Additive Manufacturing with Metals: Design, Processes, Materials, Quality Assurance, and Applications [1st ed. 2023] 3031370686, 9783031370687

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Sanjay Joshi Richard P. Martukanitz Abdalla R. Nassar Pan Michaleris

Additive Manufacturing with Metals Design, Processes, Materials, Quality Assurance, and Applications

Additive Manufacturing with Metals

Sanjay Joshi • Richard P. Martukanitz • Abdalla R. Nassar • Pan Michaleris

Additive Manufacturing with Metals Design, Processes, Materials, Quality Assurance, and Applications

Sanjay Joshi Pennsylvania State University University Park, PA, USA

Richard P. Martukanitz University of Virginia Charlottesville, VA, USA

Abdalla R. Nassar John Deere Moline, IL, USA

Pan Michaleris Pan Computing LLC State College, PA, USA

ISBN 978-3-031-37068-7 ISBN 978-3-031-37069-4 https://doi.org/10.1007/978-3-031-37069-4

(eBook)

© Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

Foreword

From the transfer of the first Additive Manufacturing (AM) system to industry in 1988, the field has grown and contributed to diverse industrial sectors. AM grew out of the automotive industry which appreciated that shortening turnaround for prototype production of polymeric parts could compress product development and result in products getting to market in shorter order. Here, the old adage, “Time is money” is fitting. The aerospace sector also demonstrated early interest in AM. The driver was cost saving associated with small production runs of complex geometries. In most cases, some type of tooling is required to create a part: a mold, die, template, or fixture. These are quite expensive and are difficult to justify if a small number of parts is produced. This results in the manufacturing cost per part due to tooling being extremely high, usually on the order of $100s to $1000s per part. AM, being a toolless technology, offers the potential for reducing cost where small runs of complex geometries are needed. This became the springboard for AM production of service parts. Over the last 30 years, AM has expanded to penetrate numerous markets: biomedical, construction, energy, space, offshore, and consumer goods. For most applications, the driver toward AM is economic. However, since the mid-1990s, there have been applications that are performance driven. AM can produce products that cannot be easily made using conventional manufacturing technologies. One broad class is geometry based. It includes incorporation of internal features, such as lattice and cellular structures. Additionally, part production resulting from topology optimization and digital artistry is enabled by AM. A second broad class is microstructurally related. For example, AM can produce discrete and continuous graded microstructures and crystallographic “texture on demand.” With the transition from rapid prototyping to service part production came the motivation to use AM technologies to produce metallic parts. The first attempts involved AM processing using low-melting point metallic feedstock in polymer AM fabricators [1] and employing indirect approaches involving metallic feedstock mixed with nonmetallic binders [2]. For the latter, post-processing was necessary to create the final metallic part. In the early 2000s, high-energy AM technology appeared commercially that enabled direct production of metallic parts from v

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feedstock including titanium, superalloys, and ferrous alloys. This is the basis for today’s metallic AM technology. From these beginnings, AM of metallic parts has grown substantially. According to the 2022 Wohlers Report, metallic feedstocks accounted for 18% of all AM feedstock in use. Metal AM fabricators have proliferated both in the number of machines and in the number of manufacturers. Wohlers reported over 3000 AM metal fabricators sold in 2022. This contrasts with less than 200 AM metal fabricators sold just 10 years previously. This represents an impressive growth of over 30% annually. This trend will undoubtedly continue for the foreseeable future. It is clear that an educated workforce must have a basic working knowledge of metallic AM part production. This book satisfies this need in exemplary fashion. The authors themselves are internationally recognized experts in the field of metallic AM. The book opens with a broad overview of metallic AM and the development of the technology. Workflow issues are considered that include solid modeling, part representation, slicing, and support structures. Design for AM of metallic parts is a crucial part of the selection process, and a chapter is devoted to this topic. The most popular AM processes for metallic AM involve fusion by a laser or electron beam power source, and these are described in detail. This includes coverage of the nature of the energy sources, analytical modeling of the beams, and material-energy interactions. Less popular AM processes are also included. Hybrid AM processes involve additive and usually subtractive processes, and these are also covered. A description is given of specific common metal alloy feedstocks, including consideration of the material’s additive-manufacturability, multiple material processing issues, and microstructural modeling. The characteristics of powder and wire forms as they impact AM are also described, both in terms of feedstock transfer and material response to processing. Post-processing is included and is an important step in metallic AM, both from a part quality standpoint and from a manufacturing cost consideration. Important service aspects are also covered in detail, including service properties and process quality and reliability. Of particular value as a teaching resource, the book includes end-of-chapter questions and discussion items, as well as a list of reference works related to the topic. This book captures the complex, multifaceted topic of metallic AM into a single, easy-to-read source. Its didactic style makes it an invaluable companion to other treatises, such as the soon-to-be-published ASM Handbook 24A, and will prove to be a valuable resource for students, practicing engineers, and technicians. Temple Foundation Professor Emeritus, The University of Texas at Austin, Austin, TX, USA August 2023

David L. Bourell

Foreword

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References 1. Manriquez Frayre JA, Bourell DL (1990) Selective laser sintering of binary metallic powder. In: Proceedings of the solid freeform fabrication symposium, The University of Texas Mechanical Engineering Department, August 6–8, 1990, pp 99–106 2. Bourell DL, Marcus HL, Barlow JW, Beaman JJ, Deckard CR (1990) Multiple material systems for selective beam sintering. US Patent #4,944,817, issued July 31, 1990

Contents

1

Introduction to Metal Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction to Additive Manufacturing with Metals. . . . . . . . . . . . . . . 1.2 Brief History of Additive Manufacturing of Metals . . . . . . . . . . . . . . . . 1.3 Classification of Additive Manufacturing Processes for Metals . . . 1.4 Benefits of Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Organization, Topics, and Use of This Book. . . . . . . . . . . . . . . . . . . . . . . . 1.6 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 5 7 9 10 11

2

Digital Processing Workflow for AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Processing Workflow for Additive Manufacturing . . . . . . . . . . . . . . . . . 2.2 AM Data Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 STL File Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 OBJ Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 AMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 3MF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Slicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 STL-Based Slicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Representation Format for Slice Files . . . . . . . . . . . . . . . . . . . . . 2.3.3 Implications of Slicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Adaptive Slicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Direct Slicing of CAD Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Part Orientation and Build Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Support Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Tool Path Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Nesting/Packing the Build . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Machine Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Post-processing of the Build . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11 Challenges in Creating the Digital Workflow . . . . . . . . . . . . . . . . . . . . . . . 2.12 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13 13 14 15 27 28 32 32 33 37 39 41 42 43 44 46 51 52 53 53 56 56 57 ix

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Metal Additive Manufacturing Processes – Laser and Electron Beam Powder Bed Fusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Laser-based Powder Bed Fusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Process Description and System Components . . . . . . . . . . . . 3.1.3 Primary Binding Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Process Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.5 Process Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.6 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.7 Microstructure and Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.8 Maintaining Process Consistency and Quality . . . . . . . . . . . . 3.1.9 Advantages and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.10 Examples of Parts and Applications . . . . . . . . . . . . . . . . . . . . . . . 3.2 Electron Beam Powder Bed Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Process Description and System Components . . . . . . . . . . . . 3.2.3 Process Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Microstructure and Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.6 Comparison Between Laser and Ebeam PBF . . . . . . . . . . . . . 3.2.7 Advantages and Disadvantages of Electron Beam Melting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.8 Example Parts and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metal Additive Manufacturing Processes – Directed Energy Deposition Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction to Directed Energy Deposition . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Powder-Based Laser DED Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Process Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Process Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Process Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.7 Microstructure and Material Properties. . . . . . . . . . . . . . . . . . . . 4.2.8 Maintaining Process Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.9 Advantages and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.10 Examples and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Wire Feed-Based DED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Electron Beam-Based Wire DED . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Laser-Based Wire DED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Wire Arc AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Resistance Heating-Based Wire Process . . . . . . . . . . . . . . . . . .

59 59 59 59 69 72 76 84 87 89 94 95 97 97 97 100 102 103 103 103 104 107 107 111 111 111 111 113 114 120 122 127 128 130 134 135 135 139 141 141 142

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4.3.5 Process Parameters for Wire DED Systems . . . . . . . . . . . . . . . 4.3.6 Materials, Microstructure, and Properties . . . . . . . . . . . . . . . . . 4.3.7 Advantages and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.8 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

143 145 147 147 148 149

Metal Additive Manufacturing Processes – Jettingand Extrusion-Based Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Binder Jetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Binder Jetting Process Description . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.4 Process Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.5 Process Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.6 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.7 Material Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.8 Advantages and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.9 Example Parts and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Material Jetting-Based Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Solution-Based Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Direct Droplet Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Extrusion-Based Fabrication of Metal Parts . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4 Process Dynamics and Parameters. . . . . . . . . . . . . . . . . . . . . . . . . 5.3.5 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Process Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.7 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

151 151 151 151 154 158 164 167 167 170 171 172 172 173 175 175 176 178 181 189 190 191 192 192

Metal Additive Manufacturing Processes – Deformation-Based AM and Hybrid AM Processes . . . . . . . . . . . . . . . . . . . . 6.1 Deformation-Based AM Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Ultrasonic Additive Manufacturing (UAM). . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.5 Process Dynamics and Process Parameters . . . . . . . . . . . . . . . 6.2.6 Bonding Principles in UAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.7 Process Workflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.8 Process Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

195 195 195 195 196 196 199 199 200 202 202

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6.3

Cold Spray Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Process Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Process Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Additive Friction Stir Deposition (AFSD) AM Process . . . . . . . . . . . . 6.4.1 AFSD Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Process Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Materials and Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4 Current Applications and Future Potential . . . . . . . . . . . . . . . . 6.5 Hybrid Additive Manufacturing Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 DED + Multiaxis Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2 Integrated PBF + 3 Axis Milling . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Deformation AM Processes + Machining . . . . . . . . . . . . . . . . 6.6 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

202 202 204 207 207 208 209 211 212 214 216 217 219 219

Design for Additive Manufacturing and Cost and Economics of AM 7.1 AM Value Proposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Design for AM (DfAM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 General Design Principles/Practices for AM (Strategic) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Specific Process-Related Considerations (Operational) . . 7.3 Topology Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Lattice Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Strut-Based Cell Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Triply Periodic Minimal Surfaces (TPMS) . . . . . . . . . . . . . . . . 7.5 Cost and Economics of AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

221 221 223

Energy Sources and Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Operating Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Laser Beam Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.3 Laser Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Electron Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Operating Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Grounding of the Substrate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 E-Beam Propagation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.4 Electron Beam Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Electric Arcs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Operating Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Arc Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

249 249 250 257 265 269 270 273 274 278 278 279 281 282 283 284

224 225 227 230 231 231 234 247 247 248

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9

Source-Material Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Lasers: Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.1 Light as an Electromagnetic Wave . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.2 Attenuation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.3 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Electron Beams: Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Elastic and Inelastic Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Arc: Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Heating and Melting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Electromagnetic Forces and Arc Pressure . . . . . . . . . . . . . . . . . 9.4.2 Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.3 Surface Tensions (Marangoni Convention). . . . . . . . . . . . . . . . 9.4.4 Buoyancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.5 Plasma Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

285 286 286 287 289 293 294 296 299 303 304 306 308 309 313 314 315

10

Feedstock Delivery and Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Powder Feedstock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.1 Powder Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.2 Powder Dynamics in Powder Bed Fusion . . . . . . . . . . . . . . . . . 10.1.3 Powder Dynamics in Directed Energy Deposition . . . . . . . . 10.2 Wire Feedstock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Wire Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 Wire Transfer Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

317 317 318 321 325 329 330 330 331 332 332

11

Mechanical Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Thermal Expansion and Contraction, Plasticity, Distortion . . . . . . . . 11.2 Residual Stress and Cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Support Structures for Mechanical Response and Their Potential Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

335 335 336

Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Rosenthal Solution for Semi-Infinite Space . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 The Method of Images and Virtual Heat Sources. . . . . . . . . . . . . . . . . . . 12.3 Eager and Tsai Gaussian Heat Source Model . . . . . . . . . . . . . . . . . . . . . . . 12.4 Computational Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.1 Heat Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.2 Elastoplastic Mechanical Response. . . . . . . . . . . . . . . . . . . . . . . . 12.4.3 Material Activation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

339 339 340 342 342 343 344 345

12

336 337 337

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12.4.4

Examples of Computational Models of Fusion-Based Metal AM Processes . . . . . . . . . . . . . . . . . . . . . . . . 348 12.4.5 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 13

Alloy Systems for Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Constitution of Alloys and Development of Microstructure . . . . . . . 13.2 Development of Strength in Metallic Systems . . . . . . . . . . . . . . . . . . . . . . 13.3 Alloy Systems for Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 Properties and Selection of Metallic Materials for Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.5 Alloys for Unique Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.6 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

359 361 366 370

14

Metallic Feedstock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 Powder Processing for Producing Feedstock . . . . . . . . . . . . . . . . . . . . . . . 14.2 Powder Characteristics and Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2.1 Physical Characteristics of Powder . . . . . . . . . . . . . . . . . . . . . . . . 14.2.2 Characteristics of a Powder Aggregate . . . . . . . . . . . . . . . . . . . . 14.2.3 Attributes of a Powder Aggregate . . . . . . . . . . . . . . . . . . . . . . . . . 14.3 Metal Powder and Binders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4 Wire Feedstock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5 Storage and Handling of Feedstock and Recycling of Powder . . . . . 14.5.1 Storage and Handling of Feedstock. . . . . . . . . . . . . . . . . . . . . . . . 14.5.2 Recycling of Powder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.6 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

383 384 391 392 403 408 413 415 417 417 419 424 424

15

Solidification During Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . 15.1 Thermal Response of Material During Processing . . . . . . . . . . . . . . . . . 15.2 Solidification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2.1 Chemical Driving Force for Solidification . . . . . . . . . . . . . . . . 15.2.2 Change in Free Energy During Heterogeneous Nucleation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2.3 Growth of the Solid Within the Liquid . . . . . . . . . . . . . . . . . . . . 15.2.4 Constitutional Undercooling and Interface Stability . . . . . . 15.2.5 Development of Microstructure During Solidification. . . . 15.2.6 Microsegregation of Solute During Solidification . . . . . . . . 15.2.7 Macrostructure and Microstructure of Additive Manufactured Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

427 427 437 441

16

374 377 380 381

445 449 459 463 470 475 478 479

Solid State Transformations and Gas Reactions During the Additive Manufacturing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 16.1 Solid State Transformations During Additive Manufacturing . . . . . 481

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16.1.1 Diffusional Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.1.2 Allotropic Reactions and Impact on Strengthening . . . . . . . 16.2 Gas and Liquid Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2.1 Gas Porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2.2 Gas and Metal Chemical Reactions. . . . . . . . . . . . . . . . . . . . . . . . 16.3 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

485 501 514 514 518 524 524

17

Modeling of Microstructure for Additive Manufacturing . . . . . . . . . . . . . 17.1 Modeling Solidification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.2 Modeling Solid-State Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

527 528 536 547 548

18

Multiple Alloy Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1 Multiple Alloy Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1.1 Alloy Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1.2 Compositional Grading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 Compatibility of Compositions for Multiple Alloy Processing . . . . 18.3 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

549 549 551 555 560 565 565

19

Post Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2 Thermal Post Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.3 Post Process Debinding and Sintering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.4 Material Removal-Based Post Processing. . . . . . . . . . . . . . . . . . . . . . . . . . . 19.4.1 Machining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.4.2 Surface Finishing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.5 Deformation (Non-material Removal)-Based Post Processing . . . . 19.6 Practical Considerations in Post Processing . . . . . . . . . . . . . . . . . . . . . . . . 19.7 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

567 567 569 575 580 581 581 584 584 587 588

20

Properties and Characteristics of Metallic Materials Produced Using Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.1 Mechanical Properties of Alloys Produced Using Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.1.1 Tensile Properties Under Static Loading . . . . . . . . . . . . . . . . . . 20.1.2 Fatigue Properties Under Cyclic Loading . . . . . . . . . . . . . . . . . 20.1.3 Toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2 Corrosion Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.3 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

591 592 597 609 616 621 627 628

Process Quality and Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633 21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633

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21.2

Traditional Process Performance Qualification Applied to Additive Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Design and Process Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Additive Manufacturing Process Performance Qualification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.3 Material Qualification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.4 Processing System Qualification . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.5 Processing Condition Qualification . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Sensor-Based Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3.1 Monitoring the Build Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3.2 Monitoring System Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3.3 Monitoring Process Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 Questions and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

634 635 635 636 636 637 638 640 640 641 645 645 645

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

About the Authors

Sanjay Joshi is Professor of Industrial and Manufacturing Engineering at Penn State University. His research and teaching interests are in the areas of ComputerAided Design and Manufacturing (CAD/CAM) with specific focus on Additive Manufacturing, Computer-Aided Process Planning, and Manufacturing Systems Design and Analysis. He has been involved in actively teaching AM at the graduate and undergraduate level for over 20 years. He has been on the faculty for 36 years, and has received several national and international research awards. Richard P. Martukanitz is Professor of Material Science and Engineering at the University of Virginia and former Fellow of Virginia’s Commonwealth Center for Advanced Manufacturing (CCAM). Prior to joining the University of Virginia, Dr. Martukanitz served as Director of the Pennsylvania State University’s Center for Innovative Materials Processing through Direct Digital Deposition (CIMP-3D) and Head of the Laser Processing Division at Penn State’s Applied Research Laboratory. He has over 40 years of experience in developing and applying laser-based additive manufacturing techniques for metallic systems. Abdalla R. Nassar is the Enterprise Additive Manufacturing (AM) Lead for John Deere, where he leads AM strategy development, R&D, and servers and the subject matter expert for the global organization. Prior to this role, he served as an Associate Research Professor and Head of the Process Physics, Analytics, and Engineering Department within the Materials Science Division of the Applied Research Laboratory (ARL) at the Pennsylvania State University. At Penn State, he developed and taught courses on Engineering and Scientific Principles of Additive Manufacturing and Laser-Materials Interactions at the graduate level. Pan Michaleris is the founder and CEO of PanOptimization LLC. In 2012, he founded Pan Computing LLC which was acquired by Autodesk in 2016. The additive manufacturing process simulation software CUBES developed by Pan Computing was commercialized as Netfabb Simulation. Dr. Michaleris became Sr. Software Architect at Autodesk and supervised the development of additive xvii

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manufacturing simulation software until 2021. He has over 30 years of experience in high-performance computing and thermo-mechanical process modeling such as additive manufacturing, welding, and thermal forming. He has a PhD in Theoretical and Applied Mechanics from the University of Illinois at Champaign-Urbana, and has worked as a Senior Research Engineer at Edison Welding Institute (EWI) from 1994 to 1997, and as Professor at the Department of Mechanical and Nuclear Engineering of The Pennsylvania State University from 1997 to 2016.

Chapter 1

Introduction to Metal Additive Manufacturing

1.1 Introduction to Additive Manufacturing with Metals The term 3D printing is often considered synonymous with the process of producing a part layer-by-layer through computer-generated commands and is used more colloquially by consumers and the media; however, industrial markets tend to use the lexicon additive manufacturing or AM to describe this technology. This is especially the case when referring to the use of various processes for producing metallic components or structures that may be used as a product or incorporated into an assembly or system and having well-defined requirements. As defined by the International Standards Organization and ASTM International through ISO/ASTM Standard 52900:21, additive manufacturing is the “process of joining materials to make parts from 3D model data, usually layer upon layer, as opposed to subtractive manufacturing and formative manufacturing methodologies” [6]. Subtractive manufacturing here refers to the creation of a shape by removal of material by operations such as milling, turning, drilling, etc. Formative manufacturing refers to the creation of shape by deformation of the shape of the raw material such as forging, bending, casting, injection molding, etc. By contrast, additive manufacturing creates the desired three-dimensional shape by successive addition of material on a layerby-layer basis through digital commands and automated motion. In the case of this discussion, the material that is added is a metal, and usually an alloy. The metallic material may be added using various starting forms or feedstock, that in many cases, is fused onto the prior layers by melting and solidification using a heat source. The type of material, the form and characteristics of the feedstock, the additive manufacturing processing conditions, and the post-processing treatments that may also be employed all play a role in the production of the final part and the resulting characteristics and properties. The potential benefits of additive manufacturing, such as the ability to produce highly complex parts, extend the design space for improved performance, and decrease cost through consolidation of parts or reduction of material, all while offering on-demand production or mass © Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_1

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customization, will continue to drive the growth of this technology in manufacturing for the foreseeable future.

1.2 Brief History of Additive Manufacturing of Metals The application of manufacturing techniques based on the creation of metallic materials to produce desired shapes is not new. The early application of welding to produce a new surface onto a substrate through “buttering” had been used since the inception of arc welding techniques, and in principle, could be considered an additive manufacturing process. Ralph Baker, working at Westinghouse Electric and Manufacturing Company developed and patented in 1920 a method for using an electric arc to create three-dimensional decorative articles in metals [1]. Other techniques, such as the stacking of metal sheets having incremental changes in shape to produce a three-dimensional surface, also had been used to create shapes in metals. However, two patents, both filed in the 1970s, are noteworthy based on their description of techniques that we view today as common additive manufacturing processes used for metals. Pierre Ciraud proposed a system in his 1971 patent that employed powder being fed into a process chamber that included a highenergy source, such as a laser, used to melt and fuse the powder into a usable form [3]. The description by Ciraud has an uncanny resemblance to the laserbased directed energy deposition process. The patent of Ross Housholder in 1979 discussed the application of powder onto a surface by scraping followed by scanning of a laser beam to selectively consolidate the powder layer by layer, which is essentially described as the laser-based powder bed fusion process [5]. Although these early patents conceptualized methods that could be viewed as precursors of additive manufacturing, they lacked certain capabilities that would eventually enable the rapid rise and adoption of this technology that is seen today, the availability of compact and sufficiently powerful computers to digitally drive the motion equipment needed to realize the concepts. The commercial availability of the two most common techniques for additive manufacturing of metals, directed energy deposition and powder bed fusion, can be traced to activities occurring in the 1990s. It should also be noted that by this time computer power was sufficiently established to not only operate complex motion required for these systems but also completely control numerous functions in a fully digital manner. One important event was the development of the selective laser sintering process by Carl Deckard and Joseph Beaman at the University of Texas [2] and commercialization of this technology under the name DTM Corporation. Around the same time, Hans Langer and Hans Steinbichler founded Electro Optics Systems, now referred to as EOS, and commercialized an early version of selective laser sintering that progressed to enable the laser to fully melt and consolidate metallic powder. In the mid-1990s, the Fraunhofer Institute for Laser Technology (ILT) developed and patented selective laser melting, which is defined as powder bed fusion today. The Fraunhofer technology was commercialized through a venture

1.2 Brief History of Additive Manufacturing of Metals

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Fig. 1.1 Two figures excerpted from the Baker Patent of 1925 entitled Method of Making Decorative Articles that utilizes an electric arc welding process [1]

by Dieter Schwarze, who founded SLM (now SLM Solutions Group AG). This venture, along with commercialization of the technology by other industry members of ILT, resulted in several major companies, such as Concept Laser-GE, Renishaw, and SLM Solutions, providing powder bed fusion systems that may trace their roots to the early work at Fraunhofer (Fig. 1.1). Although developed later, the EBM (Electron Beam Melting) process followed commercialization of selective laser melting technology. In 2002, a Swedish Company by the name of Arcam introduced their first electron beam-based powder bed fusion system, at the EuroMold Conference in Frankfurt, Germany. Due to the ability to process within a vacuum, as opposed to the laser-based powder bed fusion process which operates within an inert gas environment, the Arcam process gained significant traction in the medical implant and aerospace industries. The technology, now under the Arcam-GE banner, continues to provide high-quality parts in these sectors. Like laser powder bed fusion, the commercialization of directed energy deposition also began in the 1990s. Much of this technology was derived from laser surface deposition or cladding to impart unique properties to the surface of a material or for restoring dimensional tolerances for the repair of parts. One of the earliest commercial systems was introduced by Optomec in the mid-1990s, which was a ® venture based on LENS (Laser Engineered Net Shaping), a laser-based directed energy deposition technology, developed at Sandia National Laboratories. One of

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the co-inventors while at Sandia, David Keicher, became the first Chief Technical Officer for Optomec. Optomec Corporation has continued advancement of LENS® technologies, and with the acquisition of Huffman Corporation in 2018 can probably lay claim to the largest number of directed energy deposition systems in the field. Near the same time as the commercialization of Optomec, AeroMet technology was also being commercialized as LAMSM (Laser Additive Manufacturing), a directed energy deposition process capable of producing large structures of titanium alloy using a high-power laser [7]. The process was developed at the Applied Research Laboratory, Pennsylvania State University through funding by the United States’ Defense Advanced Research Project Agency (DARPA). Development was conducted through a joint effort by Eric Whitney of Penn State and Frank Arcella, who at the time was with Johns Hopkins University, and later helped found AeroMet in 1997 as a wholly owned subsidiary of MTS Corporation. Although AeroMet was credited with producing the first additive manufactured structures used in aerospace applications, which are currently still operational, AeroMet unfortunately ended production in 2005. With AeroMet’s demise, Sciaky Corporation, a longheld leader of electron beam welding technology, began to turn their attention towards developing the EBAM (Electron Beam Additive Manufacturing) process for producing large titanium structures using a high-power electron beam. Owing to the operation within a vacuum and the high deposition rates that may be achieved with high-power electron beams, Sciaky’s EBAM technology continues to be attractive for producing large structures for critical applications. Although relatively new to additive manufacturing, Norsk Titanium is also developing additive technology, which in this case is based on plasma welding technology, for the production of large aerospace structures in titanium alloys. Norsk began operation in 2007 and has made significant advancement in development and application of their technology for aerospace structures. Since its recent introduction, the number of additive manufacturing processes applicable to metals has grown significantly, as well as the number of manufacturers producing systems for these processes. Even within a single process, options regarding type of heat source, form of feedstock, supporting software, and numerous other details make the selection of a system challenging. However, it is this variety that promotes innovation, even if the motive is for increasing market share. It is hoped that the consolidation of manufacturers occurring within the industry will not result in the resignation of the need to continually advance the technology. Finally, it should also be noted that the above historical discussion purposely omitted, to a large extent, the sources and paths of intellectual property regarding these processes. Rather, the discussion was couched in terms of individuals and organizations that were seen as leading the development of additive manufacturing technologies for metals. As with many technologies that are highly disruptive, the patents covering key areas of additive manufacturing applicable to metals may be described as tortious and convoluted.

1.3 Classification of Additive Manufacturing Processes for Metals

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1.3 Classification of Additive Manufacturing Processes for Metals As described earlier, additive manufacturing involves the use of digital commands to automatically and selectively create successive layers of material that eventually form a three-dimensional shape. In the case of metals, the entire additive manufacturing process serves two functions: the creation of a three-dimensional form and the simultaneous formation of a functional material. However, the techniques that are employed to accomplish these two goals may vary considerably. The various processes used for additive manufacturing have been classified into seven categories based on ASTM F2792−12a, Standard Terminology for Additive Manufacturing Technologies [6]. This classification is shown in Table 1.1, along with the applicability of each process for producing metal parts, realizing that the utility of each process for producing metallic parts will represent varying degrees of market penetration, depending upon the industry and application. Also, it should be noted that although all processes may utilize metallic materials, not all metals may be appropriate for all processes. Details regarding the processes will be discussed in subsequent chapters. Shown in Fig. 1.2 is a graphical representation of the various additive manufacturing processes applicable to metals. In the figure, the processes are initially delineated by whether consolidation of the material takes place by a thermally activated process or through a deformation joining process. The thermal process for consolidation is through melting and solidification, which includes the categories of powder bed fusion and directed energy deposition. The powder bed fusion technique is considered to be the most widespread application of additive manufacturing of metals, owing to its operation in an almost fully automated environment, ability to produce highly complex shapes, and availability of processing parameters that lead to the creation of high-quality metallics. The other thermal process for metals, which also involves melting and solidification, is directed energy deposition. This process utilizes several heat sources for accomplishing deposition that may be scaled over a range of deposition rates contingent upon the available power of the heat source and size of components or structures that may be produced based on the volume of the motion envelope. As shown, there are numerous variations that rely on melting and solidifications. The other broad category of processes that involve consolidation through thermal activation is sintering, a mechanism that involves heating to a high temperature but below the melting point to cause coalescence of powder particles through a solid-state reaction. This consolidation technique is conducted post-process or after forming of the three-dimensional shape, where the powder particles are moderately bonded using a binder to achieve the form but is not fully consolidated to achieve workable strength. The various processes that require sintering are described by the means in which the binder is provided to the material to create a shape, which includes material extrusion (commonly referred to as fused deposition modeling – FDM), binder jetting, material jetting, and vat polymerization. Analogous processes

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Table 1.1 ASTM classification of additive manufacturing processes applicable to metals Process category Powder bed fusion (PBF)

Directed energy deposition (DED)

Material extrusion

Sheet lamination

Binder jetting

Material jetting

Vat photopolymerization

Brief description An additive manufacturing process in which thermal energy selectively fuses regions of a powder bed An additive manufacturing process in which focused thermal energy is used to fuse materials by melting as they are being deposited An additive manufacturing process in which material is selectively dispensed through a nozzle or orifice An additive manufacturing process in which sheets of material are bonded to form an object An additive manufacturing process in which a liquid bonding agent is selectively deposited to join powder materials An additive manufacturing process in which droplets of build material are selectively deposited An additive manufacturing process in which liquid photopolymer in a vat is selectively cured by light-activated polymerization

Applicability to metals and means of consolidation Yes, consolidation through melting and solidification

Yes, consolidation through melting and solidification

Yes, consolidation by post-process sintering

Yes, with individual sheets being joined at selective locations through a solid-state joining process, such as ultrasonic welding Yes, consolidation by post-process sintering

Yes, consolidation by post-process sintering

Yes, consolidation by post-process sinteringa

a The application of vat photopolymerization for producing metallic parts is a relatively new development

involving the layering of a soluble paste bounded by a sacrificial polymer wax are also available. Because post-process sintering involves a solid-state reaction for consolidation, when applied to metallic systems, these processes are often used for materials that have difficulty in achieving defect-free structure through solidification techniques. There is a broad category of additive manufacturing processes for metals that also involves a solid-state process for consolidation but entails a deformation joining process to consolidate material concurrently while forming a three-dimensional near-net shape. This includes the cold spay process that utilizes a high-velocity stream of powder for consolidation of the particles to create a form, ultrasonic

1.4 Benefits of Additive Manufacturing

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Fig. 1.2 Graphical depiction of classification of additive manufacturing processes applicable to metals based on material consolidation, heat source, and feedstock form

joining of stacked sheets that are simultaneously machined to form a shape, and friction stir welding with a consumable material to produce a near-net shape that would be subsequently machined.

1.4 Benefits of Additive Manufacturing The application of additive manufacturing for producing metallic components is rapidly expanding in many industries, such as aerospace, medical device, automotive and transportation, heavy industries, consumer goods, tool and die, and energy production, to name a few. This tremendous growth is being fueled by several key benefits that makes additive technology highly attractive during design and manufacturing. Although there are numerous advantages for additive manufacturing, which tend to be specific to a particular application, some of the more common benefits of the technology are noted below. • Additive manufacturing may be used to increase complexity of shapes that result in better functionality in design. The ability to produce complex shapes with fewer limits on manufacturability opens the design space and allows for design freedom in exploring unique features and alternative geometries. These

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capabilities are being applied to parts where increased design complexity may directly lead to improved product performance. It may be used to reduce weight of components and structures using topologyoptimized designs that place material where needed based on functional optimized criteria, as well as the ability to produce geometric features, such as lattice and open cell structures, that may also be used for weight reduction. These qualities are being utilized for expanding opportunities in industries that can benefit from light weighting. It allows reduced part count through redesign and combining several parts into one by additive manufacturing. The ability to reduce the number of parts in an assembly can result in decreased cost through elimination of fabrication steps, improved reliability due to removal of joints, and increased performance through improved designs. In many instances, complex geometries created by combining parts may be easily produced through additive manufacturing. Additional benefits from part count reduction is the effect on part inventory management, and reductions in supply chains. Additive manufacturing allows highly complex internal channels and features to be easily produced, which enables increased product performance via greater efficiency of flow paths, improved placement of channels resulting in greater heat transfer, or internal features that permit embedded sensors, components, and elements. These attributes are especially important for injection molding dies and heat exchangers. It is capable of creating net or near-net shapes that reduce cost by using significantly less material. This may be accomplished by minimizing the amount of material removed during machining to achieve final dimensions. This factor becomes more important as the cost of the material increases or as the difficulty in machining of the material increases. It may be utilized for direct fabrication of parts that eliminate the need for complex and expensive tooling, such as molds, patterns, and dies, that are justified through large production quantities. This quality supports the capacity for small batch production through additive manufacturing, and when combined with the ability to quickly modify designs, offers the ability for on-demand production and mass customization. Additive technologies are adept at quickly producing parts from an existing design or through the generation of a new design that ultimately results in shorter lead times. This feature is especially applicable to the use of additive manufacturing for producing replacements. Rather than maintaining an inventory of spare parts, the design files and manufacturing parameters may be utilized locally or distributed to produce replacement parts only when needed.

Given the potential of additive manufacturing to positively impact cost, performance, and availability of products, it is no wonder that the application of this technology continues to grow. At one time, the belief that the perceived higher cost associated with lower cycle times of additive manufacturing of metals would limit growth and resign additive to a niche technology. The actual outcome can

1.5 Organization, Topics, and Use of This Book

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be no further from the truth. At the time of this writing, additive manufacturing of metallic materials is projected to exhibit continued, steady, growth through the end of the 2020 decade [4]. This growth may be attributed to several aspects of the technology, a few of which include: greater familiarity and understanding of the technology, greater experience of engineers in applying additive manufacturing techniques to new designs, expansion, and naturalization of the supply chain for additive materials and services, development of standard post-process practices, greater accessibility and documentation of expected mechanical properties of material produce using these processes, productivity of additive equipment for metals, continued development and standardization of acquisition and qualification protocols for additive manufacturing of metals, and development and application of new or unique alloys capable of being utilized in additive manufacturing processes. Although the factors listed above are compelling, one of the most important features related to the future of additive manufacturing is more difficult to evaluate but is believed to have profound effects on the impending growth and adoption of the technology. This critical aspect is the ability of additive manufacturing to be fully integrated into the digital enterprise, which enables the manufacturing process to be completely synchronized with all aspects of product development. The ability to completely utilize and share digital information during market analysis, design, product development, manufacturing, quality assurance, sales, and distribution may be the most important benefit that this important technology will contribute to the future of manufacturing.

1.5 Organization, Topics, and Use of This Book The goal of this book has been to develop a comprehensive essay on the important topic of additive manufacturing of metallic materials. It is hoped that this goal was accomplished; however, one must consider the challenge in meeting this objective given the full scope and fluidity of the topic. Nevertheless, the authors, who have a combined experience of over eighty years pursuing the science and application of additive manufacturing of metals, have endeavored to achieve this goal. In addressing the range of topics that are necessary to adequately address the subject matter, the treatise has been organized based on four major perspectives regarding the technology: discussions on digital workflow and processes, processing science, materials, and post-processing, properties, and quality. The section on digital workflow and processes is self-explanatory and is intended to sufficiently describe the elements and sequences for designing, preparing, and conducting additive manufacturing, along with discussions on the various additive manufacturing processes applicable to metallic materials. Each of these discussions includes a basic description and distinction of the digital elements, processes, primary parameters that are used to control the processes, and resultant characteristics of parts produced using these methods. Also contained within this section is an introduction to design, as well as a condensed discussion of

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economics, both of which must be considered in any conversation on additive manufacturing. The transport of energy and mass plays an active role in many of these processes and, thus, is central to the conversation pertaining to the science of these processes. These discussions examine analytical and numerical techniques for representing the physics of processes, as well as the ability to describe and manage the propagation of energy within the process and interaction of energy within the material. Emphasis is placed on the constructs that support the creation of virtual simulations, which are finding so much utility for better understanding these processes. A rather large section is devoted to the material aspects of the technology, which for the case of metallic systems, is a necessity for defining, controlling, and ensuring the resultant material properties are acceptable for the intended application. This includes basic aspects of metallic systems as they relate to additive manufacturing, as well as an ample description of techniques used to produce metal feedstock and the characteristics and attributes of powder that may impact additive processing. Details concerning solidification theory and solid-state transformations are discussed and examined in terms of thermal response of the material for understanding the development and evolution of microstructure during additive manufacturing. As required, the influence of microstructure on properties, primarily through strengthening methods, is also addressed. The final section, which addresses several post-process considerations includes discussions on thermal treatments used to alter microstructure for achieving desired mechanical properties and finishing techniques often employed for attaining geometric tolerances and surface finishes. This section also entails a reasonably thorough description of anticipated properties of metallic systems produced using the common additive manufacturing processes, based on reported values within the literature. This section is concluded with a discussion on process and product reliability that includes methods and techniques utilized for ensuring quality during processing and protocols for qualifying additive manufacturing materials, systems, and processes. As mentioned earlier, the goal during the creation of this book was to develop a comprehensive exposition of the subject of additive manufacturing of metals. This goal was pursued to address two perceived needs. Firstly, a manual that could be used as a reference source for this important subject was not available, and secondly, there existed a need for a single volume that could be used for undergraduate and graduate student instruction that discusses the broad field of additive manufacturing in a fully integrated fashion.

1.6 Questions and Discussions 1. Compared to conventional metal processing technologies, what are the five key advantages of additive manufacturing? 2. Of the seven additive categories defined in ISO ASTM 52900, which would you anticipate enables the formation of a metal part with little to no porosity (>99% dense)?

References

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3. Identify successful applications of AM in industry, and explain why these applications can be considered successful? 4. What do you foresee as the future of AM as it relates to a household tool? What potential applications would make it worthwhile to have an AM machine at home? 5. What are the key attributes of a product that would make it suitable for AM?

References 1. Baker R (1925) Patent No. 1533300. Retrieved from https://www.freepatentsonline.com/ 1533300.pdf 2. Beaman J, Deckard C (1986) Patent No. US4938816A. Retrieved from https:// patents.google.com/patent/US4938816A/en 3. Ciraud PAL (1971) Patent No. DE2263777A1. Retrieved from https://patents.google.com/ patent/DE2263777A1/en 4. Global Market Monitor (2021) Metal additive manufacturing market report. Retrieved from https://www.globalmarketmonitor.com/reports/664838-metal-additive-manufacturing-marketreport.html 5. Householder R (1979) Patent No. US4247508A. Retrieved from https://patents.google.com/ patent/US4247508A/en 6. ISO (2021) Additive manufacturing – general principles – fundamentals and vocabulary. Retrieved from https://www.iso.org/standard/74514.html 7. Kobryn PA, Ontko NR, Perkins LP, Tiley JS (2006) Additive manufacturing of aerospace alloys for aircraft structures. Air Force Research Lab Wright-Patterson AFB OH Materials and Manufacturing Directorate

Chapter 2

Digital Processing Workflow for AM

2.1 Processing Workflow for Additive Manufacturing The complete workflow to convert a 3D design and its relationships to the various steps that must be successfully executed is shown in Fig. 2.1. The process begins with a 3D CAD model which can be created by several means – by designing in a 3D modeling software, reverse engineering a 3D object using scanning technology to create a point cloud and conversion of the point cloud in a 3D model, or by using sliced data such as that from a CT scan or MRI and reconstruction of a 3D model. The 3D model is then converted into a format that is suitable for use by AM. In a majority of cases, this is the STL file that is created by converting the 3D model into a format that can be read, shared, and executed by downstream software. STL files can potentially contain errors that can impact its use by the algorithms embedded in the downstream software, and hence the next step in the process is to fix and repair the STL files. Once the files are repaired and error-free, the process planning activities can begin. Process planning involves all the decisionmaking that must take place to enable the successful build of the part. The first major decision is to determine the build orientation of the part, since that has an impact on all further decisions. In fact, the determination of build orientation is tightly coupled with support generation and the resulting slices for each layer; hence, it is often performed in an interactive manner. To enable prediction of the process planning decisions on the build, simulation software may be used to analyze the results of the decisions made prior to the physical building of the part and help in fine-tuning the process planning. These simulations can be used at various stages of the AM process with different levels of granularity in the input data for the different levels of details in the simulation results. After the build direction and support structures are established, the model and support structures are sliced to create the build geometry for each layer. This information is provided to the tool path planning process where each slice is converted to a sequence of actual motions of the machine that will be used to create the solid layer. It is at this point the actual © Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_2

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Fig. 2.1 CAD to part workflow for AM

processing parameters of the machine are embedded with the motion geometry. This results in the set of instructions that form the input used to drive the machine and execute the build. The execution of the build is performed at the machine, which often must be properly set up for the build. Process parameters that are not included in the tool path, such as temperature of the build chamber, gas flow rates, recoating speed, and other machine-specific settings are part of the machine setup process that must be performed prior to the build. After the part build is completed, the final post-processes steps must be executed. These range from removal of powder, stress relieving, removal from the build plate, support removal, heat treatment, machining to improve dimensional accuracy, and others depending on the part requirements. The final step in the process is to ensure that the part quality meets the designed specifications.

2.2 AM Data Representation The data required for AM refers to all the data that is required, used, generated, captured, and exchanged throughout the AM process chain [16]. The representation of AM data is a format, method, standard, or language in a form that can be directly

2.2 AM Data Representation

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Table 2.1 Popular AM data formats Data format STL [17]

OBJ [20] AMF [4] 3MF ([1]

CLI – Common Layer Interface [5]

Source Converted from 3D CAD model, point clouds from reverse engineering, conversions from CT scan data Converted from 3D CAD model Converted from 3D CAD data, Augmentation of STL files Converted from 3D CAD data and STL files, augmented with other data to facilitate printing Slicing a 3D file

Type of data 3D data limited to geometry

3D polygonal model, color data, material, and texture 3D data including geometry, material, color, etc. 3D data including geometry, material, color, texture, and printability data 2D data presenting the geometry of each AM layer

read and interpreted by the computer systems that form the digital chain that will be handling and working with the representations. Initial representations focused on the product representation of the 3D models for use in AM with more recent efforts being focused on integrated requirements for additional process data to facilitate universal fabrication of AM parts [9]. Many data formats have been used in AM digital chain. Some of the data formats are proprietary to the vendors but publicly available for third party sources to use and develop applications. Table 2.1 provides a sampling of some of the popular and mainstream data formats.

2.2.1 STL File Format The STL file or sometimes referred to as the “Stereolithography” format or “Standard Tessellation Language” was developed by Albert Consulting Group for 3D Systems in the early years of rapid prototyping to serve as a means of transmitting the geometric data of a 3D model for use by downstream applications such as slicing algorithms to create the contour geometry for each layer to be built. It has since become the de facto standard and widely used for all additive manufacturing, along with other CAD/CAM applications. Typical CAD modelers store the 3D geometric model in their own native and sometimes proprietary formats. Given the myriad of such formats in use, this created a problem with the lack of standard representation that could be used by slicing algorithms independent of the CAD modeler used to create the 3D model. This led to the development of the STL file, which would serve as the format to transfer files from a CAD system to the slicing software. Currently, the STL file is supported by all CAD modelers and the internal native CAD format can be converted and exported to an STL file. Each CAD software has its own processing software to create the STL files.

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Fig. 2.2 Tessellation of a planar and curved object

The STL file is a representation of the tessellation of the boundary of the 3D object into planar triangular facets that collectively define the boundary of the object. Figure 2.2 shows the process of tessellation into triangles. For a planarfaced object such as a cube, where each boundary face of the cube is a bounded plane, the tessellation results in twelve triangles, with each of the six faces being tessellated into two triangles. The resulting tessellation does not introduce any additional boundary artifacts and is an exact match to the original boundary. However, when tessellating an object with a curved boundary surface, such as a cylinder, the tessellation into triangles results in a wide range of potential solutions which differ in the number of triangles and the result approximates the curved boundary. The amount of approximation error introduced is a function of the chordal deviation, which is chosen by the user within the CAD modeler used to export and create the STL file, which in turn controls the number of generated triangles that approximate the curved surface. It is important to note that the tessellation is a oneway transformation, the original data cannot be recovered from a tessellated file since all geometric information related to the original geometry is lost in the STL format. The relationship between the chordal deviation and the number of triangles generated is shown in Fig. 2.3. As the amount of acceptable chordal deviation “b” is changed, the chord length L changes based on the relationships specified in Fig. 2.3. A high-resolution STL file will have a smaller value for the deviation, hence a smaller chord length and larger number of triangles, which in turn results in a larger file size. The STL file stores the information related to all the triangle facets generated by the tessellation. As shown in Fig. 2.4, the information for each triangle includes:

2.2 AM Data Representation

17

Fig. 2.3 Relationship between chordal deviation and number of triangles Fig. 2.4 Representation of a single triangle in STL file

1. The coordinates of each of the vertices. 2. The components of the unit normal vector to the triangle. By convention, the normal vector should point outwards with respect to the 3D model. This also imposes an ordering among the listed vertices. Using the right-hand rule, the thumb points along the direction of the normal vector and the curl of the fingers imposes the counterclockwise ordering of the vertices. This information can be stored in the ASCII (human-readable) format or in a binary format. The ASCII file starts with the mandatory name of the object solid name

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Followed by an unordered list of the triangle facet information that includes the components of the normal vector n and vertices v. The x,y,z subscripts represent the x,y,z components of the normal vector and the vertex coordinates. facet normal nx ny outer loop vertex v1x vertex v2x vertex v3x endloop endfacet

nz v1y v1z v2y v2z v3y v3z

The file ends with endsolid name

The ASCII STL files can become quite large, and a binary version was developed. The binary file follows the format shown below. UINT8[80] – Header UINT32 – Number of For each triangle REAL32[3] – Normal REAL32[3] – Vertex REAL32[3] – Vertex REAL32[3] – Vertex UINT16 – Attribute END

triangles vector 1 2 3 byte count

The binary version provides an 80-character header but does not allow for using the name “solid” to prevent confusion with the ASCI file. Unlike the ASCII version, the binary version includes the number of triangles stored as unsigned integer, using 32 bits (or 4 bytes). Each triangle is described by twelve 32-bit floating-point numbers three each for the x,y,z components of the normal vector and each vertex. This is followed by a 16-bit integer (2 bytes) to record the attribute byte count. In practice, the attribute is usually set to 0 and acts as spaces between the different triangle information. In some cases, it has been used to record additional information about the triangles such as color. For proper use in AM, the STL file must follow a few specific requirements:

2.2 AM Data Representation

19

1. The STL file must be “watertight”. This means that the triangles must connect to the adjacent triangles and no triangles must be missing. This is a strong topological requirement that must meet the definition of manifold geometry. A manifold geometry in this case requires that each edge connects to two faces. 2. The normal must point to the outside. While the normal is explicitly recorded in the STL file, it can be computed from the ordering of the vertices, which are recorded in a counterclockwise manner. With respect to Fig. 2.4, the unit normal can be computed by the cross product of the vector defined from vertex V1 and V2 and the vector defined from vertex V2 to V3 as follows Unit Normal N =

.

(V2 − V1 ) X (V3 − V2 ) |(V2 − V1 ) X (V3 − V2 )|

3. The triangles generated via tessellation must follow the “Vertex to Vertex” rule. In accordance with the vertex-to-vertex rule, every triangle must share exactly two common vertices with each adjacent triangle. Each triangle must share two vertices with its neighboring triangles. Thus, a vertex of one triangle must not lie on the side of another triangle. Figure 2.5 shows an invalid STL representation and two possible ways in which it can be corrected. Since the STL files are created by the CAD modeling software, and the tessellation algorithms are vendor provided in the CAD software operating as black boxes, the quality of STL files is often vendor dependent. STL files can be fraught

Fig. 2.5 Vertex-to-vertex rule

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2 Digital Processing Workflow for AM

with issues that need to be resolved before proceeding with any downstream use of the STL file.

2.2.1.1

Working with STL Files

Generating STL Files All CAD software provide the capability to export the model as an STL file and provide the user some degree of flexibility in generating the STL file by manipulating the tessellation parameters. Figure 2.6 shows the user interaction screen for the SOLIDWORKS software when creating an STL file. Solidworks provides three Resolution choices; Coarse, Fine, and Custom. Coarse will produce a highly faceted part with larger triangles. A Fine setting will produce smaller triangles, and Custom will allow user to select the tessellation parameters. The Custom option allows the user to input values for the Deviation and Angle parameters. The deviation refers to the acceptable deviation between the generated triangle facet and the actual boundary of the part, and angle refers to the maximum allowable angle between normals of two adjacent triangles. The smaller this value, more denser the tessellation in curved surfaces.

Fig. 2.6 Solidworks dialog for creating STL files

2.2 AM Data Representation

21

Fig. 2.7 Effect of STL export settings on file size

An optional requirement on some applications of STL files requires that the object represented by the STL file be in the first octant of the coordinate system. This can be easily performed by automatic translation in the CAD system while generating the STL file. When dealing with assemblies, additional options allow for creating the STL files for the individual components as separate STL files or combining them into one single file. Combining into one single file may be useful when printing a functional assembly. It is the user’s responsibility to make sure that the appropriate clearances are provided in the assembly model. From a practical perspective, choosing the right chordal deviation should be related to its impact on the final printed part. Generally, recommended values using rules of thumb recommend about 1/20th of the printed layer height and not less than one micron. This usually results in acceptable accuracy. Using smaller values often has no impact on print quality but results in unnecessarily large STL files. File Size and Resolution As discussed earlier the size of the STL file is a function of the acceptable deviation of the triangle facet from the actual surface. In practice, there is no limit on the file size, but working and transporting large files can pose problems. Cloud-based applications may have limits on acceptable file sizes. Figure 2.7 and Table 2.2

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Table 2.2 Effect of STL export settings on file size Design model Coarse Fine Custom

STL export setting Chordal deviation – 0.005 in. Angle – 30 deg. Chordal deviation – 0.002 in. Angle – 10 deg. Chordal deviation – 0.0002 in. Angle – 0.5 deg.

Number of triangles 372

File size (bytes) binary 18,684

File size (bytes) ASCII 105,300

600

30,084

169,824

8912

445,684

2,522,120

show the impact of varying the STL file generation parameters on the file sizes and differences in file sizes between ASCII and Binary. Choosing the right set of parameters is an important first step. While there is no real answer on the right set of parameters to use, the upper limits of acceptable deviations will be dictated by the final look of the desired product, the lower limit is dictated by the ability of the tessellation software and the smallest resolvable triangle that can be printed. The physical limits on printer resolution should be considered since choosing a deviation far less than the printer resolution will have no impact on the print quality.

2.2.1.2

Errors in STL Files

The quality of STL files generated by CAD software relies heavily on the computational capabilities of the algorithms embedded in the software for tessellation. Issues such as CAD models themselves not being mathematically correct, the robustness of the tessellation algorithms, difficulty in tessellating complex geometric surfaces such as NURBS (Non-Uniform Rational B-Spline)-based models, numerical imprecision introduced by floating-point computations, lack of topological information in the STL file, often lead to errors in the STL file [11]. These errors need to be fixed to avoid problems in further processing of the STL file during slicing and preventing printing failures caused by these errors. The first step in the fixing of the errors is the detection of the types of different errors that may be encountered and subsequent fixing of the errors. The detection of the errors is performed automatically using software algorithms, whereas the fixing can be either performed automatically or manually. Automatic fixing requires the use of sophisticated algorithms and often must rely on making assumptions about the missing information. In cases where the automatic fixing does not work well, the user may have to resort to fixing the files manually. Software for manipulating STL files will provide both the capabilities. Some common errors are: 1. 2. 3. 4.

Gaps, holes, or missing facets Misoriented triangles or flipped Normal Degenerate facets Overlapping facets

2.2 AM Data Representation

23

Fig. 2.8 Gaps, holes, and missing triangles [11] (© Springer)

5. Intersecting triangles 6. Unmatched triangle sides 7. Non-manifold topology conditions Gaps, Holes, or Missing Triangle Facets Gaps, holes, or missing triangle facets refer to the missing faces that guarantee a “watertight” or topologically correct manifold object. Tessellation of connected complex curved surfaces often leads to situations where the triangles at the joints may not be properly defined, small triangles may be lost, and existence of rounding errors leading to missing triangles. Figure 2.8 shows an example of the cause of such errors [11]. Detection of gaps or missing triangles can be performed by checking the STL for validity, based on the correctness criteria for a manifold 3D object using the Euler’s rule for solids: F −E+V =2×B

.

where F is the number of faces, E is the number of Edges, V is the number of vertices and B is the number of bodies in the solid. This quick check can only reveal the presence of a gap or missing triangles. Further analysis is needed to identify the actual triangles that are missing. This requires analysis of the topology of the 3D object. Unfortunately, the STL file does not contain this information explicitly and the first step in any such algorithm is to recreate the topology of the object. The topology defines the relationships between the faces, edges, and vertices that make up the object. For a valid STL file of a 3D object, the following conditions will hold: (1) each edge will appear in two faces and (2) the edge will be oriented in opposite directions in the two faces. This can be exploited to develop a simple algorithm to detect the missing triangles [11].

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Fig. 2.9 Overlapping triangles. (Adapted from Leong et al. [11] © Springer)

Misoriented Triangles or Flipped Normal As discussed earlier, all the vertices of the triangles must be listed in a counterclockwise manner. This allows for using the right-hand rule to determine the direction of the normal. The surface normal must point to the outside of the solid. Any violation of this is referred to misoriented triangle or flipped normal. In such cases, there is disagreement between the two conditions and leads to confusion between the inside and outside of the solid object. This causes further issues in slicing and in the definition of the closed contour that will define the layer boundary of each slice. Degenerate Facets Degenerate facets result when all the triangle facet’s edges are all co-linear even though the vertices are distinct. This can arise due to round-off errors in thin triangles. Overlapping Triangles May be generated due to numerical round-off errors during tessellation [11], if the round-off tolerances are set too liberally. Figure 2.9 shows an example of overlapping facets. Intersecting Triangles Intersecting triangles occur whenever triangles cut through each other. Facets may sometimes intersect at locations other than their edges resulting in intersecting triangles, as seen in Fig. 2.10. Unmatched Triangle Sides Unmatched triangle sides are created when the vertex-to-vertex rule is violated, resulting in triangles whose vertices touch the sides of adjacent triangles, as shown in Fig. 2.11 below.

2.2 AM Data Representation

25

Fig. 2.10 Intersecting triangles

Fig. 2.11 Unmatched triangle sides

Non-manifold Geometry A 3D manifold body requires certain topological conditions to be met. All geometric entities in a manifold body must belong to the same dimensional space. For a solid object, this dimension is 3D space. Manifold models are models where the volume is well defined. They satisfy the properties that every edge belongs to two faces, faces only intersect each other at common edges or vertices, and material only exists on one side of a face. For example, a single triangle by itself in 3D space is a non-manifold geometry since it is a 2D entity with no volume. A solid cube defined by the six faces is a manifold geometry in 3D. Removal of a face from the cube results in an object that is no longer manifold. This requirement of manifold geometry enforces certain properties of a solid object, such as no open boundaries, the surface being “watertight,” and a distinct inside and outside. A nonmanifold is any geometry that doesn’t meet the requirement for a manifold. From a physical perspective, a non-manifold object can be represented in a computer model; however, it cannot be physically realized and hence cannot be manufactured by AM. Figure 2.12 shows some examples of non-manifold geometry that might be encountered in polygonal meshing.

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2 Digital Processing Workflow for AM

Fig. 2.12 Non-manifold objects

Fig. 2.13 Improved triangular mesh after decimation

Reducing File Size Files with large number of triangles can be quite large in size depending on the settings chosen for the chordal deviations. Files with large number of triangles require more processing for display as well as further computations during slicing and other operations. This may also be the case with STL files that are created from point cloud data and MRI and computer tomography files which often result in oversampled data. In such cases, decimation operations may be used to reduce the number of triangles while trying to preserve the original geometry. Figure 2.13 shows an example of decimation of a single planar face. Repairing STL Files Before using the STL files, they must be checked for errors and the errors repaired. The errors are typically fixed using software that can detect the errors and provide the capability to either automatically fix the errors or allow for manual fixing of the errors. Table 2.3 lists some of the available software for repairing and fixing STL files.

2.2 AM Data Representation Table 2.3 Software for repairing and fixing STL files

27 Software Netfabb (Autodesk) Magics Polygonica Meshmixer Meshlab Blender

Commercial/open source Commercial Commercial Commercial Open source Open source Open source

Other Limitations of STL Files The developments in the capability of AM machines and increased use of STL files have exposed additional limitations with STL files. 1. Data redundancies. Data redundancies create several problems. The first is that storing values multiple times wastes space. The second problem is that when a value changes, multiple occurrences need to be updated. The STL file requires that all the vertices be listed for each triangle. Hence, each vertex appears in two or more different triangles, leading to redundancy in representation. Furthermore, the normal can be computed from the clockwise orientation of the vertices and can be easily omitted. 2. Slow to process. The STL file does not explicitly contain any topological information related to the connectivity of the geometry. It is basically a “triangle soup” with no ordering. Common tasks that require checking for errors or properties of the solid cannot be easily conducted without first creating the topological information. This step is tedious, error-prone, and often quite slow. 3. Unit ambiguities. The STL representation does not store the units anywhere in the STL file; hence, when working with the STL file additional information needs to be provided related to the units of measurement. 4. Scale poorly. The STL files are generated using the deviations provided when creating the STL file. If an STL file is scaled up, it in effect increases the deviation resulting in an STL file with poorer resolution. 5. Cannot accommodate colors, multiple materials, or texture. There is a growing gap between what AM machines can make and what a STL file can represent. For example, newer generation of AM technology can work with colors, multiple materials, and textures but this information cannot be represented in the original STL file. These limitations with STL files have led to the need for other standard representations, that are potentially more suitable for modern AM technology.

2.2.2 OBJ Format The OBJ format was not originally intended for AM but for use in graphics to share 3D models. It was developed by Wavefront Technologies to store geometric

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information along with color and texture information [20]. Since it can store color and texture information, it was quickly adopted by AM machines capable of multicolor printing. Similar to the STL file, the OBJ files are created by the CAD software. In addition to storing tessellated polygonal geometry shapes, it can also store geometry in surface form such as Bezier curves and surfaces, non-uniform rational B-splines (NURBS) without triangular tessellation, thus resulting in more precise files and smaller file sizes. In its simplest form, the surface of the model can be tessellated into simple geometric shapes like triangles. The vertices and normal to the polygons are stored, similar to the STL file. The OBJ format also extends this concept to other simple polygons. The OBJ file format uses companion files in material template library (MTL) format. The MTL file contains text that defines the material properties such as color, and properties needed for light-reflecting computations. It also supports texture maps included as images to specify color and textures.

2.2.3 AMF The Additive Manufacturing File format was introduced in 2011, as an alternative to STL, and accepted as a standard by ISO/ASTM 52915 [4]. The primary goal was to address the limitations of the STL file and provide an XML-based format to contain native support for additive manufacturing data such as geometry, scale, color, material, lattices, duplicates, and orientation. XML was chosen as the representation since it is text-based, easy to read/write/parse, extensible and highly compressible, and editable with existing editing tools. The AMF format represents an object by a hierarchy of five elements: object, material, texture, constellation, and metadata [4]. • The object element defines a volume or volumes of material using mesh geometry, each of which is associated with a material ID for printing. It represents the object using triangular meshes similar to STL but with one major difference. It allows for curved triangles in addition to the planar triangles. The use of curved triangles allows for describing a curved surface without using too many facets, thus handling a curved surface with fewer triangles resulting in a smaller file size compared to STL. At least one object element must be present in the file. Additional objects are optional. • The optional material element defines one or more materials for printing with an associated material ID. If no material element is included, a single default material is assumed. • The optional texture element defines one or more images or textures for color or texture mapping, each with an associated texture ID. • The optional constellation element hierarchically combines objects and other constellations into a relative pattern for printing. This feature allows manufacturers to specify the relative pattern of the objects within the

2.2 AM Data Representation

29

Fig. 2.14 (a) Solid model, (b) STL mesh for a two material part

file, and allows multiple objects to be arranged within the file, specifying their location and orientation. • The optional metadata element specifies additional information about the object(s) and elements contained in the file. Information such as name, author, company, description, volume, tolerances, and much more can be easily incorporated into the data file. • As an example, consider a simple geometry of a part made of two materials, as seen in Fig. 2.14a. The STL mesh for the part is shown in Fig. 2.14b with the vertices labeled for each of the two material boundaries. In Fig. 2.15, AMF file for the example part shows a partial AMF representation for this part (the full definition of only one object is shown). The part is defined as a constellation made up of the two objects identified by the object id. Each object is identified by an id and a material id, along with color. The geometry is specified by the mesh which lists each vertex’s coordinates and a volume defined by the triangles. Each triangle is defined by three vertices listed in counterclockwise direction. A pointer to the vertex is used to point to the vertex coordinates. The units are listed in the header.

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Fig. 2.15 AMF file for the example part

A significant difference between the AMF and STL formats is the ability to use curved triangles to reduce the deviation error. The edges of the curved triangles are represented by Hermite cubic curves, defined mathematically by the vertices and the vertex normal or edge tangents, as shown in Fig. 2.16. The equation defining each edge of the curve triangle is determined by the end points and tangent at the end points and is given by the following formula: ⎡ ⎡ ⎤ ⎤ ⎤ dx 1  x1  x2     3 2 3 2 + ⎣ dy 1 ⎦ t 3 − 2t 2 + t .Q(t) = ⎣ y1 ⎦ 2t − 3t + 1 + ⎣ y2 ⎦ −2t + 3t z1 z2 dz1 ⎤ ⎡ dx 2   + ⎣ dy 2 ⎦ t 3 − t 2 dz2 ⎡

2.2 AM Data Representation

31

Fig. 2.16 Representing a triangle edge with curve using end points and tangents

Fig. 2.17 Subdivision of the curved triangles

where t is the parameter ranging from [0,1], [x,y,z] are the coordinates of the end points, and [dx ,dy ,dz ] are the tangent vectors at the end points of the curve. In the case that the normal at each vertex is specified, the tangent vectors can be computed from the normal and the vector connecting the two vectors. Given the two vertices v1 and v2 , and n1 as the normal at v1 , then the tangent at v1 can be computed such that it is perpendicular to the normal n1 and residing in the plane defined by the normal and the vector connecting the two vertices v1 and v2 . The following formula can be used to compute the tangent t1 . Define d = v2 − v1 t1 =| d |

.

− (n1 × d) × n1 | (n1 × d) × n1 |

This curved triangle can be recursively subdivided into 4n triangles by choosing the midpoint of each triangle edge curve, where n is the number of subdivisions (Fig. 2.17). Each subsequent subdivision results in reduction of the error between the actual surface and the curved triangle. A five-level deep subdivision results in 1024 triangles. These are generated on the fly and only stored temporarily during processing. A major problem with the AMF format is its slow adoption by the industry and CAD vendors, which has led to lack of software throughout the process chain. An additional problem was the lack of buy-in from the key industry players.

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2.2.4 3MF The 3MF format was developed initially by Microsoft with the goal of integrating 3D printing into their operating system and making it as simple as document printing. A consortium of key industry players from CAD vendors, equipment manufacturers, and end users representing the complete process chain has been involved in its development with the goal of “Advancing the print industry with a universal specification for 3D printing” (“3MF Specification” n.d.). According to the 3MF consortium, its goals for the 3MF file format are for it to be: Complete: Containing all of the necessary model, material, and property information in a single archive Human readable: Using common structures such as OPC, ZIP, and XML to ease development Simple: A short, clear specification, making development easy and validation fast Extensible: Leveraging XML namespaces allow for both public and private extensions while maintaining compatibility Unambiguous: Clear language and conformance tests ensure a file is always consistent from digital to physical Free: Access to and implementation of the 3MF specification is and will always be free of royalties, patents, and licensing The 3MF format represents a 3D model in a markup format that includes fundamental information necessary for a consumer to generate a physical object through additive manufacturing. It also includes optional components required to generate a physical object such as print job control instructions, describe assembly of objects to be built simultaneously, and other features. The 3MF document format follows the Open Packaging Conventions specification that also supports digital signatures and core properties. Figures 2.18 and 2.19 show the basic structure of the 3MF file format (Table 2.4). The 3MF representation of the example part shown in Fig. 2.14, is shown in Fig. 2.19. As seen in the figure, the geometry is represented by the STL mesh, along with the additional information related to part units, color, material information, etc.

2.3 Slicing The 3D models in the representation format used must be first sliced into layers since the AM process creates the part by adding material layer by layer. The result of slicing is the contour geometry that defines the material region of the layer to be built.

2.3 Slicing

33

Fig. 2.18 Structure of a typical 3MF. (Document © 3MF Corporation used with permission. https://github.com/3MFConsortium/spec_core/blob/master/3MF%20Core%20Specification.md)

Fig. 2.19 3MF 3D model representation for the example part

2.3.1 STL-Based Slicing Figure 2.20 shows the conceptual approach to slicing an STL file. The build direction is the z axis. The current layer at which the object needs to be sliced is

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Table 2.4 Parts of a 3MF document Name 3D model Core properties Digital signature origin Digital signature Digital signature certificate PrintTicket

Thumbnail

3D texture

Custom parts

Description Contains the description of one or more 3D objects for manufacturing The OPC part that contains various document properties The OPC part that is the root of digital signatures in the package OPC parts that each contains a digital signature OPC parts that contain a digital signature certificate Provides settings to be used when outputting the 3D object(s) in the 3D model part Contains a small JPEG or PNG image that represents the 3D objects in the package or the package as a whole Contains a texture used to apply color to a 3D object in the 3D model part (available for extensions) OPC parts that are associated with metadata

Relationship source Package

Required/optional REQUIRED

Package

OPTIONAL

Package

OPTIONAL

Digital signature origin Digital signature

OPTIONAL

3D model

OPTIONAL

Package

OPTIONAL

3D model

OPTIONAL

Package

OPTIONAL

OPTIONAL

© 3MF Corporation used with permission https://github.com/3MFConsortium/spec_core/blob/master/3MF%20Core%20Specification.md

represented by a plane z = zlayer . This plane intersects some of the triangles in the STL file. Since each triangle defines a plane, the slicing process is essentially a plane-plane intersection which results in a line segment that defines a boundary section of the contour that will form on the slicing plane. The overall goal of the slicing process is to create properly oriented contour geometry for each slice, that clearly demarcates the inside and outside. This contour geometry is then subsequently used for tool path planning. The basic steps performed in any slicing process require choosing the slice plane, computing the plane-triangle intersections, and assembling the resulting line segments into a closed-oriented contour, as shown in Fig. 2.21. The selection of the slicing plane can be in a constant step corresponding to the layer thickness produced by the machine resulting in uniform slicing or can be a variable based on some optimization criteria, resulting in what is termed adaptive slicing. The slicing step is the problem of finding the intersections of the individual triangles contained in the STL file with the slicing plane. The STL file is basically a

2.3 Slicing

35

Fig. 2.20 Slicing a 3D STL file

Fig. 2.21 Steps in the slicing process

“triangle soup” with no ordering; there are several potential scenarios, as shown in Fig. 2.22, that can arise when intersecting a triangle with the slice plane. 1. The plane intersects two edges of the triangle, resulting in a line segment. 2. The plane passes through a triangle vertex, resulting in a point. 3. One of the edges of the triangle lies on the slicing plane, resulting in a line segment, which is the same as the triangle edge. 4. The plane is completely above or below the triangle and there is no intersection. 5. The complete triangle lies on the slice plane. The calculation of the intersection involves intersection of each edge of the triangle with the plane (z = zi ), and can be calculated using the equation, where

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Fig. 2.22 Scenarios in plane-triangle intersections

P1 (x1 ,y1 ,z1 ) and P2 (x2 ,y2 ,z2 ) correspond to the start and end point of the triangle edge and P(X,Y,Z) is the intersection point given by the following equation set. 1 )(x2 −x1 ) X = x1 + (zi −z (z2 −z1 ) (zi −z1 )(y2 −y1 ) . Y = y1 + (z2 −z1 ) Z = zi

Intersection with the second edge of the triangle will result in another point of intersection, and the two points form the intersection polyline segment. The polyline line segments produced by slicing must be organized into one or more closed polygons that clearly demarcate the inside and outside region on each slice. This step is called the contour reconstruction step. The result of slicing must clearly identify each contour and its relational position. An example result is shown

2.3 Slicing

37

Fig. 2.23 Result of contour construction Table 2.5 Examples of proprietary slice file formats

File format SLI SLC SSL ABF CLS SLM

Vendor EOS 3D systems Stratasys Arcam Concept laser Selective laser melting

in Fig. 2.23. The convention used is to represent the vertices defining the outer contour in a counterclockwise manner, and the internal contours in a clockwise manner so that the material is always to the left when traversing the contour.

2.3.2 Representation Format for Slice Files The purpose of slicing is to generate the input required for subsequent tool path planning. Due to the tool path generation requirement, that often relies on the specifics of the machine, the software for slicing is often included in proprietary software that interfaces with the machine. Hence, most machine manufacturers implement their own slicing procedures and internal proprietary representation formats for the slices. This makes it difficult for data exchange at the slice level. Table 2.5 lists some examples of proprietary file formats. Common Layer Interface- CLI [5] was developed as a 2 ½-dimensional unambiguous format for data input to all layer-based manufacturing systems. It was intended to be independent of vendors or fabrication machines and could be adapted

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Fig. 2.24 Example ASCII CLI file format [6]. (Used with permission)

easily to accommodate conversion into vendor-specific internal data structures, thus facilitating use over wide-ranging applications without hindering data transfer between different applications and machines. The CLI format assumes that the building plane is the positive z-axis and the part is in the first octant. It defines a layer as the volume between two parallel slices and is defined by a thickness, a set of contours, and optionally hatches. The contour represents the boundaries of the within the layer and marked as internal or external contours where it is defined by closed non intersecting polylines oriented such that the material regions can be identified. The polylines are defined by a set of x,y vertex points ordered contiguously in the listed order by straight line segments. A closed polyline forms a polygon. Optionally, hatches can be included, where a hatch is an independent set of straight lines each defined by one start and one end points. The purpose of the hatch is to define support structures or filling structures. This information is represented using ASCII as well as binary file formats, using the standard syntax as defined by the CLI format. Figure 2.24 shows an example ASCII CLI file. The format for each line is KEYWORD/parameter. The header section contains information about the file, units, date, and number of layers. This is followed by the geometry section, which is listed as a stack of layers identified sequentially by the height. The first polylines are defined by a sequence of x,y coordinates of the end points of line segments. The first line segment begins at (0,0) and ends at (5,1.00). The second segment then begins at (5,1.00) and ends at (2.2,3.0), and so on. The Hatches are open line segments, the first hatch in the example is defined by start (0,2) and end (10.2,10.4), and so on. Additional polylines and hatches can be used within each layer.

2.3 Slicing

39

Fig. 2.25 Staircase effect and cusp height

2.3.3 Implications of Slicing Since the AM parts are built by approximating the part with a set of stacked layers in the build direction, this results in quantization of the part, which impacts the fidelity of the part form and introduces additional errors and side effects that impact the surface quality of the part. To evaluate the errors introduced by layering, two concepts are used to evaluate the extent of the error: cusp height error and volumetric difference. Building the part in layers creates a staircase effect on all curved and inclined surfaces. The cusp height error is defined as the maximum distance between the manufactured part and the designed surface [3] (Fig. 2.25). The cusp height depends on the layer thickness and the angle between the local surface orientation and the build direction [3] and can be calculated as h = L ∗ cos α

.

The integral of the cusp height has also been used as a good estimate for the fidelity of the built part. For triangulated surfaces, the cusp height is computed separately on each facet as the dot product between the build direction b and the triangle normal n, | cosα | = |b . n|. It is then scaled by the triangle area and normalized by the total mesh area to accommodate uneven tessellations and make it scale-independent [19]. Volumetric difference refers to the difference between the volume of the designed object and the volume of the AM manufactured part, which has also been used as a metric [12]. While both cusp height and volumetric error are used as proxies to evaluate the staircase error introduced through building in layers, they are not equivalent. Since these metrics depend on the orientation in which the part is built, they are often used to evaluate and optimize orientation and for determining the variable layer thickness in adaptive slicing.

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Additional implications of building in layers relate to the surface roughness resulting from the staircasing effect. Typical metrics of evaluating surface roughness such as mean surface roughness (Ra) is often the metric used. The surface roughness is also impacted by the direction in which the surface is facing. Upward-facing surfaces (with the z component of normal pointing in the build direction) will have a better surface finish compared to downward-facing surfaces. Additionally, the surface roughness of downward-facing surfaces will also be impacted by the support structures that may need to be added to downward-facing surfaces. How the layers are created from the slice geometry can also have an impact on the final result. The slice geometry lies on a plane, the built layer has a thickness. How the layer is created from the slice geometry can influence the actual volume that is built. The volume of the built layer can be established by either projecting the lower slice to the next top slice (bottom-up), or by projecting the upper slice to the next bottom slice (top-down). Depending on the method implemented, this can result in some layers of the built part to be larger than the actual geometry and others to be smaller depending on the curvature of the object. This problem was referred to as the containment problem in [14] and illustrated in Fig. 2.26. Layering algorithms can be created that only generate one type of containment error, positive (with extra material on all curved surfaces) or negative (all layers undersized), as shown in Fig. 2.27. Building in layers can also have an impact on the dimensional accuracy of the part. Surfaces on the part that end up lying between the slices will end being shifted to the layer above or below depending on the strategy being used to create the layer walls, which can result in loss of dimensional accuracy. Additionally, features that lie entirely between layers may completely disappear. While these issues are not as prominent when manufacturing in thin layers, the impact is magnified when working with thicker layers associated with high-volume deposition AM processes. Figure 2.28 shows the implication of this.

Fig. 2.26 Layering created from slicing

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Fig. 2.27 Layers created using positive and negative tolerances Feature Eliminated

Feature moved up

Slice Planes Printed Layer

PART

Fig. 2.28 Impact of layer thickness on features

2.3.4 Adaptive Slicing Adaptive slicing relaxes the constraint that the slicing thickness is uniform (Fig. 2.29). Thus, allowing for variable slice thickness results in fewer layers and hence, a decrease in the build time of the part, along with potential improvements in surface finish and volumetric deviations. Adaptive slicing relies on some form of objective function to establish the variable position of the next slice. Three primary criteria have been proposed – (i) Limits on acceptable cusp, (ii) surface roughness, and (iii) volumetric deviations [8].

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Fig. 2.29 Adaptive slicing and layer thickness

While the concept of adaptive slicing and non-uniform thickness layers is appealing from a perspective of reducing the build time, the actual use in practice is often limited due to several reasons. The various metrics and their implications on the final part are not well understood from a user perspective. The physical manufacturing of different thickness layers requires a good understanding of the process parameters to ensure that the process is capable of executing process parameter changes to ensure that the different layer thickness can be built, as well as ensuring that these changes in process parameters are capable of producing the material without defects and other manufacturing issues.

2.3.5 Direct Slicing of CAD Models Tessellated geometry is a first-order approximation. As seen earlier, it introduces errors caused by the chordal deviations due to the approximation by planar triangles. It was primarily developed during the early days of rapid prototyping when accuracy was not a primary concern, and the 3D CAD modeling tools were not as developed as they are today. With the push to use AM for production-ready parts, the need for accuracy has increased. Furthermore, the tessellated geometry itself introduces errors that must be fixed, and adds additional steps to the processing chain. It does not contain the topological and geometric robustness that the current generation of 3D CAD modeling tools can provide. Direct slicing of CAD models can easily be accomplished in today’s generation of CAD models. The functions required to perform direct slicing using a plane are available as cross-sectioning functions and can be implemented via macro programming or programmed routines. The geometry of each slice does not need to be limited to polylines and the actual contour geometry for each slice can be stored, and subsequently exported for tool path generation [21]. Existing CAD standards such as IGES or STEP can be used to store and share the slice information.

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2.4 Part Orientation and Build Direction Parts are built via AM, one layer at a time. The build direction in most cases is the z-axis of the machine. However, the part can be oriented with respect to the z-axis in an infinite number of ways. Part orientation describes the rotation of the part in the build space around the axes of the machine’s coordinate system. Determination of the build orientation is one of the most important steps in process planning for AM and has implications on all subsequent steps in process planning as well as the final outcome. It impacts build time, the requirement for support structures, surface roughness, geometry to be built on each layer, and hence the thermal behavior of the part as it is being built along with the impact on internal stress buildup and distortion, microstructure development as a function of the thermal behavior, and, eventually, the mechanical strength of the part [10]. The problem of choosing a build orientation is compounded by the fact that the various objectives often contradict each other. Build time: The time to build a complete part is a function of the number of layers, the time to physically build the layer geometry, and the time for preparation of the layer. Under most situations, the part build time is impacted the most by the number of layers. Build Geometry on each layer: As can be clearly seen from Fig. 2.30, the different orientations of the part in the build volume will result in very different geometry for each layer during the slicing procedure, and hence different tool paths to deposit the material. This has implications on the thermal behavior of the part as it is being built. Support Structures: For a successful built of the part, supports must often be provided to support overhanging geometry of the part and disconnected islands that may form as an artifact of building in layers. For metal additive manufacturing, support structures present significant potential for increases in material consumption, energy use, and amount of effort to remove the support structures and its consequences on surface finish. It can significantly increase the level of manual intervention necessary in an otherwise digitally automated process and negate the economics benefits. The part orientation can significantly impact this, as seen in the figure.

Fig. 2.30 Part showing three different build orientations

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Surface Roughness: As seen earlier, slicing an object results in staircasing effect on the surfaces, leading to surface roughness on the part. The amount and location of the surface roughness depend on the orientation of the past as it is built [2]. The surface roughness can be minimized by building the surface of interest in a horizontal or vertical orientation. Impact on part properties: The layering effect can result in anisotropic properties in the part. Research has shown that mechanical properties along the build direction are often lower than those in the xy plane. Selecting a good build direction is a balancing act between trying to address the various implications of the choice, such as build time, support volume, accessibility of supports for removal, protection of functional faces, distortion tendencies, postprocessing implications, and matching the part to the build volume.

2.5 Support Structures The need for support structures is heavily influenced by the process being used as well as the part orientation, and often done iteratively with the determination of the build direction. Support structures play an important role in the manufacturability of the part as well as the thermal dissipation during the build process [7]. Supports used to improve manufacturability involve the use of supports to support any overhanging and free-standing islands that may develop during the slicing process (Fig. 2.31), supports to anchor the part so it can resist mechanical forces during the build, for example, the forces encountered during the recoating process when using a metal blade in a powder bed deposition process, and ensuring stability of the part during build in cases where the balance of the part during the build needs to be maintained. Metal AM processes are accompanied by high thermal gradients, which result in residual stresses due to the high heat accumulation and rapid cooling rates. These residual stresses often result in shape distortions, and the support structures are used to enhance the rigidity of the part and prevent any part movement caused by the distortions. In some cases, the support structures may be used to remove the excessive heat accumulation from areas of the part where it could be detrimental for part properties and surface finish. Other support structures may be added to facilitate removal of the part from the build plate. While the support structures can help with these problems, they introduce their own set of challenges for AM. Adding support structures lead to wasted feedstock material since they are often not reusable, add to build time, add to additional postprocessing time and cost associated with removal of the supports and cleanup of surfaces where the support structures are attached to the part. Considerations for removal of support structure must be addressed while planning the build of the part, since in some cases access to the support structures may hinder removal of the support structures. Different geometries have been proposed for use as support structures, as shown in Fig. 2.32. General design principles for support structures follow some basic

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Fig. 2.31 Overhangs, islands and self supported features

Fig. 2.32 Different geometries for support structures

guidelines. The contact between the support structure and parts should be as small as possible and use geometry that facilitates easy removal and limit the impact on the surface being supported. The support structures should use as little material as possible to reduce material use and build effort. The design and selection of the support structures are often a tradeoff between the success of the final build, its quality, and the time and cost to remove the support structure. Minimizing the use and impact of support structures requires considerable effort. Two main approaches are often considered when addressing the support optimization problem. The first approach assumes that the design is fixed and cannot be changed. In this situation, the effort is around selecting the best build orientation, optimizing support structures, while balancing the downstream needs of support removal. Another approach is to modify the design to reduce or eliminate the need for support structures. Using the capabilities of AM to build complex geometries, the part design can be modified to reduce and eliminate the need for support structures. Topology optimization, use of lattice structures, and designing around the machine limitations can be used to reduce the support structure requirements.

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2.6 Tool Path Generation After the build orientation and support structures are determined, the part is sliced via the slicing algorithms to determine the geometry to be built on each layer. Since the support structures must build simultaneously with the part, the geometry for each build layer must also incorporate the geometry of any support structure that must be built. Tool path generation refers to the process of determining how each layer will be physically built and involves determination of the motion path of the machine components primarily the deposition head or laser that will be used to physically build the layer. In addition to generating the path sequence, this step also involves assigning the processing parameters to the path. A typical tool path for a single layer comprises two main areas – the boundary contour and the infill area. The boundary contour defines the outer boundary of the build geometry obtained by slicing. A single line of material created is characterized by the width of the line generated, which depends on the actual process being used. For a PBF and DED process, it is determined by the size of the laser spot and the melt pool that is generated and can range from 10s of microns for a PBF to several mm for a DED process. For tool path planning purposes, the width of a single line must be known. Although for machine programming purpose the center line is programmed, information on the width is necessary for proper offset of the fill contour and spacing of the hatch lines for the infill area. Spacing of the lines is referred to as the hatch spacing. Figure 2.33 shows the various parameters that define a generic tool path and some nomenclature used for extrusion-based tool paths and laser scan-based tool paths. It is the task of the tool path planner to determine the best values for these and these will depend on the actual process for which the tool path is being planned. Different strategies may be employed to create the infill region of the part. Figure 2.34 shows different infill patterns that can be used with varying amounts of infill percentage to allow for changes in part density and impact the build time. Additionally, different strategies may be used to change the number of wall contours. The selection of these strategies plays an important role in part build time, part strength, as well as implications of residual stress and success of the build. Within these overall strategies for tool paths, additional tool path considerations that influence the tool path may include where the tool path begins and ends and how it is traversed. In a simple line-based strategy, the infill region is simply filled with parallel lines that start and stop at the boundary of infill area, and separated by specified hatch spacing. The scanning path along these lines is unidirectional or bidirectional. If a completely solid part is desired, the hatch spacing must allow for a certain amount of overlap between the line widths created. In the case of a sparse infill, gaps are allowed between the lines and once again influenced by the hatch spacing selected. Parallel contours can be used to create infill regions by successively offsetting the boundary of the infill region by the hatch spacing amount. Spiral contours are an adaptation of the parallel contours where the continuity between successive contours is maintained. These approaches may not be applicable

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Fig. 2.33 Tool path planning nomenclature extrusion and laser scan

to complete regions of the part due to the complexity of the geometry and may require decomposition of the infill region into areas where different tool paths may be applicable. A tool path requires starting and stopping for each individual line, which involves acceleration and deceleration at the end points, respectively, along with compensation of the parameters to ensure that a uniform line width is created at different travel speeds. Hybrid approaches that build on the primitive tool path strategies are also often employed. Research has shown that the scan strategy can have a significant impact on the part quality (pores and voids) and on the thermal impact induced by the scanning sequence. Different scanning strategies can result in differences in residual stresses and subsequent build failures. Besides having a direct influence on residual stresses, scanning strategies determine several other outcomes, such as

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Fig. 2.34 Various infill and build strategies

tensile properties, achievable density, microstructure, and surface finish [15, 18]. These researchers have concluded from prior research that reducing the scan vector length, through subdivision of the region to be scanned, is effective in reducing the magnitude of generated thermal stresses. Common scan pattern strategies used in PBF are – stripe scanning and checkerboard each with its own set of options (Fig. 2.35). The stripe pattern is a band defined by the scan vector width (i.e., stripe width), the hatching space between adjacent tracks and the scan direction, as well as the overlap with the neighboring stripes. The chessboard pattern – or checkerboard pattern – is defined by squares like the squares on a checkerboard. This pattern of squares is defined by the side length of the square, the hatching distance between adjacent tracks, and the overlap between squares. Different scanning patterns can be implemented within each square, and the squares can be scanned in a multitude of different sequences – from random to systematic patterns. When building multiple layers, these inlayer strategies and patterns can be shifted, rotated at various angles across successive layers. Large number of permutations are possible. Additionally, each layer geometry is split into different regions based on whether there is material above or below in the layer region. Each layer may be divided into areas such as core, skin, upskin, downskin, contour, and infill. This gives the flexibility to assign different process parameters to each region. This is important because the melting process and heat transfer are different depending on the location of the material (Fig. 2.36). Figure 2.36 shows the deconstruction of a part into different regions as performed by EOS and 3D systems Expert software. Contours define the outer region of the

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Fig. 2.35 Common powder bed fusion tool path strategies

part and are usually processed with slower speeds and lower powers to generate a more stable melt pool during processing, yielding more accurate dimensions and a better surface finish. In contrast, higher laser powers and faster scanning speeds are characteristic of part infill in order to more quickly build up the bulk of the component. Between these two regions, the skin region can act as a transition region between the processing parameters used for the outer contours and the infill. However, the skin region is often excluded from processing parameter “recipes” for simplicity. Finally, up-facing and down-facing surfaces are special cases which attempt to improve the surface finish of AM parts. Like contours, up-facing surfaces are processed with slower speeds and lower powers to create a clean finish while the intent of down-facing parameters is to minimize surface-adhered particles. Each of these regions is capable of being processed with its own tailored processing parameters for laser power, scanning speed, hatch spacing, etc. It is important to note that this decomposition into different regions is typically proprietary to the software and no standards exist to ensure consistency across different software and companies. Production-oriented PBF processes are being developed with multiple lasers to significantly cut the amount of time to process each layer. Systems with multiple lasers, 2, 4, and even up to 12, have been developed and pose additional issues for consideration when generating tools. More than one laser working in close proximity raises issues related to the direct interaction of the lasers as well as

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Fig. 2.36 Part decomposition for parameter regions by EOS MAGICS and 3DS expert

the interaction of the effects produced by the lasers [13]. Emissions, ejecta, and smoke created by one laser can impact the other lasers, especially if one laser is downwind of the other. Forcing the lasers to work in zones and using gas flows to avoid the effects of emissions, and ejecta can be used to avoid some of these problems. Balancing the scan time between the lasers must also be considered to avoid reductions in productivity caused by lasers having to wait for others to finish before moving on to the next layer. The layer processing time will depend on the start time of the first laser and the finish time of the last one. The use of independent optical systems for each laser can lead to drift between the different lasers which can cause alignment issues at the overlap area of zones, especially when this area belongs to the same part. Some machines allow for full overlap allowing each laser to cover the full build plate allowing for the potential of a more efficient use of each laser. While this can significantly reduce the time to build large parts, additional

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research is necessary to fully understand the implications and limitations introduced. Strategies such as assigning each laser to a single part and positioning of parts to avoid downwind implications of gas flow can be used. When working on a single part, it may be possible to divide the part into horizontal zones for each laser to work within. The zonal boundaries pose problems in this case. To avoid discontinuities in the part boundary, a single laser may be used to create the boundary and multiple lasers working in close proximity to fill the interior. Laser interaction effects are distance related and are minimal when lasers are working further apart.

2.7 Nesting/Packing the Build After the complete set of plans are developed for a single part it is ready to be sent to the machine to build. In many cases, if the build platform has enough space, it is not uncommon to group multiple parts at the same time in the same build. This is cost-effective from an economic perspective as it minimizes the number of machine setups needed during which the machines are not useable. In some cases, nesting is usually an early design consideration in the production of metal AM. Nesting and optimal orientation can be a trade-off in some cases, and economics resulting from nesting may constrain the choice of build orientations. Nesting or packing process allows for a collection of parts to be organized on the build platform and fit in the build volume (Fig. 2.37). In some cases, the parts cannot be stacked on top of each other due to the requirements of support structures. In this case, the nesting is performed in a two-dimensional space (Fig. 2.38). For some processes, such as Fig. 2.37 3D nesting of parts for a single build. (©Materialise. Used with permission)

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Fig. 2.38 2D nesting of parts for a single build. (© Croft Additive Manufacturing Limited. Used with permission. https://www.croftam.co.uk/wp-content/uploads/2019/01/Full_Base_Plate_Shoe_ Parts.jpg)

binder jetting and ebeam powder bed fusion, where the powder itself can serve as the support, three-dimensional stacking is also possible to maximize the complete build volume. While the goal of nesting is to allow for packing as many parts as you can in the build volume, parts with specific constraints may limit some of the placement options and available degrees of freedom. Additionally, the risk of build failures and crashes must also be considered during nesting and balanced with the part nesting based just on geometric considerations. The capability for nesting is either provided by independent AM software providers or by the machine software. The Figure 2.37 shows the capability of a commercial software to perform 3D nesting for a binder jetting powder bed process and improve the utilization of the build volume.

2.8 Machine Setup Once the software steps are complete, the next step is the preparation of the machine to build the part. While the exact set of activities is machine and process dependent, this set of activities can be grouped into two sets: (1) prepping the machine to build and (2) setting up the build and environment parameters that are necessary for a successful build but not included in the tool path. For a powder bed fusion process, prepping the machine to build consists of several steps – cleaning the machine from the previous build, filling the powder hoppers, checking the build parameters of the machine, and adjustments to the machine components such as re-coater blade gaps. The build and environments parameter setting refers to tasks and machine settings that are necessary for a successful build but not included in the tool paths. This includes parameters such as recoating speed and motion, gas flow rates, chamber temperature, and oxygen levels. Some of these parameters are monitored during the build for process control purposes. In the process, diagnostics on the machines

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are possible for machines equipped with sensors and diagnostic tools. Examples of such diagnostics include melt pool monitoring to analyze size and shape of melt pool. Imaging systems can be used to monitor each layer to ensure the fidelity of each layer as it is being built.

2.9 Post-processing of the Build Once the build is complete, this set of activities is an essential component to the process. The parts need to be removed from the build chamber. It involves removing the excess powder and extraction of the build plate from the build chamber. At this stage, the part is still attached to the build plate. And the excess powder must be carefully removed. Building a metal part with rapid heating and cooling at each layer, results in parts that are thermally stressed and have high residual stress. The next step in the process is often residual stress relieving. The build plate along with the part is put into a heat-treating oven and heated to high temperature and held there for a while to help remove the residual stresses in the part. This prevents part warpage after the part is separated from the plate. Separation from the plate requires either using a band saw or EDM to cut the part and support structures from the build plate. Removal of support structures can range from simply breaking off the supports to having to cut them via EDM or CNC machining. Once the parts are removed from the build plate, and supports removed additional heat treatments may be applied to improve the part qualities. Hot isostatic pressing (HIP) may be used to remove internal porosity and increase part densification. Additional heat treatments may be necessary to improve the microstructures, and additional machining operations to improve surface finish and tolerance requirements may be necessary. The implications of post-processing after the build should be considered since it is a large factor in the processing time and cost of the part. The final step in post-processing is quality control and quality assurance to ensure that all the part specifications are met.

2.10 Simulation The workflow for AM follows a systematic approach as shown in Fig. 2.1. While a good manufacturing plan can be generated using the workflow, the feasibility of the plan working to ensure that the part is produced right the first time is still questionable, even for experienced AM users. Failure to print correctly and requiring multiple iterative builds can become time-consuming and costly. What is not obvious and clear is the implications of decisions made during the part design and process planning stages on the final part. For example, what impact will the choice of build direction have on the final part, its microstructure and properties, and potential issues during the build? What amount of distortion can be expected

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Fig. 2.39 Simulation of additive manufacturing process. Part distortion resulting from additive manufacturing process, generated by the Simufact Additive software. (Credit: Hexagon. © Hexagon. Used with permission)

during a build? Will the support structures be adequate? Given the digital nature of the process, validated simulation models can be used to evaluate the impact of the process planning decisions, quantify the uncertainty and even optimize the process via virtual experimental studies. Simulations can be used at various stages to help with choosing the right decisions to improve the probability of building it right the first time. Developing a simulation process that can accurately predict the outcomes of the AM process will help to drive the adoption of the technology. For these simulations to be viable, the results need to justify the added cost and effort. It needs to be accurate, timely, and able to predict the performance of components to be worth the added investment. Figure 2.39 shows the results of displacement simulation in Netfabb additive software tools. A precursor to developing simulations is the ability to model the process. The AM process occurs at various scales from the micro-, meso- to the macroscale. Integrating simulations across various time scales in an efficient manner is a challenging task. Simulations associated with the material-energy interaction occur at the microscale and can be used to predict the resulting microstructures. The time step associated with microlevel simulations is very small, and microlevel simulations of manufacturing a complete part may be very time- and computingintensive. Mesoscale simulations involving the actual tool path and simulating the travel of the deposition process can be used to generate thermal history of the part.

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At the macroscale, the thermal history could be used to determine the internal stresses and resulting distortions on the part. The challenge is to connect all of the different scales within a component’s design – including the top part-level, multilayer tool paths and process parameters, and melt pool level dynamics – into a complete framework, while balancing the computational workload to be able to provide reasonable results in a useful timeframe. The availability of such simulations will ultimately provide the capability for virtual evaluation of process planning decisions, make predictions on the outcome of the part and allow for rapid replanning with the goal to get it right the first time. Current generation of simulation software has focused on the macrolevel simulations that accept process parameters as input and provide results on residual stress and distortions. Figure 2.40, shows how these simulations can be used in the workflow. The figure shows the results of evaluating two different orientations for the resulting distortions. These distortion predictions can then be potentially used to make corrections to the input CAD model. The distortion simulations can also be used to evaluate different support structures and their impact on the resulting distortions and ability to prevent build crashing due to part warping.

Fig. 2.40 Part displacement as a function of orientation

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2.11 Challenges in Creating the Digital Workflow It is not uncommon for a typical workflow to include several different pieces of software: CAD software for Design, CAE software for design analysis, Topology Optimization software for design optimization, machine-specific software for slicing, tool path planning, and execution, simulation software for print process to evaluate process specifics such as how temperature changes, distortions, and stresses will impact part build, simulations to predict microstructures and material properties. One large challenge is providing an integrated and seamless workflow that does not require working across multiple CAD formats, FEA models, or topology optimization formats that do not integrate well and are often fraught with issues of file and data format incompatibility, loss of information in transfer between specialized software packages and working across various platforms.

2.12 Questions and Discussions 1. What are the steps in the workflow to go from CAD to the as-built part, and decisions at each step of the workflow? Discuss the interdependence of these steps. 2. What is the information represented in an STL file? What information is not represented in the STL file and why do you think it is necessary? 3. What are some of the considerations that must be taken into account before generating the STL file? 4. What are the errors that might be present in an STL file? What are the potential sources of these errors? What are the implications of leaving the errors in the STL file? 5. What does “Water tight” STL model mean? 6. The AMF standard is being proposed as an alternative to the STL file. How does it address shortcomings of the STL File format? 7. Consider a tetrahedron. Where the base triangle is defined by the coordinates (0,0,0), (5,10,0), and (10,0,0) and the tip vertex is defined by (5,5,10). Without modeling this on a computer, write the STL file for it. 8. What is the impact on the part build of choosing an orientation? What are some of the multiple objectives that may be under consideration when choosing a build orientation? 9. What are some of the considerations related to support structures that must be considered when dealing with the orientation problem? 10. What are the implications of slicing on the geometry of the part that will be produced? 11. Why is adaptive slicing not a commonly available feature for slicing a CAD model?

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12. What are the parameters/variables related to tool paths and their impact on the tool path? Can the tool path parameters be established independent of the machine that will be used to build the part? If not, why? 13. Discuss how the need for post-processing can influence the difference between the “as designed” part and the “as built” part. 14. List all the items that can be impacted by the choice of direction. Can all of these be satisfied simultaneously? If not, how would you determine which ones are the important ones? 15. Using the STL file and a given build orientation, how would you determine which of the triangles could potentially require support structures? Present your algorithm in the form of a flow chart.

References 1. “3MF Specification” (n.d.) Accessed 4 Feb 2020. https://3mf.io/ 2. Abdelrhman AM, Gan WW, Kurniawan D (2019) Effect of part orientation on dimensional accuracy, part strength, and surface quality of three dimensional printed part. IOP Conf Ser Mater Sci Eng 694:12048. https://doi.org/10.1088/1757-899x/694/1/012048 3. Alexander P, Allen S, Dutta D (1998) Part orientation and build cost determination in layered manufacturing. Comput Aided Des 30(5):343–356. https://doi.org/10.1016/s00104485(97)00083-3 4. ASTM F2915-12 (2012) Standard specification for additive manufacturing file format (AFM) version 1.2. ASTM Int 2013:1–15. https://doi.org/10.1520/F2915-11.2 5. CEC (1994) Common Layer Interface (CLI) Version 2.0. https://www.hmilch.net/downloads/ cli_format.html 6. Clijsters S (2017a) Development of a smart selective laser meltprocess. KU Luven. https://nam10.safelinks.protection.outlook.com/ ing ?url=https%3A%2F%2Flirias.kuleuven.be%2F1748636%3Flimo%3D0&data=05%7C01 %7Csbj4%40psu.edu%7C06e190d115af46402dae08db02d66157 %7C7cf48d453ddb4389a9c1c115526eb52e%7C0%7C0%7C638106891996381918 %7CUnknown%7CTWFpbGZs 7. Clijsters S (2017b) Support structures for additive manufacturing: a review. J Manuf Mater Proc (KU Luven). https://doi.org/10.3390/jmmp2040064 8. Dolenc A, Mäkelä I (1994) Slicing procedures for layered manufacturing techniques. Comput Aided Des 26(2):119–126. https://doi.org/10.1016/0010-4485(94)90032-9 9. Feng SC, Witherell PW, Ameta G, Kim DB (2015) Fundamental requirements for data representations in laser-based powder bed fusion. In: ASME 2015 international manufacturing science and engineering conference, MSEC 2015, vol 1, pp 1–10. https://doi.org/10.1115/ MSEC20159439 10. Hartunian P, Eshraghi M (2018) Effect of build orientation on the microstructure and mechanical properties of selective laser-melted Ti-6Al-4V alloy. J Manuf Mater Proc 2(4):69. https://doi.org/10.3390/jmmp2040069 11. Leong KF, Chua CK, Ng YM (1996) A study of Stereolithography file errors and repair. Part 1. Generic solution. Int J Adv Manuf Technol 12(6):407–414. https://doi.org/10.1007/ BF01186929 12. Masood SH, Rattanawong W, Iovenitti P (2003) A generic algorithm for a best part orientation system for complex parts in rapid prototyping. J Mater Process Technol 139(1–3):110–116. https://doi.org/10.1016/s0924-0136(03)00190-0

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13. Renishaw (2018) Multi-laser processing strategies for high-integrity component manufacture. Gloucestershire. https://www.renishaw.com/resourcecentre/en/details?data= 112228&lang=English 14. Pandey PM, Nallagundia VR, Dhande SG (2003) Slicing procedures in layered manufacturing: a review. Rapid Prototyp J 9:274–374 15. Parry L, Ashcroft IA, Wildman RD (2016) Understanding the effect of laser scan strategy on residual stress in selective laser melting through Thermo-mechanical simulation. Addit Manuf 12:1–15. https://doi.org/10.1016/j.addma.2016.05.014 16. Qin Y, Qi Q, Scott PJ, Jiang X (2019) Status, comparison, and future of the representations of additive manufacturing data. CAD Comput Aided Des 111(February):44–64. https://doi.org/ 10.1016/j.cad.2019.02.004 17. Roscoe LE (3D Systems) (1988) Stereo lithography Interface specification. Valencia, CA 18. Volpato N, Zanotto TT (2019) Analysis of deposition sequence in tool-path optimization for low-cost material extrusion additive manufacturing. Int J Adv Manuf Technol 101(5–8):1855– 1863. https://doi.org/10.1007/s00170-018-3108-1 19. Wang WM, Zanni C, Kobbelt L (2016) Improved surface quality in 3D printing by optimizing the printing direction. Comput Graph Forum 35(2):59–70. https://doi.org/10.1111/cgf.12811 20. Wavefront (1995) Wavefront advanced visualizer manual Apendix B1 Object Files (Obj). Santa Barbara, CA. http://www.cs.utah.edu/~boulos/cs3505/obj_spec.pdf 21. Zhou* MY (2005) STEP-based approach for direct slicing of CAD models for layered manufacturing. Int J Prod Res 43(15):3273–3285. https://doi.org/10.1080/00207540500097809

Chapter 3

Metal Additive Manufacturing Processes – Laser and Electron Beam Powder Bed Fusion

3.1 Laser-based Powder Bed Fusion 3.1.1 Brief History Laser-based powder bed fusion (PBF) was one of the earliest processes developed for consolidating feedstock powder in a layer-by-layer manner to create a solid part. The initial patents were based on consolidating the powder layer based on sintering using a laser beam called Selective Laser Sintering (SLS) developed and patented by Dr. Carl Deckard and Dr. Joseph Beaman at the University of Texas at Austin in the mid-1980s. (US Patent #4,863,538). A similar process was patented by Fraunhofer in Germany (US Patent # 6,215,093 B1) where instead of sintering full melting was used as the means of powder consolidation, and was referred to as Selective Laser Sintering at Melting Temperatures. This technology has evolved under different names such as selective laser melting (SLM) and direct laser melting system (DMLS – by EOS Corporation).

3.1.2 Process Description and System Components The laser-based PBF process is illustrated in Fig. 3.1. A laser beam focused on a small spot is used to scan a thinly spread layer of powder deposited on a build platform. The laser scanning is performed at controlled speeds and paths. The scanning positions and path are determined by the 2D geometry that needs to be created as defined by the slicing process of the CAD model and the generated tool paths. The thermal energy provided by the focused laser fuses the powder within the layer and to the layer below based on the primary mechanisms for binding (sintering, full melting). After completion of one layer, the build platform is lowered by the defined layer thickness and a new layer of powder is deposited by the powder © Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_3

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Fig. 3.1 Schematic of a typical powder bed fusion system

spreading mechanism using the reservoir of stored powder to deposit the powder and a recoating blade or roller to spread the powder over the build platform. The process of scanning and subsequent lowering of the powder bed is repeated until all layers are complete. The complete process is executed in an enclosed build chamber with the atmosphere in the chamber controlled for temperature as well as the gases that surround the build layer. Oxygen-free atmosphere is necessary to prevent the oxidation, and hence inert gases such as argon and nitrogen are used to fill the fill chamber and provide the low oxygen atmosphere. The gases are introduced via gas flow systems that provide gas flow across the build platform. After the part is complete, the part is completely encased in the powder. Excess powder is removed and sieved to be potentially reused. The part is attached to the build plate, and subsequently removed from the build plate. A typical laser powder bed machine has several key subsystems: 1. 2. 3. 4. 5. 6.

Powder delivery and spreading system. Gas Flow and build chamber atmosphere management. Build platform and height management. Laser, Laser delivery, focusing, and scanning system. Control System and user interface. Auxiliary equipment for powder recovery and management.

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Fig. 3.2 (a) layer creation using a blade (b) using a counter-rotating roller (c) using a slot feeder. (Adapted from Ref. [29])

3.1.2.1

Powder Delivery and Spreading Systems

A controlled volume of powder is deposited by either dropping powder from an overhead hopper, or by pushing powder up from a powder reservoir (feed bin) by a certain height. A powder feed bin contains the powder feedstock in the quantity needed to completely fill the build chamber. The feed bin contains a piston at the bottom that pushes a predetermined amount outside the build platform. This powder is then spread to create a uniform layer dictated by the desired layer thickness. This helps control the layer density, layer packing, and homogeneity. The powder is spread using recoaters such as a hard doctor blade, a soft silicone blade, or a counter-rotating roller (Fig. 3.2). Excess powder is collected in a second chamber or returned to a powder supply tank. In the overhead design, the powder is stored in overhead hoppers, and gravity is utilized to deposit the amount of powder to be spread. In some designs, just one hopper may be used, and in other two hoppers one on each side is used to facilitate bi-directional spreading. The use of bidirectional spreading can reduce the build time, due to reduced time to deposit each layer. A hard recoater blade, often referred to as doctor blade, is made from hard steel and ceramics. They allow for exerting downward pressure on the powder bed during the recoating process thus allowing for slightly higher packing density in the layer. However, in the case of larger distortions in the part during build, it may be possible that the blade collides with part and stops the build. Soft recoater blades are typically made from silicon, rubber, carbon fiber brushes, or metal rakes with flexible teeth. The flexibility of the blade provides a certain amount of give in the case of collision with the previous layers being built, due to the distortions that may be experienced due to thermal effects, residual stresses, failure of support anchors, etc. Soft recoaters can be damaged more easily. They are more suited when different parts are built on the same platform, allowing the build process to continue even if one of the parts is not built correctly. A counter-rotating roller allows for applying pressure during the layer creation process, and hence provides the highest packing density which allows for denser parts and allows for building parts with smaller delicate features that may be easily damaged by hard recoater blades. The rollers also avoid the problem of collisions in the case of layer distortions during build. While this can be construed as an

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advantage in some cases, in others it may be a disadvantage since build problems may go undetected until the build is complete.

3.1.2.2

Build Platform and Height Management

The parts are typically built on a removable build plate mounted to a platform carrier. The platform carrier provides the accurate vertical z-axis displacement, by the use of backlash-free lead screws and guide rails, which are used to manage the layer thickness of the deposited powder and subsequent built layer thickness. The building platform carrier provides the mounting and adjustment for leveling of the build plate. Reference positioning pins, holes, and holding screws are used for precise and reproducible location of the build plate. It may also include a build plate heating module to reduce temperature gradients between the building platform and the part to reduce internal stresses and ensure a good bonding of the first few layers. The heating module also helps in removing any moisture from the powder and to maintain the part at a constant temperature during any interruptions in the building process to ensure maximum process reliability. The build plate material and size are often functions of the build material. Typical thickness ranges from 22 to 36 mm. The surface of the build plate is typically machined or ground.

3.1.2.3

Gas Flow and Build Chamber Atmosphere Management

The main purpose of this system is to generate and maintain an inert atmosphere and create the gas flow necessary to remove contaminants from the build platform and chamber. A simple way to do this is to simply fill the build chamber with inert gas and purge the existing air by displacing all of the original atmosphere. This is inefficient and wastes a lot of inert gas to drop the oxygen levels to desired values (typically below 1000 ppm or 0.1%). Another approach is to first create a vacuum to remove the existing air and then backfill with the inert gas of choice. This is less waste full, and faster. Another advantage of the vacuum and purge method is that it can extract the trapped air from the powder feedstock container. Gas flow in PBF systems provides the following functions [20]. (i) Prevent Oxidation: An oxygen-free atmosphere is critical in processing metals and reactive materials, to prevent the formation of oxides and altering the chemical composition. The metals when processed are in a molten state and any oxygen present in the atmosphere can lead to changes in alloy chemistry, resulting in changes in mechanical properties. Inert gas atmospheres, such as argon and nitrogen, are used in processing metals. For reactive materials such as Ti6Al4V and AlSi10Mg, argon is the preferred inert gas. Nitrogen and oxygen can be absorbed into the material as interstitial elements, (ii) Removal of emissions: The laser interaction with the powder bed results in the creation of a melt pool. The creation of this melt pool often results in the

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formation of vapor plume that contains ejecta from the weld spatter, smoke, and powder particles. The spatter is caused by the high energy beams creating localized boiling and superheating causing melt pool instabilities through recoil pressure and vapor entrainment of surrounding particles leading to vaporization and ejection of material. The vaporized material also rapidly solidifies in the chamber atmosphere causing the formation of nanoparticulate condensate that can coat the insides of the build chamber. The gas flow across the powder bed should be designed to remove this from the melt pool region so that there is no obstruction with the laser path, as well as prevent any splatter from landing on the regions of the powder bed that have yet to be melted. The hot splatter landing back on the powder bed can create agglomerates of powder particles which may not fully melt or create subsequent problems with spreading the next layer. This imposes requirement on the gas flow, such as consistency of flow across the powder bed, and gas flow velocity enough to remove the emissions but not disturb the surface of the powder bed.

3.1.2.4

Laser, Laser Delivery, Focusing, and Scanning Systems

Powder bed systems using lasers as the energy source rely on directing a focused laser spot to heat and melt the powder layer. A molten pool is created and is moved over the powder bed by moving the laser, through a process called scanning. The molten pool rapidly solidifies once the laser energy is moved to a different location. The process depends on the ability to provide the required energy density while maintaining the quality of the focused laser spot, in terms of beam power, spot diameter, scanning velocity, and positioning accuracy. Figure 3.3 shows the schematics of a complete laser system. Lasers typically used in powder bed systems are typically CO2, Nd:YAG, and ND:YAG fiber lasers ranging in power from a few hundred to a few thousand watts. A typical laser system consists of a lasing medium, source for pumping energy, and an optical resonator cavity. The lasing medium is placed in the optical resonator, and external energy is supplied to the pumping medium. The optical resonator amplifies the light by stimulated emission of photons, created by the population inversion required for lasing. The output of the laser light is characterized by the wavelength, output power, type of output – continuous or pulsed, and life of the lasing medium. Lasers are monochromatic with all the energy being in a narrow bandwidth concentrated around a single wavelength. Lasers are coherent, where all the phases of the electromagnetic radiation are in the same phase. They also have a low divergence and are highly collimated beams. For more details on lasers refer to Chap. 8. Table 3.1 provides data on the commonly used laser systems for AM. The CO2 lasers are gas lasers, the gas state gain medium is CO2 , fills the discharge tube, and is electrically pumped to provide the energy required for lasing. The long wavelength results in several limitations for metal due to low light absorption in the infrared region. The CO2 lasers in this wavelength cannot be delivered with optical fibers, and often require bulky optics for beam delivery. Nd:YAG lasers

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Fig. 3.3 Schematic of a typical laser delivery system. (Redrawn with permission Special Optics)

Table 3.1 Commercially used laser systems for AM Laser Wavelength (μm) Efficiency Output power Operation mode Fiber delivery Maintenance period

CO2 laser 10.6 5–20% Up to 20 kW Continuous & Pulse Not possible 2000 hr

Nd:YAG laser 1.06 10–20% Up to 16 kW Continuous & Pulse Possible 10,000 h

Yb-fiber laser 1.07 10–30% Up to 10 kW Continuous & Pulse Possible 25,000 hr

Adapted from [16]

(neodymium-doped yttrium aluminum garnet laser; Nd3+ :Y3 Al5 O12 laser) are a type of solid-state laser using rod-shaped Nd:YAG crystals as a solid gain medium. Diode lasers are used for pumping, and are more efficient compared to Xenon

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Fig. 3.4 Irradiance distribution in a Gaussian laser beam

flash lamp-based pumping mechanisms. For AM use, the Nd:YAG lasers are being replaced by more efficient and compact Yb-fibers, due to the wider absorption bands and higher efficiency. There are several critical parameters that are laser-related and can have an impact on the process. The operating wavelength of the laser is important since different materials interact differently with the laser wavelength. The laser energy is absorbed by the powders differently. For metal powders the shorter wavelengths have higher absorptivity and hence Nd:YAG and Yb-fiber lasers are more commonly used. For polymer powders, the absorptivity is higher at longer wavelengths and hence CO2 lasers are a better choice. The operating wavelength also impacts focusing. The focused spot size is proportional to the wavelength due to the diffraction limits. The laser power defines the input energy and must be able to provide the energy threshold for sintering and melting. The laser power and the area of the focused spot size define the power density (Irradiance) of the focused laser spot (in Watts/area2 ), as defined by Power Density =

Laser Power(P )

.

Crosssectional area of the focused spot



π d2 4



The laser operation can be classified as continuous or pulsed. In a continuous laser, the laser power is constant independent of time, whereas in a pulsed laser, the output power is emitted in short pulses at a fixed frequency. Laser beams typically have a Gaussian intensity profile, as shown in Fig. 3.4. The irradiance decreases exponentially as the distance from the center of the beam increases, as defined by the equation. The “beam diameter” is defined as the distance across the center of the beam for which the irradiance (E) equals 1/e2 of the maximum irradiance (1/e2 = 0.135), ω is beam radius, and r is the distance from the center.

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Fig. 3.5 Schematic of a laser focusing system

r

E = Emax e−2( ω )

2

.

Higher power fiber delivered lasers typically employ a multi-mode beam and result in a “top hat” energy distribution after fiber delivery, whereas, lower power single mode beams of a ytterbium laser, where the laser source may also be the fiber delivery system, can provide a Gaussian energy distribution upon leaving the fiber. This distribution is typical for lower power ytterbium lasers used for the PBF process. The generated laser beam is focused using optical systems to create the focused spot. The smaller the focus diameter is the greater the beam is focused, and results in higher power density at the focus. A smaller focus spot also allows for finer detail. For a Gaussian beam, the propagation of the beam through the optics retains the Gaussian properties. A schematic of a focusing optical system is shown in Fig. 3.5. After the focus, the beam begins to spread out. The Rayleigh length indicates the distance from the focus at which the cross-sectional area of the beam is doubled, Fig. 3.6. A longer Rayleigh length means a smaller degree of divergence. Two times the Rayleigh length is frequently referred to as “depth of field.” The focal length of the lens or focusing mirror refers to the distance from the lens center or the mirror to the focal point of an ideal parallel ray. The smaller the focal length is, the greater the beam is focused and smaller the focus diameter, Rayleigh length, and image distance. The Rayleigh range ZR is defined as ZR =

.

π Wo2 λM 2

The smallest spot size that can be achieved, is usually limited by diffraction. Diffraction is a natural and inescapable result of the wave nature of light, is present in all optical systems, and determines the ultimate theoretical limit on their performance, given by the formula

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Fig. 3.6 Parameters of a focused laser beam

Spot diameter (limited due to diffraction) 2Wo =

.

4M 2 λf πD

where: M2 = beam mode parameter. For Gaussian Beam M2 = 1 λ = laser wavelength f = focal length D = beam input diameter at lens (measured at 1/e2 point) The depth-of-field (DOF) or depth of focus is defined as the distance through which satisfactory definition can be maintained when a lens is in focus at a particular distance. There is a general agreement that “satisfactory definition” is maintained as long as the spot size remains smaller than 1.4 times its smallest size. This distance is also called the Rayleigh range (Fig. 3.6). The DOF is therefore equal to twice the Rayleigh range of the focusing system and is given by

DOF = 2ZR =

.

  8λ f 2 2 M π D

Most laser-based systems use a pair of rotating galvanometric mirror systems to direct the laser beam to the XY locations on the powder bed, Fig. 3.3. Since the positions on the powder bed are generated by the rotation of the mirrors, the beam length, angles, and cross-section of the beam when it hits the powder layer are different depending on the XY position of the beam when using spherical lenses. As we move away from the center, the beam length increases and the beam crosssection changes from a circle to a larger ellipse. The focus point is no longer on the surface of the powder bed, and lies on the arc created by the focal length (Fig. 3.7a) (“F-Theta Lenses Tutorial” [8]). This must be compensated and corrected. Three methods are used to do this.

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Fig. 3.7 Focus using (a) spherical Lens, (b) flat field lens (c) F-theta Scanning Lens [8]. (Modified from https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=10766)

(i) Flat Field Scanning Lens Standard flat field scanning lenses (Fig. 3.7b) provide a flat field, but require complicated electronics to obtain a uniform scanning speed since the distance traveled by the laser spot is not a linear function of the scan angle (θ), in fact y = f *tanθ (ii) F-Theta Systems The F-theta system is a multi-element lens that focuses the beam onto a flat plane. The focal length varies with the angle of the incident beam. F-Theta lenses (Fig. 3.7c) are designed both to form an image on a flat plane and to provide a linear relationship between the scan length (y) and the scan angle (θ), in accordance with the following so-called F-Theta condition y = f *θ. F-Theta lenses satisfy the previous relationship thanks to a special corrected built-in negative distortion (barrel type). The size of the working fields depends on the lens’ focal length and is given by L = f *2θ. For instance, a focal length of 163 mm provides a scan area with a size of 115 × 115 mm, while f = 250 mm provides a 176 × 176 mm scan area. One problem with using F-theta lenses with high-power laser systems is the generation of heat in the lenses, along with some absorption in the lens, which leads to loss of power. Temperature changes in the lenses can lead to variations in focal length. (iii) Dynamic Focusing Systems As seen in Fig. 3.8, these systems use a lens in the beam line before the galvanometer mirrors and move it relative to the source location to create the change in the focal length.

3.1.2.5

Control System and User Interface

A process computer with associated process software is used to manage and control the build process and the system’s measuring and control components. It also provides the user interface necessary to operate the machine. Most control systems

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Fig. 3.8 Dynamic focusing system

Fig. 3.9 Primary binding mechanisms in powder bed fusion processes [15]. (Redrawn)

employ a graphical user interface (GUI) that allows the various subsystems to be managed and monitored, as well as a main program that interacts with the various subsystems during continuous operation of the system. Since the control system also utilizes a path plan for deposition of a single layer or the entire build, the system must be capable of interfacing with software that is utilized for creating, and hopefully simulating, preprogrammed motion commands. Additionally, the control system allows for setting some process parameters that are typically not set in the path planning software to be set. These include parameters such as gas flow rates and chamber temperatures to be set manually.

3.1.3 Primary Binding Mechanisms The layers of powder that are deposited in PBF systems, need to be fused or bound to create a solid layer. The main differentiator of the various process that can be used to fuse the powder layers is the primary mechanism that provides the binding. The primary binding mechanisms that can be potentially used have been described by Kruth et al. [15], as shown in Fig. 3.9.

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Fig. 3.10 Sinter neck formation between particles prior to densification. (P. R. German [11] used with permission)

3.1.3.1

Solid-state Sintering

Solid-state sintering refers to the bonding and densification of powder particles by the application of heat. Solid-state sintering takes place below the melting temperature of the powder, and bonding occurs by atomic diffusion between adjacent powder particles. Sintering temperatures range between 50–80% of melting temperatures of bulk material. Sintering follows a progression of steps. Initially, contact between the particles is created by the adhesive forces pulling the powder particles together. During heating, initial bonding occurs at the contact point between particles and results in the formation of necks (Fig. 3.10). With increasing temperatures or longer times, the necks grow and the particles pull together to create a denser structure. As the process continues, it results in the creation of grains several times larger than the initial particle size and several of the particles fuse to form a single grain. The coalescing of the power particles into grains results in shrinkage and reduction in the pores between adjacent powder particles. Mass transport by diffusion is the underlying mechanism driven by the reduction in total interface energy as the system achieves thermal equilibrium. Since the total surface of the powder layer is a function of powder particle size, smaller particles with the larger surface-to-volume ratio sinter more rapidly than larger particles and can sinter at lower temperatures. Powder particle size, temperature, temperature gradients, and sintering time impact the rate of sintering as well as the result of sintering [12]. In a typical AM process, solid-state sintering is a relatively slower process compared to fusion by melting, hence most AM processes focused on producing fully dense metal parts without the use of secondary sintering processes, use full melting as the primary means of fusion of metal particles. The effects of solid-state sintering can also be seen as secondary effects in a full melting-based process. Powder regions surrounding the part being built, experience increase in temperature due to thermal conductive heat dissipation through the

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powder bed. The loose powder surrounding the part being built can reach sintering temperatures and lead to agglomeration of powder particles thus increasing the size of the powder particles in subsequent reuse of the powder. The particles need to be sieved and removed to maintain the particle size distribution. Further, some of these sintered particles can adhere to the boundary of the part resulting in skin growth on the boundary that can impact the final dimensions and surface finish of the part.

3.1.3.2

Chemically Induced Sintering

Chemically induced sintering relies on the use of chemical reactions between powders or the atmosphere to create the bond between the powder particles. These chemical reactions can be triggered thermally or by exposure to the atmosphere, and typically result in either the generation of heat for the sintering process or byproducts of the reactions to physically bind the powder particles. While this method is not popular in commercial use of AM, research examples using SiC and other ceramics such as Al2 O3 and ZnSiO4 have been demonstrated at Fraunhofer Institute. When heating the SiC particles to high temperatures, the SiC partially disintegrates into Si and C. The free Si forms SiO2 which acts as binder between SiC particles.

3.1.3.3

Liquid Phase Sintering

Liquid Phase sintering relies on using blended and alloyed powders where one of the components remains solid throughout the process and a binder material that is liquified to form the liquid phase which upon solidification binds the solid particles. In mixed powders, the liquid is formed by the lowest melting point powder, and in alloyed powder, the liquid phase is formed by heating to a temperature between the liquidus and solidus temperatures. High diffusion rates are associated with the liquids given fast sintering or lower temperatures. Several different approaches have been used to create the powders for use where the LPS is the dominant binding mechanism. 1. Mixed Powders – Separate binders and structural material powders are blended together. In the case of mixed powders, the lower-temperature melting powder (binder) first undergoes solid-state sintering. Further heating leads to melting of the liquid that dissolves the sinter bonds, wets the solid (structural material), and penetrates between the solid grains via capillary action to induce grain rearrangement. The binder particles are usually smaller than the structural ones, and the high surface-to-volume ratio of the binder in combination with its lower melting points favors the melting of the binder. 2. Composite grains using both the binder and structural material within each individual powder grain can be manufactured by mechanically alloying a mixture of powders. Composite grains often result in higher green density and better surface roughness.

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3. Coated Grains – The structural material is coated with the binder material. In this case, the laser power is preferentially absorbed by the binder material and melts the binder material. Coated powders can be created with polymer as well as metal coatings. In the earliest use of laser sintering for metal parts, DTM corporation used polymer-coated steel in the formulation of the Rapid Steel powder. When using polymer-coated particles, in some cases an additional step is needed to burn the polymer coating and create a “brown” part which then undergoes a full sintering operation.

3.1.3.4

Partial Melting

In cases where there is no distinction between binder and structural material, partial melting can be used as a binding mechanism. When the supplied heat is not enough to melt the whole particle, only the outer shell of the particle may undergo melting while the core remains solid. The molten material acts as the binder for the unmolten parts of the powder.

3.1.3.5

Full Melting

To obtain fully dense metal parts the current approach with PBF systems is to perform full melting. Full melting avoids the need for additional sintering and densification steps. It requires the use of higher energy density. A wide range of metals can be processed; however, large differences in the processing requirements of the materials exist. The proper processing parameters need to be determined, often experimentally to successfully work with different materials given the wide range of material properties such as melting point, laser absorption, surface tension, liquid viscosity, material phase changes, etc.

3.1.4 Process Dynamics Starting from the feedstock material in this case the powder, the powder particle size and morphology affect the density and consequently the mechanical properties of the parts produced in a PBF process. Once the powder layer has been spread, the creation of the layer involves scanning the powder bed with a focused laser beam to create the required geometry on the layer as defined by the slicing process. The general progression of the creation of a solid part in PBF is shown in Fig. 3.11. The process is complex and involves many different interacting physical phenomena, as shown in Fig. 3.12. The process begins by absorption of the laser energy by the powder layer exposed to the focused laser spot. Not all the energy is available to be absorbed, some of it is lost due to reflection at the powder surface. The absorbed energy increases the powder temperature and the thermal energy

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Fig. 3.11 Progression in the formation of a solid part in PBF

Fig. 3.12 Interacting physical phenomenon that influences the PBF processes

spreads by heat diffusion. When the temperature exceeds the solidus temperature of the metal, the solid-fluid phase transformation starts to create the melt pool. When the local liquid phase fraction exceeds a given threshold value dictated by the temperature, the solid starts to behave as a liquid. The surface tension of the liquid drags more powder into the melt pool. Surface tension and capillary forces influence the formation of the “bead” or track formed by the traveling energy source. The heat input is dissipated through radiation, convection, and conduction through the powder bed. As the beam moves away from the melt pool, the removal of the heat leads to rapid solidification of the material. The material also undergoes

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some solidification shrinkage. The melt pool dynamics (discussed later) also play an important role in the process. The energy from the laser is first absorbed by the powder. The absorption efficiency of lasers depends on the wavelength of the laser as well as the reflectivity of the powders used. Figure 3.13 below shows the absorption efficiency of different bulk materials to the wavelength of lasers. The reflectivity of the powders is generally lower than that of the bulk solid due to multiple reflections inside the powder bed. Ray tracing simulations and modeling have been used to model the reflectivity and identify the factors that impact it [4]. As seen in Fig. 3.14, the reflectivity of the powder also increases at the solid-liquid transformation [13].

3.1.4.1

Melt Pool Evolution

Figure 3.15 shows the schematic plot of the general phenomena and actions that influence the PBF process. The absorbed laser energy is converted to heat and begins the formation of the melt pool. Initially, the powder particle surface heats up quickly, followed by a homogenization phase where the heat diffuses from the particle surface to the core. When the metal temperature is higher than the melting point, a melt pool is formed. The heat is transferred from the melt pool to its surroundings by radiation, conduction, and convention. The conduction mainly occurs through the surrounding powder and the already-solidified material below the layers and adjacent to the layers. Convection occurs due to the surface tension, buoyancy, and vaporization in the melt pool. The temperature gradient in the melt pool from the center of the laser beam to the outer parts of the melt pool creates

Fig. 3.13 Absorption efficiency of different materials to different laser wavelengths [10]. (https:// go.additive.ge.com/rs/706-JIU-273/images/GE%20Additive_EBM_White%20paper_FINAL.pdf. Image credit GE Additive, used with permission)

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Fig. 3.14 Reflectivity evolution during the static melting, with laser power 320 W, 90 micron thick layer of stainless steel powder, and 10 ms radiation time. (Reproduced from Ref. [13] used with permission of the Laser Institute of America) Fig. 3.15 Various phenomena influencing the process dynamics in power bed fusion [5]. (© Springer)

surface tension gradients that induce liquid flow from the low surface tension to the high surface tension areas (inside to outside) and is called the Maragoni flow. Changes in material density with temperature also cause fluid flow outwards. As the melt surface temperature increases it may result in the evaporation of alloys in the material that have low boiling points. Reduced pressure above the melt pool can also reduce the boiling point of some of the elements, further contributing to evaporation losses. The high-temperature metal vapors and hot gases and above the molten pool apply pressure to the melt pool as it expands. This is called the recoil pressure and is responsible for the outward movement of the liquid in the melt pool. With high enough recoil pressure, a cavity called the keyhole is formed. It has also

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been recently shown [3] that the vapor flows result in local pressure drops above the melt pool and create a lateral gas flow which can pull particles from the powder bed into the melt pool, which created a denudation zone around the scanned area, where the number of particles is reduced. As the laser beam scans and creates the tracks there are ejecta produced that are basically (i) ejected powder particles due to the rapid expansion of gas in the particle spaces and (ii) molten spatter from the melt pool when the forces in the melt pool (Marangoni forces, and recoil pressures) exceed the surface tension. The vapors produced by the vaporization can also condense forming fumes and condensates. These by-products when expelled can cause quality issues when they land in areas of the powder bed that has yet to be scanned and create defects in parts. Further, they can also pass through the laser causing shadowing effects by absorbing the laser radiation and scattering causing defocusing of the laser thus reducing the energy input to the power bed. The inert gas flow that runs across the powder bed also serves the purpose of removing the ejecta and moving them to the gas outlet. Figure 3.16 [17] shows an interesting series of time series Xray radiographs obtained during the processing of a single track of Invar 36 powder under the processing conditions of P = 209 W, v = 13 mm/s and line energy density of 16.1 J/mm. Figure 3.16a shows the melt track morphology at 3 key stages. Figure 3.16b shows the formation of the melt pool and the denuded zone shown in yellow dashed line. The laser beam causes metal vaporization, generating a recoil pressure at the interaction zone (blue dotted arrows) while indirectly heating up the surrounding argon gas (red arrows). The molten pool/track grows while enlarging the denuded zone by molten pool wetting and (c) and vapor-driven powder entrainment (orange dotted semi ellipse) which can lead to the formation of powder spatter (purple dotted circle) and droplet spatter (its trajectory path is indicated by the green arrows) as seen in (d) and (e). After the laser switches off at t = 334 ms, pores nucleate, coalesce, and collapse, resulting in an open pore (pink dotted line). The figures are all shown with a scale bar of 250 microns

3.1.5 Process Parameters Process parameters such as laser power, exposure time, scanning speed, layer thickness, and building direction show a strong influence on the quality of the parts produced; including surface microstructure, mechanical properties, fatigue strength, hardness, density, and surface roughness. Proper understanding and control of these parameters are necessary for the development of the process. A large number of materials can be processed by PBF systems; however, the processing parameters settings and acceptable ranges will vary for different materials and have to be determined for each material and feedstock properties. These parameters along with others shown in Fig. 3.17, can all be adjusted independently making the parameter selection and optimization a rather sophisticated problem.

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Fig. 3.16 Time series radiographs showing the dynamics in the melt pool [17]. (©Springer)

The main scan-related process parameters shown in Fig. 3.18, determine the amount of exposure received by the powder bed. These parameters include laser power (P) the total energy emitted by the laser per unit time measured in Watts, scanning speed or velocity (v) the speed at which the spot is moved across the powder bed, spot size (d) diameter of the focused laser beam, hatch spacing (h) the distance between adjacent scan vectors selected to allow a small amount of overlap for remelting of previous fused line and ensuring the resulting lines are connected, and layer thickness (t). These parameters can be used to characterize the process by establishing relationships between the process parameters. Power Density =

.

Laser Power area of focused laser spot

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Fig. 3.17 Principal processing parameters involved in laser melting processes

Volumetric energy density is the amount of energy supplied to the powder particles per unit volume Ev =

.

P hvt

where P is the laser power in (W), v is the scanning speed in (mm/s), h is the hatch spacing in (mm), t is the layer thickness in (mm), and Ev is the volumetric energy density in (J/mm3 ). The surface energy density is given by

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Fig. 3.18 PBF scan-related process parameters

Es =

.

P hv

The energy density required for melting a certain material depends on the thermal properties of the material and is estimated by the following equation: Em = cρ (Tm − Ta )

.

where c is the specific heat capacity in (J/kg K), ρ is the material density in (kg/mm3 ), Tm is the melting temperature in (K), Ta is the ambient temperature in (K), and Em is the melting energy density in (J/mm3 ). A dimensionless ratio between the volumetric energy density and the required energy density for melting can be defined as the (e) ratio. e=

.

Ev Em

This ratio describes the relationship between the energy density of the laser source and the energy required for melting the metal powder.

3.1.5.1

Determining Proper Process Parameters

Successful additive manufacturing by PBF requires proper setting of the process parameters. This is even more critical during serial production when repeatability is key to avoiding quality issues that may arise. The process parameters must be established for each material alloy since the thermal response will be different for different materials. The goal of the proper parameters is to provide a fully dense component, and often density is used as the first criteria in establishing the process parameters. As seen in Fig. 3.17, there are a lot of parameters that can influence the final results of the process. To establish the main scanning parameters, several

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Fig. 3.19 P-V graph showing different process outcomes

of the other parameters are fixed, such as powder-related parameters (particle size distribution, chemistry), layer thickness, and laser spot size. Thus, simplifying the problem to only a few parameters such as laser power, scan speed, and hatch distance. Parametric investigation is typically conducted by depositing single tracks and tuning laser power and scan velocity. The parameter choices are plotted in P-V space, where the laser power (P) is plotted against scanning velocity (V), as shown in Fig. 3.19. Scanning too fast with lower laser power results in lower exposure of the powder and can lead to lack of fusion. Scanning with high power and low scanning velocities can lead to overexposure-related issues such as overheating causing deeper penetration and keyhole formation. High laser power and higher speeds can result in faster build times, but there may be regions where the melt pool does not create continuous lines and breaks up to create the balling effect. The balling phenomenon in laser melting of powder results in the formation of spheroidal beads due to insufficient wetting and surface tension of the molten material [18]. Balling can be reduced significantly by keeping oxygen levels at 0.1%, by applying a combination of high laser power and low scanning speed, and by repeated application of laser to break up the oxide films. Figure 3.20 shows an example of single tracks generated with different laser power and scanning speed. In some cases, a humping effect is seen at high velocities and high power as seen in Fig. 3.21. Once the single-track parameters are established, complete layers and multiple layers are deposited and analyzed for density. When depositing single layers, hatch spacing is established to ensure that there is sufficient overlap between adjacent single tracks. Additionally, the layer may be broken down into different regions for processing such as contour, up skin, down skin, and core (infill) as seen in Fig. 3.22. Different set of parameters are used for each of the regions to improve the surface finish of the build. For example, the boundary may be created by using contours (one or more contours) and the internal core regions may be filled using various scanning strategies.

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Fig. 3.20 Single-track processing map for the first powder bed fusion layer at different laser power and velocities. (Reproduced from [13] used with permission of the Laser Institute of America)

Up skin are areas of the layer above which there is no other layer to be exposed. Down skin are regions of the layer that lie directly on the powder bed (and may or may not need support structures). Down skin regions of the layer may require using different parameters since they do not sit on existing layers but rather on the powder bed and have different heat dissipation properties. The down skin portion of the layer are particularly sensitive to the amount of heat input due to the fact they are built on top of the powder, and heat conduction is different, resulting the formation of dross and warping. Large overhang regions that exceed the ability of the machine to successfully build the layer require adding support structures. Support structures eventually will need to be removed and can add considerable cost during the postprocessing steps. It should be noted that the definition of the up skin and down skin are functions of the part orientation chosen for the build. Different hatch patterns can be used for the infill. Typical pattern includes using a stripe with a small width, instead of completely scanning the full width of the layer

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Fig. 3.21 Cross-section of single tracks at different speeds and power. (Reproduced from [13] used with permission of the Laser Institute of America)

Fig. 3.22 Different regions of a part layer

geometry as seen in Fig. 3.23. Overlapping stripes are used to complete the layer [2]. Checkerboard is another pattern used to fill the layer. The checkerboard can be random, and different strategies can be employed within the checkerboard square, such as parallel or parallel zig zag. The checkerboards can also be randomly scanned to potentially reduce the effect of internal stresses. These scanning effects results in different heat input on the layer which can influence the resulting microstructure [2] and residual stresses [23, 28]. Figure 3.24 shows examples of various scan strategies. During scanning of a sing line, the mirrors in the galvanometers need to be accelerated and decelerated to provide the change in velocity needed at the beginning and end of each scan line. This changes the processing conditions due to changes in the velocity and hence the energy density. To avoid this situation from

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Fig. 3.23 Stripe scanning for infill [2]. (©Springer)

Fig. 3.24 Different scan patterns used for tool paths

occurring in the part, and to keep the acceleration and deceleration portions out of the layer geometry, skywriting options may be provided. During skywriting, the laser is turned off while the acceleration and deceleration are taking place outside the part and then turned on at the start of the path on the part. As seen in Fig. 3.25, the dashed line is the skywriting area of the path where the beam is turned off, and the solid line shows the scan with constant velocity. When building multiple layers, the scan patterns for subsequent layers are often rotated by a fixed angle or offset. For example, the stripe pattern may be rotated by 60 degrees for each subsequent layer. Checkerboard scanning patterns can be offset.

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Fig. 3.25 Skywriting

3.1.6 Materials The feedstock for metal PBF is metallic powders that can be produced by a variety of processes such as gas atomization, water atomization, mechanical reduction, and various chemical reactions. All of these powder production methods impart characteristics associated with the powder, such as size, morphology, purity, and production yield, that may impact cost and use for additive manufacturing. The characteristics and attributes of the powder used as feedstock can directly and indirectly impact the additive manufacturing process [6]. Evaluating the usefulness of a powder for use in laser PBF systems requires evaluation of the properties of the powder. ASTM standard F3049-14 identifies several powder characteristics such as size distribution, morphology, chemical composition, flowability, and apparent density. Understanding the effect of these characteristics on final built part quality is fundamental for further development and improvement of the AM technology. One characteristic of powder that is cited frequently as an important characteristic is the flowability of the powder. Flowability of the powder is affected by a large number of powder characteristics, as seen in Fig. 3.26. Spherical powder particle morphologies are preferred since they generally have better flow properties. Various sizes may be preferred to allow for better packing density in the powder layer. Typical powder size ranges from 10-60 microns with typical layer thickness of 20–60 microns. Table 3.2 shows example of materials available for the EOS 290 machine with a 400 W laser. Materials typically available from machine manufacturers come with process parameter sets that allow these materials to be used on the machine. For further details on the feedstock materials and their properties, refer to Chap. 14. Given the high cost of powders, and only partial use of the complete powder bed, after the build, the powders are typically recycled. The used powder is sieved and reused, sometimes mixed with new powder. The process of recycling requires the use of specialized equipment. The amount of time the powder can be reused is

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85 rate of flow through an orifice shear strength

permeability

cohesive strength

flow energy

flowability

angle of repose

compressibility Hausner ratio

avalanching behavior

flow properties

wall friction

static dynamic

bulk density

morphology electrostatic interaction surface tension

powder properties

interparticle forces friction

van der Waals

composition

PSD

moisture content

interlocking

Fig. 3.26 Factors affecting the flowability of powders [32]. (©Springer)

Table 3.2 Sample materials currently available from EOS (https://www.eos.info/03_systemrelated-assets/material-related-contents/material_pdf/eos_materials_overview_metal_en.pdf) Steel

Product EOS maraging steel

Material type MS1 AMS6514, 18Ni300Series

EOS stainless steel GP1

Stainless steel 17-4 / 1.4542

EOS stainless steel 316 L

1.4441, UNS S31673, F138

EOS stainless steel 17-4PH

1.4542, UNS17400, A564M

Application Injection molding tools, mechanical engineering parts Functional prototypes and series-production parts, mechanical engineering, and medical technology Engineering parts for corrosive environments can be used for medical parts (e.g., endoscopy and orthopedics) Acid and corrosion-resistant engineering parts, medical instruments (surgical tools, orthopedic instrumentation) (continued)

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Table 3.2 (continued) Product EOS nickel alloy IN718

Material type UNS N07718, AMS 5662, AMS 5664, 2.4668, NiCr19Fe19NbMo3

EOS nickel alloy IN625

UNS N06625, AMS 5666, AMS 5599, 2.4856, NiCr22Mo9Nb

EOS cobalt chrome MP1

UNS R31537, ISO 5832-4, ASTM F75, ISO 5832-12, ASTM F1537

EOS cobalt chrome SP2

“Type 4” CoCr dental material as per ISO 22674

Titanium

EOS titanium Ti64 EOS titanium Ti64 grade 5 EOS titanium Ti64ELI EOS titanium Ti64 grade 23

Ti6Al4V, ISO5832-3, ASTM F1472, ASTM F2924, ASTM F3302 Ti6Al4V ELI, ASTM F136, ASTM F3001, ASTM F3302

Aluminum

EOS Aluminum AlSi10Mg

AlSi10Mg

Copper

EOS copper cu

High purity copper

Refractive materials

EOS tungsten W1

Pure tungsten

Nickel

Cobalt chrome

Application Load-bearing components for high-temperature applications up to 700 ◦ C, good potential for cryogenic applications Components for service in corrosive environments, good potential for cryogenic applications Medical implants with high wear and corrosion resistance, high-temperature components in aerospace Class IIa medical device in accordance with annex IX rule 8 of the MDD 93/42/EEC Series production parts in aerospace, medical and automotive Series production parts in medical (spinal cages, tibial trays, patella, etc.) Functional prototypes and series production in mechanical engineering, automotive, hydraulics, and aerospace industries Heat exchangers, electronics, variety of industry applications requiring good conductivity Thin-walled parts for use in guidance structures in X-ray imaging such as anti-scatter grids

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not currently dictated by any standards, but based primarily on user experience and studies on powder reuse. There is significant evidence that suggests that processing of powder during additive manufacturing results in some alterations of the physical and chemical characteristics of the powder; however, the linkage between these changes and the effect on properties of the material produced using reused powder is less direct. For further details on powder recycling and use, see Chap. 14.

3.1.7 Microstructure and Properties The solidified microstructure is governed by thermal conditions such as temperature gradient (G) and solidification rate (R) during solidification, along with the material phases developed during the process. This is primarily due to the high speed of motion of the energy source along with the complex scanning paths that are used for hatching and contouring for producing the slice geometries. The process also requires many layers for producing the final build, and the production of each layer imparts its own thermal response within the material. During processing, the thermal response of the material being created at the current layer entails thermal cycles involving rapid heating and cooling due to the thermal fields generated by the moving source of energy. Figure 3.27 shows an example of the thermal cycles in a part introduced by the process. It should be noted that these profiles will be different for different process parameters, scan strategies, and points at which it is being measured, but the general shape and behavior are illustrative.

Fig. 3.27 Thermal cycles for 10 layers at a point within a blade structure built using the powder bed fusion process using N07718 (IN718) alloy [27]. (©Springer)

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Fig. 3.28 Figure showing different microstructures depending on the thermal gradients and cooling rates [7] (used with permission)

The peak temperature at positions near the energy source exceeds the liquidus temperature of the material and results in melting, followed by rapid solidification as the source moves away from the material. This results in melting and solidification of the added material, the powder layer, and substrate during PBF. Hence, solidification is responsible for establishing the initial microstructure of the material. Figure 3.28 depicts the expected growth morphologies based on the thermal gradient with the liquid and the growth rate of the interface [14]. The growth morphologies illustrated in the figure, planar, cellular, columnar dendritic, and equiaxed dendritic are common morphologies observed during solidification in powder-based and directed energy-based AM processes. The rapid heating and cooling followed by the remelting creates high internal stresses and also thermally affect diffusional processes like grain growth, phase transformations, and precipitation phases in alloys, resulting in a non-equilibrium microstructure. To ensure bonding with the layers below, the melt pool is typically adjusted to penetrate 3–5 layers deep. The generated microstructures can span several layers. Figure 3.29 shows the tracks formed by the various scans, and the different microstructures and grains created. The microstructures produced during the solidification process greatly influence the mechanical properties of laser metal deposited parts. The processing parameters also have a role to play in the resulting microstructure and hence the mechanical properties. The process-structure-property relationships define the interactions and the resulting properties. AM process tends to produce anisotropic properties due to the layer-based strategy for building parts. Figure 3.30 shows the mechanical properties of Ti6Al4V ELI in 2 build orientations, vertical and horizontal. The figure also shows the changes in properties after stress relieving and annealing heat treatments. Further details related to microstructure formation and modeling are discussed in Chap. 17.

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Fig. 3.29 SEM image showing several tracks and microstructure formed [27]. (© Springer)

Fig. 3.30 Tensile properties of Ti6Al4V ELI in different build orientations and after heat treatments [33]. (©Springer)

3.1.8 Maintaining Process Consistency and Quality In the metal PBF AM process, a number of issues can occur that can significantly impact the quality of the part. Proper selection of feedstock material, process parameters, and build planning can all have an impact on part quality. Issues such as porosity, residual stress, density, warping, cracking, and poor surface finish can significantly impact the success of the build as well as the final usability of the part. 3.1.8.1

Powder Delivery and Spreading-Related Issues

The build problems associated with recoaters can be reduced by the positioning of parts on a build platform (Fig. 3.31). Some good guidelines are (i) not positioning

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Fig. 3.31 Avoiding recoater issues. (Adapted from Ref. [21]) (used with permission)

the parts parallel to recoater to minimize the contact length between the part and the recoater. Having the recoater contact a corner first rather than a long edge. (ii) Avoid putting parts right behind each other. In cases of interference between the recoater and the part in front, the powder bed layer behind the part may be affected causing build problems in the part behind – such as uneven powder layer and shorting of powder in the layer. (iii) Avoid simultaneous contact with recoater. Reducing the amount of contact with the recoater by offsetting the parts minimizes the impact of the recoater blade on the parts. (iv) Position the highest parts closest to the front. The powder bed quality is usually better in the front than in the back. Positioning taller parts towards the front also helps with saving powder on longer builds which also contain smaller parts. Once the smaller parts are finished building, the taller parts in the front only require depositing powder in the region of the tall part, and hence can save on powder and pausing for refills.

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Fig. 3.32 Powder shorting during build [9]. (Used with permission from SFF Proceedings)

Fig. 3.33 Powder layer defects caused by recoating [9]. (used with permission from SFF Proceedings)

The powder delivery and spreading mechanism can be the source of several errors that may arise during the build [9]. Powder shorting: If the powder reservoir is insufficiently packed before the build process or the so-called “charge amount” (i.e., the amount of powder swept across the bed during each pass of the recoater blade) is set too low to account for powder consolidation during processing, powder shorting may occur. This results in a nonuniform powder layer as seen in Fig. 3.32. Adherence of particles to recoater: Partially fused clumps of powder or spatter from the melt pool may adhere to the recoater blade and get plowed across the powder bed during recoating. This leads to troughs within the powder and a nonuniform powder layer, Fig. 3.33. Damage to recoater blade: Impact of the recoater blade with the previously build part layers and can lead to damage such as nicks and gouges that show up on the powder layer in the form of striations and variations in layer thickness.

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Fig. 3.34 A set of cubes manufactured at different process parameter settings showing the changes in porosity with change power (v = 800 mm/s and power from 90-360 W). (With permission from Elsevier)

Recoater blade bounce: The recoater blade may also “bounce” on impact and create a rippling effect before settling, leading to regular perturbations in powder thickness.

3.1.8.2

Porosity/Density and Lack of Fusion

Porosity is the occurrence of small voids forming in the part during the build process. The part density is inversely related to porosity. The lower the porosity the higher the part density that can be achieved. These voids can significantly impact the mechanical properties of the part along with the failure modes. Pores, especially those near the surface are critical and act as crack initiators severely impacting fatigue strength. Porosity can arise from several sources. Particle size distribution can also impact the porosity of a printed part. A wider particle size distribution may allow fine particles to fill spaces between larger particles. Porosity can occur due to improper selection of process parameters. Different pore formation mechanisms have been identified in PBF, with the three most common forms related to process parameters being keyhole mode pores, metallurgical or gas pores, and lack-of-fusion pores. When the energy density is too high, it creates a deep melt pool and causes a vapor depression to form in the melt pool. Due to high liquid flow velocities, it can cause the melt pool to close in on itself and trap the vapors during the cooling process thus creating pores. In gas-atomized powders, gas pockets can form within the powder feedstock itself and may be transferred to the final part during the build. At low energy density, the metal particles may not fuse leading to porosity caused by lack of fusion. Figure 3.34 shows an example of how process parameters can impact porosity.

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Fig. 3.35 Some examples of porosity caused by gaps in tool paths [9]. (With permission from SFF Proceedings)

At high-power densities, spatter ejection and subsequent embedding of ejected particles into the powder bed can also lead to inclusions and lack of fusion around these inclusions. Powder particles larger than layer thickness, due to ejecta and agglomeration of powder are another source of porosity. Loose powder packing during the spreading of the powder has also been attributed as a potential source of porosity. The process of scanning each layer can also lead to porosity caused by improper overlap between hatch vectors especially where the infill hatch vectors meet the boundary. Figure 3.35 shows an example of porosity. Porosity from a variety of these sources can be controlled and effectively eliminated by manipulating AM process variables. Porosity less than .2–.5% can be achieved by proper selection of process parameters.

3.1.8.3

Thermal/Residual Stress-Related Effects

Residual stresses are introduced into the part as a result of thermal effects created by solidification of the melt pool, heating and cooling, and repeated expansion and contraction that occurs during the layered building process. The residual stress manifests itself as distortion in the part geometry, warping and curling of the build layers, cracking, and separation from the supports. Figure 3.36a shows the distortion during build causing the part to interfere with the recoater blade and failed build. Figure 3.36b shows separation of the part from the support structures due to the internal stresses. Such a separation during the build can lead to build failures.

3.1.8.4

Chemistry-Related Effects

Improper selection of process parameters and operating conditions can also lead to chemical changes in the part. Exposure to oxygen and humidity can cause metal alloys to change composition. For instance, as oxygen increases in Ti-6Al4 V titanium, the aluminum content may decrease. In a metal alloy, in which multiple metals are alloyed, the metal with the lower melting point could potentially evaporate in the process. In the case of Ti-6Al-4 V, titanium has a much higher

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Fig. 3.36 Examples showing impact of thermal effects and residual stress [9]. (With permission from SFF Proceedings)

melting temperature than aluminum, and it’s possible to alter the composition of the material during the AM process.

3.1.9 Advantages and Limitations Powder bed systems are capable of high-resolution parts, and depend on the laser spot size, melt pool size, and layer thickness. Feature resolutions of 40-70 microns are possible. A downside to using small layer thickness is the process time to build parts. Larger number of layers are needed, which necessitates larger number of recoating operations which are slow, thus impacting build time. Complex geometry can be made allowing for building of lattice structures, topology-optimized geometry, and intricate cooling channels. However, care must be taken to ensure that the power can be easily removed, as well as the support structure accessibility. This requires careful upfront planning. The typical build platform for PBF is small roughly 300 × 300 × 300mm. Scaling this to a larger build size is limited by the optics and powder spreading capabilities. Newer machines with multiple lasers are currently available. The use of multiple lasers can speed up the layer scanning time as the build platform size increases. Large bed PBF machines with upto 1 meter build area are recently being developed with up to 12 lasers. Another issue is the cost of the powder and the amount of powder that is required to be loaded into the machine. Cost of machines and auxiliary equipment for powder handling is high. Setup times to switch powders is high and this is often counteracted by using dedicated machines for each powder. Nesting parts to utilize the full 3D volume is often not possible without creative use of supports. Multiple material parts are generally not possible, although a recent approach to recoating by Aerosint has shown an example of dual

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material part. Limited number of materials are currently available, but more are under development.

3.1.10 Examples of Parts and Applications Powder bed systems have been used in a large range of industries, and the use and applications are only limited by the user’s imagination and the technology limitations. Table 3.3 shows a few examples of the use of PBF systems in a range of

Table 3.3 Example parts using laser powder bed fusion Application/industry GE leap engine / aerospace engines

Example part

https://3dprintingindustry.com/news/ge-atlas-metal-3dprinter-announces-development-of-worlds-largestpowder-bed-3d-printing-116490/ (used with permission from GE Additive) Heat exchangers

https://www.3dsystems.com/aerospace-defense/heatexchangers (credit 3D systems, Inc. used with permission) Medical implants

https://www.3dsystems.com/healthcare/device-designand-development?ind=medical (credit 3D systems, Inc. used with permission) (continued)

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Table 3.3 (continued) Application/industry Patient-specific custom implants

Example part

https://www.3dsystems.com/device-med (credit 3D systems, Inc. used with permission) Lightweight structures

https://pr.themanufacturer.com/additivemanufacturing-research-experts-at-oerlikon-lindeand-tu-munich-to-develop-high-strengthlightweight-aluminum-based-alloy/ (credit Oerlikon, used with permission) Tooling with conformal cooling channels

https://www.3dsystems.com/sites/default/files/ 2019-09/3d-systems-conformal-cooling-datasheeten-letter-web-2019-08-27_0.pdf (credit 3D Systems, used with permission) Lattice structures

https://insights.globalspec.com/article/7447/factorsto-consider-when-3d-printing-or-additivemanufacturing-metal-parts (used with permission from Autodesk)

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industries. Some of these may just be prototypes or notional parts indicating what is possible. The trend is obvious – the move towards functional parts either in small batches or mass production.

3.2 Electron Beam Powder Bed Process 3.2.1 Brief History A 1993 Patent (SE 9301647) described the principle of melting electrically conductive powder, layer by layer, with an electron beam (ebeam), for manufacturing three-dimensional bodies (Larson 1993). In 1997 Arcam AB was founded and the company continued the development on its own, with the objective to further develop and commercialize the fundamental idea behind the patent. The process was commercialized by ARCAM AB Corporation in Sweden, and recently acquired by GE Additive.

3.2.2 Process Description and System Components Figure 3.37 shows a typical configuration of the ebeam AM machine. It is very similar in concept to the laser PBF process with similar machine hardware and architecture, except the energy source is replaced by a focused ebeam. The process steps are also very similar to that of a laser PBF, hence only the major differences are highlighted here. An additional step of intermediate heating is introduced after the deposition of the powder layer. The complete process is executed in a vacuum.

3.2.2.1

Ebeam Generation and Delivery System

The main energy source for the melting of the powder is the focused ebeam spot that is moved in the x,y plane. The ebeam is generated using an electron gun. The typical structure of the ebeam generator and delivery system is shown in Fig. 3.37. Negatively charged electrons are emitted from a thermionic cathode, typically a heated tungsten or Lanthanum hexaboride LaB6 filament placed in a Wehnalt cylinder with an exit aperture through which the electrons can exit. The electrostatic fields between the filament and the Wehnalt cylinder provide initial focusing of the beam and act as an electrostatic lens. Tungsten filament-based cathodes were used in the earlier machine and replaced by LaB6 in the newer more recent machines. The tungsten filaments tend to increase the beam diameter when power exceeds 1 kW. The beam produced with LaB6 is much more stable at higher power. The exiting electrons are accelerated towards a positive anode by applying a high voltage, called

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Fig. 3.37 Schematic of the ebeam machine (GE whitepaper, Inside Electron-Beam Melting). (Used with permission GE Additive)

the acceleration voltage. The anode has a central hole through which the electrons exit. A fraction of the electrons goes through the anode, forming the initial electron beam. The beam current is determined by these electrons. The electron beam exiting the anode is then shaped by the beam-forming components – a stigmator to correct for astigmatism in the beam and focusing system for focusing the beam. A beam deflection system provides the ability to deflect the beam and move it around in the x,y plane. Since the electrons in the beam are negatively charged the manipulations

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are performed by electromagnetic coils and no moving parts are used. The lack of moving parts might require less maintenance. The energy of the resulting beams is measured in keV (thousands of electron volts) or MeV (million electron volts). Another key parameter is the beam current, measured in milliamps (mA), and is a measure of the number of electrons in the beam in a given amount of time. The power of the ebeam system is measured in Watts and computed as Power = Current X Energy. The beam current is usually between 1 and 50 mA, with acceleration voltages in the range of 60-100KeV, resulting in a maximum beam power of about 3 kW. The beam diameter can be focused to around 100 microns. Using electromagnetic beam control with no moving parts, the beam positions can be changed at extremely fast speeds up to 8000 m/s. The kinetic energy of the resulting beam is equal to the potential difference between the cathode and the anode. The electron’s kinetic energy is transformed into heat when it strikes the powder bed and provides the heat for fusion. Under an accelerating voltage of 100 kV, the kinetic energy of an electron accelerated through a potential difference of V volts can be calculated by .

1 mv 2 = eV 2

where e = electron charge (1.6 × 10−19 C), m is the mass of the electron (9.11 × 10−31 kg) and v = velocity, V is the potential difference, the resulting velocity of the electrons striking the work surface is  v=

.

 2eV = m

2 × 1.6 × 10−19 × 100 9.11 × 10−31

= 7.26 × 106 m/s

The spatial energy distribution in the ebeam is a Gaussian similar to that of the laser. Other profiles are also possible.

3.2.2.2

Vacuum System

The electron beam generation and use are both performed under vacuum. The operational vacuum for the electron beam generation is between 10−5 and 10−6 mbar. The working chamber environment for ebeam powder bed systems provides a base pressure of 5 × 10−5 mbar or better throughout the build process. A small helium partial pressure (controlled vacuum) of 4 × 10−3 mbar is applied to prevent electrostatic discharge and smoke events. Working in a vacuum environment also promotes higher levels of cleanliness in the build chamber and higher energy efficiency. The low oxygen levels in the build chamber reduce the buildup of oxides, allows for processing reactive materials, and eliminate the need for laminar flow of inert gas typically required in laser PBF systems.

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3 Metal Additive Manufacturing Processes – Laser and Electron Beam Powder. . .

Powder Feeder and Spreading

The powder is stored in 2 hoppers one on each side of the build plate. A raking system is used to spread the powder. Unlike a hard doctor blade, the rake is made of spring steel and has a very fine-toothed structure, making it more flexible than a doctor blade. A calibrated amount of powder is dispensed by the powder feeder and spread over the build area by the rake. A sensor system allows for measuring the deposited powder and determines the number of passes of the rake to ensure layer uniformity. Bi-directional spreading of the powder reduces the powder spreading time.

3.2.2.4

Intermediate Heating Steps

After spreading the powder, the powder layer is preheated by high-speed scanning with a defocused electron beam several times across the layer. This helps to maintain the temperature in the build volume and to slightly sinter the powder particles. This is necessary to increase the electrical conductivity of the powder to reduce the possibility of powder discharge (or “smoke”) due to the repulsion of electrostatically charged powder particles. The electrons of the beam transfer the charge to the powder grains causing the concentration of negatively charged powder particles that repel causing “powder explosions” or “smoke”. The heating process produces parts with lower residual stresses and hence better production of parts prone to cracking and thinner cross-sections. Entire builds can be kept at elevated temperatures up to 1000 ◦ C. This also reduces the amount of energy needed to reach the melting point resulting in a faster process and increased productivity. This also eliminates the need for post-process heat treatment. The preheating temperatures depend on the material being used. The intermediate heating step is applied to the full powder bed surface and creates a partially sintered powder bed. A defocused ebeam is used to rapidly scan the surface of the newly deposited powder layer in incrementally increasing power, thereby gradually increasing the temperature and allowing the sintering to take place. Since the complete layer of powder is partially sintered, the sintered powder acts as a support structure and reduces the need for complex mechanical support structures. Supports used primarily provide a means for heat removal to ensure even build temperatures, and do not need to be strongly embedded into the part to hold the part to prevent effects of high residual stresses. The process also allows for building stacked parts to make use of the full 3D build volume thus increasing productivity.

3.2.3 Process Dynamics The primary mechanism for creating the heat required for melting is through the transfer of energy from the kinetic energy of the electrons to heat energy. Once

3.2 Electron Beam Powder Bed Process

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Fig. 3.38 Path of electrons [19]

the electrons strike the powder surface, a variety of elastic and inelastic collisions between electrons and atoms in the powder sample are produced. A large percentage of the electrons begin to lose energy to the powder bed as they penetrate further into the powder bed. Some electrons bounce back from the surface without any loss of energy (elastic collisions), and are called backscattered electrons. Atoms with larger atomic numbers have a higher probability of producing backscatter. The electrons that penetrate may free some additional electrons in the powder, released as secondary electrons. Ignoring the secondary electrons, the component of energy absorbed by the powder is defined by the absorption coefficient = (1- % of backscatter). Figure 3.38 shows the path of the electrons. A major advantage of using electrons is due to the higher absorption efficiency as compared to a laser, especially for materials with higher reflectivity. By deceleration of the electrons in the powder, the momentum of the electrons will be transferred to the powder particles. This results in 2 physical actions, (i) the spreading of the powder also called “smoke” due to its appearance as a cloud of displaced powder and (ii) creation of the melt pool. The spreading of the powder can be attributed to two physical actions. The impulse caused by the striking electrons could cause a spreading of the powder. However, it is shown in [22] that the impulse caused by the striking electrons is not an applicable cause of powder spreading. The electrostatic charge of the powder particles was shown to be the primary cause for

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the effect on the spreading of the powder. Several different methods were proposed to address this. The roughening up of the build plate to increase the contact surface area and hence provide a greater surface for the dissipation of the electron charge. The preheating and mild sintering that accompanies it increases the electrical conductivity of the powder. Enlarging the build platform and making it thicker also enhanced the flow of the electrical charge. Electrical resistance to the grounding was increased by using a copper electrode directly from the powder to ground. The powder used was switched from gas atomization which causes spherical grains and was replaced with water-atomized grains to increase the variety of shapes to increase electrical conductivity. On entering the substrate, the electrons spread radially and the effective beam diameter changes by the amount of the spread. Additionally, the repulsion from the charged powder may cause some diffusion of the beam increasing the focused spot size. The computations for power density, volumetric energy density, and surface density are identical to those for the laser. The energy is dissipated by the incident electrons into the material and converted into heat to melt the powder particles and form the melt pool. The melt pool created is about 3–4 times deeper than the layer thickness to allow for connected layers. The melt pool traverses along a path defined by the tool path to solidify the geometry on each layer. The tool path parameters such as hatch spacing, power, scanning velocity, and layer thickness all govern the size of the melt pool influence the process and governs the formation of the material microstructure. The building of the part by successive layers results in rapid and directional solidification, leading to the formation of epitaxial grains in the direction of the build layers. The two-step heating process used maintains the part and powder bed at elevated temperatures (up to 700 ◦ C-1000 ◦ C) and hence reduces the cooling rates. This also reduces some of the internal residual stresses in the part. An effect of building in a vacuum at high melting temperatures is the depletion of some alloying constituents due to the high vapor pressure. The loss of the alloying elements due to uneven evaporation can be more significant in the ebeam as compared to the laser-based PBF due to the higher beam power and temperatures in the melt pool. Research has shown that the final content of the alloying elements is sensitive to energy input and beam velocity. Increasing energy density with constant velocity leads to higher evaporation rates due to increased melt pool size, and surface temperatures. Aluminum loss as high as 1.5% was reported at high energy density and low scan speeds with close line spacing [26].

3.2.4 Materials Similar to laser-based systems, starting feedstock is powder, typically with spherical morphology, high flowability, high packing density, and no internal porosity.

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Typical particle sizes range from 45–100 μm for layer thickness of 50–100 μm. Commercially available machines currently use Ti6Al4V grades, Inconel 718, Tool Steel, and TiAl. Researchers have used many other powders. Recycling of powder for an ebeam process is also slightly different, due to the different process characteristics. The ebeam process involves preheating each powder layer and slight sintering, a sintered cake of powder will be created. This cake will be kept at the preheating temperature through the whole build, which in many cases is several hours. The powder is at higher temperature than expected, due to the pre-sintering as well as exposure of the powder cake to a rather large temperature for long build times [24, 31].

3.2.5 Microstructure and Properties The formation of microstructure in ebeam powder bed follows the process similar to the laser-based powder bed. The rate of cooling is however slower due to the higher temperature of the powder bed. This leads to differences in formation of the microstructure. The EBM process can take 5–80 h to cool below 100 ◦ C after layer melting is completed, depending on part size and geometry, so an additive manufactured part may experience a significant amount of annealing and recrystallization within the AM process chamber. The different sets of parameters used for different areas of the parts lead to different microstructures in the layers. Figure 3.39, shows the different Beta grain structures created in different regions of the part [1]. For further details on microstructure and properties, refer to Chaps. 17 and 18.

3.2.6 Comparison Between Laser and Ebeam PBF Table 3.4 shows the comparison between laser PBF and ebeam based on commercially available machines, modified from [30].

3.2.7 Advantages and Disadvantages of Electron Beam Melting Ebeam PBF can produce parts with very high density and higher purity due to the operation in vacuum. Higher scanning speeds make it a faster process. Beam splitting can allow for production of multiple parts simultaneously. Parts have less

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Fig. 3.39 Diagram showing different B grain structures generated by contour pass and infill [1]. (© Springer)

thermal stress and require less support. The complete 3D volume can be filled to allow better use of the build volume. The build size is limited with the largest machine having a build volume of about 350 × 350 × 380 mm. Ebeam machines have a higher cost and limited availability of materials.

3.2.8 Example Parts and Applications Ebeam-based PBF part applications overlap considerably with those of laser-based processes. The main difference lies in the surface finish, resolution, and dimensional tolerances. The reduced need for supports allows for different lattice geometries to be created without concerns for support removal (Table 3.5).

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Table 3.4 Comparison between Laser PBF and ebeam Characteristics Energy source Energy transfer mechanisms

Laser-based PBF Laser beam Laser photon energy converted to thermal energy

Beam power Minimum spot size Layer thickness Volumetric build rate

100-400 W 30–250 microns 20–100 microns 10–50 cc/hr. (highly material dependent). Depends on f theta lens, and number of lasers

Maximum build volume

Beam scanning speed Materials

Powder feedstock size Processing atmosphere

Powder preheating strategy Powder preheating temperature Powder removal from finished part

Surface finish Residual thermal stresses Geometric tolerance Minimum feature size Equipment cost

0.3–1.0 m/s Stainless and maraging steel; aluminum, cobalt-chromium, and titanium alloys; but also: Polymers, ceramics, cermets Relatively fine (mean particle size: 30 μm) Inert gas (argon; nitrogen)

Limited to platform preheating by infrared heaters Lower (T: 100 ◦ C–200 ◦ C) Vacuum cleaning (sufficient for removing loose powder)

Fair to good (Ra: 4–11 μm) High Good (±0.05 to ±0.1 mm) 40–200 μm Cheaper

EBEAM-based PBF Electron beam Kinetic energy of electrons is converted into thermal energy 3KW -6 KW 100 microns 50–200 microns 50–90 cc/hr. (material-dependent) Depends on the deflection capability and astigmatism correction 8000 m/sec Metals (conductive materials only) of Ti6Al4V grades, Inconel 718, tool steel, TiAl Relatively coarse (mean particle size: 70 μm) Vacuum (chamber pressure 5 × 10−4 mbar, build atmosphere 4 × 10−3 mbar helium) Defocused ion beam scanning Higher (T: 700 ◦ C–1000 ◦ C) Sandblasting with similar powder (required for detaching partly sintered powder) Poor to fair (Ra: 25–35 μm) Low Fair (±0.2 mm) 100 μm Expensive

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Table 3.5 Examples of Parts using ebeam PBF Application / Industry Lattice structures

Parts

https://3dsourced.com/guides/electron-beam-melting-ebm/ Turbine blades

https://www.ge.com/reports/future-manufacturing-take-look-insidefactory-3d-printing-jet-engine-parts/ (used with permission from GE Additive) Medical implants

https://www.ge.com/additive/ebm (used with permission GE additive) Copper components

https://www.canadianmetalworking.com/canadianmetalworking/ product/metalworking/new-materials-from-ge-additive-arcam-helpunlock-potential-of-electron-beam-melting (used with permission from GE Additive)

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3.3 Questions and Discussions 1. What are the main components of a powder bed fusion additive manufacturing process? What is the role of each of these main components, and how they might influence the process? 2. What are some of the common lasers used in powder bed systems? 3. What are the main components of the laser delivery systems, along with the operational parameters of interest? 4. What are some of the typical defects that may be encountered in PBF systems and how are they related to the process parameters? 5. What are the major differences between laser and ebeam-based powder bed fusion systems? 6. What is the role of gas flow in powder bed fusion-based processes? 7. What are the scan-related parameters and how are they related to the energy density? 8. Discuss the need for support structures in both laser- as well as ebeam-based systems. 9. What are some of the types of materials used in powder bed fusion systems? 10. How are residual stresses created in powder bed systems and what are the implications of residual stresses and their role and impact?

References 1. Antonysamy AA, Meyer J, Prangnell PB (2013) Effect of build geometry on the β-grain structure and texture in additive manufacture of Ti6Al4V by selective electron beam melting. Mater Charact 84:153–168. https://doi.org/10.1016/j.matchar.2013.07.012 2. Arısoy YM, Criales LE, Özel T, Lane B, Moylan S, Donmez A (2017) Influence of scan strategy and process parameters on microstructure and its optimization in additively manufactured nickel alloy 625 via laser powder bed fusion. Int J Adv Manuf Technol 90(5– 8):1393–1417. https://doi.org/10.1007/s00170-016-9429-z 3. Bidare P, Bitharas I, Ward RM, Attallah MM, Moore AJ (2018) Fluid and particle dynamics in laser powder bed fusion. Acta Mater 142(January):107–120. https://doi.org/10.1016/ j.actamat.2017.09.051 4. Boley CD, Khairallah SA, Rubenchik AM (2017) Calculation of laser absorption by metal powders in additive manufacturing. Additive Manufacturing Handbook: Product Development for the Defense Industry 54:507–517 5. Cheng B, Loeber L, Willeck H, Hartel U, Tuffile C (2019) Computational investigation of melt pool process dynamics and pore formation in laser powder bed fusion. J Mater Eng Perform 28(11):6565–6578. https://doi.org/10.1007/s11665-019-04435-y 6. Cooke A, Slotwinski J (2015) Properties of metal powders for additive manufacturing: a review of the state of the art of metal powder property testing. In: Additive manufacturing materials: standards, testing and applicability. KU Luven. https://lirias.kuleuven.be/1748636?limo=0 7. DebRoy T, Wei HL, Zuback JS, Mukherjee T, Elmer JW, Milewski JO, Beese AM, WilsonHeid A, De A, Zhang W (2018) Additive manufacturing of metallic components – process, structure and properties. Prog Mater Sci. https://doi.org/10.1016/j.pmatsci.2017.10.001

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8. F-Theta Lenses Tutorial (n.d.) Accessed February 27, 2020. https://www.thorlabs.com/ newgrouppage9.cfm?objectgroup_id=10766 9. Foster BK, Reutzel EW, Nassar AR, Hall BT, Brown SW, Dickman CJ (2015) Optical, layerwise monitoring of powder bed fusion. Solid Freeform Fabrication Proceedings:295–307. https://doi.org/10.1017/CBO9781107415324.004 10. GE (2017) Inside Electron-Beam Melting 11. German, Prof Randall (2019) Thinking about metal binder jetting or FFF? Here is (almost) everything you need to know about sintering. Metal AM:2019 12. German RM (1996) Sintering theory and practice. Wiley 13. Gunenthiram V, Peyre P, Schneider M, Dal M, Coste F, Fabbro R (2017) Analysis of laser–melt pool–powder bed interaction during the selective laser melting of a stainless steel. J Laser Appl 29(2):022303. https://doi.org/10.2351/1.4983259 14. Kou S (2002) Welding metallurgy, 2nd edn. Wiley 15. Kruth J-P, Mercelis P, Van Vaerenbergh J, Froyen L, Rombouts M (2005) Binding mechanisms in selective laser sintering and selective laser melting. Rapid Prototyp J 11(1):26–36. https:// doi.org/10.1108/13552540510573365 16. Lee H, Lim CHJ, Low MJ, Tham N, Murukeshan VM, Kim YJ (2017) Lasers in additive manufacturing: a review. Int J Precis Eng Manuf Green Technol 4(3):307–322. https://doi.org/ 10.1007/s40684-017-0037-7 17. Leung CL, Alex SM, Atwood RC, Towrie M, Withers PJ, Lee PD (2018) In situ X-ray imaging of defect and molten pool dynamics in laser additive manufacturing. Nat Commun 9(1):1–9. https://doi.org/10.1038/s41467-018-03734-7 18. Li R, Liu J, Shi Y, Wang L, Jiang W (2012) Balling behavior of stainless steel and nickel powder during selective laser melting process. Int J Adv Manuf Technol 59(9):1025–1035. https://doi.org/10.1007/s00170-011-3566-1 19. Mahale TR (2017) Electron beam melting of advanced materials and structures, mass customization, mass personalization. NC State University. https://repository.lib.ncsu.edu/handle/ 1840.16/4943 20. Saunders M (2017) Gone with the wind – how gas flow governs LPBF performance. Article 1–14. https://doi.org/10.1097/00000542-196201000-00083 21. Materialise (2017) Metal 3D printing: how to counter the impact of recoaters two types of recoaters. https://manufacturing.report/Resources/Whitepapers/170ac942-e67a-44b3-bbb52248db3321c3_Paper_Metal_3DPrinting_Recoaters.pdf 22. Milberg J, Sigl M (2008) Electron beam sintering of metal powder. Prod Eng 2(2):117–122. https://doi.org/10.1007/s11740-008-0088-2 23. Mugwagwa L, Dimitrov D, Matope S, Yadroitsev I (2019) Evaluation of the impact of scanning strategies on residual stresses in selective laser melting. Int J Adv Manuf Technol 102(5– 8):2441–2450. https://doi.org/10.1007/s00170-019-03396-9 24. Petrovic V, Niñerola R (2015) “Powder recyclability in electron beam melting for aeronautical use.” Edited by Prof Richard Degenhardt, Dr Leslie J. co. Aircr Eng Aerosp Technol 87(2):147–155. https://doi.org/10.1108/AEAT-11-2013-0212 25. Plessis, Anton du (2019) Effects of process parameters on porosity in laser powder bed fusion revealed by X-ray tomography. Addit Manuf 30(July):100871. https://doi.org/10.1016/ j.addma.2019.100871 26. Pobel CR, Osmanlic F, Lodes MA, Wachter S, Körner C (2019) Processing windows for Ti6Al-4V fabricated by selective electron beam melting with improved beam focus and different scan line spacings. Rapid Prototyp J 25(4):665–671. https://doi.org/10.1108/RPJ-04-20180084 27. Promoppatum P, Shi-Chune Yao P, Pistorius C, Rollett AD, Coutts PJ, Lia F, Martukanitz R (2018) Numerical modeling and experimental validation of thermal history and microstructure for additive manufacturing of an Inconel 718 product. Prog Addit Manuf 3(1):15–32. https:// doi.org/10.1007/s40964-018-0039-1

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Chapter 4

Metal Additive Manufacturing Processes – Directed Energy Deposition Processes

4.1 Introduction to Directed Energy Deposition Directed energy deposition (DED) is a major category of processes used for additive manufacturing of metallic materials. Instead of using a powder layer, like the PBF processes, the material is deposited directly at the melt pool created by the energy source. The melt pool is moved over the surface by moving the energy source to create a single layer. The surface is not restricted to a planar layer, the process can be used to build 3D shapes on any starting surface. Hence it can be used for part restoration and repair by adding material layer by layer to existing surfaces of a part. Various heat sources (laser, ebeam, plasma arc, electric arc) have been utilized for the DED process, as well as various forms of feedstock (powder, wire) that represent the deposited material. Figure 4.1 shows a classification of the different types of energy and feedstock used in the various DED processes. DED processes have the capability to deposit large amounts of material while trading off on the feature definition. Shown in Fig. 4.2 is a schematic illustrating the contrasting nature of deposition rate and feature definition associated with the DED process. Also shown in the figure is the regime typically defined for the PBF process for comparison. Hence, these processes are often used in conjunction with post-process machining. Consideration is usually given to balancing the amount of material that may be deposited with what may be machined to minimize the overall manufacturing time.

4.2 Powder-Based Laser DED Process 4.2.1 Brief History The DED processes trace their roots back to the use of welding as an additive manufacturing process, and patents alluding to the process can trace their roots to © Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_4

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4 Metal Additive Manufacturing Processes – Directed Energy Deposition Processes

Fig. 4.1 Classification of DED processes

Fig. 4.2 Schematic showing the effect of deposition rate and feature quality associated with the DED process at increasing source energy. (With permission from ASM International)

Kratky’s (1937) production of hard metal alloys. Patent # US 2076952 and Harter I (1942) “Method of forming structures wholly of fusion deposited weld metal. Patent # US 2299747A”. Using this approach to repair parts was patented by Mehta PP, Otten RR, Cooper EB (1988) “Method and apparatus for repairing metal in an article. Patent # US 4743733A.” The use of this technique to make AM parts was developed and patented by Sandia National Lab and referred to as the LENS (Laser Engineered Net Shape) process. Since its development, it has been referred to as laser cladding, direct metal deposition (DMD), laser melt deposition (LMD), and blown powder technology.

4.2 Powder-Based Laser DED Process

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Fig. 4.3 Laser-based DED process schematics

4.2.2 Process Description The powder-based DED systems typically use lasers as the power source, and powder as the form of feed material. A deposition head is used to focus the beam while directing the powder into the melt pool created as shown in Fig. 4.3. The deposition head is mounted in a machine capable of positioning the head in 3D space to create a moving head and deposition framework. The machine motion platform used is often similar to a 3- or 5-axis CNC machine. The deposition head can also be mounted to a robot providing further degrees of motion to the positioning of the deposition head. A single layer is created by moving the head over a prescribed surface along a specified tool path under the guidance of a computer-controlled positioning system. Successive deposition of layers on top of each other creates the 3D solid. Since the process works with molten metal, the atmosphere surrounding the heated part must have low oxygen content to prevent oxidation of the material. A shielding gas is used to create an oxygen-free atmosphere. In an enclosed machine construction, this is provided by flooding the build chamber with inert gas in a manner similar to PBF systems. When the head is mounted in a robot arm, the shielded atmosphere around the melt pool is created by introducing the shielding gas through the deposition head. The powder is delivered to the melt pool via powder feeders and supply lines through the deposition head.

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4.2.3 System Components 4.2.3.1

Deposition Head

Deposition heads are primarily used for laser-based DED. A coaxial design is typically used where the laser is focused through the center, and the powder is delivered through multiple nozzles concentrically located around the laser beam. An outer shroud gas passage is used to feed the shielding gas, especially in applications that do not use a hermetically sealed chamber. Additionally, water or gas cooling may be included to reduce the damage to the optics and tips due to heat build-up. The inert gas is also commonly used within the deposition head for laser-based DED systems to minimize contamination of optics due to spatter and vaporized material, as a carrier gas for powder feeding, and as an ancillary cover gas for protecting the molten metal during processing. Figure 4.4 shows a schematic of the deposition head.

Fig. 4.4 Schematics of a deposition head used in laser-based DED systems. (With permission from ASM International)

4.2 Powder-Based Laser DED Process

4.2.3.2

115

Laser and Laser Delivery

Several types of industrial lasers have been used for DED, such as ytterbium fiber, Nd:YAG, direct diode, and CO2 lasers, but most DED processing systems utilize lasers having a characteristic wavelength near 1 μm or 1000 nm due to the improved absorptivity of near-infrared electromagnetic radiation with metals and transmissivity within an optical fiber. Most modern systems use fiber lasers that are capable of multi-kWatt power. The laser delivery and optics have similar properties and requirements as the PBF systems. A typical delivery system requires a beam from the laser source, the focusing of the beam onto the end of the fiber, the transmission of the beam through the fiber, and the recollimation and focusing of the beam at the deposition head. The focal length, the distance between the final optic and the focused laser beam, is determined by the curvature of the focusing optic, while the radius of the focused spot, or similarly the spot diameter, is a function of the magnification (m), the radius of the delivery fiber and the characteristics of the laser source. Higher power fiber delivered lasers typically employ a multi-mode beam and result in a “top hat” energy distribution after fiber delivery [7], whereas, lower power single-mode beams of a ytterbium laser, where the laser source may also be the fiber delivery system, can provide a Gaussian energy distribution upon leaving the fiber. Laser power used for DED may be between 500 W and 10 kW, with increased power resulting in increased deposition rates. Increasing power allows for an increase in deposition rate; however, it comes at the cost of feature definition. Smaller features are more difficult to produce at higher power and high deposition rates. An approximate relationship to estimate the maximum deposition rate per kilowatt of power for lasers in the 1 mm range is 1 kg of deposited material per 1 kW of power. Although lasers are capable of being focused on very small spots, the laser deposition process usually uses a defocused or diffuse beam at the interaction plane, since the larger laser spot increases the potential deposition area and lower power densities are adequate for surface melting. Metal powder is typically used for laser-based DED since the larger surface area associated with the powder particles improves energy absorption during laser interaction.

4.2.3.3

Powder Feed and Delivery Systems

Powder used for the DED process is typically between 50 and 150 microns in diameter to provide sufficient flowability from the power feeding system, through the feeding conduit, and to the feeding nozzle(s). The powder is housed in sealed reservoirs remotely located from the deposition head. A powder feed system is used to meter and supply the powder. Several mechanisms have been developed but most utilize a revolving wheel having cavities or scoops that are used to capture powder from the powder hopper or reservoir and provide it to the powder conduit. The rotational speed of the wheel and the volume of the cavities dictate the mass feed rate, in kg/hr. (lbs/hr), of powder that is fed to the deposition head and feed nozzles.

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Fig. 4.5 Schematics of powder delivery. (With permission from ASM International)

To facilitate flow of the powder through the powder conduits pipes, a carrier gas, often an inert gas such as argon, is used to assist the powder in flowing through the conduit to the laser deposition head. Figure 4.5 shows one such configuration. Shown in Fig. 4.5 is a diagram of a complete system used for feeding powder from a hopper to the laser deposition head. This system utilizes a rotating metering wheel to control mass flow rate to provide powder to a coaxially fed nozzle; however, a manifold is also used to provide the powder at four locations at the nozzle to aid uniformity of powder at the interaction area. Also note that in this case, the laser is providing deposition with a defocused beam that is created by processing below the plane of focus. Once at the head, various configurations are used to direct the powder to the laser beam and interaction region of the substrate for deposition. One or multiple nozzles are used, as well as an annular, coaxial arrangement for providing powder to the laser beam for deposition. When a single nozzle is used, it may be directed at the leading edge of the laser interaction area, with the powder flowing into the beam and the diffuse laser spot. In many instances, multiple nozzles are used to provide a more uniform flow of powder to the interaction area and to increase the amount of powder material for deposition. Relatively high deposition rates may be achieved using one large nozzle to preplace powder ahead of a manipulated beam that is scanned transverse to the primary motion or circularly manipulated around an axis of primary motion. Although this technique offers the ability for high deposition rates, it is limited to simple motion of the deposition head or only the substrate to control placement of the powder ahead of the beam. When multiple nozzles are used, they may be placed at various positions along the circumference of the laser

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beam. The most common use when separate nozzles are employed is to separate the nozzles at 90◦ quadrants. Two nozzles, one at the leading edge and one at the rear of the molten pool, can be used to provide one type of powder at the front and another powder type at the rear. This technique has been used to produce deposits representing a metal matrix composite, where the metallic powder is added at the leading edge to create the deposit and the hard particles, such as a carbide, are fed into the molten pool at the rear to avoid extremely high temperatures and slow dissolution of the hard particles. As mentioned above, a coaxially fed powder using two concentric nozzles that form an annular ring around the deposition head is also employed. One technique utilizes this approach with increased carrier gas flow rates to propel powder as a stream into the beam for processing when the deposition head is not parallel to gravity. This technique has been shown to be useful for “out of position” processing when the deposition head may significantly depart from the gravity vector, but at relatively low deposition rates.

4.2.3.4

Motion Systems

Unlike PBF systems where the laser spot only moves on a single plane, and the positioning of the spot is controlled by galvanometer-driven systems, in DED systems the entire processing head moves relative to the substrate. Motion devices for DED systems may involve movement of the processing head, movement of the substrate or component, or a combination of motion involving the processing head and substrate. Motion requirements are dictated by the complexity of the paths used to form the part geometry, or deposition geometry in the case of restoring material to an existing part. In many instances, these requirements include the motion for creating the layer geometry, as well as any angular motion needed to maintain the perpendicularity of the processing head and the deposition path. Laser- and arc-based DED systems may utilize rectilinear or articulating systems, commonly referred to as gantry or robotic systems, respectively. Rectilinear devices are defined by the length, accuracy, velocity, and weight capacity of motion. Commonly used rectilinear systems comprise three axes for X, Y, and Z motion, with X and Y representing horizontal motion relative to the processing base or substrate and the Z-axis defining the vertical motion of the processing head. This configuration provides basic motion for layered processing in an X and Y plane and the Z-axis is indexed to provide deposition for each layer. This system may suffice for building simple geometric shapes having minimal changes in the Z-axis; whereas more complicated shapes, especially involving continuous changes in the Z-axis, require additional axes of motion to assure that the processing head is maintained perpendicular to the deposited molten metal. This typically requires two additional rotational degrees of freedom, or a rotation and tilt, to achieve the desired motion. Examples of rectilinear systems for providing threeaxes motion for building a simple shape and five-axes of motion for producing a more complex shape are shown in Fig. 4.6.

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Fig. 4.6 (a, b) With permission from ASM International. (c) Common designation of robot axis. (With permission from Yamaha Motor Corporation, USA)

Articulating systems, such as robots, may also be utilized for motion of the deposition head and the substrate. Shown in Fig. 4.6 are common designations for the axes used for industrial robotic systems. Although robotic devices are usually not as accurate in movement as rectilinear systems, they may provide the necessary accuracy for most deposition applications. Also, when a robotic system is integrated with additional motion devices, such as in Fig. 4.6b, showing integrated rotation and tilt, highly complex motion between the deposition head and the substrate or part may be achieved. Movement of a robotic system may be conducted using several methods with the pendant being used for general positioning and teaching simple paths. Complex motion for many DED applications, especially when additional axes are integrated into the system, requires specialized off-line programming packages. Many of these software systems also have the capability to recreate path motion directly from design files and conduct simulation of the created paths prior to processing. Although software for driving these systems is improving, the integration and interaction of software utilized for various steps that are required for conducting the DED process are not as robust as those used for PBF processes.

4.2.3.5

Processing Space or Chamber

The materials that may be processed within a DED system are dictated by the processing environment of the system, and may consider the propensity of the liquid metal to oxidize, absorption of gaseous species within the liquid pool, or detrimental reaction of the metal with gaseous species at elevated temperatures, but below the

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melting temperature. Examples include the formation of oxides on the surface of the molten pool for many alloy systems, absorption of hydrogen into the molten pool when processing aluminum, and absorption of oxygen and nitrogen at elevated temperatures for titanium alloys. Hence, systems utilized for DED employ various methods to control the environment during processing to minimize or eliminate these detrimental reactions. This includes processing within a vacuum or an inert gas environment, as well as local shielding using an inert gas similar to welding. Laser-based DED systems may utilize either a controlled environmental chamber or an open processing system that relies on local inert gas shielding. Whether a controlled or open environment is employed will limit the materials that may be effectively processed with these systems. Materials that are reactive to the potential presence of gas species, such as titanium alloys with oxygen and nitrogen, will require a processing chamber capable of producing a controlled atmosphere. Processing in a controlled environment requires the processing head and any motion equipment to be within a sealed chamber. The chamber is then purged with inert gas, argon is normally employed, to displace and vent air from the system. Once the desired environment is reached, measured by the level of residual oxygen within the system, a gas purification system is typically used to constantly recirculate the inert gas and any gas by-products produced during processing through a “scrubber” that reacts and removes oxygen from the processing environment. Residual oxygen within the processing chamber is measured using a gas analysis system that continually samples the chamber environment to report residual oxygen, which may be anywhere from 5 to 500 ppm, with the lower levels being preferred. These systems normally employ a coulometric sensor that measures oxygen based on a degree of an electrolysis reaction, which needs to be maintained and calibrated periodically. When using a laser-based DED system in an open environment, the alloys being deposited must be capable of melting and solidification under local inert gas shielding. This technique has been successfully applied to processing of ferrous, stainless steel, nickel-based, and aluminum alloys, to name a few. This method is usually applied to processing of large components or structures, where the scale of the motion system would pose significant challenges for operating in an enclosed chamber. Processing in an open environment requires adequate shielding to be applied locally through the use of a gas nozzle within the processing head. The flow rates of the gas used for shielding should be sufficient to enable uniform coverage of the deposition area, while not producing turbulence and aspiration of the outside environment to the liquid metal. Improved shielding may be accomplished through the use of ancillary shielding, either through additional nozzles or a gas shroud around the deposition nozzle. These ancillary shielding devices may utilize a diffuser technique, which provides uniform laminar gas flow, to provide consistent and stable gas coverage over a large area.

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Control System

The control system for a DED process must be capable of digitally directing all of the subsystems, as well as controlling and responding to various safety interlocks and commands. This is achieved through a central processor, which is included in systems designed specifically for DED processing. In most instances, processing parameters and path plans are set and controlled through the use of a digital build plan. However, it is not unusual for some parameters, such as gas flow rate or rate of feedstock introduction, to be set manually with the control system used to activate “on and off” instructions. For electron beam-based DED processing, the high-speed digital deflection system is utilized to create “raster patterns” that can be customized for specific applications. The raster pattern size, shape, and frame time are user programmable, and once created allow all inputs to be written into a fixed process agreement under CNC control. Most control systems employ a graphical user interface (GUI) that allows the various subsystems to be managed and monitored, as well as a main program that interacts with the various subsystems during continuous operation of the system. Since the control system also utilizes a path plan for deposition of a single layer or the entire build, the system must be capable of interfacing with software that is utilized for creating, and hopefully simulating, preprogrammed motion commands.

4.2.4 Process Dynamics Similar to the PBF process, the powder-based laser DED process relies on creating a layer by moving a melt pool over a surface. The main difference is that the surface is not limited to a planar surface and there is no powder bed layer; instead, powder is added to the melt pool created on an existing substrate. A stream of powder is fed coaxial to the laser beam. Movement of the melt pool results in rapid solidification and formation of individual tracks of deposited material. The powder particles absorb some of the laser energy, which are heated as they travel into the melt pool created by the focused laser beam. The fraction of energy absorbed by the powder particles results in heating of the powder particles. The temperature depends on several factors, such as particle size, velocity, thermal properties of the powder, and power density of the laser beam. Not all the powder ends up in the melt pool, and the fraction of captured powder is referred to as the capture efficiency, which also depends on several factors, such as size of the melt pool, powder velocity, etc. Calorimetric measurements of the partitioning of energy during the process show that the bulk absorption coefficient (β), which provides the ratio of the component of energy with respect to the total energy supplied to the system is an important parameter [10]. The energy balance equation shows the various components of how the input energy Qin is distributed. Some of it is absorbed by the powder (Qdep ), some is absorbed by the substrate (Qabs ), some is reflected by the substrate (Qref ), and some of it is lost through the powder due to the powder capture efficiency (Qlost ).

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Qin = Qabs + Qref + Qdep + Qlost

.

βabs + βref + βdep + βlost = 1

.

β must be determined through specialized experiments involving calorimetry [12]. However, based on previous research, β may be estimated. The bulk absorption coefficient for laser-based DED has been experimentally measured, and due to changes in the reflection of the beam with various materials has been shown to be sensitive to the wavelength and the material being processed, as well as laser power [12]. Results of these measurements have shown that β for laser-based DED using a ytterbium fiber laser operating at 1 kW and powder as the feedstock was 0.42 and 0.37 for alloys Ti-6Al-4V and Inconel 625, respectively [10]. It is also important to note that the results of these experiments revealed that under these conditions, 27% of the total energy provided by the laser was lost by the Ti-6Al-4V powder and 19% was lost by the Inconel 625 powder due to a portion of the heated powder not being captured within the deposit and ejection of superheated powder (spatter) from the deposit. The absorbed energy results in the creation of the melt pool. The dynamics within the melt pool affect the characteristics of the final deposition. The melt pool temperature/morphology is affected by forces such as surface tension, Marangoni convection effects, and metal vapor recoil. When the vapor recoil force exceeds the liquid/gas surface tension force near the periphery of the melt pool, the melt pool is expulsed. The recoil force increases with temperature faster than the surface tension force, therefore, as the process parameters are varied to increase the bulk temperature near the melt pool, mass loss due to boiling in the melt pool is possible. Flow dynamics and geometrical evolution of the liquid melt pool have been suggested to have strong relationships with the subsequent mechanical properties of additively manufactured parts. The depth of the melt pool is selected so that it penetrates one or more layers to provide the adhesion required between layers. For the directed energy deposition process, the substrate material may be different than the material being deposited, and under this condition, the composition of the melt is based on the compositions of the deposition and material diluted within the substrate. The composition for a i , may be determined particular alloying addition within the melt, denoted as .Cmelt by measuring the area of the melted region of the substrate and the deposit. If it is assumed that the cross-sectional area does not change significantly, the area of the two regions may be used to determine the composition of the alloying addition within the melted region based on the contributions from the deposited material and the substrate. This method is shown schematically in Fig. 4.7. It should be noted that when the alloying composition of the substrate is sufficiently different than the deposition material, subsequent deposits will cause a gradual change in composition related to successive dilution from each layer. This becomes more important when creating functionally graded materials.

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Fig. 4.7 Schematic showing the computation of the dilution effect

The complete layer is formed by the overlapping tracks whose trajectory is determined by the tool path for each layer. The complete part is formed by subsequent deposition of layers stacked on top of each other. The thermal history of the part is determined by the process parameters and tool path used. The thermal history influences the formation of microstructure and hence the material properties.

4.2.5 Process Parameters The parameters may be used to assess and compare the thermal response of the material during processing, anticipated build rates and productivity of the process, and potential for producing defects during processing. Shown in Fig. 4.8 is an illustration of the laser-based DED process defining important processing parameters. Although the laser-based process is shown in Fig. 4.8, the parameters of interest are applicable to all variants of the DED process. The fundamental parameters defined within Fig. 4.8 include: power (P) provided by the energy source, velocity (V) of the moving heat source, diameter (dspot ) of the energy source projected onto the substrate, mass flow rate (M) of the feedstock provided during processing, and spacing (S) between adjacent deposition beads (also called hatch spacing). One particular relationship that includes three of the fundamental parameters is the local energy density that defines the energy available for melting and deposition of material during DED processing. Similar to powder bed fusion systems, the local energy density (Ed ) may be described by: Ed =

.

βP V dspot

where β is the bulk absorption coefficient that accounts for the total energy that is absorbed during melting and deposition, P is power (in W) delivered from the heat source, V is velocity of the moving heat source (in cm/s), and dspot is the diameter

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Fig. 4.8 Illustration of the laser-based DED process defining important processing parameters: laser power (P), velocity (V), mass feed rate (M), spot size of the energy source (dspot ), and hatch spacing (H). (With permission from ASM International)

of a circular heat source (in cm) at the substrate. Using the suggested units, Ed is expressed in J/cm2 and describes the energy projected onto the substrate during movement over a unit of time. The total energy contribution for an entire layer (EL ) may also be determined based on: EL = βP t

.

where t is the total time that the energy source is activated during creation of the layer. If time is expressed in seconds, EL is measured in Joules. The primary process parameters are used in combination to establish important characteristics of the deposit, which is illustrated in Fig. 4.9 for a laser-based DED process for two adjacent deposits or two tracks produced using constant power (P1 = P2 ), velocity, and spot size with a spacing that provides sufficient overlap. These characteristics include penetration depth into the substrate (Dsub ), width of the deposit (Wdep ), and height of the deposit (Hdep ). Also illustrated in the figure is the spot diameter of the energy source (dspot ) and the energy distribution of the source, shown as a “top hat” distribution in the figure. The fundamental parameters are selected and used to establish deposition characteristics deemed adequate for the process. The parameters that define the energy density, along with mass feed rate (M) of the feedstock (reported in g/s) directly influence the amount and geometry of the material deposited, as well as the depth of melting into the substrate. Typically,

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Fig. 4.9 Schematic of a laser-based DED process showing important characteristics for two adjacent deposits produced using constant power, velocity, and spot size with a spacing that provides sufficient overlap. (With permission from ASM International)

power and spot size are selected to maximize deposition width, while power, mass feed rate, and velocity play an important role in establishing the height of the deposit. These parameters also impact feature definition, with smaller spot sizes and power-increasing feature resolution. Although larger spot sizes and power may be used to increase deposition width and rates, a minimum energy density is always required for sufficient melting of the substrate, which limits the maximum spot size based on the available energy of the source. Figure 4.10 [3] depicts the influence of width and thickness of layer deposits produced using laser-based DED. Single track deposits were produced using a direct diode laser with gas atomized (GA) and plasma rotary electrode process (PREP) Ti6Al-4V alloy powder being deposited at a constant velocity of 5 mm/sec using a coaxial feeding nozzle. The results of these experiments conducted using a laser power of 800 and 1000 watts show the effect of changing powder flow rate on deposition width and layer thickness for the two powders. These results demonstrate the strong influence of mass flow rate on increasing layer thickness; whereas, minor changes in deposition width are observed at increasing powder flow rates. During multiple depositions, the correct selection of hatch spacing is crucial for achieving optimal height representing multiple depositions and ensuring adequate melting into the substrate and prior deposit. These conditions are also illustrated in Fig. 4.9. The practical height of the combined depositions or the layer is shown as the Hlayer and is based on the minimum deposition height in Region

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Fig. 4.10 Influence of power and mass flow rate of powder on deposition width and height for a laser-based DED process for alloy R56400 (Ti-6Al-4V) [2]

A representing the overlap, whereas Region B in the figure represents sufficient melting or remelting into the substrate from the prior deposition. Proper hatch spacing or overlap distance is an important parameter that directly impacts lack of fusion defects at the intersections of adjacent tracks, and an approach developed by Kelly for determining proper hatch spacing has been used successfully and is illustrated in Fig. 4.11 [8]. This method assumes that an optimal hatch spacing provides an adequate overlap of deposition tracks while not applying an excessive number of tracks. The contact angle of the deposit, shown in Fig. 4.11 as α, is dependent upon the material being deposited, and optimal hatch spacing for a given set of material and parameters may be identified through experimentation designed to equal the cross-sectional area of the overlap in penetration and the area between the deposited tracks, shown as areas A1 and A2 in Fig. 4.11. Results of single-track experiments utilizing a laser-based DED process with Ti-6Al-4V alloy to measure deposition width based on mass flow rate of powder are shown in Fig. 4.12. As seen in the figure, increasing mass flow rate significantly increased deposition height with little impact on width. Calculated hatch spacings for the measured

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Fig. 4.11 Establishing proper hatch spacing [8]. (With permission from ARL Penn State)

Fig. 4.12 Results of experiments using laser-based DED for measured deposition heights and widths and calculated hatch spacing based on these values [8]. (With permission from ARL Penn State)

heights and widths of the deposits are also shown in Fig. 4.12. These calculations were derived using simple geometric considerations assuming an elliptical shape of the deposit based on contact angle, height, and width to equalize areas A1 and A2. It should also be noted that the primary parameters discussed earlier, through the corresponding local energy density also influence other aspects of the process. Higher local energy densities generally result in deeper penetration and melting of the substrate and slower solidification and cooling rates of the deposited material, while higher layer energies produce higher substrate temperatures between layers. The dwell time (time when the heat source is off) between deposition layers also strongly influences the substrate temperature during the build process.

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4.2.6 Materials The vast majority of metal systems and alloy materials are being used for directed energy deposition. This includes a broad range of ferrous-based alloys, nickel-based alloys, titanium alloys, aluminum alloys, and cobalt-chromium alloys (Table 4.1). One important consideration for DED processing of a material is it resistance to cracking during or immediately after solidification. For many existing alloys, the “weldability” of the material is a desirable manufacturing characteristic that has been evaluated and defined, and because welding is in many ways similar to DED, the weldability of an alloy is usually a good indication of whether the material may be easily processed using DED.

Table 4.1 Some commonly used alloys for directed energy deposition for various applications Alloy system Steels

Examples of applicable alloysa T20813 (H13) ® CPM 9V

Stainless steels

S30403 (304L), S30880 (308L), S31603 (316L) S42000 (420), S43100 (431) S17400 (17-4 PH)

Nickel

N06625 (IN625) N07718 (IN718)

Titanium

R56400 (Ti-6Al-4V) R50400 (Titanium Grad 2 or Commercially Pure)

Aluminum

A92319 (2319) A94047 (4047) Al-Si10Mg

Cobalt-chromium

R30006 (Cobalt Alloy 6)

General characteristics and potential applications Tool steel for repair and building 3D components Tool steel for repair Austenitic stainless steels for 3D components Martensitic stainless steels for repair Precipitation strengthened alloys for repair or creation of 3D components Both alloys provide good high temperature and corrosion resistance and are applicable to the repair and production of 3D components High specific strength and corrosion resistance for repair and 3D components and structures Good corrosion resistance for repair and 3D components All of these alloys provide moderate strength and are applicable to the repair and production of 3D components and structures Moderate strength, high wear resistance, and good corrosion resistance for deposition on surfaces and production of 3D components

a When possible, UNS designations are utilized with their trade, grade, or common name in parentheses

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4.2.7 Microstructure and Material Properties The DED process utilizes a heat source to melt, deposit, and solidify feedstock using predetermined paths in a layer-by-layer manner to build two or three-dimensional shapes. Hence, the response of the materials, the feedstock, and the substrate begins with solidification and is followed by solid-state transformations that occur during successive heating and cooling cycles associated with the layers. Solidification and solid-state transformations at a position within the build geometry are governed by the thermal cycles representing these positions, and these thermal cycles are dictated by the local energy density, the paths used for deposition of each layer, the dwell time between layers, the thermophysical properties and mass of the substrate, and build geometry. The microstructures obtained through DED can be predicted using the two important parameters, thermal gradient G and cooling rate R which are heavily influenced by the process parameters. Micrographs representing the N06625 (IN625) deposits for the four different energy densities are shown in Fig. 4.13. All of the micrographs display a columnar dendritic solidification morphology for alloy N06625 (IN625) produced under these conditions; however, measurement of secondary dendrite arm spacing indicated changes based on energy density, with an increase in arm spacing with higher energy densities. Although solidification begins the process of establishing microstructure of the alloy during the DED process, the repetitive heating and cooling cycles that are present during the build process also play an important role in solid-state transformations that are responsible for the evolution of the initial microstructure. These solid-state reactions will be dependent upon the alloy being processed. As seen in the thermal cycles at a position within the build will exhibit the highest peak temperatures during the deposition of that material, and as subsequent layers are produced, the peak temperature at this position will decrease due to the source of energy being further from that point. This is illustrated in Fig. 4.20, which depicts measured temperatures in the first layer during laser-based DED with R56400 (Ti6Al-4V) alloy powder and substrate to produce a single-track, five-layer build, as shown in Fig. 4.14. Also shown in the figure is the solidus and liquidus temperatures defining melting and solidification. Figure 4.15 shows macrographs of the five successive layers for the R56400 (Ti-6Al-4V) alloy and corresponding temperature cycles of Fig. 4.14. The position within the first layer representing the thermal cycle is also indicated on the micrographs as an open circle. The large columnar grains exhibited within the deposits after the first layer are due to directional solidification in the favorable crystallographic growth direction, which is driven by heat flow towards the substrate. The favorable growth direction is maintained in subsequent layers due to epitaxial growth from the previous layer and results in a continuation of the columnar growth through subsequent layers. This phenomenon is also seen in deposition of nickelbased alloys.

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Fig. 4.13 Micrographs representing N06625 (IN625) alloy produced using a laser-based DED process and four energy densities to produce one track [11]. (With permission from Elsevier)

Micrographs of the material representing the first layer after production of five successive layers for the R56400 (Ti-6Al-4V) alloy and a schematic showing the probable phases that have been formed are shown in Fig. 4.16. This shows the effect of changes in microstructure and material phases as subsequent layers are deposited. The above examples are used to illustrate how microstructures are formed influenced by the process. For more details and the science that impacts this refer to Chaps. 15, 16, and 17. The mechanical properties of parts will be directly influenced by the chosen processing parameters and the resulting microstructure. Table 4.2 shows the properties of various alloys fabricated by DED process on an Optomec LENS machine as reported by [6], and compared to wrought properties.

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Fig. 4.14 Measured temperatures during laser-based DED of R56400 (Ti-6Al-4V) alloy during production of a single-track, five-layer build [11]. (With permission from Elsevier)

4.2.8 Maintaining Process Consistency Although proper selection of parameters is critical in establishing a suitable DED process, potential variability of processing conditions may also influence deposition characteristics and, ultimately, quality of the build. Most of the parameters are set by digital control and, under normal conditions, provide very little variability during processing. This includes power, velocity, and hatch spacing. However, three factors that may vary during prolonged processing should be addressed and involves the mass flow rate of feed material, distribution of the feed material in the energy interaction area, and diameter of the spot at the surface of the build. The mass flow rate of the feedstock may be set by the control system for the process or manually at the feeding system. As for any feedstock and feeding system, measurement of flow rate for a particular powder or wire may be easily performed by assessing the mass or weight of the material through the system over a defined period of time, and the results may be used to establish “calibration curves” for mass flow rate for a particular material and setting on the feeding unit. Stability of mass flow rate for powder as a feedstock is challenging. Variability of powder during processing may be caused by changes in the surface characteristics of the powder over time and ability of the feeding system to provide consistent and uniform flow during processing. Some powder may be sensitive to reactions of the powder surface with the environment during storage or within the powder reservoir over prolonged processing times. An example of this situation is the potential hydration reaction of aluminum alloys with moisture. Not only does this reaction change the mass of the powder material but it also affects the interaction of particles, which may impact flowability and ultimately flow rates. Hence, not only is it important to develop

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Fig. 4.15 Macrographs of five successive layers for the R56400 (Ti-6Al-4V) alloy with the position at the first layer representing the composite temperature cycle being indicated on the micrographs as an open circle [11]. (With permission from Elsevier)

“calibration curves” for a particular material but to also periodically assess the flow rate of a material if it has been stored for extended time or if there is a change in the material supplier. Stable interaction of the energy source with the feedstock requires constancy of the mass flow rate, as well as stable and uniform distribution of the feedstock within the interaction area. Using powder as feedstock, placement and uniformity of the distribution of the powder leaving the feeding nozzle or nozzles requires periodic maintenance to ensure uninterrupted feeding and proper alignment between the laser beam and convergence of the powder stream. This is especially important for achieving minimal levels of lack of fusion defects due to poor overlap, as well

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Fig. 4.16 Micrographs of material representing the first layer after production of five successive layers for R56400 (Ti-6Al-4V) alloy and a schematic showing the probable phases that have been formed [11]. (With permission from Elsevier)

as for producing high feature quality and good surface finish. Figure 4.17 shows a photograph of powder feeding within a laser-based DED system employing four feeding nozzles and a schematic depicting beam and powder characteristics in the energy interaction area. The schematic of the powder stream shown in the figure was created from specialized photographic imaging of actual powder feeding for this system. Alignment of the feeding system and the energy source may be performed

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Table 4.2 Some commonly used alloys tensile properties via laser-based DED process [6]. ©Springer Properties Process 316 SS 304 SS PH13-8Mo H13 Ti-6Al-4V IN 600 IN 625 IN 718

YTS, MPa ® LENS 434 324 634 1462 931 428 614 1117

WRT 234 276 621 1448 855 – 400 1158

UTS, MPa ® LENS 758 655 1324 1703 965 731 931 1400

WRT 586 – 931 1724 931 – 834 1379

Elongation, % ® LENS WRT 45–70 50 70 55 13 14 3 12 16 10 40 – 38 37 16 20

Fig. 4.17 Photograph of powder feeding within a laser-based DED system employing four feeding nozzles and a schematic depicting beam and powder characteristics in the energy interaction area. (Photograph and schematic courtesy of CIMP-3D, Penn State. With permission from ARL Penn State)

by producing an alignment target on the substrate that requires motion in the X and Y coordinates, followed by close inspection of the position of the deposit with respect to the energy interaction. Periodic inspection, alignment, and cleaning of nozzles to maintain consistent and uniform feeding are essential for retaining uniformity and reliability of the deposition during processing with powder as the feedstock. Another aspect of the DED process that may hinder consistency is the variability of spot size during processing of components that are relatively tall. As described earlier, the energy source is focused and projected onto the substrate, and if the position of the focusing optics relative to the existing position of the substrate is altered sufficiently, the spot size will change and vary the energy density. This may be caused by variability of the accumulated deposition height over numerous build layers. It is not unusual for the actual build height to be smaller than the planned

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height based on numerical control in the Z orientation. As the build progresses, variability of the focal position may cause inconsistency in the degree of penetration into the substrate, as well as width and position of the current deposit. The use of height sensing to accurately determine the position of the current layer in Z has been used to minimize this condition. Another source of variability in deposition height is due to changes in the fluidity of the molten material during processing due to heat accumulation. This results in changes in the height of the deposit along its length. A closed-loop control of power from the source based on continuous measurements of the diameter of the molten pool has alleviated this condition when this type of control is available. Periodic measurements of build height and calibration of the build plan may be necessary when producing components having many build layers and a large dimension in the Z orientation. Common defects observed in DED process are: Porosity and lack of fusion – Similar to powder bed fusion, porosity defects can be produced by three main mechanisms. If operating at high-energy densities, the process may operate in keyhole mode melting, and the keyholes formed can become unstable and collapse, leaving spherical voids inside the deposit that consist of entrapped gases. Gas Atomized powders can have entrapped gases in the powder particles which can result in microscopic pores in the part. Shielding gases or alloy vapors can also get trapped in the molten pool during solidification [4]. Lack of fusion defects can be caused by inadequate penetration of the molten pool of an upper layer into either the substrate or the previously deposited layer. Cracks and delamination – Solidification cracks similar to those seen in welding, are formed by tensile stresses from shrinkage during solidification and the thermal effects. If the tensile stresses exceeds the strength of the material, cracking shows at the grain boundaries. Delamination is the separation of two consecutive layers which is caused by the residual stresses at the layer interfaces exceeding the yield strength of the material. Residual stresses – Deposition of hot liquid on a cooler substrate or prior deposited layers results in high-temperature gradients, thermal strain, and residual stresses. The residual stresses lead to distortions of the part, potential delamination, warping and dimensional issues. Chemical Compositional Changes – The high temperatures experienced in the process may lead to vaporization of some of the alloying elements. This can be a problem when producing high-quality components since the changes can affect the microstructure and mechanical properties.

4.2.9 Advantages and Limitations The laser-based DED process provides several advantages over the powder bed fusion systems. The ability to deposit on existing surfaces makes the process suitable for repair applications where the material can be deposited to build up worn or

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broken surfaces. Additionally, the process can be executed using multiple axes allowing for deposition of non-planar layers, thus eliminating the need for support structures. Using multiple powder feeders allows for creating functionally graded materials and alloys by compositional change of the powder. The process allows for deposition of larger layer thickness and hence higher deposition rates can be achieved using higher power lasers and powder feed rates. The process can also be made to operate using shielding gases instead of using a completely enclosed environmentally enclosed chamber which allows the process to be used in hybrid DED and machining systems. The main limitations stem from some of the advantages. Higher deposition rates limit the feature size that can be created and hence always require post-machining operations to achieve dimensional and tolerance requirements. The powder capture efficiency of the process can be low leading to high powder loss.

4.2.10 Examples and Applications Table 4.3 shows several examples of parts produced by the DED process.

4.3 Wire Feed-Based DED Instead of using powder as the feedstock material, an alternative approach is the use of feedstock in the form of wire. In the case of using powder feed DED, there is a significant amount of powder that does not end up in the melt pool. Using a wire avoids this issue. Other advantages to using wire instead of powder, include cheaper cost of feedstock, and unlike powders handling of feedstock is not needed. Additionally, the use of wire avoids many of the challenges associated with powders such as control of particle size or distribution, which affect process performance. The wire-based DED processes draw heavily on their roots in the welding industry, and theoretically, all forms of welding processes can be used to create the additive layers to make a 3D part. The energy sources used can range from laser, electron beam, Plasma, and electric arc. These processes share a lot of common features. The energy efficiency of the energy sources can vary significantly. Laser has a poor energy efficiency (2–5%), electron beam has slightly higher efficiency (15–20%), but the process must be executed in a high vacuum environment. The efficiencies of arc welding process can be as high as 90% and the equipment is considerably cheaper [5]. The arc welding-based processes are also termed as WAAM (Wire and Arc Additive Manufacturing). These processes are capable of high metal deposition rates and high efficiencies, and hence suitable for large structural components especially in aerospace and defense applications. Metal deposition rates up to 9 kg/h have been reported using

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Table 4.3 Examples of parts produced by DED Application/industry Buildup on existing surface

https://engineeringproductdesign.com/wp-content/uploads/ direct-energy-deposition.jpg. With permission Trumpf Group Multi-axis fabrication with no support structure IN 718

? https://www.rpm-innovations.com/uploads/1/2/0/6/ 120630585/718-case_orig.png. With permission RPM Innovations, Inc. 6 diameter (150 mm) Continuous Dual Wall Fabrication 0.065 (1.5 mm) wall thickness Inconel 625

https://www.rpm-innovations.com/uploads/1/2/0/6/ 120630585/625-dual-wall-duct-2_orig.jpg. With permission from RPM Innovations

high-energy sources such as 10 kW lasers, and gross deposition rates range from 7 to 25 lbs. (3.18–11.34 kg) of metal per hour, depending upon the selected material and part features with 40 KW ebeam systems. While the process offers the potential for very high deposition rates and fast build times for large structures this comes at the cost of certain tradeoffs. The high rates of deposition limit the ability to create

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Fig. 4.18 Types of wire feed-based DED processes

small feature sizes. The high deposition rates result in larger melt pools which are more difficult to control when depositing on positions that are not flat. Large melt pools also affect the size and resolution of features that can be printed. The high heat input also results in large amounts of residual stresses in the part and must be carefully managed to ensure a successful build. The process may need to be stopped to add additional heating processes to reduce the residual stress and prevent parts from large distortions and cracking during the build. Large layer thicknesses lead to very rough surfaces. At best, these processes are near-net shape processes that require post-process machining to address the limitations. Due to the roughness of the surface and net shape of the material, these processes must be followed with machining to achieve the dimensional size and surface roughness to make the part useable. Wire-based DED processes can be classified based on the type of energy source used, as seen in Fig. 4.18. All of these different energy sources have been utilized in commercially available AM processes. Structurally, all processes in this category use a conceptually similar architecture as shown in Figs. 4.19 and 4.20. The end effector, the welding torch or laser/ebeam welding gun, and wire delivery nozzle are mounted at the end of a multi-axis robot or a gantry-type system. Additional positioning table with multiple positioning axes, which support the platform for the part to be built, can be used. The power source is the primary distinguishing component. It provides the necessary power to generate the heat to liquefy the metal at the end of the torch so that the metal bead required to build the part can be deposited. Depending on the power source there may be different requirements placed on the system, and these are discussed later in the sections on each of the different sources of power. A wire feeder supplies the welding gun with the wire typically stored in a spool. Shielding gases are delivered through the welding gun. An insulation disc is required between the torch or any mechanical breakaway and the tool mounting plate on the robot. The mechanical breakaways provide for the welding gun to disconnect from the robot in the event of a collision, to protect it from damage. The power supply for the operation of the process is required for the energy source. A separate robot controller

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Fig. 4.19 Photograph of a robot-based wire arc-based DED process [9]. (Open source)

Fig. 4.20 Photograph of a processing chamber for an electron-beam-based DED system capable of relatively large build volumes. (With permission from Sciaky Inc.)

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Fig. 4.21 Schematic of the Ebeam Wire DED process. (With permission from Sciacky)

is integrated with the power supply, wire feeder, energy source, positioning table, and feedback devices that may be included for process monitoring.

4.3.1 Electron Beam-Based Wire DED 4.3.1.1

Process Overview

A focused electron beam (similar in principle to the ebeam PBF process) is used to provide the energy source for the process. Unlike the PBF process, the electron beam is not positioned by deflection, but rather by mounting the ebeam gun on an articulating arm that can be positioned in xyz space through the use of positioning devices such as linear and rotational axis under CNC control, as seen in Fig. 4.20. The schematic of the process is shown in Fig. 4.21. High-energy electron beams are commonly used for the DED process to facilitate higher deposition rates. It is not uncommon for electron beam-based DED systems to operate at high-power output, between 15 and 50 KW. The complete process is performed in vacuum; hence the entire chamber must be sealed during the process. Electron beam DED uses pumps to evacuate the air from the processing chamber, thus producing a vacuum environment that typically ranges between 1.33 × 10−2 mbar and 1.33 × 10−3 mbar (10−3 –10−4 Torr). These low pressures are enough to greatly minimize the presence of residual gas species within the chamber. The volume of the processing chambers for electron beam-based DED may be as small as 0.8 m3 and up to several m3 ; however, these chambers must be built to withstand the hydrostatic forces present due to the differential pressures between the outside and inside environments. The degree of vacuum required, and the size of the chamber influences the time required to pump down to vacuum levels; however, the contemporary use of high pumping

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rate systems enables the vacuum environment to be achieved relatively quickly. Shown in Fig. 4.20 is a photograph of a processing chamber for an electron beambased DED system capable of relatively large build volumes. This system provides five axes of motion and can achieve an operating vacuum of 10−3 mbar (10−4 Torr) in approximately 20 min of pumping. The use of ebeam also allows for large standoff distances from the work piece. The wire feeding system is also contained within the chamber, and delivers the wire to the melt pool. In case of large diameter wire, additional straightening of the wire may be required. The machines can be equipped with multiple wire feed nozzles utilized with a single EB gun. This allows for higher deposition rates, as well as the potential to independently feed different metal alloys to create super alloys and graded material parts, leading to potentially higher material performances.

4.3.1.2

Process Dynamics

The electron beam wire DED process behaves very similar to electron beam welding in a lot of respects, and has similarities to the ebeam-based powder bed process. The power available for the process depends on the physical interaction of the electron with the substrate and melt pool. Electrons striking the surface are scattered elastically and inelastically. The inelastic scattering is accompanied by energy loss. Not all the beam electrons transfer their kinetic energy to the work piece. Some percentage of electrons do not contribute to the energy transfer and are termed backscattering loses. The efficiency of power transfer depends on these losses and can vary with the material and beam power. The backscatter of the electrons has also been used as an image acquisition device for monitoring the process.

4.3.1.3

Process Parameters

Establishing the process parameters of wire-based ebeam process requires understanding the fundamental relations between the variables in a very complex physical process. Maintaining a stable melt pool is critical to the process, and similar to the other ebeam processes controlling the melt pool dimensions and melt pool characteristics is critical for controlling the process. The approach for understanding the process variables is similar to the ebeam PBF. The energy density, and wire feed rate along with other wire-related parameters such as orientation and height with respect to the workpiece are important process parameters. During solidification, the weld beads are formed. Knowing the behavior of single bead profiles opens the capability for finding an optimum overlapping distance, which is an important input for the path planning for a complete layer. The solidification process leads to the microstructural evolution and leads to the mechanical properties of the work part. The solidification process also creates the residual stresses within the part. Since the process parameters for all the wire-based arc process are quite similar, they are discussed together in Sect. 4.3.5.

4.3 Wire Feed-Based DED

4.3.1.4

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Materials

The ebeam process by Sciaky uses a wide range of materials such as Titanium and Titanium alloys, Inconel 718, 625, Tantalum, Tungsten, Niobium, Stainless Steels (300 series), 2319, 4043 Aluminum, 4340 Steel, Zircalloy, 70-30 Copper Nickel, and 70-30 Nickel Copper. The process is especially well suited for refractory materials. The feedstock is in the form of wire, which is considerably cheaper and easier to manage compared to powder.

4.3.2 Laser-Based Wire DED The laser-based wire DED systems are very similar in design to the ebeam-based systems, except that the energy source used is a laser and process does not require execution in a vacuum. The fundamental basics of the laser, process parameters, and materials are the same as discussed for other processes. Often high-power laser 10 KW or more have been used to achieve higher deposition rates.

4.3.3 Wire Arc AM The wire arc processes use popular welding techniques such as Gas metal arc welding (GMAW) known as the MIG (metal inert gas) welding process, gas TIG (Tungsten Inert Gas) arc welding (GTAW), and Plasma Arc Welding (PAW). The process has been demonstrated for use in AM since the early 90s (Baker R.: “Method of making decorative articles”; US patent no. 15333001925.) although the first patents on the process were filed as early as 1925 (Acheson R.: “Automatic welding apparatus for weld build-up and method of achieving weld build-up”; US patent no. 49527691990). Wire Arc AM (WAAM) is attractive since the hardware used is commercially available off-the-shelf welding equipment, such as power sources, torches, and wire feed systems. Motion systems are typically provided by standard multi-axis robots and gantry systems equipped with CNC control. The three main classes of welding process are illustrated in Fig. 4.22. In GMAW, the consumable metal wire is used as an electrode to form the electric arc between the wire and the grounded workpiece. A shielding gas is supplied through the wire feed nozzle to provide the inert gas atmosphere necessary to prevent the formation of the metal oxides. The deposition path and parameters are controlled. The GTAW process differs primarily in how the electrode is used. A nonconsumable tungsten electrode is used to provide the electric arc. A separate wire material is fed into the melt pool using the wire feed mechanism. The weld is

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4 Metal Additive Manufacturing Processes – Directed Energy Deposition Processes Plasma gas

Shielding gas

Electrode wire Tungsten electrode

Nozzle

DC Power

Arc

Shielding gas

DC Power Weld pool Nozzle

Workpiece

Plasma arc

Weld pool

(a) Tungsten electrode

Workpiece

(c) Nozzle Contact tube Shielding gas

Wire

Arc

(b) Fig. 4.22 Schematic of the arc-based process [5]. (a) GMAW, (b) GTAW, and (c) Plasma Arc. (Copyright Springer)

shielded from the atmosphere using an inert gas shield. Typically, Argon and Helium are used, depending on the materials being processed. Plasma arc welding also uses a tungsten electrode to generate the arc. The positioning of the electrode is such that the plasma arc formed is separated from the shielding gas envelope using a unique torch design. The plasma is forced through a nozzle that constricts the arc, and different operating modes can be created by varying the bore diameter and plasma gas flow rates. The plasma arc process is generally more precise than GTAW.

4.3.4 Resistance Heating-Based Wire Process A recent development in wire-based DED process is the use of resistance heating to melt the wire and create the melt pool and deposition bead. An electrical current is applied to the wire. When the current flows through the wire heat energy is generated

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Fig. 4.23 Schematic showing use of resistance heating for melting. (https://doi.org/10.1016/ j.mattod.2018.07.001. Under Creative Commons License)

in the wire melting the wire and creating a molten drop of material (Fig. 4.23). The amount of heat generated depends on the resistance of the wire, the amount of current and the time for which the current flows (H = I2 Rt). This process is commercialized by Digital Alloys and termed Joule Printing. Using thin diameter wires (0.9 mm), higher resolution can be achieved with this process.

4.3.5 Process Parameters for Wire DED Systems The process performance in terms of mechanical properties (strength, hardness, residual stresses) microstructure (grain size, growth orientation, etc.) along with dimensions, surface finish, and quality are strongly influenced by the process parameters. Input parameters for the process include beam power, beam pattern, wire feeding direction and angle, wire feed rate, desired layer thickness, source power, and welding speed. The input parameters have been shown to have coupled interactions that currently require trial and error, and expert human experience, to find desirable combinations.

4.3.5.1

Wire Feeding Angle and Direction

The wire feed orientation is shown by α in Fig. 4.24, along with the position of the feed with respect to the melt pool influences the material transfer and the quality of the deposit. This is often dependent on the material and power of the energy source. Wire is normally fed into the front edge of the laser interaction area, but this limits

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Fig. 4.24 Wire feed angle and feed directions [5]. (©Springer)

the full range of motion for complex paths since the deposition head must always be positioned to place the wire at the leading edge of beam motion.

4.3.5.2

Wire Feed Rate and Weld Speed

The wire feed rate and weld speed are generally limited by the available power and also influence the size of the melt pool and height of the deposit. When the wire feed rate is set at high levels, the energy source may not be able to fully melt the wire, while exposing the melt pool to excessive power may result in evaporation of some of the alloys. The energy per unit length of track (EL in J/mm) is the combined effect of the laser/ebeam/arc power (P) in Watts and welding speed V in mm/sec, and defined as EL = P/V. The deposited volume per unit length Dvol is determined by the welding speed V (mm/sec) and wire feed rate Wfr (mm/sec), and the cross-sectional area (A) of the wire. Dvol = A∗ Wf r /V

.

The key to successful deposition is the creation of continuous track with acceptable dimensions. Depending on the combination of process parameters, three different process characteristics have been observed (i) wire dripping (ii) smooth wire transfer, and (iii) wire stubbing [1]. Figure 4.25 shows an example of these. Tracks with smooth deposition were observed when the wire tip melted at the point or close to the point of intersection with melt pool. At very low wire feed rates, the wire tip interacts too long with the laser beam such that the absorbed energy melts the wire tip before interacting with the melt pool. This produces the effect of intermittent dripping of the molten wire. When the wire feed is high for a fixed combination of speed and laser power, the interaction of the wire with the laser was short and the wire entered the melt pool in nearly solid form resulting in the collision of the wire with the solid substrate at the base of the melt pool. This is called wire stubbing. A process map created by varying the conditions can

4.3 Wire Feed-Based DED

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(a)

Wire dripping

(b)

Smooth wire deposition

(c)

Wire stubbing

Fig. 4.25 Deposits of Inconel 625 wire [1]. (©Springer)

Fig. 4.26 Different Tool Path Strategies. (With permission from WAAM Cranfield University)

be created to establish the boundaries of the processing parameters. This will be different for different materials, and hence needs to be established for each alloy. Different path-planning strategies can be used to build the complete path. Figure 4.26 shows examples of different path strategies that may be employed in the building of a part. Path planning can have a significant impact on final part properties and mechanical properties.

4.3.6 Materials, Microstructure, and Properties Any metallic material that can be welded and available in wire form can be used. Similar to the other AM process based on melting, for a given material, the

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Fig. 4.27 (a) Macrostructure showing epitaxial grains (b) microstructure from the top layer of the build region showing a fine α  morphology; (c) typical microstructure of the majority of the wall between the bands showing a coarser Widmanstätten structure; and (d) the microstructure between two neighboring bands showing a transition from a coarse to a fine Widmanstätten structure [13]. (Copyright Springer)

solidification morphology of the deposited material mainly depends on the velocity of solidification (R) and the temperature gradient (G). In a study by [13], the macrostructure, and mechanical properties of a Ti6Al-4V alloy after WAAM deposition were investigated. As seen in Fig. 4.27, the microstructure of the arc-deposited Ti-6Al-4V was characterized by epitaxial growth of large columnar prior-β grains up through the deposited layers. Macroscopic banding, corresponding to each layer height, was also observed in the as-deposited samples, but was not seen in the top five layers. These banded structures have been formed as a result of the heat-affected zone or repeated thermal cycle that develops as each new layer is deposited. Tensile tests on the specimens showed significant effect of sample orientation [13]. The average yield strength (YS), ultimate tensile strength (UTS), and strain to failure from the baseline tests were 950 MPa, 1033 MPa, and 11.7%, respectively. In comparison, the samples tested from the vertical build direction exhibited a lower strength, with a mean yield strength of 803 MPa and UTS of 918 MPa. The tensile strength properties were, therefore, only moderately anisotropic. However, greater asymmetry was seen in the ductility data, which were much worse when measured in the horizontal direction.

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Fig. 4.28 Distortion caused by high deposition rates in Electron beam Wire Process. (With permission from Sciaky Inc. https://d2n4wb9orp1vta. cloudfront.net/cms/brand/ MMS/2019-MMS/MMS0419-AdditiveInsights-1.jpg; width=550;quality=60)

4.3.7 Advantages and Limitations These processes are capable of depositing large amounts of material rapidly. They support the use of large molten melt pools, which often create problems. Surface tension can create rounded deposits resulting in loss of deposition accuracy, high surface roughness, and sagging due to gravity. However, since the parts are usually post-machined these issues can be mitigated by using the process to produce nearnet shapes followed by subsequent machining. A metric often used to evaluate the efficiency of the process when compared to machining is the “buy to fly” ratio. The amount of material deposited compared to the bulk material required for machining. These processes tend to be a lot more efficient in terms of material use. The process is also suitable for repair and buildup material on damaged surfaces. Multiple materials can be incorporated using multiple wire feeds. The processes also introduce large amounts of thermal stresses and creative approaches to handle the buildup of residual stress during the build process must be applied. These can involve building on both sides of the build plate and incorporating the build plate into the part. Figure 4.28 shows an example of a part made with ebeam wire process and resulting distortion due to residual stresses. The effect of residual stresses reduced by building on both sides of the plate is shown in Fig. 4.29.

4.3.8 Examples Table 4.4 shows examples of parts manufactured by the DED process.

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Fig. 4.29 Reducing the effect of Residual stress by building on both sides of build plate. (With permission from Sciaky Inc. https:// d2n4wb9orp1vta.cloudfront. net/cms/brand/MMS/2019MMS/mms-0419additiveinsights-2-.jpg; width=860)

4.4 Questions and Discussions 1. What are the major categories and classifications of DED processes? 2. Describe the operation of powder-based DED systems. 3. Survey the current manufacturers of powder-based laser DED systems, and discuss the range of capabilities commercially available. 4. Identify the main process parameters that might be encountered in a powderbased laser DED process. 5. What are some of the main defects in powder-based DED processes, and what is their relationship to process parameters? 6. Compare the powder-based laser DED processes to a powder bed fusion laser process, in terms of speed, capability, resolution and feature size, support generation, and removal. 7. How does Sicaky’s wire-based ebeam DED process differ from the powderbased DED process? 8. How do the arc welding-based wire DED processes differ from the wire-based ebeam process? 9. Residual stresses can play an important role in DED processes. Discuss various ways in which the effects of residual stresses can be mitigated and addressed. 10. Survey the current manufacturers of arc-based wire DED processes, and discuss the range of commercially available capabilities.

References

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Table 4.4 Examples of parts Examples Plasma arc titanium parts, by Norsk Titanium, followed by subsequent machining

With permission from Norsck Titanium Ebeam wire deposited part and subsequently machined, Sciaky.

With permission from Sciaky Inc.

https://additive-manufacturing-report.com/wp-content/ uploads/2019/10/WAAM.png. With permission WAAM from Cranfield University

http://fitnik.tech/public/img/technologies/waam3.jpg. With permission from WAAM Cranfield University

References 1. Abioye TE, Folkes J, Clare AT (2013) A parametric study of inconel 625 wire laser deposition. J Mater Process Technol 213(12):2145–2151. https://doi.org/10.1016/ j.jmatprotec.2013.06.007 2. Ahsan MN, Pinkerton AJ (2011) An analytical–numerical model of laser direct metal deposition track and microstructure formation. Model Simul Mater Sci Eng 19(5):55003. https://doi.org/10.1088/0965-0393/19/5/055003 3. Ahsan MN, Pinkerton AJ, Moat RJ, Shackleton J (2011) A comparative study of laser direct metal deposition characteristics using gas and plasma-atomized Ti–6Al–4V powders. Mater Sci Eng A 528(25):7648–7657. https://doi.org/10.1016/j.msea.2011.06.074

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4. DebRoy T, Wei HL, Zuback JS, Mukherjee T, Elmer JW, Milewski JO, Beese AM, WilsonHeid A, De A, Zhang W (2018) Additive manufacturing of metallic components – process, structure and properties. Prog Mater Sci. https://doi.org/10.1016/j.pmatsci.2017.10.001 5. Ding D, Pan Z, Cuiuri D, Li H (2015) Wire-feed additive manufacturing of metal components: technologies, developments and future interests. Int J Adv Manuf Technol 81(1–4):465–481. https://doi.org/10.1007/s00170-015-7077-3 6. Griffith ML, Ensz MT, Puskar JD, Robino CV, Brooks JA, Philliber JA, Smugeresky JE, Hofmeister WH (2000) Understanding the microstructure and properties of components fabricated by laser engineered net shaping (LENS). MRS Proc 625:9. https://doi.org/10.1557/ PROC-625-9 7. Hunter BV, Leong KH (1997) Improving fiber-optic laser beam delivery by incorporating GRADIUM optics. Appl Opt 36(13):2763–2769. https://doi.org/10.1364/AO.36.002763 8. Kelly S (2011) Development of repair procedures for Ti-6Al-4V alloy 9. Köhler M, Fiebig S, Hensel J, Dilger K (2019) Wire and arc additive manufacturing of aluminum components. Metals. https://doi.org/10.3390/met9050608 10. Lia F, Park J, Tressler J, Martukanitz R (2017) Partitioning of laser energy during directed energy deposition. Addit Manuf 18:31–39. https://doi.org/10.1016/j.addma.2017.08.012 11. Lia F, Park JZ, Keist JS, Joshi S, Martukanitz RP (2018) Thermal and microstructural analysis of laser-based directed energy deposition for Ti-6Al-4V and inconel 625 deposits. Mater Sci Eng A 717:1–10. https://doi.org/10.1016/j.msea.2018.01.060 12. Martukanitz RP, Melnychuk RM, Stefanski MS, Copley SM (2004) Dynamic absorption of a powder layer. In: ICALEO 2004 – 23rd international congress on applications of laser and electro-optics, congress proceedings. https://doi.org/10.2351/1.5060217 13. Wang F, Williams S, Colegrove P, Antonysamy AA (2013) Microstructure and mechanical properties of wire and arc additive manufactured Ti-6Al-4V. Metall Mater Trans A 44(2):968– 977. https://doi.org/10.1007/s11661-012-1444-6

Chapter 5

Metal Additive Manufacturing Processes – Jetting- and Extrusion-Based Processes

5.1 Binder Jetting 5.1.1 Brief History The binder jetting process traces its roots back to the patent by MIT professors Dr. Emanuel Schas and Dr. Michael Cima in 1993. The technology was also known as inkjet printing and 3D printing. The process shares some similarities with the inkjet printers where a document inkjet printer selectively deposits ink onto a paper, the 3D inkjet printing process deposits the binder (used as ink) onto a layer of powder. Extrude Hone Corporation, obtained an exclusive license for MIT’s technology in 1996. Since then, the company has developed and commercialized metal binder jetting systems, with the first 3D printer, ProMetal RTS-300, delivered to Motorola in 1999 [1] ExOne, was spun off from Extrude Hone in 2005, and has continued the development of this technology. Digital Metal was founded in 2012 and started offering its metal binder-jetting technology as a service in 2013. HP introduced its version of the process in 2018.

5.1.2 Binder Jetting Process Description Binder Jetting is an additive manufacturing process in which a liquid binding agent is selectively deposited to join powder particles (Fig. 5.1). Unlike the full meltingbased processes where heat (laser and ebeam) is applied to provide the energy for melting, the metal binder jetting processes proceed in a two-step manner, where the first step is the creation of the green part followed by the sintering process. The steps involved in a complete binder jetting process are shown in Fig. 5.2. The powder layer is spread across the build platform. The build chamber may be maintained at an elevated temperature to accelerate the development of the binder and to evaporate © Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_5

151

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Fig. 5.1 Binder jetting machine schematics. (https://www.digitalalloys.com/wp-content/uploads/ 2019/07/Binder-Jetting-Schematic-Diagram.png. Image courtesy of Freeman Technology Limited)

the liquids in the binding agent. The binders are selectively deposited by the print heads based on the geometry generated for each slice. The binders are dried to increase the cross-linking and to allow for the spreading of powder for the next layer and prevent sticking onto the rollers used for spreading. Successive lowering of the build platform and deposition of a new powder layer followed by the binder deposition continues until the complete part is built. The final solid object created by the action of the binding agent is termed the “green” part, where the powder particles are merely being held by the gluing action of the binding agent (Fig. 5.3). These parts are often fragile, weak, and brittle. Once all the layers of the part are completed, there may be additional curing involved to improve the green strength of the part before being handled for subsequent processing. The decaking or depowdering process involves extraction of the green part from the powder bed. The green parts are then moved to a sintering oven where the excess binder is burned out and sintering process allows for the metal particle to metal particle bonding to take place. On completion of the sintering process, the part is allowed to cool and further post build finishing operation may be performed. The binder jetting process decouples the printing from the densification process (sintering), hence the high thermal stresses and anisotropic microstructures seen in full meltingbased powder bed fusion processes can be avoided. The binder jet process uses the surrounding powder to support overhanging part structures and does not require support structures for building complex parts. The process can be easily scaled to larger powder beds by using multiple print heads and nozzles.

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Fig. 5.2 Schematic of the process steps in the binder jetting process. (https://www.ifam. fraunhofer.de/en/technologies/metal-binder-jetting-from-prototype-to-series-production/jcr: content/contentPar/sectioncomponent/sectionParsys/textwithinlinedimage/imageComponent1/ image.img.4col.large.jpg/1642775910833/metal-binder-jetting-individual-process-steps.jpg. © Fraunhofer IFAM) Fig. 5.3 Micrograph of cross-section of an HP Metal Jet green part showing metal particles and cured binder (red arrows) [12]. (© Copyright 2022 HP Development Company, L.P (used with permission))

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5.1.3 System Components 5.1.3.1

Powder Spreading Systems

The binder jetting process shares the step of creation of the powder layer with the powder bed fusion process. The standard binder jet processes use a roller for powder spreading and compaction. Innovative approaches have been developed to speed up the process of layer creation to allow for creation of large machines and faster processes. Powder particle size plays an important role in the final density of the parts produced by this process. Ultra-fine particles, can sinter together to form a dense, uniform microstructure that is required for high quality and performance. These ultra-fine powders pose challenges for spreading, since they are prone to clumping, creating dust clouds when spreading rapidly. Depositing droplets of binders at high speeds can result in creating ripples and powder displacement due to the impact of the binder droplet. ExOne has developed special Triple ACT (Advanced Compaction Technology) for dispensing, spreading, and compacting metal powders (Fig. 5.4). It uses an ultrasonic vibratory hopper with a changeable dispensing screen for different powders and releases controlled dose of powder as it moves across the build platform. To enable even spreading of the powder, a knurled roller is used to increase the friction or engagement with the surface of the powder and allows for even and consistent spreading. The density of the powder is increased by compacting with another roller, that provides the right amount of pressure to increase the density while not damaging the layers below. The goal of the powder delivery and spreading systems is to provide a good packing density in the deposited layer. Packing density is defined as the ratio of powder volume to the given volume of powder and air in a predefined volume, according to the equation. Packing Density =

.

Volume of powder Volume of Powder + Volume of air

In this case, the predefined volume is the volume of the deposited layer (area of the layer X thickness).

5.1.3.2

Inkjet Droplet Deposition

Once the powder layer is created the next step is the deposition of the binders, which are the ink for the printing process. The binders are deposited using inkjet printheads, to provide precise placement of the binder droplets. Capillary forces pull the binders into the interstices between the metal particles to produce a uniform binder distribution.

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155

Fig. 5.4 Exone technology for powder spreading and compaction [7]. (With permission Exone)

Several different technologies have been used in the development of print heads, classified as continuous droplet printing and droplet on-demand systems. In continuous inkjet printing (Fig. 5.5), an inkjet is broken into drops using pulses from a piezoelectric crystal. The ink droplets required for printing are charged by an electrode as they break off from the inkjet. The charged droplets pass through an electrostatic field between deflector plates, a combination of speed and charge determines the position of the droplet on the substrate. The uncharged droplets are collected by a catcher and the printer re-circulates the remaining ink. Drop-on-demand (DoD) print heads usually have an array of nozzles, each of which ejects ink drops from the ink chamber only when required. An actuator is used to create the rapid change in the cavity volume and imparts momentum to the

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5 Metal Additive Manufacturing Processes – Jetting- and Extrusion-Based Processes

Fig. 5.5 Continuous inkjet printing [14]. (© IOP Publishing. Reproduced with permission)

ejected drop. Wave propagation in the ink and the geometry of the cavity behind the nozzle have significant effects on the size and frequency of droplet ejection. The ejection forces must overcome the surface tension effects that hold the liquid in place in the chamber behind the nozzle. Before the next drop is ejected the ink chamber must refill and wave propagation stabilizes so as to not impact the formation of the next drop. With DOD, drop volumes are in the range of 1 pico liter - 1 nano liter, with corresponding diameters in the range of 10–100 μm. Drops are ejected on demand at rates up to about 20 kHz [6]. The two most common means to trigger the ejection are thermal-based and piezo electric-based. Thermal droplet on-demand systems rely on thermal energy to generate a vapor bubble, that is used to push the droplet out of the ink chamber (Fig. 5.6a). Also called the “bubble jet”. The chamber is filled with ink, heating element is fired, and leads to the formation of a vapor bubble due to the boiling. The expansion of the bubble pushes the liquid out of the chamber. The heating elements then cool off, collapsing the vapor bubble and ink refills the chamber. The frequency at which the heating and cooling can be cycled controls the droplet deposition rate. The material chosen as the ink can potentially lead to degradation due to the cyclical thermal loading, and hence the formulation must be carefully tailored. The piezo droplet on-demand systems use piezo crystals that expand when voltage is applied (Fig. 5.6b). The chamber fills with ink, and a voltage is applied at a frequency ranging from 1 to 20 kHz, to generate pressure (acoustic) waves that are propagated within the ink chamber. Droplets are generated at the acoustic frequencies. New ink keeps the chamber filled. DoD print heads have been more popular in binder jetting processes due to their higher resolution, repeatability, and robust operations. Figure 5.7, shows an example of the print head used by HP binder jet printers. The thermal inkjet is based on design proven in HP’s paper printers. Each printhead produces a 108-mm (4.25-inch) print swath with two independent columns of 5280 nozzles that are spaced 1200/inch in each column. There are two independent supply ports for HP Binding Agent and two built-in pressure regulators. These printheads

5.1 Binder Jetting

157

Fig. 5.6 (a) Thermal droplet on demand, (b) Piezo droplet on demand 1

2 Scan

Electrical interconnect

zzles X 2 no in) 5.280 (4.25 m m 8 10

1

2

1/1200 in 320 mm (12.6 in)

HP Blinding Agent supply parts (2)

Pressure regulators (2) Print carriage with two print bars

Fig. 5.7 Example print head used in HP’s binder Jet printers [12]. (© Copyright 2022 HP Development Company, L.P. used with permission)

are designed for easy replacement. Multiple printheads can be combined to create larger printing areas. The print heads are capable of precisely depositing up to 630 million nanogram-sized drops per second of a liquid binding agent onto a powder bed. The resolution of the inkjet printers is often stated in dots per inch (dpi), and defines the details and precision of the printed surfaces. The resolution for the HP printer is stated as 1200 × 1200 dpi. A common problem with using binders as ink is the clogging of the print nozzles. Redundant nozzles are used to avoid the defects

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5 Metal Additive Manufacturing Processes – Jetting- and Extrusion-Based Processes

caused by clogged print nozzles. As shown in Fig. 5.7, four nozzles are aligned to print in the same 1200 × 1200 dot area and is called 4 times nozzle redundancy. The health of the print nozzles is monitored by print head service stations and can be checked before, during, and after printing, and redundancy can be activated to account for malfunctioning print nozzles.

5.1.4 Process Dynamics 5.1.4.1

Droplet Formation and Droplet Substrate Interaction

A key to proper understanding of the process dynamics is to develop a comprehensive understanding of the dynamics of droplet formation, control of droplet geometry and size, the velocity of the ejected droplet, the droplet path, and impact behavior with the substrate. This is important to ensure repeatability of the process, and to provide the necessary control to produce quality printed parts. Generation of droplets is a complex process, that starts by the formation of the initial jet. The droplet head shape initially changes from cylindrical to spherical as it travels further down from the nozzle. This stretches to the formation of an approximately spherical droplet and a long-connected tail that continues stretching until it breaks. Part of the tail that stays connected to the nozzle may get pulled into the nozzle, and the remainder of the tail undergoes break up due to the instabilities in the thin tail. During this process, small satellite droplets may also be formed as the tail collapses. The final drop forms a spherical drop and eventually impacts the surface where it is deposited (Fig. 5.8). The size of the droplets influences the resolution of the process. The smaller the droplet the higher the resolution of printing, and smaller the deposited volume.

(I)

(II)

(III)

(IV)

(V)

(VI)

(VII)

(VIII) Ligament length (µm)

1400 1200

Break off

Lb

1000

Stretching

Collapsing

800 600

Initial 400 jet 200

Final drop D

0 0

40

80 120 160 200 240 280 320 360 400 Time after emergence (µs)

Fig. 5.8 Formation of a droplet [10]. (Reprinted with permission of IS&T: The Society for Imaging Science and Technology sole copyright owners of The Journal of Imaging Science and Technology)

5.1 Binder Jetting

159

Fig. 5.9 Relationship between nozzle diameter, droplet size, and volume [16]. (With permission from Microdrop Technologies)

Figure 5.9 shows the influence of the droplet size and volume based on the nozzle diameter. Research has also shown that decreasing nozzle diameter decreases the droplet volume; however, viscous resistance increases and energy loss grows rapidly. Increasing binder viscosity has a larger effect on velocity drop compared with increasing velocity by changing nozzle cross-sectional area [22]. While the formation and behavior of the liquid drops is a complex process, it can be characterized by several dimensionless numbers, and threshold conditions [6]. Reynolds number : the ratio of inertia to viscosity

.

Weber Number : the ratio of inertia to surface tension

.

Ohnesorge Number :

.

Oh =

Re =

νρa η

We =

ρaν 2 γ

√ We Re

where ρ is density, η is dynamic viscosity, γ is surface tension, ν is velocity, and a is a characteristic length (typically droplet diameter). The limiting factor for drop generation is the influence of the fluid/air surface tension at nozzle. This leads to a minimum velocity for drop ejection.  νmin =

.

4γ ρdn

1/2 where dn is nozzle diameter.

Reformulating in terms of Weber number, the minimum Weber number for drop ejection to overcome the surface tension at the nozzle is given below, and must exceed 4.  We = vmin

.

ρdn λ

1/2 >4

The ejected drop impacts the surface, and ideally must impact such that it leaves a single isolated spread drop. A typical reaction to the droplet impacting the surface is to create splashing. The threshold at which splashing occurs was established as:

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5 Metal Additive Manufacturing Processes – Jetting- and Extrusion-Based Processes

 .

We Re > f (r)

f (r) is a function of surface roughness, for a smooth surface, f (r) = 50 Based on these equations and assumptions of fluid behaving in a linear Newtonian manner, a parameter space map has been constructed to show fluid properties that are suitable for drop on-demand systems and has been empirically verified (Figs. 5.10 and 5.11). The interaction between the droplet and the surface is controlled by several physical process and can be driven by inertial forces, capillary forces, and gravitational forces, and can also be characterized by the physical constants. Typically, the allowed ranges of physical properties are as follows: viscosity η (1–25 cP), surface tension σ (20–50 dyne per cm), ink density ρ (0.9–1.1 g mL−1 ), and preferably the particle size should be smaller than 1 micron.

5.1.4.2

Droplet Substrate Interaction

Once the drop lands on the substrate, the binder droplet needs to spread on the powder surface and fill in the gaps between the powder particles to provide the binding. The droplet must spread on the surface and also penetrate into the powder layer in excess of the layer thickness to create the adherence with the previously built layers. The rheological properties of the binder and the surface properties of the substrate will influence this process. The spreading of the droplet is affected by

Fig. 5.10 Parameter space for printable fluids [6]. (Open access under creative commons license)

5.1 Binder Jetting

161

Fig. 5.11 Feasible space for droplet on-demand printing [15]. (Used with permission)

the kinetic energy of the droplet impact and a secondary state due to the wetting and capillary action. The initial spreading is a function of droplet density and size along with the droplet impact velocity, and occurs in a few microseconds. The secondary spreading is related to the Ohnesorge number. If Oh 1 then the final droplet size will be large for systems with large droplets and small contact angles (dictated by surface tension of ink). This final spreading phenomenon can take many seconds to reach equilibrium, by which time other droplets may have impacted or drying may have progressed significantly [6] Positioning of the droplet is also a critical aspect of the process. The print head does not contact the substrate. The moving print head, along with the ejection velocity, creates a horizontal component to the droplet velocity. This impacts the droplet flight path that controls the final drop velocity as well as the position of the droplet on the surface (Fig. 5.12). At very low printing speeds (0,012–0.06 m/s) the droplet horizontal velocity is negligible. In the case of high printing velocities (0.06–1.0 m/s) the horizontal component of the velocity leads to change in the flight path and the angle at which the droplet impacts the substrate. Controlling the droplet flight path becomes more challenging as the size of the droplet decreases and increases in print head velocity. Small variations in droplet ejection velocity and air turbulence can impact the flight path and landing position. To minimize the effect of air turbulence, and ambient temperature higher-resolution printing systems use

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5 Metal Additive Manufacturing Processes – Jetting- and Extrusion-Based Processes

Fig. 5.12 Droplet release from print head [17]. (With permission from author)

enclosed build chambers. Print heads are also placed close to the surface, to reduce the time of flight and shorten the droplet flight path [17]. Recent research on real-time observation of binder jetting printing process using highspeed X-ray imaging [20] provides an interesting view into the process. DoD print heads were observed during the printing process. Figure 5.13a shows the droplet formation for 2 consecutive droplets. Both the droplet geometries display the approximately spherical droplet head followed by a long thin tail. Three to five satellite droplets were also observed for each droplet. The separation between the droplets was measured between the droplet head positions in the frame just before they impacted the powder bed. The measured separation between consecutive droplets was 49.34 ± 0.62 μm which was very close to the separation set in the printer operation software. The measured velocity of the droplet head was 7.74 ± 0.06 m/s, slightly lower than the designated velocity of 8 m/s. The observed velocity for the last satellite for each droplet was 6.30 ± 0.05 ms−1 . The tail of the droplet was observed to break up near the end, forming smaller satellite droplets. The length of the droplet tail before breakup was 703.16 ± 7.08 μm (measured from 38 droplet images). The satellite droplets were observed to drift away from the droplet head in the direction of the print-head motion. The separation between the impact points for the droplet head and the satellite droplet was 15.12 ± 0.55 μm. Figure 5.13b, shows the image sequence showing the evolution of the droplet during flight. The generation of the satellites is clearly visible. Figure 5.14, shows the behavior of the powder bed after the droplet impact. The impact of the droplet on the surface depicts the changes in the powder bed due to movement and ejection of powder particles caused by the impact of the binder droplet and subsequent momentum transfer between the droplet and powder particles. Most of the binder droplet momentum was used to deform the powder

5.1 Binder Jetting

163

Fig. 5.13 Xray image of droplet formation in binder jetting process [20]. (©Springer)

bed, while a small percentage of the momentum (≈2%) contributed to ejection of the powder particles from the powder bed. The penetration of the binder into the powder bed is not shown here. Other studies have shown that the impact of droplets on powder beds results in crater geometries [19]. The powder characteristics have a significant influence on this behavior. For larger spherical free-flowing particles, the impact cratering is the primary source of disturbance in the powder bed. For smaller poorly flowing particles, the cohesive forces between the particles increase, and the momentum from the droplet impact is transferred deeper into the powder bed. The ejection behavior of powder particles also depends on the size and morphology of powder particles. Two mechanisms govern the ejection behavior of particles: larger particles have better flowability, and they are easier to displace from the powder bed. On the other hand, due to larger mass, each ejected particle accounts for more momentum for larger particle sizes.

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5 Metal Additive Manufacturing Processes – Jetting- and Extrusion-Based Processes

Fig. 5.14 Evolution of Interaction depth 30 micron 316 stainless powder [20]. (©Springer)

Agglomeration was also observed in powders with small particle sizes 1 Mpa) and low-pressure cold spray (> ZR , the beam radius .ω (z) ≈ |z| × Θ. For clarity we have denoted the full divergence angle, as .ΘF ull = 2Θ, as shown in Fig. 8.9. The question still remains on how to manipulate such a laser beam using optics. Assume that .z = 0 now represents the plane at which a beam of radius .ω0,in exits a laser. Typically, the first task is to collimate such a beam to reduce its far-field divergence angle to a value close to zero. If a collimating lens with a focal length of .fcol is placed in the far field region (.z >> ZR ), then to a first approximation, it is sufficient to place the optic at .z = fcol . Note again that .fcol >> ZR . Such a configuration, depicted in Fig. 8.10, will result in a roughly collimated beam with a radius, .ωcol , of ωcol ≈

.

fcol λ . π ω0,in

(8.21)

Naturally, if the collimated beam were allowed to propagate an arbitrary distance then focused with a second optic having a focal length .ff ocus , a new laser waist would form at a distance of .ff ocus from the second optic to a waist radius of ω0,f ocus ≈

.

ff ocus λ . π ωcol

(8.22)

Combining Eqs. (8.22) and (8.21), it can then be readily observed that the ratio of the focused and original beam waists are

.

ω0,f ocus ≈ ω0,in

ff ocus λ π ωcol fcol λ π ω0,in

=

ff ocus . fcol

(8.23)

8.1 Lasers

261

Fig. 8.10 Propagation of a 1070 nm wavelength beam with an initial waist .ω0,in = 0.5 mm that is collimated by a .fcol = 50 mm lens and focused by a .ff ocus = 100 mm lens

As an illustration, the propagation of a 1070 nm wavelength beam with an initial waist .ω0,in = 0.5 mm that is collimated by a .fcol = 50 mm lens and focused by a .ff ocus = 100 mm lens is shown in Fig. 8.10. Here, the ratio of the focused to initial beam waist is .ff ocus /fcol = 2.

8.1.2.3

The ABCD Matrix Method

It should be noted that the preceding approximations assume a thin lens. Also the equations assume that the beam between the collimating and focusing lenses does not diverge. While this approximation may suffice for rough approximation, more care should be taken when designing real optical systems. To this end, the ABCD matrix method, which will now be introduced, offers a better approximation. For a Gaussian beam which travels through an optical system, the ABCD matrix method allows computation of the size, .ω0,out and location .dout of an output beam waist given an input beam waist and wavelength. See Fig. 8.11. The justification and derivations for this method are beyond the scope of this work but are described in many textbooks on quasioptical system—for instance, see [3]. Here we will simply describe the method and its application.  AB is known for an optical system, the output beam If the ABCD Matrix . CD waist location is dout = −

.

(Adin + B) (Cdin + D) + ACZR2 (Cdin + D)2 + C 2 ZR2

(8.24)

262

8 Energy Sources and Propagation

Fig. 8.11 Propagation of Gaussian beam though an optical system defined by an ABCD matrix

and the output beam waist is ω0,out = 

ω0,in

.

(8.25)

(Cdin + D)2 + C 2 ZR2

Most common optical elements have an associated ABCD matrix, which can be looked up. Several common matrices are listed in Table 8.1. One of the more useful features of the ABCD Matrix approach is that multiple optical elements can be combined to form a single ABCD Matrix. This is done by arranging the matrix for each optical component in order from right to left

.

AB CD

 Combined

AB = CD



AB ... CD n

 2

AB CD

 (8.26) 1

where the right-most matrix is the first optical element and the left-most matrix is the last, nth, optical element. The combined ABCD matrix is calculated by matrix multiplication of the elements. Let’s reexamine the propagation of a 1070 nm wavelength beam with an initial waist .ω0,in = 0.5 mm that is collimated by a .fcol = 50 mm lens and focused by a .ff ocus = 100 mm lens we previously showed in Fig. 8.10. Now, solving with the ABCD Matrix method, we first find the ABCD matrix  optical element. The  for each 1 0 first optic is the collimating lens with .ABCDcol = . Propagation through 1 − fcol 1

 1d . Finally, the matrix for the focusing free space must also be accounted for: . 01

8.1 Lasers

263

Table 8.1 Common optical elements with associated ABCD matrix Optical element A medium with constant index of refraction (e.g., free space) for a distance d Fat mirror

Thin lens with focal length of f

A lens of thickness t surrounded by free space, where n is the refractive index of the lens, .R1 is the radius of curvature of the first surface, and .R2 is the radius of curvature of the second surface

 lens is .ABCDf ocus =

.

1

1 − ff ocus

ABCD matrix   1d . 01   10 . 01   1 0 . − f1 1     1 0 1 0 1 t . n−1 n 1−n 1 01 R2 1 R1 n n

 0 . The combined matrix is this 1

      −ff ocus 1 0 1d 1 0 AB fcol = = 1 d−ff ocus − ff ocus 1 0 1 − f1 1 CD −f col f f f ocus col

0 1 f ocus

− fffcol ocus

 . (8.27)

Plugging in numerical values we find   1 0.1 AB m = −10 0 CD

.

(8.28)

Now plugging A,B,C, and D into Eqs. (8.24) and (8.25), we find dout = 0.0958 m

(8.29)

ω0,out = 9.894 × 10−5 m

(8.30)

.

and the output beam waist is .

We thus find that the simplified approach used earlier under predicts the laser waist by just 1% and overpredicts the distance between the focusing lens and the waist by about 4.4%. These are fairly small errors; however, recall that we applied the estimates under the conditions where the focal length of the collimating lens was much larger than the Rayleigh range of the input beam and the focal length of the focusing beam was also much larger than the Rayleigh range of the output beam. If these assumption were not true, our error would have been significantly greater (Fig. 8.12).

264

8 Energy Sources and Propagation

Fig. 8.12 Calculation of beam waist and location using ABCD matrix

8.1.2.4

Propagation of Non-Gaussian Beams

All our analysis thus far has assumed a Gaussian beam; however, real laser beams are never perfectly Gaussian. To estimate the propagation of real laser beams, we introduce a beam quality factor called M-squared, .M 2 , where an .M 2 = 1 represents a perfect Gaussian beam. A summary of key equations which incorporate the M-squared correction is provided in Eqs. (8.32)–(8.35). Note that ABCD matrix method can also be directly used for non-Gaussian beams, so long as the Msquared correction is incorporated into the Rayleigh range calculation (Eq. 8.32). A comparison of the propagation of beams with M-square values of 1 and 2 is sown in Fig. 8.13. Notice that, for the same initial beam waist, the far-filed divergence of the non-Gaussian beam is M-square time that of the Gaussian beam. Also notice that the Rayleigh range of the non-Gaussian beam is 1/M-square times that of the Gaussian beam. Another quantity sometimes used to characterize the quality of a laser beam is known as the beam parameter product (BP P ). The BP P is equal to the waist radius times the half divergence angle: BP P =

.

ω0 ΘF ull . 2

(8.31)

For a Gaussian beam, a multiplication of the beam waist with the half divergence angle, Eq. (8.20), simply yields .λ/π . This is the lowest possible BP P value possible for a laser beam. A non-Gaussian beam can be said to have a BPP of .M 2 times that of an ideal Gaussian, .BP P = M 2 λ/π . A summary of key equations for the propagation of non-Gaussian beams (.M 2 > 1) follows:

8.1 Lasers

265

Fig. 8.13 Comparison of the propagation of a Gaussian (.M 2 = 1) and non-Gaussian beam with an .M 2 = 2. Both beams have a 1070 nm wavelength beam with an initial waist .ω0,in = 0.5 mm that is collimated by a .fcol = 50 mm lens and focused by a .ff ocus = 100 mm lens

ZR =

.

 π ω02 . M 2λ

Θ = M2

.

λ . π ω0



2     2 λz z 2 M . = ω0 1 + 1+ .ω (z) = ω0 ZR π ω02 f

.

(8.32)

(8.33)

(8.34)

λ

M 2 πf ocus ff ocus ω0,f ocus ωcol . = ≈ λ f fcol ω0,in M 2 π ωcol0,in

(8.35)

8.1.3 Laser Types There are dozens of types of laser systems used in industry [4–6]. Most often, a laser is categorized by its lasing medium, output power range, and temporal behavior during operation (continuous (CW) or pulsed). In AM fusion processes, the most commonly employed laser systems include:

266

8 Energy Sources and Propagation

Fig. 8.14 Common laser types and wavelengths

• fiber lasers doped with rare-earth metal ions like ytterbium (Yb.3+ ), erbium (Er.3+ ), or thulium (Tm.3+ ), • neodymium-doped (ND.3+ ) yttrium aluminum garnet (Nd:YAG) lasers, and • semiconductor-based diode lasers. Historically, carbon dioxide (CO.2 ) lasers were also widely used. The wavelengths of some common lasers are illustrated in Fig. 8.14. Perhaps the mostly commonly employed laser type in fusion AM is the fiber laser [7]. The lasing medium for such lasers is a glass fiber doped with rare-earth metal dopants. The dopants within the glass are essential to the lasing process. In fact, population inversion and stimulated emission actually occur between energy levels of the dopant, not the silica glass. The glass is little more than a transparent medium to hold the rare-earth metals. Typically, the lasing medium (i.e., the doped glass fiber) is pumped using one or more diode lasers. The pumping laser travels through an inner cladding, made of glass with a slightly lower index of refraction than the core fiber, such that the lasing beam is trapped within the inner, lasing fiber via total internal reflection while the pumping beam travels though both the core and inner cladding. The outer cladding traps the pumping beam via total internal reflection. At both ends of the fiber, dielectric mirrors, usually consisting of a fiber Bragg grating (FBG), allow the laser beam to oscillate within the laser cavity. At the fiber output, the FBG has a reflection index less than unity allowing the beam to escape. See Fig. 8.15 for an illustration of the makeup of a fiber laser. Often, a secondary, delivery fiber is coupled to the fiber output to transmit the beam to collimating, directing, and focusing optics.

8.1 Lasers

267

Fig. 8.15 (a) A fiber laser is made up of an inner, lasing core doped with a rare-earth metal, an outer core through which the pumping laser passes, and an outer cladding. (b) An illustration of pumping of a fiber laser via multiple fiber-coupled diode lasers

Ytterbium, erbium, and thulium-doped fiber lasers emit light in the near-IR regime, at wavelengths around 1 to 2 .μm. Significant advantages of fiber lasers include simple beam delivery though a single fiber-optic cable, low maintenance costs, and fairly reliable operation. A wide variety of laser powers and output beam profiles are also available. Single-mode ytterbium-doped fiber lasers, outputting Gaussian (i.e., TEM.00 ), beams around 1070 nm wavelengths are available at hundreds of watts and often used in powder bed fusion AM processes. Multi-kilowatt lasers, with multi-mode outputs, are also commonly used in laser processing and high-power directed energy deposition AM. Another type of laser which emits in the near-IR regime (at a 1064 nm wavelength) is the Nd:YAG laser. The lasing medium is typically arranged within the laser cavity as a several centimeter long Nd:YAG rod, pumped by a flash lamp. A diode laser together with a disk geometry can also be used to increase pumping efficiency and beam quality. Both configurations are illustrated in Fig. 8.16. A significant advantage of the disk laser geometry is direct, conduction cooling of the lasing medium through the a heat sink which is bonded to the Nd:YAG disk. It is noteworthy that commercially available, high-power Nd:YAG lasers predated fiber lasers by about a decade. As such, many of the laser optics originally developed for the Nd:YAG output wavelength of 1064 nm were readily substituted later on for fiber lasers. Both laser types can also readily use commercial optical fibers for beam delivery. Electrically pumped semiconductor lasers are also an attractive option for metal AM. How such lasers operate is a bit outside the scope of the current work— see [4, 6, 8]. It is however sufficient to say that semiconductor lasers are similar

268

8 Energy Sources and Propagation

Fig. 8.16 (a) A rod, flash lamp pumped Nd:YAG laser. (b) A diode pumped Nd:YAG disk laser

to light-emitting didoes (LEDs) in that an electric current is applied across a p-n transition, where the n-region is doped with atoms such as to produce an excess number of unbounded electrons, while the p-region contains a deficit of electrons (i.e., holes). See Fig. 8.17. The recombination of electrons and holes at the p-n transition produces photons. To produce a resonator, mirrors are created at the ends on the semiconductor by cleaving and polishing. In some cases the fiber ends are also coated to enhance reflections at specific wavelengths. Today, semiconductor lasers are used widely for illumination and optical communication, as pumping sources, and for numerous other applications; however, their use in AM is less common. Two significant disadvantages of such lasers are limited availability at power .>100 W (though multiple lasers can be stacked/combined to multiply power) and a large beam divergence. The latter is a consequence of a small resonator cross section (see Fig. 8.17). Nevertheless semiconductor lasers are now available across the visible to IR spectrum and are gaining popularity for use in laser processing and AM. The final laser we will mention in passing is the carbon dioxide (CO.2 ) laser. The lasing medium for this laser is CO.2 , hence the name. While still widely used in the laser processing industry for applications including cutting, welding, and forming, it is now rarely used for fusion AM. The loss of market share in metal AM processes is largely due to the output wavelength, 10.6 .μm, which precludes beam delivery

8.2 Electron Beams

269

Fig. 8.17 A simplified front and side views of a semiconductor laser

using fiber optics and is reflected by metal surface to a much greater degree than the shorter wavelengths outputs of fiber, Nd:YAG, or semiconductor lasers.

8.2 Electron Beams Another common source for DED and PBFAM is the electron beam (e-beam). Though the operating principles for electron beams were known in the early twentieth century, it was not until past the middle of the century that they were utilized for welding [9]. In that sense, both laser and e-beam technology are relatively new material processing technologies. Additional similarities include their abilities to produce very powerful beams which can be applied over areas as small as several microns, resulting in intensities exceeding gigawatts per square meter. One advantage of electron beam, in contrast with laser-based, processes is that much of the electrical energy consumed is converted directly into output beam power. This is known as wall-plug efficiency and is estimated to be on the order of 70% for modern e-beam systems. Compare this with most laser beam systems, which are typically well below 50%. It should however be noted that the total energy consumption in laser versus e-beam processes is difficult to quantify. For instance, significant energy is consumed in some e-beam powder bed fusion AM systems due to preheating of the build chamber to hundreds degrees Celsius prior to processing. Today, commercial AM systems which use electron beams include the GEowned Arcam EBM PBFAM process and the Sciaky EBAM DED process. The contrast between these systems is striking. The Arcam system is typically used to produce parts on the order of tens to hundreds of millimeters in size, while the Sciaky system is designed to build very large parts on the order of meters in size. Nevertheless, as we will discuss in the next section, the technology underlying the production and direction of the electron beam is similar in both cases: electrons

270

8 Energy Sources and Propagation

Fig. 8.18 Key components of an electron beam system for fusion AM. Adapted from [10]

are generated by a high-temperature filament, accelerated toward a substrate using a strong electric field, and rapidly directed and rastered using magnetic optics. As with most electron beam processes, both Arcam and Sciaky systems also operate under very low pressures so that electrons can travel from the filament to the substrate without being scattered or absorbed by gases in between. Key components of an electron beam system are illustrated in Fig. 8.18.

8.2.1 Operating Principles The first step in constructing an electron beam system is to generate free electrons. To do this, one can heat a metal filament to very high temperatures. This process, of freeing electrons from a metal by heating, is known as thermionic emissions. To explain this process, we should briefly discuss the arrangement of electrons within a metal.

8.2.1.1

Thermionic Emissions

Electrons within metal, unlike those involved in ionic or covalent bonds in a dielectric, are not tightly bound to particular atoms. We can think of metals as being held together using metallic bonds, in which a uniform “sea of free electrons” is shared by positively charged metal ions—see Fig. 8.19. Another way to think of electrons within a metal is as particles within a deep potential well. At rest (i.e., a temperature of absolute zero), energy levels within the well up to an energy equal to the Fermi energy level, .EF , are occupied. That is, the probability that an electron occupies any energy state below .EF is equal to one, while the probability that an electron occupied any energy above .EF is zero.

8.2 Electron Beams

271

Fig. 8.19 Electrons within a metal can be thought of as a seal of electrons holding together positively charged atoms

Fig. 8.20 Electrons within a metal can be thought of as being trapped in a deep potential well. As the temperature of the metal increases, the probability of electrons having an energy greater than the sum of the Fermi energy and work energy becomes non-zero

However, as the metal is heated, electrons gain energy and begin to occupy states above .EF . This is illustrated in Fig. 8.20. The probability of electrons occupying a certain energy state, follows the Fermi-Dirac distribution F (E) =

.

1 + exp

1 

E−EF kB T

,

(8.36)

where E is the energy state of interest and T is the temperature of the metal. If the energy gained by an electron, already at the Fermi energy, exceeds the energy barrier of the metal (.We ), such that F (EF + We ) > 0,

.

(8.37)

there is a non-zero probability that the electron will escape. We must also account for the chance that a portion of electrons with sufficient energy to escape the potential

272

8 Energy Sources and Propagation

well will be reflected back. That is, there is a non-zero reflection coefficient .r(E) required by quantum mechanics. The current density caused by electrons escaping the metal, J (amperes per square meter), follows Richardson’s law, named after Nobel prize winner Owen Richardson:  J = (1 − r) AT 2 exp

.

 −We . kB T

(8.38)

The coefficient A is known as Richardson’s constant and depends on the filament material. It is on the order of .1.2 × 106 A/(m.2 K.2 ). Of course there are other ways to cause electrons to escape the potential well. One method is by using incident photons with an energy .hν > We ; this is known as the photoelectric effect. Another method is to affect potential well itself by applying an electric field. For practical e-beam applications to fusion AM processes however, thermionic emissions are our primary interest. The most common way to cause thermionic emissions is to resistively heat the filament by applying a voltage across a metal, typically tungsten, filament.

8.2.1.2

Accelerating Voltage

Once freed from the filament via thermionic emissions, the free electrons must be directed and accelerated toward a substrate. This is accomplished by applying a strong electric potential (i.e., voltage) between the negatively charged filament (the cathode) and a grounded anode, as shown in Fig. 8.18. The acceleration of electrons is governed by the Lorentz force F = me a = −qe E − qe (v × μH) ,

.

(8.39)

where .me is the mass of an electron, .qe ≈ 1.602 × 10−19 coulombs is the charge of an electron, a is its acceleration, .E is the electric potential between the filament and the anode (V/m), .v is the velocity of the electron, .H is the magnetic field strength (A/m2 ), and .μ is the magnetic permeability, which is .μ0 ≈ 1.257 × 10−6 H/m in a vacuum. For now, let’s ignore the magnetic field. The energy gained by the electron in the presence of an electric field is 

 ΔE =

.

F · ds = −qe

E · ds = qe V ,

(8.40)

 since the electric potential, .V = − E · ds volts. Note that this energy is entirely kinetic; the electric potential has been converted to fast-moving electrons heading toward the substrate with an energy of . 12 me v 2 = qe V . For this reason, we often refer to energy in terms of electron volts (1 eV = .qe × 1 V .≈ 1.602 × 10−19 J). So far, we have considered only one free electron. But, of course, many electrons are emitted by the heated filament, producing a current density according to Eq.

8.2 Electron Beams

273

(8.38). Using Eq. (8.38), together with the filament surface area, we can estimate the total current, I amps, emitted. The power of the electron beam, P , can then be calculated as P =

.

dE dNe d = Ne qe V = qe V = I V , dt dt dt

(8.41)

since the electric current I is by definition equal to the charge of an electron times e the number of electron generated per unit .qe dN dt . It can therefore be surmised that the energy of an electron beam is controlled by the acceleration voltage, and its average power is controlled by both the acceleration voltage and the cathode heating voltage (i.e., filament temperature). To further control the flow of electrons, a control grid (i.e., biased cup or Wehnelt cylinder) is also typically used. By varying the electric potential between the filament and bias cup, the flow of electrons can be reduced or stopped—setting the bias cup to a high negative potential relative to the filament is said to “pinch off” the flow of electrons by repelling electrons back toward the cathode. Essentially, controlling the control grid bias voltage allows control of the area of the tip capable of emitting electrons which are attracted toward the anode. In practice, modulation of the grid cup voltage is typically used to adjust the beam current and size of the electron beam (the area of the filament emitting electrons). Thus, control grid voltage is key to modulating the power of the electron beam without affecting the acceleration voltage.

8.2.1.3

Magnetic Focusing and Deflection

The final requirements for practical application of an electron beam are focusing and deflection. Focusing is accomplished by a magnetic lens. Similarly, defection is accomplished using magnetic coils. Both operate based on the Lorentz force, Eq. (8.39). Though we did not prove so in our prior analysis concerning the energy gained by electrons, the magnetic field does not actually impart any energy to the electrons. It does however affect its path. A key advantage of electron beams over lasers is the ability to focus and deflect the beam dynamically at rates exceeding hundreds of kilohertz.

8.2.2 Grounding of the Substrate Before moving on, one additional consideration should be noted: it is critical that the substrate remain grounded (i.e., at an electrical potential of zero) during processing. Because the purpose of the electron beam is to accelerate and direct negatively charged electrons toward the substrate, it is easy to accumulate negative charges and thus affect the nearby electric field. Local charging can thus effect the beam power,

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location, and size. To prevent this, the substrate must be grounded to dissipate the charge. Processing of materials with a significant surface oxide or poorly conducting powders can be particularly problematic—more on this later.

8.2.3 E-Beam Propagation The flow of electrons within an e-beam system can be thought of as analogous to photons in an optical system. We will speak of lenses and focal lengths in much the same way. A key difference however is that while photons can, to a first approximation, be thought of as traveling along straight rays, electron motion, in the presence of a magnetic field, follows the law of Lorentz, Eq. (8.39). In the case of a static electric field where .E = E0 zˆ and .H = 0, the electron simply travels along a straight line opposite to the direction of the electric field x(t) = x0 , y(t) = y0 , z(t) = z0 + v0 t −

.

q0 E0 , 2me

(8.42)

where .(x0 , y0 , z0 ) represents the initial position and .v0 is the initial velocity of the electron. Consider static electric and magnetic fields both parallel to the z direction, respectively, .Ez and .Hz . The motion of the particle in vacuum will follow:  dvx −qe  vy μ0 Hz , = dt me

(8.43)

dvy −qe = (−vx μ0 Hz ) , dt me

(8.44)

dvz −qe Ez . = dt me

(8.45)

.

.

.

Along the z direction, the electron again simply travels opposite to the direction of the electric field and is not affected by the magnetic field. Solving the equations of motion perpendicular to z by integrating twice yields .

    x(t) = rg sin ωg t + φ0 + x0 − rg sin φ0 ,

(8.46)

    y(t) = rg cos ωg t + φ0 + y0 − rg sin φ0 ,

(8.47)

.

where .φ0 is an arbitrary initial phase and .rg is known as the gyroradius and is proportional to the speed perpendicular to the magnetic field, .v⊥0

8.2 Electron Beams

275

Fig. 8.21 Motion of an electron in a uniform electric and magnetic field parallel to the z axis

rg =

me v⊥0 . qe me

(8.48)

ωg =

qe μ0 H . me

(8.49)

.

The gyrofrequency, .ωg , is .

This tells us that the electron will accelerate along the x and y directions simultaneously, much like a rotating ball held by a sting. The Lorentz force, .(qe v⊥0 μ0 Hz ), pulls the electron toward the center of the gyroradius, while the   centrifugal force, . me v⊥0 /rg , pulls the electron outward. All the meanwhile, as we discussed, along the z direction, the particle will also accelerate opposite to the electric field (recall that the electron is negatively charged). An illustration of this motion is provided in Fig. 8.21. In general, calculation of the motion of electrons is a spatially varying magnetic field is complicated and requires numerical solutions. But let us at least attempt to visualize the effect of magnetic lenses and deflection coils. Specialized textbooks cover the topic in detail [11, 12]. Based on what we’ve already established, we can say that the electrons travel opposite to the electric field lines and around the magnetic field lines. The task of a magnetic lens is to cause convergence of the magnetic field lines and in so doing focus the envelope of electron motion as shown in Fig. 8.22. For a thin coil with a radius, R, much larger than its cross section, the focal length, f , of the coil can be approximated as [11]

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8 Energy Sources and Propagation

Fig. 8.22 Motion of an electron in a uniform electric and magnetic field parallel to the z axis

.

3π q 2 μ2 (I N )2 1 , = 2020 f 16 me |qe V0 |R

(8.50)

where I is the current flowing though the coil, N is the number of coil turns, and .V0 is the constant electrical potential between the cathode and anode. Similar to focusing of the electron beam, deflection can be achieved using magnetic fields generated by solenoids. However, in contrast to focusing, the magnetic field now needs to be at least partially orthogonal to the travel direction of the electrons. A common quadrupole arrangement is shown in Fig. 8.23, where two pairs of electromagnetic coils are placed opposite to one another; each generates opposite magnetic field lines. This mimics the arrangement of two permanent magnets along the horizontal axis, with the north faces facing one another, and two permanent magnets along the vertical axis, with the south faces facing one another. By varying the strength of the magnetic field generated by each coil, the beam can be deflected.

8.2 Electron Beams

277

Fig. 8.23 Deflection of an electron by a quadrupole magnet Fig. 8.24 The propagation of an ensemble of electrons forms a beam envelope analogous to the propagation of a laser

It would be far too cumbersome to consider the trajectory of each individual electron within an electron beam system. Most often, the distribution of electrons is assumed to be Gaussian and considered to propagate though space much like a laser beam (Fig. 8.24)—recall that we have already discussed the Gaussian distributions in Sect. 8.1.2.1 (Eq. 8.17). Unfortunately, there appears to be no standard method for reporting electron beam size—some use the .1/e2 definition that is common with laser beams, and some use .1/e, while still others report the full width at half maximum (FWHM). As with lasers, the beam parameter product (BP P ) is also an invariant for electron beams. The BP P is also termed the beam emittance (.ϵ) and follows the same definition as for a laser: it is equal to the beam waist radius times the half divergence angle, or in terms of the diameter, .d0 , and full divergence angle, .ΘF ull : ϵ=

.

d0 ΘF ull . 4

(8.51)

It is calculated from the ratio of the beam parameter product (BPP) of the beam to that of a Gaussian beam with the same accelerating voltage.

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8 Energy Sources and Propagation

8.2.4 Electron Beam Systems All the components we’ve thus far discussed—the filament, bias cup, anode, focusing, and deflection optics—make up what is termed the electron gun. To prevent oxidation of the filament and contamination, the gun portion is kept isolated from the rest of the processing chamber either using a thin metal window or valved off from the rest of the system when not under vacuum. Here, we shall refer to both the gun and the processing chamber holistically as the electron beam system. Electron beam systems are typically categorized according to the operating acceleration voltage and vacuum level. For fusion AM processes, acceleration voltages are relatively moderate, at around 60 kV—commercial electron beam welding machines can operate at more than twice this value. Beam currents are also moderate, at around hundreds of milliamps, producing output powers on the order of 5 to 10 kW. Some DED systems, such as those available from Sciaky, Inc., can operate at powers exceeding tens of kilowatts, while powder bed fusion systems, such as those from General Electric Company, generally operate around 6 kW. Most electron beam systems employee a tungsten (W) filament. Tungsten has a work function of approximately 4.5 eV (.7.2 × 10−19 J). Operating temperatures around 2500 to 3000 K are typical, with a corresponding current density values on the order of 2 to 3 A/cm2 . This current can be affected using the control grid bias voltage, which is kept between zero and negative voltage set at several kilovolts relative to the tungsten cathode. There is little published information regarding the optics used within commercial electron beam AM systems; however, many settings can be assumed to be typical. Most systems for fusion AM appear to focus electron beams to spots on the order of 100s of microns in diameter and are capable of deflecting the electron beam at very high (100s kHz to MHz) rates. These high-speed deflections enable complex paths and enable production of a single or multiple simultaneous melt pools. The latter case gives the illusion of multiple beams processing simultaneously and is sometimes called multi-beam processing or beam splitting. A high vacuum (.< 10−4 mbar) is also maintained in all commercial AM system. This is of course required to prevent absorption, attenuation, and scattering of the electron beam by atmospheric gas. A unique feature of the powder bed fusion systems available from GE is that after pumping down to a high vacuum, the system is backfilled with helium gas to a pressure of (.≈ 10−3 mbar) to reduce the effect of charge buildup on the powder and substrate [13].

8.3 Electric Arcs While not capable of competing with the high intensities and small spot sizes available from laser and electron beam sources, electric arcs are nevertheless very attractive for AM of large structures, where cost and speed are more important

8.3 Electric Arcs

279

Fig. 8.25 A plasma, consisting of ions and free electrons, forms between the electrodes of an arc. Electrons are accelerated toward the anode, while ions are accelerated toward the cathode

than minimum feature size and accuracy. Electric arcs are also an old technology, considered a novelty in the 1800s; they were later used for lighting around the turn of the century and then became ubiquitously used for repair and construction in the early to mid-1900s. Nikolai Benardos and Stanislaw Olszewski are generally credited with first developing and demonstrating joining of metal parts via electric arc welding [14] around 1885. It is of course no surprise that the explosion in the development of electric arc sources for welding coincided with the development and expansion of the electric power grid, starting in the late 1800s and early twentieth century.

8.3.1 Operating Principles Like an electron beam source, electric arcs operate based on the application of a high voltage difference between a negatively charged cathode and a positively charged anode. A key difference however is that the process does not take place in a vacuum; nor is the cathode heated to generate free electrons. Rather, the process relies on the breakdown (ionization) of gases between the cathode and electrode followed by subsequent acceleration of electrons toward the anode and ions toward the cathode. An illustration of arc process is provided in Fig. 8.25.

8.3.1.1

Arc Formation

As the electrons and ions are accelerated toward the anode and cathode, respectively, they collide with neutral gases, forming more charged species via impact ionization. The plasma generated between the electrode is thus self-sustained by the voltage difference and resulting current between anode and the cathode. As charges are accelerated, they gain a kinetic energy between successive collision of .mv 2 /2 =  qE · ds, where q is the charge, .E is the electric field, and .s is the path between collisions. For electrons, this energy is equal to .qe V , where V is the voltage

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8 Energy Sources and Propagation

difference between collision. Additional electrons are provided by the cathode though a combination of processes, including thermionic emissions.

8.3.1.2

Arc Plasma Properties

Both near the cathode and anode regions, a sharp change in the electric field is observed. These transition regions, known as the cathode and anode drop, account for the majority of resistance within the circuit formed by external voltage, electrodes, and plasma. The bulk of the plasma, the plasma column, also exhibits a linear voltage change. Once formed, the length of the plasma column thus affects the energy and current of species and consequently heat input into the electrodes. The thermal plasma which forms between the anode and cathode is highly nonuniform. Generally, temperatures within the plasma are less than an electron volt (1 eV, equivalent to .≈ 11,604 K). However, temperature, as discussed in Sect. 8.1.1, is a tricky term. In complete thermodynamic equilibrium, a single temperature defines the amount of radiation, the distribution of excited states, degree of ionization, and particle speeds within the plasma. In other words, there is a single temperature, T , which defines the Planck radiation (Eq. 8.1), the Boltzmann distribution (Eq. 8.3), and the degree of ionization (defined by the Saha equation). This single temperature also defines the speed of species within the plasma, which follows the Maxwell-Boltzmann distribution    m 3/2 mv 2 2 .f (v)dv = 4π v exp − (8.52) dv, 2π kT 2kT where v is the speed and m is the mass of the particle. Achieving complete thermodynamic equilibrium would require trapping all particles and radiation from escaping—this is clearly not possible with an electric arc. In some cases, one can however argue that over a very small region of the plasma, while we may not be able to account for escaping radiation (Eq. 8.1), there are sufficient, rapid interactions between neighboring species such that the distribution of excited states, degree of ionization, and particle speeds within a small neighborhood are defined by a local temperature. This assumption of local thermodynamic equilibrium (LTE) is what enables us to talk about the temperatures within the plasma, though in many cases this is too presumptuous [15, 16]. Energy from the arc is transferred to the electrodes via the collision of energetic electrons and ions. This results in significant heating. It is this heating that is useful in fusion AM processes. The anode, as it is bombarded by energetic electrons, generally attains higher temperatures than the cathode. Arc energy transfer is discussed in more detail in Sect. 9.3.

8.3 Electric Arcs

281

Fig. 8.26 Examples of arc welding systems: gas metal arc welding, gas tungsten arc welding, non-transferred arc welding, and transferred plasma arc welding. Adapted from [10]

8.3.2 Arc Systems Arc systems can take many forms. Common fusion AM systems are based on traditional arc welding processes, which employee a shielding gas together with a wire feed system. Variants of tradition gas metal arc welding (GMAW or MIG), gas tungsten arc welding (GTAW or TIG), and plasma arc welding (PAW) are all viable sources for fusion AM processes. What differentiates these processes are the arrangement of electrodes, the methods for wire feeding, and types of electric circuits employed. In GMAW- and GTAW-based AM processes, a voltage is applied between an electrode and substrate. Meanwhile an inert gas flow (e.g., argon, helium, or nitrogen for some materials) surrounds the electrode and shields the melt pool from oxidation. The key difference between the two processes, as shown in Fig. 8.26, is the use of a non-consumable electrode in GTAW rather than the consumable electrode used in GMAW welding. Non-consumable electrodes are made up of refractory metals, typically tungsten, which vaporize and erode slowly during processing. In contrast a consumable electrode is continuously fed and melted

282

8 Energy Sources and Propagation

during GMAW. A consumable electrode offers the advantage of incorporating a coaxial wire delivery system directly into the processing head. Either system can utilize an AC or DC voltage supply, though DC supplies are more typical. One advantage of this arrangement is that the substrate or electrode wire can be made the anode (positively charged)—this results in a more focused distribution of heat input into the substrate. Typical kilowatt power supplies provide operating currents in the range of hundreds of amps and a potential difference on the order of tens of volts. In the GMAW process, faster wire melting and a higher feed rates can be obtained by positively charging the wire, which causes a concentrated bombardment of electrons. Closed-loop control of arc voltage and current in combination with a wire feeder controller are also commonly employed to enhance process stability and maintain the desired current and arc column length. Both GMAW and GTAW produce an energy input on the order of .106 –108 W/m2 into the substrate. Plasma arc welding processes are distinguished by the confinement of the plasma below the non-consumable electrode. As shown in Fig. 8.26, the two variants of plasma arc welding include transferred arc welding and non-transferred arc welding. In plasma arc welding processes, a wire feedstock is typically employed, though a powder can also be delivered using a coaxial nozzle. In transferred arc welding, the plasma formed between the non-consumable electrode and the substrate is constrained by a nozzle. Often, a DC power supply provides a negative voltage to the electrode, relative to the substrate. The constricting nozzle results in a more stable, longer, and focused plasma plume. Because heating of the substrate results both from the kinetic energy of electrons (the anode spot) and interaction with the thermal plasma, the net energy density directed to the substrate is up to two orders of magnitude greater than typical in GMAW and GTAW. Non-transferred arcs remove the substrate from the welding circuit altogether. The arc is formed between the non-consumable electrode and a constricting nozzle. The flow of gas through the constricting nozzle still directs the plasma toward the substrate; however, the plasma is more dispersed than in transferred arc welding. Additionally, heating is not provided by the anode spot, resulting in less energy being transferred to the substrate.

8.4 Summary Lasers, electron beams, and electric arcs are all viable sources for metal fusion AM processes. Of the three, lasers are the most popular. Laser operation requires stimulated emissions, population inversion, and a resonator. These principles are widely applicable, resulting in many commercially available laser sources. Light produced by a laser is directional and monochromatic, which enables the focusing of energy to small spots, ranging from tens of microns to several millimeters.

8.5 Questions and Discussions

283

Electron beams offer an alternative to laser sources. Key requirements for the operation of e-beams include thermionic emissions, the presence of an accelerating voltage, and the use of magnetic focusing and deflection optics. During operation, the presence of a vacuum within the chamber prevents beam absorption and scattering. High-speed deflection of the beam, at rates on the order of hundreds of kilohertz, is a significant advantage over laser sources. Today, e-beam sources are available for both powder bed fusion and directed energy deposition processes. Electric arcs are inexpensive and well-established for melting large volumes. Arc processes rely on the generation of a thermal plasma, which transfers energy to the underlying substrate. Variants of electric arc methods include gas metal arc, gas tungsten arc, and plasma arc processes. Though output intensities are lower than possible with laser or electron beam processes, total power output of several kilowatts is achievable and sufficient for producing weld pools on the order of millimeters to centimeters in size.

8.5 Questions and Discussions 1. What are the required elements for (a) laser, (b) electron-beam, and (c) electric arc operation? 2. Compare and contrast the advantages and disadvantage of each source. 3. Consider a Gaussian laser beam with a wavelength of λ and a 1/e2 beam radius, at the exit of the laser beam, of ω0,L . Assume that ω0,L represents a beam waist located right at the exit of the laser. (a) What is the far-field divergence angle? (b) If the laser was non-Gaussian, with an M-squared value of M2 , what is the effect of the far-field divergence angle? (c) If the laser is focused by an arbitrary optical system, how would you calculate the location and size of the output beam waist? 4. Compare and contrast the advantages and disadvantage of common types of laser systems. 5. Is it necessary or important to keep an electron beam system under vacuum? Why or why not? 6. Compare and contrast the focusing and propagation of an electron beam with that of a laser beam. 7. Describe the various types of electric arcs available. Compare and contrast their advantages and disadvantages. 8. How does plasma form and how is it sustained during the operation of a electric arc? Describe why plasma properties are important.

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References 1. Einstein A (1917) The quantum theory of radiation. Physikalische Zeitschrift 18:121 2. Planck M (1901) On the law of the energy distribution in the normal spectrum. M Planck Ann Phys 4:553 3. Goldsmith P (1998) Quasioptical systems: Gaussian beam quasioptical propogation and applications. Wiley-IEEE Press, New York 4. Webb CE, Jones JDC (2003) Handbook of laser technology and applications, vol II. CRC Press, Boca Raton 5. Steen WM, Mazumder J (2010) Laser material processing. Springer London, London 6. Eichler HJ, Jürgen E, Oliver L (2018) Lasers - basics, advances and applications, vol 220. Springer series in optical sciences. Springer Nature Switzerland AG, Switzerland 7. Pinkerton AJ (2016) Lasers in additive manufacturing. Opt Laser Technol 78:25–32 8. Thyagarajan K, Ghatak A (2011) Lasers. Graduate texts in physics. Springer US, Boston, MA 9. St. W˛eglowski M, Błacha S, Phillips A (2016) Electron beam welding – techniques and trends review. Vacuum 130:72–92 10. Nassar AR, Reutzel EW (2020) Energy sources for fusion additive manufacturing processes. In: ASM handbook, vol 24, pp 24A–4E. ASM International, Detroit 11. Molokovskij SI, Suškov AD (2005) Intense electron and ion beams. Springer, Berlin. OCLC: 254248546 12. Rose HH (2009) Geometrical charged-particle optics. Springer series in optical sciences, vol 142, 1st edn. Springer, Berlin. OCLC: 845416587 13. Gong X, Anderson T, Chou K (2014) Review on powder-based electron beam additive manufacturing technology. Manuf Rev 1:2 14. De Benardos N (1887) Process of and apparatus for working metals by the direct application of the electric current., Patent No. 363320. Retrieved from https://patents.google.com/patent/ US363320A/en 15. McWhirter RWP (1968) A survey of phenomena in ionized gases. Invited papers presnted at Vienna, International atomic energy agency. In: Departures from local thermodynamic equilibrium 16. Wendelstorf J (2000) Ab initio modelling of thermal plasma gas discharges (electric arcs). Ph.D., Technische Universität Braunschweig, Braunschweig, Germany

Chapter 9

Source-Material Interactions

Be it light, an electron beam, or a thermal plasma, the purpose of all energy sources in fusion AM processes is to melt metal. That is, to transfer energy, which is rapidly thermalized and causes a phase change in the material. This is in contrast to primary photochemical processes such as vat polymerization, wherein bonding results primary from a chemical reaction induced by photons. Additional exceptions to this rule are cold fusion processes, such as ultrasonic welding and friction-stir processes. However, we will not detail such photochemical or cold bonding methods here. Rather, we will focus on thermally induced heating and melting by lasers, electron beams, and arcs. By treating the process as purely thermal, we can limit the timescales of interest to those necessary for thermal diffusion to occur (greater than hundreds of picoseconds). Simplifying the matter further, we can even neglect many of the details of energy transfer and assume heat source of a suitable magnitude, size, and distribution. However before this treatment, we must first understand a bit about source-material interactions and how energy is reflected and absorbed by a substrate—that is, the subject of this chapter. To tackle the topics of source-material interactions, this chapter is structured as follows. First, we detail models for laser, electron beam, and arc absorption, respectively. Where appropriate, we present simplified model of metals and dielectrics and describe interactions at the surface and within the bulk of the material. Next, we deal with heating and melting. The discussion is, in general, source agnostic, with a focus on underlying principles. In addition, peculiarities associated with each energy source are detailed.

© Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_9

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9.1 Lasers: Energy Transfer 9.1.1 Light as an Electromagnetic Wave Light incident on a material may be reflected, absorbed, and/or attenuated. The degree to which each of these mechanisms occurs is a function of the boundary conditions imposed by the material system and the surrounding environment. To determine the degree of reflection, absorption, and attenuation, it is most convenient to treat light as an electromagnetic wave. An electromagnetic wave incident on a dielectric can be thought of as causing the bound electrons within to oscillate. Let us consider a wave oscillating in the x direction and propagating along the z direction Ex (z, t) = E0 exp (j (ωt − kz)),

.

(9.1)

√ where .E0 is the amplitude [V/m], .j = −1 is the imaginary unit, .ω is the angular frequency of oscillation [Hz], t is time [s], and k is known as the wave number [1/m]. Here, representing the wave using complex notation is more convenient than using a cosine or sine function: .Ex (z, t) = E0 cos (ωt − kz). However, both notations are interchangeable, following Euler’s theorem: .

exp (j φ) = cos (φ) + j sin

(9.2)

Strictly speaking, .cos (φ) = 21 exp (j φ) + 12 exp (−j φ) = Re (exp (j φ)). For convenience, we typically neglect to explicitly state the complex conjugate or real notations and simply write the oscillating wave as in Eq. (9.1). The wave described in Eq. (9.1) is said to be linearly polarized. That is, as time passes and the wave propagates along the positive z direction, the electric field oscillates only along one axis, x, perpendicular to the wave vector, .k. A wave incident on a surface is said to be p-polarized if the electric field oscillates within the plane of incidence defined by the wave vector and the vector normal to surface. If the wave oscillates perpendicular to the plane of incidence, it is said to be spolarized—see Fig. 9.1. Of course it is possible for the wave to have components both parallel and perpendicular to the plane of incidence. If we consider a wave propagating in the z direction, such that it is incident on a substrate with a normal vector in the x-y   plane, .Ex (z, t) = Es + Ep = (E0x + E0y exp (j (ωt − kz)) represents a linearly polarized wave with both p- and s-polarized components. Applying a .π/2 phase shift to one of the wave’s components causes the electric field direction to rotate, resulting in an elliptical wave. If the magnitude of the electric field of both the pand s-components are equal, the wave is said to be circularly polarized. In fact, any polarization can be considered as the sum of linearly polarized waves. Light’s polarization is of great practical importance as we will soon see. While non-laser sources typically produce light that is randomly polarized, many lasers produce linearly polarized light.

9.1 Lasers: Energy Transfer

287

Fig. 9.1 Definition of p- and s-polarization. Within the plane of incidence, defined as containing the surface normal and wave vector, .k, p-polarized light contains an electric field parallel to the plane on incidence. S-polarized light has an electric field perpendicular to the plane of incidence

9.1.2 Attenuation Regardless of polarization, when light is incident onto a substrate, the oscillation of electric field causes the electrons in a dielectric to vibrate. This motion causes both attenuation and a change in phase of the wave. Both effects can be modeled using a complex wave number: k˜ = kr − j k = β − j α

(9.3)

.

the real part of the complex wave number, .kr or .β, describes a change in the phase of the wave, while .ki or .α described the attenuation of the wave. This can be readily observed if we substitute .k˜ into Eq. (9.1): Ex (z, t) = E0 exp (j (ωt − z (β − j α))) = E0 exp (j (ωt − zβ)) exp (−αz). (9.4)

.

Exponential decay of the wave amplitude is therefore caused by .α, the attenuation coefficient, while the .β term affects the phase within the oscillating component of the wave. Calculation of the .α and .β terms is straightforward if the complex permittivity, .ϵ ˜ = ϵreal + ϵi , of the material is known    μϵreal ˜ .α = Re j k = ω 2 





˜ = ω μϵreal .β = Im j k 2

 1+  1+

ϵi

− 1.

(9.5)

ϵi + 1, ϵreal

(9.6)

ϵreal

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9 Source-Material Interactions

where .ω is the angular frequency of the wave .ω = 2πf = 2π c/λ. For dielectrics and non-magnetic metals, the permeability can be approximated as equal to the permeability of free space .μ = μ0 = 4π × 10−7 H/m. Electrons within a metal, unlike within an dielectric, are not strongly bound. Rather, they are free to flow between atoms within a “sea of electrons.” The mobility of electrons in this sea is characterized by the electrical conductivity, .σ . As such, for a metal, the attenuation and phase coefficients are functions of the electrical conductivity:    μϵ ˜ .α = Re j k = ω 2    μϵ ˜ .α = Im j k = ω 2

 1+

 σ 2 − 1. ωϵ

(9.7)

1+

 σ 2 + 1. ωϵ

(9.8)



For practical calculations, .α and .β for non-magnetic metals can be calculated assuming a permittivity approximately real and equal to the permittivity of free space, .μ ≈ μ0 . A term closely related to the attenuation coefficient is the skin depth, .δ. The skin depth is a measure of how far an electromagnetic wave penetrates into a material and is the point at which the electromagnetic field decays by a value of .1/e. That is, .E(δ, t) = E0 exp (j (ωt − δβ)) exp (−1). Thus, the skin depth is simply equal to .1/α. For most metals and optical and infrared wavelengths, the skin depth is on the order of tens of nanometers.   σ >> 1 around or below near-IR frequencies For very good conductors . ωϵ Eqs. (9.7) and (9.8) can be further approximated to  α=β=

.

ωμσ . 2

(9.9)

We now have a means of estimating the degree to which an electromagnetic field is absorbed into a material. However, this is not the same as estimating the attenuation of laser intensity! For one thing, while an electromagnetic field is measured in volts per meter, intensity is measured in watts per meters squared. It is therefore essential to not confuse the electromagnetic absorption coefficient, .α, with the optical absorption coefficient. To find the relationship between the electromagnetic and optical absorption coefficients, we must first relate the electromagnetic field strength (V/m) to its intensity (W/m.2 ). The relationship between intensity and the strength of electromagnetic field is defined by the time-averaged pointing vector

.

〈S〉 =

1 E02 , 2 η0

(9.10)

9.1 Lasers: Energy Transfer

289

where .η0 is known as the intrinsic impedance of free space .η0 = 120 π ohms. In laser optics, the time-averaged pointing vector defines the intensity of a laser beam in watts per square meters. So, if the electromagnetic field strength is defined by Eq. (9.4), then it’s intensity must be I (z) =

.

E02 exp (−2αz). 2η0

(9.11)

Note that in Eq. (9.11), the time terms have disappeared—remember, it’s the timeaveraged intensity—and we are left with a .2α exponential decay along the z direction. We can therefore state that the optical absorption coefficient equals .2α. Confusingly, it is not uncommon for various authors to use letter .α to denote the optical, rather than electromagnetic, absorption coefficient. Here, we will do our best to avoid this confusion by always denoting .2α as the optical absorption coefficient. It is also common to use a complex index of refraction .(n), ˜ rather than a wave number to describe a material’s optical characteristics n˜ = n + ikext ,

(9.12)

.

where n is the real part of the index of refraction and .kext is known as the extinction coefficient. The wave number is related to the index of refraction by 2π n˜ 2π n 2π kext ωn˜ = = +j . (9.13) k˜ = c λ λ λ σ  For very good conductors . ωϵ >> 1 and low frequencies (around or below nearIR), .

 Re (n) ˜ = Im (n) ˜ = n = kext = c

.

μσ 2ω

(9.14)

9.1.3 Reflection Use of the complex index of refraction is particularly useful in estimating reflection coefficients at the interface between two media, .n˜ 1 and .n˜ 2 . The optical reflection coefficients for s- and p-polarized light at an angle of incidence of .θi and angle of transmission of .θt are   2 2   2  n˜ 1 cos θi − n˜ 2 1 − n˜ 1 sin θi      n˜ 1 cos θi − n˜ 2 cos θt  n˜ 2    .Rs =    n˜ cos θ + n˜ cos θ  =  2   1 i 2 t  n˜ 1  n˜ 1 cos θi + n˜ 2 1 − n˜ sin θi  2

(9.15)

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9 Source-Material Interactions

Fig. 9.2 Reflection coefficients as a function of angle of incidence for laser wavelengths of 1070 nm and 10.6 .μm incident on a titanium substrate in air. Data is based on complex indexes of refraction reported by Ordal et al. [1]

2   2     2  n˜ 1 1 − n˜ 1 sin θi − n˜ 2 cos θi     n˜ 1 cos θt − n˜ 2 cos θi  n˜ 2    .Rp =    n˜ cos θ + n˜ cos θ  =     2 1 t 2 i    n˜ 1 1 − nn˜˜ 1 sin θi + n˜ 2 cos θi  2

(9.16)

Recall our previous discussion regarding the difference between electromagnetic and optical coefficients. Notice the squared term in both .Rs and .Rp equations. This is a consequence of these equations representing the optical coefficients. Representation of the electromagnetic coefficients would not include the square terms. As shown in Fig. 9.2, for the case of .n˜ 1 = 1, the s-polarized component of light experiences a minimum, while the p-polarized component does not. For randomly or circularly polarized light, the effective reflection coefficient is an average of s and p polarization and denoted as R. For normal incidence onto a very conductive metal at low frequencies, where .n ˜ 1 = 1 and .n˜ 2 = n, ˜ the equations simplify significantly:    1 − n˜ 2  . R =  1 + n˜ 

.

(9.17)

And given that in this case, both the real and imaginary components of the index of refraction are approximately equal:

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291

Fig. 9.3 Laser light incident on a powder bed experiences many reflections, resulting in an increase of the effective absorption coefficient [2]

 1 2 =1− .R = 1 − n c

8ω . μσ

(9.18)

This is termed the Hagen-Rubens relationship and roughly approximates the reflection coefficient for conductive metals at wavelengths longer than a few microns. So far, we have discussed bulk reflection and attenuation properties of metals. That is, we have ignored surface effects—of which there are many. Surface roughness results in many angle of incidence, effectively scattering the incident light and often resulting in a net increase in absorption. Surface oxides, with optical constants quite different than the underlying metal, can also result in an increase in light absorption. The absorption and attenuation coefficients are also significantly affected in the case where a laser is incident on a powder bed. As illustrated in Fig. 9.3, the laser is reflected into gaps between the powder particles resulting in multiple reflection and absorption events; thus, the size distribution of powder particles has a direct influence of the effective beam absorption and attenuation (Fig. 9.4).

292

9 Source-Material Interactions

Fig. 9.4 The effective absorption and attenuation coefficients of metal powder are a function of particle size. Adapted from [2]

9.1.3.1

Absorption

Any light not reflected by a metal is either absorbed or transmitted. Given that most metals have a skin depth less than tens of nanometers at visible and infrared wavelengths, transmission need not be considered for a substrate with a thickness greater than hundreds of nanometers. Effectively, the sum of the transmission and reflection coefficients is unity, .R + A = 1. As a first approximation, it may be convenient to assume that the absorption and attenuation coefficients are temperature-independent. In reality however, both are dependent upon the temperature and phase of the material. For most metals, as temperature increases, the absorption coefficient increases. This is consistent with the simplified Hagen-Rubens model, since the static electric conductivity of most metals is roughly inversely proportional √ to temperature (.σ ∝ 1/T ). Thus as electric conductivity decreases .A = 1 − R ∝ T . To simplify matters, it is not uncommon to assume an absorption coefficient which linearly increases with temperature: A(T ) = A0 + A1 (T − T0 )

.

(9.19)

Knowing the reflection coefficient and absorption coefficient enables calculation of absorbed energy at a given depth: Q (z) = I0 (1 − R)(2α) exp (−2αz).

.

(9.20)

It is important to note that we have assumed that light is represented by a plane electromagnetic wave with infinite extents perpendicular to the wave vector. This

9.2 Electron Beams: Energy Transfer

293

means that the incident light source must be infinite in the plane parallel to the substrate. Of course this is not possible. In reality however, the beam intensity will of course decay as a function of beam radius as discussed in Sect. 8.1.2.1. Nevertheless, assuming a region with an intensity of .I0 , the power density absorbed at a depth z can be calculated using Eq. (9.20). Note that .Q (z) is in watts per cubic meter; Q is ∞ often simply called the heat source. Note that that . 0 Q(z)dz = AI0 .

9.2 Electron Beams: Energy Transfer As discussed in Sect. 8.2.1.2, charges within an electron beam have a kinetic energy equal to the accelerating voltage within the e-beam gun, . 12 me v 2 = qe V . We may imagine these fast-moving electrons as seeing a substrate as being made up of many small nuclei around which there are somewhat bound electron clouds. Interactions between the e-beam and electron cloud may be elastic or inelastic. As illustrated in Fig. 9.5, elastic collisions lead to a change in direction (i.e., scattering) but do not affect the energy of the e-beam. In contract, inelastic collisions are those which reduce the kinetic energy of the e-beam electrons.

Fig. 9.5 Fast-moving electrons may be elastically or inelastically interact with matter. Elastic collisions may result in a change of direction, but not change of energy, while inelastic collisions affect both the energy and direction of the electron

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9 Source-Material Interactions

9.2.1 Elastic and Inelastic Collisions The probability of an elastic interaction is a function of the elastic scattering cross section, .σelastic (E). The elastic scattering cross section is a function of the incoming electron’s kinetic energy and the effective diameter of the atom with which it is interacting σelastic (E) ∝

.

π a02 , 2

(9.21)

where .a0 is an effective diameter that is proportional to the atomic number of the atom. Thus, unsurprisingly, large atoms with many orbiting electrons are more likely to scatter an electron beam. For e-beam processing, we are typically more interested in inelastic collisions. These are the collisions which result in thermalization of energy (i.e., heating) within the material. Inelastic collisions can involve a wide range of interactions, not all of which will immediately contribute to heating, including excitation of waves within the electron cloud (plasmon excitation), secondary electron generation, bremsstrahlung radiation (x-rays) generated due to deceleration of the e-beam, inner-shell ionization resulting in x-rays or Auger electrons, and excitation of lattice oscillations (phonon excitation). Possible e-beam interactions are sketched in Fig. 9.6.

Fig. 9.6 Electron beam scattering and thermalization processes

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295

Fig. 9.7 A semi-empherical model of e-beam interactions with an aluminum substrate. The energy dissipation volume of (a) single electrons and (b) an e-beam with a width of w. (c) The percentage of back-scatterred (.ηB ), transmitted (.ηT ), and absorbed (.ηA ) electrons as a function of depth (z). (d) The absorbed energy fraction (.EA /E0 ) from the incoming beam as a function of depth along with the rate of energy absorption (.d(EA /E0 )dz), also known as the depth-dose profile. Used with permission from [3]

9.2.1.1

Absorption

The sum of energy transferred from the e-beam via inelastic collisions, minus energy lost due to escaping electrons and radiation, heats the substrate. Collisions take place within an energy dissipation volume that is wider than the size of the incoming electron beam as a result of scattering. In a thin substrate, electrons may also be transmitted though the substrate. Of course the e-beam absorption, back-scattering, and transmission coefficients must sum to unity: .ηA + ηB + ηT = 1. However this simple relationship is complicated by the fact that back-scattered electrons may escape from some depth within the substrate, as illustrated in Fig. 9.7. Accounting for the total energy absorbed and the size of the energy dissipation volume is non-trivial and often requires simulation of many electron paths via Monte Carlo methods. Semi-empherical methods have however been developed and provide a reasonable model [3]. Such models assume a bulb-shaped interaction region, wherein electrons experience repeated inelastic and elastic interactions. Note that for materials with high atomic number, the shape compresses to a semi-circle due to more frequent interactions near the surface. Backscattering events within the depth of the material may result in escaping electrons until a saturation depth

296

9 Source-Material Interactions

Fig. 9.8 Depth-dosage curves for copper. Experimental data from [4, 5] are compared with semi-empherical model results of [3]. Used with permissions from [3]

is reached. This saturation depth is illustrated in Fig. 9.7c around a depth of 30 microns, upon which the fraction of backscattered electrons reaches a steady-state value of .ηB,0 . If the energy of back-scattered electrons reflected back from deeper layers are ignored, the fraction of absorbed electrons, and corresponding fraction of absorbed energy within a layer (.EA (z)/E0 ) at a depth of z can thus be approximated as [3]

 

EB,0 ET (z) EA (z) = 1 − ηB,0 . . 1 − ηT (z) E0 E0 E0

(9.22)

The derivative of Eq. (9.22) provides depth-dose profile for the material. This represents the rate of energy absorption as a function of depth. Notice that, as shown in Fig. 9.7, there is a point below the surface of the material at which the rate of energy absorption is maximized—this is quite different than for laser absorption, where energy is attenuated exponentially through the depth of the material. Interestingly, the depth-dose curve is significantly affected by the electron-beam’s angle of incidence, as illustrate in Fig. 9.8. This may have practical consequences for electron beam additive manufacturing where the beam is diverted at large angles to process large areas.

9.3 Arc: Energy Transfer During arc welding, electric power (current times voltage) is used to accelerate electrons and ions, resulting in plasma formation. As we discussed in Sect. 8.3, collision of the excited charged particles and neutral, along with radiation from the arc, onto the substrate results in significant heating and melting. The efficiency with

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297

which the electrical power, used to generate the arc (.P = I V ), is transferred to the substrate is depended on the configuration of the arc system (i.e., the arrangement of electrodes, method of wire feeding, type of shielding gas employed, etc.). Joule (i.e., ohmic or resistive) heating is the primary mechanism by which electrical energy is transferred to the arc. That is, repeated electron accelerations and collisions within the arc, due to the voltage difference between the cathode and anode, result in thermalization of the energy (i.e., random motion of the species within the plasma following Planck’s equation). The energy transfer mechanisms at the arc-substrate interface are numerous. Consider the simplest case of a TIG process with a negatively charged electrode and a positively charged substrate; the contributions to substrate (anode) heating are as follows: • Work function: Energy released by electrons condensing (i.e., entering the metal lattice) at the anode. • Electron drift (Thomson effect): Inelastic collisions between electrons moving toward the substrate due to a temperature gradient. • Anode potential drop: acceleration of electrons due to local electric potential near the surface of the anode. • Ion recombination: Energy lost to do ionization or gained due to ion recombination at the anode. • Conduction: Heat transfer due to a gradients in the temperatures of electrons and heavy particles (e.g., ions and neutrals). • Radiation: UV, visible, and IR emissions generated by plasma and absorbed by the substrate • Evaporation: Loss of energy at the anode due to material evaporation. Some of these processes are illustrated in Fig. 9.9.

Fig. 9.9 Heat transfer mechanisms within a TIG process

298

9 Source-Material Interactions

Fig. 9.10 Heat flux to an anode surface. Modeled for an atmospheric-pressure TIG process with at a current of 200 A and a argon mass flow of 0.2 g/s. Used with permission [6]

For a TIG process using a direct current and an electrode that is negatively charged—often referred to as a DCEN TIG process—electrons condensing at the anode are the greatest contributor to heating. Note that this flow is directly proportional to the electron current at the anode (electron-condensation heat flux .= Je We , where .Je is the flow of electrons normal to the anode surface). Modeled contributors to the heat flux on an anode surface for an atmospheric-pressure TIG process with at a current of 200 A and a argon mass flow of 0.2 g/s are illustrated in Fig. 9.10 [6]. Note that radiation and evaporation losses are ignored, as these are thought to account for only a few percent of the heat transfer. The total heat transferred to the substrate, .Qa , is thus [7] Qa = Qelec + Qcond + Qrad ,

.



5 kB Te Qelec = Je We + Va + + Ji (Ei − We ), 2 qe

.

Qcond = −ke

.

dTh dTe , − kh dz dz

(9.23) (9.24)

(9.25)

where .Qelec accounts for energy transferred by the flux of electrons (.Je ) and ions (.Ji ), .Qcond is conduction from electrons and heavy particles due to a gradients in the temperatures, and .Qrad is radiative heat transfer. The overall efficiency (.η) of substrate heating can be defined as the fraction of power transferred to the substrate over the total energy input into the arc (.Parc = I V ). That is, .η = Qa /Parc . It should be clear from the discussion thus far that transferred arc processes are generally more efficient than non-transferred processes. In non-transferred arc welding, energy is only transferred via thermal and radiative processes and doesn’t include energy transfer by a flux of charged particles. Modeling of the heat transference efficiency for a particular process is not easy; values are generally calculated via calorimetry. Rough efficiency for nontransferred plasma arc processes is on the order of 0.4–0.5; increased efficiency is observed with gas tungsten arc (.η = 0.6–0.7) and gas metal arc (.η = 0.8–0.9)

9.4 Heating and Melting

299

processes [8]. Note however that values vary significantly depending on the specific parameters used for processing. As indicated in Fig. 9.10, the heat flux reaching the substrate W/m.2 is usually assumed to be Gaussian. Note that the heat flux is analogous to the intensity distribution of a laser or electron beam source (Eq. (8.17)). The welding source heat flux can be modeled as

  VI r2 exp − 2 .q(x, y) = η (9.26) = q0 exp −Cr 2 , 2 2π reff reff where .reff is the effective radius of the arc. Both the efficiency .η and the effective radius .reff are depended on the composition of the arc, its geometry, and applied power [9]. It is also not uncommon in the arc welding literature to use a concentration coefficient, C, instead of an effective radius and to define .q0 as the amplitude of the heat flux. Interestingly, it is not typical to directly use this heat flux to model arc-based processes; rather, as will be discussed in forthcoming chapters, embedded points or volumetric heat sources provide better comparisons to experiments. This is partly due to rapid fluid motion within the melt, which rapidly transfers heat within the melt.

9.4 Heating and Melting Regardless of the process by which heating occurs, three regimes can be considered: heating, conduction-mode melting, and keyhole mode melting. These are illustrated in Fig. 9.11. At intensities on the order of .105 W/cm.2 and interactions time of tens to hundreds of milliseconds, most metals will experience little melting. Under these conditions, we can typically assume temperature-independent material properties (e.g., a constant laser absorption coefficient) and need not consider a phase change. In this case, we need only consider conduction within the material and assume simple boundary conditions: no convection, no heat loss due to thermal radiation, no mass loss through melt ejection, and constant pressure. Under these simplified conditions, determining the degree of heating within the material involves solving the heat equation.

Fig. 9.11 Heat transfer mechanisms within a TIG process

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9 Source-Material Interactions

Fig. 9.12 Phase transitions from lower to higher enthalpy

ρ(T )cP (T )

.

 dT (x, t) + νs ▽T (x, t) = ▽ (κ(T )▽T (x, t)) + Q(x, t), dt

(9.27)

where .ρ is the material density, .cp is the specific heat at constant pressure, .νs is the speed of the heat source across the surface of the substrate, .κ is the thermal conductivity, and Q is the rate of volumetric energy absorption into the substrate. Solutions to the heat equation will be discussed in Chap. 12. Once melting occurs, things quickly become more complicated, and we are now faced with a moving solid-liquid boundary and at least one phase transition. Phase transitions involve a change in the system’s enthalpy. For a system with a constant mass and pressure, the enthalpy represents the heat absorbed or released. As illustrated in Fig. 9.12, melting, vaporization, and plasma formation successively increase the enthalpy of a system. To melt a material, it must absorb energy at least equal to the enthalpy of fusion (i.e., latent heat of fusion), .LM , times the mass of the melt plus the energy required to raise the material’s temperature from room temperature to the melting point. The minimum power required to melt a volume V of material within an interaction time of .τ is thus   V ρcp (Tm − T0 ) + ρLM , (9.28) .Pmin = τA where .Tm is the melting temperature and A is the energy source’s absorption coefficient. At the melt-vapor interface, the application of a concentrated heat flux induces melting and vaporization. The vapor imparts a downward pressure on the liquid, often termed the recoil pressure. This downward force causes a divot in the surface of the melt and drives flow from the center to the edges of the pool. Additional melt flow is caused by Marangoni convection, which is a function of the gradient of the surface tension as function of temperature. If the velocity of the melt toward the pool edge is greater than the capillary pressure holding droplets to the edges of the melt pool, melt ejection will occur. Within the melt pool, the outward flow toward the edges of the pool together with buoyancy forces drives a current, as illustrated in Fig. 9.13. In transferred arc processing, electromagnetic forces caused by the current field and resulting magnetic effects also induce flow within the melt. As the intensity of the energy source increases, the vapor pressure can become so great that a deep vapor cavity forms within the melt (Fig. 9.14). This is known as keyhole mode or depression mode melting. The transition from conduction mode

9.4 Heating and Melting

301

Fig. 9.13 Melting, vaporization, and melt ejection during processing with an intense source

Fig. 9.14 Melting and vaporization in keyhole mode melting. A keyhole cavity is maintained by the pressure of the metal vapor evaporating from the front of the keyhole

to keyhole mode is somewhat nebulous. As already noted, a depression in the melt pool nearly always forms during melting. As the depression deepens, heat input into the part can no longer be considered as originating from a source at the surface of the substrate. Rather, it is more akin to a line or cylindrical source buried within the melt. Within the vapor cavity, a thermal plume, emanating from the front and bottom of the cavity, maintains the keyhole and transfers heat to the melt. In laser-based AM processes, the beam experiences multiple reflections within the keyhole. Absorption of the laser energy by the thermal plume via inverse Bremsstrahlung is also a significant contributor at IR wavelengths. Both factors lead to a rapid increases in the absorption coefficient with increasing laser intensity. Such an increase in absorption is illustrated in Fig. 9.15 [10]. Similarly, with electron beam sources, electrons reflected by the front of the keyhole can be reabsorbed, resulting in an increase in the beam absorption coefficient. Vaporization during electric arc AM

302

9 Source-Material Interactions

Fig. 9.15 Measured 316 L stainless steel plate (a) absorption vs laser power at a speed of 500 mm/s together with (b) and (c) cross-sectional discs measured with a scanning speed of 500 mm s1. (b) Cross sections of the tracks with the laser power listed below each track cross section. Linearly increasing (I), rapid transient (II), and saturation (III) regions of laser absorption are highlighted. Used with permission [10]

also forms a vapor depression; however it is rare for a deep keyhole to form owning to the lower peak intensity, relative to laser and e-beam processes. Regardless of the energy source, flows in molten pool lead to convective heat transfer within. The flows thus contribute to the depth and profile of AM deposits. Mechanisms which contribute to flow include [11]: • • • •

electromagnetic forces and arc pressure, evaporation, surface tension (Marangoni convention), and buoyancy.

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303

9.4.1 Electromagnetic Forces and Arc Pressure Electromagnetic forces are important in electric arcs. This is a consequence of the Lorentz force Eq. (8.39), which rewritten in terms of the charge density, .ρe , and current density, J , is expressed as F = ρe E + (J × μH) .

.

(9.29)

In the case of arc welding, the magnetic field is self-induced by the arc. In the case of transferred arc welding, where current flows between the substrate and an electrode, much of the current flow is along the axis normal to the substrate, .Jz . This axial current induces an azimuthal magnetic field, .Hθ . The interaction of .Hθ with the axial and radial components of the current density, .Jz and .Jr , applies forces on the melt. A radial, squeezing force results from .Jz × μHθ , while a downward force results from .Jr × μHθ . Modeling of the resulting convection within the melt pool forces is quite complex [12–14] and indicates that electromagnetic forces play a key role in convection within the melt and significantly affect the size and shape of the resulting melt pool. Another consequence of electromagnetic forces in arc processes is on confinement and direction of gas flow within the arc. Just as a Lorentz force is applied directly to the melt as a consequence of the electric current-induced magnetic field, a Lorentz force also affects the arc. In the case of transferred arc welding, where the substrate is the anode, the Lorentz force pinches and constrains the arc. As explained by Lin and Eagar [15], a pressure builds up within the arc to balance the constraining effect of the Lorentz force, .J × μH. Due to the higher current density at the cathode, a pressure difference will then form between the cathode and the substrate. This effect is illustrated in Fig. 9.16. The result is a flow within the arc toward the surface of the melt and an effective static pressure distribution at the surface of the melt [15, 16]: Parc

.



−r 2 μ0 I 2 exp = . 2 2 2reff 4π 2 reff

(9.30)

Arc pressure is a also a function of the gas nozzle geometry along with the geometry and location of the electrode and/or filler material. Nozzle restrictions, present in plasma arc welding (see Fig. 8.26), can lead to flow velocities on the order of hundreds of meters per second. This leads to a significant arc pressure at the surface of the melt. The location of the electrode, relative to the substrate, also influences arc pressure. In the case of a consumable electrode in a transferred process, the distance between the electrode and substrate fluctuates as the consumable electrode melts and feeds into the melt. This results in fluctuation in arc length, the current density, and thus the pressure induced by the arc. Processes which utilize a non-consumable electrode together with a filler wire can also experience fluctuations in arc pressure due to current flow between the electrode and the filler wire.

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9 Source-Material Interactions

Fig. 9.16 An illustration of forces affecting the arc and melt in transferred arc processes

In arc processes, gas flow toward and above the melt can be on the order of hundreds of meters per second. This flow is thought to result in a hydrodynamic drag force on the surface of the melt. This drag force induces a shear stress on the surface of melt, directing it from the center toward the sides of the pool. It has been argued that this drag force, particularly in cases where the arc length is long, can lead to an increase in convection within the melt and the formation of a shallow center with accompanying deep side lobes [11, 17].

9.4.2 Evaporation Melt flows are also caused by the pressure gradient across the weld, resulting from vaporization at surface of the melt. When a heat source is used for melting, vaporization always takes place. The dynamic vapor pressure, which is often termed the recoil pressure, .pr , is the pressure, above the atmospheric pressure, exerted on the surface of the melt as a result of vaporization. Estimation of the recoil pressure is possible by relating it to the saturation vapor pressure. The saturation vapor pressure, .psat , is defined as the pressure exerted by evaporating gases within a closed container. It is a function of temperature as defined by the ClausiusClapeyron relationship

Psat = P0 exp

.

 U U , − T TB

(9.31)

9.4 Heating and Melting

305

a Lv where .P0 is the ambient pressure, .TB is the boiling temperature, and .U = M Na kB . Here, .Ma is the atomic mass of the vapor, .La is the latent heat of vaporization, .Na is the Avogadro constant (.6.02214 × 1023 mol.−1 ), and .kB is the Boltzmann constant. It should be noted that in many formulations, U is expressed as . LRv , where .Lv is the latent heat of vaporization expressed in joules per mol and R is the gas constant J (.≈ 8.314 Kmol ). The Clausius-Clapeyron relationship however is generally not as accurate as more empirical formulations. In part, this is because a constant, rather than temperature-dependent, heat of vaporization is assumed within the equation. More empirical formulations append fitting coefficients within the Clausius-Clapeyron relationship. For instance, Semak and Matsunawa [18] report the recoil pressure as

Pr = APsat (T ) = AB0

.

exp (−U/T ) , √ T

(9.32)

where A and .B0 are experimentally determined constants and T is the temperature at the surface of the melt. Anisimov and Khokhlov [19] approximate the recoil pressure for the cases where the surface temperature is close to the boiling point as exp (−U/T ) Pr = 0.56Psat = 0.56  . TBoiling

.

(9.33)

In the case of laser and electron beam processing, the role of recoil pressure is quite significant. The vapor pressure significantly contributes to the depressions in the top surface of the melt. The depression formed by vaporization along with flows within the melt are shown for conduction- and keyhole mode melting in Figs. 9.17 and 9.18 [20]. As shown in Fig. 9.18 [20], in keyhole mode melting, a deep vapor depression is maintained, and significant flow is present along the walls of the keyhole. Near the keyhole, significant material flows from the walls from the walls of vapor cavity to the edges of the melt. Assuming a uniform intensity distribution at the surface of a liquid, we can use the Bernoulli equation to relate the recoil pressure to the speed of the displaced liquid [18]: pr =

.

2 ρm vm . 2

(9.34)

In keyhole mode melting, vaporization primary occurs at the front of the keyhole, where the laser interacts with the melt. The front of the keyhole is thus subject to rapid evaporation and runaway instabilities. At some translation speeds, local instabilities can result in the formation of “humps” in the keyhole walls, leading to a significant asymmetry in the keyhole geometry [21]. Such runaway instabilities along with any other processes which causes rapid closure of the keyhole (i.e., keyhole collapse) can lead to the trapping of vapor bubbles within the melt. When

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9 Source-Material Interactions

Fig. 9.17 X-ray imaging and flow description in conduction-mode laser melting. Used with permission [20]

trapped bubbles do not rise and break the surface of the melt, they remain in the solidified material as spherical pores (i.e., keyhole-induced porosity). Rapidly vaporization also induces drag forces on the surface of the melt. This effect is similar to that observed in arc welding, where a fast vapor/plasma flow induces a shear stress on the surface of melt, directing it from the center toward the sides of the pool. In laser-based processes, the velocity of the vapor/plasma flow is approximately an order of magnitude less than that observed in arc processes; nevertheless, the density within the vapor is likely much higher than in an arc, possibly resulting in a comparable drag force on the melt [11]. Within a keyhole, drag forces may also significantly contribute to melt flow along its surface.

9.4.3 Surface Tensions (Marangoni Convention) Marangoni convection describes the motion of a fluid along a boundary due to a surface tension gradient. At a liquid-gas interface, surface tension, .γ (N/m), drives liquids to minimize their surface area. This is due to the cohesion of liquid molecules

9.4 Heating and Melting

307

Fig. 9.18 X-ray imaging and flow description in keyhole mode laser melting. Used with permission [20]

to one another being stronger than the adhesion of the liquid to the gas. For most dγ liquids, as temperature increases, the surface tension decreases: . dT < 0. Within a pool of liquid where the surface tension decreases with temperature, material will be pulled from the hot toward the cold regions. Sometimes, this is termed thermo-capillary convection, though Marangoni convection is the more popular description. In fusion AM processes, where the center of the melt pool is the hottest region, Marangoni convection thus drives a radial flow of the melt toward dγ the pool edges. This is of course assuming that . dT < 0. dγ Under some conditions, the assumption that . dT < 0 is however not valid. Surface-activated elements such as sulfur in steels can reverse the trend, causing dγ . dT > 0. This causes flow from the edges of the pool toward its center. Such flows can lead to an increase in melt pool depth. Some common AM alloys, such as nickel alloy 718, also exhibit a transition from a positive to a negative slope of surface tension with increasing temperature. In laser-based directed energy deposition AM of nickel alloy 718, it has been proposed that this effect leads to a change in fusion zone geometry with increasing laser power [22]—see Fig. 9.19.

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9 Source-Material Interactions

Fig. 9.19 Surface tension as a function of temperature curve for nickel alloy 718 and resulting Marangoni flow together with fusion zone profiles for laser-based DED AM using (a) low power and high speed, (b) medium power and medium speed, and (c) high power and low speed. Used with permission from [22]

Another phenomena related to surface tension is the agglomeration of melt at the edges of the pool. As illustrated in Figs. 9.14 and 9.16, flow at the surface of the pool can lead to protuberance at the edge of the pool with a radius of curvature equal to .Rm . The protuberance is held within the melt pool by a capillary pressure equal to .γ /Rm pressure. In laser welding, the interplay between recoil pressure and surface tension leads to oscillations within the pool [23]. And in cases where the dynamic pressure of the melt exceeds surface tension, .

2 ρm vm γ > , Rm 2

(9.35)

melt ejection occurs. Modeling and simulation results, carried out by Ly et al. [24], demonstrating melt ejection during a laser powder bed fusion process are shown in Fig. 9.20.

9.4.4 Buoyancy Buoyancy is yet another mechanism which contributes to flows within the melt. As with any liquid within which a density gradient exists, denser regions will tend to sink, while less dense regions will rise. In a melt, density variations are a result of the temperature increase above the melting point, .ρ = ρ0 (1 − β(T − Tm )), where .ρ0 is the density at the melting temperature .Tm and .β is the liquid volumetric thermal

9.4 Heating and Melting

309

Fig. 9.20 Experimental (a)–(c) and simulation (d)–(g) results of laser-based powder bed fusion AM atop a bare stainless steel 316 L plate. A protuberance at the edge of the pool forms then escapes as a spherical ejecta. Used with permission from [24]

expansion coefficient (m3 /m3 K). Thus, the buoyancy body force (per unit volume) within the melt is FB = ρgβ (T − Tm ) ,

.

(9.36)

where g is the standard gravitational acceleration (.≈9.8 m/s.2 ) and T is the temperate above the melting point. The contribution of buoyancy within the melt is however though to be minor in arc welding [13, 25] and laser or e-beam processes with small melt pools [11].

9.4.5 Plasma Interactions We have already discussed plasma in the context of AM processes utilizing electric arcs—see Sect. 8.3.1. Plasma interactions should also be considered in laser-based AM. In laser-based processes, plasma interactions may lead to energy absorption, scattering, and heat transfer to the substrate via re-radiation and collisions between excited species and the substrate [26–29]. This is particularly important for processes utilizing CO2 lasers at powers on the order of kilowatts.

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9 Source-Material Interactions

The degree to which a plasma interacts with laser light varies according to the laser and plasma properties. Plasma consist of charged particles interacting collectively via long-range coulomb forces. To assess the degree to which interactions are likely, we must first define some key plasma parameters. Assuming a plasma with a maximum degree of ionization of one, the distance over which coulomb forces influence other charges is the Debye Length, .λD .

λD =

.

ϵ0 k B Te ne qe2

1/2 (9.37)

.

where .Te is the electron temperature in Kelvin, .n0 = ne = ni is electron and ion density (plasma density), .kB is the Boltzmann constant, .qe is an electron’s charge, and .ϵ0 is the permittivity of free space. The Debye length defines the region over which a local charge perturbation will be shielded; that is, for a distance greater than the Debye length, the plasma is electrically neutral. We should note that this definition is, at best, a rough approximation which doesn’t account for temperature differences between electron, ions, and excited species. A second critical plasma parameter is the plasma frequency, .ωp . The plasma frequency is related to the thermal velocity of electrons, .ve , and the Debye length by ωp =

.

ve = λD



n0 qe2 ϵ0 m e

1/2 ,

(9.38)

where .me is the electron mass and .n0 is the plasma density. Since charge neutrality is typically assumed, the plasma density is equal to the electron density which is equal to the ion density, .n0 = ne = ni . If an electric field causes an electron to be displaced from its ideal shielded location, neighboring electrons will adjust to shield this nonequilibrium field. The resulting oscillations describe the plasma frequency, .ωp . If an incident electromagnetic field propagates at a frequency less than the plasma frequency, electrons can quickly adjust, and the wave decays within a distance on the order of the electromagnetic skin depth, .δ c , δ= 2 ωp − ω2

.

(9.39)

where c is the speed of light and .ω is the angular frequency of incident electromagnetic field. Laser light (i.e., an electromagnetic field) with a frequency greater than the plasma frequency may pass though the plasma. But as the frequency of the laser approaches that of the plasma, the light absorption will increase. For electromagnetic fields with a frequency below the plasma frequency, most of the electromagnetic energy is absorbed at the outer skin of the plasma—much like a metal.

9.4 Heating and Melting

311

Plasma can be formed near the focal point of a laser beam via three mechanism. The first is photoionization, wherein a neutral, A, absorbs a single photon with an energy (.hν) exceeding the neutral’s ionization energy (ionization potential): hν + A → e− + A+ .

.

To photoionization say a titanium atom (first-degree ionization energy of 6.83 eV), a wavelength less than 182 nm would be required. So, photoionization alone is not a likely mechanism to produce plasma. Another improbable means to achieve ionization is through multiphoton absorption. This mechanism allows ionization via simultaneous absorption of two or more photons with a combined energy exceeding the neutral’s ionization potential Nhν + A → e− + A+ ,

.

where N is the required number of photons necessary to a exceed the ionization energy. To ionize a ground-state titanium atom using a 1070 nm wavelength laser would require simultaneous absorption of 6 photons. This is possible but highly unlikely to occur. The third mechanism by which breakdown can occur at IR and optical frequencies is cascade (i.e., avalanche), breakdown. Here, free electrons accelerated by a laser’s electromagnetic field, .e−∗ , collide with neutrals resulting in ionization and a doubling of the number free electrons: e−∗ + A → 2e− + A+ .

.

Inelastic collisions between neutrals and electrons, accelerated by the laser’s electromagnetic field through inverse bremsstrahlung absorption, hν + e− + A → e−∗ + A,

.

continue to produce more electrons until a sufficient density of ions is achieved. At this point, the plasma is heated through the more efficient [30] electron-ion inverse bremsstrahlung process hν + e− + A+ → e−∗ + A+ ,

.

resulting in a sharp increase in the degree of ionization and sustainment of the plasma [31]. Cascade breakdown is the most likely mechanism for plasma formation in laserbased AM processes. At a sufficient laser intensity, plasma forms primary in the vaporizing metal. In the presence of a substrate, as is always the case in fusion AM process, plasma formation is more likely due to a number of possible mechanisms [31–33]:

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9 Source-Material Interactions

• Vaporization results in a partially ionized, dense metal vapor above the melt pool. • Free electrons are released from the melt due to thermionic emissions. • Reflection from substrate result in a local increase in electric field, reducing the ionization threshold. The presence of surface defects or thermally isolated regions can also reduce the threshold for plasma formation—though these are likely to only play a role at the beginning of laser tracks. A final possible means for plasma formation at low intensities, which is not typically discussed, are interactions between the laser beam and thermally isolated spatter and powder particles suspended above the melt. If generated and sustained, plasma will absorb laser light via the inverse bremsstrahlung effect. The optical inverse bremsstrahlung absorption coefficient, .αI B , at IR frequencies is [34] αI B =

.

3.1 × 10−7 Zn2e ln Λ 3/2 ω 2 Te

1−

1 ωp2 ω2

1/2 ,

(9.40)

where all units are in practical cgs units. .Te is the electron temperature in electron volts, Z (set equal to one for first-degree ionization) is the ionic charge, .ne is the electron density in .cm−3 , .ωp is the laser’s angular frequency (.2π ν), .ωp is the 3/2 plasma frequency, and .ln Λ ≈ 23 − ln(ne2 ZTe ) [35] is the coulomb logarithm for electron-ion collision under most conditions of interest. In applying Eq. (9.40) appropriately, it is imperative to use the cgs units noted above. Unfortunately, there is a paucity of research addressing laser-materials interactions at and above the melt pool for laser-based AM processes. Nevertheless, the laser-processing literature suggests a potentially strong influence of laser-plume and plume-melt interactions. Plume interactions have been shown to play a dominate role in CO.2 laser welding of steels [36, 37] and titanium [37]. Plume parameters have also been used to monitor weld quality [38, 39]. Plume has also been shown to significantly participate in the energy-transfer during laser-nitriding processes [29]. That being said, most of the works on the influence of plasma plume utilize a CO2 laser, rather than the more common fiber lasers used in metal AM. Inverse bremsstrahlung absorption is inversely proportional to the square of the frequency of radiation (Eq. (9.40)). Therefore, one should expect absorption to be about two orders of magnitude less with a Fiber or Nd:YAG laser (.λ ≈ 1 micron), as compared with CO2 laser (10.6 .μm). There is however evidence that in laserbased AM of metals, even when using laser sources emitting near 1 .μm and laser intensities as low as .105 W/cm2 , plumes of significant size can occur. High-speed images captured during single-track (a, b) and multi-track, multi-layer AM (c) deposition of Ti-6Al-4V, using a ytterbium-doped fiber laser (1.07 .μm wavelength), are shown in Fig. 9.21 [40]. It has also been observed that size and shape of the fluctuating plume vary in both DED [40, 41] and PBF processes [42, 43]. Rough order of magnitude values for the temperature and density within a laser-produced plasma are .Te ≈1 eV and .n0 =1016 cm-3 [26–28, 42, 44]. The reader may have

9.5 Summary

313

Fig. 9.21 High-speed imaging of a directed energy deposition. (a), (b) Representative image of AM of a Ti-6Al-4V single track with using a powder flow rate of 3 g/s, a laser power of 450 W and processing speeds of (b) 7.94 mm/s and (c) 10.58 mm/s. (c) A transient plume and (d) associated optical emission spectra observed during AM of a Ti-6Al-4V block using a 2 g/min flow rate and 425 W. (b) and (c) adapted with permission from [40]

noticed that we have used “plume” and “plasma” interchangeably. The degree of ionization within the plume can sometimes be a contentious issue—as such, many authors use the term “plume” rather than plasma to indicate that they have not proven that significant free electrons and ionization exists.

9.5 Summary In this chapter we explored foundational concepts related to source-materials interactions and resulting effects of heating, melting, and vaporization. In particular we considers laser, electron beam, and electric arc sources. The degree of laser light reflection and absorption can be estimated given the beam polarization and the optical properties of the matter with which it is interacting. Namely, the complex index of refraction is used to define both reflection at the surface and beam attenuation within. An electron beam’s interaction with a substrate drastically differs from laser beam absorption. Electron accelerated within the beam may either

314

9 Source-Material Interactions

elastically or inelastically collide within the substrate. Inelastic collision leads to energy thermalization and heating within the material. Electric arcs present yet another set of transfer mechanisms. Heating of the substrate is achieved through a combination of electron interactions, heavy particle interactions, and radiation. Whichever source is considered, the particular configuration and properties of each significantly affect the types and degrees of interactions. In fusion AM processes, sources are used to heat and melt the substrate and feedstock material. At sufficiently high source intensities, melting occurs. The surface and shape of the melt are dependent on present electromagnetic forces, evaporation, surface tension, and buoyancy. Under high laser and electron beam intensities, deep vapor cavities are observed in the melt. This transition to keyhole mode melting is accompanied by a sharp increase in process efficiency but may also lead to instabilities within the melt. Plume or plasma formation may also occur during laser processing at high intensities, particularly when utilizing long wavelength lasers. Plumes-laser interactions may affect energy transfer to the melt. The details discussed here provide a simplified framework for understanding the many phenomena and possible interactions in fusion AM processes.

9.6 Questions and Discussions 1. What effect does laser wavelength have on a material’s reflection coefficient? How does one approximate the reflection coefficient for a metal with a known complex index or refraction? 2. Are electron beam reflections more or less likely in aluminum than in a steel substrate? Why or why not? 3. Consider an AM process wherein a vapor depression is formed in the melt. (a) Explain the mechanism where by which such a depression may form? (b) If we assume that the laser interacts with the front edge of the keyhole, forming an angle of incidence of θ , what is the resulting effect on the beam absorption and reflection coefficient? (c) Is keyhole mode melting more or less likely to occur with arc-based processes? 4. What are the key processes which contribute to melt flow in fusion AM processes? 5. Under what conditions is melt ejection likely to occur? What are possible consequences of melt ejection? 6. How might plasma plumes form in laser-based processes?

References

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References 1. Ordal MA, Bell RJ, Alexander RW, Newquist LA, Querry M (1988) Optical properties of Al, Fe, Ti, Ta, W, and Mo at submillimeter wavelengths. Appl Opt 27(6):1203–1209 2. McVey RW, Melnychuck RM, Todd JA, Martukanitz RP (2007) Absorption of laser irradiation in a porous powder layer. J Laser Appl 19(4):214–224 3. Klassen A, Bauereiß A, Körner C (2014) Modelling of electron beam absorption in complex geometries. J Phys D Appl Phys 47(6):065307 4. Cosslett VE, Thomas RN (1965) Multiple scattering of 5–30 keV electrons in evaporated metal films III: Backscattering and absorption. Br J Appl Phys 16:779–796 5. Lockwood GL, Ruggles LE, Miller GH, Halbleib JA (1987) Calorimetric measurment of electron energy deposition in extended media—theory vs experiment. In: Sandia Report SAND79-0414, Sandia National Laboratories 6. Amakawa T, Jenista J, Heberlein J, Pfender E (1998) Anode-boundary-layer behaviour in a transferred high-intensity arc. J Phys D Appl Phys 31(20):2826–2834 7. Choi HK, Gauvin WH (1982) Operating Characteristics and Energy Distribution in Transferred Plasma Arc Systems. Plasma Chem Plasma Process 2(4):361–386 8. Dupont JN, Marder AR (1995) Thermal efficiency of arc welding processes. Welding Research Supplement 74(12):406s–416–s 9. Tsai NS, Eagar TW (1985) Distribution of the heat and current fluxes in gas tungsten arcs. Metall. Trans. B 16(4):841–846 10. Trapp J, Rubenchik AM, Guss G, Matthews M (2017) In situ absorptivity measurements of metallic powders during laser powder-bed fusion additive manufacturing. Appl. Mater. Today 9:341–349 11. Matsunawa A (2002) Science of laser welding—Mechanisms of keyhole and pool dynamics. In Proceedings of ICALEO 2002, p 290, Phoenix AZ 12. Kou S, Wang Y (1986) Computer simulation of convection in moving arc weld pools. Metall Trans A 17:2271–2277 13. Kumar A, DebRoy T (2003) Calculation of three-dimensional electromagnetic force field during arc welding. J Appl Phys 94:1267–1277 14. Nemchinsky VA (1996) The distribution of the electromagnetic force in a welding pool. J Phys D Appl Phys 2:2659–2663 15. Lin ML, Eagar TW (1986) Pressures produced by gas tungsten arcs. Metall Trans. B 17(3):601–607 16. Cao Z, Yang Z, Chen XL (2004) Three-Dimensional Simulation of Transient GMA Weld Pool with Free Surface. Weld J 83:169–s 17. Matsunawa A, Shinichiro Y, Yutaka A (1988) Convection in weld pool and its effect on penetration shape in stationary arc welds. Q. J. Jpn. Weld. Soc. 6(4):455–462 18. Semak V, Matsunawa A (1997) The role of recoil pressure in energy balance during laser materials processing. J Phys D Appl Phys 30(18):2541 19. Anisimov SI, Khokhlov VA (1995) Instabilities in laser-matter interaction. CRC Press, Boca Raton 20. Guo Q, Zhao C, Qu M, Xiong L, Hojjatzadeh MSH, Escano LI, Parab ND, Fezzaa K, Sun T, Chen L (2020) In-situ full-field mapping of melt flow dynamics in laser metal additive manufacturing. Addit Manuf 31:100939 21. Matsunawa A, Semak V (1997) The simulation of front keyhole wall dynamics during laser welding. J Phys D Appl Phys 30(5):798–809 22. Kistler NA, Nassar AR, Reutzel EW, Corbin DJ, Beese AM (2017) Effect of directed energy deposition processing parameters on laser deposited Inconel ® 718: External morphology. J Laser Appl 29:022005 23. Semak VV, Hopkins JA, McCay MH, McCay TD (1995) Melt pool dynamics during laser welding. J Phys D Appl Phys 28(12):2443–2450

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24. Ly S, Rubenchik AM, Khairallah SA, Guss G, Matthews MJ (2017) Metal vapor micro-jet controls material redistribution in laser powder bed fusion additive manufacturing. Sci Rep 7(1):4085 25. Tanaka M (2004) An introduction to physical phenomena in arc welding processes. Weld Int 18(11):845–851 26. Pirri AN, Root RG, Wu PKS (1978) Plasma energy transfer to metal surfaces irradiated by pulsed lasers. AIAA J 16(12):1296–1304 27. Rockstroh TJ, Mazumder J (1987) Spectroscopic studies of plasma during cw laser materials interaction. J Appl Phys 61(3):917–923 28. Mo´scicki T, Hoffman J, Szyma´nski Z (2006) Modelling of plasma plume induced during laser welding. J Phys D Appl Phys 39(4):685–692 29. Nassar AR, Akarapu R, Copley SM, Todd JA (2012) Investigations of laser-sustained plasma and its role in laser nitriding of titanium. J Phys D Appl Phys 45(18):185401 30. Raizer YP (1991) Gas discharge physics. Springer, Berlin 31. Hermann J, Boulmer-Leborgne C., Mihailescu IN, Dubreuil B (1993) Multistage plasma initiation process by pulsed CO< inf> 2 laser irradiation of a Ti sample in an ambient gas (He, Ar, or N< inf> 2). J Appl Phys 73(3):1091–1099 32. Bäuerle D (2011) Laser processing and chemistry. Springer, Berlin 33. Arzuov MI, Barchukov AI, Bunkin FV, Konov VI, Prokhorov AM (1975) Self-maintenance of a continuous optical discharge in gases near solid targets. Sov J Quantum Electron 5(5):523– 525 34. Johnston TW (1973) Correct values for high-frequency power absorption by inverse bremsstrahlung in plasmas. Phys Fluids 16(5):722 35. Huba JD (2004) NRL: plasma formulary. Technical report, DTIC Document, Virginia 36. Ancona A, Spagnolo V, Lugara PM, Ferrara M (2001) Optical sensor for real-time monitoring of CO2 laser welding process. Appl Opt 40(33):6019–6025 37. Szymanski Z, Kurzyna J, Kalita W (1997) The spectroscopy of the plasma plume induced during laser welding of stainless steel and titanium. J Phys D Appl Phys 30(22):3153 38. Sibillano T, Ancona A, Rizzi D, Mezzapesa F, Konuk AR, Aarts R, Huis in ’t Veld B, Lugarà PM (2012) Spectroscopic closed loop control of penetration depth in laser beam welding process, pp. 82390S–82390S–8 39. Collur MM, DebRoy T (1989) Emission spectroscopy of plasma during laser welding of AISI 201 stainless steel. Metall Mater Trans B 20(2):277–286 40. Stutzman CB, Nassar AR, Reutzel EW (2018) Multi-sensor investigations of optical emissions and their relations to directed energy deposition processes and quality. Addit Manuf 21:333– 339 41. Nassar AR, Starr B, Reutzel EW (2015) Process monitoring of directed-energy deposition of Inconel-718 via plume imaging. In: Proceedings of the Solid Freeform Fabrication Symposium, pp. 284–294. Austin, TX 42. Bidare P, Bitharas I, Ward RM, Attallah MM, Moore AJ (2018) Fluid and particle dynamics in laser powder bed fusion. Acta Mater 142:107–120 43. Nassar AR, Gundermann MA, Reutzel EW, Guerrier P, Krane MH, Weldon MJ (2019) Formation processes for large ejecta and interactions with melt pool formation in powder bed fusion additive manufacturing. Sci Rep 9:5038 44. Akarapu R, Nassar AR, Copley SM, Todd JA (2009) Numerical model of a laser-sustained argon plasma. J Laser Appl 21:169

Chapter 10

Feedstock Delivery and Dynamics

Feedstock characteristics are of utmost importance to resulting chemistry, microstructure, and mechanical properties of an AM part. After all, it is the melted and solidified feedstock that comprises the AM material. Metal powders are the most commonly used in fusion AM DED and PBF processes. Wire feedstocks are also frequently used in wide area AM processes, where high deposition rate are favored. This chapter focuses on feedstock behavior and interactions in AM fusion processes. We introduce the topic by first providing a brief discussion of powder properties; a more detailed discussion is provided in Chap. 14. Next, details of powder dynamics within powder bed fusion and directed energy deposition processes are provided. Finally, we deal with wire characteristics and transfer modes commonly observed with wire-fed processes.

10.1 Powder Feedstock In both DED and PBF processes, powder feedstocks characteristics and delivery influence the resulting AM component geometry, density, thermal history, and microstructure. However, the question of how a particular powder property is linked to final component characteristics or even how powder properties influence feedstock delivery is very difficult to answer. We cannot hope to begin to answer these questions without first uncovering key powder properties. Common Production Methods Specific powder characteristics are functions of the constituent materials and production method, along with environmental variables. Many powder production methods exist. Low-cost production methods include mechanical milling, water atomization, and chemistry-based reduction or precipitation. These methods, while

© Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_10

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low-cost, also produce highly irregular powder particles. Unfortunately, DED and PBF processes require powders that either flow or spread easily and consistently. For metal AM, the most popular powder production methods are gas atomization and plasma rotating electrode process (PREP). Of the two, gas atomization produces a wider range of particle sizes but is also generally less expensive and is commercially used to produce a wide range of alloys. In contrast, PREP powders are more expensive but are generally more spherical and have higher purity. PREP powders can also be produced with a smaller range of particle sizes; diameters ranging between one to a few hundreds microns are typical. In gas atomization, molten metal flows through a small diameter orifice. Highpressure gas impinges on the flow generating fine droplets. Depending on material reactivity, either nitrogen or argon gas is commonly employed. Droplet size, and hence the resulting particle size, can be based on process variables, including nozzle geometry, gas and melt flow rates, and chamber pressure. The PREP process utilizes an electric arc between a non-consumable tungsten electrode and a rotating, consumable electrode. As the rotating, consumable electrode melts, small molten droplets are dispersed due to the centrifugal force. Variants of the PREP process utilize an electron beam or laser to melt the tip of the rotating consumable metal. These and other centrifugal processes produce larger powders than atomization processes with a narrow size distribution and are often used to produce very spherical, reactive powders (e.g., titanium alloys) for DED processes.

10.1.1 Powder Characteristics In AM production environment, strict powder sampling and analysis procedures must be followed. Recommended powder sampling procedures, as specified in [1], are used to capture a representative sample of powder. This is particularly important given that many powder measurements utilize very small fraction of feedstock. Powder increments are collected from across the available feedstock, blended, and a representative, composite sample is collected.

10.1.1.1

Specific Powder Properties

The characteristics of a powder can either refer to specific or bulk properties. Specific properties, such as those shown in Fig. 10.1, refer to measurable properties that can be attributed to individual powder particles. Such properties include powder chemistry, constituent phases, shape, and size. Individual powder particles within a lot will be within ranges of these properties. As such, one typically refers to the distributional of a given property. For instance, particle size distribution is measured for a representative quantity of powder.

10.1 Powder Feedstock

319

Fig. 10.1 Some measurable, specific properties of powder particles

Particle size distribution (PSD) is nearly always sought for AM powders. Standard methods for determining PSD include sieve analysis [2] and light scattering [3]. In sieve analysis, a set of sieves are stacked, with the sieves arranged from those having the largest opening to those having the smallest. Next, the collection of sieves is placed in a shaker for some time (on the order of 15 min), and, finally, the weight fractions of powder between each set of sieves are measured. Laser light scattering methods are based on Fraunhofer diffraction and/or Mie scattering assuming spherical particles dispersed in a fluid. For nonspherical powders, the size should be interpreted as an effective radius. Metal powders rarely contain perfectly spherical particles. Possible particle shapes are near infinite and difficult to define quantitative—few standards exist defining powder morphology or shape. Inspection and classification of particle shape are generally based on inspection using optical or scanning electron microscopes (SEM). It should be clear that such measurements are based on a twodimensional projected image of a particle. Measurements of the projected diameter, its relationship to an effective diameter, and classifications of particle shape are little changed from when originally proposed in the early twentieth century [4]. In addition, particles can also be classified based on their circularity, how closely they approximate a circle; convexity, a measure of the a particle’s surface roughness; and elongation, the ratio of a particles width to its length [5]. Similar to particle morphology, analysis of particles microstructure is conducted using microscopy. An SEM equipped with an energy-dispersive x-ray spectroscopy (EDX) can also be used to estimate individual particle chemistry. Systems recently available from RJ Lee Group enable automated SEM and EDX measurements of large numbers of individual particles. This provides both an estimate of the PSD and ranges for particle morphology and chemistry. More typically, bulk chemistry is assessed using inductively coupled plasma mass spectrometry or inductively coupled plasma atomic emission spectroscopy. Measurement of porosity within individual powder particles also relies on imaging techniques. Cross sections of powder particles can be obtained via embedding in a mounting medium followed by grinding and polishing. Recently, high-resolution x-ray computed tomography of powder particles has become practical for mea-

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10 Feedstock Delivery and Dynamics

Fig. 10.2 Some measurable properties of bulk powder

surement of external morphology and internal pores [6]. If pores are not surface connected, gas pycnometry can also be used to measure absolute volume of a collection of particles. Given a known particle size distribution and the theoretical density, the percentage of trapped pores within the powder can be estimated.

10.1.1.2

Bulk Powder Properties

Specific powder properties contribute to bulk properties, many of which are provided in Fig. 10.2. Because bulk properties are a function of all specific particles as well as their interactions, determining bulk behavior based on specific properties is nontrivial and rarely attempted for real powders. To complicate matters further, powder properties are also a function of handling and storage. In particular, moisture can dramatically influence surface properties and chemistry. This can significantly degrade powder flowability. Electrostatic charging is also a potentially dangerous consequence of improper handling. In both PBF and DED processes, powder flowability, in addition to powder chemistry and particle size distribution, is perhaps the most critical factor in determining the suitability of a feedstock. Hall flow measurements of powder flow [7] provide an indication of flowability. Powders which do not flow well (i.e., take a long time to flow or fail to start flowing once the funnel orifice is unblocked) are unlikely to produce a consistent flow using commercially available DED powder feeders or to spread well during PBF recoating [8]. Another practically consequential measurement, particularly for powder bed processes, is powder density. Both apparent and tap density are significant. Apparent powder density—the density of loose packed powder—can be measured in conjugation with hall flow rate [7]. Tap density is based on the compaction of powder by tapping a container until no further increase in density is observed [9].

10.1 Powder Feedstock

321

Fig. 10.3 Powder consolidation in PBFAM

10.1.2 Powder Dynamics in Powder Bed Fusion 10.1.2.1

Densification

The volume occupied by a fully dense solid is less than that occupied by a powder, whether the powder is loosely packed (as measured by its apparent density) or packed (as measured by its tap density). Consequently, a recoated powder layer with a thickness of .ΔZpowder , once melted, will produce a solidified, fully dense layer of height .ΔZsolid . This is illustrated in Fig. 10.3. It then follows that .ΔZpowder > ΔZsolid . One important consequences of this phenomena is that the so-called charge percentage, defined as the thickness of powder applied over the build plate relative to the set layer thickness, must always be greater than 100%. On most laser PBFAM systems, the charge percentage is controlled by the upward motion of the powder supply platform. If the surface areas of the build and powder supply platforms are equal, the charge amount is defined as the upward, incremental motion of the supply platform relative to the downward, incremental motion of the build platform over a layer. An insufficient charge percentage results in short feeding, wherein a portion of the build plate is left bare or with a thickness less than the set layer thickness. To avoid the possibility of short feeding, builds containing components with large cross-sectional areas, relative to the total build plate area, are typically provided a charge percentage on the order of 200% or greater. It should be apparent that a second consequence of densification is that the solidified layer thickness is not necessarily equal to the set layer thickness. In fact, the solidified layer thickness will likely oscillate from layer to layer. Additional phenomena, discussed later in this chapter, complicate the simple model presented

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10 Feedstock Delivery and Dynamics

Fig. 10.4 Powder denudation zone (referred to as “zone of powder consolidation”) observed in single-track laser PBFAM depositions [10]

in Fig. 10.3: denudation and entrainment of powder near the melt pool; spatter and melt ejection; and, losses via spillover, unintended suction of powder into gas recirculation systems and charging (i.e., “smoking”) effects in electron beam PBF.

10.1.2.2

Denudation

In PBFAM single-track depositions, powder-free region next to solidified track boundaries have long been observed [10]—see Fig. 10.4. This phenomenon is a consequence of entertainment within a gas flow driven by evaporation at the surface of the melt [11, 12]. The evaporation caused by the source-melt interaction (see Sect. 9.4.2) results in a strong jet of metal vapor flowing outward, normal to the melt surface. The vapor flow also induces a gas flow along (i.e., parallel to) the powder bed, which entrains surrounding powder [12, 13] as illustrated in Fig. 10.6. Powder surrounding the melt is thus dragged into the vapor flow. A portion of powder particles are subsumed within the melt, while some particles are ejected upward. Among the ejected particles, some cross the path of the laser beam and are melted or vaporized, some are heated by the metal vapor plume, and still others are ejected with little heating. Gas flow perpendicular to the powder bed results in drag (i.e., frictional) forces on individual powder particles which drives denudation. The drag force on a spherical particle can be used to roughly model denudation [13]. According to Stokes law, drag on a small sphere, of radius R, within a fluid, with a dynamic viscosity of .η, and a fluid speed of .vrel relative to the particle is Fd = 6π ηRvrel .

.

(10.1)

10.1 Powder Feedstock

323

Fig. 10.5 Flow past a spherical particle

This simplified model is illustrated in Fig. 10.5. If we equate the force required to accelerate a sphere to the drag force, we find that 4 dvrel ρp π R 3 = 6π(vg − vp )ηR, 3 dt

.

(10.2)

where .ρp is the particle density and .vrel = (vg − vp ) is the relative velocity of the gas flow. Assuming a constant gas velocity, .vg , we find that 

 2ρp R 2 t .vp − vg = C exp − , τ= , τ 9η

(10.3)

where C is a constant. Equation (10.3) may be interpreted to mean that given sufficient time (.t >> τ ), where .τ is the entrainment time, the relative velocity of the particle will approach the gas velocity, resulting in a relative gas velocity of zero. Solving explicitly for the particle velocity, and applying an initial condition of .vp (t = 0) = 0 (i.e., an initially stationary particle), we find that    t .vp = vg . 1 − exp − τ

(10.4)

Of course, this simple model is incomplete. Particles within the powder bed are not fully immersed in the gas flow. Rather they are held, by gravity, within the powder bed and will resist the gas flow-induced drag through friction with the substrate and neighboring particles in the powder bed.

10.1.2.3

Spatter

Spatter is commonly observed in powder bed fusion processes. We have already discussed one mechanism for spatter: melt ejection. As discussed in Sect. 9.4, melt

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10 Feedstock Delivery and Dynamics

Fig. 10.6 Powder denudation is a result of vaporization-induced gas flow, resulting in subsumed particles as well as cold and hot ejecta, as described by Ly et al. [13]

ejection occurs when the dynamic pressure within the melt exceeds surface tension, resulting in detachment of droplets from the melt pool. Melt ejection tends to generate ejected melt droplets on the order 25–100 microns in diameter [13]. Entrained powder particles are a second mechanism for spatter formation. As shown in Fig. 10.6, a portion of entrained particles, which are not subsumed in the melt, are ejected. Many of these particles appear hot or molten [13, 14]. These entrained particles have a size distribution representative of the feedstock powder. The pressure within the processing chamber strongly impacts the size and shape of the vapor plume and hence the degree and envelope of powder entertainment [14]. Random, inelastic collision of powder particles mid-air and on the surface of the powder and parts have been observed to result in spatter particles much larger than the feedstock [15]. Such collisions not only occur between two neighboring entrained particle, but also between ejecta generated from distant location. Coalescence of partially sintered spatter particles by the vapor plume has also been observed [15]. In electron beam processes, charging of the powder bed can also lead to spatter generation. Due to a native oxide surface layer surrounding metal powder and gaps between individual particles, the conductivity of the powder is much lower than bulk metal. Without proper grounding, the powder bed becomes negatively charged when subjected to stream of electrons (i.e., an electron beam). Under e-beam processing, powder thus becomes charged and particles repel one another, leading to spatter formation—this phenomenon is commonly termed “smoking.” Several methods are used to reduce the potential for spatter formation in electron beam PBF: grounding

10.1 Powder Feedstock

325

of the powder bed, increasing the conductivity of the powder bed by heating it to a temperatures (on the order of several hundred degrees Celsius), and sintering the powder bed using a low beam current prior to selectively melting each layer [16–18]. Interactions between spatter generated during powder bed fusion processes can significantly affect the process. Large spatter particles have been observed to perturb the melt pool geometry and have been hypothesized to be responsible for a portion of seemingly random (i.e., random or rogue) lack-of-fusion defects in otherwise dense components [15]. Mid-air interactions between ejected particles and the laser beam can also lead to attenuation of energy arriving to the melt below, essentially shadowing or blocking the laser beam [15].

10.1.3 Powder Dynamics in Directed Energy Deposition Powder-blown directed energy deposition relies on the introduction of gas-fluidized powder into a liquid melt. Gas fluidization is the process of using a, typically inert, gas, like argon, to carry and direct powder from a powder feeder to a deposition head, equipped with one or more nozzles—see Fig. 10.7. Of course, given the need for a gas fluidization, powder-blown DED is typically limited to use with laser or arc sources. In both cases, the source forms a melt, within which the powder is fed. The source also heats, and in some processes melts, the powder as it is directed toward the melt.

Fig. 10.7 Two variations of powder-blown DED deposition heads: a four-nozzle powder blown and a coaxial deposition head. Both variants direct gas-fluidized powder toward a melt pool

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10 Feedstock Delivery and Dynamics

Fig. 10.8 DED powder flow characteristics. Key variables which affect the DED process include the powder envelope, relative locations of the laser and powder focus, and relative location of the substrate

Multiple nozzles (i.e., discontinuous coaxial) and cylindrical nozzles (i.e., continuous coaxial), illustrated in Fig. 10.7, enable additive manufacturing independent of the in-plane translation direction of the substrate relative to the deposition head. This is in contrast to off-axis, non-concentric nozzles, which direct powder ahead on the melt pool and are rarely used for additive manufacturing. The powder flow profile exiting the deposition head strongly affects the DED process. Key characteristics, as shown in Fig. 10.8, include the overall powder mass flow rate and powder envelope profile, particularly the location and size of the powder flow envelope at focus and at the substrate. Note that the tip of the flow nozzles is typically used as reference point. On many DED systems, the stand-off positions of the powder focus and laser focus, relative to the nozzle tip, are fixed or rarely adjusted. Currently, there are no standard rules regarding the appropriate position of the laser or powder focus, relative to the substrate position. While some operators place the laser focus and/or powder focus at the substrate, many do not. Further it is important to appreciate the effect of the substrate on powder scattering. The total amount of powder consolidated into a deposited track—the powder capture efficiency—is a function of the powder density, the melt pool size, and the powder temperature; the latter two variables are influenced by heating and scattering of the laser beam within the powder flow envelope.

10.1 Powder Feedstock

10.1.3.1

327

Powder Flow Stream

The powder flow envelope (i.e., structure) from the coaxial nozzle forms consists of three regimes: converging, focus, and diverging. Powder exiting the nozzle converges, driven by pressurized carrier gas, toward a focal point. The structure of the converging flow is influenced by the nozzle geometry, carrier gas flow rate, and the powder mass flow rate, along with the flow of the coaxial gas flow. Additional spreading of the powder occurs due to particle collisions and gravity. Many of these effects have been modeled and experimentally verified [19–24]. At the focus of the powder flow, the density of particle is most concentrated. Here, a Gaussian distribution of powder particles is generally assumed and has been experimentally verified [20]. The powder concentration, in terms of particles per area, at the powder focal point is thus NP articles (r) = N0 exp

.

−2r 2 , ω2

(10.5)

 where .r = x 2 + y 2 is the distance from the z axis, along which the powder travels and .ω0 represents the .1/e2 radius of the powder stream at the focal point. The maximum concentration of the powder is .N0 . Similar to a Gaussian laser intensity distribution, the maximum, .N0 , can be rewritten in terms of the total number of total particles, .Ntotal , .N0 = 2N . An illustration of experimentally measured powder π ω2 flow distribution near the powder focus is provided in Fig. 10.9.

Fig. 10.9 Gaussian Powder Flow Distribution measured on an Optomec LENS MR-7 system equipped with four symmetric nozzles. Data adapted from [25]

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10 Feedstock Delivery and Dynamics

Fig. 10.10 Three dimensional reconstruction of powder flow incident onto a flat substrate. Data adapted from [25]

The powder flow stream, and the powder distribution within, can be experimentally verified using illumination of a plane through the powder stream together with an imaging system. An early implementation of such a system utilized broadband illumination together with a cylindrical optic [20]. More recent implementations utilize laser lines and high-speed imaging systems and enable three-dimensional profiling of the particle distribution within the stream [25]. The substrate distance also strongly influences the distribution and shape of the powder stream [26]. The local geometry of the substrate (e.g., a flat versus a thinwalled structure) also strongly impacts the shape and distribution within the powder stream [24]. As shown in Fig. 10.10, the local substrate results in powder scattering back toward the laser beam.

10.1.3.2

Source-Powder Interactions

Powder-source interactions play a key role in the energy transfer to the melt. In the case of a laser source, laser power to the substrate is attenuated by the powder particles through absorption and reflection. However, not all attenuated energy is lost. Heated particles, which become consolidated into the solidified track, return some energy back to the melt. Modeling of the source-powder-substrate interactions is non-trivial. Using simplifying assumptions, such as a sparse density of powders, where one particle does not shadow any other particle, analytical [27] models have been developed. More complex, three-dimensional numerical models, which include powder heating, phase changes [28], and substrate interactions [29], show that laser beam attenuation

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329

increases with the powder mass flow rate and the powder concentration. For conditions typical of laser-based, powder-blown DED processes, attenuation is generally on the order of 15–25% [28]. However, for very low powder to gas flow rate volume (on the order of 1:1000), the beam can be assumed to not be attenuated by the powder [30]. Powder-blown DED systems can also utilize arc sources. While not widely used for AM of complex structures, these powder-blown arc-based processes (e.g., plasma transferred arc processing, plasma cladding, plasma spraying) have been used for several decades for wide-area cladding of surfaces, often using hard-facing materials [31]. Interactions between the arc and powder stream lead to significant heating and melting of the powder as it travels toward the substrate. In essence, the result is the spattering of partially to fully molten droplets against a heated or molten substrate.

10.1.3.3

Powder Catchment Efficiency

Ultimately, powder which is consumed by the melt forms the solidified track. The percentage of powder which is consumed divided by the total amount of powder exiting the deposition head is the powder capture efficiency. The capture efficiency (i.e., catchment efficiency or the fraction of entrapped powder) is calculated by dividing the mass of a deposit by the mass of blown powder used to form it. In the case of laser-based processes, early investigations [30] showed that the powder captured in the melt is a function of the size of the melt pool and the powder flow rate. In particular the melt pool width relative to the powder stream diameter strongly influences the capture efficiency. For many processes, capture efficiencies on the order of 25% are typical. However, using a powder stream diameter approximately twice the melt width can increase capture efficiency to .∼ 80% [32]. With a tightly focused powder stream, such that the stream diameter is on the order of the melt pool width, the efficiency can approach 1 [32]. Arc-based, powder-blown processes also, generally, exhibit high capture efficiency, exceeding 70% [33].

10.2 Wire Feedstock While catchment efficiency for powder-blown process is variable, wire-based DED systems have the advantage of full incorporation of the feedstock into the melt. Control of the wire feed rate drives the mass of material injected into the melt. As discussed in Sect. 8.3.1, various wire feeding arrangements are possible with arc-based processes. Metal arc welding (GMAW or MIG) use the feed wire as a consumable electrode, typically inserted coaxial to the deposition head. In contrast, gas tungsten arc welding (GTAW or TIG) and plasma arc welding (PAW) utilize an off-axis wire feed into the front of side of the melt pool. Similarly laser and

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10 Feedstock Delivery and Dynamics

Fig. 10.11 Cast is the approximate diameter of an unrolled length of wire removed from a spool when placed on a flat surface. Helix is the vertical distance separating the ends of the wire

electron beam systems typically use an off-axis wire feeder. Note that coaxial wire feed systems are also gaining popularity for use with a laser source. Such system rely on a arrangement of lasers beams coaxial to the wire or optical manipulation of the laser to form a ring around the wire.

10.2.1 Wire Characteristics Critical to any wire feed process is the precise positioning and introduction of wire into the melt. Commercial wire feeders can be adjusted to specify a wire feed geometry and for feedback-controlled wire speeds. A practical concern is dithering of the wire between the feeder and the melt pool. As such, wires are typically straightened as they are fed. The cast and helix of the wire, defined graphically in Fig. 10.11, influence the feeding accuracy and precision. As such, in addition to wire diameter, wire feeding systems specify limits on wire cast and helix.

10.2.2 Wire Transfer Modes Wire is introduced into the melt via several transfer modes. While researchers differ on the terminology used in defining these modes [34, 35], metal transfer is generally categorized as contact or free-flight transfer. Contact transfer, also categorized by some as bridging transfer, involves intermittent or continuous contact between the wire and the molten pool. In contrast, in free-flight transfer, the wire melts and is conveyed to the melt via droplets or a spray. Within each category, numerous transfer modes are possible, as illustrated in Fig. 10.12. Metal transfer within the GMAW processes, which utilize a consumable electrode, is sensitive to the wire material, diameter, feed rate, shielding gas, processing voltage, current, and induced electromagnetic forces and may exhibit any of the modes illustrated in Fig. 10.12. Transfer of material to the melt is thus influenced by the externally applied feeding forces on the wire, electromagnetic forces, gravity, and surface tension. These forces also influence metal transfer in GTAW processes. However, the decoupling of arc formation from the wire feed system somewhat

10.3 Summary

331

Fig. 10.12 Metal transfer modes in gas metal arc processing. Based on classifications proposed by Iordachescu and Quintino [34] and Scotti [35]

simplifies metal transfer. Primary transfer modes in GTAW include globular and full or partial bridging transfer. These are also the primary transfer modes in laser and electron-beam processing. The temperature and feed profile of the wire can also be customized to control the sizes of deposited material and the depth of the melt pool. Hot-wire systems resistively heat the wire via a current flow. Such system require closed circuit between the wire and the substrate; full or partial bridging transfer is thus required. Hot-wire systems enable high-rate deposition with reduced requirements on the input source power. Cold metal transfer can also be employed for low-speed deposition of individual droplets. Such systems utilize precise feeding and retraction of the wire; once a short circuit is detected, the wire is retracted, and the weld is allowed to cool.

10.3 Summary In this chapter we covered key characteristics of powders and wires in the context of metal fusion AM. Powder and wire properties must be considered in any AM process, regardless of the utilized heat source. In particular, powder flowability and spreadability are key quality indicators for powder-blown and powder bed processes, respectively. Both, together with the energy source properties, strongly impact the complex melt-powder-source interactions. Wire-fed processes also involve complex interactions and metal transfer modes, which are sensitive to processing conditions. Successful application of powder or wire-based AM processes requires characterization and control of the feedstock properties and its delivery to the melt.

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10.4 Questions and Discussions 1. Consider a laser PBFAM process wherein a set layer thickness of t is specified. Assume that the recoater and build platform surface areas both equal A. If the powder tap density is ρp and the solid bulk density is ρs , what is the minimum theoretical charge percentage as a function of build cross-sectional area, relative to the total build platform area? 2. Identify key specific and bulk properties of powder feed stock? How might each property affect a powder-blown DED process? How might each property affect a powder bed process? 3. Describe the catchment efficiency for powder-blown and wire-fed DED processes. 4. What are the key metal transfer modes in wire-fed arc AM?

References 1. ASTM International (2015) ASTM B215-15—Standard Practices for Sampling Metal Powders. Standard ASTM B215-15, West Conshohocken, PA 2. B09 Committee (2016) Test Method for Sieve Analysis of Metal Powders. Technical report, ASTM International, New York 3. B09 Committee (2017) Test Method for Particle Size Distribution of Metal Powders and Related Compounds by Light Scattering. Technical report, ASTM International, New York 4. Heywood H (1937) Numerical definitions of particle size and shape. J Soc Chem Ind 56(7):149–154 5. Nouri A, Sola A (2018) Metal particle shape: a practical perspective. Met Powder Rep 73(5):276–282 6. Bernier F, Tahara R, Gendron M (2018) Additive manufacturing powder feedstock characterization using X-ray tomography. Met Powder Rep 73(3):158–162 7. B09 Committee (2020) Test Methods for Flow Rate of Metal Powders Using the Hall Flowmeter Funnel. Standard, ASTM International, Pennsylvania 8. Snow Z, Martukanitz R, Joshi S (2019) On the development of powder spreadability metrics and feedstock requirements for powder bed fusion additive manufacturing. Addit Manuf 28:78–86 9. B09 Committee (2015) Test Method for Tap Density of Metal Powders and Compounds. Standard, ASTM International, Pennsylvania 10. Yadroitsev I, Gusarov AV, Yadroitsava I, Smurov I (2010) Single track formation in selective laser melting of metal powders. J Mater Process Technol 210(12):1624–1631 11. Khairallah SA, Anderson AT, Rubenchik A, King WE (2016) Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater 108:36–45 12. Matthews MJ, Guss G, Khairallah SA, Rubenchik AM, Depond PJ, King WE (2016) Denudation of metal powder layers in laser powder bed fusion processes. Acta Mater 114:33– 42 13. Ly S, Rubenchik AM, Khairallah SA, Guss G, Matthews MJ (2017) Metal vapor micro-jet controls material redistribution in laser powder bed fusion additive manufacturing. Sci Rep 7(1):4085 14. Guo Q, Zhao C, Escano LI, Young Z, Xiong L, Fezzaa K, Everhart W, Brown B, Sun T, Chen L (2018) Transient dynamics of powder spattering in laser powder bed fusion additive

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manufacturing process revealed by in-situ high-speed high-energy x-ray imaging. Acta Mater 151:169–180 15. Nassar AR, Gundermann MA, Reutzel EW, Guerrier P, Krane MH, Weldon MJ (2019) Formation processes for large ejecta and interactions with melt pool formation in powder bed fusion additive manufacturing. Sci Rep 9:5038 16. Sigl M, Lutzmann S, Zaeh MF (2006) Transient physical effects in electron beam sintering. In: Solid Freeform Fabrication Symposium Proceedings, vol 17, pp 397–405 17. Kahnert M, Lutzmann S, Zäh MF (2007) Layer formations in electron beam sintering. In: Solid Freeform Fabrication Symposium Proceedings, vol 18 18. Cordero ZC, Meyer HM, Nandwana P, Dehoff RR (2017) Powder bed charging during electronbeam additive manufacturing. Acta Mater 124:437–445 19. Lin J (2000) Numerical simulation of the focused powder streams in coaxial laser cladding. J Mater Process Technol 105(1):17–23 20. Lin J, Steen WM (1998) Design characteristics and development of a nozzle for coaxial laser cladding. J Laser Appl 10(2):10 21. Balu P, Leggett P, Kovacevic R (2012) Parametric study on a coaxial multi-material powder flow in laser-based powder deposition process. J Mater Process Technol 212(7):1598–1610 22. Kovaleva I, Kovalev O, Zaitsev A, Smurov I (2013) Numerical simulation and comparison of powder jet profiles for different types of coaxial nozzles in direct material deposition. Phys Procedia 41:870–872 23. Pan H, Liou F (2005) Numerical simulation of metallic powder flow in a coaxial nozzle for the laser aided deposition process. J Mater Process Technol 168(2):230–244 24. Zekovic S, Dwivedi R, Kovacevic R (2007) Numerical simulation and experimental investigation of gas—powder flow from radially symmetrical nozzles in laser-based direct metal deposition. Int J Mach Tools Manuf 47(1):112–123 25. Nassar AR, Reutzel EW, Brown SW, Morgan JP, Morgan JP, Natale DJ, Tutwiler RL, Feck DP, Banks JC (2016) Sensing for directed energy deposition and powder bed fusion additive manufacturing at Penn State University. In: Gu B, Helvajian H, Piqué A, (eds) Proceedings of the SPIE 9738, Laser 3D Manufacturing III, p 97380R 26. Ibarra-Medina J, Pinkerton AJ (2011) Numerical investigation of powder heating in coaxial laser metal deposition. Surf Eng 27(10):754–761 27. Liu J, Li L, Zhang Y, Xie X (2005) Attenuation of laser power of a focused Gaussian beam during interaction between a laser and powder in coaxial laser cladding. J Phys D Appl Phys 38(10):1546–1550 28. He X, Mazumder J (2007) Transport phenomena during direct metal deposition. J Appl Phys 101(5):053113 29. Ibarra-Medina J, Pinkerton AJ (2010) A CFD model of the laser, coaxial powder stream and substrate interaction in laser cladding. Phys Procedia 5:337–346 30. Powell J (1983) Laser Cladding. Ph.D., University of London, London 31. Diaz VV, Dutra JC, D’Oliveira ASCM (2012) Hardfacing by plasma transfer arc process. Weld Int 26(2):87–95 32. Lin J (1999) A simple model of powder catchment in coaxial laser cladding. Opt Laser Technol 31(3):233–238 33. Hardfacing, weld cladding, and dissimilar metal joining. In: Olson DL, Siewert TA, Liu S, Edwards GR (eds) Welding, Brazing and Soldering, pp 789–829. ASM International, New York (1993) 34. Iordachescu D, Quintino L (2008) Steps toward a new classification of metal transfer in gas metal arc welding. J Mater Process Technol202(1–3):391–397 35. Scotti A (2012) A scientific application oriented classification for metal transfer modes in GMA welding. J Mater Process Technol 212(6):1406–1413

Chapter 11

Mechanical Response

The heating and cooling cycles generated by the heat source in metal AM can generate residual stress and distortion. Residual stresses in combination with stress concentrations or defects, such as voids or inclusions, can lead to cracking for certain materials. Support structures are often used to restrict distortion of the part; however, they may lead to increased residual stresses and support structure failure.

11.1 Thermal Expansion and Contraction, Plasticity, Distortion Residual stress and distortion in metal AM is caused by the localized heating at the melt/sintering region resulting in thermal expansion which is restricted by the surrounding colder material. This causes plasticity formation which upon cooling manifests as residual stress and distortion. The three-bar analog, often used to exemplify the formation of residual stress and distortion in welding, is also applicable to metal AM. Figure 11.1, [1] illustrates three bars connected at both ends by rigid blocks. The middle bar represents the area under the localized heating to melt the metal, while the other two bars represent the surrounding cooler metal. Before the heat source is applied, all bars have the same temperature and zero stress (Fig. 11.1a). During heating and melting, the middle bar thermally expands due to the elevated temperature (Fig. 11.1b). Since the rigid blocks connect all bars, the expansion of the middle bar pulls the cold bars into tension resulting in compressive stresses in middle bar. The elevated temperature and partial melting of the middle bar results in reduced yield strength and thus compressive plastic deformation. Upon cooling, all bars return to the same temperature. If the middle bar was not connected to the end blocks (Fig. 11.1c), it would be shorter after cooling due to the negative plastic deformation. However, since the middle bar is connected to the end blocks (Fig. 11.1d), its contraction © Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_11

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Fig. 11.1 Three-bar analogy for formation of thermomechanical distortion [2]. (a) Room temperature. (b) Heated middle bar. (c) Return to room temperature, middle bar not connected. (d) Return to room temperature, middle bar connected. (With permission from ASM International)

compresses the side bars into compression resulting in contraction (distortion) of the three-bar assembly. Repeated heating and cooling cycles occur during metal AM in different regions of the part resulting in complex residual stress and distortion patterns. As discussed further in Sect. 12.4, finite element analysis can be used to provide an insight or predict the residual stress and distortion in metal AM.

11.2 Residual Stress and Cracking Residual stresses in metal AM tend to be high, often near the yield stress of the material. Depending on the material ductility; the formation of defects, such as voids caused by either lack of fusion or keyholing; and the part geometry, the residual stress may result into cracking as illustrated in Fig. 11.2. AM of titanium alloys is typically prone to cracking, especially for large and bulky parts.

11.3 Support Structures for Mechanical Response and Their Potential Failure Support structures can be used to reduce part deformation during AM and thus minimize post process distortion. However, the supports need to be sufficiently strong to support the stresses that are developed during manufacturing. For example, in the part shown in Fig. 11.3, support structures are used below the flange of the part. As shown in the figure, the part/support interface failed during processing resulting in excessive distortion.

References

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Fig. 11.2 Cracking in metal AM

Fig. 11.3 Support structure failure

11.4 Questions and Discussions 1. What is the three-bar analogy for formation of thermomechanical distortion? 2. What is the purpose of mechanical support structures?

References 1. Michaleris P (2011) Introduction to welding residual stress and distortion. In: Minimization of Welding Distortion and Buckling, pp 3–22. Elsevier, Amsterdam 2. Michaleris P (2011) Welding fundamentals and processes, vol 6A, chapter. Thermomechanical Effects of Fusion Welding, pp 146–151. ASM International, Materials Park

Chapter 12

Analytical Models

Analytical models for the simulation of temperature evolution in metal AM are based on the Rosenthal solution [1] of a point source moving on an infinite half space with a constant speed, which was originally developed for welding. Currently, there are no analytical models for mechanical effects in metal AM.

12.1 Rosenthal Solution for Semi-Infinite Space As shown in Fig. 12.1, for a fixed reference frame .(x, y, z) attached to the semiinfinite solid, and a reference frame .(x1 , y1 , z1 ) attached to a heat source moving along the x axis, the distance traveled is .ξ = vt. As derived by Rosenthal in Ref. [1], for temperature-independent material properties, the steady-state temperature T solution is q −vξ 1 −vR e 2α e 2α 4π k R q 1 −vR e 2α T (x, y, z) = T0 + 4π k R

T (x, y, z) = T0 +

.

for ξ > 0.

(12.1)

for ξ < 0

(12.2)

where .T0 is the initial temperature, q is the heat source power, R is the distance of point .(x, y, z) from the moving source, k is the thermal conductivity, and .α = k/CP is the thermal diffusivity, with .CP the specific heat. The Rosenthal solution is simple and easy to compute as compared to computationally expensive numerical methods such as finite element analysis (FEA) or finite difference (FD) methods. The limitations of the Rosenthal solution are as follows:

© Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_12

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Fig. 12.1 Reference frame for Rosenthal moving point source solution [2] (With permission from ASME)

• It assumes constant material properties with respect to temperature. • It only accounts for the steady portion of the moving source. The addition of the transient component of the solution is presented in [2–4]. • It assumes constant power at constant speed. • It assumes a semi-infinite part. • It results into infinite temperatures at the heat source location.

12.2 The Method of Images and Virtual Heat Sources Rosenthal in [1] also derived the steady-state solution of a moving point source in a solid bounded by planes using the method of images or mirrors. For example, as illustrated in Fig. 12.2, to account for a plate of finite thickness d instead of a semiinfinite space, a mirrored heat source can be applied to a depth .−d below the actual plate. The application of the mirrored heat results in an adiabatic boundary condition at the bottom of the actual plate, meaning that there is no heat transfer along the n direction, which is equivalent to a plate of finite thickness d. The method of images can also be used to extend the Rosenthal solution into simulating more complex geometries. For example, Li et al. [2] used two additional mirrors to simulate the AM of a single bead wall of width w on a substrate of thickness d as illustrated in Fig. 12.3. Similarly to using images or mirror heat sources to account for geometries bounded by planes, virtual heat sources can be used to account for finite length heat sources. As illustrated in Fig. 12.4, a negative heat source can be used starting at point B to account for that the real heat source is turned off. Similarly multiple real and virtual heat sources can be used to simulate the AM of a single bead wall as shown in Fig. 12.5.

12.2 The Method of Images and Virtual Heat Sources

341

Fig. 12.2 Illustration of a mirrored heat source to account for a plate thickness d [2] (With permission from ASME)

Fig. 12.3 Illustration of mirrored heat sources to account for wall of width w [2] (With permission from ASME)

Fig. 12.4 Illustration of virtual heat source to account for heating turned off [2] (With permission from ASME)

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Fig. 12.5 Illustration of virtual heat sources to account stacking several layers of heating lines [2] (With permission from ASME)

12.3 Eager and Tsai Gaussian Heat Source Model As seen from Eqs. (12.1) and (12.2), the temperature T becomes infinite at the point source location (.R = 0) which is caused by assuming a point heat source rather than a distributed one. To alleviate this limitation, Eagar and Tsai developed a Gaussian distributed moving heat source model based on the Rosenthal solution [5].

12.4 Computational Models Computational methods can account for nonlinear material response, complex geometry, and mechanical effects in metal AM. Similarly to analytical, the computational methods for metal AM have their origins in welding. However, as demonstrated in [6] since in AM most of the analysis domain is added metal rather than base plate, AM imposes additional requirements such as consistent material activation and numerical complexity. Figure 12.6 illustrates the typical analysis flow of thermomechanical analysis for AM. Starting with the process parameters (heat source spot size, power, travel speed, hatch spacing, layer thickness, etc.), a heat transfer analysis is required to compute the temperature history during the process. Depending on the material, the temperature history can be used as input to microstructural analysis to compute resulting material composition, morphology, and material properties. Then, the temperature history and mechanical properties are used in a mechanical analysis to compute stress and deformation. As shown in Fig. 12.6, the thermal, microstructural, and mechanical analysis can be coupled. For example, if support structures fail during the process, the heat transfer is affected resulting in coupling of the thermal and mechanical analyses.

12.4 Computational Models

343

Fig. 12.6 Outline of thermomechanical modeling [7] (With permission from ASME)

12.4.1 Heat Conduction Neglecting transport and assuming a Lagrangian (stationary) reference frame, the energy balance results in the following expression: ρCp

.

∂T = ∇ · (k∇T ) + Q ∂t

(12.3)

where .ρ is the mass density, .Cp is the constant pressure-specific heat, T is the temperature field, .t is time, .k is the temperature-dependent thermal conductivity, and .Q is the volumetric internal heat generation rate. The initial condition for the heat transfer problem is an initial temperature field .T = T0 at an initial time .t = t0 throughout the volume V of the part. The boundary conditions consist of prescribed temperatures .Tp and prescribed surface heat fluxes .qp , on two disjoint surfaces .

T = Tp

on surface ST for all t.

(12.4)

−k∇T · n = qp

on surface Sq for all t

(12.5)

where .n is the unit free surfaces. The two surfaces .ST and .Sq satisfy normal vector to the relations .ST Sq = S and .ST Sq = ∅. Surface radiation .qrad is applied to the prescribed surface heat flux as follows:   qrad = εσ Ts 4 − T∞ 4

.

(12.6)

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where .ε is the surface emissivity, .σ is the Stefan-Boltzmann constant, and .Ts is the surface temperature of the workpiece, and .T∞ is the ambient temperature. Surface convection .qconv is applied to the prescribed surface heat flux as follows: qconv = h(Ts − T∞ )

.

(12.7)

where h is the convective heat transfer coefficient. The initial-boundary value problem of Eqs. (12.3)–(12.7) can be numerically solved by either finite difference or finite element methods.

12.4.2 Elastoplastic Mechanical Response For a mechanical problem, the governing force equilibrium equation is ∇ ·σ =b

.

(12.8)

where .σ is the second-order stress tensor and .b are the body forces such as gravity. The mechanical constitutive law is σ = Cϵ e

.

(12.9)

where .C is the fourth-order material stiffness tensor and .ϵe is the second-order elastic strain tensor. In addition to elastic strain .ϵe , plastic strain .ϵp and thermal strain .ϵt also contribute to total displacement ϵ = ϵe + ϵp + ϵt =

.

 1 ∇u + (∇u)T 2

(12.10)

where u is the displacement vector. ϵ t = ϵt j.

(12.11)

.

ϵt = α(T − T ).  T j= 111000 ref

(12.12) (12.13)

where .α is the thermal expansion coefficient and .T ref is the reference temperature. The plastic strain is computed by enforcing the von Mises yield criterion and the Prandtl-Reuss flow rule f = σm − σy (ϵq , T ) ≤ 0

.

(12.14)

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345

ϵ˙ p = ϵ˙q α.

T ∂f α= ∂σ

.

(12.15) (12.16)

where f is the yield function, .σm is Mises’ stress, .σy yield stress, .ϵ q is the equivalent plastic strain, and .α is the flow vector. The initial condition for the mechanical problem is an initial displacement vector field .u = u0 at an initial time .t = t0 throughout the volume V . The boundary conditions consist of prescribed displacements .up and prescribed traction vectors .tp , on two disjoint surfaces u = up

on surface Su for all t.

(12.17)

σ · n = tp

on surface Sf for all t

(12.18)

.

where  .n is the unit normal  vector to the surface and the surfaces satisfy the relations Su Sf = S and .Su Sf = ∅.

.

12.4.3 Material Activation In most AM methods, the volume of the part and thus the analysis domain keep increasing as material is added on. Two material activation methods are most common as originally introduced in welding modeling [6, 8–10] : (1) the quiet and (2) the inactive element method. Quiet Element Method In the quiet element method, the FEA mesh includes the entire part geometry from the start of the process simulation. Initially, elements representing added metal regions are assigned properties so they do not affect the analysis significantly. For heat transfer analyses, the thermal conductivity k is set to a lower value to minimize conduction into the quiet elements, and the specific heat .Cp is set to a lower value to adjust energy transfer to the quiet elements, while for mechanical analyses, the elastic modulus E is low value to reduce the stiffness of the quiet elements kquiet = sk k.

(12.19)

Cp quiet = sCp Cp.

(12.20)

Equiet = sE E

(12.21)

.

where .kquiet , .Cp quiet , and .Equiet are the thermal conductivity, specific heat, and elastic modulus of the quiet elements and .sk , .sCp , and .sE are their corresponding scaling factors. Initially all elements representing added metal regions are assigned

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Fig. 12.7 1D example for quiet method element activation [6] (With permission from Elsevier)

sk , .sCp , and .sE values less than 1. As the process progresses, elements are activated by switching the scaling factors to 1. The advantage of the quiet element method is that it is simple to implement; however, the choice of the scaling factors can effect the accuracy of the computed results. The 1D example shown in Fig. 12.7 is used in [6] to quantify potential errors of the quiet element method in the heat transfer analysis of AM. The length of the bar is set to 10 mm and the cross section to 1 mm.2 . The thermal conductivity k is set to 0.05 W/mm/.◦ C, the specific heat .Cp to 1000 kJ/Kg/.◦ C, and the density .ρ to −6 kg/mm.3 . The half left of the bar is set to be active at all time, while the right .10 half is set to be inactive or quiet for times 0 to 0.1 s and then switched to active. A heat source Q of 1 W/mm.3 is applied to the left half of the bar for times 0 to 0.1 s. Figures 12.8 and 12.9 show the temperature results at 0.1 and 10 s, respectively. As seen in the figures, for .sk = 0.0001 and .sCp =0.01 , the solution starts to converge to the analytical solution. If the values of .sk and .sCp become even smaller, there is risk for numerical instabilities depending on the level of numerical precision used in the calculations. .

Inactive Element Method In the inactive element method, the elements representing added metal regions are removed from the analysis, and only nodal degrees of freedom corresponding to active elements are considered. As the process progresses, nodes and elements are added to the simulation. As shown in [6], elements need to activated at the initial temperature rather than the interpolated; otherwise artificial energy is generated in the analysis. Since the inactive element method does not require property scaling, it is more accurate and numerically stable. However, it requires constant renumbering of the nodal degrees of freedom and equation reordering. Hybrid Element Method In a [6], a hybrid quiet/inactive element activation method was proposed for AM modeling. In this approach, the analysis commences with all AM elements in an inactive state. Then, elements are switched to quiet on a layer by layer basis. The elements are then activated by the heat source as in the quiet element activation approach. Equation renumbering occurs only during layer activation, resulting in faster run times and equivalent results.

12.4 Computational Models

Fig. 12.8 1D quiet element method results at .t = 0.1 s [6] (With permission from Elsevier)

Fig. 12.9 1D quiet element method results at .t = 10 s [6] (With permission from Elsevier)

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12.4.4 Examples of Computational Models of Fusion-Based Metal AM Processes 12.4.4.1

DED

Figure 12.10 shows the heat flow during DED processing. The moving electron beam, laser beam, or electric arc are typically modeled as a moving heat source. The heat conducts into the part and fixturing (not pictured). For electron beam processes, the only surface losses are due to radiation because the process is performed in a vacuum, while for laser and arc processes, surface convection heat losses are present on the free surfaces. As seen in the figure, more elements are added as the process progresses and the free surface continuously evolves, implying that the surface boundary conditions also continuously evolve. Numerical simulation of the directed energy deposition processes is similar to the simulation of multi-pass welding [6, 11, 12]. For large and complex parts, the simulation can become computationally expensive as both the mesh size and the number of time increments required to account for the movement of the heat source become excessive. Figure 12.11 shows a large part (3.81 m long build plate) what was simulated using a moving source FEA thermomechanical approach [12]. Figure 12.12 shows the final simulated distortion, and Fig. 12.13 compares the simulated distortion to the measured distortion of the experimental build along the x-z plane.

Fig. 12.10 Heat flow in DED

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Fig. 12.11 Large workpiece (3.8-m-long substrate) used for experimental model validation [12] (With permission from ASME)

Fig. 12.12 Displacement magnitude (mm) results (2x magnification) [12] (With permission from ASME)

Fig. 12.13 Experimental and simulated distortion results (mm) in the x-z plane [12] (With permission from ASME)

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Fig. 12.14 Heat flow in PBLF [13] (With permission from Elsevier)

12.4.4.2

Powder Bed Fusion

Figure 12.14 shows the heat flow during powder bed fusion AM. The laser (or electron) beam is acting as moving heat source, which conducts into the part, surrounding powder, and substrate. Radiation heat losses occur on the top surface for all processes. Additional surface convection occurs in laser-based processes. Moving Source Simulations In powder bed AM processes, the heat source is smaller than that of the DED processes, resulting in very fine meshes and too many time increments for moving source analyses. Spatial adaptivity can reduce the number of degrees of freedom and can make simulation of a few layers feasible [14]. Figure 12.15 shows a within-the-layer adaptivity scheme, where a fine mesh is used at the heat source and at the high temperature gradient locations, while element coarsening is allowed elsewhere. Such type of adaptivity is applicable to thermal analyses only because in mechanical analyses there is a permanent wake of plastic strain behind the heat source path. Figure 12.16 shows an across-thelayers adaptivity scheme, where the top layer is kept fine and coarsening is allowed below. This type of adaptivity is applicable to both thermal and mechanical analyses because after processing of a layer is completed, the plastic strain and associated stress field homogenize. This type of adaptivity was used in [14] to simulate the AM of a .6.3 × 6.3 × 2.3 mm volume as shown in Fig. 12.17. In situ displacement measurements were obtained as presented in [15]. Both adaptivity schemes allow the simulation of the moving heat source on a few layers. However, the number of time increments required to simulate the manufacturing of complex parts is prohibitive for moving source analyses of large and complex parts (Figs. 12.18 and 12.19).

12.4 Computational Models

Fig. 12.15 Within the layer adaptivity in moving source thermal analyses

Fig. 12.16 Across-the-layers adaptivity [16] (With permission from Elsevier)

351

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Fig. 12.17 Final mesh of moving source simulation of powder bed processing a .6.3×6.3×2.3 mm volume [14] (With permission from Elsevier)

Fig. 12.18 Syy residual stress simulated by moving source simulation of powder bed processing a .6.3 × 6.3 × 2.3 mm volume [14] (With permission from Elsevier)

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353

Fig. 12.19 Comparison of simulated and in situ measured distortion during the AM of a .6.3 × 6.3 × 2.3 mm volume [14] (With permission from Elsevier)

Process Agglomeration Hodge et al. [17] used a process agglomeration approach where a larger than the actual heat source and powder layer thickens was used in moving source simulations. For D, R, v, the actual layer thickness, laser radius, and travel speed, respectively, the agglomerated values .D ' , .R ' , and .v ' were computed as follows D ' = sD.

.

R' D'

=

R . D

v' = v

(12.22) (12.23) (12.24)

where s is a scaling factor. In [17] setting .s = 20 reduced both spatial and temporal descetization sufficiently to enable the moving source simulation of the part. Layerwise Lumped Heat Models In an effort to simulate powder bed AM of actual parts, some investigators adopted a layerwise lumped heat model approach, where the process was simulated introducing groups of layers and then applying the process energy over the group of layers using either an elevated initial temperature or an equivalent heat source [18].

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Fig. 12.20 Multiscale distortion approach for PBLF [16] (With permission from Elsevier)

Fig. 12.21 Multiscale distortion approach for PBLF [16] (With permission from Elsevier)

Multiscale Models In an effort to further accelerate the simulation times and allow the simulation of large and complex parts, a multiscale approach was implemented in Autodesk Netfabb Simulation software. Reference [16] presents the implementation and validation of the approach. Figure 12.20 illustrates the analysis flow. Process parameters and nonlinear material properties are the input into a small-scale moving source analysis. The small-scale analysis is a weakly coupled thermo-elastoplastic analysis and captures the complex thermal and mechanical interaction between the individual deposited layers. The output from the small-scale model is used as input into a weakly coupled thermomechanical part-scale model, where groups of layers are introduced in the model sequentially. Figure 12.21 shows a comparison of computed and experimental distortion on the large part of Fig. 12.22.

12.4 Computational Models

355

Fig. 12.22 Multiscale distortion approach for PBLF [16] (With permission from Elsevier)

Effect of Powder Part scale thermal models of powder bed processes most often do not include the powder, to reduce the model size and improve computational efficiency. Heat conduction into the powder is either ignored or modeled as surface convection. Although the thermal conductivity of powder is typically two orders of magnitude lower than the conductivity of the part, some of the powder still absorbs part of the process energy, especially in parts with thin sections. In the surface convection approach, the appropriate equivalent convection coefficient is unknown. Furthermore, convection may not be suitable if parts are stacked close together, resulting in heat transfer between the parts. In [13] a systematic study was performed to identify the efficacy of using convection to model heat losses into the powder (Fig. 12.23). Results from models of parts and surface convection (Fig. 12.23b) were compared to models of parts surrounded by powder (Fig. 12.23c). It was found that the equivalent confection coefficient depends on the part thickness and part thermal conductivity; see Fig. 12.24. Layerwise Inherent Strain Models The concept of inherent strain was introduced in the 1980s to compute welding distortion [19, 20]. As shown in the three-bar analog of Fig. 11.1, the thermal cycle of the process introduces compressive plastic strains near the heated region. In the inherent strain approach, rather than performing a thermomechanical simulation, a negative strain is applied in the heated regions in an elastic analysis. In additive manufacturing, the approach simply involves introducing groups of layers in the model with an applied negative (inherent) strain. The applied inherent strain can be determined either experimentally or computationally. In the experimental approach, a (calibration) sample is built. The sample is then cut-off the substrate, and the resulting distortion is measured. Then, a simulation of the sample is performed to identify the applied inherent strain that results in the same distortion as that measured. Then, the same inherent strain is used in other geometries built with the

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Fig. 12.23 Powder effects in modeling powder bed processes: (a) part geometry, (b) part model without powder, (c) part and powder model [13] (With permission from Elsevier)

same processing conditions. In the computational approach, a thermomechanical simulation is performed instead of a calibration built to either identify or directly compute the inherent strain [21]. Although the inherent strain approach is computationally efficient for computing distortion in large parts, it can be only qualitatively accurate as the inherent strain depends on the part geometry [21].

12.4.5 Questions and Discussions 1. What are the limitations and advantages of analytical models of AM processing?

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357

Fig. 12.24 Equivalent convection coefficient for powder in PBLF [13] (With permission from Elsevier)

2. What are the limitations and advantages of computational models of AM processing? 3. What type (scale and size) of computational models have been proposed for DED processes? 4. What scale of computational models have been proposed for PBLF processes? 5. How is powder modeled in PBLF processes?

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References 1. Rosenthal D (1946) The theory of moving sources of heat and its application to metal treatments. Trans. ASME 68(8):849–866 2. Li J, Wang Q, et al. (2018) An analytical computation of temperature field evolved in directed energy deposition.J Manuf Sci Eng 140(10):101004 3. Cao Z, Dong P, Brust F (2000) A fast thermal solution procedure for analyzing 3d multi-pass welded structures. Weld Res Counc Bull 455(1):12–21 4. Perret W, Schwenk C, Rethmeier M (2010) Comparison of analytical and numerical welding temperature field calculation. Comput Mater Sci 47(4):1005–1015 5. Eagar TW, Tsai NS (1983) Temperature fields produced by traveling distributed heat sources. Weld J 62(12):346–355 6. Michaleris P (2014) Modeling metal deposition in heat transfer analyses of additive manufacturing processes. Finite Elem Anal Des 86:51–60 7. Michaleris P (2011) Welding Fundamentals and Processes, vol 6A, chapter Thermomechanical Effects of Fusion Welding, pp. 146–151. ASM International, Materials Park 8. Lindgren, L-E, Runnemalm H, Nasstrom MO (1999) Simulation of multipass welding of a thick plate. Int J Numer Methods Eng 44(9):1301–1316 9. Lindgren L-E, Hedblom E (2001) Modelling of addition of filler material in large deformation analysis of multipass welding. Commun Numer Methods Eng 17(9):647–657 10. Lindgren LE, Michaleris P (2005) Modeling of welding for residual stresses. In: Lu J (ed) Handbook on residual stress, vol 2, pp 47–67. SEM, New York 11. Heigel JC, Michaleris P, Reutzel EW (2015) Thermo-mechanical model development and validation of directed energy deposition additive manufacturing of ti–6al–4v. Addit Manuf 5:9–19 12. Denlinger ER, Irwin J, Michaleris P (2014) Thermomechanical modeling of additive manufacturing large parts. J Manuf Sci Eng 136(6):061007 13. Li C, Gouge MF, Denlinger ER, Irwin JE, Michaleris P (2019) Estimation of part-to-powder heat losses as surface convection in laser powder bed fusion. Addit Manuf 26:258–269 14. Denlinger ER, Gouge M, Irwin J, Michaleris P (2017) Thermomechanical model development and in situ experimental validation of the laser powder-bed fusion process. Addit Manuf 16:73– 80 15. Dunbar AJ, Denlinger ER, Heigel J, Michaleris P, Guerrier P, Martukanitz R, Simpson TW (2016) Development of experimental method for in situ distortion and temperature measurements during the laser powder bed fusion additive manufacturing process. Addit Manuf 12:25–30 16. Gouge M, Denlinger E, Irwin J, Li C, Michaleris P (2019) Experimental validation of thermomechanical part-scale modeling for laser powder bed fusion processes. Addit Manuf 29:100771 17. Hodge NE, Ferencz RM, Vignes RM (2016) Experimental comparison of residual stresses for a thermomechanical model for the simulation of selective laser melting. Addit Manuf 12:159– 168 18. Papadakis L, Loizou A, Risse J, Bremen S, Schrage J (2014) A computational reduction model for appraising structural effects in selective laser melting manufacturing: a methodical model reduction proposed for time-efficient finite element analysis of larger components in selective laser melting. Virtual Phys Prototyping 9(1):17–25 19. Ueda Y, Murakawa H (1984) Applications of computer and numerical analysis techniques in welding research. Trans. JWRI 13(2):165–174 20. Ueda Y, Kim YC, Yuan MG (1989) A predictive method of welding residual stress using source of residual stress (report I) characteristics of inherent strain (source of residual stress). Trans JWRI 18(1):135–141 21. Bugatti M, Semeraro Q (2018) Limitations of the inherent strain method in simulating powder bed fusion processes. Addit Manuf 23:329–346

Chapter 13

Alloy Systems for Additive Manufacturing

Metallic systems, in the form of alloys, comprise the largest use of materials for engineered components and structures. This is primarily due to the wide variety of properties and characteristics that are exhibited by metallic systems, and because of this, metal alloys are natural choices for applications in a wide variety of industries, which includes transportation, energy, aerospace, recreational products, and medical devices, to name a few. Shown in Fig. 13.1 is a graph showing the ultimate tensile strength and toughness for various metals and other common material systems utilized for industrial applications [1]. As illustrated in the figure, the combination of good strength and toughness of certain alloys, such as high alloy steels, titanium alloys, and nickel alloys, enables these materials to be applied to a wide range of applications requiring high durability. In instances where high specific strength or high specific stiffness is a necessity, such as in many applications within the aerospace industry, aluminum and titanium alloys are well represented. These properties are shown in Fig. 13.2 for alloys and several classes of materials, where the specific properties signify the material’s strength or stiffness in terms of density [1]. Although metals do not possess the highest specific properties, which is currently reserved for composite and ceramic materials, the combination of good specific strength and stiffness coupled with high toughness makes metal alloys attractive for these types of applications. There are also very specific applications where metallic materials are extremely well suited, and examples include service at high temperatures, which is illustrated in the data of Fig. 13.3 [1], or electrical conductivity. Metallic systems used under high temperature conditions include titanium and nickel alloys, as well as the high-temperature refractory metals: tungsten, zirconium, niobium, tantalum, rhenium, and molybdenum. Copper and aluminum alloys are commonly used in applications requiring good electrical, and thermal, conductivity. Based on the excellent combination of properties and unique characteristics of metals, they have found widespread acceptance in many industries and in many instances are the materials of choice for products having critical performance requirements. © Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_13

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Fig. 13.1 Strength and toughness of several material systems used for engineered components and structures. (Figure courtesy of Granta Design Ltd., Cambridge, UK [1])

Because of their extensive use, metallic systems play a central role in additive manufacturing. However, the appeal of metals for additive processing has created a dichotomy. The relatively low production rates inherent in additive manufacturing processes drive application for metals to high-value products, and this typically implies high performance requirements for the parts. In turn, this places significant requirements on the additive manufacturing process to meet a level of process reliability and material quality that is necessary for these applications. The additive manufacturing process simultaneously forms a three-dimensional shape while also creating the material, and for metals, not only is the form and fit of the component of importance but also its functionality. Significant attention must be paid to ensure that the metallic material selected and the additive manufacturing process used are capable of producing a consistently high quality of material. This is a necessity, since the operating stresses under loading, both static and dynamic, for many applications involving metal parts and structures are sufficiently high and may result in crack propagation and potential failure with the presence of defects. The design of metallic components for additive manufacturing also requires that a sound statistical basis be used to establish expected mechanical properties for the

13.1 Constitution of Alloys and Development of Microstructure

361

Fig. 13.2 Graphs showing stiffness and strength versus density for several classes of materials: (a) Young’s modulus versus density and (b) strength versus density. (Figure courtesy of Granta Design Ltd., Cambridge, UK [1])

various processes and materials. For many alloys that have been produced through additive manufacturing, mechanical properties must also consider the orientation of the material within the process, which can be highly anisotropic.

13.1 Constitution of Alloys and Development of Microstructure The properties and characteristics displayed by alloys are a product of the composition and processing of the material, which defines the microstructural features that are responsible for producing these properties. Once the composition of the alloy is defined, relationships that govern the process, microstructure, and resultant properties are used to optimize the performance of the material system. Alloys are mixtures of various elements that are added to or present in a principal metallic element to establish a microstructure that displays characteristics that are superior to

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13 Alloy Systems for Additive Manufacturing

Fig. 13.3 Strength versus maximum service temperature for various materials. (Figure courtesy of Granta Design Ltd., Cambridge, UK [1])

the pure element. Common examples of alloy systems used extensively in industry include small amounts of carbon added to iron for increasing strength, copper added to aluminum for improving strength, and molybdenum and cobalt additions to nickel for increasing resistance to corrosion and increasing strength. The most common method for obtaining a relatively uniform distribution of alloying additions is through melting of the mixture followed by solidification. Once the composition is established, various thermal and mechanical processes are then used to fashion the material into usable forms while also developing a microstructure within the material that is suitable for providing the desired properties. The distinct phases that may be present within a material system over a composition and temperature range may be defined through the use of a phase diagram, which represents the thermodynamically stable phases under equilibrium conditions. Although pressure is also required for establishing thermodynamic stability, for most material engineering purposes the pressure is assumed to be 1 atmosphere. Shown in Fig. 13.4 is a binary phase diagram representing a twocomponent system of A and B. Also, superimposed on the phase diagram is a hypothetical alloy representing a small amount of B, as the solute, within A, the solvent. As shown by the diagram, for any composition representing the A and B

13.1 Constitution of Alloys and Development of Microstructure

363

Fig. 13.4 Binary phase diagram for an alloy system representing A and B components

mixture, the phases that are stable at any temperature are defined by the regions delineated by the phase boundaries. It is important to note that the term “phase” is used to describe several attributes of the material, but in each case, it represents material that is chemically uniform and having distinct physically properties. The discreet phases defined in the diagram of Fig. 13.4 include all compositions at the appropriate temperatures that are completely liquid, L, solid solutions of B within A, α, and solid solutions of A within B, β. In addition, mixtures of these phases are also shown, as with α + L, β + L, and α + β. An important location within the phase diagram is the eutectic point, which at the eutectic temperature, Te , and the eutectic composition, represents equilibrium of all phases. The transformation that occurs during cooling through the eutectic point, at the eutectic composition, is represented as: liquid → α (solid solution) + β (solid solution)

.

The two phases that are present below the eutectic temperature are both solutions containing the solute atoms within the atomic lattice of the solvent. The solute atoms may substitute for solvent atoms or may fit between the interstitial region between the solvent atoms. In the case of α, the atoms of element B are incorporated into the atomic lattice of A and vice versa for β. However, the mixture that is formed from the two solid solutions, α + β, represent distinct phases which, in many instances, are manipulated to obtain a microstructure that displays enhanced characteristics over the pure elements. The single-phase regions for α or β below the eutectic temperature are bounded by the line representing the maximum solid solubility for β in α, the α-solvus line, and α in β, the β-solvus line.

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Fig. 13.5 Binary phase diagram for an alloy system representing A and B components

Based on the composition of the hypothetical Alloy A-B, a vertical line is used to identify phases that would be present within this alloy at various temperatures. If a composition of Alloy A-B was heated into the liquid region, or melted, and allowed to cool, initial solidification of the alloy will begin at the liquidus temperature, Tl . With continued cooling below Tl , solidification would proceed by increasing the fraction of solid α within the liquid until complete solidification at the solidus temperature, Ts . The development of a potential solidification morphology for the hypothetical alloy is illustrated in Fig. 13.5. In this example, the solidification process is represented by a liquid solution of A with some B being deposited onto a solid substrate. Initial solidification begins at the substrate through rapid extraction of heat from the liquid and promotion of heterogeneous nucleation of the solid at the surface. As cooling continues, a solid network is continually developed and is controlled by the direction of heat extraction and local conditions near the liquid and solid interface. In the example in Fig. 13.5, a cellular solidification morphology developed with the growth of the cells being in the direction of major heat extraction from the substrate. It is also important to note at this time that the composition, or content of A and B, within the solidifying cells and the intercellular regions may be quite different from the alloy composition.

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365

Further cooling below the solidus temperature results in reactions between α and β within the solid state. Using the above hypothetical alloy system, solid state reactions that may occur after solidification could involve the transformation of α to a mixture of α + β upon cooling below the α-solvus line and subsequently α + β to α during reheating above the solvus line. If the crystallographic structures of α, representing α with β in solid solution, and β as a discreet phase are similar, the reaction that occurs during cooling below the α-solvus or heating above the α-solvus will be diffusion-controlled based on the mobility of the A and B atoms. This type of reaction is referred to as non-allotropic phase transformation where the crystallographic structure remains unchanged during the transformation, as opposed to an allotropic transformation where the reactants and products may represent different crystallographic structures. In this example, cooling from the α region that is bound by the solidus and solvus lines to the α + β region would result in nucleation and growth of a separate βphase within an α matrix by long-range diffusion of A and B atoms. Figure 13.5 also illustrates a potential microstructure that could result upon cooling below the solvus into the two-phase region due to nucleation and growth of β in α. In this example, a fine distribution of β is formed within the solidified cells representing a composition of the α and β solid solution. This is one example of the development of microstructure based on the composition of an alloy, which in this case could signify β as a precipitation strengthening phase within the alloy. Since many of the transformations that occur during solidification and cooling in the solid state are governed by the rate of the reaction, or kinetics, the time it takes for the liquid and solid to cool plays a significant role in determining the potential and extent of operative transformations. This includes the morphology and scale of the solidified structure formed from the liquid, as well as the solid state transformations that occur as temperatures span the phase boundaries upon heating and cooling. The faster the cooling, the lesser time available for the growth of features, typically resulting in finer microstructures. However, it should be noted that the rapid and successive heating and cooling cycles experienced during many of the additive manufacturing processes pose difficulty in applying conventional kinetic analysis for many reactions important in establishing microstructure and resultant properties. Fortunately, special techniques have been developed that enable a reasonable assessment of the development and evolution of microstructures for important alloys used in additive manufacturing. The above discussion briefly introduced the implication of temperature and cooling of an alloy through solidification and transition of phases in the solid during thermal excursions common in additive manufacturing process. The phase diagram that represents phases present based on composition and temperature for an alloy system may be utilized to examine potential transformations and phases that could result during heating and cooling and potential microstructural features represented by the material. However, this assessment does not directly address the impact of these features on the properties of the material.

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13.2 Development of Strength in Metallic Systems Engineered metallic systems are polycrystalline and the ability of the material to resist stress and deformation is a function of the structure and substructure of the individual grains and the aggregate. Strength may be defined as the materials’ ability to resist plastic deformation under an applied stress state, and this deformation is governed by the creation and movement of dislocations, which are defects within the crystalline lattice. Hence, strengthening of the material may occur when conditions are imposed that impede motion of dislocations. There are several mechanisms that are used to hinder movement of dislocations in metals and result in increasing strength of the material by increasing the stress required for dislocation motion. In many instances, a combination of these methods is used to fully develop strength in a particular alloy. Of these strengthening mechanisms, four are of particular interest and relevant to materials used in additive manufacturing and include grain boundary strengthening, solid solution strengthening, precipitation strengthening, and phase transformation strengthening. Because of the inherent atomic disorder at grain boundaries, dislocation glide across the boundaries is hampered, and by increasing the density of grain boundaries, strength may be increased. Based on this phenomena, the Hall-Petch relationship states that increased strength associated with grain boundary strengthening is proportional to the average diameter of grains within an alloy, which is defined as: σy = σo +

.

k (d)1/2

(13.1)

where σ y the yield strength associated with grain boundary strengthening, σ o is a constant for a metal and is related to the resistance to dislocation movement without grain boundaries, k is also a material-specific coefficient, and d is the average grain diameter. As seen by the Hall-Petch relationship, strength will increase as grain size decreases. Solid solution strengthening relies on the addition of certain alloying elements as solute atoms that may substitute within the atomic lattice of the solvent or be interstitially incorporated between atoms within the lattice. The distortion of the lattice generated by the solute atoms acts to impede the motion of dislocations within the lattice. Increasing strength using this method is effective with increasing solute content up to the solid solubility limit. Precipitation strengthening utilizes a thermal treatment to increase solubility during heating to an elevated temperature, which upon rapid cooling from this temperature results in a supersaturated solution that may drive nucleation a growth of a second phase. The resultant fine distribution of second phase particles can interact and hinder dislocation motion, thus increasing strength through precipitation strengthening. The heating and cooling to achieve this condition is conducted as a thermal treatment (heat treatment). Phase transformation strengthening relies on an allotropic alteration in crystal structure during transformation of phases through changes in temperature. The

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distortion of the lattice field associated with the alteration of the crystalline structure acts to impede dislocation motion. This type of strengthening is used extensively in ferrous alloy having moderate to high levels of carbon, where a thermal treatment (heat treatment) is used to form the γ-phase (austenite) at elevated temperature followed by rapid cooling or quenching that transforms the face-centered cubic (FCC) austenite to a body-centered tetragonal (BCT) crystal structure, referred to as martensite. The distortion of the lattice from forming martensite results in significant obstruction to dislocation movement and high strength and hardness. This example also points out an important aspect of the mechanical properties of a material; many applications for a material require an optimal combination of properties and may necessitate compromises in properties, such as having sufficient strength but good ductility. In the case of the phase transformation of steels, the martensite is typically “tempered” at a moderate temperature that reorients the lattice and decreases the strength of the material but increases its ductility and toughness. As mentioned previously, a combination of strengthening mechanisms is typically used to develop mechanical properties of an alloy system and is based on the alloying elements added for certain characteristics, such as corrosion resistance, or specifically for improving mechanical properties. A good example may be found in ferrous alloys. The phase transformation of austenite to martensite, with the appropriate thermal treatment, may be used to achieve a wide range of strength (and hardness) with higher carbon steels. In addition to carbon, a wide variety of additional elements may be added to high carbon steels, such as chromium, tungsten, molybdenum, vanadium, and cobalt, to produce a material that may be useful for a variety of applications. These alloys develop excellent properties through a combination of phase transformation strengthening, solid solution and precipitation strengthening, and grain boundary strengthening mechanisms. Many of the elements employed in these alloys are used for forming fine precipitates of nitride, carbides, or intermetallic compounds that when combined with appropriate heat treatments exhibit an optimal mix of hardness, strength, toughness, and wear resistance suitable for demanding applications, such as tooling and dies, aerospace components, engine components, fasteners, and mechanical device components. Additions of nickel and chromium are utilized in combination with carbon in stainless steel alloys to achieve high corrosion resistance. Austenitic stainless steels contain fairly low levels of carbon (below 0.10%) and manganese but appreciable amounts of nickel (8–10%) and chromium (up to 18%). Nickel and chromium additions provide exceptional corrosion resistance in these alloys, but the nickel and manganese also act to stabilize austenite within the microstructure, which precludes phase transformation hardening of these alloys. However, these alloys may achieve moderate strengths through a combination of solid solution strengthening with carbon and nitrogen and work hardening during fabrication into shapes. In some instances, additional elements, such as titanium or vanadium, are added to promote precipitation strengthening through the formation of fine carbides or nitrides [2]. The combination of good strength, ductility, and toughness, as well as good formability and weldability, enables the austenitic stainless steels to be used in a

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very wide range of applications, which includes cookware, automotive trim, piping, tanks, chemical processing equipment, and architectural applications, to name a few. The martensitic stainless steels contain carbon between 0.1% and 1.0%, high levels of chromium (11–18%), and typically, no nickel. As the name implies, these alloys are capable of forming martensite upon phase transformation strengthening by heat treating and can develop high strength and toughness while also exhibiting good corrosion resistance. Some alloys also contain molybdenum, copper, and vanadium for further strengthening by precipitation of carbides and intermetallic compounds. A few grades contain small amounts of sulfur to improve machinability. The martensitic stainless steels may exhibit moderate to very high strength and hardness based on the alloy and thermal treatment, but in general, they do not display the corrosion resistance of stainless steels containing nickel. These alloys are used in a broad range of applications that include cutlery and surgical instruments, steam and gas turbine blades, molding dies, bearings, and bushings, as examples. Many nickel-based alloys fall into the category of materials referred to as superalloys, which are based on nickel, nickel-iron, and cobalt. These alloys have been developed for service in severe environments, such as applications requiring combinations of high corrosion, temperature, oxidation, and stress. Superalloys based on nickel and nickel iron may contain a variety of additions that include chromium (5–25%), molybdenum, tungsten, titanium, cobalt, tantalum, and rhenium. Alloys based on cobalt may have many of the same constituent, but also contain high levels of chromium (19–30%). These alloys are primarily strengthened by a combination of solute and precipitate strengthening from alloying additions, with the specific compositions being developed to meet high performance requirements under unique service conditions [3]. Superalloys have been developed to meet the demands of the gas turbine engine industry and are utilized in this application as turbine blades, disks, and combustion chambers. However, there are other applications where these alloys are employed, which include the use of the nickel and nickel-iron alloys for energy generation and cobalt-chromium alloys for orthopedic implants. A variant of cobalt-chromium alloys is also used for surface deposition for applications requiring improved wear and corrosion resistance. Titanium alloys undergo an allotropic transformation from the β-phase, which displays a body-centered cubic (BCC) crystalline structure at elevated temperatures, to α at lower temperatures, which represents a hexagonal closed packed (HCP) structure. Hence, titanium alloys are categorized as α, α + β, or β alloys, depending on the predominate phases present after cooling to room temperature. Commercially pure (CP) titanium is composed of the α-phase at room temperature and exhibits lower strength but higher ductility and corrosion resistance [4]. Additions to titanium are used to stabilize either the α-phase, β-phase, or both during cooling below the β to α transformation temperature (beta transus temperature). Aluminum is a common addition to stabilize α, as well as with the addition of oxygen and nitrogen, and vanadium, molybdenum, silicon, and tantalum can be used to stabilize β. The most common titanium alloy contains 6% aluminum and 4% vanadium and forms a mixed α + β microstructure at room temperature. Strengthening of α + β alloys may involve solid solution strengthening and precipitation, and if

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the rate of cooling from the beta transus is sufficiently rapid, may also involve a transformation strengthening effect [5, 6]. Because of competition between the nondiffusional allotropic and diffusional transformations, these alloys tend to exhibit complex microstructures. Titanium alloys have a distinct combination of high specific strength and good ductility, along with good corrosion resistance and high temperature resistance, but are costly. Hence, titanium alloys are primarily used in aerospace and other high-value applications. Examples of these applications include aerospace structures, turbine engine blades, disks, rings, fasteners, and orthopedic implants. Aluminum alloys provide moderate to good strength and low density while providing good general corrosion resistance. Depending upon the alloying additions, aluminum alloys are strengthened through a combination of solid solution and precipitation strengthening and work or strain hardening. Aluminum alloys are categorized by the principal alloying additions [7]. For wrought products representing plate, sheet, extrusions, and forging, these categories include the 1XXX series alloys representing pure aluminum, 2XXX series alloys containing copper and usually magnesium, the 3XXX series alloys containing manganese, the 4XXX series primarily containing silicon, the 5XXX series alloys containing magnesium, the 6XXX series containing magnesium and silicon, and the 7XXX series alloys containing zinc, magnesium, and copper. Aluminum casting alloys have a somewhat similar classification based on major alloying elements corresponding to additions of copper, silicon, magnesium, and zinc. Almost all aluminum alloys utilize strain hardening during production to improve strength to some degree; however, most alloys also employ solid solution and precipitation strengthening to fully develop properties. The 3XXX and 5XXX series are strengthened by solid solution strengthening and strain hardening, and the 2XXX, 6XXX and 7XXX series alloys are primarily strengthened by forming second phase precipitates resulting from alloying additions and thermal treatments. The 4XXX series alloys, which have been developed for use as welding and brazing filler material, rely on dispersion strengthening of the aluminum-silicon eutectic phase during solidification. Because of the wide range of properties and characteristic available in aluminum alloys, they are utilized extensively. The 3XXX, 5XXX, and 6XXX series alloys represent moderate strength and good corrosion resistance and formability and are used throughout the automotive, shipbuilding, and chemical industries, whereas the 2XXX, 7XXX, and certain 6XXX alloys are capable of relatively high strength from precipitation strengthening and are used to achieve improved performance, such as in applications involving automotive and aerospace components and structures. However, because of the relatively wide solidification temperature range, high coefficient of thermal expansion, and change in volume upon solidification, many of the precipitation-strengthened alloys that contain higher levels of alloying additions may be prone to cracking during solidification. Copper alloys are usually employed to take advantage of the high thermal or electrical conductivity that is inherent in these alloys. Copper alloys also have good corrosion resistance. Copper alloys represent some of the earliest developed metal systems, such as through the addition of tin with small amounts of phosphorus

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impurities to produce bronze. Today, various alloying elements are added to copper to produce a wide assortment of alloys having specific properties and characteristics. This includes tin, zinc (to produce brass), aluminum, nickel, and silicon, to name a few. Similar to aluminum alloys, copper alloys may utilize several strengthening mechanisms to develop properties, with strain hardening, in combination with other methods. However, copper alloys representing higher purity, which also exhibit the greatest electrical conducting, are primarily strengthened by work or strain hardening. In addition to the strain hardening effect from processing used to produce shapes, copper alloys are also strengthened by solid solution and precipitation strengthening means. The early bronze alloys relied on tin for achieving higher strength through a substitutional sold solution mechanism. Other elements that may impart solid solution strengthening in copper are zinc, manganese, nickel, and silicon. High strengths and good ductility in copper alloys may also be obtained through precipitation strengthening through additions of chromium, nickel, and zirconium. The combination of good electrical and thermal conductivity, along with good corrosion, ductility, strength, and its ability to be easily formed, makes copper and its alloys ideal for a wide range of suitable applications. This includes ammunitions, radiators, condensers, heat exchangers, piping, electrical components, valves, and fasteners and hardware. However, it should be noted that some copper alloys contain small levels of beryllium that may be hazardous if its dust or fumes are inhaled.

13.3 Alloy Systems for Additive Manufacturing As stated earlier, the use of metallic systems, in the form of alloys, is pervasive in products touching every aspect of our world, and thus, they form a major group of materials being utilized in additive manufacturing. The range of alloys being applied is highly diverse and is based upon the distinctive properties and characteristics that are required for the intended application. Because of the wide assortment of alloys that will be discussed, the unified numbering system (UNS) will be employed for identifying and simplifying the discussion of specific alloys in an orderly manner. The UNS scheme for designation of alloys involves a prefix letter that represents a major alloy series, followed by five digits that identify the alloy, based on composition, within that family. Shown in Table 13.1 is the major series used to designate alloys within UNS [8]. For the purposes of discussing specific alloys, the UNS designation will be employed but followed by the most common other trade or grade name in parentheses. The vast majority of materials that are being used for producing engineered components through additive manufacturing are metallic systems or alloys. This includes a broad range of ferrous based alloys, nickel-based alloys, titanium alloys, aluminum alloys, cobalt-chromium alloys, and copper alloys, to name a few. However, one important consideration for additive processing of metals is the resistance of the alloy to cracking during or immediately after solidification. For

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Table 13.1 Unified numbering system (UNS) categories [2] UNS series A00001 to A99999 C00001 to C99999 D00001 to D99999 E00001 to E99999 F00001 to F99999 G00001 to G99999 H00001 to H99999 J00001 to J99999 K00001 to K99999 L00001 to L99999 M00001 to M99999 N00001 to N99999 P00001 to P99999 R00001 to R99999

S00001 to S99999 T00001 to T99999 W00001 to W99999 Z00001 to Z99999

Metal type(s) Aluminum and aluminum alloys Copper and copper alloys (brasses and bronzes) Specified mechanical property steels Rare earth and rare earthlike metals and alloys Cast irons AISI and SAE carbon and alloy steels (except tool steels) AISI and SAE H-steels Cast steels (except tool steels) Miscellaneous steels and ferrous alloys Low-melting metals and alloys Miscellaneous nonferrous metals and alloys, such as: M1xxxx – Magnesium alloys Nickel and nickel alloys Precious metals and alloys Reactive and refractory metals and alloys: R03xxx – Molybdenum alloys R04xxx – Niobium (columbium) alloys R05xxx – Tantalum alloys R3xxxx – Cobalt alloys R5xxxx – Titanium alloys R6xxxx – Zirconium alloys Heat- and corrosion-resistant (stainless) steels Tool steels, wrought, and cast Welding filler metals Zinc and zinc alloys

many existing alloys, the “weldability” of the material is a desirable manufacturing characteristic that has been evaluated and defined, and because welding is in many ways similar to additive manufacturing, the weldability of an alloy is usually a good indication of whether the material may be easily processed using additive techniques. The production of parts through additive manufacturing requires that the metallic material used for deposition be resilient to solidification or thermally induced cracking, while also capable of developing engineering properties that are required for the intended application of the component or structure. However, it should be noted that the selection of an alloy for additive manufacturing necessitates that the material is available in a form that may be used for one of these processes, i.e., powder or wire. As mentioned earlier, because of the similarities of welding and additive manufacturing, many alloys that are currently being used in processes that utilize wire as a feedstock rely on alloys available as spooled welding electrode. In the case of processes that utilize powder as a feedstock, the powder industry has responded to the needs of additive manufacturing by making available alloys in powder form based on the demand of the industry. In some cases, powder alloys that

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Table 13.2 Some commonly used alloys for additive manufacturing for various applications Alloy system Tool steels

Examples of applicable alloysa T20813 (H13) ® CPM 9 V

Stainless steels

S30880 (308L), S31603 (316L) S42000 (420), S43100 (431) S17400 (17-4 PH)

Nickel

N06625 (IN625) N07718 (IN718)

Titanium

R56400 (Ti-6Al-4V) R50400 (titanium grade 2 or CP-commercially pure)

Aluminum

A92319 (2319) A94047 (4047) Al-Si10Mg

Cobalt-chromium

R30006 (cobalt alloy 6)

Copper

C11000 (Cu-ETP) C18150

General characteristics and potential applications Tool steel for repair and building 3D components Tool steel for repair Austenitic stainless steels for 3D components Martensitic stainless steels for repair Precipitation-strengthened alloys for repair or creation of 3D components Both alloys provide good high temperature and corrosion resistance and are applicable to repair and production of 3D components High specific strength and corrosion resistance for repair and 3D components and structures Good corrosion resistance for repair and 3D components All of these alloys provide moderate strength and are applicable to repair and production of 3D components and structures Moderate strength, high wear resistance, and good corrosion resistance for deposition on surfaces and production of 3D components Commercially pure copper for high thermal and electrical conductivity High strength alloy for 3D components

a When possible, UNS designations are utilized with their trade, grade, or common name in parentheses

have been used for other established processes, such as plasma spraying or plasma transferred arc welding, are being applied to additive manufacturing. Although there are many alloys and material systems that are applicable to additive manufacturing, many of the current and planned applications for metals involve several alloy systems and commonly available alloys. Shown in Table 13.2 is a list of common alloy systems and alloys used in additive manufacturing. This list is not intended to be all inclusive but only meant to illustrate the assortment of alloy systems that are being applied to additive manufacturing. There is a wide range of ferrous alloys used for the various additive processes and includes tool steels [9– 12] for restoration of dimensions for repair and production of components, as well

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as various classes of stainless steel. Several alloys representing the austenitic grade stainless steels [13–15] are especially relevant for building components and large structures due to their inherent ability to resist cracking, whereas the higher strength and hardness of the martensitic grade stainless steels [16, 17] and the precipitationstrengthened alloys [18] are finding acceptance for restoration where high hardness and wear resistance are needed, as well as for production of net-shaped parts for high stress applications. Nickel-based alloys [19–22] are being applied to various applications within the aerospace industry for repair of high-value components or production of three-dimensional (3D) shapes due to their high temperature strength and oxidation resistance and good corrosion characteristics. Several titanium alloys [19, 23–25] are also being applied to additive manufacturing for aerospace applications based on properties that are similar to those of nickel-based alloys, with the added benefit of higher specific strength. One important consideration during processing of titanium alloys is assuring low gaseous species, such as oxygen, within the processing environment to suppress solid solution strengthening and decreased ductility caused by absorption at elevated temperature. Because of this condition, electron beam-based additive processes are finding favor for processing of titanium alloys. Several aluminum alloys [26–28] that display low sensitivity to solidification cracking are being used for additive manufacturing for repair and restoration, as well as for creating 3D parts and structures. Because aluminum alloys may be prone to hydrogen absorption while molten and subsequent formation of gas porosity during solidification, potential moisture contamination of powder feedstock and low moisture content within the processing environment should be closely monitored. Some of the earliest applications of additive manufacturing for restoring or improving properties at the surface of components requiring high wear resistance have employed cobalt-chromium alloys [29–31]. Because of the combined resistance to wear, corrosion, and heat, additive manufacturing of these alloys is also being utilized for aerospace components and medical implants. The excellent thermal and electrical conductivity of copper-based alloys is also spurring applications in additive manufacturing of these materials [32, 33]. Because additive manufacturing is utilized for creating two-dimensional features for the addition of material onto surfaces or three-dimensional features for producing net and near net shapes, the metallic systems applied to these processes may be discussed based on the application. Addition of material onto a surface may be used for restoring dimensions to an existing part or adding a material onto the surface for imparting special characteristics. In the case of restoring dimensions to an existing component, consideration of the material to be added involves metallurgical compatibility with the alloy representing the component, as well as meeting various mechanical and physical properties of the existing material. When additive manufacturing processes, such as directed energy deposition, are selectively applied to a surface for imparting unique local characteristics, such as improved wear resistance or corrosion, the deposited material must also have metallurgical compatibility with the underlying substrate, while also displaying the desired characteristics of interest. The production of net or near net shape parts through additive manufacturing requires that the metallic material used for

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deposition be resilient to solidification or thermally induced cracking, while also capable of developing engineering properties that are required for the intended application of the component or structure. However, it should be noted that the selection of an alloy for these processes necessitates that the material is available in a form that may be used as feedstock for additive manufacturing, i.e., powder or wire. Because of the similarities of welding to the directed energy deposition process, many alloys that are currently being used for deposition processes that utilize wire as a feedstock rely on alloys available as spooled welding electrode. In the case of directed energy deposition using powder as a feedstock, the powder industry has responded to the needs of additive manufacturing by making available alloys in powder form based on the demand of the industry. In some cases, powder alloys that have been used for other established processes, such as plasma spraying or plasma transferred arc welding, are being applied to DED.

13.4 Properties and Selection of Metallic Materials for Additive Manufacturing The selection of an alloy for producing a component or structure using additive manufacturing is based on the ability of the material to develop the properties and characteristics that are required for the intended application. Achieving the desired properties is not only a function of the selected alloy, but is also dependent upon the specific additive manufacturing process, as well as the post-process operations applied to the component or structure. As discussed earlier, applications that dictate the use of metallic materials typically have high performance requirements, and these prerequisites assume the process is capable of producing material of a known quality that will meet these requirements. There are many properties that have been defined to quantitatively describe the response of a material under various loading conditions; however, several are commonly used and are appropriate for this discussion. Customary properties of interest include density, strength, hardness, toughness, fatigue strength, and resistance to corrosion, and in most instances, it is the combination of these characteristics that is of importance for a particular application. Strength may be defined by the ultimate tensile strength at failure or the yield strength when permanent deformation occurs. The choice of what strength is significant is made during design and broadly indicates the level of durability required by the component, with yield strength being used for applications requiring long-term stability and resilience. Although hardness, for many metals, is directly related to the strength of the material, it is accurately a measure of the resistance of the surface to deformation and is determined using special tests. Materials exhibiting high hardness have been developed specifically for applications that require high resistance to surface deformation, i.e., wear resistance, and usually are not well suited for conditions requiring high strength and toughness.

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Toughness is also used to describe the durability of the material under loading and is defined by the energy expended per unit volume during deformation prior to fracture. Toughness is quantitatively described through integration of the area under the stress-strain curve during loading to failure:  toughness =

f

σ d

.

(13.2)

0

where  is strain,  f is strain at failure, and  is stress, with toughness being expressed as energy per unit volume. As strength is an indication of the force required for deformation (yield strength) or failure (ultimate tensile strength), toughness is the amount of energy absorbed before failure. For applications where failure may lead to catastrophic consequences, fracture toughness is used to describe the ability of the material to resist fracture. This criterion may include the resistance of the material for initiation of fracture at a stress concentration, as well as the propagation of an existing crack leading to failure. In the case of propagation of a crack, fracture mechanics is utilized to determine the potential for cracks or flaws to lead to unstable growth and potential catastrophic failure and is appropriate for distinguishing a critical flaw size under various stress states. The parameter that is used to describe the potential for rapid growth of a crack having specific geometry under a particular applied stress is the stress intensity factory, K, with the critical stress to propagate a crack under plane strain condition during Mode I loading, KIc , representing the fracture toughness under those conditions. It will be seen in further discussions that the use of this approach has a particular value for analysis of additive manufactured parts that may contain small flaws and are of interest for use in critical applications. Many applications require the component or structure to continually operate under cyclic loading conditions, which may involve fatigue of the material. This includes operational conditions that impose high stress levels over a limited number of cycles, low cycle fatigue, and lower levels of stress over a much longer duration of operation, high cycle fatigue. Low cycle fatigue (LCF) may result when applied stresses repeatedly exceed the yield strength of the material, but with relatively long intervals between peak stresses. Under LCF, high cyclic stresses result in elastic and inelastic strains, with the latter causing plastic deformation and potential failure before 105 cycles. High cycle fatigue (HCF) entails cyclic stress that generates only elastic strain but with potential failure occurring at greater than 105 cycles, and in many instances, failure under HCF will require a much greater number of cycles. Shown in Fig. 13.6 is a chart showing the results of cyclic fatigue testing under axial loading at several maximum stress levels along with the associated number of cycles to failure. The data having arrows associated with the points indicate that fatigue failure did not occur at that stress and the test was terminated. These are also referred to as “runouts.” The fitted line representing the data exhibits a characteristic sinusoidal curve for HCF. The horizontal line that has been added to the chart has been established statistically and represents the endurance limit for the material and reflects the specimen geometry and the loading conditions for the

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Fig. 13.6 Chart showing data for cyclic fatigue testing under axial loading based on maximum applied stress and number of cycles to failure (solid line has been fitted to the data)

test. The sinusoidal or S-N curve becomes asymptotic near the endurance limit. The endurance limit is also termed the fatigue limit or the fatigue strength at a specific number of cycles and is a property that represents the level of stress that may be applied under cyclic loading without fatigue failure. Many alloys exhibit this behavior and enable an accurate delineation of the endurance limit. This includes ferrous-based alloys, titanium alloys, and nickel-based alloys; however, aluminum and copper alloys do not provide a distinct limit for fatigue endurance. Characteristics that define an alloy’s sensitivity to corrosion are based upon tests that measure the corrosion rate through weight gain and identification of a corrosion product for an alloy within a specific environment, such as alternate immersion in a salt solution or continuous atmospheric exposure. Electrochemical corrosion tests are also extensively employed and utilize electrical potential and current to determine the rate of oxidation and reduction reactions of the material. By nature, electrochemical corrosion tests require less material and provide very quantitative data regarding corrosion reactions. In many instances the design and application of engineered components or structures require very specific properties that combine several conditions that may simultaneously act on the alloy and stress states that are dependent on the component. Examples of these combined test requirements and properties include the fracture toughness while in the presence of a corrosion environment and the fatigue strength that may be associated with various notches or surface conditions. Finally, in instances where the mass of the material also plays an important role for its use, specific strength is applied to account for the load-bearing capacity and density.

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13.5 Alloys for Unique Requirements As alluded to in the previous discussions, there is a large assortment of alloys that may be applied to additive manufacturing, with the selection of a particular alloy being dictated by the properties and characteristics required for the intended application. In certain instances, an application will require certain characteristics that may only be met by an alloy or material that possess unique attributes. Examples where unique materials are being utilized in additive manufacturing for imparting distinctive qualities include the use of refractory metals for high temperature service and metal matrix composites for high wear resistance at surfaces. Refractory metals, such as tungsten, tantalum, rhenium, niobium, and molybdenum, exhibit the highest densities and melting temperatures of metallic systems, which makes these materials attractive for applications involving high temperatures [34]. The ability of refractory metals to operate at high temperature also provides good elevated temperature creep resistance, and generally, they also exhibit high hardness and good corrosion resistance making them ideal for extremely aggressive environments. Tungsten and molybdenum also have a comparatively high thermal conductivity, tungsten being on par with some aluminum alloys. Melting temperatures of pure niobium and molybdenum exceed 2400 ◦ C, and tungsten, tantalum, and rhenium have melting temperatures above 3000 ◦ C. Refractory metals also exhibit low vapor pressures and high vaporization temperatures. These materials are also subject to oxidation at high temperatures and in the presence of relatively low levels of oxygen. Because of the high melting temperatures, commercial forms are produced using powder metallurgy, based on powder produced from chemical processes, which are then compacted into shapes and sintered at an elevated temperature to consolidate the particles and create a usable material. Final finishing usually requires special machining and grinding techniques. The unique qualities of refractory metals, which pose difficulties for traditional fabrication processes, make them especially attractive for creating net shapes through additive manufacturing techniques. Although refractory metals are used in pure form for very high-temperature applications, these materials are also alloyed for increased structural strength. In many instances refractory alloys are alloyed with other refractory metals for controlling grain size and grain boundary strengthening while maintaining relatively high elevated temperature service [35]. Examples of this include tungsten alloyed with rhenium or molybdenum and niobium alloyed with zirconium or molybdenum. Additional strengthening of selective refractory alloys is accomplished by alloying for solid solution strengthening and dispersion strengthening. Chromium and titanium are used for solid solution strengthening of molybdenum and dispersion strengthening through the formation of fine carbides by the addition of zirconium and carbon in niobium or titanium, zirconium, and carbon in molybdenum. The unique characteristics of refractory metals and alloys that enable these materials to be applied to specialized applications also must be considered during processing by additive manufacturing. The high melting temperatures require

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higher local energy densities for sufficient melting when using powder bed fusion techniques, and the sensitivity to oxidation at elevated temperatures, such as during melting and solidification, requires close control of oxygen levels during processing. Because of the higher energy densities available and the ability to process within a vacuum, the electron beam powder bed fusion process is ideally suited for processing of refractory materials. For larger structures, the electron beam-based directed energy deposition system has been used for processing of moderately large structures using refractory metals. However, cracking has been reported during powder bed fusion processing, in inert gas and vacuum, of molybdenum and tungsten and has been attributed to oxide formation during solidification leading to brittle grain boundaries, which reinforces the need for controlling oxygen levels during processing of these materials [36]. Metal matrix composites (MMCs) are another class of specialized materials that are routinely used in additive manufacturing. These materials rely on a composite strengthening mechanism that involves a matrix and reinforcement component representing two distinct materials. In many instances, MMCs are deposited locally onto surfaces for obtaining high wear resistance while retaining the strength and toughness of the substrate material. There are also applications where MMCs are being used to produce three-dimensional shapes to produce components having other unique characteristics found in many of these materials, such as high modulus or stiffness. As mentioned, MMCs rely on a matrix material and a reinforcement material to obtain unique properties and characteristics, with the interface between the two materials being sufficient to enable transfer of stresses under load. The strength of the matrix material, which is controlled by various strengthening mechanisms described previously, also plays a role in determining the properties of MMCs. However, the scale of the interaction between the matrix and reinforcement components that influences composite strengthening is at the macro-level and not at the microstructural level responsible for strengthening of the matrix. Matrix materials used for MMCs are typically known alloy systems, such as ferrous, aluminum, titanium, and nickel alloys, which are suitable for incorporating the reinforcement material. The suitability of the matrix material for a specific reinforcement material is based on retaining the reinforcement during melting and solidification, obtaining a defect-free matrix network, and developing a cohesive interface between the matrix and reinforcement [37]. The composite strengthening effect is based on the reinforcement material exhibiting significantly improved properties over the matrix alloy. Hence, reinforcement materials are generally ceramic materials that exhibit high properties, such as strength and modulus, but are difficult to produce and shape into usable forms. For most MMCs used in additive manufacturing, the reinforcement material is of a discontinuous form, as opposed to continuous fibers that are more common in polymer-based composite systems. The discontinuous reinforcement materials may be round or faceted particles or whiskers having higher aspect ratios [38]. Examples of reinforcement materials include oxides, carbides,

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and nitrides, although other reinforcement materials are also utilized. The properties that may be displayed by MMCs are dictated by the properties of the matrix and reinforcement materials, the proportion or “loading” of the reinforcement component within the material system, and the morphology and orientation of the reinforcement within the matrix [39]. The application of MMCs in additive manufacturing is accomplished using primarily two formulation techniques. In one technique the composite system representing the matrix and reinforcement material is processed through additive manufacturing to retain a significant portion of the reinforcement material. This approach may involve melting and solidification of the matrix material while preserving a significant portion of the unmelted reinforcement, such as with the powder bed fusion or directed energy deposition processes, or consolidation of the matrix and reinforcement materials followed by sintering of the matrix while retaining the reinforcement, such as with the binder jetting process. This method is referred to as ex-situ formulation, since the composite system is established prior to processing. The second technique, signified as in-situ formulation, involves the creation of the composite system through reactions that occur at high temperatures, such as during powder bed fusion or directed energy deposition processes that involve melting and solidification. In this case, the material that is processed contains elements that may react during processing to produce the desired composite structure upon cooling from elevated processing temperatures. As will be seen, even in instances of ex-situ formulation and processing, the potential for reactions between the matrix and reinforcement materials at high temperatures may also result in in-situ formulations based on the creation of additional phases [40]. However, it should be noted that in-situ reactions typically result in a finer scale of the second phase than true composite strengthening and are primarily responsible for increasing the properties of the matrix through dispersion strengthening. Shown in Fig. 13.7 are micrographs of two MMCs produced using the directed energy deposition process for improving the wear resistance at the surface of components [41]. Figure 13.7a represents WC particles as a reinforcement in a N06625 (IN625) alloy matrix formed ex-situ as a preblended powder used for deposition, and Fig. 13.7b denotes remnants of faceted TiC in a matrix of martensitic stainless steel alloy S42000 (420). The TiC in S42000 composite structure was initially formulated ex situ using a preblended powder but also involved partial melting of the TiC within the liquid pool and reformation of TiC and Ti(C,N) during solidification and cooling under an argon and nitrogen processing gas mixture. The remnants of the original TiC particles in the micrograph are shown as dark gray, faceted particles, and the Ti(C,N) that was formed in situ is shown as fine spherical particles present throughout the matrix material. The ability to retain the initial reinforcement material is governed by the thermodynamic stability of the reinforcement and matrix alloy compositions and the period of time that the molten pool is liquid.

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Fig. 13.7 Micrographs of metal matrix composite deposits representing (a) deposition of an ex situ composite deposited onto a substrate through the use of a powder blend containing nickel alloy N06625 (INC625) and WC particles and (b) TiC formed ex situ and in situ in a martensitic stainless steel alloy N07718 (IN718) matrix

13.6 Questions and Discussions 1. List and discuss the material properties and characteristics that are usually considered for applications in various industries, such as transportation, energy, aerospace, recreational products, and medical devices. 2. Define and discuss attributes of metallic systems that encourage or hinder the broad use of these materials for additive manufacturing. 3. Provide an example of a ternary phase diagram for a three-component system and discuss how it is used to define phases that may form upon cooling from the solidus temperature. 4. Discuss why the Hall-Petch relationship may not be adequate for describing the strength of metals having extremely fine grain size. 5. Define and briefly discuss the active strengthening mechanisms for martensitic stainless steels and precipitation-strengthened steels. 6. Explain why cobalt-chromium alloys are so readily available in powder form and austenitic stainless steels are so easily available as wire for feedstock in additive manufacturing. 7. Discuss how the material property KIC is used for determining suitability of an alloy for critical applications. 8. Define and discuss a composite strengthening relationship that may be used to describe the strength of boron-nitride particles in an aluminum alloy matrix that is being developed as a material for use in additive manufacturing.

References

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References 1. Lovatt AM, Shercliff HR, Withers PJ (2000) Material selection and processing. wwwmaterials.eng.cam.ac.uk/mpsite. Accessed Aug 2019 2. Karjalainen LP, Taulavuori T, Sellman M, Kyröläinen A (2008) Some strengthening methods for austenitic stainless steels. Steel Res Int 79. https://doi.org/10.2374/SRI08SP040-79-2008404 3. Goodfellow A (2018) Strengthening mechanisms in polycrystalline nickel-based superalloys. Mater Sci Technol 34:1–16. https://doi.org/10.1080/02670836.2018.1461594 4. Poondla N, Srivatsan TS, Patnaik A, Petraroli N (2009) A study of the microstructure and hardness of two titanium alloys: commercially pure and Ti–6Al–4V. J Alloys Compd 486:162– 176 5. Kawabe Y, Mune S (1991) Strengthening and toughening of titanium alloys. ISIJ Int 31:785– 791 6. Ahmed T, Rack HJ (1998) Phase transformations during cooling in α+β titanium alloys. Mater Sci Eng A 243:206–211 7. Hatch JE (1984) Aluminum: properties and physical metallurgy. ASM International 8. Oberg E et al (2004) Machinery’s handbook, 27th edn. Industrial Press Inc., p 440. ISBN 08311-2700-7 9. Bailey NS, Katinas C, Shin YC (2017) Laser direct deposition of AISI H13 tool steel powder with numerical modeling of solid phase transformation, hardness, and residual stresses. J Mater Proc Tech 247:223–233. https://doi.org/10.1016/j.jmatprotec.2017.04.020 10. Wang W, Pinkerton AJ, Wee LM, Li L (2007) Component repair using laser direct metal deposition, Proceedings of the 35th international MATADOR conference. Springer, London. https://doi.org/10.1007/978-1-84628-988-0_78 11. Xue L, Chen J, Wang SH (2013) Freeform laser consolidated H13 and CPM 9V tool steels. Metallogr Microstruct Anal 2:67–78. https://doi-org.proxy01.its.virginia.edu/10.1007/s13632013-0061-0 12. Kattire P, Paul S, Singh R, Yan W (2015) Experimental characterization of laser cladding of CPM 9V on H13 tool steel for die repair applications. J Manuf Process 20:492–499 13. Bassoli E, Denti L, Gatto A, Emilia R, Sewell NT (2018) Directed energy deposition of steel 316L: effects of build orientation. Int J Mech Eng Technol (IJMET) 9(8):438–446 14. Sciammarella FM, Najafabadi BS (2018) Processing parameter DOE for 316L using directed energy deposition. J Manuf Mater Process 2:61 15. Melia MA, Nguyen HA, Rodelas JM, Schindelholz EJ (2019) Corrosion properties of 304L stainless steel made by directed energy deposition additive manufacturing. Corros Sci 152:20– 30 16. Martukanitz RP, Babu SS (2004) Development of advanced coatings for laser modifications through process and materials simulation. In: Proceedings of the international conference on materials processing and design: modeling, simulation, and applications. American Institute of Physics, pp 1539–1546 17. Fang JX, Dong SY, Wang YJ, Xu BS, Zhang ZH, Xia D, Ren WB, He P (2017) Microstructure and properties of an as-deposited and heat treated martensitic stainless steel fabricated by direct laser deposition. J Manuf Process 25:402–410 18. Adomako NK, Noh S, Oh CS, Yang S, Kim JH (2019) Laser deposition additive manufacturing of 17-4PH stainless steel on Ti-6Al-4V using V interlayer. Mater Res Lett 7:259–266 19. Lia F, Park JZ, Keist JS, Joshi SB, Martukanitz R (2018) Thermal and microstructural analysis of laser-based directed energy deposition for Ti-6Al-4V and Inconel 625 deposits. Mater Sci Eng A 717:1–10. https://doi.org/10.1016/j.msea.2018.01.060 20. Dinda GP, Dasgupta AK, Mazumder J (2009) Laser aided direct metal deposition of Inconel 625 superalloy: microstructural evolution and thermal stability. Mater Sci Eng A 509:98–104 21. Chen B, Mazumder J (2017) Role of process parameters during additive manufacturing by direct metal deposition of Inconel 718. Rapid Prototyp J 23:919–929

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22. Zhang YN, Cao X, Wanjara P, Medraj M (2013) Fiber laser deposition of INCONEL 718 using powders. In: Materials science and technology conference and exhibition 2013, MS and T’ 13, vol 1, pp 37–49 23. Saboori A, Gallo D, Biamino S, Fino P, Lombardi M (2017) An overview of additive manufacturing of titanium components by directed energy deposition: microstructure and mechanical properties. Appl Sci 7:883 24. Dutta B, Froes F (2017) The additive manufacturing (AM) of titanium alloys. Metal Powder Rep 72:96–106 25. Baufeld B, Dutilleul T, Widdison R (2018) Wire based electron beam additive manufacturing. In: 70th IIW annual assembly and international conference, Shanghai, China 26. Lathabai S (2018) Fundamentals of aluminium metallurgy: recent advances. additive manufacturing of aluminium-based alloys and composites. Woodhead Publishing Series in Metals and Surface Engineering, pp 47–92 27. Martin JH, Yahata BD, Hundley JM, Mayer JA, Schaedler TA, Pollock TM (2017) 3D printing of high-strength aluminium alloys. Nature 549:365–369 28. Caiazzo F, Alfieri V (2019) Simulation of laser-assisted directed energy deposition of aluminum powder: prediction of geometry and temperature evolution. Materials 12:2100 29. Singh R, Kumar D, Mishra SK, Tiwari SK (2014) Laser cladding of Stellite 6 on stainless steel to enhance solid particle erosion and cavitation resistance. Surf Coat Technol 251:87–97 30. Kathuria YP, Tsuboi A (1996) Laser cladding of Stellite #6: a detailed analysis. In: Proceedings of lasers, optics, and vision for productivity in manufacturing I. Besancon, France. https:// doi.org/10.1117/12.251166 31. Zhang X, Cui W, Li W, Liou F (2019) Effects of tool path in remanufacturing cylindrical components by laser metal deposition. Int J Adv Manuf Technol 100:1607–1617. https:// doi.org/10.1007/s00170-018-2786-z 32. Zhang G, Chen C, Wang X et al (2018) Int J Adv Manuf Technol 96:4223. https://doi.org/ 10.1007/s00170-018-1891-3 33. https://www.nasa.gov/marshall/news/nasa-3-D-prints-first-full-scale-copper-rocket-enginepart.html. Accessed Aug 2019 34. Briant CL, Banerjee MK (2016) Refractory metals and alloys. In: Reference module in materials science and materials engineering. Elsevier 35. Wesemann I, Hoffmann A, Mrotzek T, Martin U (2010) Investigation of solid solution hardening in molybdenum alloys. Int J Refract Met Hard Mater 28(6):709–715. https://doi.org/ 10.1016/j.ijrmhm.2010.05.010 36. Braun J, Kaserer L, Stajkovic J, Leitz KH, Tabernig B, Singer P, Leibenguth P, Gspan C, Kestler H, Leichtfried G (2019) Molybdenum and tungsten manufactured by selective laser melting: analysis of defect structure and solidification mechanisms. Int J Refract Met Hard Mater 84:104999. https://doi.org/10.1016/j.ijrmhm.2019.104999 37. Baxter WJ (1992) The strength of metal matrix composites. Metall Trans A 23:3045–3053. https://doi.org/10.1007/BF02646122 38. Kaczmar JW, Pietrzak K, Włosi´nski W (2000) The production and application of metal matrix composite materials. J Mater Process Technol 106:58–67. https://doi.org/10.1016/ S0924-0136(00)00639-7 39. Aikin RM (1997) The mechanical properties of in-situ composites. J Metals 49:35–39 40. Fereiduni E, Ghasemi A, Elbestawi M (2019) Selective laser melting of hybrid ex-situ/insitu reinforced titanium matrix composites. Mater Des 184:108185. https://doi.org/10.1016/ j.matdes.2019.108185 41. Babu SS, Martukanitz RP, Parks KD, David SA (2002) Toward prediction of microstructural evolution during laser surface alloying. Metall Mater Trans A 33A:1189–1200

Chapter 14

Metallic Feedstock

Feedstock provides the added material for additive manufacturing processes and almost exclusively is in the form of powder or solid wire. In many instances the selection of the alloy for the process is not only based on the desired properties and characteristics of the fabricated material but also on the availability of a suitable alloy in one of these forms. Materials that are frequently used for additive manufacturing of three-dimensional components are available in these common forms, but in many instances, materials that are used for local deposition have adopted alloys that have been employed in more traditional processes for surface modifications, such as wire for arc welding or powder for plasma spraying. Powders are used in a range of sizes in many additive manufacturing processes for metals. Powder material is utilized for powder bed fusion, binder jetting, material extrusion, and powder-based directed energy deposition processes, whereas wire feedstock is used exclusively for directed energy deposition. The characteristics of the powder and wire used in additive manufacturing can influence the repeatability of the process and properties of the fabricated material. Hence, the quality of the feedstock used for the additive manufacturing process is an important consideration. Because of the relatively large amount of material utilized to produce the final components or structures, the cost of the feedstock is also an important factor and should always be contemplated alongside quality.

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14.1 Powder Processing for Producing Feedstock Metallic powders are used extensively in additive manufacturing, as well as in many other industries. To meet this demand, the production of metallic powders relies on a wide variety of processes that depend upon the metal or alloy being produced. Broadly, these processes include atomization, mechanical reduction, and various chemical reactions, and depending upon the process may use pre-alloyed material or a chemical reduction of a metallic compound to achieve the metallic powder. All of these powder production methods impart characteristics associated with the powder, such as size, morphology, purity, and production yield, that may impact the cost and use for additive manufacturing. Rather than examining all the production methods applicable to metallic powders, primary processes used for metals, alloys, and composite reinforcement materials that form the bulk of the additive manufacturing industry are discussed. Based on the desirable attributes of the atomization process, such as size, shape, and compositional control, it is by far the most prevalent process for producing metallic powder for additive manufacturing. There are several types of atomization that may be used to produce metallic powder and they may be categorized by the medium or method that is used to disrupt and separate a molten metal stream into droplets that solidify into particles [1]. These categories are water atomization, gas atomization, vacuum atomization, and centrifugal atomization. As one would expect, the various processes produce powders having distinctive characteristics based on the metal being processed. In the case of water, gas, or vacuum atomization, the molten metal that serves the atomizer is provided by a furnace that has used pig (bulk alloy cast for use in solidification processes), scrap, and master alloys to obtain the desired composition for the melt. Common furnaces used for melting are electric arc with an air or inert gas atmosphere or induction under inert gas or vacuum, with the type of furnace being dependent upon the metallic system being melted. Reactive metals, such as titanium or aluminum alloys, and alloys requiring low impurity levels, such as nickel-base super alloys, are melted in inert gas or vacuum, with vacuum melting provided the lowest contamination. Once the correct chemistry for processing is established, the molten metal is transferred to the atomizer to provide a liquid metal stream for processing. For higher production processes, the liquid metal, having an appropriate superheat, is transferred through the use of a tundish or transfer vessel. Lower production or experimental capabilities, as well as with vacuum processing, may include the furnace as an integral component of the atomizer. Depending upon the material and the method, the molten metal is allowed to free flow, which is commonly used for water atomization, or is backfilled with gas, which is employed for inert gas atomization, to force the liquid through a nozzle as a molten metal

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Fig. 14.1 Schematics of the water atomization and gas atomization processes for producing metal powders. (Image of water atomization courtesy of AMETEK Metals Corporation and image of gas atomization courtesy of Carpenter Additive)

stream to the atomizer. In the case of water atomization, a high-pressure stream of water is used to strike the liquid stream near the exit of the nozzle and disintegrate the stream of liquid metal into droplets. Gas atomization uses a similar approach except high-pressure gas, such as air, argon, or nitrogen, is injected at the nozzle exit and the rapidly expanding gas causes the liquid metal to fragment and form droplets. Shown in Fig. 14.1 are schematics of water and gas atomization that is used for producing metal powder. Upon atomization, the liquid droplets rapidly cool and solidify within the atomization chamber and are allowed to pass to the collection vessel. In the case of gas atomization, cooling of the metal particles is assisted using a gas medium, such as air, nitrogen, or argon. Although simple in principle, a host of parameters used for the atomization process is adjusted for a particular powder material, size, and yield. Parameters that influence the process and characteristics of powder produced during atomization include properties of the liquid metal, medium used for atomization, temperature of the liquid metal during processing, pressure used to force the liquid metal through the nozzle, and method of cooling the liquid droplets. Along with the above considerations, the design of the orifice and impingement angle of the atomization nozzle also plays an important role in helping to control the size distribution and shape of the powder being produced, as well as productivity of the process. Flow rate of the gas used for atomizing also plays an important role in the size of the powder produced, with higher flow rates favoring production of smaller particles. Because atomization produces powder having a distribution of size, after

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atomization the powder is sieved to common size distributions required for various processes. This could include powder having a size range between 10 and 50 μm for powder bed fusion processes and powder between 50 and 150 μm for directed energy deposition processes being produced during the same atomization process. A typical atomization process is regulated to produce powder having the most useful powder size distribution at the highest production rate.

Sieves and Sieve Size Sieving is frequently used to screen or filter a collection of small particles to a predefined size range. This is simply performed by allowing the particles to pass through a sieve having a certain mesh or opening size. The larger particles remain above the sieve and the particles that are smaller than the mesh size are allowed to pass through the sieve and be collected. By using multiple sieves having different mesh sizes, a quantity of particles may be produced having a known size distribution. Mesh size is a US measurement standard that defines the number of opening sizes within the sieve or screen, and the mesh number is the number of opening per inch of distance represented by the sieve. The standard mesh numbers used within the US for common mesh sizes and opening size are shown. As observed, the larger the mesh number, the smaller the opening size and smaller the particles that may pass through the mesh. Note that the mesh size is not a precise measurement since opening size is the function of the wire diameter used to create the mesh and it only provides sorting on a two-dimensional basis. Some industries have adopted and still use a powder size measurement in terms of mesh number, such as “+325–100” to represent powder being larger than 0.044 mm and smaller than 0.149 mm. (continued)

14.1 Powder Processing for Producing Feedstock

Photograph courtesy of Dual Manufacturing Inc.

U.S. Standard Mesh Mesh Number 20 25 30 35 40 45 50 60 70 80 100 120 140 170 200 230 270 325 400 500 635

Opening Size (in.) (mm) 0.0331 0.841 0.0278 0.710 0.0232 0.595 0.0197 0.500 0.0165 0.400 0.0139 0.355 0.0117 0.300 0.0098 0.250 0.0083 0.210 0.0070 0.177 0.0059 0.149 0.0049 0.125 0.0041 0.105 0.0035 0.088 0.0029 0.074 0.0024 0.063 0.0021 0.053 0.0017 0.044 0.0015 0.037 0.0010 0.025 0.0008 0.020

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Fig. 14.2 The plasma-rotating electrode process (PREP) for producing metal powder

A form of centrifugal atomization that utilizes a plasma-rotating electrode process (PREP) is used for producing high-quality powder in reactive metals, such as titanium [2]. The material to be atomized is in the form of a rod that is rotated at high speed and is continuously fed to a non-consumable tungsten electrode. The process is conducted under an argon or helium gas environment, and when an electric current passed between the metal electrode and the tungsten electrode, an electric arc-induced plasma is formed that causes melting of the metal electrode. The high speed of rotation results in centrifugal forces that eject the molten metal as droplets that are deposited onto a circumferential collection chamber. A schematic of the PREP process is shown in Fig. 14.2. Although PREP may be used to produce high-quality powder based on metal purity and particle sphericity, it is considered a more costly process. Water atomization is the most cost-effective means for producing powder for additive manufacturing; however, it is most suitable for metals and alloys that do not react with water. Water atomized powder of metals having a sensitivity to oxidation can be affected by oxygen generated during dissociation of the water during atomization and may produce surfaces on the powder having a relatively thick oxide. Also, because of the turbulence that is experienced during the liquid metal and water interaction, the morphology of water atomized powder is more irregular and departs from a spheroidal shape, many times exhibiting lager agglomeration of smaller particles. Water atomization is very appropriate for low-cost ferrous alloys and may also be used for nickel, copper, and the noble metals. Water atomization is never used for aluminum- or titanium-bearing alloys since the water molecule disassociates on contact with the molten material and liberates hydrogen gas, which is explosive. Water atomization offers a means for producing austenitic stainless steel alloys at a lower cost when compared to inert gas processing. Gas atomization produces a less violent reaction during atomization and produces powder generally

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having greater sphericity; although, depending upon processing conditions, powder produced by gas atomization may exhibit satellites of smaller particles attached to larger powder. Gas atomization of powder, depending upon processing parameters, may also entrap the atomization gas as pores within the powder, which may lead to potential porosity during the additive manufacturing process [3]. Depending upon the method used for melting, the chemical purity of gas atomized powder is usually very good. Nitrogen gas atomization is a lower cost production method when compared to atomization using inert gas but may result in absorption of nitrogen in the liquid metal during processing. This must be considered when obtaining powder for additive manufacturing of metals and alloys where the final microstructure may be influenced by high levels of dissolved nitrogen, such as the formation of retained austenite in the presence of nitrogen in ferrous alloys that are expected to predominately form martensite upon cooling. This may be alleviated through atomization using inert gases, primarily argon, which also increases cost associated with the production of the powder. As mentioned previously, the greatest control of composition is provided by vacuum melting and atomization and is used to produce powder having exceptionally low impurities. The PREP process employing a plasma and inert gas during centrifugal atomization produces powder having a high degree of chemical purity and very good control of sphericity. Shown in Fig. 14.3 are scanning electron micrographs of powder representing common alloys and powder production methods used for additive manufacturing. The production of powders for metals, alloys, and materials having high melting temperatures is typically produced using other techniques. Materials within this category that are applicable to additive manufacturing are refractory metals, such as tungsten, molybdenum, and tantalum, for producing three-dimensional components, as well as various hard particles, such as carbides, nitrides, and borides, used for producing metal matrix composite coatings. Production of powder representing refractory metals begins with extraction of the metal with impurities from ore. These compounds are then reduced through one or more chemical reactions to produce the pure material in a powder form [4]. The powder produced using this method tends to be irregular in shape, but similar to other production techniques, sieving may be used to achieve the correct size distribution. If high-quality scrap refractory metal is available, grinding and milling may be used to produce powder. Material constituting hard particles also have high melting temperatures and must be processed by alternate powder production methods. Various chemical reactions are used to create compounds representing the materials that are eventually processed into powder or particulates. Examples of these type of processes are the elevated temperature reactions of plant-based SiO2 with C to form SiC and the carburization of W to form WC. In many instances, crushing, grinding, and milling are used to further reduce the particles in size and may be followed by sieving to the desirable size distribution. The mechanical reduction in size produces particles that are highly faceted and commonly are of very fine size since these materials are usually compacted and sintered to produce usable shapes, and the sintering process is accelerated by shorter diffusional distances exhibited by fine particles.

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Fig. 14.3 Micrographs obtained by scanning electron microscopy of powder representing alloy R56400 (Ti-6Al-4V) atomized using argon gas, R56400 produced using the plasma-rotating electrode process (PREP), N07718 (IN718) atomized with argon gas, R30006 (Co-Cr) atomized with nitrogen gas, S43100 (SS 431) atomized with argon, and S43100 atomized using water (images courtesy of the Applied Research Laboratory, Pennsylvania State University)

A special technique, spheroidization, also may be used to alter powder produced by methods that do not provide spherical particles. Spheroidization uses high energy of a plasma formed using a high electrical current or an induction coil, with both techniques using an ionizing gas, such as argon. The process results in partial melting of the particles that are injected through the plasma, and the surface tension of the outer melted layer is used to modify the shape of angular or irregular powder to a near spherical shape. The process is applicable to a wide range of materials and has been applied to various metal powders, as well as powder representing refractory metals, carbides, nitrides, and oxides. The spheroidization process slightly reduces the mean size of the powder being modified.

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14.2 Powder Characteristics and Attributes The characteristics and attributes of the powder used as feedstock can directly and indirectly impact the additive manufacturing process [5]. Many of these characteristics and attributes may be measured using techniques that range from simple measurements to complex analytical tests, while some features of the powder are extremely difficult to ascertain. Although there are many opinions regarding the influence of powder on the additive manufacturing process, often supported by sound rationale, in many instances these relationships lack the exact experimental observation and evidence that support the premise. Much of this is due to the difficulty in directly measuring the condition of interest within the process; however, strides are being made in numerical modeling and advanced imaging techniques that may help further understand the importance of powder characteristics and attributes on the additive manufacturing process. The characteristics of the powder may be used to define the particulate material and may be described within three categories: the physical characteristics, the bulk chemical characteristics, and the surface chemical characteristics. The attributes of the powder describe the qualities that are displayed due to the interaction of particles as an assembly, as well as the interaction of the powder with the process. Tests to measure powder characteristics are well defined and standardized, and because of the maturity of the powder metallurgy industry, techniques for measuring the attributes of particle interaction have been developed and utilized for many years. However, the examination of powder interaction during the process is more difficult to accurately ascertain. Because the characteristics of the powder determine its attributes, both concurrently influence the additive manufacturing process. The attributes of the powder, which describe the various traits related to the movement and compaction of the powder as a bulk assembly due to particle-to-particle interaction, may provide the most observable effects on the process by influencing flowability, spreading, and packing of the powder during processing. However, there are instances when a characteristic of the powder is not easily detected during the process, such as impurities formed on the surface of the powder during processing or storage that lead to internal defects within the material produced during the additive manufacturing process. The following discussion will define the basic characteristics used to describe a powder, as well as the ramification of those characteristics on the attributes of the powder that may influence the process. Tests or techniques that provide quantitative information will be stressed; however, in some instances a qualitative description may be employed due to ease in defining the trait or lack of a quantitative method.

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14.2.1 Physical Characteristics of Powder Physical characteristics of the powder may be categorized as traits related to the individual particles and the properties reflecting the powder as an aggregate of particles. Although many of these characteristics are based on measurements of individual particles, the expression of these characteristics must account for the broader sampling of the aggregate, such as size of particles being represented by the size distribution of the collection. The physical characteristics of the powder may be defined as the shape, size, and density of the powder, mostly determined by an aggregation of particles dispersed within the test apparatus.

14.2.1.1

Shape of Powder Particles

The shape of a powder is most readily determined by imaging the powder at a suitable magnification. Optical microscopy is a low-cost means of obtaining this information, but the improved depth of field of scanning electron microscopes to provide a more three-dimensional representation is used quite often to determine the typical shape of a powder sample. A qualitative description of powder shape may be easily provided through association with common forms having recognizable descriptors. Shown in Fig. 14.4 are various two-dimensional images of shapes that may be used to describe and characterize powder material used for additive manufacturing. Under the proper atomizing conditions metallic powder is typically spherical or granular in shape; whereas hard particles representing carbides, nitride, or borides may exhibit an acicular, flake, angular, irregular, or aggregated appearance, depending upon the material and the means of production. Shown in Fig. 14.5 are

Fig. 14.4 Two-dimensional images of shapes that may be used to describe and characterize powder material used for additive manufacturing

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Fig. 14.5 Representative scanning electron microscope images of two metallic powders that are spherical in shape and TiC particles exhibiting an angular morphology. (Images courtesy of the Applied Research Laboratory, Pennsylvania State University)

representative SEM images of two metallic powders that are spherical in shape and TiC particles exhibiting an angular morphology. Also observed from the images in Fig. 14.4, powder morphologies do not always display a scale of size similar in all dimensions. Examples of this condition are powder that exhibit an acicular shape where the diameter of the rod-like particles may be much smaller than the length, and flake-shaped powder that is very thin in relation to the other dimensions. This may impact how the particle size is defined, as well as sieving of the powder to a redefined size. As in many of the characterization techniques that are employed for determining properties of a powder, the method of sampling should be sufficient to represent the powder being characterized. Considering the method used for distinguishing the shape of a given powder, it should be obvious that characterization should be of a sufficient sample size to represent the powder, as well as ensuring that the collection represents the powder population. This should include sampling of multiple containers in a random fashion, assuming they represent the same lot of powder, and at varying depths or after thorough mixing. To assess the statistical relevance of the characterization technique, the weight of the sample may be compared to the total weight of the powder population being sampled. Once a sufficient sample population is obtained, images from optical or electron microscopy may then be used to qualitatively characterize the shape indicative of the powder. The use of a shape reference, such as that found in Fig. 14.4, may be used to qualitatively define the shape of the powder. When greater definition of shape is required, automated analysis techniques of the powder images may be employed to provide quantitative information. These techniques utilize images of a collection of particles obtained from an optical microscope or a SEM that are analyzed using image processing algorithms to provide a quantitative parameter describing the shape of each individual particle, as well as the average values describing the entire assembly of particles. The test may be performed on a single image or multiple images of particles that have been dispersed under the camera’s field of view, as a static measurement, or imaged continually as dispersed particles are allowed to flow across the field of view, as a dynamic measurement. Shown in Fig. 14.6

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Fig. 14.6 Technique and equipment for dynamic measurement and analysis of particle shape. (Image courtesy of Microtrac MRB)

are a technique and equipment that utilizes a two-camera method for dynamic optical image analysis for particle shape. Using this technique, the powder is passed through the field of view through free fall, dispersion by an air stream, or a liquid dispersion for imaging at two magnifications. Analysis is conducted on the images and parameters are defined that describe the shape of the individual particles and the collection of powder. The automated image analysis is used to generate values representing the individual particle shapes in terms of various parameters, such as roundness, circularity, aspect (length to width) ratio and symmetry, as well as various descriptions of particle size. As a simple approach, the analysis may use a perfect sphere as a reference by comparing the measured ratio of a particle’s boundary length to crosssectional area to that of a sphere, with higher values indicating greater irregularity in shape. The data representing the entire sample size may be viewed based on a percentage of the sample for each range of particle size and provides a cumulative distribution of size of the particles. Similar distributions may be used based on the shape calculated parameters, and summary data for the various shape parameters may also be provided.

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14.2.1.2

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Size of Powder Particles

The size of the powder is also an important characteristic for additive manufacturing. Realizing that the size of the powder or aggregate always represents a range, statistical means are used to define the distribution of the entire sample. As discussed previously, sieving using an assortment of sieve sizes and image analysis may be used to determine the size distribution of a powder sample. In the case of sieving, the size categories are determined by the sieve sizes that are progressively used to sort the powder, and the weight percentage of the powder for each size category is used to construct a histogram based on the weight of the powder for the various size classes represented by the sieves. Size distributions using imaging techniques employ a similar categorization technique, but the size distribution is usually shown as percent volume based on a total that is derived from an approximation of volume determined from each particle. Shown in Fig. 14.7 is a notional size distribution based on the cumulative weight for a few thousand particles of a powder sample. The distribution shown in the figure was based on the powder being sieved using seven sieves with openings at 10 μm intervals from 10 to 70 μm. After sorting the powders within these size categories, the powder within each sieve was weighed and plotted for each size category. This data is shown in the figure as bars reflecting the weight for each size category and represents a size histogram. A line has also been fitted to the histogram, shown as a dashed line. The cumulative weight of the powder at each size category can be used to determine the weight percent based for each size, and this is also shown on the graph as the solid line. This line represents the cumulative size distribution of the sampled powder. Along with the entire size distribution curve, it is common to report the size distribution for powder based

Fig. 14.7 Size distribution based on the weight of a powder sample

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on the cumulative weight or volume at the 10%, 50%, and 90% values, which are depicted in the figure as d10 , d50 , and d90 , respectively. Based on the measured distribution of the data in the figure, 10% of the powder is less than 27 μm (d10 ), 90% of the powder is less than 52 μm (d90 ), and the median powder size is 38 μm (d50 ). Note that the size distribution in Fig. 14.7 suggests a normal or Gaussian distribution, and under this condition, the median is equivalent to the mean or average size of the powder. However, not all powder size measurements may yield data representing a normal distribution, with some being skewed to the lower or larger sizes, or even bimodal and having two size maximums. When the distribution is skewed to the larger sizes, being right-skewed or having positive skewness, it may be represented as a log-normal distribution. The most common method today for efficiently determining powder size distributions involves the use of laser diffraction as a static measurement. In this technique, one or two lasers, depending upon the size range for measurement, are directed at particles dispersed within the sample chamber. The particles cause scattering of the laser radiation in all direction and form circular rings on a detector. The diameter of the rings is inversely proportional to the size of the particle responsible for the scattering, such that an inversion algorithm may be used to enable the diameter of the powder to be determined from the scattering image. The intensity of the scattered light is a function of the particle size in relation to the laser wavelength, with higher intensities being generated when the particle is much smaller than the wavelength, and hence the use of multiple lasers to extend the size range that may be detected. By measuring many particles within the sample, a complete powder size distribution may be generated. Shown in Fig. 14.8 is a schematic of the laser diffraction technique within a system designed for measuring powder size distributions. Shown in Fig. 14.9 is an example of size distribution data generated using the laser diffraction method for measuring the size distribution of a powder. In the example, the data reflects a log-normal distribution for the powder.

14.2.1.3

Density of Powder Particles

The density of the powder as a physical characteristic signifies the soundness of individual particles representative of the powder under study and is not the density of an aggregation of powder particles, such as the packing density, the latter being examined during the discussion on powder attributes. Under most production conditions, the metallic powder used for additive manufacturing is very sound and represents the density of the bulk alloy. However, since the vast majority of powder used for additive manufacturing is produced using a form of atomization, there is the potential to absorb or entrap either the gases used for atomization or a gas by-product of the atomization process. Although care is taken to control the atomization process to minimize entrapped gas, it has been theorized and supported by observation that higher atomization energies and gas velocities may lead to undesirable melt fragmentation that allows gas entrainment within the powder [6]. It has also been observed that under conditions that favor gas entrapment, porosity

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Fig. 14.8 Schematic of laser diffraction being used for measuring powder size distributions of a powder sample. (Image courtesy of Malvern Panalytical)

Fig. 14.9 An example of a size distribution obtained by the laser diffraction method for a powder sample. (Courtesy of Malvern Panalytical)

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Fig. 14.10 Scanning electron micrographs of N07713 alloy powder having a size of 45–106 mm produced by (a) inert gas atomization with high kinetic energies showing porosity in 21% of the particles and (b) argon gas atomization with lower kinetic energies showing pores in only 4% of the powder. (Images used with permission; copyright 2018 Elsevier Ref. [8])

increases as a function of powder size, with a large increase in dissolved gas and porosity found in powder diameters above 75 μm [7]. Common techniques applicable for detecting internal porosity within particles are optical or electron microscopy, and more analytical techniques available for measuring the soundness of powder include gas pycnometry and micro-computed tomography. In the case of optical or electron microscopy, a sample of powder is encapsulated within mounting material and the powder and mounting material is polished to observe cross sections of individual particles that have intersected the surface of the mount. Optical or electron images are used to interrogate the particles for evidence of internal porosity. The exact volume of internal pores within the particles requires a stereological correction since individual particles are sectioned at different depths. Shown in Fig. 14.10a are SEM micrographs from Anderson et al., using the backscattered imaging technique, for powder of Ni-based superalloy N07713 (MAR-M-247) that had been inert gas atomized using relatively high kinetic energy and having a size range of 45–106 μm [8]. The micrographs were obtained from mounted specimens that have been prepared metallographically and exhibit 21% of the particles having internal porosity. Figure 14.10b shows similar

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SEM micrographs for powder representing the N07713 alloy that had been argon gas atomized yielding a similar size range but atomized using lower kinetic energies where only 4% of the powder displayed internal porosity. Other techniques are also available for accurately measuring powder density. Gas pycnometry, mostly using helium, involves a special apparatus that can accurately determine the total volume of an assembly of particles. Prior to pycnometry, a small sample of powder is weighed to determine its mass. The powder sample is then placed into the pycnometer chamber having a known volume. A calibrated volume of gas at a known pressure from a second chamber is then introduced to the sample chamber and the new pressure is measured. Using the combined gas law, the measured pressure is used to adjust the reference volume, which is then subtracted from the known volume of the chamber to determine the volume of the powder sample. Density is then calculated using the mass obtained during weighing. The calculated density is then compared to the density of the bulk material. Because of the inherent variability that may be associated with powder sampling and testing, several tests should be employed for increasing accuracy of the measurement. Moisture on the surface of the powder may also influence the results of gas pycnometry measurements. Micro-computed tomography has also been used to assess powder density. With this method, a sample of powder is placed in a container having a low radiation cross section, such as a polymer. Similar to computed tomography (CT), micro-CT employs many perspectives using radiographic projection and digital reconstruction software to obtain three-dimensional images based on the density of the material being interrogated; micro-CT uses lower x-ray energies and greater magnification to achieve higher feature resolution, potentially below the 1 μm range. This enables micro-CT to generate images of a collection of powder at a definition that enables internal voids to be determined. Image analysis software that is usually associated with this technique may also be used to determine the total volume of the powder and the volume of voids based on changes in contrast to the images; however, accurate determinations of density require calibration of the algorithms used for image analysis, since changes in image contrast may also be caused by other factors not related to internal voids, such as local changes in composition or changes in attenuation of a polychromatic beam (having a range of energies) as it passes through the sample.

14.2.1.4

Composition of Powder

Because of the importance of establishing the accurate composition of a metal, there are various standardized methods applicable to determining the bulk chemical composition of metals and most are applicable to powder. More common methods include inductively coupled plasma-mass spectroscopy (ICP-MS), optical emission spectroscopy (OES), energy-dispersive x-ray spectroscopy (EDS), and xray fluorescence spectroscopy (XRF). All of these techniques are applicable to compositional determinations of metals, not only in powder form, and they all

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have various traits that make a specific test more appropriate depending upon the elements of interest, accuracy required, and circumstance, such as availability and cost. Although it is not the intention of this discussion to describe in detail these techniques, a discussion on what methods that may be applied to the various metal powders used in additive manufacturing is appropriate, as well as a brief introduction to spectroscopy, which is an important component to many of these techniques. Another important factor that is relevant to the selection of the method employed for chemical analysis is whether the assay is to be performed on the powder itself or material that has been produced using melting and solidification of the powder. When the composition is needed for evaluation or certification of the powder, the approach should be obvious. Whereas analysis of material produced using the powder is generally easier to conduct, it may not provide an accurate representation of the powder chemistry due to evaporation during melting of alloying elements having high vapor pressures. However, this approach may be applicable to certain determinations of chemical composition. As mentioned, spectroscopy plays a role in many of the techniques used for measuring elemental composition. Spectroscopy involves the measurement of intensity of a response as a function of wavelength or frequency during the interaction of a material with electromagnetic radiation. The source of the interaction may be due to atoms and ions produced by a plasma (ICP-MS and OES) or characteristic xrays ejected from the material (EDS and XRF), and the response data is normally shown through an emission spectrum as a function of the wavelength, frequency, or energy. The intensity of the response for a given element is utilized with appropriate standard response data to provide the concentration of that element. The source of energy for ICP-MS is a plasma created by an electromagnetic coil with an argon carrier gas, and the sample is typically a liquid solution, such as an acid, that is used to dissolve the sample. A high voltage electric arc is used to create the plasma during OES, and the sample to be tested usually represents a flat surface having an area of up to 100 mm2 . It is quite common for scanning electron microscopes to also incorporate an EDS detector, which uses the electron beam to cause emission of characteristic or secondary x-rays. Because of the finely focused electron beam, EDS is considered a microanalysis technique. The XRF method for chemical analysis utilizes an x-ray source to bombard the specimen and generate characteristic or secondary x-rays and may be used as a semi-microanalysis technique. However, as with EDS, the XRF energy source may be scanned to generate compositional data over an area. In the case of EDS, the high resolution of the electron beam allows the technique to be used for identifying the changes in elemental composition at the microstructural scale. The frequency or energy spectrum that is obtained from these tests is used to identify the presence of elements, and the intensity of the peaks is compared to data from standards to determine the quantity, usually as a percentage, of the respective elements. In the case of EDS, the spectra represent a characteristic energy of the x-rays produced when there is a transition of electrons from the inner shells of the atoms. This transition occurs when the material is bombarded with x-rays from a primary source that results in the emission of secondary x-rays having

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Fig. 14.11 Spectrum obtained from energy-dispersive x-ray spectroscopy of stainless steel alloy S31603 (316L) powder showing energy peaks representing elements present within the alloy. (Image courtesy of the Applied Research Laboratory, Pennsylvania State University)

characteristic energies that represent elements within the material. This response is shown as lines at specific energies representing electron transitions from one atomic energy level to another energy level. Each transition creates a characteristic x-ray having an energy that reflects the difference in energies between the transition levels or subshell levels. Energies that are often used include the transition of electrons from the L to K shells (Kα energy lines having two subshells), M to K shells (Kβ energy line), M to L shells (Lα energy lines having two subshells), and the N to L shells (Lβ energy line). The characteristic x-ray energy lines are associated with specific elements that are present, and the intensity of the lines, depending upon the reference data that is available, may provide a qualitative or quantitative indication of the amount of the individual species present. Shown in Table 14.1 are characteristic energies in electron volt (eV) for electron transitions from x-ray fluorescence emission for selective elements. Shown in Fig. 14.11 is a spectrum obtained from energy-dispersive x-ray spectroscopy of stainless steel alloy S31603 (316L) powder showing energy peaks representing elements present within the alloy. The line energies illustrated in the figure may be used with appropriate software and standards to provide the total composition of the alloy based on the individual constituents that are present. It should be noted that the various forms of spectroscopy are extremely useful for determining the composition of metallic materials, including powder. However, these techniques do have some limitations. Although these techniques are applicable to a large number of elements present in many alloy systems, all elements are not

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Table 14.1 Characteristic x-ray fluorescence emission energies in electron volts (eV) of selected elements Element Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Rb Sr Zr Nb Mo Tc Ru Rh

.Kα1

.Kα2

.Kβ1

.Lα1

.Lα2

.Lβ1

54.3 108.5 183.3 277.0 392.4 524.9 676.8 848.6 1040.98 1253.60 1486.70 1739.98 2013.70 2307.84 2622.39 2957.70 3313.80 3691.68 4090.60 4510.84 4952.20 5414.72 5898.75 6403.84 6930.32 7478.15 8047.78 8638.86 13,395.3 14,165.0 15,775.1 16,615.1 17,479.3 18,367.1 19,279.2 20,216.1

848.6 1040.98 1253.60 1486.27 1739.38 2012.70 2306.64 2620.78 2955.63 3311.10 3688.09 4086.10 4504.86 4944.64 5405.51 5887.65 6390.84 6915.30 7460.89 8027.83 8615.78 13,335.80 14,097.90 15,690.90 16,521.00 17,374.30 18,250.80 19,150.40 20,073.70

1071.10 1302.20 1557.45 1835.94 2139.10 2464.04 2815.60 3190.50 3589.60 4012.70 4460.50 4931.81 5427.29 5946.71 6490.45 7057.98 7649.43 8264.66 8905.29 9572.00 14,961.30 15,835.70 17,667.80 18,622.50 19,608.30 20,619.00 21,656.80 22,723.60

341.3 395.4 452.2 511.3 572.8 637.4 705.0 776.2 851.5 929.7 1011.70 1694.13 1806.56 2042.36 2165.89 2293/16 2424.00 2558.55 2696.74

341.3 395.4 452.2 511.3 572.8 637.4 705.0 776.2 851.5 929.7 1011.70 1692.56 1804.74 2039.90 2163.00 2289.85 2420.00 2554.31 2692.05

344.9 399.6 458.4 519.2 582.8 648.8 718.5 791.4 868.8 949.8 1034.70 1752.17 1871.72 2124.40 2257.40 2394.81 2538.00 2683.23 2834.41

Data provided by Refs. [8, 9]

detectable. In many instances, light elements, having atomic numbers lower than 11 (sodium), pose difficulties for ICP-MS, EDS, and XRF, but carbon, nitrogen, oxygen, phosphorus, and sulfur may be detected by OES.

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When fine powder is employed in additive manufacturing processes that rely on melting and solidification for consolidation, a relatively large amount of surface area contributes to the formation of the molten pool. Constituents on the surface of powder may represent oxides, as well as organic species, such as moisture or by-products of the reaction of water vapor with the oxide on the powder surface. The chemical species, the low level of the species that may be present, and the location of the element or compound at the surface require specialized techniques for interrogation. In many instances, the interest is not only detecting elements but also potential molecules, which may represent organic compounds that may disassociate upon melting to elemental species that may form gas porosity within the melt. This includes compounds containing hydrogen, oxygen, and nitrogen, as examples. The subject of surface chemistry analysis is a discipline in itself and subject to many intricacies, capabilities, and skills related to specialized procedures. However, there are two techniques that are relevant to metal powders, secondary ion mass spectroscopy (SIMS) and x-ray photoelectron spectroscopy (XPS). Both techniques can provide elemental and molecular information for constituents at the near surface, between 1 and 10 nm in depth. They may be used to determine elements, residues, or compounds on the surface, with the exception of free hydrogen. It should be noted that these are highly specialized techniques that often require skilled interpretation of the results. Gas-containing species, which may be present in molecular form at the surface, or dissolved gas within the metal, are also of interest for metallic powders. During processing, hydrogen, nitrogen, and oxygen may be absorbed within the molten pool and form gas pores upon solidification. The particular gas species that results in porosity will depend upon the metallic system, such as hydrogen in aluminum alloys and nitrogen and oxygen in steels. A standard technique that is utilized to measure the total amount of gas is the inert gas fusion technique that melts a small amount of material in an inert gas. The total amount of gas that is extracted after melting is then analyzed using infrared absorption or high-sensitivity thermal conductivity to measure the amount of gas present. Three common gas species are routinely measured: hydrogen, nitrogen, and oxygen. The initial weight of the sample interrogated is used to determine a percentage of gas within the specimen in percent or parts per million. This technique determines the total gas present, including gas dissolved within the metal powder, as well as gas species that may have been liberated from the surface during heating of the sample to the melting temperature.

14.2.2 Characteristics of a Powder Aggregate There are several characteristics that define the powder assembly that are more difficult to measure directly but nevertheless are important physical traits that help define the bulk characteristics of the powder. Because of the importance of these characteristics on assessing the ability of powder to be used in a consistent

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Fig. 14.12 Schematic illustrating several mechanisms that may influence particle motion through increasing cohesive strength between powder particles. (Image courtesy of Freeman Technology Ltd.)

and reliable manner, it is worthwhile to examine the physical aspects of particle interaction while offering rationale regarding the influence of powder characteristics on these attributes. Two important aspects of powder during additive manufacturing are flow and packing. The flow of powder, be it within the hopper, feeding lines, or nozzle prior to injection into heat source for directed energy deposition or along the base plate due to movement of the recoater blade for powder bed fusion, may be described based on resistance of powder to flow initiation as a quasi-static condition or bulk flow operating within a dynamic regime [8]. For both cases, the bulk motion of the powder assembly may be described based on the cohesive strength between particles, frictional forces between particles and their surroundings, and the density of the assembly. Shown in Fig. 14.12 is a schematic of several mechanisms that may restrict particle motion by influencing the cohesive strength of powder particles in a collection. In the case of frictional forces between particles flowing against each other, surface roughness may impact the level of friction acting on the particles. Friction also plays a role when particles flow past walls or surfaces, such as feeding tubes or a flat build plate. Smoother surfaces provide less friction. Forces due to interlocking of individual particles may also impede flow when powder shape favors this type of interference. Interparticle forces, due to Van der Waal forces leading to greater particle-to-particle attraction or electrostatic forces that may act to attract

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or repel particles, may also impact cohesive strength and flow. Bridging between particles, such as with the presence of moisture molecules, may also increase cohesive strength between particles. Generally, increasing the cohesive strength of the powder assembly will decrease the flowability of the powder, with freer flowing powder being observed with larger particles being spherical in shape and having low moisture content [9]. Forces acting to facilitate flow of powder are due to gravity acting on stationary particles and inertia of moving particles, which may be enhanced by fluidization of the powder through the use of a flowing gas. Smaller particles and powder material having a lower density result in smaller gravitational forces when compared to the cohesive forces and generally decrease the flowability of a powder. The packing density of the powder, which describes the degree in which the powder assembly is consolidated, may be defined as the sum of the volume of all individual particles to the volume that the particles occupy: i=n ρp =

.

i=0

V

p

Vi

(14.1)

 p where . i=n i=0 Vi is the summation of volume of all particles that are contained within a volume of space, V. With a suitable density of the metal signifying the powder, packing density may also be expressed as mass per volume in g/cm3 . Packing density is dependent upon several factors related to characteristics of the powder, such as shape, as well as the means that is used to form the particle assembly. Hence, several packing densities have been established based on the method that was used to arrange the particles within a given volume. This includes the aerated density representing the lowest density achieved by gravity, the apparent density representing a poured powder, and the tap density which characterizes the powder density after some form of vibration. Both aerated and apparent densities are considered a random close packing of the powder. Shown in Table 14.2 are values for packing densities for random close-packed particles having different shapes using data from Carson et al. [10]. As illustrated in Table 14.2, packing density is a function of particle shape, with spherical and near-spherical particles typically exhibiting a packing density in the range of 0.60. However, it should be noted that the packing densities of Table 14.2 reflect a random close packing and may be influenced by consolidation of particles under external forces. Also, higher packing densities may be achieved with spherical particles by utilizing a bimodal size distribution where the smaller particles are able to fit within the interstitial areas of the larger particles. Packing densities that result in greater difficulty for particles to rearrange within the assembly, while still maintaining loose random packing, will typically decrease the flow of the aggregate. However, the characteristics that affect the flow also influence the packing density of a powder, such that the sole effect of packing density under conditions considered random close packing on flowability may not be easily ascertained. Nevertheless, packing density, as measured under controlled

406 Table 14.2 Packing densities for random close-packed particles having various shapes [10]

14 Metallic Feedstock Particle shape Spheres Spheroids Disks Cubes Parallelepiped Rounded aggregates Crushed aggregates Short fibers

Random close packing density 0.60–0.64 0.58–0.61 0.63 0.76 0.51–0.67 0.59–0.63 0.50–0.57 0.48

conditions that attempt to mimic the function of the powder within the processing system, is one of the most widely used technique for determining the suitability of a powder for use. Tests have been developed to measure important mechanical parameters related to the flow of powder as a bulk material. Many of these tests utilize a rheometer to gauge the flow of powder under applied forces and hence measure the rheology of the powder aggregate as a continuum. Typically, the powder is externally loaded and the resistance to motion of the bulk powder is measured as a normal and shear stress required for initiation and continuation of flow. The results of these tests can provide direct indications of flowability, as well as generating information that may be applied to define important parameters used in mechanics analysis of the powder as a bulk solid [11, 12]. This analysis involves a relatively simple examination of force equilibrium to determine the influence of external forces on plastic deformation or flow of the bulk solid. Cohesive forces, representing adhesion between particles of the aggregate, act to oppose plastic deformation, with deformation or flow representing shear zones at various planes within the solid. Figure 14.13 describes this approach schematically from the analysis of Tomas [13]. In the top figure, points representing flow for normal and shear stresses under a biaxial stress state are plotted to define a yield locus. The plot represents the linear portion of the shear stress versus normal stress data. The slope of the yield locus signifies the internal friction of the solid, and the intersection of the locus with the normal stress at zero (τ c = 0) represents resistance to shear due to cohesive forces between particles in the absence of external normal stress. Although present but not shown in the schematics of Fig. 14.13, cohesive forces also exist between particles. The resistance to shear, described by the slope and intersect at τ c , is strongly dependent upon the cohesive stress developed through history of stress on the aggregate, as well as chemical reactions that may occur over prolonged periods. By employing Mohr’s circle for resolving the principal stresses at consolidation of the powder, the major stress in the vertical direction and the minor stress in the horizontal direction of the aggregate may be determined. If it is assumed that the vertical stress does not include shear, the compressive stress, σ c , representing the compressive strength of the aggregate may be defined from the intersection of the semi-circle when τ = 0. This value is a characteristic of the cohesive strength of the consolidated aggregate under uniaxial compression and is also referred to as

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Fig. 14.13 Schematic of biaxial stress states for a powder aggregate under shear and normal stress. (Figure adapted from original and used with permission, Copyright 2003 Trans Tech Publications Ref. [13])

the unconfined yield strength of the bulk solid. Utilizing a similar approach during consolidation of powder within a contained cylinder, the consolidation stress, σ 1 , may be determined from the maximum principle stress at τ = 0 and defines the conditions of the powder at the end of consolidation. The ratio of the uniaxial compression strength and the consolidation stress have been defined as the flow function, FF, for the bulk material [14]: FF =

.

σ1 σc

(14.2)

Shown in Fig. 14.14 is a graphical description of data for FF adopted from Schulze [15] based on the values that described the flow function, the unconfined yield strength as a function of the consolidation stress, as curve A. Also shown in the figure are regions indicating the classification of flowability, with the boundaries being represented by straight lines having a constant ratio of consolidation stress to unconfined yield strength [14, 15]. It must also be reiterated that the compressive strength of the aggregate is dependent upon the consolidation history. An example of this dependency is illustrated in Fig. 14.15, where the flow function for curve B in the figure represents powder after a storage period and the development of additional cohesive strength.

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Fig. 14.14 Flow diagram based on stress measurements of a powder aggregate. (Figure adapted from Schulze with permission, copyright 2021 Springer Ref. [15])

Fig. 14.15 Hall flow meter. (Image courtesy of Qualtech Products Industry)

14.2.3 Attributes of a Powder Aggregate The attributes of an aggregate of powder are measured properties that describe the interaction of particles and, in a practical sense, depict the qualities that influence the transfer, packing, and processing of the bulk powder. Ideally, these attributes are controlled by the physical and chemical characteristics of the powder and the powder aggregate. Obvious examples of powder qualities that may be important in additive manufacturing of metals include the consistency in the flow of powder within feeding lines and nozzles for directed energy deposition and the uniformity

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of recoating and powder packing during the powder bed fusion and binder jetting processes. Because of the difficulty in quantifying these traits during processing, techniques have been developed to gauge and determine attributes that may be used to describe the behavior of the bulk powder under similar conditions. Common attributes are the flowability and packing efficiency of the powder aggregate and simple tests have been developed to determine these attributes. Although these tests provide empirical information, they serve as a means of establishing baseline parameters that may be compared to process effectiveness. In all cases, these tests are used to measure attributes and qualities of the powder as an aggregate. As alluded to above, more complex tests have also been developed to measure the rheometric characteristics of a powder aggregate with the goal of relating these characteristics to attributes that define the quality of the powder for processing. Flowability and packing efficiency are two common attributes used to describe powder, and hence, simple tests have been developed to easily measure these attributes. Note that the definition of flow and packing of powder in this discussion is only indirectly related to the principles regarding these conditions described previously. Flow and packing as attributes of a powder aggregate are qualities obtained from standard tests that may or may not reflect the use of the powder in additive manufacturing processes. Nevertheless, they provide an indication of the basic traits of the powder at a point in time. Although there are variants of these tests, the most common are discussed with the goal of describing the basic principle of operation and the information that is provided. The Hall flow meter is a simple test used to measure flow and apparent density of a powder. The Hall test uses a standard funnel having a 30◦ angle and a 2.54 diameter orifice. A set amount of powder based on weight is allowed to flow through the funnel and the time for completion is measured. Shorter periods of time for the entire powder sample to pass through the orifice indicates better flowability. The Hall flow meter is shown in Fig. 14.15. Flowability of powders that cannot easily flow through the Hall meter may be measured in a similar manner through the use of a Carney funnel, which is similar to the Hall funnel but has an orifice diameter of 5.08 mm. Another attribute that may be determined using the Hall flow meter is the static angle of repose. Figure 14.16 is a schematic of the determination of the static angle of repose for a powder aggregate. The angle of repose is established by feeding the powder through the Hall funnel onto a circular plate of known diameter, D. The bottom of the Hall cup may be used for this type of measurement. The powder is allowed to flow until the diameter is filled. The height of the powder, h, deposited onto the plate is measured and the angle of repose, θ r , is calculated using the following relationship:  θr = arctan

.

2h D

 (14.3)

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Fig. 14.16 Measuring the angle of repose for a powder aggregate

However, it should be noted that several test factors may influence the angle of repose, such that the most reliable comparisons are based on measurements conducted using the same test configuration and parameters. The Hall flow meter may also be used to ascertain apparent density, density of the loose powder, through a standard cup that may be filled using the Hall funnel. After filling the cup, the weight of the powder and cup is measured. Since the cup has a standard weight and volume, the weight of the powder may be determined and dividing the powder weight by the known volume of the cup enables the tap density to be expressed. Along with the apparent density, the tap density representing some level of consolidation of the power is also frequently determined for a powder aggregate. The tap density is measured in a similar fashion as the apparent density but after consolidation by “tapping” or vibration. Based on the consolidation of particles with the volume, the tap density is always higher than the apparent density of a powder. Because the degree of consolidation has a strong influence on the tap density, the means used to induce packing of the powder should be controlled. Tap density may be obtained for a moderate consolidation by physically tapping the Hall cup during filling. Other techniques use vibration during filling of a graduated volume using a predetermined weight of powder to more fully consolidate the powder. As with apparent density, the mass of the powder divided by the volume that the powder occupies provides the tap density. Powder rheometers are being used to characterize powders applicable to additive manufacturing. The expectation in using these devices is that quantifiable data related to the mechanics of dynamic powder flow would be obtained and could be used to relate the test results to actual conditions found during processing. Most rheometers used for measuring powder attributes are of the rotational or shear type. Shown in Fig. 14.17 is a powder rheometer that is finding acceptance for examining powders used in additive manufacturing. This particular device utilizes rotating blades that also travel vertically in a helical path to measure the resistance to rotation, in torque, and vertical movement, in force. The continuous measurement of these values is also illustrated in the figure. The continuous measurement of torque and vertical force is used to calculate the energy gradient for work expended

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Fig. 14.17 Powder rheometer for measuring various properties of powders. (Images courtesy of Freeman Technology Ltd.)

to move through the powder as the blade rotates and moves vertically. From the area under the energy gradient curve, the total flow energy representing the resistance of the powder to flow may be determined. Through minor changes in the test configuration, various powder characteristics may be ascertained. This includes forced flow and unconfined flow of powder, powder conditioning and consolidation, shear rate sensitivity during flow, and shear cell measurements for determining unconfined yield strength and consolidated stress associated with a powder. Although powder rheometers are seen as a valuable tool for developing a greater basis for understanding the qualities and characteristics of powder, there remains a need for establishing direct relationships for properties and characteristics obtained from these tests for many of the conditions found in additive manufacturing processes. The tests described above provide, in many instances, quantitative and reliable data regarding the attributes of a powder aggregate at that point in time; however, the real interest from an additive manufacturing standpoint is how will the powder behave under the conditions that are operative within the processing system. Practical traits of the powder within the system may include the ability to feed and provide consistent mass flow rates within relatively long lengths of feeder tube in directed energy deposition, capacity to be spread over the build plate in a uniform manner for hundreds or thousands of cycles for binder jetting or powder bed fusion, and being able to produce and maintain a homogeneous blend of powder representing a metal alloy and hard particles for depositing a MMC material. Hence, there is usefulness to be able to relate the attributes of a powder obtained under more controlled conditions to performance during additive processing. Ideally, if relationships are available that accurately depict the influence of powder characteristics on attributes, and with the extension to powder performance within the system, closer control of powder may be used to further increase the reliability of the additive manufacturing

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process. Further, the attributes of a powder feedstock may not be static with storage, handling, and recycling, and the ability to assess the current state of a powder is also of importance for controlling the process. The question remains: how can the powder attributes be used to help control powder feedstock for additive manufacturing? Historically, much of the work conducted on the mechanics of powder flow has been directed at bulk flow properties of powder, such as through hoppers, outlets, and large feeding lines, whereas the requirements for powder flow in additive manufacturing are quite different. Nevertheless, several observations regarding powder mechanics and power attributes may be applied to additive processing. The cohesiveness of a power does impact feeding. As discussed previously, higher cohesive strength requires higher shear forces for inducing plastic yield and flow. Moisture content plays an important role in increasing cohesiveness with many alloy systems and particularly when the material exhibits a hygroscopic nature [9], such as with aluminum alloys containing magnesium, zinc, and lithium. Although there does not appear to be a clear relationship between particle size and shape, cohesiveness typically increases with smaller particles. Storage time of a powder may also increase cohesiveness through chemical reactions, such as hygroscopy, and compaction. Similar to the cohesiveness, frictional properties are also an important factor in flow of a powder. This includes frictional forces between particles, as well as friction of the powder with walls and flow lines. As with cohesiveness, moisture and storage also increase friction, and smaller particles are generally more frictional than coarser powder. Angular powder also has higher frictional forces than rounded powder, and powder having a wider size range also exhibits great interparticle friction [9]. Obviously, the surface of the metallic particles, which always exhibits some degree of oxide, may act to decrease friction due to the higher hardness of oxides. However, as was discussed, the chemical reactions at the surface of particles are not only dictated by oxide formation and may involve additional chemical reactions that can influence friction and cohesive forces. Wall and faces may also increase or decrease friction between particles and the surface. This may be observed during the initial recoating of powder onto a smooth build plate for powder bed fusion, where some amount of friction is useful for providing a uniform coating. This is mitigated by using a rougher surface through machining or laser scribing of the plate prior to processing. In many instances, inert gas is used to fluidize the gas stream when feeding in relatively smaller lines and over longer distances. This serves to decrease compaction and friction during feeding. Based on these observations, it is anticipated that tests designed to measure certain attributes of a powder aggregate would be indicative of flowability and packing, and this is partially correct. The Hall flow test provides a coarse indication of flow under gravity but does not represent forced fluidized flow found in feed lines. It may suggest bulk flow indicative of recoating, but the creation of a thin layer from a mass of powder moved across a surface by a recoating blade is significantly more complicated. Correspondingly, the apparent density may provide insight into the capacity of the powder to efficiently pack during recoating. The angle of repose is a measure of the frictional forces between particles and flow

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without cohesion. As with other attributes, the presence of moisture may affect the angle of repose, with moisture increasing the angle. Powder shape also influences the angle of repose, by increasing frictional forces for irregular shapes. The angle of repose does not directly relate to flow but may have ramification to the ability of the powder to spread, such as with recoating. Snow et al. had observed during controlled experiments that the angle of repose was statistically correlated with the ability of three different Al-Si10Mg alloy powders to spread and evenly coat the base plate while reproducing the powder bed fusion process [16]. In this case, powder exhibiting a lower angle of repose provided more uniform coverage during recoating. Segregation of particles, due to particle size during feeding and recoating or composition during blending, may be present in processing of powder during additive manufacturing. Segregation occurs through several mechanisms. Sifting causes smaller particles to move more easily through the aggregate during bulk movement and results in finer particles settling to the lower region of the aggregate. The drag force due to friction at a surface is higher for smaller particles and may lead to variation in velocity of powder during movement and segregation. Powder blends of components having significant change in density of the material may also segregate due to higher gravitational forces and changes in frictional forces and cohesive forces associated with the component powders. In the case of powder blends, there are several techniques that are used for mixing of powders for achieving a homogeneous blend. A very simple technique utilizes a rotating drum that continuously avalanches and mixes the powder components of the blend. It should be noted that these techniques may produce a homogeneous blend, but the mixture may still result in segregation during processing through hoppers, lines, and nozzles.

14.3 Metal Powder and Binders Metal powders are also used with binders in the binder jetting process, material jetting process, and material extrusion of metals. In the case of the binder jetting process, fine powder is spread over the build plate to create a layer similar to the powder bed fusion process; however, rather than melting the powder with a high energy source, a binder solution is selectively printed onto the powder layer to represent the slice geometry. The process is repeated layer by layer to produce a “green” component that exhibits minor strength from the binder and must be sintered to fully consolidate the metal powder. The material jetting process utilizes fine powder suspended in a solution of the binder with water or a solvent to directly print the slice geometry. As with binder jetting, the process is repeated to produce a green component that is sintered to develop its full strength. The material extrusion process used to produce a metallic component employs a filament composed of metal powder and binder. Similar to material extrusion of polymers, the filament is extruded at an elevated temperature using a predetermined path to deposit material

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and form the slice geometry. Again, sintering is used to fully consolidate the material. For all of these processes, post-process sintering also includes a debinding thermal treatment that is used to pyrolyze the binder and is followed by a higher temperature sintering process for consolidation of the individual metallic particles. This process also results in significant shrinkage of the component that is proportional to the amount of binder originally present in the part. Because of the nuances of the additive manufacturing processes that utilize these systems, the size of powder and the binder formulations may be quite different for each technique. Powder size is chosen to facilitate the use of the powder within the process and the formulation of the binder must account for delivery and permeability of the binder, as well as its cohesiveness and ability to be removed prior to sintering. Hence, the formulation of the optimal binder for a particular material and process is involved. In general, binder formulations for the binder jetting process involve a polymer binder with a carrier of water or solvent. The binder and carrier solution allow the binder to be sprayed onto the powder layer using fine printing nozzles. During processing, the carrier evaporates and the binder is cured thermally by local heating or through irradiation with an ultraviolet (UV) source. The ability of the remaining binder to provide cohesion with the powder particles is controlled by the volume, wettability, and cured strength of the binder and the interparticle spacing of the powder aggregate. The binder jetting process requires the powder to be evenly spread across the build area similar to the powder bed fusion process, and as such, metal powders used for binder jetting are typically in the range of 10–50 μm in diameter. However, the sintering process is diffusion controlled and is accelerated by shorter diffusion distances found with powder that are smaller in size. Given the potential interactions mentioned above, it is not surprising that the binder system and characteristics of the powder may influence important aspects of the material produced with the binder jetting process. This includes the green strength directly after processing and the final volume and strength of the component after post-process sintering [17]. Shown in Fig. 14.18 is a schematic of powder by Mostafaei et al. after processing (as-printed) and during stages of post-process sintering, along with micrographs of the consolidated material [18]. The nickel-based alloy N06625 powder used for the evaluation represented three size distributions obtained by sieving, and a water-based binder that included 10% by volume ethylene glycol monobutyl ether and 10% by volume ethylene glycol was used at a 60% binder saturation to provide bonding within the 100 μm powder layers. After processing the density of the green components was measured to be 52% for powder having a 16 to 63 μm distribution (d10 = 19 μm and d90 = 57 μm), 45% for powder having a 16 to 25 μm distribution (d10 = 16 μm and d90 = 29 μm), and 48% for powder having a 53 to 63 μm distribution (d10 = 38 μm and d90 = 64 μm). After printing, the material was sintering in a vacuum furnace at temperatures between 1225 and 1300 ◦ C for 4 h. As illustrated in the figure, the initial powder having a relatively wide distribution provided less interstitial space compared to the two powders that were finer or coarser but having narrower distributions. The material jetting process typically uses a binder and carrier consisting of approximately 50% water. The powder is suspended within the binder and carrier

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Fig. 14.18 Schematic and micrographs depicting three sizes of N06625 alloy powder processed using the binder jetting process and post-process sintered. (Figure used with permission, copyright 2019 Elsevier, Creative Commons Attribution 4.0 License, Ref. [18])

mixture as an “ink” and is deposited using fine printing nozzles. The powder, which can constitute up to 50% by weight in the carrier, tends to be relatively small and may range between 1 and 25 μm in diameter. Metallic filaments used in the material extrusion process employ powder and binder systems developed for the metal injection molding industry and hence, employ a slightly different arrangement. These materials normally contain higher levels of paraffin and are formed into pellets that are then extruded through a die into a thin filament between 0.8 and 1.5 mm in diameter for use in the material extrusion process. A typical binder composition is 50% powder with 65% paraffin, 30% polypropylene, and 5% steric acid. As discussed, all of these processes require a thermal treatment for pyrolyzing the binder prior to sintering.

14.4 Wire Feedstock Solid wire feedstock having a diameter of between 0.9 and 2.3 mm is used for directed energy deposition processes employing a laser, electron beam, and electric arc as the heat source. Because of its similarity to welding processes, wire feedstock for additive manufacturing typically utilizes “filler metal” produced for welding. Wire feedstock is produced by a sequential process of casting, rolling, and drawing

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Fig. 14.19 Primary processes used to produce wire feedstock Fig. 14.20 Scanning electron microscope image of 1.5 mm diameter wire feedstock of titanium alloy R56400. (Courtesy of Kyle Snyder and the Applied Research Laboratory, Pennsylvania State University)

of wire to the final diameter. This process is shown schematically in Fig. 14.19. An important aspect of fabricating wire feedstock is the final drawing and spooling operations. Drawing is accomplished using various types of lubricants depending on the metal that is being processed; however, almost all of the lubricants are hydrocarbon-based and provide a source of contamination on the surface if not cleaned properly prior to spooling. High-quality wire feedstock exhibits shallow die lines from the drawing operation and minimal residual drawing lubricant. Shown in Fig. 14.20 is a SEM image of the surface of 1.5 mm diameter wire feedstock of titanium alloy R56400 exhibiting minor die lines from drawing.

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Many suppliers of steel welding wire provide a thin copper coating on the wire by cladding the billet with a copper jacket prior to rolling and drawing. The copper is bonded to the steel during thermal and mechanical processing, resulting in a very thin layer. The thin coating provides improved electrical conductivity for electric arc welding processes and decreases corrosion of the surface during shipping and storage.

14.5 Storage and Handling of Feedstock and Recycling of Powder Storage of feedstock material used for additive manufacturing processes should not be taken lightly. Proper storage is important to retain the original quality and attributes of all feedstock, and in the case of powder, additional considerations for safety within the manufacturing environment should always be considered. In the case of powder, the large surface area associated with particulate material imparts a high degree of reactivity with the surrounding environment that may lead to undesirable reactions during storage. This is especially the case for moisture in air, which may result in dissociation of water molecules and chemical absorption at the powder surface. Obviously, the nature of the powder surface plays an important role in these reactions, and in many instances, these reactions are dictated by a very thin oxide layer that may be formed during the production of the powder. The ability to recycle or reuse powder is also extremely important for establishing economic viability for additive manufacturing processes, and hence, significant attention has been placed on the influence of processing on the physical characteristics, chemical characteristics, and attributes of recycled powder, as well as the properties of the material produced using recycled powder. The impact of processing on the powder is dependent upon the specific additive manufacturing process. Processes that utilize thermal energy for melting, such as powder bed fusion or directed energy deposition, may result in partial melting and agglomeration of powder particles during processing and alteration of chemical composition, as well as the formation of additional oxide, whereas in the binder jetting process, the use of a binder for partially consolidating powder may also cause agglomeration of powder due to the presence of excess binder. The ability to treat used powder by sieving aids in minimizing dramatic changes in particle size and plays an important role in being able to reuse powder without altering the additive manufacturing process.

14.5.1 Storage and Handling of Feedstock Powder is typically provided in hermetically sealed containers containing a desiccant to absorb residual moisture. This type of packaging has been designed

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to provide sufficient stability for the powder over relatively long periods while remaining sealed. However, once opened, virgin powder is susceptible to absorption of moisture and potential addition of other contamination during handling and storage. Therefore, opening of containers of new powder should only be conducted when necessary, such as for inspection, sampling, and use. Powder should be stored in an area that provides a controlled environment for temperature and humidity, with standard heating, ventilation, and air conditioning of industrial operations usually being sufficient. The temperature for storage should be controlled to minimize fluctuations and should be similar to the temperature in the processing area. Humidity should be controlled within a range that minimizes static electrical discharge by being too low and diminishes the potential for moisture absorption by being too high. A range of between 30% and 50% relative humidity typically satisfies these requirements for metal powders used in many additive manufacturing processes. Storage of spooled wire follows many of the same requirements of powder, and although solid wire is not as surface reactive as powder, storage should be in a dry environment to minimize moisture absorption on the surface. A common condition that may plague powder or wire that is open to the environment is transportation of feedstock from a cold to warmer environment. If wire of powder is opened and stored or transported at low temperatures and brought to room temperature quickly, the temperature of the feedstock may be below the dew point temperature at the warmer environment causing condensation to form at the surfaces. One means of removing moisture from powder is to heat the powder in a vessel to a relatively low temperature, between 35 and 45 ◦ C, using some form of conductive heating while being evacuated to create a soft vacuum. The moisture within the powder is vaporized, opposite to the effect of condensation, and removed through the evacuation of gas. Agitation of the powder during heating may also be used to continuously provide fresh powder for evacuation. Although low moisture content may result from this process, attributes of the powder, such as flowability or packing, may also be altered based on the reduction of potentially coherent forces. It must also be noted that handling of metal powders necessitates additional safety and hygienic requirements which should be reviewed prior to the installation and operation of additive manufacturing systems [19–21]. Such precautions during storage, handling, and use may include personal protection to prevent inhalation and contact of fine metal particles, prevention of fire and explosion of fine metal powder, especially for reactive metals, and suitable disposal of used powder. Because safety and hygiene requirements for installation and operation of equipment may vary based on local, state, and federal regulations, the cognizant authority within an organization, which may be an industrial hygienist, safety officer, or other equivalent authority, should be consulted during the planning stages, which should include the development of a thorough hazard analysis covering all facets of installation of equipment, operation of the process, and storage and handling of powders. The local fire marshal or similar authority should also be consulted early in the process to ensure that local and state requirements are met. An initial introduction to safety and hygiene requirements for safe handling of metal powder may be found in the

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above references, and the systems provider should always be expected to provide information regarding the safe use of their equipment.

14.5.2 Recycling of Powder Up to 75% of powder used in additive manufacturing processes are not consumed by consolidation on the build. This creates significant difficulty in achieving economic viability for additive manufacturing of metals, since powder may represent a major cost component of the process. To address this issue, powder is typically recycled or reused. This includes the collection and reuse of unfused metal powder from the powder bed fusion process and powder-based directed energy process, as well as unbonded powder from the binder jetting process. However, because of the potential alterations to the physical characteristics, composition, and processing attributes of recycled powder, the reuse of powder should consider the requirements of the products that will be produced using recycled powder, the potential degradation of powder during reuse, and the impact of powder degradation on product performance [22, 23]. Several investigations have confirmed an increase in the upper size range of powder after processing, as well as increased levels of oxygen. The increase in size may be attributed to agglomeration of particles during melting under a high energy heat source. In the case of powder bed fusion, small particles are heated rapidly and may result in coalesces of adjacent particles that result in an agglomeration of particles having a larger size than the initial distribution. The rapid heating also results in recoil forces that result in the expulsion of the agglomerates from the molten pool and this phenomenon has been observed during high speed imaging of the powder bed fusion process [24]. The rise in oxygen content may be associated with oxidation, which is also due to processing under a high energy source [22, 23]. Although processing during powder bed fusion is conducted in a controlled environment, the high temperatures experienced within the liquid pool thermodynamically drive oxidation even at very low oxygen levels. In the case of directed energy deposition where the powder stream is fed through the high energy beam, the potential for partial melting and agglomeration of particles, as well as for oxidation, is readily prevalent [25]. There is significant evidence that suggests that processing of powder during additive manufacturing results in some alterations of the physical and chemical characteristics of the powder; however, the linkage between these changes and the effect on properties of the material produced using reused powder is less direct. The most observed consequence of processing of powder during additive manufacturing is agglomeration that increases the upper range of particle size and may be accompanied by increased oxidation of powder that had interacted with the heat source, with the degree of oxidation being dependent upon the oxidation potential of the material. Figure 14.21 depicts SEM images from Slotwinski et al. showing alloy S174000 (17-4 PH) powder obtain from sieve residue after recycling

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Fig. 14.21 Scanning electron microscope images of alloy S174000 (17-4 PH) powder obtained from sieve residue after recycling. (Figure used with permission of Dr. John Slotwinski, National Institute of Standards and Technology Ref. [26])

Fig. 14.22 Laser diffraction measurements for diameters of alloy S174000 (17-4 PH) powder after reuse and sieving up to 8 cycles. (Figure used with permission of Dr. John Slotwinski, National Institute of Standards and Technology Ref. [26])

[26]. Agglomeration of particles is readily evident. Figure 14.22 shows the results from laser diffraction measurements from this study for powder diameters after reuse and sieving at 80 μm for up to 8 recycles. Also shown in the figure are the original diameters of the virgin S174000 (17-4 PH) powder at the three mass fractions of 10, 50, and 90%. The measured values from Fig. 14.22 illustrate the increase in diameter of the powder particles after reuse, especially after the 5th recycling, even though the powder was sieved to reclaim all powder below 80 μm. The large, agglomerated particles that result from processing may be easily filtered during post-process treatment by sieving. The increase in oxygen associated

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with oxidized material may or may not have an effect depending on the material being processed. Titanium is sensitive to solid solution strengthening by the absorbed oxygen but oxygen has little effect on nickel-based alloys. Also, there are other potential alterations that may occur that are more difficult to ascertain. The use of powder requires handling and, in the case of powder bed fusion, processing in an environment that may have been at moderately elevated temperature. This may alter the rheological properties of the powder that may influence processing attributes, such as spreadability and packing, which may have an indirect impact on the process. These combined effects complicate the influence of recycled powder on the quality of material produced. Nevertheless, the use of recycled powder is common. Although there are instances when only new or virgin powder is utilized in the powder bed fusion process due to the need to maintain initial powder characteristics and powder lot traceability, it is not only common but a necessity to reuse powder in this process. Depending upon the design and density of the components to be built, the amount of powder that is consumed and consolidated into parts during the process may range from 25% to 75%, and conversely, the amount of powder that is expended during the process but available for reuse is between 75% and 25%. The powder available for recycling includes remnant powder surrounding the consolidated parts and powder remaining in reservoirs or hoppers. Powder bed fusion systems utilize three primary modes for collection and treatment of powder for recycling: systems where the powder is internally collected and treated, systems that require manual collection and external treatment of powder, and systems that provide a combination of internal and external treatment. Although strides are being made by system developers to provide a closed system for powder handling and recycling, the most common method today utilizes some form of manual collection followed by powder treatment. For manual collection of unused powder, utilizing protective equipment for minimizing inhalation of fine particles, the powder is carefully collected for treatment to prepare it for reuse. The powder that is surrounding the parts and remaining on the build platform would be exposed to the high-energy heat source and would be expected to contain particles that had been agglomerated, whereas the powder remaining in the reservoirs would be considered to be less contaminated. Whether these powders are handled differently is a matter of choice, but some form of powder management that defines the percentage of virgin powder and used powders that are blended for reuse should be established. Treatment of used powder primarily involves sieving for reestablishing the correct particle size range for processing. Although sieving is commonly employed for removal of agglomerated particles larger than the original distribution, sieving may also be used to eliminate small particles for establishing a minimum size. An example for treatment of used powder having an initial size distribution of d10 = 15 μm and d90 = 45 μm would be sieving using a 50 μm screen opening to filter all particles less than 50 μm. Sieving equipment used for reclaiming fine powders include vibratory mechanisms that enable fine powder to be screened rapidly. After treatment, the powder should be packaged immediately and stored

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properly. Depending upon quality requirements, the powder may also be sampled and characterized for powder size and potentially other characteristics deemed critical for maintaining consistency of the process and quality of parts. Although the treatment of powder is a viable method for reuse, there are limitations on the number of times that powder may be recycled. This appears to be due to the accumulated effect of processing cycles on the characteristics of the reused powder. Nezhadfar et al. have shown that reuse of alloy S174000 (17-4 PH) powder in the powder bed fusion process showed an initial increase of approximately 20% in strain at failure and reduction of area during axial tensile testing of parts produced after 5 recycles and a 6–8% decrease in those properties after 15 recycles, compared to the virgin powder [27]. The increase after the first five recycles was attributed to a decrease in powder cohesion and improved spreading of the powder. A more extensive evaluation was conducted by Jacob et al. on the same alloy also using the powder bed fusion process [22]. The results of this evaluation showed similar tensile properties of material produced using powder recycle 11 times when compared to the original virgin powder. Grainger studied the reuse of alloy R56400 (Ti-6Al-4V) powder using the powder bed fusion process up to 38 recycles [28]. In this study, a single lot of powder was repeatedly utilized. After each cycle, the powder was treated by sieving and reused. The powder was also characterized by physical and chemical characteristics. Sieving of the powder was able to maintain the proper size distribution for processing, while each recycle was found to increase the oxygen and nitrogen content of the powder. Oxygen increased from approximately 700 ppm for the virgin powder to 1300 ppm after the 38 build. Tensile properties of the material produced using the recycled powder showed a slight increase, from approximately 1000 MPa for the virgin powder to about 1100 MPa after the 38 recycles. However, percent elongation or reduction in area from the tensile tests was not reported. The results of these evaluations, as well as other data that has not been published, indicate that if proper treatment is used for recycled powder, satisfactory mechanical properties may be achieved after recycling of powder for the powder bed fusion process. Although most of the studies have involved static tensile tests, increased mechanical property data under dynamic testing, fatigue, and fracture toughness, is needed to confirm the number of times various alloys powders may be reused. An important aspect of powder recycling is the ability to establish and maintain powder lot traceability related to powder use. This is especially important when utilizing powders representing various manufacturing lots. Shown in Fig. 14.23 is a chart showing the use of recycled and virgin powder during a five-build cycle. The initial build, Build 1, was produced using 75% of previously recycled powder and 25% of new or virgin powder. The previously recycled powder is assumed to represent different material than the new powder. After every build, the powder is recycled and refreshed with 25% of virgin powder. The recycled powder after each build is also identified as a new production lot of powder which identifies the source and percentage of the powders that constitute the lot. This traceability is shown in the bottom of the chart to identify the powder used to produce each build. The percentage of powder representing the virgin powder used to produce each of the

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Fig. 14.23 Chart showing recycling of powder during five production builds illustrating powder lot traceability and powder use within the builds

five builds is also calculated based on 25% addition of new powder mixed with 75% of recycled powder from the previous build. As illustrated, based on the 25% refresh of virgin powder, the amount of virgin powder used for each build increases from the initial 25% to 77% for the fifth build. Being able to track the powder during production is an important tool for maintaining and controlling the quality of the process. With additional information on the source powder, such as chemical composition, the composition of built components may be estimated based on the powder used to produce the builds. The directed energy deposition processes may also benefit from the reuse of powder but the ability to collect the powder after processing is more difficult than the powder bed fusion process. Rather than having a contained processing compartment, the directed energy deposition process is usually conducted in a larger workspace with less control for powder accumulation. This creates greater difficulty in gathering powder for recycling and also increases the potential for contamination of powder during the collection process. Aside from maintaining cleanliness in the process area, stainless steel or aluminum foil on the processing table may be used for capturing powder while minimizing contamination. The foil may be changed when processing different materials to avoid alloy contamination. Thin processing

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trays fabricated from stainless steel may also be used to capture powder during the directed energy deposition process. The treatment of powder after collection is similar to treating powder from the powder bed fusion process. Sieving is employed to filter larger agglomerated particles.

14.6 Questions and Discussions 1. Contrast the differences between the gas atomization process using inert gas and the plasma-rotating electrode process. Based on the differences in the two processes, discuss the differences in the powder that the two processes produce. 2. Illustrate graphically how two powders that have the same d10 and d90 values may be very different in terms of the individual size distributions. 3. Discuss three techniques that may be used to ascertain the density of powder particles. 4. Discuss how individual powder particles may interact and how these interactions influence the flow of the powder aggregate. 5. Explain in layman’s terms how the angle of repose for a powder sample can be used to describe the flowability of the powder aggregate. 6. Discuss in general terms what is meant by the physical characteristics of powder particles, characteristics of a powder aggregate, and attributes of a powder aggregate. How are these descriptors of powder related? 7. Using the shear stress versus normal stress diagram, sketch the response of two powders on the diagram that reflect different flow functions, one powder displaying easy flowing characteristics and the other powder being very cohesive. 8. Describe in detail the components that comprise the filament feedstock that is used in the material extrusion process with a metallic filament. 9. Name and discuss three important aspects of powder that may change during storage and how these alterations may impact the performance of the powder in an additive manufacturing process. 10. Discuss why it is important to document the sources of powder that may be used in an additive manufacturing process. What features of the powder should be documented for this purpose?

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23. Tang H, Qian M, Liu N, Zhang X, Yang G, Wang J (2015) Effect of powder reuse times on additive manufacturing of Ti-6Al-4V by selective electron beam melting. J Metals 67:555–563 24. Nassar AR, Gundermann MA, Reutzel EW, Guerrier P, Krane MH, Weldon MJ (2019) Formation processes for large ejecta and interactions with melt pool formation in powder bed fusion additive manufacturing. Sci Rep 9 25. Terrassa K, Haley J, MacDonald B, Schoenung J (2018) Reuse of powder feedstock for directed energy deposition. Powder Technol 338:819–829. https://doi.org/10.1016/ j.powtec.2018.07.065 26. Slotwinski JA, Garboczi EJ, Stutzman PE, Ferraris CF, Watson SS, Peltz MA (2014) Characterization of metal powder used for additive manufacturing. J Res Natl Inst Stand Technol 119:460–493. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4487284 27. Nezhadfar P, Soltani-Tehrani A, Sterling A, Tsolas N, Shamsaei N (2018) The effects of powder recycling on the mechanical properties of additively manufactured 17-4 PH stainless steel. In: Proceedings of the 29th annual international solid freeform fabrication symposium 28. Grainger L (2016) How much can you recycle metal additive manufacturing powder. Des Eng. https://www.design-engineering.com/features/additive-manufacturing-powder

Chapter 15

Solidification During Additive Manufacturing

Producing functional components in metallic materials through additive manufacturing must consider not only form and fit, but also function, and in many instances, the functionality of the part will be governed by its mechanical properties, which in turn are closely defined by the process and resultant microstructures. For processes that involve selective melting and solidification (powder bed fusion) or melting and deposition (directed energy deposition), the metallurgical transformations that take place within the material during the additive manufacturing process control the development and evolution of microstructures, with the resultant microstructure having significant influence on the mechanical properties of the material that is produced. Although the transformations that may occur during these processes are as diverse as the alloys utilized, they may be broadly described in two categories, transformation involving solidification of the liquid into a solid and various transformations within the solid state. All of the metallurgical transformations that are operative under powder bed fusion and directed energy deposition are highly dependent upon the repetitive and complex thermal transients that are the consequence of these additive manufacturing processes. Additive manufacturing methods that rely upon subsequent processing to fully consolidate the material, such as the binder jetting and material jetting, rely on the post-process sintering process to consolidate material and establish the final microstructure.

15.1 Thermal Response of Material During Processing Additive manufacturing processes that involve in situ melting and solidification of metallic materials for producing engineered components involve relative complex motion between the heat source and the substrate to produce the various layers that eventually constitute the final part. The digital process that is used to accomplish this begins with a CAD model translated into a STL file or other suitable file format, © Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_15

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which defines the part geometry. The digital description of the part is then utilized to create slice files that drive the motion of the additive manufacturing system to produce two-dimensional layers necessary for creating the part geometry. The motion required to produce an individual layer is usually complex, involving a range of motions over a two-dimensional plane. The result of this complex motion is a thermal cycle within the material that is highly dependent upon the location within the material relative to the path of the heat source. Although powder bed fusion and directed energy deposition of metals involve the repetitive creation of layers through melting and solidification of material, there are major distinctions between the two processes which have ramifications to the thermal response of the material during processing. Directed energy deposition processes involve a lower velocity of motion at higher power where the added material is either powder that is provided coaxially to a laser beam or wire directed into the interaction region between the electron beam and the substrate. Heating and melting simultaneously occur within the feedstock and the substrate beneath the beam. Exchange of energy encompasses the direct transfer between the energy source and the material, as well as mass and energy transport. In the case of powder bed fusion techniques, a lower power laser or electron beam is rapidly scanned over a pre-deposited powder layer to melt and solidify the surface. The exchange of energy for laser beam processing is the interaction of photons with electrons within the material, whereas the transfer of energy for electron beam processing is governed by the kinetic energy of the accelerating electrons being transformed to heat upon collision with the material. For both the directed energy deposition process and the powder bed fusion process, as the heat source moves relative to the substrate, the thermal fields generated within the material follow the heat source and change during acceleration or deacceleration, as well as changes to the motion vector. For the underlying material near the path of the heat source, this results in rapid heating, and melting directly below the heat source, followed by rapid cooling. Temperatures directly beneath the heat source will also result in some degree of evaporation of the liquid, and preferential evaporation will occur for high vapor pressure species within an alloy. Shown in Fig. 15.1 are results from numerical simulations showing the thermal response at a point in the material located at the surface of the build plate during production of the simple “blade” geometry using the laser-based directed energy deposition process to deposit R56400 (Ti-6Al-4 V) alloy as a powder. The production of the blade was conducted using two adjacent tracks and 19 layers. The motion of the heat source for the first track was reverse to produce the adjacent track and all motion was preprogrammed to be conducted in a continuous manner with little time between tracks and layers. The upper image in the figure illustrates the blade geometry used for the simulations after several layers, and the red point at the center of the image indicates the position on the substrate represented by the thermal response curves. Also shown on the thermal response curves are the liquidus and solidus temperatures (Tl and Ts ) for the R56400 (Ti-6Al-4 V) alloy used for the deposits. Melting at the point of interest occurred during the first two tracks for Layers 1 and 2 that were directly over the point. The starting temperature

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Fig. 15.1 Results of numerical simulation showing thermal response for laser-based directed energy deposition at a single point during the production of a blade geometry (simulation results by PanX and courtesy of PanOptimization)

for each track is based on the cooling from the prior track and may be considered the “background temperature.” Several factors influence the rate of heating and cooling, peak temperatures achieved, and the background temperature between layers during the directed energy deposition process. These factors include the thickness and physical properties of the substrate, the physical properties of the deposition material, the heat input or energy provided by the source, the path of motion of the heat source, and the time between production of subsequent layers, or dwell time. The fluence, f, may be used to represent the amount of energy of the source that is distributed during the process and may be represented as:

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15 Solidification During Additive Manufacturing

f =

.

βP Vd

(15.1)

where β is the bulk absorption coefficient, P is power, V is velocity, and d is the diameter of the source of energy projected to the part. The fluence defines the amount of energy that is distributed over the surface of the substrate over unit time and is described in the accompanying sidebar, along with two other common definitions of energy used in additive manufacturing. For fluence, if the power is expressed in watts, velocity in cm/s, and diameter of the source energy on the substrate in cm, f is defined in terms of J/cm2 . As stated above, there are many factors responsible for determining the thermal effect in the material during directed energy deposition, but some of the most controllable parameters are associated with the energy input used for the process. In particular, this is the power and velocity of the heat source and the resultant fluence. Figure 15.2 demonstrates the impact of the fluence, based on changes in power and velocity, on the thermal response of the material during the laser-based directed energy deposition process. The data shown in the figure was obtained by measuring the temperature at the surface of a N06625 (IN625) alloy substrate using tungsten-rhenium thermocouples while depositing the same alloy directly over the thermocouple position [1]. The four conditions, employing two laser powers and two velocities, used to produce the single track deposits are shown in Table 15.1 and resulted in four fluences of 1.2, 2.3, 2.9, and 5.8 kJ/cm2 . All of the thermal responses exhibited rapid heating as the heat source approached the thermocouple position, followed by relatively rapid cooling as the source passed over and beyond the thermocouple. However, the most rapid heating rates were associated with the

Fig. 15.2 Measured temperatures showing heating, solidification, and cooling of N06625 (IN625) alloy during laser-based directed energy deposition to produce of one layer using four energy fluences. (Figure used with permission; copyright 2018 Materials Science and Engineering [1])

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Table 15.1 Processing parameters for laser-based directed energy deposition of single tracks of alloy N06625 (IN625) produced using four local energy densities [1] Powder and substrate material N06625 (IN625)

a Absorption

Sample number In 1 In 6 In 7 In 8

Laser powera (W) 2000 2000 1000 1000

Scan velocity (cm/s) 1.06 0.42 1.06 0.42

Beam spot size (cm) 0.3 0.3 0.3 0.3

Powder flow rate (g/min) 25.9 25.9 25.9 25.9

Energy fluence (J/cm2 ) 2327 5831 1164 2916

coefficient used in calculation for fluence was based on a measured value of 0.37

two conditions employing the higher scan velocity of 10.6 mm/s for the heat source, Samples In 7 and In 1. The rate of cooling decreased with increases in the energy fluence used during the process, with both scan velocity and power influencing cooling rates.

Description of Energy During Processing A quantitative description of the amount of energy used in additive manufacturing processes that utilize a moving heat source is important for comparing processing conditions, developing relationships for process effects and resultant microstructures, and conducting thermal analysis. There are several expressions that are used for defining energy input during processing, and they are all capable of describing the relative energy provided to the substrate. However, it is imperative that there is an understanding of what is described by the parameter, especially when values are being compared using different energy input descriptions.

(continued)

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The fluence, f, is an accurate representation of the energy projected to the material for processing and is a well-established parameter within the laser processing industry. Fluence is defined as the energy projected onto the material over a unit time and is expressed through power (P), diameter (d), and velocity (V) of the heat source. It may also account for the energy absorbed over that area through the use of the bulk absorption coefficient, β. Fluence has units of energy per area. The local energy density, .EdL , sometimes referred to as the energy density, is similar to fluence but utilizes the hatch spacing, h, to define the width of the area exposed to the source. It is not a true density, since it does not represent a volume of mass. It is expressed in units of energy per area. The energy density, Ed , is utilized to describe the total energy that has been absorbed and used for melting in the material. The determination of energy density does require information regarding the geometry of the melted region, width (w) and depth (z). Although the energy density does not typically include the absorption coefficient, because it is meant to portray energy (continued)

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absorbed for melting, the coefficient should be utilized in this expression to indicate the ratio of energy that was absorbed within the material to the total energy presented. The use of the hatch spacing and powder layer thickness in powder bed fusion is also employed to describe the energy absorbed within this layer and substitutes for width and depth of melting. These substitutions eliminate the need for determining melt pool geometry. The energy density is defined in terms of energy per volume.

These experiments were conducted on plates that were 1 cm in thickness and 15 cm in length. The thickness and length of the plates in relationship to the concentrated heat source enabled three thermocouples along the center of the plate to be used to replicate the thermal cycles. This is due to a phenomenon long recognized in welding technology referred to as the quasi-steady state condition, which is illustrated in Fig. 15.3. Under situations that satisfy the quasi-steady state condition, the thermal response of a material subjected to a moving heat source may be considered constant when referenced from the center of the heat source. In the figure, isotherms for specific temperatures are shown around a heat source moving at a constant velocity along the centerline of a plate at three times during the movement. The temperatures exhibit a thermal wave around the heat source as it moves along the plate. After the initial transient condition, caused by reduced conduction and addition of surface heat losses associated with the edge of the plate, the thermal response in the plate is constant at distances and angles from the center

Fig. 15.3 Illustration of the quasi-steady state condition for thermal response of a material when subjected to a moving heat source

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15 Solidification During Additive Manufacturing

of the heat source, which displays the quasi-steady state condition. One important aspect that is also illustrated in the figure is the change in the thermal profile early in the process, i.e., the initial transient condition. The temperature profiles around the heat source at this time, t1 , are compressed and reflect higher thermal gradients [2]. This condition may result in higher temperatures within melt during directed energy deposition, which may lead to changes in the surface tension and viscosity of the pool and alterations in the deposit geometry during the initial portion of the track. Establishment of the quasi-steady state condition essentially defines a constant thermal history in the material under the path of motion within this regime. This simplifies, to some degree, the complexity of the thermal response of the material. However, as pointed out earlier, the regime when the quasi-steady state condition is operative is dependent on various factors, but nevertheless, it serves as an important tool for analysis of microstructures in additive manufacturing. It also provides for a simplified, analytical solution, when appropriate, for conducting analysis of the thermal response of a material under a moving heat source [3]. It must also be noted that the quasi-steady state condition is based on relatively homogenous temperatures within the substrate prior to processing. As production of layers proceeds during the directed energy process, particularly with the use of complicated path plans, the temperatures present within the underlying material may exhibit a wide range of starting temperatures that can negate the use of the quasi-steady state condition for analysis. The nature of the powder bed fusion process results in thermal responses within the material that are significantly more rapid and complex than that of the directed energy deposition process. This is primarily due to the high speed of motion of the energy source along with the complex scanning paths that are used for hatching and contouring for producing the slice geometries. The process also requires many layers for producing the final build, and the production of each layer imparts its own thermal response within the material. Shown in Fig. 15.4 are thermal cycles obtained from numerical simulations at a point within a blade structure that was produced using N07718 (IN718) alloy powder and the laser-based powder bed fusion process [4]. The blade structure was 100 mm wide, 90 mm long, and 72 mm high, and the point within the material and represented by the thermal response data was located halfway along the width, length, and height of the blade. Process parameters used during the simulation included a scanning velocity of 960 mm/s, laser power of 291 W, diameter of the laser spot of 84 μm, and thickness of the powder layer of 40 μm. The scan paths that were used during processing involved an 11 mm hatch length and a 0.11 mm hatch spacing. The scanning path for hatching was alternately conducted exactly at 0◦ and 90◦ to the long axis of the blade. Shown in Fig. 15.5 is the scan pattern for hatching of alternate layers in the vicinity of the point within the blade represented by the thermal cycles in Fig. 15.4. The square region in the center of the blade, which also encapsulates the point of interest, indicates the 7 scan paths that are represented by the thermal data for 11 layers. The point of interest was at the surface of the first layer, and 10 additional layers were produced above the point.

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Fig. 15.4 Thermal cycles for 10 layers at a point within a blade structure built using the powder bed fusion process using N07718 (IN718) alloy. (Figure adapted with permission; copyright 2018 Progress in Additive Manufacturing [4])

Fig. 15.5 Scan paths in the vicinity of the point represented by the thermal cycles for a point within a 5 mm thick blade (the hatch spacing is not scaled and has been enlarged)

The thermal response in Fig. 15.4 shows 7 peaks produced for each layer with the highest peaks associated with the first layer and coincided with the point of interest. The seven thermal peaks associated with the first layer were produced when the energy source was scanned adjacent and directly over the point of interest. Several hatches during each scan were sufficiently near the point of interest to result in

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15 Solidification During Additive Manufacturing

Fig. 15.6 Three views of the thermal fields near the energy source after achieving the quasisteady state condition based on the results of numerical simulation. (Figure used with permission; copyright 2018 Progress in Additive Manufacturing) [4]

heating and cooling, and these hatches are indicated within the shaded region of Fig. 15.5. Also superimposed on the thermal cycles from the initial layer are thermal cycles produced using nine additional scans employed to produce subsequent layers above the point of interest. Based on an approximate liquidus temperature for 1600 ◦ C for alloy N07718 (IN718), melting only occurred when the laser passed directly over the point during creation of the first layer. Subsequent layers also produced progressively lower peak temperatures, but the background temperature resulting during interlayer cooling continued to increase, approaching 500 ◦ C after the creation of ten layers. The thermal fields surrounding the moving heat source obtained from the numerical simulation for the first layer after achieving the quasi-steady state condition are also shown in Fig. 15.6. The perspectives in the figure show isotherms on the top face of the layer, at the longitudinal midplane, and transverse at a plane along the length that exhibited the maximum depth of melting. As illustrated in the figure, the melt pool formed under the energy source is highly elongated. Utilizing the liquidus temperature of 1660 ◦ C to establish the boundary, the melt pool dimensions are shown to be 1000 μm in length, 160 μm in width, and 74 mm in depth. Although the thermal response of the material during the directed energy deposition and powder bed fusion processes exhibits similar characteristics, such as rapid heating and cooling due to the moving energy source, the time scale of the thermal cycles for each process is significantly different. This is due to the large difference in the velocities of the energy source used with these processes. The energy used for directed energy deposition and powder bed fusion is also quite different and also influences the heating and cooling rates within the material. Shown in Table 15.2 are typical parameters and calculated fluence used for a variety

15.2 Solidification

437

Table 15.2 Typical processing parameters and energy fluence used for directed energy deposition (DED) and powder bed fusion (PBF) processes Process Laser PBF EB PBF Low-energy laser DED High-energy laser DED EB DED

Power (W) 400 1000 1000

Typical absorption coefficient 0.5 0.9 0.5

Scan velocity (cm/s) 100 100 3

Spot size of energy (cm) 0.008 0.01 0.2

Energy fluence (J/cm2 ) 250 900 833

6000

0.5

1

0.5

3000

10,000

0.9

1

2.0

4500

of directed energy deposition and powder bed fusion processes. The parameters in the table illustrate the wide range of power, velocity, and spot size of the energy source used for these processes and reflect the broad range for their respective energy fluences. In general, high rates of cooling will be exhibited with high scan velocities and lower power that results in low fluence, whereas lower cooling rates are associated with low scanning speeds and higher power, which results in high energy fluence. It will also be seen that the cooling rates associated with the process influence the resultant microstructure by establishing the solidification morphology, segregation of constituent during solidification, and solid state reactions that may occur post-solidification. The continuous heating and cooling cycles that transpire during the entire build process also drive potential solid state transformations within the material.

15.2 Solidification During processing, the thermal response of the material being created at the current layer entails thermal cycles involving rapid heating and cooling due to the thermal fields generated by the moving source of energy. The peak temperature at positions near the energy source exceeds the liquidus temperature of the material and results in melting, followed by rapid solidification as the source moves away from the material. This results in melting and solidification of the added material being deposited, as with directed energy deposition, or the powder layer and substrate during powder bed fusion. Hence, solidification is responsible for establishing the initial microstructure of the material. Solidification of a material involves an increase in atomic ordering through a decrease in thermal energy associated with the material. It occurs in a pure metal when the material is cooled from an elevated temperature that had resulted in melting to the melting or freezing temperature. For alloys, the melting temperature, or freezing temperature, is described by a range of temperatures that are bounded by the liquidus temperature, when solidification starts, and the solidus temperature,

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15 Solidification During Additive Manufacturing

Fig. 15.7 The solvent-rich portion of a binary phase diagram showing the temperatures and compositions of interest during solidification of an alloy

when solidification is complete. This is illustrated in Fig. 15.7, which shows a portion of a binary phase diagram and temperatures representing the liquidus and solidus as a function of alloy composition. The diagram indicates an alloy having a solute content of Co and having a liquidus temperature of Tl and a solidus temperature of Ts . Also illustrated in the figure is the solute concentrations during equilibrium solidification at an arbitrary temperature T*. During initial solidification at Tl , the first solid to form will have a composition of CS , which is lower than the initial composition of the liquid, Co , at Tl . Conversely upon cooling to Ts , the solid that now forms will represent a composition of CL , which is higher than the composition of the liquid. At temperatures between Tl and Ts , such as at T*, the fraction of phases participating in solidification at any temperature may be determined user the lever rule, which assumes complete diffusion of solute in the solid and liquid. With this assumption for the present, the determination of the fraction of solid, fs , and the fraction of liquid, fL , at any temperature between the liquidus and solidus may be shown through the lever rule to be: fs =

C L − Co C L − CS

(15.2)

fl =

Co − CS C L − CS

(15.3)

.

and .

15.2 Solidification

439

where CL is the equilibrium composition of solute at the liquidus, CS is the equilibrium composition of solute at the solidus, and Co is the composition of solute for the alloy. An evaluation of the above equations indicates that the lever rule describes the fraction of solid during solidification as having a linear relationship between the liquidus and solidus temperatures. During initial solidification of an alloy having a composition Co at Tl , the fraction solid, fS , is zero, with the fraction liquid, fL , being 1 and the liquid at the interface will have a solute concentration of Co . Conversely, during the terminal stage of solidification at Ts , fS is 1 and the concentration of solute in the solid at the interface is also Co . The overall description of solidification under these conditions would be a planar solidification front with a constant concentration of solute, Co , in the solid and liquid. In actuality, these assumptions are overly simplistic for conditions of interest and actual alloys, which severely limits the analysis for describing the phase fraction and composition during solidification for most metallic systems and processing conditions. Solidification of alloys during additive manufacturing involves rapid heating and cooling due to the moving energy source. The material under the source is usually superheated above the liquidus and begins to cool rapidly as the source of energy passes and the material begins to conduct heat from the molten pool into the substrate. Cooling on the surface of the liquid pool also takes place through convective and radiative heat losses. A schematic showing the Tl and Ts isotherms in a transverse section of the pool immediately after the energy source has passed is shown in Figs. 15.8 and, Fig. 15.9 depicts the heating and cooling curve within the material during the process in relation to the phase diagram and the liquid, two-phase zone, and solid present near the liquid and solid interface. Regarding the cooling rates within the liquid, in most instances, conduction dominates heat removal from the liquid and the highest cooling rates are associated with the liquidsolid interface in the substrate. Cooling rates decrease with distances from the Fig. 15.8 Schematic showing the cross section of material depicting the liquidus and solidus isotherms and process conditions responsible for cooling of the melt

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Fig. 15.9 Hypothetical cooling curve for additive manufacturing process in relation to phase diagram for an alloy and the liquid, two-phase zone, and solid material at the interface of the melted region and the substrate

liquid and solid interface to within the liquid pool. The cooling curve of Fig. 15.9 represents a point within the substrate that undergoes heating above the liquidus and rapid cooling through the solidification range to the solid. Upon initiation of solidification, the increase in atomic ordering developed within the solid during solidification results in the release of energy referred to as the latent heat of fusion, a thermodynamic property also defined as the enthalpy of fusion. The exothermic nature of the latent heat of fusion during solidification interrupts the temperature during cooling, resulting in a thermal arrest.

Dilution of the Substrate and the Deposition Material During deposition of material for the directed energy deposition process or melting of the powder layer in the powder bed fusion process, the region that forms the melt zone is formed through melting of new material and material representing the underlying substrate. In the case of the powder bed fusion process, the melted material within the substrate is compositionally identical to the new powder layer that had been melted, and hence, the composition with the melt zone does not change. However, for the directed energy deposition process, the substrate material may be different than the material being deposited, and under this condition, the composition of the melt is based on the composition of the material that was added and the material melted or diluted within the substrate. The composition for a particular alloying addition i within the melt, denoted as .Cmelt , may be determined by measuring the area (continued)

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441

of the melted region of the substrate and the deposit. If it is assumed that the cross-sectional area does not change significantly, the area of the two regions may be used to determine the composition of the alloying addition within the melted region based on the contributions from the deposited material and the substrate. This method is shown schematically below. It should be noted that when the alloying composition of the substrate is sufficiently different than the deposition material, subsequent deposits will cause a gradual change in composition related to successive dilution from each layer. This may also be used to purposely grade composition from the substrate to the deposition material.

15.2.1 Chemical Driving Force for Solidification The driving force for solidification, as with many physical systems, is the minimization of free energy of the system. Under constant pressure, the change in Gibbs free energy, ΔG, of a system may be expressed as: ΔG = ΔH − T ΔS

.

(15.4)

where H is enthalpy, T is temperature, and S is entropy of the system. Enthalpy is a state function that describes the equilibrium state of the system based on the internal energy required to create the system, as well as the pressure and volume that is occupied by the system, but this is ignored under constant pressure. Entropy, also a state function, defines the degree of atomic disorder within the system. Thus, assessing the change in Gibbs free energy associated with the reaction of a volume of liquid transforming to a solid for a pure metal at temperature TM may be used to describe aspects of the reaction that satisfies local thermodynamic equilibrium. Based on this reaction, the change in free energy of the volume at equilibrium between of liquid and solid may be shown as: ΔGV = GL − GS = 0

.

(15.5)

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15 Solidification During Additive Manufacturing

and HL − HS − TM (SL − SS ) = 0

.

(15.6)

may be used to define the state of equilibrium between the liquid and solid at TM . The expression HL − HS is the change in enthalpy associated with the phase transformation between the liquid and solid phase and defines the latent heat of fusion, ΔHf . Similarly, SL − SS describes the entropy of fusion, ΔSf . Therefore, ΔGV = ΔHf − T ΔSf = 0

.

(15.7)

and ΔHf TM

ΔSf =

.

(15.8)

It may also be shown under that under these assumptions  ΔH = ΔHf +

T

ΔCp dT

(15.9)

ΔCp dT TM T

(15.10)

.

TM

and  ΔS = ΔSf +

.

T

where ΔCp is the difference in the heat capacity of the liquid and solid phase at constant pressure. Utilizing the expression for the change in free energy as a function of enthalpy of fusion and the temperature-dependent entropy of fusion, it may be shown: ΔGV = ΔHf − T ΔSf

(15.11)

ΔHM TM

(15.12)

.

or ΔGV = ΔHf − T

.

and   T 1− .ΔGV = ΔHf TM or

(15.13)

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443

 ΔGV = ΔHf

.

TM − T TM

 (15.14)

and substituting ΔT for TM − T yields:  ΔGV = ΔHf

.

ΔT TM

 (15.15)

From the above, it directly follows that: ΔGV = ΔSf ΔT

.

(15.16)

or ΔT =

.

ΔGV ΔSf

(15.17)

The above relationship for ΔT defines the degree of undercooling below TM required to enable equilibrium to be established between the liquid and solid, thus allowing initiation of solidification. The relationship also indicates that the degree of undercooling is proportionate to the driving force for solidification. Figure 15.10 illustrates the effect of the change in free energy on the driving force for solidification through the stability of the liquid and solid for a pure metal solidifying at a single temperature and a binary alloy having two components that solidify over a range of temperature between the liquidus and solidus. In both

Fig. 15.10 Schematic representation illustrating the driving force for solidification as the reduction in free energy at near the melting temperature for a pure alloy (left) and at the liquidus (TL ) and solidus (TS ) temperatures for a binary alloy (right). (Figure on the left adapted and used with permission, copyright 2020 Wiley, Creative Commons Attribution 4.0 International [5]; and figure on the right adapted and used with permission, copyrighted 1991 Elsevier [6])

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Fig. 15.11 Gibbs free energy curves for all concentrations at temperature T* for a eutectic system

examples, the phases being at local equilibrium at a particular temperature are indicated by the minimization in the Gibbs free energy. Recalling that G = H − TS, it may also be shown that the difference between the enthalpy and Gibbs free energy in the diagrams is the entropy of the system, with entropy increasing with temperature and indicating greater disorder. Shown in Fig. 15.11 is a phase diagram for a eutectic system and the corresponding Gibbs free energy curves for compositions at temperature T*, which defines a temperature between the liquidus and solidus. The minimum free energy at a particular concentration indicates the phases at equilibrium at T*. Note that the solid and liquid at equilibrium at this temperature is defined by the tie-lines at the tangent points between the minimum free energies for solid α, solid β, and the liquid phase. The discussion so far details the need for some degree of undercooling to initiate a change of state representing a volume of liquid to the solid; however, there are other considerations regarding initiation and sustainment of solidification relevant to additive manufacturing processes that also entail a change in the free energy of the system. This includes the establishment of stable nuclei of solid material and

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445

the continued growth of the solid within the liquid. In addition to the chemical energy of the system, these considerations would involve the change in surface energy associated with the curvature of a favorable nuclei, ΔGS , and the change in free energy related to undercooling of the liquid based on a compositional gradient within the liquid, ΔGT [7]. Although the change in the Gibbs free energy accompanying the chemical transformation of the liquid to the solid will be negative, the additional change in free energy related to ΔGS and ΔGT will be positive. Based on these considerations, the total change in free energy during solidification applicable to additive manufacturing processes may be expresses as: ΔG = −ΔGV + ΔGS + ΔGC

.

(15.18)

15.2.2 Change in Free Energy During Heterogeneous Nucleation Although formation of a stable nuclei during solidification may involve homogeneous nucleation at high undercooling within the melt, additive manufacturing processes that entail melting and solidification of material on a substrate rely on heterogeneous nucleation of the solid on a relatively rough surface and require a much lower degree of undercooling. Although undercooling, driven by change in chemical free energy, is required to form the solid, the contribution of surface energy accompanying heterogeneous nucleation at the substrate surface reduces substantially the undercooling for initiation of solidification. The formation of the initial nuclei is also facilitated by epitaxy or the continued arrangement of atoms in the initially formed solid that corresponds with the crystallographic structure of the underlying substrate and results in lower misfit energy during atomic ordering. The crystallographic orientation of the solid during subsequent growth may also be influenced by epitaxy. In most metals, when the deposition material possesses the same crystallographic structure as the substrate, the favorable crystallographic orientation for growth is the direction. Initiation of the solid at a point on the substrate may be viewed as the formation of a hemispherical cap having a radius, r, and a contact angle between the substrate surface, θ [8]. This is illustrated in Fig. 15.12. The total change in free energy accompanying the formation of the nuclei may be described by the change in chemical free energy through a reduction in per unit volume during transfer of atoms from the liquid to the solid and the contribution of interfacial energy created by the new interface between the liquid and solid: ΔG = −ΔGV + ΔGS

.

(15.19)

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15 Solidification During Additive Manufacturing

Fig. 15.12 Spherical cap of solid nucleated on the surface of a substrate from the liquid. (Figure adapted and used with permission; copyright 2018 http://tec-science.com [8])

The surface of the hemispherical cap is a function of the contact angle θ , which is determined by the surface tension between the liquid and the substrate, γ L − Sub ; solid and the substrate, γ S − Sub ; and the solid and the liquid, γ S − L . It may be shown that by employing a force balance based on the analysis by Young, the specific surface tensions may be used to define the wetting angle, cosθ , in terms of θ : cosθ =

.

γL−Sub − γS−Sub γS−L

(15.20)

The volume of the hemispherical cap may also be expressed in terms of the radius and contact angle: V =

.

 π 2 − 3cosθ + cos3 θ r 3 3

(15.21)

where the contact angle function, f (θ ), is defined as:   f (θ ) = 2 − 3cosθ + cos3 θ

.

(15.22)

It follows that the decrease in chemical free energy for a volume of a solid nuclei formed from the liquid is: ΔGV = V • GV

.

and recalling that ΔGV = ΔHf ΔT/TM , the substitutions yield:

(15.23)

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447

  ΔH ΔT  π f 3 2 − 3cosθ + cos θ r 3 .ΔGV = 3 TM

(15.24)

in which the above describes the change in chemical energy for the reduction in volume of the liquid forming the solid nuclei having a radius of r and a specific heat of fusion of ΔHf and requiring an undercooling of ΔT. The change in surface free energy related to the formation of the nuclei, ΔGS , may be defined by the creation of surface representing the nuclei formed into the liquid and the change in surface energy due to the formation of the nuclei on the surface of the substrate. The surface energy of the newly created hemispherical cap into the liquid, ΔGS, S − L , may be determined based on the new area and the surface tension between the solid and liquid, such that: ΔGS,S−L = 2π γS−L (1 − cosθ ) r 2

.

(15.25)

The change in energy due to forming the hemispherical nuclei on the substrate, ΔGS, S − Sub , may be shown to be:   GS,S−Sub = −π γL−Sub cosθ − cos3 θ r 2

.

(15.26)

and the sum of the above two relationships provides the determination for the total change in surface free energy in forming the hemispherical nuclei. Applying manipulation and employing Young’s relationship, the total surface energy may be shown as:   2 3 2 .ΔGS = 2π γS−L (1 − cosθ ) r − π γS−L cosθ − cos θ r (15.27) or   ΔGS = π γS−L 2 − 3cosθ + cos3 θ r 2

.

(15.28)

The total change in free energy for nucleation of the hemisphere, accounting for the contributions of ΔGV and ΔGS , may now be determined: ΔG= −

.

   ΔH ΔT   π f + π γS−L 2 − 3cosθ + cos3 θ r 2 2 − 3cosθ + cos3 θ r 3 3 TM (15.29)

and may be simplified to represent the classical description: 

4π .ΔG = − 3



ΔHf ΔT TM



 

2 − 3cosθ + cos3 θ r + 4π γS−L r 4 (15.30) 3

2

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15 Solidification During Additive Manufacturing

The expression in the left bracket above represents the free energy change during homogeneous nucleation, with the right bracket being the wetting factor that indicates the variation in free energy required for heterogeneous nucleation. The wetting factor will be between zero and 1. The effect of contact angle of nuclei for nucleation based on the wetting factor is shown in Fig. 15.13 [8]. The critical radius for nucleation, rc , under heterogeneous nucleation may be derived by minimizing the differential of ΔG with respect to r: d (ΔG) =0 dr

.

(15.31)

and   

  2 − 3cosθ + cos3 θ ΔHf ΔT 2 rc + 8π γS−L rc . −4π =0 TM 4

(15.32)

which is commonly shown as: rc =

.

2γS−L ΔGV

(15.33)

Based on classical nucleation theory, the rate of heterogeneous nucleation, Ihet , may be defined based on meeting the critical energy barrier, ΔGcrit , to form a nucleus of critical size:

Fig. 15.13 Influence of the wetting factor on contact angle of nuclei. (Figure used with permission; copyright 2018 http://tec-science.com [8])

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449

Ihet

.

  ΔGcrit = ZJ N exp − kB T

(15.34)

where Z is the Zeldovich factor that defines the probability that the nuclei will grow and not dissolve, N is the number of sites available for nucleation, J describes the rate in which atoms attach to the nuclei, and kB is Boltzmann’s constant. This formulation is based on Ihet representing the number of nucleation events per volume per unit time. The parameters on the right of the expression prior to the exponential term describe the kinetics of the nucleation event, where the exponential term defines the energetic requirements. Evaluating the above expressions shows that the radius of a nucleus to initiate stable nucleation is inversely proportional to the degree of undercooling, and that the critical radius for a nucleus at a given undercooling decreases as the surface tension between the solid and liquid decreases. This would represent good wetting between the liquid and solid and would be indicative of deposition of a single alloy system, often found in additive manufacturing. The smaller contact angle associated with good wetting also represents a smaller wetting factor, which may be shown to decrease the activation energy required for nucleation. Also, as the critical radius and potential solidification morphology decrease, such as that found in powder bed fusion processing, the impact of minimizing interfacial energy, which is proportional to the surface tension between the liquid and solid, becomes more significant. The inherent number of nucleation sites available at the surface of the substrate for additive manufacturing processes also has a direct impact on increasing the rate of nucleation during solidification. In general, heterogeneous nucleation is readily active in solidification during additive manufacturing but plays a progressively larger role in processes that utilize high velocities of the energy source that lead to high solidification rates and fine solidification morphologies.

15.2.3 Growth of the Solid Within the Liquid The prior discussion focused on the thermodynamic driving force for establishing a stable nucleus of the solid on the surface of the substrate under local equilibrium conditions, which is an important component for initiating the solidification process. However, once stable nuclei are achieved, the growth of the solid within the liquid or the solidification front becomes the dominant mechanism in establishing the morphology of the solidified material and, ultimately, microstructure. The growth of the solid within the liquid is still impelled by minimizing free energy, but the rate of growth and shape of the solidification front may be influenced by several factors, which include the rate of heat extraction, thermal gradient within the liquid, curvature of the solid and liquid interface, and compositional gradients within the liquid and solid. It will also be shown that the distribution of alloying constituents will be altered by how these additions respond to the solidification event. As in many engineering analyses, the dominant factors that govern a reaction are specific

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15 Solidification During Additive Manufacturing

to a particular process, and hence, the development of the solidification front during additive manufacturing will be discussed in terms of characteristics inherent to these processes. As described earlier, additive manufacturing processes that involve local melting and solidification of metals, such as displayed in powder bed fusion and directed energy deposition, utilize a moving energy source to form the layer in a predetermined manner. Energy is applied to the material and substrate for melting and extraction of heat is accomplished through conduction to the substrate, as well as surface heat losses due to convection and radiation as the build geometry grows above the build plate. Conduction of heat is driven by thermal gradients in the conduction path, with the rate of dissipation being controlled by the thermal diffusivity of the material. The highest rate of heat extraction occurs during the initial layers when the substrate temperature is relatively low. As layers are added, the underlying material increases in temperature and results in decreasing thermal conduction, which is illustrated in the thermal responses shown in Figs. 15.1 and 15.4. As the height of the build increases during directed energy deposition, additional surface area is created to encourage radiative and convective losses. However, surface heat losses at the walls of the build are suppressed by the continued addition of surrounding powder during the powder bed fusion process with surface heat transfer occurring only on the top layer. Although specific processing conditions, such as the energy used for deposition, the use of auxiliary preheating, dwell time between layers, geometry of the build, and material thermal and physical properties, may influence the rate of heat extraction, the various powder bed fusion and directed energy processes may be characterized based on the ability to remove heat during processing. In general, the rate of heat extraction and subsequent cooling for these processes, in highest to lowest rate of extraction, are laser-based powder bed fusion, electron beam-based powder bed fusion, low-energy laser-based directed energy deposition, moderate-energy laser and electron beam directed energy deposition, and high-energy electron beam directed energy deposition. Based on the above discussion, there are direct implications of the additive manufacturing process to the growth of the solidification front. The use of the moving heat source and the ability of the substrate and surrounding environment to promote cooling result in relatively high rates of heat extraction near the solidification front. Also, the continuous addition of energy from the source to the melt and the substantial mixing within the liquid, which entails mass and energy transport, typically provides a positive thermal gradient within the molten pool; the temperature within the liquid ahead of the solidification front is higher than the temperature at the solid and liquid interface. In combination, these conditions facilitate directional solidification at the front that follows the primary flow of heat at the interface. Local equilibrium at the front requires some level of undercooling for continued development of the solid, and under these circumstances, the growth of the solid in the liquid and the establishment of the solidification morphology may be described by the degree of undercooling associated with the curvature of the solid and liquid interface and the compositional gradient within the liquid.

15.2 Solidification

15.2.3.1

451

Curvature at the Solid and Liquid Interface

Because of heterogeneous nucleation at discreet points on the surface of the substrate, initial solidification will exhibit some degree of curvature at the interface. When small perturbations of the solid begin to grow, the contribution of interfacial energy associated with the growing surface is relatively high in comparison to the enthalpy of the solid. This results in a marginal increase in the total free energy and acts to slightly decrease the local equilibrium solidification temperature, thus enabling the growth of the solid within the liquid to be maintained. For a spherical nucleus of solid having a radius r growing within the liquid, the increase in free energy may be shown as: ΔGV =

.

2σ r

(15.35)

where σ is the interfacial energy of the liquid and the solid. Recalling the relationship for undercooling during solidification may be expressed as: ΔT =

.

ΔGV ΔSf

(15.36)

and substituting for ΔGV yields: 2σ r

(15.37)

2σ rΔSf

(15.38)

ΔT ΔSf =

.

or ΔTr =

.

The above relationship is the Gibbs-Thompson equation which describes the degree of undercooling that may be associated with a spherical perturbation of solid growing into the liquid. The above may be further simplified as: ΔTr =

.

2𝚪 r

(15.39)

where Γ is the Gibbs-Thompson coefficient defined as: 𝚪=

.

σ ΔSf

(15.40)

The analysis by Stefanescu has shown that utilizing the common value of 10−7 K-m for Γ , which is applicable for many metals, yielded an undercooling of 0.2 ◦ C that was required to achieve a stable solid with a radius on the order of 10 μm [7]. Based on this small scale of feature, it is reasonable to believe undercooling due

452

15 Solidification During Additive Manufacturing

Fig. 15.14 Scanning electron microscope image of the solidification morphology for the laser-based powder bed fusion process with a Co-29Cr-6Mo alloy. (Figure used with permission; copyright 2018 Elsevier [9])

to curvature of the solid may be operative and contributory in initiating the fine microstructures observed from the powder bed fusion process. Shown in Fig. 15.14 is a SEM image of the solidification morphology in a Co-29Cr-6Mo alloy produced using a laser power of 280 W in the powder bed fusion process [9]. The demarcation of the final melt pool and the underlying material is readily shown, along with small grains on the order of a few microns that were formed during initial solidification. The small grains were quickly replaced by a cellular structure, which also indicates a strong epitaxial growth direction in the small chill grains and the final cellular structure. Conversely, the larger microstructural features observed in other additive manufacturing processes preclude undercooling due to curvature being active. Although curvature for providing undercooling sufficient for stable initiation of growth is applicable to the rapid cooling rates of the powder bed fusion process, the influence of compositional gradients within the liquid for controlling solidification morphology is also pertinent to all of the materials and processes used for additive manufacturing that involves melting and solidification.

15.2.3.2

Compositional Gradient Within the Solid and Liquid and Partitioning of Solute

The discussion will now turn to the impact of a compositional gradient within the liquid in front of the solid and liquid interface. It is well established that the effect of local composition of solute near the interface can have a profound effect on the development of the solidification morphology. The influence of changes in composition at the interface has a direct impact on solidification temperatures, and

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453

this phenomenon is referred to as constitutional undercooling or supercooling. The consequences of local composition during solidification are not only important for establishing growth conditions for the solid and liquid interface, but also have ramifications to partitioning or redistribution of alloying species during solidification and lead to alloying segregation with the microstructure. Hence, the discussion will begin with how composition may change during solidification. The exact composition of the material at the solidification front is an important factor for understanding the development of the solidification morphology and evaluating the segregation of alloying additions during solidification. The potential for segregation of alloying additions can be viewed based on the equilibrium partition coefficient that describes the redistribution of a particular solute species at the solidification interface. The equilibrium partition coefficient, ki , may be described for each solute species, i, through: ki =

.

CS CL

(15.41)

where CS is the composition of the solid in equilibrium with the liquid at the solidification interface and CL is the composition of the liquid in equilibrium with the solid at the interface. Conservation of solute must also be maintained, such that if the fraction of solid is defined as fS and the fraction of liquid is defined as fL , then it follows: CS fS + CL fL = Co

(15.42)

fS + fL = 1

(15.43)

.

and .

If the liquidus and solidus lines are linear and possess a constant slope, the amount of solute in equilibrium at the solidus during initial solidification, at fS = 0, may be shown to be kCo , and the concentration of solute at the liquidus during the terminus of solidification, at fL = 0, is Co /k. Whether the partition coefficient is less than or greater than 1 may be determined from the phase diagram for the particular solute species of interest based on the slope of the liquidus and solidus lines being positive or negative. In cases where k 1, the solute is absorbed within the solid through diffusion and very little is redistributed with the liquid. This is illustrated in Fig. 15.15. It may also be shown that the partition coefficient is constant only when the slope of the liquidus line is constant; however, even though for many alloys the slope of the liquidus line is not constant, analytical analyses typically assume k is constant. Under the above assumptions and conditions, i.e., linear liquidus and solidus lines, complete diffusion or mixing of solute within the solid and the liquid, and

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15 Solidification During Additive Manufacturing

Fig. 15.15 Examples of sections of phase diagrams showing slope of liquidus and solidus lines and effect on partition coefficients

chemical equilibrium at the solid and liquid interface, the local composition during solidification may be anticipated. Shown in Fig. 15.16 is the expected composition for a planar interface in terms of solute concentration for an alloy system shown on the left of Fig. 15.15 (k < 1) and having an initial concentration of solute of Co during equilibrium solidification. The local concentration of solute in the figure is depicted by the solid blue lines representing the concentration profiles during initial solidification, at temperature T*, and during the terminal stage of solidification. Recalling the above relationships regarding conservation of solute for equilibrium solidification, during the terminal phase, fS = 1, fL = 0, and CS = Co . Hence, under these conditions, the composition at the planar interface after solidification may be seen to be Co , with some departure during initial and final solidification. Although solute content at equilibrium provides deviation from the initial solute concentration, complete diffusion or mixing in the solid and liquid ensures the final composition is at Co . Complete diffusion within the solid and liquid ensures chemical equilibrium at the interface and no segregation of solute would be expected. Also, note that conservation of solute must be maintained and is illustrated by the area of the solute profiles. Although this example is useful for illustrating how solute participates in the solidification process, it is not realistic regarding most material systems and processing conditions. One of these assumptions will now be relaxed to reflect a situation that is somewhat more realistic, limited diffusion within the solid. Under the rapid cooling experienced during additive manufacturing, thermally driven diffusion within the solid would expect to be limited. In this case, it is assumed that there is no diffusion in the solid and complete mixing in the liquid. Because of

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455

Fig. 15.16 Diagram showing local concentration of solute profile (blue line) for a binary alloy having a partition coefficient less than 1 during equilibrium solidification with complete diffusion in the solid and complete diffusion and mixing in the liquid

limited diffusion within the solid, the ability to strictly follow the solidus boundary composition will be hindered, such that chemical equilibrium within the system will not be maintained; however, local equilibrium at the interface is assumed. Shown in Fig. 15.17 are solute profiles, depicted as the blue line, of a planar interface for an alloy system with k < 1 and having an initial concentration of solute of Co under conditions of no diffusion in the solid and complete mixing in the liquid. Because k is less than 1, with CS also being less than CL , as liquid is transformed to the solid during solidification, solute atoms at the interface are rejected from the solid, and perfect mixing in the liquid ensures that the rejected solute is readily distributed. As solidification proceeds, the increasing level of solute within the liquid eventually results in the eutectic reaction. Under these conditions, solidification results in redistribution and segregation of solute. Initial solidification will represent a solid having lower levels of solute equal to kCo , with the final stage of solidification being solute-rich. Under the conditions described above, it was assumed that no solute diffuses into the solid and there is complete mixing of solute within the liquid. There is departure from chemical equilibrium in the system but local equilibrium exists at the interface. The use of .CS∗ and .CL∗ is now used to define the non-equilibrium composition of the solid and liquid, respectively. Based on the level rule, the composition of the liquid during solidification would be directly related to temperature and would not account for solute redistribution during solidification. Hence, under these conditions, the solute that is rejected by the solid is defined by the composition of the liquid, .CL∗ ,

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15 Solidification During Additive Manufacturing

which in this case is equal to the equilibrium composition, CL . However, due to limited diffusion within the solid, the composition of the solid, .CS∗ , will not equal the equilibrium concentration, CS . By assuming equilibrium at the advancing solidification interface, the nonequilibrium redistribution of solute described by the composition of solute in the solid and liquid may be defined. The approach is shown graphically in Fig. 15.18, which describes known compositions based on local equilibrium at the solid and liquid interface. Based on the above, a mass balance near the interface provides:

Fig. 15.17 Diagram showing local concentration of solute profile (blue line) for a binary alloy having a partition coefficient less than 1 during near equilibrium solidification with no diffusion in the solid and complete mixing in the liquid Fig. 15.18 Compositional gradient near the solid and liquid interface, along with the approach for determining composition of the liquid during solute redistribution

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457

.

∗  CL − CS∗ dfS = (fL ) dCL

(15.44)

where .CS∗ represents the non-equilibrium composition. Realizing that the partition coefficient under non-equilibrium conditions may be represented by: k=

.

CS∗ CL∗

(15.45)

and recalling conservation of solute, fS + fL = 1, with .CL∗ = CL , the mass balance may be shown as: CL (1 − k) dfS = (1 − fS ) dCL

.

(15.46)

Establishing the boundary condition that .CL∗ = 0 during initial solidification (fS = 0): 

fS

dfS 1 = 1 − fS 1−k

.

0



CL dC Co

L

CL

(15.47)

which yields: .

CL = Co (1 − fS )k−1

(15.48)

CS∗ = kCo (1 − fS )k−1

(15.49)

and .

The above derivation provides a means of estimating solute redistribution during non-equilibrium conditions, as well as the concentration within the solid during solidification, using the equilibrium partition coefficient. The results of the derivation represent the Scheil equation (Scheil-Gulliver), which was the earliest attempt to describe solute redistribution during solidification. Shown in Fig. 15.19 are graphical examples based on the Scheil relationship showing the change in concentration of solute in the solidified material, .CS∗ , as a function of solid fraction of solid, fS , for several partition coefficients that are less than or greater than 1. The fraction solid will proceed from 0 to 1 during the solidification event. By definition, the slope of the solidus and liquidus lines defines the value of the partition coefficient (recall Fig. 15.15). Partition coefficients less than 1 signify an increasing equilibrium concentration of solute at the interface as solidification proceeds. By contrast, partition coefficients greater than 1 indicate a decrease in solute at the interface as solidification progresses. It will be shown that this has significant ramification to solute redistribution and potential segregation resulting from the solidification event. Also, note that when the partition coefficient is less than 1,

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15 Solidification During Additive Manufacturing

Fig. 15.19 Concentration of solute during solidification based on the Scheil relationship for several partition coefficients that are less than or greater than 1.

the eutectic reaction limits the ability of fS to reach the value of 1 at the terminus of solidification. It is important to understand the assumptions that govern the derivation of the Scheil equation, complete mixing in the liquid, limited diffusion within the solid, local equilibrium at the interface, and linear solidus and liquidus boundaries of the phase diagram. It is important to also note that the Scheil equation, in many instances, provides a reasonable attempt to portray solute partitioning under non-equilibrium solidification, but depending upon material and processing, it may depart significantly from actual conditions. Although it continues to be used extensively, other derivations have also been developed to account for some of the deficiencies in the Scheil approach. The above case for solidification, which assumes equilibrium at the interface, no diffusion in the solid, and perfect mixing in the liquid, may depict additive manufacturing processes under certain conditions, and although there is expected to be significant mixing in the molten pool, it is not perfect. Of particular importance is the thin boundary layer next to the solid that extends into the fluid. This layer acts to decrease mixing very near the solid and liquid interface and results in reduced mixing of the rejected solute. Under this condition, it would be anticipated that the solute would be enriched at the solid and liquid interface with greater uniformity away from the interface. This non-equilibrium condition is illustrated in Fig. 15.20. The rejection of solute at the interface, coupled with the boundary layer for limiting mixing, results in solute enrichment ahead of the solidification front. The level of solute within the liquid at the interface is no longer equal to the equilibrium concentration under these circumstances, such that .CL∗ must be defined and is not equal to CL . When the partition coefficient is greater than 1, solute is absorbed within the solid, such that the boundary layer is solute poor. This is illustrated in Fig. 15.21 [10].

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459

Fig. 15.20 Diagram showing local concentration of solute profile (blue line) for a binary alloy having a partition coefficient less than 1 during non-equilibrium solidification with no diffusion in the solid and limited mixing in the liquid with a boundary layer at the interface

Fig. 15.21 Representation of solute redistribution ahead of the solidification front when the partition coefficient is less than and greater than 1. (Figure adapted with permission; copyright 2008 Minerals, Metals and Materials Society [10])

15.2.4 Constitutional Undercooling and Interface Stability The redistribution of solute and the enrichment at the interface have a significant implication to the stability of the interface and the resultant growth morphology during solidification. The enrichment of solute near the interface is responsible for lowering the solidification temperature in this region. The reduction in temperature due to the local change in composition is termed constitutional undercooling or supercooling. Figure 15.22 graphically describes this phenomenon. In the figure, the influence of solute enrichment on the local liquidus temperature ahead of the interface and the accompanying zone of constitutional undercooling are illustrated.

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15 Solidification During Additive Manufacturing

Fig. 15.22 Graphical description of constitutional undercooling ahead of the solidification interface

Due to solute enrichment, the liquidus temperature of the material slightly ahead of the interface is lower than the thermal gradient within the liquid, resulting in an energetic driving force for solidification. As demonstrated in Fig. 15.22, constitutional undercooling can only occur when the liquidus temperature of the material representing the enriched boundary layer is higher than the actual temperature within the liquid. This criterion may also be described by comparing the gradients of the local liquidus temperatures and temperatures within the liquid, or: .

dTl dCL < dx dx

(15.50)

Assuming a boundary moving at a steady state and having a velocity of ν, the gradient of solute within the enriched boundary layer at the solid and liquid interface (x = 0) may be defined as: 

dCL .m dx

 =− x=0

 v ∗ CL − CS∗ DL

(15.51)

where m is the slope of the liquidus boundary and DL is the diffusion coefficient for solute within the liquid. Realizing that .CL∗ = Co /k and .CS∗ = Co :

15.2 Solidification

461

 .

dCL dx

 x=0

mCo (1 − k) =− k



v DL

 (15.52)

Therefore, the thermal gradient within the liquid for achieving constitutional undercooling requires: .

mCo (1 − k) dTi < dx k



v DL

 (15.53)

The above relationship forms an important criterion for describing growth morphologies during solidification. Constitutional undercooling describes whether the interface will remain stable during growth, and when combined with other undercooling requirements, such as for curvature of the interface, it plays an important role in defining the solidification structure as a function of material and processing parameters. Figure 15.23 illustrates the application of constitutional supercooling based on hypothetical conditions that involve solidification of an alloy under three processing conditions that would result in varying thermal gradients within the liquid. In this case, the liquidus gradient associated with the material is described as a rate of change with the ordinate axis indicating the change in liquidus temperature. The liquidus gradient for this alloy (at 0.020 cm/s) is shown as the blue line and the three thermal gradients (at 300, 100, and 10 ◦ C.cm) are shown as black lines in the figure. Based on this scenario, the processing condition that produced the thermal gradient of 300 ◦ C/cm would not result in undercooling in this alloy system. Under these circumstances, a planar solidification front would be anticipated based on the lack of constitutional undercooling. In the case of the two processes that produced thermal gradients of 100 and 10 ◦ C/cm, constitutional undercooling would be expected. Fig. 15.23 Example of applying constitutional undercooling based on hypothetical conditions for an alloy and three thermal gradients during solidification

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15 Solidification During Additive Manufacturing

The undercooling ahead of the interface for these conditions is illustrated by the shaded areas. The degree of undercooling would be an indication of the stability of the interface, with greater undercooling providing the potential for greater interface perturbations. A cellular morphology would be anticipated for the thermal gradient of 100 ◦ C/cm, and a more complex morphology, such as a columnar dendritic morphology, would be predicted for the process condition resulting in the thermal gradient of 10 ◦ C/cm. A more useful form for employing constitutional undercooling is obtained by defining the thermal gradient within the liquid as Gth , and through minor manipulation and employing .ΔT = CL∗ − CS∗ , an expression for the critical requirements for undercooling may be shown as:  .

Gth v

 = crit

ΔT DL

(15.54)

In this form, the ratio of the thermal gradient within the liquid to the growth velocity of the interface critical for achieving constitutional undercooling may be expressed in terms of parameters governed mostly by the material, the difference in the liquidus and solidus temperatures, and the diffusion rate within the liquid. The caveat “mostly” is used since convection within the liquid, which is also dictated by processing conditions, will also influence the diffusion coefficient, DL . When constitutional undercooling is viewed in this manner, the degree of interface stability and the resultant solidification morphologies may be categorized for a particular alloy composition. This is graphically illustrated in Fig. 15.24, which Fig. 15.24 Graphical representation of expected growth morphologies for an alloy during solidification based on thermal gradient within the liquid and growth rate of the interface. (Figure adapted with permission; copyright 2002 Wiley & Sons, Inc. [10])

15.2 Solidification

463

was adapted from Kou and depicts the expected growth morphologies based on the thermal gradient with the liquid and the growth rate of the interface [11]. The growth morphologies illustrated in the figure, planar, cellular, columnar dendritic, and equiaxed dendritic, are common morphologies observed during solidification and exhibit increasing instability of the interface. Constitutional undercooling provides opportunity for small perturbations along the solid interface to continue to grow into the liquid, and high degree of constitutional undercooling coupled with undercooling associated with curvature of the interface enables complex growth morphologies to be achieved. Factors that promote constitutional undercooling are small gradients within the liquid, high growth rates of the interface, large diffusion coefficients of solute within the liquid, and steep gradients representing the liquidus and solidus boundaries.

15.2.5 Development of Microstructure During Solidification Because of the high growth rates associated with the rapidly moving energy source used for additive manufacturing, some level of constitutional undercooling is always expected and is an important aspect of the development of the microstructure during solidification. As described earlier, the thermal gradient within the liquid and the growth rate of the interface may be used to indicate the degree of constitutional undercooling associated with solidification. Although undercooling will almost always be operative, the wide range of growth rates and thermal gradients experienced in additive processes result in a wide range of morphologies and solidification microstructures that may be developed. During movement of the energy source, melting and solidification follow the advancement of the source, and thus, the growth rate of the interface, R, is related to the velocity of the energy source, V, through: R = V cosθ

.

(15.55)

where θ is the angle normal to the apparent solid-liquid interface and the direction of the energy source. The thermal gradient within the liquid is not as easily determined. Heat transfer analyses using analytical or numerical means may be used to estimate Gth , but these techniques are difficult for obtaining accurate values of temperatures near the interface. In the case of directed energy deposition, using detailed numerical modeling in conjunction with thermal measurements, Lia et al. have shown that the thermal gradient was found to be inversely proportional to the fluence of energy used to produce the build [1]. The importance of this reasoning is that the degree of constitutional undercooling, and resultant solidification morphologies, may be estimated based on parameters known during processing. Shown in Fig. 15.25 are results of these experiments in terms of Gth and R values, as well as graphical representation for Gth being replaced with the relationship based on the fluence or local energy density, Ed , and R being replaced with the scan velocity, V. The data

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15 Solidification During Additive Manufacturing

Fig. 15.25 Results of experiments to determine Gth and R for laser-based directed energy deposition of N06625 (IN625). (Figure used with permission; copyright 2018 Elsevier [1])

represented in the figure is based on experiments using a laser-based directed energy deposition process for alloy N06625 (IN625) and conducted at 1 and 2 kW of laser power and scan velocities of 4.2 and 10.6 mm/s. The as-built microstructures in all cases exhibited a columnar dendritic morphology and are illustrated in Fig. 15.26. This is indicated by the columnar structure containing secondary dendritic arms. The elongated columnar dendritic structure may be seen to grow in the Z direction or build height, which was in the path of the maximum heat transfer to the base plate. Also note that the columnar dendritic features show a distinct angle in the direction of movement of the heat source, representing the X direction. The wide range of energy input and scanning speeds associated with additive manufacturing processes undoubtedly result in vastly different Gth and R values and corresponding solidification morphologic structures and scale of structures. An example of this fact is when the solidification morphology of material produced by directed energy deposition is compared to that of powder bed fusion. This is illustrated in Figs. 15.27 and 15.28. Fig. 15.27 depicts the solidification microstructure for N06625 (IN625) obtained through optical techniques, and the micrographs in Fig. 15.28 are based on the work of Marchese et al., which shows the as-built microstructure of N06625 (IN625) produced using a laser-based powder bed fusion process through optical and electron microscopy techniques [12]. The very fine scale of the microstructure produced using powder bed fusion is evident, with the solidification morphology being cellular. The high energy density and velocity of the laser during the powder bed fusion processing results in extremely steep thermal gradients and rapid growth rates within the molten pool which drive the development of a cellular growth morphology. It may be surmised that the power of the heat source during additive manufacturing processes involving melting and solidification is inversely proportional to the thermal gradient of the liquid pool, and it has been indicated that the velocity of the energy source is directly related to the growth rate of the solid and liquid interface. Based on these two assumptions, the former being somewhat reasonable, the prediction of the solidification morphology may be defined based

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Fig. 15.26 Microstructures of as-built N06625 (IN625) deposits produced using laser-based directed energy deposition at four fluences or local energy densities that exhibit a columnar dendritic solidification morphology. (Figure used with permission; copyright 2018 Elsevier [1])

on two primary process parameters, power and velocity of the energy source. This approach may be used to define the processing region indicative of the solidification morphology based on power and velocity. Shown in Fig. 15.29 is an example of a map for N06625 (IN625) alloy based on microstructures representing various directed energy deposition processes. The data for laser-based directed energy deposition by Lia et al. [1] has been supplemented with additional data representing N06625 (IN625) material produced by laser, electron beam, and arc-based directed energy [13–15]. The thermal gradient was estimated based on power, velocity, and diameter of the energy source according the relationship depicted in Fig. 15.25. All of the deposited material representing the data within the figure was reported to exhibit a columnar dendritic microstructure. Also superimposed on the data is a calculated boundary for the transition from a cellular to columnar dendritic

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Fig. 15.27 Microstructure of N06625 (IN625) deposits in the as-built condition that was produced using laser-directed energy deposition with X being the direction of deposition and Z being the build height. (Courtesy of F. Lia, Applied Research Laboratory, Pennsylvania State University)

Fig. 15.28 Microstructure of N06625 (IN625) deposits in the as-built condition that was produced using powder bed fusion: (a) optical micrography showing multiple deposits, (b) higher magnification optical micrograph showing cellular solidification morphology, (c) scanning electron micrograph depicting the transverse view of cellular structure, and d) scanning electron micrograph showing the edge view of cells. (Figure used with permission; copyright 2018 Elsevier [12])

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Fig. 15.29 Graph showing columnar dendritic morphology for alloy N06625 (IN625) produced using directed energy deposition including laser (L-DED), electron beam (EB-DED), and arcbased (A-DED) processes [13–16]

morphology, established for INC690 alloy by Blecher et al. [16]. Even though alloy INC690 is higher in alloy content than INC625, it serves as a reasonable estimation for identifying the columnar dendritic region for this alloy system. Isolines for scale of microstructural features are also shown in Fig. 15.29. The general trend indicates that when scan velocity or thermal gradient is decreased, the size of features that define the microstructure, such as cell spacing or secondary arm spacing of dendrites, will increase. This may be rationalized by noting that the product of G and R represents the solidification rate, in ◦ C/s, and a decrease in either of these parameters will result in a decrease in the solidification rate. This is also accompanied by longer times for solidification to be completed and sustained growth of developing features. Although the above discussion implies that G and R are constant for a particular process and set of process parameters, that is rarely the case. Conditions often lead to changes in G and R and accompanying variation in solidification morphology within a build cycle. Several factors may alter the solidification rate within a given process. This includes geometric effects that influence the local solidification growth rate, increased temperature of the substrate that acts to decrease the thermal gradient, and changes in the rate of thermal dissipation during prolonged processing that may affect the thermal gradient, as well as the growth rate. The latter may be due to higher temperatures within the underlying material that results in reduced thermal conduction or increasing surface area that enhances surface heat losses through convection and radiation. Shown in Fig. 15.30 is a schematic of deposition being produced under moderate scanning velocities, such as with directed energy deposition, showing development of the solidification structure. For simplicity, a cellular solidification mode is illustrated. In the case of a moving energy source, the growth rate of the

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Fig. 15.30 Schematic of a deposit being produced for a process having a moderate velocity of the heat source showing development of the solidification structure for longitudinal and cross-sectional views (T1/2 is one-half the melting temperature)

solidification front, defined by the solidus and liquidus temperatures for an alloy, moves proportionally with the source, with heat being dissipated behind the path of movement. The growth direction is opposite of the direction of principle heat extraction. However, the geometry of the solid and liquid interface limits the growth velocity of the front, R, directly below the source of energy where the angle of the front normal to the direction of movement is steep (recall R = Vcosθ ). Hence, rate of growth at the bottom or side of the pool approaches zero. Because of this condition, solidification below the energy source primarily serves as initial nucleation sites with growth occurring behind the energy source and accompanied by higher solidification velocities. The change in velocity of the solidification front can result in a variation of the solidification morphology lower in the deposit. This is especially applicable to early build layers when the relatively cold substrate also results in high thermal gradients, Gth . Alterations in microstructure due solely to changes in the thermal gradient are also prevalent under many additive manufacturing conditions. Shown in Fig. 15.31 is a schematic from Foster showing micrographs at three positions within a build of N06625 (IN625) alloy produced using laser-based directed energy deposition depicting changes in solidification morphology based on height [14]. Three deposition passes were used for each layer. As distance from the substrate increased, the background or preheat temperature of the layer increased and resulted

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Fig. 15.31 Images of build with N06625 (IN625) alloy produced using the laser-based directed energy deposition process showing solidification morphology based on position within the build. (Figure used with permission of Bryant Foster and the Applied Research Laboratory, Pennsylvania State University, copyrighted 2015 Bryant Foster [14])

in a decrease in thermal gradients during deposition and lower solidification rates. This resulted in a slightly coarser solidification morphology, evident by the moderate increase in secondary dendritic arm spacing, as the distance from the substrate increased. Lower thermal gradients result in slower solidification rates and greater time for growth of these features. Under these conditions, the potential alteration in microstructure could be anticipated based on changes in the thermal gradient. It should be noted that during extended processing with the directed energy deposition process, which results in high background temperature, not only are modifications to the scale of solidification features possible but also a potential change in the type of solidification morphology, such as transitioning from columnar dendritic cell to equiaxed morphology, as described in Fig. 15.24.

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15.2.6 Microsegregation of Solute During Solidification Most of the discussion until now has purposely discussed solidification in terms of morphology, which primarily describes the shape of the solidifying front. Although solidification morphology is extremely important in defining the shape of the solidifying network, a full description of the microstructure requires morphology and constitution, and solidification also plays a vital role in establishing the local composition within the microstructure. One aspect of this effect is based upon partitioning of solute during solidification, which describes the solute enrichment or solute reduction ahead of the solid-liquid interface and can be described by the value of the partition coefficient of the solute species. The partition coefficients for many alloying additions are less than 1 and will involve enrichment at the interface. However, there are instances when the coefficient for an alloy species is greater than 1, which results in solute being absorbed within the interface. These two conditions are illustrated in Fig. 15.21. When the partition coefficient is less than 1 for a particular solute, that species is rejected by the moving interface and results in an enrichment. Eventually, the enhanced level of solute ahead of the front is trapped between competing solidification features and results in segregation at the solidification boundaries. Conversely, for partition coefficients of solute species that exhibit values greater than 1, that solute is absorbed within the solidification front and causes an increase in concentration internally to the solidification features. When the partition coefficient is close to 1, little compositional segregation is expected. Shown in Table 15.3 are reported partition coefficients for constituents of interest within a few alloy systems relevant to additive manufacturing [17–24]. Several material systems in the table represent the partition coefficients for binary alloys of the major solvent component, such as δ-iron or nickel, with one solute species. The binary alloys of δ-iron and γ-iron are shown and represent the hypoeutectoid steels having less than 0.8% carbon and hyper-eutectoid steels having greater than 0.8% carbon. In some instances, compositions of an alloy are indicated with the accompanying partition coefficients for the alloying additions, such as the N06625 (IN625), N07718 (IN718), and R56400 (Ti-6Al-4 V) alloys. As the partition coefficients further depart from a value of 1, greater enrichment at the feature boundaries (when k < 1) or greater absorption within the solidification features (when k > 1) is expected. The inter-partition coefficients for the solvent in the table, such as nickel in the Ni-22Cr-9Mo-3.5Nb alloy, are assumed to be close to unity. The values in Table 15.3 should be considered with caution, since partition coefficients of a constituent are dependent upon the entire composition of an alloy, and as discussed earlier, partition coefficients may vary depending upon the degree of non-equilibrium during solidification. Nevertheless, the values in the table provide a first glimpse for solute segregation for constituents within an alloy during solidification. Since the partition coefficient is by definition the ratio of the solute concentration within the solid to the concentration within the liquid during solidification, computation of the phase diagram using thermodynamic principles is

2.7

Partition coefficient of constituent, ki Fe C Mn Si Ni Cr 0.19 0.76 0.77 0.34 0.78 0.52 0.87 1.02 0.89 0.62 1.12 1.05 1.03 1.19 1.16 0.60 0.50 0.70

*Binary alloys, **N06625 (IN625) alloy, ***N07718 (IN718) alloy

δ-Fe* γ-Fe* Fe-Ni Fe-Cr-Ni Ni* Ni-22Cr-9Mo-3.5Nb** Ni-19Cr-5Nb-18Fe-3Mo*** Ti* Ti-6Al-4 V Al-Cu Cu-Ni

Alloy system

0.57 1.00 0.85 0.78 1.50

Mo

0.70 0.60

Ti 0.14 0.07

1.45

0.79

Cu

S 0.05 0.04

0.06 0.13

P 0.23 0.13 0.12

1.60

O 0.02 0.02

Table 15.3 Reported partition coefficients of constituent in a few alloy systems relevant to additive manufacturing

1.58

N 0.28 0.54

H 0.32 0.45

1.05 (Al)0.92 (V)

0.39 (Nb) 0.40 (Nb) 0.35 (Nb)

Others

17

17 17 18 19 20, 21 22 23 20 24

Ref.

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a powerful tool for fairly accurate assessment of partition coefficients for simple, as well as complex systems. Figure 15.32 represents schematics depicting the potential influence of the partition coefficient on segregation of solute during solidification. The figure characterizes solidification under conditions that result in cellular and columnar dendritic morphologies with the partition coefficient of a solute species being less than or greater than unity. Also shown in the figure are arrows indicating the direction of solute that is being rejected (k < 1) or absorbed (k > 1) at the solid and liquid interface during solidification. The material having a composition that is high in solute is represented in the figure as a darker phase, while the solvent being leaner in solute is shown as the lighter phase. The solute that is rejected or absorbed results in microsegregation within the microstructure where the local composition significantly departs from the composition of the alloy. This segregation may result in the boundaries between solidification features or the core of the features containing higher concentration of solute. In many instances,

Fig. 15.32 Schematics of potential solute segregation for cellular and columnar dendritic solidification for solute having a partition coefficient (k) less than and greater than unity (red arrows indicate the direction of solute redistribution at the interface)

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Fig. 15.33 Optical micrographs at two magnifications of a transverse cross section of N06625 (IN625) material deposited using an arc-based directed energy deposition process. (Figure used with permission; copyright 2016 Elsevier [25])

multiple solute species having similar partition coefficients may contribute to the formation of a separate phase representing the microsegregation. This is particularly true for binary, ternary, and quaternary eutectic phases, which forms a compositional path during solidification. In other instances, the local concentration of solute species may react during the terminal stage of solidification or undergo solid state transformations directly after the solidification event. Shown in Fig. 15.33 are optical micrographs by Wang et al. that represent N06625 (IN625) material deposited using an arc-based directed energy deposition system [25]. The process utilized a gas tungsten arc to deposit N06625 wire using a local energy density of approximately 65 J/mm2 and maintaining an inter-pass temperature of 50 ◦ C. The micrographs in the figure are cross sections that were perpendicular to the direction of travel with the z-orientation being along the build height obtained at two magnifications. The micrographs represent material at the mid-height of a build that was approximately 5 cm high. The image acquired at the higher magnification clearly indicates a columnar dendritic microstructure for the deposited material. In that micrograph, the columnar dendritic growth morphology is seen as the white phase and portrays cores and secondary arms of dendrites. Figure 15.34 is a scanning electron micrograph of the deposited material, along with element maps obtained by energy-dispersive x-ray spectroscopy for various constituents present with the N06625 alloy [25]. The core regions of the primary dendrites and the secondary arms are shown in the scanning electron micrograph as a light gray matrix with small white islands that represent regions between secondary dendrite arms. The light areas within the element maps indicate higher concentrations of a particular element. Based on these maps, the matrix exhibits high concentrations of niobium and chromium, with lesser amounts of

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Fig. 15.34 Images of N06625 (IN625) deposit showing (a) scanning electron micrograph and element maps for (b) Nb, (c) Mo, (d) Ti, (e) Cr, (f) Fe, and (g) Ni. (Figure used with permission; copyright 2016 Elsevier [25]) Table 15.4 Results of energy-dispersive x-ray spectroscopy and initial composition of wire (weight percent) for the N06625 (INC625) alloy conducted by Wang et al. for Spots A and B shown in the micrograph of Fig. 15.33 [25] Description Spot A (interdendritic regions) Spot B (matrix material) Wire used to produce the deposit Partition coefficients for N06625 alloy

Ni 44.9 65.0 64.2 1.05

Cr 20.4 27.3 22.6 1.03

Mo 14.5 4.4 8.7 0.85

Nb 18.2 1.5 3.5 0.40

Fe 1.2 1.3 0.3 1.12

Ti 0.8 0.4 0.2 0.60

molybdenum. The islands representing the interdendritic regions appear to reflect higher concentrations of niobium and molybdenum. Given the partition coefficients for elements within the N06625 (IN625) alloy, interdendritic segregation of niobium (kNb = 0.40), titanium (kTi = 0.60), and chromium (kCr = 0.85) would be expected. Wang et al. also conducted a more detailed analysis by conducting quantitative measurements using the energy-dispersive x-ray spectroscopy of two spots defined by A and B in the electron micrograph. The results of this analysis are shown in Table 15.4, along with the reported composition of the wire used to produce the material and the partition coefficients for this alloy from Table 15.3. The composition of the matrix (Spot B) is relatively similar to the initial starting composition of the wire in terms of nickel and chromium, which have partition coefficients close to 1. The interdendritic region (Spot A) indicated enrichment of species with partition coefficients less than 1, which included niobium, titanium, and molybdenum. These findings support the generally well-known observation of segregation during solidification in several nickel-base alloys that may result in the detrimental interdendritic formation of the Laves phase that may form as (Ni,Cr)2 (Nb,Co), as well as precipitates of niobium and titanium carbides [22, 25, 26].

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15.2.7 Macrostructure and Microstructure of Additive Manufactured Metals As alluded to, additive manufacturing processes that involve melting and solidification utilize a broad range of energy for the heat source, and this inherently results in a wide span of thermal gradients, interface growth rates, and solidification rates within the material. The two extreme conditions are the powder bed fusion process that employs a highly focused beam moving at extremely high rates, at meters per second, and a directed energy deposition process operating at very high power, up to 25,000 W, that creates a large pool moving at a relatively low speed. There are also various processes that fall between these extremes, which encompasses directed energy deposition processes operating at low to moderate power and travel velocities. The result of this wide variety of processing conditions is an assortment of scale and microstructural features exhibited by the material that is produced. This is due to the large difference in solidification conditions associated with the processes, as well as the solid state transformations of the microstructure that occur post-solidification during subsequent heating cycles. Shown below are several examples that illustrate the variation in microstructures that may be present in additive manufactured metals. Figure 15.35 represents optical macrographs and a micrograph of a build with R56400 (Ti-6Al-4 V) alloy produced using a laser-based directed energy deposition process with powder. The entire build was produced utilizing many layers with each layer produced using 14 passes, all passes using a fluence of approximately 0.1 J/mm2 . An absorption coefficient of 0.5 was estimated for calculating the fluence. The macrographs indicate large columnar prior β grains formed during solidification, which is typical of this alloy. These large prior β grains are formed initially by epitaxial growth from the substrate and grow as columns opposite the axis of heat flow, which is into the substrate by conduction. The columnar growth continues during each deposition pass by continuing the epitaxy from the previously deposited material. The macrograph at the center of the figure clearly shows the long, columnar grains that have grown vertically in the build direction, the z-orientation. Also shown in this micrograph are “shadows” that delineate the various passes used to deposit the material. These shadows are caused by solid state transformations in the underlying material during each deposition pass and are similar to the heat-affected zone of weldments. The primary solid state transformation upon cooling is the transformation of the high temperature β-phase to acicular martensite, α’, during rapid cooling. The acicular α’-phase is seen in the micrograph on the right in the figure. The optical macrograph and micrograph of Fig. 15.36 also represent a build with R56400 (Ti-6Al-4 V) produced using a laser-based directed energy deposition process with powder, but at a fluence of 23 J/mm2 (β = 0.5). The build was produced using five layers with one pass per layer. The large columnar grains are also exhibited in the macrograph. These prior β grains have a width slightly larger than the grain in Fig. 15.35; however, the morphology of the grains indicates some

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Fig. 15.35 Optical macrograph and micrographs of R56400 (Ti-6Al-4 V) produced using a laserbased directed energy deposition process with a local energy density of 0.1 J/mm2 . (Images used with permission of Dr. Shawn Kelly and the Applied Research Laboratory, Pennsylvania State University)

competition during growth, as well as curvature towards the build walls, which also contributed to cooling. The last pass representing the top surface has formed a few equiaxed grains due to the low thermal gradient caused by the high background or inter-pass temperature associated with the prior deposits. The micrograph also exhibits acicular martensite that had transformed from the elevated temperature βphase during cooling. Shown in Fig. 15.37 are optical micrographs of R56400 (Ti-6Al-4 V) produced using the powder bed fusion process. Figure 15.37a represents material created using a laser-based powder fusion process at a fluence of 3.0 J/mm2 (β = 0.5) [27], and Fig. 15.37b denotes material produced using an electron beam-based powder bed fusion process conducted at approximately 2.0 J/mm2 (β = 0.9) [28]. The smaller scale of microstructural features for material produced using the laserbased powder bed fusion process is readily observable when compared to the directed energy deposition process for this material. Evidence of elongated prior β grains is observed in the laser-based process, Fig. 15.37a, as well as a very fine acicular martensite, α’, that was formed during rapid cooling but after solidification. Although the electron beam-based powder bed fusion process was conducted at a low fluence, the preheating of between 650 to 700 ◦ C that is typically used for this process resulted in significantly lower thermal gradients and cooling rates. The

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Fig. 15.36 Optical macrograph (left) of R56400 (Ti-6Al-4 V) produced using a laser-based directed energy deposition process with a local energy density of 23 J/mm2 and optical micrograph (right) within deposition showing the grain boundary region. (Figure used with permission; copyright 2018 Materials Science and Engineering [1])

Fig. 15.37 Optical micrographs of R56400 (Ti-6Al-4 V) by Cepeda-Jiménez et al. produced using the (a) laser-based powder bed fusion and (b) Rafi et al. using the electron beam-based powder bed fusion processes. (Figure (a) used with permission, copyright 2018 Elsevier [27] and figure (b) used with permission, copyright 2013 Springer [28])

resultant microstructure for the R56400 material, shown in Fig. 15.37b, reflects these conditions by exhibiting much larger prior β grain boundaries, denoted by the white boundary regions in the micrograph, as well as relatively large laths of α that formed post-solidification at lower cooling rates than the martensitic α’ that was shown earlier.

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Fig. 15.38 Optical micrographs of material produced using the laser-based powder bed fusion process for (a) stainless steel alloy S31603 (316L) and (b) aluminum alloy Al-10Si-0.5Mg (Figure (a) used with permission, copyright 2019 Elsevier [29] and figure (b) used with permission, copyright 2018 Elsevier [30])

The fine microstructural features associated with the laser-based powder bed fusion are also illustrated in Fig. 15.38, which shows optical micrographs of stainless steel alloy S31603 (316 L) (Fig. 15.38a) and aluminum alloy Al-10Si0.5 Mg (Fig. 15.38b) [29, 30]. In both instances, the micrographs display a region having boundaries between passes. The S31603 alloy appears to exhibit columnar grains with a fine cellular substructure. Epitaxial growth between passes is seen with the S31603 material, which probably represents , the easy crystallographic growth direction for this alloy system. The aluminum alloy also appears to show cellular growth. In both cases, extremely fine equiaxed grains are exhibited at the boundary, which may be remnants of nucleation.

15.3 Questions and Discussions 1. Discuss the effect of changes in the energy fluence and energy density used during the directed energy deposition on the resulting cooling rates that may be experienced by the material. 2. Describe what is meant by the quasi-steady state condition and how that condition may be used to simplify the thermal analysis of additive manufacturing of a material. What are the limitations to the quasi-steady state condition? 3. Show using basic relationships how the degree of undercooling is proportional to the driving force for solidification, and how this may be related to the disorder of the system. 4. Show mathematically how the above relationship may be modified to account for curvature of the interface between the solid and liquid.

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5. Discuss how the change in free energy for nucleation during solidification is influence by the ability of the liquid to wet the solid. 6. Derive the relationships for composition of the solid during initial solidification and composition of the liquid during terminal solidification in terms of the partition coefficient. 7. Discuss how the effects of solute diffusion in the solid and solute mixing and diffusion in the liquid may influence solidification behavior and what conditions may be considered most appropriate for solidification during additive manufacturing. 8. Based on classical solidification theory, describe what factors dominate the development of morphology during solidification. 9. Using alloy S42000 (420) as a hypothetical system, discuss what alloying additions would be expected to be found in intergranular and intragranular regions. 10. Discuss in detail what microstructures would be anticipated after conducting a directed energy deposition process and a powder bed fusion process.

References 1. Lia F, Park JZ, Keist JS, Joshi SB, Martukanitz RP (2018) Thermal and microstructural analysis of laser-based directed energy deposition for Ti-6Al-4V and Inconel 625 deposits. Mater Sci Eng A 717:1–10. https://doi.org/10.1016/j.msea.2018.01.060 2. Wu CS, Yan F (2003) Numerical simulation of transient development and diminution of weld pool in gas tungsten arc welding, modelling simul. Mater Sci Eng 12:13–20 3. Steuben JC, Birnbaum AJ, Michopoulos JG, Iliopoulos AP (2019) Enriched analytical solutions for additive manufacturing modeling and simulation. Addit Manuf 25:437–447. http:/ /www.sciencedirect.com/science/article/pii/S2214860418303877 4. Promoppatum P, Yao S, Pistorius P, Rollett A, Coutts P, Lia F, McCandless A, Sweny R, Martukanitz R (2018) Numerical modeling and experimental validation of thermal history and microstructure for additive manufacturing of an Inconel 718 product. Progress in Additive Manufacturing 3:15–32 5. Kurtuldu G, Löffler J (2020) Multistep crystallization and melting pathways in the freeenergy landscape of a Au–Si eutectic alloy. Advanced Science:7. https://doi.org/10.1002/ advs.201903544 6. Ohsaka K, Lin JC, Trinh EH, Perepezko JH (1991) Free energy change of off-eutectic binary alloys on solidification. Scripta Met 25:945–948 7. Stefanescu D (2009) Equilibrium and non-equilibrium during solidification, chapter 2 in science and engineering of casting solidification. Springer:5–24 8. https://www.tec-science.com/material-science/solidification-of-metals/heterogeneousnucleation/. Accessed Feb, 2020 9. Darvish K, Chen ZW, Phan MAL, Pasang T (2018) Selective laser melting of Co-29Cr-6Mo alloy with laser power 180–360W: cellular growth, intercellular spacing and the related thermal condition. Mater Charact 135:183–191. https://doi.org/10.1016/j.matchar.2017.11.042 10. Seo S, Lee J, Yoo Y, Jo C, Miyahar H, Ogi K (2008) Solute redistribution during planar and dendritic growth of directionally solidified Ni-based superalloy CMSX-10. Proceedings of Superalloys 2008, TMS, pp 277–286 11. Kou S (2002) Welding metallurgy, 2nd edn. Wiley

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12. Marchese G, Lorusso M, Parizia S, Bassini E, Lee J, Calignano F, Manfredi D, Terner M, Hong H, Ugues D, Lombardi M, Biamino S (2018) Influence of heat treatments on microstructure evolution and mechanical properties of Inconel 625 processed by laser powder bed fusion. Mater Sci Eng A 729:64–75 13. Dinda GP, Dasgupta AK, Mazumder J (2009) Laser aided direct metal deposition of Inconel 625 superalloy: microstructural evolution and stability. Mater Sci Eng A 509:98–104 ® 14. Foster B (2015) Characterization of Inconel 625 and Ti-6Al-4V laser deposited builds manufactured with varying dwell times. Masters Thesis, Pennsylvania State University 15. Alberti E, Bueno B, D’Oliveira A (2015) Additive manufacturing using plasma transferred arc. Journal of Advanced Manufacturing Technology 83:83 16. Blecher J, Palmer T, Debroy T (2013) Solidification map of nickel-base alloy. Metall Mater Trans A 45:2142–2151 17. Ueshima Y, Mizoguchi S, Matsumiya T, Kaijioka H (1986) Analysis of solute distribution in dendrites of carbon steel with δ/γ transformation during solidification. Metall Trans B 17B:845–859 18. Narayan C (1980) Ternary partition coefficients in Fe-Ni-X alloys-implications on the solidification of iron meteorites. Lehigh University Lehigh Preserve 19. Kobayashi Y, Todoroki H, Mizun K (2019) Problems in solidification model for microsegregation analysis of Fe–Cr–Ni–Mo–Cu alloy. ISIJ Int 59(2):277–282 20. Massalski T, Murray J, Bennett L, Baker H (1986) Binary alloy phase diagrams. ASM 21. Tanaka T, Norio I, Akihiro K, Takamichi I, Zen-ichiro M (1991) Equilibrium partition coefficients between solid and liquid phases and activity coefficients of solute elements in Ni base binary dilute alloy. Z Met 82:836–840 22. Silva C, Miranda C, Motta M, Farias J, Alonso CD, Ramirez A (2013) New insights on the solidification path of an alloy 625 weld overlay. J Mater Res Technol 2:228–237. https:// doi.org/10.1016/j.jmrt.2013.02.008 23. Nastac L, Valencia J, Tims M, Dax F (n.d.) Advances in solidification of IN718 and RS5 alloys. https://www.tms.org/superalloys/10.7449/2001/Superalloys_2001_103_112.pdf 24. Inoue H, Ogawa T (1995) Weld cracking and solidification behavior of titanium alloys. Weld J 21 25. Wang F, Sun Q, Wang H, Liu J, Feng J (2016) Effect of location on microstructure and mechanical properties of additive layer manufactured Inconel 625 using gas tungsten arc welding. Mater Sci Eng A 676:395–405. https://doi.org/10.1016/j.msea.2016.09.015. http:// www.sciencedirect.com/science/article/pii/S0921509316310772 26. Sawai T, Ueshima Y, Mizoguchi S (1990) Microsegregation and precipitation behavior during solidification in a nickel-base superalloy. ISJJ In 30:520–528 27. Cepeda-Jiménez C, Potenza F, Magalini E, Luchin V, Molinari A, Pérez-Prado M (2020) Effect of energy density on the microstructure and texture evolution of Ti-6Al-4V manufactured by laser powder bed fusion, vol 163. Materials Characterization, p 110238 28. Rafi H, Nadimpalli K, Gong H, Starr T, Stucker B (2013) Microstructures and mechanical properties of Ti6Al4V parts fabricated by selective laser melting and electron beam melting. J Mater Eng Perform 22:3872–3883 29. Bertoli U, MacDonald B, Schoenung J (2019) Stability of cellular microstructure in laser powder bed fusion of 316L stainless steel. Mater Sci Eng A 739:109–117 30. Qin H, Fallah V, Dong Q, Brochu M, Daymond M, Gallerneault M (2018) Solidification pattern, microstructure and texture development in laser powder bed fusion (LPBF) of Al10SiMg alloy. Mater Charact 145:29–38

Chapter 16

Solid State Transformations and Gas Reactions During the Additive Manufacturing Process

During additive manufacturing, the material undergoes many thermal cycles, and depending upon the location within the build and in relation to the moving heat source, the thermal cycles may exceed the melting temperature or represent heating and cooling below the melting temperature. Melting and solidification occur directly below the path of the moving source of energy, whereas the material that is some distance from the heat source, either radially or at depth, experiences elevated temperatures below the melting point and may undergo solid state transformations.

16.1 Solid State Transformations During Additive Manufacturing Solid state metallurgical transformations take place near the heat source and can have a profound influence on the evolution of microstructure within the material, as well as the resultant properties and characteristics at these locations. Shown in Fig. 16.1 are measurements of the thermal response of R56400 (Ti-6Al-4V) alloy deposits illustrated in Fig. 15.36, which was produced using a laser-based directed energy deposition process using five deposition passes [1]. The temperature for the five passes was obtained for the material at the surface of the substrate for all passes. The thermal excursions were measured by utilizing embedded high-temperature thermocouples within the substrate and conducting five experiments under identical conditions to produce successive layers. Also shown in the figure is the solidus and liquidus temperatures defining melting and solidification, as well as the β transus temperature, demarcating the transition of β to α during cooling and α to β during heating. Figure 16.2 signifies macrographs representing the deposits after each pass, and the location representing the measured thermal response is shown as a circle in the macrographs [1]. The first pass resulted in melting and solidification in this region, and although not obvious in the macrograph, the microstructure of © Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_16

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16 Solid State Transformations and Gas Reactions During the Additive. . .

Fig. 16.1 Thermal response of alloy R56400 (Ti-6Al-4V) during five passes using a laser-based directed energy deposition process with powder. (Figure used with permission; Copyright 2018 Elsevier [1])

the material within the region had undergone modification during each thermal cycle. These repetitive heating and cooling cycles that are present during the additive manufacturing process play an important role in continually modifying the microstructure through solid state transformations. These solid state reactions will be dependent upon the alloy being processed and may include allotropic transformations, such as heating above and cooling below the β-transus temperature in the R56400 alloy, as well as diffusional reactions involving nucleation and/or growth, such as with the transformation of α ' into a mixed microstructure consisting of α + α ' + β phases in the above example. The above example is used to illustrate an approach for ascertaining the development and evolution of microstructures for a particular alloy during additive manufacturing. In most instances, the exact thermal response of the material within a build is not available; however, these thermal excursions may at least be envisioned. With additional insight regarding transformations that may be operative within an alloy system, the effect of the process on the development and evolution of microstructure may be estimated. This includes the potential for variation in microstructure within a complex build, as well as directionality of microstructure and anisotropy of properties. This is especially important for alloys that may be utilized in service without significant post-process thermal treatments, such as utilizing only a low temperature stress relief. In cases where post-process thermal treatments are used to establish the required microstructure for the intended application, inhomogeneity and anisotropy within the build may still be an important aspect of microstructure evolution during processing.

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Fig. 16.2 Optical macrographs of five layers representing deposits of R56400 (Ti-6Al-4V) material produced using the laser-based directed energy deposition process illustrating the position of the thermal response in Fig. 16.1. (Figure used with permission; Copyright 2018 Elsevier [1])

Since the desired mechanical properties of a material provide the motivation for controlling microstructure, the strengthening mechanisms that are used for various metallic systems offer an initial approach for ascertaining the impact of the process on the material. Shown in Table 16.1 are the strengthening mechanisms employed for several alloy systems of interest for additive manufacturing. Generally, the principal strengthening mechanisms employed for the alloy systems of Table 16.1 are the allotropic transformations for steels and titanium alloys, solid solution strengthening for austenitic stainless steels, some nickel-base alloys, and cobaltchromium alloys, and precipitation strengthening for many aluminum alloys, certain nickel-based alloys, and copper-nickel-tin alloys. It should also be noted that two of

Allotropic formation of martensite

S31603 (316L)

S17400 (17-4PH)

S43100 (431)

Austenitic stainless steels

Precipitationstrengthened stainless steels Martensitic stainless steels

Copper-nickel-tin alloys

Cobalt-chromium alloys Aluminum alloys

Titanium alloys

C72900 (Cu-18Ni-8Sn)

R56400 (Ti-6Al-4V) R30006 (cobalt alloy 6) Al-Si10Mg A92319 (2319)

Nickel-based alloys N06625 (IN625) N07718 (IN718)

Allotropic formation of martensite Precipitation strengthening with Cu and Cr

K93120 (A538)

Maraging steels

Solid solution strengthening with Nb and Mo Precipitation strengthening by Ni3 Nb (γ '') Allotropic formation of martensitic alpha (α ' ) Solid solution strengthening with Cr and W Precipitation strengthening by Mg2 Si (β ' ) for Al-Si10Mg and CuAl2 (θ ' ) for A92319 Precipitation strengthening by Ni3 Sn

Solid solution strengthening with C and N

Grain boundary strengthening (Hall-Petch) Grain boundary strengthening (Hall-Petch)

Grain boundary strengthening (Hall-Petch)

Allotropic formation of martensite Precipitation strengthening with Ni3 Ti and Ni3 Mo

Example of alloys Primary strengthening mechanism Additional strengthening mechanism T72302 (H13) Allotropic formation of martensite

Alloy systems Tool steels

Solutionizing, quenching, and aging for precipitation

Solutionizing, quenching, and aging for precipitation

Annealing above or below the β-transus

Comments on heat treatments for strengthening Austenitization, quenching to produce martensite followed by tempering Austenitization, quenching to produce martensite and aging for precipitation Controlled C content to minimize corrosion sensitization due to chromium carbides Austenitization, quenching to produce martensite and aging for precipitation Austenitization, quenching (air) to produce martensite followed by tempering Solutionizing, quenching, and ageing for precipitation

Table 16.1 Primary strengthening mechanisms associated with several metallic systems commonly used in additive manufacturing

484 16 Solid State Transformations and Gas Reactions During the Additive. . .

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485

these systems, the maraging steels and precipitation-strengthened stainless steels, rely on the allotropic transformation and precipitation for achieving high strength, while the strength of many of these alloy systems is also influenced by grain boundary strengthening. Based on these principal strengthening mechanisms, the analysis of potential microstructural modifications that may govern the resultant properties and characteristics of materials produced by additive manufacturing processes may be performed. This analysis must consider the thermal response of the material, which is driven by the additive process and part geometry, along with the specific alloy being processed. As with the discussion on the development of solidification morphologies, this examination requires a degree of understanding of the solid state reactions that are responsible for establishing microstructure, which will be approached based on the reactions that impact the primary strengthening mechanisms. The development of microstructure in metallic systems involves transformations that alter the amount and character of the phases present within the system. In many instances these transformations occur at temperatures that follow the solidification event and hence are referred to as solid state transformations. As discussed earlier, the phase diagram for a particular alloy system may be used to define the phases present at temperatures for a particular composition within the system. Although the phase diagram, which is based on equilibrium within the chemical system, defining the spatial characteristics of phases that constitute the microstructure requires additional information concerning the rates of reactions within the system. This is especially true for processes that involve non-isothermal conditions, such as found in additive manufacturing. For many alloys, anticipating the alteration and distribution of phases that comprise the microstructure is dictated by the atomic mobility between constituents and may be defined in terms of the diffusional rate of the reactions. In other instances, the speed of a reaction is not determined by the rate of atomic diffusion but is driven by an allotropic reaction that is dominated by thermal activation at a particular temperature. The best example of an allotropic reaction is the transformation of γ -iron (austenite), which represents a facecentered-cubic lattice structure, to body-centered-cubic α-iron (ferrite) when cooled below the austenite temperature. This forms the dominant method of strengthening for many alloys known as steels.

16.1.1 Diffusional Reactions Many metallurgical transformations are driven and controlled by the rate of atomic diffusion of species within the alloy, and because atomic mobility is thermally induced, all of these processes involve elevated temperatures. This includes the development of microstructure based on the thermal response of the material during the additive manufacturing additive manufacturing process, as well as post-process thermal treatments used in conjunction with the additive process. Auxiliary thermal treatments are extensively used as part of the additive manufacturing enterprise.

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16 Solid State Transformations and Gas Reactions During the Additive. . .

Thermal stress relief is almost always employed for minimizing thermally induced residual stress within the build and utilizes atomic mobility for inducing dislocation motion leading to annihilation and reduction of stress. Numerous post-process thermal treatments are used to modify and control the microstructure of additive manufactured material for improving mechanical properties or other characteristics. Many of these processes are diffusional and include: homogenization used to obtain a more uniform compositional distribution within the material, solutionizing to achieve a solid solution for subsequent precipitation, aging that is utilized to control the nucleation and growth process for forming strengthening precipitates, and tempering used to decompose and modify the martensitic structure for improved toughness. Finally, additive manufacturing processes that employ post-process sintering for full consolidation of material, such as the binder jetting and material jetting processes, rely on diffusional controlled sintering for bonding of particles to form a coherent, dense structure.

16.1.1.1

Precipitation Reactions

Precipitation reactions that are governed by diffusional transformations were discussed earlier in a more general sense to introduce the concept of alloy constituency and the implication to microstructural development. The topic was introduced using a binary phase diagram that was only defined by the concentration of solute, but nevertheless, appropriate for many alloys that are strengthened through precipitation of a second phase. Shown in Fig. 16.3 is the quasi-binary phase diagram for the aluminum-Mg2 Si system. It is referred to as “quasi” since the system actually represents three components but the magnesium and silicon behave as a single component, Mg2 Si, at relatively dilute concentrations. The phase diagram was constructed based on the composition of aluminum casting alloy A13560 (A356), which has a nominal composition of Al-7Si-0.35Mg [2]. Although this alloy is somewhat leaner in composition than the Al-10Si-0.5Mg alloy commonly used for additive manufacturing, it may serve to describe the development of microstructure for this system. Also indicated in the figure is the concentration of Mg2 Si based on the nominal composition of the Al-10Si-05Mg alloy, and assuming that the amount of Mg2 Si will be limited stoichiometrically by the amount of Mg present. This results in approximately 0.8 weight-percent Mg2 Si for an alloy containing 0.5% magnesium, with the excess silicon available to form as primary silicon. Also shown in the figure are schematics of microstructures that would be present above and below the solvus boundary separating the α and α + β phase fields. The precipitation reaction relies on the ability of the system to accept a relatively large amount of solute in solution at elevated temperature with a much lower solubility being exhibited at lower temperatures. In the case of the aluminum-Mg2 Si system, the β-phase (Mg2 Si) dissolves into solution above the solvus, and upon rapid cooling to below the solvus produces an unstable supersaturated solution that will precipitate β within an α matrix through a sequence of nucleation and growth. The complete precipitation reaction for the aluminum-Mg2 Si system may be described as:

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Fig. 16.3 Section of the quasi-binary phase diagram for the aluminum-Mg2 Si system

  αss → α + GP → α + β '' → α + β ' → α + β Mg2 Si

.

(16.1)

where GP is Guinier-Preston zones that represent enriched regions of magnesium and silicon atoms and β ' and β '' are intermediate phases of the equilibrium Mg2 Si. The intermediate phases, β '' and β ' , have atomic arrangements that are different from the equilibrium phase, β, owing to the coherent nature of the atomic arrangement during the early stages of the precipitation reaction. Initial nucleation is strongly affected by surface energy, similar to the discussion during solidification, whereas the growth of the precipitates is influenced by the need to minimize strain energy between the growing precipitates and the surrounding lattice. This results in the β '' being needle shaped and β ' being rod-like, with the length of these phases being between 0.01 and 0.1 μm (100–1000 Å). The thermal treatment that is utilized for achieving the optimal strength for these types of alloys involves a solutionizing process that heats the material to above the solvus temperature, followed by rapid cooling or quenching to achieve supersaturation. Nucleation of small clusters of atoms occurs almost immediately after quenching but controlled growth of a uniformly distributed network of very small particles is accomplished by a low-temperature thermal process referred to as aging, which is a precipitation treatment. The temperature and time that is used during aging is selected to obtain the largest number density of precipitates that have the ideal size to impede dislocation motion. A schematic illustrating the size and distribution of precipitates during aging is shown in Fig. 16.4 for the under-aged, peak-aged, and over-aged conditions. As seen in the diagram, peak aging provides an optimal distribution of number and size of precipitates for interaction with dislocations, whereas over-aging results in further growth of some

488

16 Solid State Transformations and Gas Reactions During the Additive. . .

Fig. 16.4 Aging curves for precipitation strengthening showing schematics for microstructures in the under-aged, peak-aged, and over-aged conditions

precipitates at the expense of others. At the extreme over-aged condition, very large precipitates representing the equilibrium Mg2 Si form within grains, as well as on grain boundaries. Also illustrated in the schematics is the effect of aging temperature on the strengthening response of the material, which demonstrates the effect of temperature on growth kinetics. Higher aging temperatures increase diffusivity of solute enabling higher rates of growth; however, there is a point where increasing temperature no longer increases the reaction rate. The decreasing rate of the reaction at temperatures that approach the solvus is due to reduction in supersaturation, which helps to drive the overall reaction. The rate of nucleation for the precipitation reaction, I, may be described by:  I = Ke exp

.

−ΔGcrit kT



 exp

−ΔQm kT

 (16.2)

where Ke is the pre-exponent factor that is related to the number of atoms that is participating in the nucleation event per unit volume, ΔGcrit is the energy barrier for reaching the critical radius, ΔQm is the energy barrier for providing mobility of atoms for crossing the interface, kB is Boltzmann’s constant, and T is temperature. The first term on the right describes the thermodynamic barrier for nucleation, while the second term defines the kinetic barrier and follows the classical Arrhenius-type equation for a reaction rate. As the temperature approaches the solvus temperature,

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489

Fig. 16.5 Graph illustrating the rate of a reaction as a function of time and temperature

the thermodynamic driving force is decreased due to lower supersaturation within the system, whereas the kinetic driving force increases with temperature due to greater atomic mobility. Once nucleation is initiated, the rate of growth, J, is dependent upon thermal activation and, similar to the second term for nucleation, may be expressed as:  J = A exp

.

−ΔQg kT

 (16.3)

where A is a constant that is dependent upon the vibrational frequency of the lattice and distance across the interface (usually related to atomic spacing of the matrix) and Qg is the activation barrier for mobility of atoms for attaching to the growing cluster. As may be anticipated, the rate of the precipitation transformation, T, is a function of the rates for nucleation and growth. The combined influence of the rates of nucleation and growth on the overall transformation rate for the precipitation reaction is shown graphically in Fig. 16.5. The curve for the overall rate of the precipitation reaction reveals the characteristics of nucleation and growth discussed above and indicates that the highest rate of the reaction will occur at an intermediate temperature, provided that a sufficient degree of supersaturation is present after cooling from above the solvus temperature. The degree of supersaturation is closely linked to the rate of cooling from the above the solvus, and rapid cooling impedes the diffusional process for nucleation and results in the supersaturated solid solution. In practice, the rates of a precipitation reaction (α → α + β) for an alloy composition may be determined by isothermal experiments that involve rapid quenching from above the solvus temperature to a lower temperature and held for a period of time, followed by quenching to room temperature. When several holding temperatures and times are included, and utilizing a method for assessing

490

16 Solid State Transformations and Gas Reactions During the Additive. . .

Fig. 16.6 The impact of nucleation rate and growth rate with temperature on the overall reaction rate for the precipitation process

the fraction of β that is transformed, the rate of the reaction may be defined based on the characteristic related to the amount transformed. Several methods may be used to estimate the fraction of β transformed and include quantitative microscopy, determination of strength or hardness, or electrical resistivity measurements, to name a few. The results of these types of experiments produce a characteristic curve which defines the fraction transformed over temperature and time, a timetemperature-transformation (TTT) curve. These types of curves are also referred to as C-curves because of the similarity to the overall transformation curve shown in Fig. 16.6. This type of representation for an alloy and a reaction, in this case a diffusion-controlled precipitation reaction, is extremely useful for estimating the effect of cooling or heating on the characteristic used to define the amount transformed for the reaction. Shown in Fig. 16.7 are curves by Liu et al. showing the influence of time and temperature on microhardness for an Al-10Si-5.5Mg alloy produced using a high-pressure die casting process having cooling rates near 103 ◦ C/s [3]. Since the degree of the transformation is represented as a change in property, such as microhardness, transformation data shown in this fashion is also referred to as a time-temperature-property (TTP) diagram. The data represents material after casting, which was solutionized at 500 ◦ C and cooled to intermediate temperatures and held at various times, followed by quenched in water and aging at 170 ◦ C for 2.5 h. The percent completion of the precipitation reaction was estimated based on microhardness measurements. Hence, the curves also reflect iso-hardness at the respective degree of completion, and the 99.5% curve represents achieving full strength from the precipitation reaction. The data of Fig. 16.7 represents hardness of the material after discontinuous cooling below the solvus followed by aging and signifies the degree of the precipitation

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491

Fig. 16.7 Completion of the precipitation reactions at 99.5%, 90%, and 80% based on microhardness for an Al-10Si-0.55Mg alloy obtained by solutionizing, holding at intermediate temperatures for various times, followed by quenching and aging at 170 ◦ C for 2.5 h. (Figure adapted with permission; Copyrighted Mengyun Liu and published in Materials MDPI [3])

reaction completed after aging. Under these conditions, the precipitation reaction is being assessed based on the reaction kinetics at the intermediate temperatures and times, along with subsequent isothermal aging. It may be utilized to determine the impact of rate of cooling from the solvus temperature on the final harness after aging. When used in this manner, the technique is referred to as quench sensitivity analysis and provides a means of determining the impact of quench rate from a thermal process on the ability of the alloy to respond to aging. As the cooling rate from the solvus temperature is decreased, the level of supersaturation is diminished, and the reaction kinetics slow, such that the isothermal aging process is only able to achieve a portion of the maximum hardness. This is indicated by the curves representing completion of the reaction at 90% and 80%. However, this type of information also provides an indication of the extent of the precipitation reaction after heating at temperatures below the solvus. Experiments utilizing material quenched from the solvus and reheated and held at intermediate temperatures and times may provide kinetic data similar to the results of Fig. 16.7 for use in evaluating the strengthening due to the precipitation reaction based only on reheating. Repetitive heating to temperatures near the “nose” of the curves will drive the precipitation reaction. In the case of the Al-10Si-0.55Mg alloy, operating at sustained temperatures in the range of 250–450 ◦ C intensifies the rate of reaction and may lead to peak strength, as well as over-aging and a reduction in strength when sufficient time was spent in this range of temperatures.

492

16 Solid State Transformations and Gas Reactions During the Additive. . .

These diagrams may also depict multiple reactions, providing insight into important transformations that govern the microstructure and properties of an alloy. Shown in Fig. 16.8 is a TTT diagram from Oradei-Basile and Radavich for N07718 (IN718) alloy in the wrought condition [4]. The C-curves were developed by solutionizing specimens above the solvus temperature, quickly cooling to intermediate temperatures and held for various times. The specimens were then quenched in water and examined under optical and electron microscopy to identify temperatures and times that represent precipitation of γ ' , γ '' , and δ within a γ matrix. As shown in the figure, initial nucleation and growth of γ ' and γ '' occur most readily at temperatures in the 750–900 ◦ C range and at high cooling rates. The γ '' phase, which has a chemical composition of Ni3 Nb and forms as thin disks on the (001) planes of the γ matrix, is the primary strengthening precipitate for the alloy [5]. The γ ' phase, representing Ni3 (Al,Ti) that forms as round precipitates, also contributes to strengthening of the system. The δ phase, which is chemically identical to γ '' but having a different lattice structure, nucleates and grows at grain boundaries at longer times at temperature at the expense of γ '' . Because δ forms on grain boundaries while decreasing the amount of γ '' present within the matrix, it is not considered a favorable phase. At all but a very high temperature, in the 900 ◦ C range, the precipitation of the strengthening phases is relatively slow, such that high cooling rates experienced with additive manufacturing along with lower background temperatures result in little precipitation but a matrix that maintains its supersaturation. Because the rate of a reaction may be strongly influenced by local composition and microstructural scale, the TTT diagrams should reflect the material of interest.

Fig. 16.8 The TTT diagram for N07718 (IN718) alloy indicating precipitation of γ ' , γ '' , and δ in the wrought condition. (Figure adapted with permission; Copyright 1991 The Minerals, Metals & Materials Society [4])

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Fig. 16.9 The pseudo-TTT diagram for N07718 (IN718) alloy prepared as a casting, homogenized at an elevated temperature, and heated and held at intermediate temperatures. (Figure adapted with permission; Copyright 1989 The Minerals, Metals & Materials Society [6])

Shown in Fig. 16.9 is a pseudo-TTT diagram by Carlson and Radavich for N07718 (IN718) alloy representing cast material [6]. The reaction kinetics for the γ '' and δ phases were developed using cast material after a homogenization treatment at elevated temperature, followed by reheating and holding at temperatures between 649 and 1093 ◦ C. Optical and electron microscopy were used for phase characterization, and x-ray diffraction and EDS were employed to aid in phase identification and chemical analysis. The significant segregation that occurred during casting necessitated the identification of reaction products occurring within dendrites, as well as at interdendritic regions. Under these conditions, the precipitation of δ would occur at higher temperatures when compared to the wrought material, and precipitation of γ '' , both within dendritic and interdendritic regions, requires longer times at temperature. The data represented in Figs. 16.8 and 16.9 indicates the difficulty for the precipitation strengthening reaction to be operative for this alloy during the additive manufacturing process. For the wrought material or the cast material, the nose of the γ '' curve, which would reflect the highest rates of γ '' precipitation, is located at 360 and 1500 s, respectively. When this is compared to the thermal cycles that may be experienced in additive manufacturing processes, as shown in Fig. 15.4 for the laser-based powder bed fusion process, the times at elevated temperature in the range of interest are not sufficient to promote the precipitation reaction for these alloys. This is much different than the precipitation reaction for the Al-10Si0.55Mg alloy shown in Fig. 16.7. In this case, the precipitation of the β-phase, and more accurately β '' , occurs in very short time, such that repetitive heating cycles during additive manufacturing may not only lead to strengthening precipitation but continued growth that would result in over-aging of the material.

494

16 Solid State Transformations and Gas Reactions During the Additive. . .

The discussion on precipitation has stressed the use of isothermal data, established at a constant temperature, where information obtained from experiments enables the construction of reaction maps that are operative at those temperatures. In this case, the rate constant that defines the fraction transformed is principally a function of temperature. Although this approach, with significant experimental data, provides important information that offers insight into potential transformations that may occur under non-isothermal conditions, it lacks the capabilities for more in-depth analysis. The development of quantitative relationships that enable the reaction to be simulated under non-isothermal conditions, especially important for the continuous heating and cooling during additive manufacturing, will also be addressed during examination of techniques for modeling of microstructure. However, an important concept will now be introduced that allows the extraction of additional information from isothermal data for use under continuous heating and cooling conditions. In practicality, there is utility to define the reaction when the path is not constant, i.e. the transformation occurring at a single temperature (isothermal). For the purpose of this discussion, the degree of a reaction may be formalized through [7]: dx = f (x, T (t)) dt

.

(16.4)

where x is the fraction transformed, t is time, and f (x, T(t)) is a functional having kinetic dependence on x, as well as a function which defines the time and temperature path of the reaction, T(t). Under isothermal conditions, T(t) is constant and f (x, T(t)) is only dependent upon x. The path is fixed at a single temperature over time and the rate constant for the reaction is in the form of an Arrheniustype relationship that is exponentially dependent upon temperature. If it is assumed that the transformation rate is a state function that is independent of the thermal path used to reach that state (the transformation occurring at varying temperature or being non-isothermal) the reaction may be expressed in terms of a relationship that utilizes additivity [8]:  .

t

dt =1 0 τ (x0 , T )

(16.5)

where t is the total time for the non-isothermal transformation and τ (x0 , T) is the time for the isothermal transformation to achieve x0 at temperature T. The reaction rate is only dependent upon x and T [9]. The above expression indicates that if the reaction obeys additivity, the total time required to achieve a specific fraction transformed under non-isothermal conditions may be determined by adding the fractions of time required to reach the specific fraction obtained isothermally until the sum equals unity. An important assumption for this approach is that nucleation occurs early in the reaction, which in many cases may be applied to heterogeneous nucleation where rapid nucleation may lead to “site saturation” [8].

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Without derivation, the volume fraction transformed under isothermal conditions may be described by the Johnson-Mehl-Avrami-Kolmogorov (JMAK) relationship:   x (τ, T ) = 1 − exp −k(T )τ n(T )

.

(16.6)

where k(T) and n(T) may be temperature dependent, although n(T) is often presumed to be independent of temperature. The parameter k(T) can be defined as:   −ΔH (16.7) .k(T ) = k0 exp kB T where in the above two expressions, n, k0 , and ΔH are the JMAK parameters that detail the operative nucleation and growth processes. The parameter n is referred to as the Avrami exponent and typically is between 1 and 3, whereas k0 describes the nucleation phenomena and ΔH is the effective activation energy for nucleation and growth [10]. The isothermal JMAK relationship also assumes site saturation for nucleation. The above analysis allows the use of isothermal reaction kinetics to be applied to non-isothermal conditions, notably the use of transformation data from TTT diagrams to situations involving continuous cooling or heating. Although the manipulation and use of the above relationships will become more obvious for modeling of transformations that govern the development of microstructure during thermal cycles in additive manufacturing, limited use of the above associations will be utilized to introduce continuous-cooling-transformation diagrams. Under cooling at a constant rate, q, and assuming a simple isokinetic reaction, the additivity relationship may be expressed as:  q=

T

.

Ti

dθ τ(x, θ )

(16.8)

where θ is the temperature during cooling (q = dθ /dt) and T is the transformation temperature. The equivalent time under isothermal conditions to achieve a specific fraction transformed at a temperature, τ (x, T), may be determined for cooling at a constant rate, q(x, T), using the following [7]:



∂T .τ(x, T ) = q(x0 , T ) ∂q



x0

1 q(x, T )

(16.9)

The method for establishing the fraction transformed under a constant cooling rate with a constant transformation rate (isokinetic) is shown graphically in Fig. 16.10 [7]. In this case, the isothermal time for cooling to achieve the amount transformed at x = 0.01 for two rates, q2 and q1 , is determined using the above

496

16 Solid State Transformations and Gas Reactions During the Additive. . .

Fig. 16.10 Determination of fraction transformed during cooling at a constant rate based on analysis utilizing isothermal transformation data. (Figure adapted with permission; Copyright 2005 Elsevier [7])

relationship. The initial temperature, Ti , is assumed to be above the transformation temperature. The use of transformation maps based on continuous cooling is an important tool for establishing the impact of cooling from an elevated temperature process on the resultant microstructure and properties for an alloy. These maps, referred to as continuous-cooling-transformation (CCT) diagrams, are similar to TTT diagrams but relate transformations directly to cooling rates. As discussed previously, the information obtained from TTT diagrams, along with the use of additivity, enables non-isothermal information to be extracted from isothermal data. However, similar to experiments used to establish TTT diagrams, an empirical determination of a CCT diagram for a particular alloy is often employed. Shown in Fig. 16.11 is a CCT diagram established experimentally and indicates the transformation to γ '' during continuous cooling for alloy N07718 (IN718) [11]. Also superimposed on the graph are isothermal transformations for γ '' formed at dendrite cores and within the interdendritic region from the TTT experiments described for Fig. 16.9 [6]. The CCT information captured in Fig. 16.11 was obtained by homogenizing wrought material at 1180 ◦ C for 24 h, followed by cooling at controlled rates and metallurgical analysis of phases present. Three cooling curves representing rates of 13.4, 9, and 4 ◦ C/s are also represented in the figure. One obvious observation from the CCT diagram is the relatively slow cooling rates required to form the strengthening phase, γ '' , for this alloy. Also note that the CCT curve is lower and to the right of the TTT curves, which is due to early portions of the transformation

16.1 Solid State Transformations During Additive Manufacturing

497

Fig. 16.11 Continuous-cooling-transformation diagram for N07718 (IN718) alloy representing wrought material and homogenized at 1180 ◦ C for 24 h and cooled at various rates (cooling curves shown for 13.4, 9, and 4 ◦ C/s). (Figure adapted with permission; Copyright 1989 and 1992 The Minerals, Metals & Materials Society [6, 11])

during continuous cooling occurring at elevated temperatures and representing lower reaction rates. Although nucleation and growth reactions are common for many phases in metallic systems, some being by design and others being undesirable, when this mechanism is utilized for strengthening, the size of these precipitates is extremely small. This scale is necessary for these fine particles to beneficially interact with dislocations during the imposition of strain. Shown in Figs. 16.12 and 16.13 are transmission electron micrographs, obtained using the high angle annular dark field scanning technique, from Zhou et al. representing samples of N07718 (IN718) alloy produced using the powder bed fusion process in the as-built and post-process heattreated condition, respectively [12]. Figure 16.12, representing the X-Z cross section for the as-built material, illustrates the fine cellular structure, approximately 1 μm in diameter, developed during solidification (Fig. 16.12b). Selected area diffraction patterns (SADP) were obtained within the cellular region (Fig. 16.12b) and at the cell boundary (Fig. 16.12c). The SAPD within the cell indicated only the γ -phase of the matrix, whereas the pattern from the cell boundary exhibited the γ -phase and what was believed to be the Laves phase, an intermetallic phase of Ni and Nb, Mo, and Ti formed by segregation during solidification. Using energy-dispersive x-ray spectroscopy (EDS), the region demarcated in Fig. 16.12d was qualitatively mapped for elemental concentration (Fig. 16.12e). In Fig. 16.12e, the boundary around the cell exhibits concentration of Nb, Mo, and Ti, which supports the observation by SADP, as well as the partition coefficients of these elements from Table 15.3.

498

16 Solid State Transformations and Gas Reactions During the Additive. . .

Fig. 16.12 Transmission electron micrographs of a sample of N07718 (IN718) alloy produced using the powder bed fusion process and in the as-built condition. (Figure used with permission; Copyright 2019 Elsevier [12])

The TEM images for the N07718 (IN718) specimen that had been post-process heat treated by solutionizing at 980 ◦ C followed water quenching and two-step aging at 720 ◦ C for 8 h and 620 ◦ C for 8 h is shown in Fig. 16.13. These images indicate significantly less segregation with a structure having well defined grain boundaries (Fig. 16.13a). Figure 16.13a also exhibits blocky plates, believed to represent the δ-phase near the boundaries based on the SADP of Fig. 16.13c and the elemental mapping of Fig. 16.13e. Also seen faintly in the micrograph of Fig. 16.13b is a network of very fine precipitates believed to be γ '' , which is indicated as a superlattice between the main γ -matrix reflections of Figure 16.13f. These fine precipitates are also believed to be γ '' as disks viewed on edge with diameters of approximately 20 nm. As alluded to earlier, the size required for strengthening precipitate, in this case γ '' , requires an extremely fine scale that allows dislocation interaction within the atomic lattice. Shown in Fig. 16.14 are transmission electron micrographs at two magnifications from Sweny et al. of an experimental aluminum alloy (Al-4.9Cu-1.4Ag-0.2Mg) designed to respond to precipitation strengthening after additive manufacturing [13]. The micrographs represent material that was produced using the laser-based directed energy deposition and post-process solution heat treated and aged to the peak hardness. Shown in the micrographs are θ ' (Al2 Cu) precipitates that formed as plates on the (001) planes of the aluminum matrix. Two orthogonal variants of the precipitates are shown on edge, as defined in the associated diffraction patterns. The

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Fig. 16.13 Transmission electron micrographs of a sample of N07718 (IN718) alloy produced using the powder bed fusion process and post-process solution heat treated and aged illustrating the fine scale of precipitates within this alloy. (Figure used with permission; Copyright 2019 Elsevier [12])

θ ' precipitates are approximately 50 nm in diameter. Not depicted in the electron micrograph of Figure 16.14 but present within the alloy was a variation of the θ' phase having Ag atoms, the Ω-phase, which also formed as plates but on the (111) planes. Shown in Fig. 16.15 are the results of hardness measurements on this alloy after post-process aging only and post-process solutioning at 510 ◦ C followed by water quench and aging at 160 ◦ C for various times. After complete solutionizing and quenching, the material exhibited a classical aging curve associated with precipitation strengthening. Hardness was found to significantly increase with aging time to a peak hardness after 20 h, followed by over-aging with prolonged times. The material responded marginally to post-process aging due to little supersaturation remaining from the relatively slow cooling rates of the directed energy deposition process. The results from post-process aging are indicative of precipitation occurring during the relatively slow cooling of the additive manufacturing cycles and would also be indicative of the response of the AlSi10Mg alloy. The mechanism of precipitation strengthening requires higher solubility at an elevated temperature and a lower solubility at lower temperatures, with the rate at which the metal cools from the elevated temperature providing the driving force for the nucleation and growth phenomena. Because of the cooling rate dependency, alloys that rely on precipitation strengthening have a wide range of responses to additive manufacturing processes that utilize melting and solidification. The

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Fig. 16.14 Transmission electron micrographs at two magnifications of an experimental alloy (Al-4.9Cu-1.4Ag-0.2Mg) showing θ ' (Al2 Cu) precipitates in the peak-aged condition, with the diffraction pattern obtained for the [001] zone axis. (Figure used with permission; Copyright 2018 Rebecca Sweny and published in Journal of Material Science & Engineering, Creative Commons Attribution 3.0 License [13])

Fig. 16.15 Aging curves for an experimental aluminum alloy (Al-4.9Cu-1.4Ag-0.2Mg) produced using the directed energy deposition process after post-process aging only at 160 ◦ C for various times (PPA) and after solution heat treatment at 510 ◦ C followed by water quench and aging at 160 ◦ C for various times (SHT+A). (Figure adapted with permission; Copyright 2018 Rebecca Sweny and published in Journal of Material Science & Engineering, Creative Commons Attribution 3.0 License [13])

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strength that may be developed in the as-built condition is a function of the kinetics of the specific alloy and the characteristic cooling rates of the process. Alloys that have slow kinetics within the cooling regime of the additive manufacturing process, such as the N07718 (IN718) alloy, will not respond sufficiently to the precipitation reaction. Conversely, alloys that are sensitive to quench rate for maintaining supersaturation during cooling, such as the AlSi10Mg alloy, also will be impeded in developing full strength. Although these alloys may not provide sufficient strength in the as-built condition, they will respond to post-process heat treatments for generating a favorable microstructure and recovery of properties. However, it should be noted that post-process thermal treatments for many commercial alloys used in additive manufacturing were developed based on wrought material. Since the heat treatment process involves diffusion of alloying species, the solidified structure of additive manufactured material may require optimization of the heat treatment process for these materials. Although this is discussed further under the chapter on post-processing, an example of a modification of the heat treating practice for additive manufactured alloys is a longer time for solutionizing that allows for greater chemical homogenization of the solidified structure.

16.1.2 Allotropic Reactions and Impact on Strengthening Allotropic transformations of certain metallic system involve a change in crystal structure during changes in temperature. Although this type of transformation is not considered diffusion controlled, other reactions that may also be operative in these materials may be governed by diffusion of atomic species. The most known materials that rely on an allotropic transformation for developing strength are steels based on alloys of iron. Iron has three allotropic forms depending on temperature, which include δ-iron that has a BCC structure upon solidification at 1538 ◦ C, γ -iron that forms at 1394 ◦ C and represents an FCC crystal structure, and α-iron that exists as BCC and forms from γ at 912 ◦ C. The α-phase remains thermodynamically stable under equilibrium conditions to room temperature. Of particular interest for strengthening in this system is the transformation that occurs during cooling from the FCC γ -phase, also defined as austenite, to the BCC αphase, referred to as ferrite. The γ -phase can contain up to 2% carbon in solid solution and decomposes upon cooling to several features that are based on the phases present, as well as the mixture and morphology of these phases that constitute the microstructure. As with the precipitation reaction discussed earlier, the rate of cooling and specific composition of the alloy plays an important role in the development of microstructure and resultant mechanical properties. Shown in Fig. 16.16 is the equilibrium phase diagram for the iron-carbon system by Föll illustrating microstructures that would be present at various temperatures and concentrations of carbon. The discussion will concentrate on hypoeutectoid steels, having carbon content less than the eutectoid concentration of 0.76%, since

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16 Solid State Transformations and Gas Reactions During the Additive. . .

Fig. 16.16 Equilibrium phase diagram for the iron-carbon system along with potential phases and microstructures that may be present at various temperatures and concentration of carbon. (Figure used with permission of Professor Helmut Föll, University of Kiel; Original figure from https:// www.tf.uni-kiel.de/matwis/amat/iss/kap_6/illustr/s6_1_2.html and accessed February, 2023)

steel alloys used in additive manufacturing generally contain lower levels of carbon due to their resistance to cracking upon cooling. Specifically, the transformations that occur with a steel having a composition of approximately 0.2% carbon, shown as the far-left vertical green line in the figure, will be reviewed. Solidification occurs with partitioning of carbon at boundaries and the formation of δ at approximately 1500 ◦ C. The grain size of δ will be dependent upon the rate of solidification. The δ transforms upon cooling to austenite at approximately 1490 ◦ C, with the FCC γ phase representing a solid solution of γ with carbon. Upon further cooling to below the γ → α + γ transformation temperature at approximately 830 ◦ C, also defined as the Ae3 equilibrium transformation temperature, the γ will begin to decompose. An initial reaction will be the formation of pockets of ferrite at the austenite grain boundaries, which will be driven by diffusion of carbon. As cooling continues within the α + γ region, the ferrite will grow and thicken into the adjacent austenite grains. Further cooling of the Fe-0.2C alloy below the Ae1 temperature, also known as the eutectoid temperature at 727 ◦ C, will result in the austenite becoming completely unstable and transforming from FCC to BCC through a displacive mechanism that involves a mass shift of atoms that results in the BCC structure, along with significant strain energy needed to accommodate this arrangement. The displacive

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transformation is initiated by the transformation temperature, but atomic diffusion is still operative. The products of the transformation will involve two phases, α (or ferrite) and Fe3 C, also called cementite; however, these two phases may form several microstructural features having vastly different mechanical properties, and the morphology and distribution of the relatively soft ferrite and hard cementite within the microstructure will determine these properties. The lower solubility of carbon in the ferrite will help drive reactions involving carbon. At the lower carbon content of 0.2%, the remaining austenite will transform to a lamellar arrangement of ferrite and cementite through a diffusional growth process from the parent austenite. The lamellar feature is referred to as pearlite and forms in proportion to the level of carbon to the eutectoid composition of 0.76% carbon. A microstructure containing high amounts of pearlite displays relatively low strength but good ductility. At higher carbon content and faster cooling rates, the displacive reaction is more active, and microstructural features are governed by transformations that rely less on diffusion. At high cooling rates, diffusion of carbon within austenite is limited, and the displacive transformation of FCC to BCC results in a highly strained lattice retaining a high supersaturation of carbon. The microstructure formed in this fashion is designated as martensite, denoted as α ' , which forms as thin plates within the prior austenite grain to minimize the strain energy of the lattice. Because equilibrium is not maintained at the high cooling rates, a small amount of austenite is also retained at room temperature. Due to the high carbon saturation, residual strain energy, and extremely fine structure, martensite exhibits high strength and low ductility. Because of this, martensite is usually tempered at a relatively low temperature to marginally decrease strength but increase toughness. Similar to martensite but formed at slightly lower cooling rates, bainite develops as an acicular structure within the austenite grains followed by carbon diffusion into the remaining austenite and results in plates of cementite between ferrite. Bainite has less strength than martensite but has higher ductility. The microstructure that results from decomposition of austenite when cooling below the transformation temperature is strongly dependent upon the cooling rate and the chemistry of the alloy. Although three phases participate in the reaction, namely, austenite, ferrite, and cementite (γ , α, and Fe3 C), the proportion, size, shape, and distribution of these phases are all important in defining the response of the microstructure under stress. Carbon is a basic alloying constituent in steels; however, many other alloying additions are used for specific purposes. These alloying additions may change the temperatures at which transformations begin, altering the rates of cooling necessary for achieving features that provide high strength, such as martensite and bainite, or directly increase the strength of the individual microstructural features. In some instances, the additions also contribute to strength beyond the decomposition of austenite. Elements such as nickel, manganese, cobalt, copper, and nitrogen are austenite stabilizers and extend the range of temperatures in which austenite may exist. This is accompanied by lowering the Ae3 and Ae1 temperatures resulting in greater likelihood of retaining metastable austenite at room temperature. Steels containing nickel and manganese are the principal additions to austenitic stainless steels, such as S31603 (316L), which is extensively used in

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16 Solid State Transformations and Gas Reactions During the Additive. . .

additive manufacturing. It should also be mentioned that the potential for nitrogen absorption during processing may alter transformations in steels strengthened by martensite. An example of this phenomena is the difficulty of alloy S17400 (174 PH) powder that had been atomized with nitrogen and additively manufactured with nitrogen cover gas to achieve a certain desired hardness, defined as H900, after solution heat treatment and aging. Additions of chromium, tungsten, molybdenum, vanadium, aluminum, and silicon are considered ferrite stabilizers and decrease the temperature range for austenite. Ferrite stabilizers increase the Ae3 and Ae1 temperatures and promote ferrite in the final microstructure. Alloying additions of chromium and nickel are used extensively for increasing corrosion resistance in steels by the formation of a passive Cr2 O3 layer and form the broad category of stainless steels. Martensitic stainless steels contain primarily chromium and small amounts of carbon to enable the martensitic transformation. As mentioned above, chromium and nickel with low levels of carbon are used for austenitic stainless steels. Carbide-forming elements, such as chromium, tungsten, vanadium, molybdenum, niobium, tantalum, and cobalt, are also used for strengthening by precipitation of fine metal carbides. These elements are used in tool steels, martensitic steels, and precipitation-strengthened stainless steels. Copper is also used for precipitation strengthening of the precipitation-strengthened stainless steels. Similar to diffusional reactions, continuous-cooling-transformation diagrams may also be used for estimating microstructures after cooling for alloys that undergo an allotropic transformation. When applied to many ferrous alloys, the CCT diagrams are more complicated due to the number of phases that may be operative and the variety of microstructural features that result from cooling at varying rates. Shown in Fig. 16.17 is a theoretical CCT diagram for a steel near the eutectoid composition of 0.76% carbon. Three different cooling rates starting from a temperature above the Ac3 temperature and within the austenite region are superimposed on the diagram to show phases, transformations, and resultant microstructures associated with varying cooling rates. The Ac3 temperature is now used to demarcate the γ to α and Fe3 C phase boundary, in lieu of Ae3 , since this temperature defines the transformation temperature upon cooling and may not follow equilibrium. As mentioned earlier, three phases, austenite, ferrite, and cementite (γ , α, and Fe3 C), participate in austenite decomposition; however, the microstructure may vary significantly depending upon the cooling rate. At high cooling rates, diffusion of carbon in iron is limited and the reaction is dominated by the displacive transformation of FCC to BCC and forming primarily martensite beginning at the martensite start temperature, Ms . At moderate cooling rates, bainite is established through the displacive transformation along with diffusion of carbon. At low cooling rates, diffusion plays a greater role in establishing the microstructural features, with allotriomorphic ferrite and cementite transforming to pearlite through diffusion of carbon. Hence, rapid to moderate cooling that may be associated with additive manufacturing processes typically leads to microstructures in the as-built condition representing martensite or bainite, which may be useful for applications requiring high strength, hardness, and wear resistance.

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Fig. 16.17 Theoretical continuous-cooling-transformation diagram for a ferrous alloy. (Figure adapted from original created by Slinky Puppet; Wikimedia Commons: Creative Commons BY3.0, https://commons.wikimedia.org/w/index.php?curid=15888815)

Fig. 16.18 Continuous-cooling-transformation diagrams for T72303 (H13) tool steel and S43100 (431) martensitic stainless steel. (Adopted with permission of SIJ Metal Ravne [14])

Shown in Fig. 16.18 are two CCT diagrams adopted from diagrams from the SIJ Group, which is a good source of CCT diagrams for ferrous metals [14]. The CCT diagrams are for T72303 (H13) tool steel and S43100 (431) martensitic stainless steel, both representing wrought material. Cooling curves indicative of a range of cooling anticipated in additive manufacturing processes are also overlaid on the diagrams. The graphs indicate that for all of the cooling rates shown, martensite forms the principal microstructural feature and the ferrite and cementite transformations are completely suppressed. In the case of T72303, the alloy is

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16 Solid State Transformations and Gas Reactions During the Additive. . .

Fig. 16.19 Microstructures that may be present after additive manufacturing processing for several types of steels. (Figure used with permission; Copyright 2020 Elsevier [15])

used for die applications requiring high wear resistance and strength at elevated temperatures, and alloy S43100 has been used extensively for repair and additions on ferrous materials for locally increasing wear and corrosion resistance. Given the wide range of ferrous materials used for additive manufacturing, the microstructures representing these alloys are extremely diverse, but it is hoped that the discussions of allotropic transformations of steels and diffusional reactions provide a basic understanding of the development of microstructures for these alloys. The excellent review by Bajaj et al. is used to summarize the discussion of potential microstructures that may develop during additive manufacturing of ferrous alloys and is shown graphically in Fig. 16.19 [15]. The prospective microstructures for these steels are shown for conventional wrought material forms, as well as additive processing using the laser-based powder bed fusion and directed energy deposition processes. The assumptions for these conditions are that additive manufacturing exhibits relatively high cooling rates, and powder bed fusion provides higher rates than directed energy deposition. Ferrous-based alloys have been used during the discussion of an allotropic transformation because they represent the most widely used materials within this category, and they typically portray the development of relatively complex microstructures. However, there is another alloy system that undergoes an allotropic transformation that is extremely relevant to additive manufacturing. The α and β titanium alloys, such as R56400 (Ti-6Al-4V), also undergoes an allotropic transformation. In this case, the high temperature β-phase is body-centered cubic above the β transus temperature, and upon cooling from this temperature, the BCC

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β-phase transitions to a hexagonal close-packed (HCP) crystal structure consisting of α and β phases. The α and β phases are metastable upon cooling and β typically accounts for between 20% and 50% of the microstructure at room temperature. The work-horse alloy in this system is R56400, containing nominally 6% aluminum, as a α stabilizer, and 4% vanadium, as a β stabilizer. Gaseous elements relevant to additive manufacturing, oxygen and nitrogen, also act to stabilizer α and may be absorbed during processing. These gaseous species, along with hydrogen, may also result in interstitial solid solution strengthening in titanium alloys [16]. Typically, microstructures exhibiting higher proportions of α display higher strength and greater amounts of β demonstrate better ductility. Similar to the allotropic transformation and diffusional effects in steels, the rate of cooling from the β region strongly influences the reactions and may result in complex microstructures. Although substantial, the research on the martensitic reaction in α and β titanium alloys does not have the luxury of over 100 years of research, and certain aspects of the reactions at high cooling rates have not been fully explained. Nevertheless, a general understanding of the products of the decomposition of β under varying cooling rates has been developed. Shown in Fig. 16.20 is a composite CCT diagram for alloy R56400 based on the prior work of Ahmed et al. [17], Kuang [18], and Sieniawski et al. [19]. The diagram has been constructed to express potential regions for transformations based on reported microstructures and should be considered approximate when delineating transformation mechanisms. As mentioned earlier, the β phase BCC is stable above the β transus temperature. Cooling below this temperature at rates greater than 400 ◦ C/s results in the transformation of β to martensitic α ' , which displays an HCP structure caused by distortion of the original BCC lattice through a shear displacement, similar to the martensitic transformation in steels. The α ' -phase forms within prior β grains as very fine plates oriented orthogonally and exhibits an acicular morphology [17]. At cooling rates between 400 and 100 ◦ C/s, an α '' -phase also begins to form preferentially at the prior β grain boundaries while retaining the α ' . The α '' represents an orthorhombic structure and is reported to form through a massive transformation involving heterogeneous nucleation and volumetric, shortrange diffusion [20]. The α '' -phase is also referred to as α m . Although α '' has a different crystal structure, they are identical in composition, which is an indication of the massive transformation. Cooling from above the β transus at a rate less than 100 ◦ C/s involves competition between the massive transformation of α '' and the diffusional reaction of β → α + β, with cooling rates below 3 ◦ C/s being dictated strictly by the latter. Cooling rates between 100 and 20 ◦ C/s show progressively less intergranular α '' formed and proportionally more α at prior β grain boundaries. At the lower cooling rates within this range, the α '' may also exhibit large blocky regions that have grown from a prior β boundaries into grain [20]. Cooling rates less than 3 ◦ C/s result in nucleation of α at grain boundaries, followed by intragranular growth of α as parallel laths interspersed with plates of retained β within the prior β grains. The microstructure of α and β formed at the lower cooling rates is referred to as Widmanstatten α and exhibits a “basketweave” appearance.

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Fig. 16.20 A composite continuous-cooling-transformation diagram for alloy R56400 (Ti-6Al4V) constructed based on prior research [17–19]

In general, cooling rates achieved during additive manufacturing may range between 104 and 102 ◦ C/s, depending upon the process and parameters, and hence, a variety of microstructures would be expected for additive manufacturing of alloy R56400. Based on the diagram of Fig. 16.20, at very high cooling rates associated with the laser-based powder bed fusion process, martensitic α ' with some β retained may be anticipated, whereas, under slower cooling, represented by the directed energy deposition process, microstructures between α '' , α, and β may be expected, depending upon processing conditions. Shown in Fig. 16.21 are optical micrographs of R56400 material produced using a laser during the powder bed fusion and directed energy deposition processes [21, 22]. The micrograph of material produced using powder bed fusion (Fig. 16.22a) exhibits an acicular martensitic α ' microstructure and potentially the presence of α '' , whereas the microstructure representing the directed energy deposition process (Fig. 16.22b) also has attributes of an acicular structure, but much coarser than the material produced by powder bed fusion. The microstructure for the directed energy deposition material was reported to contain α ' , α, and β (and probably α '' ). It must be reiterated that the microstructure that results from a build sequence is not only based on the cooling rate from a transformation temperature, but also reactions that may occur during multiple thermal cycles below transformation temperatures. An example of five thermal cycles for material in the first layer was shown earlier (Fig. 16.1) for directed energy deposition of alloy R56400 alloy, and the micrograph for the directed energy deposition process in Fig. 16.21 represents the material produced under these conditions [1]. The thermal cycles from the earlier

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Fig. 16.21 Optical micrographs of R56400 (Ti-6Al-4V) showing the as-built microstructure for the (a) laser-based powder bed fusion process and (b) laser-based directed energy deposition process. (Figure a: Used with permission; Copyright 2016 Elsevier [21], and Figure b: Used with permission of Dr. Jaime Keist and the Applied Research Laboratory, Pennsylvania State University [22])

Fig. 16.22 Thermal cycles of five-layer deposition using the directed energy deposition process and alloy R56400 (Ti-6Al-4V) superimposed on CCT diagram

figure have been superimposed on the CCT diagram for the R56400 alloy and are shown in Fig. 16.22. It should be noted that the time scale for the thermal cycles does not correspond to the time scale of the CCT diagram, since it is logarithmic. The peak temperatures may be compared directly to the CCT diagram, although the peaks for the first two layers have been truncated to fit within the diagram. As seen

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16 Solid State Transformations and Gas Reactions During the Additive. . .

in the figure, the first three deposits resulted in peak temperatures well above the β transus, and based on cooling rates of between 100 and 200 ◦ C/s for these deposits, a mixed microstructure containing the martensitic α ' , α '' , and retained β would be expected. However, the peak temperatures in the material after the fourth and fifth layer were below the β transus and for a short period of time could result in the decomposition of the initial α ' to α and β. Shown in Fig. 16.23 are optical micrographs, data regarding peak temperatures and cooling rates, and results of x-ray diffraction (XRD) for material in the first layer after each subsequent deposition layer. The three micrographs in Fig. 16.23 represent the material in the first layer after deposition of one, three, and five deposits and are also noted in the thermal cycles of Fig. 16.22. All of the micrographs indicate an acicular microstructure of α’ but cannot discern the subtleties that may have occurred after the fourth and fifth layer. However, results of XRD did indicate a change in lattice ratio, c/a, after the fifth layer. The c/a ratio is a measure of the average lattice distortion due to atomic packing for the HCP structure and may indicate the proportion of α and β present. As seen in Fig. 16.23, the c/a ratios for the first four layers that exceeded or approached the β transus followed by rapid cooling were similar and found to be between 1.5910 and 1.5930, whereas the c/a ratio for the material that had undergone all five thermal transients exhibited an appreciable increase in the ratio, with an average measurement of 1.5964. The higher lattice ratio would signify a greater amount of β within the microstructure, which was also indicated by the substrate material having a mixed α and β microstructure. Although solidification plays an important role in establishing the initial microstructure in material produced using additive manufacturing processes that rely on melting and solidification, there is also a host of solid state transformations that take place post solidification. These transformations are driven by the complicated thermal transients that occur within the material during processing and can be instrumental in defining important microstructural features and characteristics that dictate mechanical properties. Many of these transformations are both time and temperature dependent and are governed by diffusional reactions, whereas several important materials, notably, many ferrous alloys and the popular titanium alloy containing Ti-6Al-4V, rely on allotropic transformations that are highly temperature dependent for achieving desirable microstructures and properties. In actuality, most engineered metallic systems utilize a combination of these methods for defining their microstructures. The use of CCT diagrams, which are applicable to diffusional and allotropic transformations, provides insight into the potential phases and microstructures that may be formed during cooling. By estimating the thermal transients that may be occurring within the material, which may be as simple as continually measuring the background or preheat temperature during processing and utilizing the melting temperature as the peak temperature, a general representation of the thermal history that is seen within the part may be envisioned. Comparing this visualized thermal response to the CCT diagrams provides a powerful tool for anticipating potential microstructures that may be developed during the process. This approach may also

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Fig. 16.23 Optical micrographs, thermal cycle information, and results of x-ray diffraction for deposited material representing R56400 (Ti-6Al-4V) alloy after five subsequent layers produced using the laser-based directed energy deposition process. (Figure used with permission; Copyright 2018 Elsevier [1])

provide an indication of how processing conditions, such as energy of the source, scan velocity, and dwell time between layers that would be utilized to impact transformations and control microstructure. Obviously if results from analytical or numerical process models are available to predict thermal history, these may be used in a similar fashion. One final point of interest, which is imperative and involves the morphology and orientation of the grain structure in additive manufactured materials, must be addressed. Using the simplest description, grains within a metal are defined by regions having the same crystallographic orientation. There is often a degree of misorientation of the lattice structure between grains, and boundaries are also usually chemically different from the intragranular area. As discussed during solidification, epitaxial growth from the substrate into the solidifying material may easily occur during additive manufacturing and successive solidification events may carry the initial crystallographic orientation beyond several deposition layers to form long, columnar grains. This type of grain structure is illustrated in Figs. 15.35 and 16.2, and because of the common orientation or texture of the structure, the properties associated with the material may be very directional or anisotropic. Although high levels of anisotropy are usually associated with directionality of mechanical properties, it may also impact other properties and characteristics, such as preferential corrosion. Almost all processed material exhibits some degree of

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non-random orientation of its crystal structure; however, the initial epitaxy during heterogeneous nucleation and the combination of thermal gradients and growth velocities that lead to columnar growth opposite the direction of heat transfer make additive manufacturing especially sensitive to this condition. The easy growth orientation for many metals having cubic unit cells, in terms of their Miller indices, is associated with the [100] direction and the (001) orthogonal planes, and this orientation is generally found in the build direction for additive manufactured metals. By utilizing techniques to measure the crystallographic orientation of many grains, a statistical distribution of the collective orientations may be used to assess the degree of texture of the material in relation to the additive manufacturing processing direction. Two techniques, XRD and electron backscattered diffraction (EBSD), are very common techniques used to evaluate the orientation of polycrystalline material. In XRD, a focused monochromatic beam of x-rays is introduced to the sample and diffract at certain angles based on the atomic positions within the lattice structure of the material. The material is usually tilted using a goniometer and rotated during irradiation, which allows the intensity of certain lattice reflections for a particular orientation to be measured. The distribution of the intensities at the various angles of diffraction enables the primary crystallographic planes to be determined, and the angle of diffraction may be related to the spacing of the atomic planes through Bragg law. If the surface of the sample, which provides a reference to the processing direction, is known in regard to the diffraction angle, a qualitative or semi-quantitative indication of a preferred crystallographic orientation or texture may be identified. In a somewhat similar manner, the EBSD technique utilizes the focused electron beam in a SEM to cause backscattering of some electrons that contain a pattern that may be indexed through the Bragg relationship. This indexing is usually performed automatically using algorithms that define the crystallographic orientation of the material within the sampling region. The EBSD method may also be used to scan a relatively small area or interrogate various positions within a sample to provide a map of crystallographic orientation. A common means of viewing the potential texturing within polycrystalline material is the use of a pole figure, which specifies the distribution of a particular crystallographic plane within the grains of the material as a stereographic projection. The specimen surface is used as a reference for the material within the projection and is denoted at the center of the pole diagram. If there is no preferred orientation, the reflection of the specific lattice plane should be random, whereas if a preferred crystallographic orientation of the grains within the material exists, the distribution of the plane will be clustered at locations on the pole diagram that may be referenced to the sample orientation. Shown in Fig. 16.24 are two notional pole figures for the (100) crystallographic plane in a specimen having no preferred orientation, or random orientation, and a specimen showing a strong crystallographic orientation related to the build direction and normal to the build direction. Figure 16.25 depicts results from Ding et al. based on EBSD of four specimens representing alloy N07718 (IN718) deposits produced using the electron beambased powder bed fusion process [23]. Longitudinal specimens were removed from

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Fig. 16.24 Pole figure for the (100) plane showing random and preferred or textured distribution of the diffraction pattern

Fig. 16.25 Results of electron backscatter diffraction (EBSD) for four specimens representing alloy N07718 (IN718) produced using the electron beam-based powder bed fusion process showing orientation maps for the scan direction (a, b, c, d), orientation maps for the build direction (e, f, g, h), and pole figures for each specimen. (Figure used with permission; Copyright 2019 Elsevier [23])

each of the deposits and viewed based on the scan direction (Fig. 16.25a–d) and the build direction (Fig. 16.25e–h). Specimens 1 and 12 displayed a mixed grain structure of smaller and larger grains, whereas Specimens 10 and 23 exhibited the

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more common columnar grain morphology. Also shown in the figure are pole figures for each specimen in terms of the scan direction (SD) and build direction (BD). All specimens showed a strong texturing related to the crystallographic orientation in the 001 plane.

16.2 Gas and Liquid Reactions Additive manufacturing that involves melting and solidification of metals may involve gas reactions within the molten pool. The principal reaction is the dissolution of the gas molecule at the gas-liquid interface, followed by absorption within the liquid. The dissolution of a diatomic gas molecule to a monatomic gas atom lowers the energy for the smaller atom to be absorbed within the pool. In many instances, the solubility of the gas species within the liquid metal increases with increasing temperature enabling large amounts of the gas to be absorbed and held in solution. Upon cooling, the solubility is significantly decreased and helps to drive, potentially, two reactions, the formation of gas pores and/or the reaction of the gas to form insoluble compounds.

16.2.1 Gas Porosity Various gases may be present during processing. This includes inert gases used purposely for shielding of the molten metal, such as argon, helium, and nitrogen. Although nitrogen is used for some applications, it is not an inert gas. Other gas species may also be present during processing and may be considered contaminants, such as oxygen and hydrogen. The inert gases argon and helium, also called the noble gases, are not reactive, since the combination of electron in the valence shell for these elements does not easily allow participation in chemical reactions. However, the other gases that may be present, albeit in small quantities, may undergo reactions that may be detrimental to the material. The most common is the disassociation and absorption into the liquid and the formation of gas pores upon cooling. The most common gases that may be available for forming porosity are oxygen, nitrogen, and hydrogen, and the potential for forming pores with the individual gases changes based on the specific metallic system being processed. As an example, under equilibrium conditions, the reaction of hydrogen gas with a liquid metal may be described as: H ⇌

.

1 H2 (g) 2

(16.10)

and the change in Gibbs free energy for the reaction in terms of the partial pressure of the gas above the liquid, .pH2 , and the activity of the dissolved gas species in the liquid metals, aH , is:

16.2 Gas and Liquid Reactions

515

 ΔG = ΔG + RT o

.

1/2

pH 2 aH

(16.11)

At equilibrium, the overall change in free energy is null, such that: ΔGo = RTlnKa

.

(16.12)

where ΔGo is the change in free energy for the system in the standard state and Ka is the equilibrium constant and may be expressed as: 1/2

Ka =

.

pH 2 aH

(16.13)

If it is assumed that at low concentrations the dissolved gas acts ideally, and hence, aH is equal to the concentration of gas in the liquid, [H], it then follows: .

1/2

[H ] = KpH2

(16.14)

The above relationship is referred to as Sievert’s law and describes the amount of gas that may be absorbed within the liquid at equilibrium based on the partial pressure of the gas above the liquid. A new constant, K, has been introduced and is related to the equilibrium constant, Ka . Equation 16.14 indicates that under equilibrium conditions the amount of gas in the liquid increases as the partial pressure of the gas above the liquid increases. In general, this describes the phenomenon; however, as was pointed out earlier, the rapid heating and cooling during additive manufacturing may not result in equilibrium conditions being operative. Under nonequilibrium conditions, an effective constant, Keff , may be used to better define the efficiency of gas absorption under specific conditions. An important aspect for a gas to form porosity within a metallic system is the solubility of the gas in the liquid. Once the gas species is absorbed into solution within the liquid, the reduction in the gas solubility during cooling drives a concurrent process of recombination to the diatomic state and the nucleation of a gas pore, a combination referred to as desorption. Although some amount of the gas will remain in solution, the excess created at the lower solubility will be available to form pores. Once porosity is formed within the liquid, the pore may grow by further desorption of gas species near the pore and liquid metal interface. Low resident time within the liquid, an artifact of high solidification rates, minimizes pore growth. Under lower solidification rates, pores that are formed within the liquid may be expelled through buoyancy or through fluid flow within the liquid pool. However, the relatively high solidification rates experienced in additive manufacturing processes tend to negate expulsion of porosity from the liquid. Gas species having appreciable levels of solubility in iron at temperatures above the liquidus include oxygen, nitrogen, and hydrogen. The solubilities of these gas are significantly higher than that in solid iron, and under certain circumstances, this

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16 Solid State Transformations and Gas Reactions During the Additive. . .

difference may drive the formation of porosity during solidification [24]. However, there are competing reactions that may take place, and these reactions may be dependent upon the alloying additions that are present. In stainless steels, dissolved oxygen may form Cr2 O3 , and steels containing manganese and silicon have an affinity to form MnO and SiO. Nitrogen within high alloyed steels containing chromium, vanadium, molybdenum, or titanium can form CrN, VN, MoN, or TiN. Finally, hydrogen dissolved in molten steel may not precipitate as a pore but diffuse atomically within the matrix. Nevertheless, when gas pores are observed in steels during additive manufacturing, the potential presence of oxygen or nitrogen should be considered. Aluminum alloys are especially sensitive to hydrogen-based porosity during solidification. As discussed earlier, the solubility of hydrogen in the liquid is much greater than the solubility in the solid, and in the case of aluminum, competing gasmetal reactions are minimal, such that high levels of hydrogen absorbed within the liquid may be available to form pores during solidification. Also, because hydrogen may be present in various forms during additive manufacturing, the contributions of hydrogen should be based on a primary source within the system if porosity is prevalent [25]. Sources of hydrogen within the additive manufacturing system may include moisture that has chemically absorbed on the surface of powder and moisture within the inert gas. Nickel-based alloys also exhibit high solubility of nitrogen, oxygen, and hydrogen in the liquid when compared to the solid state and have the potential to form gas porosity. The addition of chromium, molybdenum, and tungsten, which are common alloying additions to nickel, has been reported to increase the solubility of nitrogen in the liquid for these alloys [26]. Although titanium alloys display moderate solubility for oxygen and nitrogen, it also exhibits a high reactivity for these elements and readily forms a stable oxide or nitride. Titanium is somewhat unusual since it exhibits a relatively high solubility for hydrogen in the solid state when compared to the melting temperature. However, the solubility of liquid titanium increases at temperature above the melting point. Although the dynamics of dissolved hydrogen in titanium appear complex, there is considerable anecdotal evidence that suggests that hydrogen plays a role in the formation of gas porosity [27]. Another aspect of porosity in titanium alloys containing aluminum, such as alloy R56400 (Ti-6Al-4V), is the potential for the high vapor pressure of the aluminum addition to form a pore at high temperatures within the liquid. Although porosity has been observed in the processing of the R56400 alloy using electron beam-based directed energy deposition within a vacuum, the exact source of the porosity has not been completely resolved. However, the potential for vaporized aluminum to form pores during solidification remains a possibility. Copper alloys may be susceptible to absorption of oxygen and hydrogen, whereas nitrogen has very little solubility in liquid copper. In the case of oxygen, the solubility in the liquid is over 40 times higher than the solid copper (70 ppm versus 2 ppm) and provides a strong driving force for gas porosity. Electrolytic tough pitch (ETP) copper is produced using relatively high amounts of oxygen, between 200 and 400 ppm, for deoxidizing the melt and some oxygen remains as a residual that may

16.2 Gas and Liquid Reactions

517

Fig. 16.26 Images of porosity and lack of fusion in directed energy deposition of alloy R56400 (Ti-6Al-4 V). (Figures used with permission of the Applied Research Laboratory, Pennsylvania State University)

be available to form porosity. However, the presence of oxygen in the liquid may also have the potential for forming copper-oxide, Cu2 O. Alloys of copper that are considered for welding and additive manufacturing may contain aluminum, silicon, manganese, or titanium to act as a deoxidizer during processing. One important aspect of this phenomenon is the correct identification of pores related to gas absorption. There also exists other defect that may be similar in size to gas porosity that does not involve absorption of gas and the formation of pores during solidification. These include lack-of-fusion defects and pores related to instability of the vapor cavity during high energy density processing, such as with lasers and electron beams. Gas-induced porosity is typically round and smooth when viewed using microscopy techniques, whereas lack-of-fusion defects, by nature of its formation, are angular. Pores caused by instability and collapse of the vapor cavity or keyhole may be more rounded than lack of fusion, but these types of defect usually are near the deepest penetration region of the deposit and can exhibit multiple pores along the length of the deposit as the vapor cavity periodically collapses and becomes reestablished. Shown in Fig. 16.26 are images showing gas porosity associated with additive manufacturing of alloy R56400 (Ti-6Al-4V), as well as an example of a lack-of-fusion defect. Locations of porosity within the material may also provide an indication of a potential source. Porosity that is scattered throughout the build material may suggest contaminated powder as the source, whereas porosity near the substrate or inter-pass areas may signal improper cleaning and preparation of the substrate surface.

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16 Solid State Transformations and Gas Reactions During the Additive. . .

16.2.2 Gas and Metal Chemical Reactions As has been mentioned above, gases dissolved in the liquid metal also may react with other constituents to form insoluble compounds, as well. The competition for consuming the gas species ultimately is resolved by the reaction that results in the greatest reduction in free energy at the temperature of interest, and although the rate of a favorable reaction must always be considered, these reactions usually occur at high temperatures, which tend to have high rates. Therefore, the reactions that transpire are typically driven by energetics. The equilibrium condition for oxygen in the presence of a liquid metal may be shown as: .

2a 2 M(l) + O2 (g) ⇌ Ma Ob (s) b b

(16.15)

and depending upon conditions, the change in free energy associated with the system will determine if the reaction will proceed and in what direction according to: 2/b

ΔG = ΔGo + RTln

.

aMa Ob  2/β  aM pO2

(16.16)

where in the above relationships, ΔGo is the standard free energy of formation of the oxide, .aMa Ob is the activity of the oxide and is assumed to be 1 for a pure material in its standard state, aM is the activity of the metal having oxygen in solution, and .pO2 is the partial pressure of oxygen in the system. Under these conditions, the equilibrium constant may be described as: Ka =

.

2/β aM

1   pO2

(16.17)

If the change in free energy is negative, the reaction is considered spontaneous and will proceed to the right and the oxide will form. If under the conditions of interest, the free energy is positive, the reduction of the oxide to the metal will occur. To further simplify the analysis for the purpose of determining the relative reactivity of gas species within a liquid metal, the metal with dissolved oxygen is assumed to be an ideal solution (Raoult’s law), and the activity of the metal with oxygen in solution is equal to the mole fraction of gas in solution. With this generalization, the equilibrium constant is inversely proportional to the partial pressure of the gas within the system, and Eq. 16.16 may be used to relate the change in free energy as a function of temperature. Knowing the standard free energy of formation and determining the overall change in free energy on a mole fraction basis enables various metal oxide reactions to be graphically presented. These types of depictions are known as Ellingham diagrams. It should also be noted that a similar

16.2 Gas and Liquid Reactions

519

Fig. 16.27 Free energy of formation as a function of temperature for selected oxides. (Figure adapted with permission; Copyright 2016 Stanley M. Howard [28], Thermodynamic data from Thomas B. Reed [29])

approach is applicable for the change in free energy associated with a liquid metal reaction with nitrogen gas. Although the reaction of carbon with liquid metal is not a gas-metal reaction, the reaction to form a carbide is also similar to Eq. 16.15, except that the partial pressure for the reaction species, carbon, is replaced by the activity of carbon, which is related to its concentration in the metal system. Shown in Figs. 16.27, 16.28, and 16.29 are Ellingham diagrams for selected oxides, nitrides, and carbides, respectively, that had been constructed by S. M. Howard [28] utilizing thermodynamic data for oxides and nitrides by Reed [29] and carbides by Jasthi [30]. The figures represent change in free energy based on a gram formula weight (gfw), which represents the atomic weight in terms of the mole ratio of the molecule, and temperature is shown in terms of absolute temperature, in keeping with the thermodynamic measure of temperature in Kelvin. It should also

520

16 Solid State Transformations and Gas Reactions During the Additive. . .

Fig. 16.28 Free energy of formation as a function of temperature for selected nitrides. (Figure adapted with permission; Copyright 2016 Stanley M. Howard [28], Thermodynamic data from Thomas B. Reed [29])

be mentioned that the diagrams shown in the figures are used only to illustrate the approach for estimating potential reactions and any application should be based on a rigorous thermodynamic analysis. These diagrams may be used to indicate the stability of the reaction and the product based on temperature of the reactions and partial pressure of oxygen (for oxides), partial pressure of nitrogen (for nitrides), or activity of carbon (for carbides). In the case of carbon, the assumption of carbon forming an ideal solution with the metal allows the activity at dilute levels to be equal to the concentration of carbon within the system. Based on the change in free energy for the reaction, while not considering kinetics, reactions that are thermodynamically possible may be pondered. Reactions that are lower in the diagram indicate a greater negativity in the change in free energy and are considered more stable or preferred than reactions that are higher

16.2 Gas and Liquid Reactions

521

Fig. 16.29 Free energy of formation as a function of temperature for selected carbides. (Figure adapted with permission; Copyright 2016 Stanley M. Howard [28], Thermodynamic data assembled by B. Jasthi [30])

in the diagrams. The reaction of oxygen and carbon to form carbon monoxide is also shown in the diagram for oxides, since it may be used to reduce oxides within the melt when carbon and oxygen are present at elevated temperatures. As an example, using Fig. 16.28 for nitrides for an iron system containing chromium, niobium, and titanium, trace nitrogen levels having a partial pressure of 10−10 and a liquid temperature of 1673 K (1400 ◦ C) would favor the formation of TiN over Nb2 N, CrN2 , and Fe4 N. This analysis is accomplished by drawing a line from the zero point in the upper left side of the diagram to the partial pressure of gas, or activity in the case of carbon, found adjacent to the right ordinate. The intersection of this line at the temperature of interest indicates what metal-gas reactions could be viable, with the most preferred reaction being lowest on the Ellingham. In actuality, more than one nitride may form, and based on this example, it is not surprising that high alloyed steels containing chromium, vanadium, molybdenum, or titanium

522

16 Solid State Transformations and Gas Reactions During the Additive. . .

form various nitrides. With the presence of carbon, there is also the potential to form various carbon-nitride compounds with these elements, as well. Knowing the components present within the system and the temperature of interest, these types of diagram provide a glimpse of potential reactions that may be relevant. Through the use of detailed free energy calculations, utilizing accurate thermochemical data [31, 32] or current thermodynamic software packages, potential reaction products, such as oxides, nitrides, carbides, and hydrides, may be examined based on the concentration of elements within the system and reaction temperatures. This approach provides a powerful tool for ascertaining the potential for forming reaction products that may occur, given the components within a system and the reaction temperature are known, as well as for identifying processing conditions that had resulted in unexpected compounds determined through examination. The initial discussion regarding these reactions alluded to the formation of compounds that form during processing of liquid metal in the presence of a gas that could be considered contaminants, but as was pointed out in the example, gas or a compound containing a gas species is purposely introduced in some instances during the production of an alloy to form beneficial compounds. In many instances, these compounds can provide improvements in strength by forming small particles within the material. Utilizing the same principles that are applied to the making of an alloy, additive manufacturing offers the opportunity to also introduce beneficial constituents through gas reactions with the liquid during processing. Shown in Fig. 16.30 are the results of microstructural analysis of material deposited on an alloy G41400 (AISI 4140) substrate [33]. The deposited material was produced using the directed energy deposition process by traversing a diffuse laser beam over a preplaced powder layer of martensitic grade stainless steel alloy S43100 (431), while also injecting TiC particles into the rear of the melt pool. Deposits were produced in this manner while employing various shielding gases. The objective was to evaluate material that could ultimately be used to replace Co-Cr alloys for imparting high wear resistance at the surface of components. The initial material design entailed the use of a high strength stainless steel alloy with the addition of TiC as hard particles. Computational thermodynamics was used to identify potential material systems that would provide minimal dissolution of the hard particles within the liquid metal. However, thermodynamic analysis also indicated the potential for forming additional hardening phases by processing with a reactive atmosphere containing nitrogen. The results showed that not only was a large portion of the original TiC retained within the deposits, but when the TiC was dissolved in the presence of shielding gas containing N2 , using air or a combination of argon and nitrogen gas, the tendency was to form a fine distribution of titanium carbonitrides. Some of the larger carbonitride particles are shown in the figure and were confirmed by EBSD. The benefit of the fine distribution of these particles is also illustrated in the microhardness measurements of deposits produced in this manner with varying amount of N2 within the shielding gas, which is illustrated in Fig. 16.31 [34].

16.2 Gas and Liquid Reactions

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Fig. 16.30 Macrographs and micrographs of deposits produced using a martensitic stainless steel alloy S43100 (431) powder with 20% (by weight) TiC particles while employing various shielding gases (arrows indicate fine carbonitrides). (Figures reproduced from Babu et al. [33] with the permission of AIP Publishing)

Fig. 16.31 Results of microhardness testing showing average hardness for deposition material created using martensitic stainless steel alloy S43100 (431) powder with 20% (by weight) TiC particles and produced using various shield gases. (Figure used with permission; Copyright 2006 Elsevier [34])

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16 Solid State Transformations and Gas Reactions During the Additive. . .

16.3 Questions and Discussions 1. Discuss the various strengthening mechanisms that are operative in tools steels, austenitic stainless steels, martensitic stainless steel, and precipitation-hardened stainless steels. Given the reactions used for strengthening these materials, which alloys would likely be hardened by the additive manufacturing process, and which alloys would probably require post-process thermal treatments? 2. Describe in detail the development of microstructure for an aluminum alloy containing silicon and magnesium, with a weight percent of Mg2 Si of 0.8, during relatively rapid cooling from above the liquidus temperature to room temperature. 3. Explain why the overall rate of a precipitation reaction occurs at an intermediate temperature between the solvus and room temperature. Sketch a precipitation reaction having a completion of 90% in terms of time and temperature. 4. Using the thermal response illustrated in Fig. 16.1 for a directed energy deposition process, discuss how this thermal response would influence the development of microstructure for alloy N07718 (IN718). Discuss how the microstructure could evolve if the process utilized 30 layers instead of 5. 5. Describe how cooling rates from the solidification temperature drive the establishment of microstructure and strength for a martensitic stainless steel alloy being employed for addition on the surface of a component requiring wear resistance. 6. Discuss how microstructure would be developed for alloy R56400 (Ti-6Al-4V) during additive manufacturing using the laser-based directed energy deposition process and the laser-based powder bed fusion process. 7. The driving force for porosity formation during solidification of aluminum alloys in the presence of hydrogen has been shown to be the dramatic reduction in hydrogen solubility within the liquid as compared to the hydrogen solubility of the solid. Define potential sources of hydrogen during powder bed fusion of aluminum alloys. 8. Describe the cause, morphology, and impact of porosity and lack of fusion defects. 9. Define the partial pressure of nitrogen that would enable the formation of TiN within a melt pool of pure titanium. 10. Discuss the results shown in Fig. 16.31 based on the measured hardness of the material and the process conditions used to produce the deposits.

References 1. Lia F, Park JZ, Keist JS, Joshi SB, Martukanitz RP (2018) Thermal and microstructural analysis of laser-based directed energy deposition for Ti-6Al-4V and Inconel 625 deposits. Mater Sci Eng A 717:1–10. https://doi.org/10.1016/j.msea.2018.01.060

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2. Rajan JI (2017) Development of ultrafine grained A356 aluminum alloy by severe plastic deformation and studies on its deformation behavior and machinability. https://doi.org/10.13140/ RG.2.2.12032.74241 3. Liu M, Zhang X, Breton F, Chen X (2019) Investigation of the quench sensitivity of an AlSi10Mg alloy in permanent mold and high-pressure vacuum die casting. Materials MDPI. https://www.mdpi.com/1996-1944/12/11/1876/pdf 4. Oradei-Basile A, Radavich J (1991) A current T-T-T diagram for wrought alloy 718. In: Loria EA (ed) Superalloys 718, 625 and various derivatives. The Minerals, Metals & Materials Society, pp 325–335 5. Maj P, Adamczyk-Cieslak B, Slesik M, Mizera J, Pieja T, Sieniawski J, Gancarczyk T, Dudek S (2017) The precipitation processes and mechanical properties of aged Inconel 718 alloy after annealing. Arch Metall Mater 62:1695–1702 6. Carlson R, Radavich J (1989) Microstructural characterization of cast 718. In: Loria EA (ed) Superalloy 718-metallurgy and applications. The Minerals, Metals & Materials Society 7. Rios P (2005) Relationship between non-isothermal transformation curves and isothermal and non-isothermal kinetics. Acta Mater 53:4893–4901. https://doi.org/10.1016/ j.actamat.2005.07.005 8. Cahn JW (1956) Transformation kinetics during continuous cooling. Acta Metall 4:572–575 9. Liu F, Yang C, Yang G, Zhou Y (2007) Additivity rule, isothermal and non-isothermal transformations on the basis of an analytical transformation model. Acta Mater 55:5255–5267. https://doi.org/10.1016/j.actamat.2007.05.041 10. Ruitenberg G, Woldt E, Petford-Long A (2001) Comparing the Johnson-Mehl-AvramiKolmogorov equations for isothermal and linear heating conditions. Thermochim Acta 378:97– 105 11. Garcia C, Lis A, Loria E, DeArdo A (1992) Thermomechanical processing and continuous cooling transformation behavior of IN-718. In: Antolovich SD, Stusrud RW, MacKay RA, Anton DL, Khan T, Kissinger RD, Klarstrom DL (eds) Superalloys. The Minerals, Metals & Materials Society 12. Zhou L, Mehta A, McWilliams B, Cho K, Sohn Y (2019) Microstructure, precipitates and mechanical properties of powder bed fused inconel 718 before and after heat treatment. J Mater Sci Technol 35(6):1153–1164 13. Sweny R, Tressler J, Martukanitz R (2018) Development and evaluation of an advanced aluminum alloy for additive manufacturing. J Mater Sci Eng 7. https://doi.org/10.4172/21690022.1000505 14. SIJ Group. https://steelselector.sij.si/steels/PK2SP.html. Accessed 9 Apr 2020 15. Bajaj P, Hariharan A, Kini A, Kürnsteiner P, Raabe D, Jägle E (2020) Steels in additive manufacturing: a review of their microstructure and properties. Mater Sci Eng A 772:138633 16. Issariyapat A, Visuttipitukul P, Song T, Umeda J, Qian M, Kondoh K (2020) Strength-ductility improvement of extruded Ti-(N) materials using pure Ti powder with high nitrogen solution. Mater Sci Eng A 779:139136 17. Ahmed T, Rack H (1998) Phase transformations during cooling in α+β titanium alloys. Mater Sci Eng A 243:206–211 18. Kuang Y (2004) Generation of TTT and CCT curves for cast Ti-6Al-4V alloy. MS thesis, George A. Smathers Libraries, University of Florida 19. Sieniawski J, Ziaja W, Kubiak K, Motyka M (2013) Microstructure and mechanical properties of high strength two-phase titanium alloys. In: Sieniawski J, Ziaja W (eds) Titanium alloys. InOpen 20. Lu S, Qian M, Tang H, Yan M, Wang J, St John D (2016) Massive transformation in Ti–6Al–4V additively manufactured by selective electron beam melting. Acta Mater 104:303–311 21. Sallica-Leva E, Caram R, Jardini A, Fogagnolo J (2016) Ductility improvement due to martensite α' decomposition in porous Ti–6Al–4V parts produced by selective laser melting for orthopedic implants. J Mech Behav Biomed Mater 54:149–158 22. Keist J (2023) Personal communications, January

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23. Ding X, Koizumi Y, Aoyagi K, Kii T, Sasaki N, Hayasaka Y, Yamanaka K, Chiba A (2019) Microstructural control of alloy 718 fabricated by electron beam melting with expanded processing window by adaptive offset method. Mater Sci Eng A 764:138058 24. Feichtinger H, Zheng X, Rennhard C (1990) Measurements of nitrogen solubility in iron and iron-nickel alloys, using a new temperature gradient method. Mater Technol 61:26–29 25. Martukanitz RP, Michnuk PR (1982) Sources of porosity in gas metal arc welding of aluminum alloys. Aluminium 58:276–279 26. Kowanda C, Speidel M (2003) Solubility of nitrogen in liquid nickel and binary Ni–Xi alloys (Xi=Cr, Mo, W, Mn, Fe, Co) under elevated pressure. Scr Mater 48:1073–1078 27. Huang J, Warnken N, Gebelin J, Strangwood M, Reed R (2012) On the mechanism of porosity formation during welding of titanium alloys. Acta Mater 60:3215–3225 28. Howard SM (2016) Ellingham diagrams: standard Gibb’s energies of formation. South Dakota School of Mines and Technology 29. Reed TB (1971) Free energy of formation of binary compounds. MIT Press, Cambridge, MA 30. Jasthi B. Thermodynamic data assembles in collaboration with S. M. Howard. South Dakota School of Mines and Technology 31. Stull DR, Prophet H (1971) JANAF Thermochemical Tables, NSRDS-NBS 37. U.S. Department of Commerce, National Bureau of Standards 32. JANAF Thermochemical Tables, U.S. National Institute for Standards and Technology. https:/ /janaf.nist.gov/ 33. Martukanitz RP, Babu SS (2004) Development of advanced coatings for laser modifications through process and materials simulation. AIP Conf Proc 712:1539. https://doi.org/10.1063/ 1.1766747 34. Babu SS, Kelly SM, Murugananth M, Martukanitz RP (2006) Reactive gas shielding during laser surface alloying for production of hard coatings. Surf Coat Technol 200:2663–2671. https://doi.org/10.1016/j.surfcoat.2005.02.160

Chapter 17

Modeling of Microstructure for Additive Manufacturing

The use of analytical and numerical techniques for modeling and simulation can be a powerful tool for providing greater insight into microstructural development of the material during additive manufacturing. Applications of this approach may include determining the potential variability of microstructure and properties associated with thermal cycles representing a complex shape and path plan, identifying processing conditions that favor the establishment of desirable microstructures, determining requirements for material grading to minimize non-desirable phases during multiple material processing, and exploring the impact of non-equilibrium conditions on resultant microstructures, to name a few. However, an important aspect of utilizing these types of models is having a reasonably accurate description of the thermal history of the material during processing. This may be accomplished by physical measurements of temperature at strategic locations and extrapolation to other regions within the part or utilizing an independent or coupled thermal model to define expected temperatures at various locations during processing. In some situations, temperature is considered constant while approximating the phenomena of interest. In many instances, microstructural models are used to predict the establishment and progression of microstructure based on predefined transformations that are anticipated. As discussed previously, these transformations typically fall into two categories, the initial development of microstructure during solidification and modification of the microstructure through solid-state transformations during repetitive heating and cooling cycles. Although there are a variety of techniques utilized to model microstructure, the following discussions will introduce a few methods that have been employed for simulating non-isothermal events during additive manufacturing. Rather than providing a complete discourse of these techniques, the approach is to introduce the subject while reinforcing the potential application of these methods.

© Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4_17

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17.1 Modeling Solidification Solidification involves a change in state of the material, which transforms the liquid to a solid based on increased atomic ordering during cooling. For the additive manufacturing processes of interest, a moving source of energy is used to selectively melt material, which is followed by solidification with the passing of the energy source. Cooling during solidification is primarily driven by heat transfer through conduction of heat from the liquid to the cooler metal substrate. Within the liquid, heat transfer is accompanied by mass transport within the molten pool due to Marangoni forces and buoyancy. As cooling proceeds, nucleation and growth of the solidification front occurs parallel but opposite to the thermal gradients exhibiting the highest rate of heat extraction. Under these circumstances, the full mathematical representation of melting and solidification can be quite complex and involve the simultaneous calculation of energy and mass transport, continuous demarcation of the free surface associated with the changing liquid boundary, and determining local composition during solidification while maintaining conservation of composition within the liquid. As with many engineering problems, certain assumptions may be used to simplify the analysis as long as the limitations posed by these assumptions are known and appropriate to the application of the model. One technique that has demonstrated usefulness in describing the evolution of morphology and composition during solidifying is phase field (PF) modeling, which considers the relaxation of energy within the system to its lowest potential over time. Benefits of the PF approach are that it provides visual two- or three-dimensional spatial information regarding the microstructure, it is capable of incorporating numerous constraints that impact energy within the system, and it can conserve global composition during local calculations of concentration. Also, the technique employs a diffuse interface between the liquid and solid rather than a sharp interface that is used for classical solidification analysis. However, one important weakness of the PF method is that the time variable or kinetic relationships must be calibrated independently. A thorough review of PF as it applies to solidification may be found in Boettinger et al. [1]; however, a brief introduction is warranted. Modeling of solidification using the PF technique involves two field equations that may be used to describe the timedependent evolution of the phase field parameter, φ, and concentration, c, which in the simplest forms are shown below: ∂c = Mc C (1 − C) ∇ 2 . ∂t

.



∂f ∂c



  ∂f ∂φ = −Mφ − εφ2 ∇ 2 (φ) ∂t ∂φ

(17.1)

(17.2)

where Mc is the mobility related to solute concentration, Mφ is mobility associated with the interface of φ, C is concentration, εφ is the gradient energy coefficient

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529

that may be defined based on an angle normal to the interface for anisotropy, and ∇ 2 is the Laplacian operator for the variational derivative of energy in x and y space (for two-dimensional analysis). Equation 17.1 is known as the CahnHilliard or the conserved Ginzburg-Landau equation, and Eq. 17.2 is referred to as the Allen-Cahn or non-conserved Ginzburg-Landau equation. The Cahn-Hilliard relationship inherently conserves concentration through the use of the free energy function. These equations enable the determination of concentration and phase field parameter, with the phase field parameter representing a continuous function between the liquid or solid, in terms of time and position. Both relationships assume a decrease in the free energy of the system over time and are coupled through the use of the free energy density. The formulation of the free energy density, f (∅, C, T), is a critical aspect of the computational process and is a function of phase field parameter, concentration, and temperature. The energy density is typically fitted as a function of two components, g(φ) and p(φ). The g(φ) component provides the energy density as a function of the free energy based on composition and forms a double well that maintains the function equal to zero when the p(φ) component is equal to 1 for the liquid or 0 for the solid. A simple representation for the g(φ) and p(φ) components is shown in Fig. 17.1 [1]. The double-welled characteristic for g(φ) is illustrated in the figure when φ is equal to 0 and 1. The smooth function between p(φ) = 0 at φ equal to 0 (for the solid) and p(φ) = 1 at φ equal to 1 (for the liquid) is also illustrated. The function ensures that ∂f /∂∅ = 0 when ∅ is 1 representing the liquid or 0 for the solid. When dealing with an alloy system, the energy density function becomes more complex. The chemical free energy for the system, f, may be defined for an alloy containing A and B as a regular solution as [1]:

Fig. 17.1 Simplified description of the two functions, g(φ) and p(φ), that are utilized to formulate the free energy density. (Figure adapted with permission; Copyright 2002 Annual Reviews [1])

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17 Modeling of Microstructure for Additive Manufacturing

f(∅, C, T ) = (1 − C) fA (∅, T ) + Cf B(∅, T ) + RT [(1 − C) ln (1 − c) + C ln C] + C(1 − C) {ΩS [1 − p (φ)] + ΩL p (φ)} (17.3)

where ΩL and ΩS are the regular solution parameters for the liquid and solid and p(φ) is used to define the phase between the liquid and solid as a function between 1 and 0. The free energy of the system at a temperature may be described using classical thermodynamic analysis or for all temperatures of interest using computational thermodynamic packages. The free energy, of course, is directly related to the phase diagram, and this dependency is illustrated in Fig. 17.2 for a binary eutectic system at three temperatures within the solidification range. For an alloy system, the free energy density is constructed based on the chemical free energy of the system over the concentration and temperature range of interest. Additional considerations, discussed above, are also employed to formalize the function, f (∅, C, T). The double well constraint for p(∅) is imposed, along with temperature-dependent chemical free energy that enables the construction of a surface function having dependency on the phase field parameter (∅), concentration (C), and temperature (T). A graphical example of a free energy density is shown in Fig. 17.3 using the required constraints, along with a projection of the free energy curves at temperatures that fall within the solidification range from Fig. 17.2. The free energy density shown within the figure is representative of the function that would be obtained using Eq. 17.3 for an alloy forming a regular solution with a solution parameter being much less than zero [1]. The development and use of the free energy density function enables the determination of concentration and phase field parameter present across the interface

Fig. 17.2 Free energy as a function of concentration for a binary alloy at the liquidus temperature (∅ = 1), temperature in the mushy zone (∅ = 0.5), and solidus temperature (∅ = 0) for a eutectic system

17.1 Modeling Solidification

531

Fig. 17.3 Graphical depiction of the free energy density as a function of the phase field parameter (φ), concentration (C), and temperature (T) (above left), along with the projection of the common tangent to the surface of f (φ, C, T) that includes the three free energy diagrams for the system shown previously (above right). (Figures adapted with permission; Copyright 2002 Annual Reviews [1])

between the liquid and solid utilizing Eqs. 17.1 and 17.2, respectively. Employing the free energy density, the two functionals, ∂f /∂C and ∂f /∂∅, are evaluated and utilized in the appropriate field equations to calculate the concentration and phase field parameter based on position. For a single temperature, the concentration of the diffuse interface between the solid and liquid will follow the compositions defined as the hatched line at the base of the ∅ and C plane for the free energy density function shown in Fig. 17.3. The tangent plane, also shown in the figure, defines the function for use far from the interface and has the properties of ∂f /∂C equal to zero and ∂f /∂∅ equal to a constant. The result of these constraints is to not alter the concentration or phase field parameter at positions remote of the interface. The field Eqs. 17.1 and 17.2 are used to determine changes in phase field parameter (∅) and concentration (C) over space by relaxation of free energy over time. The free energy density describing the system is used as a functional within the field equations to calculate composition and phase field parameter within the computational domain as a function of time. The relationship for determining the phase field parameter (Eq. 17.2) may be expressed as: .

  ∂f ∂∅ = Mφ ε2∅ ∇ 2 ∅ − ∂∅ ∂t

(17.4)

and replacing the Laplace operator in spatial derivative form for two-dimensional analysis provides: .

  2   ∂ ∅ ∂ 2∅ ∂f ∂∅ 2 − = M∅ ε∅ + ∂t ∂∅ ∂x 2 ∂y 2

(17.5)

532

17 Modeling of Microstructure for Additive Manufacturing

The above equation may be approximated using numerical techniques, such as finite differencing. Using the time-forward, center differencing, explicit approach, Eq. 17.5 may be approximated through:  ∅n+1 i,j

=

∅ni,j

+ ΔtM∅ 

.

2 +ε∅

 2 ε∅

∅ni+1,j + ∅ni−1,j − 2∅ni,j

∅ni,j +1 + ∅ni,j −1 − 2∅ni,j Δy 2

Δx 2 

∂f − ∂∅





(17.6)

where n is an index denoting the time increment for ∅ beginning at n = 0 at t = 0 and the indices i and j represent spatial discretization of x and y, respectively. Numerical implementation of the above requires a computational grid to be generated, as well as the free energy density function to be established and evaluated. Shown in Fig. 17.4 is a schematic for a portion of a computational grid depicting nodes that would be applicable for the numerical calculations using Eq. 17.6. The time increment is selected to satisfy the stability criteria for providing convergence of the numerical method, which is related to the minimum grid-spacing, Δx and Δy, and the mobility coefficient, M∅ , according to:

Fig. 17.4 Schematic of a computational grid with nodes and that may be used for implementing the numerical scheme for phase field calculations

17.1 Modeling Solidification

533

0
3 500 KB/s 63 MB/ 1 image

Unknown

36 M pixel × 14 bits 640 × 286 MB/s 1–3 512 × 14 bits 640 × 14.3 GB/s 1–3 512 × 14 bits 16 bits 200 KB/s 1–3

~9 s

~0.5 ms

~0.5 ms

~50 μs

The detailed sensing methods span many orders of magnitude both temporally and spatially. A summary of typical sensor systems, unitized in metal powder bed AM processes, is provided in Table 21.1. As discussed in this section, when selecting, integrating, and utilizing any sensor, care must be exercised in determining the appropriate protocols for data transfer, analysis, and storage. In many cases, sensor outputs are difficult to interpret – this is particularly the case for photodiode and acoustic data. Rather than estimating physical metrics, many have pursued machine learning. Supervised and unsupervised neural networks [18, 19, 35, 50–52] and convolutional neural networks—which are especially popular when acoustic sensor data are an input—are trained to predict build quality [53, 54]. ML has also been used with inter-layer imaging of powder bed fusion (i.e., layer-wise imaging) strategies, employing visible [18, 19, 55, 56] and IR cameras [57], to identify anomalies [18, 19, 57]. Regardless of the sensing technology or analysis method used, alignment of sensor and post-process inspection data is critical to determine the reliability of the quality monitoring system. This is, however, not trivial for several reasons: • Uncertainty in registering time-series data to a spatial domain relies on deep knowledge of time delays and spatial distortions, which may be difficult to ascertain. • The spatial resolution and uncertainty in post-process inspection data (e.g., computed tomography or serial sectioning data) may be vastly different than the spatial resolution of sensor data.

644

21 Process Quality and Reliability

Fig. 21.4 A robust data alignment framework is necessary for implementation of sensor-based quality control

• AM parts experience distortion, which adds additional uncertainty in alignment of post-process inspection data. • Fusion AM processes rely on repeated heating and melting of the same area or voxel. As such, voids or anomalies, which may have been accurately detected, may be eliminated on subsequent passes. • Voids and inclusions formed within the melt pool are mobile. They can be carried into regions of the melt which do not exactly align with their position upon detection. A pathway to data alignment, which considers the points above, is illustrated in Fig. 21.4. Here, X-ray computed tomography (XCT) data is used as ground truth to train a flaw detection model which uses time-series data as an input. Note that the procedure can be extended to spatial sensor data as well. Parallel tasks of registering XCT and time-series data to a common coordinate system must first take place. In this case, the common coordinate system is defined by the component geometry, extracted from CAD, a boundary representation (e.g., STL), or the build plan. With XCT data, it may be necessary to use a best-fit strategy to account for part distortion and variation in the as-built geometry. Similarly, time-series data requires accounting for timing delays, the size of the region from which data are collected, and distortions. Even though XCT is claimed as ground truth, it is not always easy or obvious as to how to identify flaws or features within the dataset. Regardless of the method used, the accuracy and precision of flaw detection must be considered, and, if possible, the presence of flaws should be confirmed through secondary means (e.g., manual inspection). As already noted, uncertainties associated with the location of flaws should also be estimated. Based on the uncertainty associated with XCT flaw location, along with uncertainty in time-series data, it is wise to consider overlapping regions or voxels of data for comparison. To enable this, time-series

References

645

data can be rasterized to form a three-dimensional dataset for each sensor modality and neighborhoods (e.g., tiles) extracted. Only then is it wise to leverage statistical or machine learning toolsets which use sensor data as a predictor of flaws.

21.4 Summary Traditional process performance qualification approaches, with some modifications, can be successfully applied to metal additive manufacturing. This requires a cycle of design verification, process definition, material qualification, qualification of the processing system, and continuous performance qualification. Sensor-based quality monitoring enables accelerated qualification. Today, many commercial systems incorporate in situ process sensors and, in some cases, closed-loop control. In the coming years, continued development of methods and data analytics are likely to lead to greater assurance in process and part quality.

21.5 Questions and Discussions • Describe the key steps in developing an AM process performance qualification regimen. • List two potential in situ sensing methods for each of the following metal AM processes: laser powered bed fusion, arc-based directed energy deposition, and laser directed energy deposition.

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Index

A ABCD matrix, 264 Abrasive flow machining, 583 Absorption, 65, 68, 72, 74, 101, 115, 118, 119, 250–252, 278, 283, 285, 286, 288, 289, 291, 292, 295, 296, 299–302, 309–313, 328, 373, 389, 403, 417, 418, 430–432, 437, 470, 475, 504, 514–517, 551, 572 Absorption coefficient, 101, 120–122, 288, 289, 291, 292, 299–301, 312, 430–432, 437, 475, 551 Acoustic sensors, 643 Adaptive slicing, 34, 39, 41–42, 56 Additive friction stir welding, 7, 207 Additivity, 494–496, 538–540, 542, 545 Agglomeration of powder, 71, 93, 417 Aging, 486–488, 490, 491, 498–500, 504, 570, 571, 573, 574, 605, 614, 619, 622, 625 Allotropic transformations, 365, 368, 482, 483, 485, 501, 504, 506, 507, 510, 570, 595 Alloy phases, 362–364 Alloys, 1, 62, 112, 167, 199, 307, 318, 336, 359, 383, 427, 481, 529, 549, 570, 591, 636 Alloy substitution, 551–555, 559, 565 Aluminum alloys, 119, 127, 130, 208, 209, 359, 369–373, 376, 377, 380, 384, 403, 412, 478, 483, 484, 498, 500, 516, 524, 555, 558, 570, 592, 593, 596 AM benefits, 1, 7–10, 206, 221, 224, 235, 238, 565 AM definition, 1 AMF file format, 15–28, 32, 37, 38 Amount transformed, 490, 537, 539

Analytical models, 339–357 Angle of repose, 409, 410, 412, 413, 424 Anneal, 570, 573, 574, 603, 607, 620 Anodic polarization, 622–626, 628 Applications, 2, 15, 70, 114, 171, 195, 221, 259, 300, 331, 340, 359, 461, 482, 527, 549, 570, 592, 635 A priori, 536, 538 Arc, 2, 67, 111, 185, 215, 249, 279, 285, 318, 348, 372, 383, 473, 606, 647 Arc pressure, 302–304 As-built, 56, 57, 464–466, 497, 498, 501, 504, 509, 535, 543, 544, 569, 571, 572, 596, 599–604, 606–608, 613–616, 619, 620, 625, 626, 644, 646 Aspect ration of powder particles, 70, 378 ASTM classification of AM processes, 5–7 ASTM/ISO Standard Terminology for AM, 5 Atomic mobility, 485, 489, 576, 578 Atomization, 84, 102, 134, 317, 318, 384–386, 388, 389, 396, 398, 424 Austenite, 367, 389, 485, 501–504, 554, 563 Avrami component, 495, 537

B Balling, 80 Barrel finishing, 582, 583 Benefits of AM, 1, 7–9, 206, 221, 224, 235, 238, 564 Beta-transus temperature, 368, 482, 506, 507, 580, 603, 604, 607, 620 Binder, 5, 52, 71, 151, 213, 247, 379, 427, 486, 567, 597

© Springer Nature Switzerland AG 2023 S. Joshi et al., Additive Manufacturing with Metals, https://doi.org/10.1007/978-3-031-37069-4

651

652 Binder jetting, 5, 6, 52, 151–171, 192, 213, 247, 285, 379, 411, 413–415, 417, 419, 427, 486, 567, 575, 597, 608, 610, 611 Binder saturation, 166, 414 Blending powders, 558 Book overview and use, 9–10 Boundary conditions, 256, 299, 340, 348, 457 Breakdown potential, 626 Build orientation, 13, 43, 45, 46, 51, 56, 57, 88, 89, 224, 225, 233, 241, 247, 597, 609, 614, 616, 618 Build plan, 134, 638–640 Bulk chemical characteristics of powders, 85, 391, 408, 422, 638 Bulk properties, 318, 320, 332 Buoyancy, 75, 300, 302, 304, 308, 309, 314, 317, 528, 562 Burnishing, 586

C Cahn-Hilliard equation, 529, 547 Camera-based systems, 642 Carbide, 117, 367, 368, 377, 378, 389, 390, 392, 474, 484, 504, 519–522, 559, 625 Carrier solution, 414 Cast, 235, 330, 371, 384, 493, 599, 625, 626 Catchment efficiency, 329, 332 Cellular growth, 464, 478 Centrifugal finishing, 583 Characteristics, 1, 9, 10, 49, 84, 87, 103, 105, 115, 121, 123, 124, 127, 130, 132, 133, 140, 144, 159, 163, 164, 167, 182, 186, 190, 225, 289, 317–321, 326, 330, 331, 359, 361, 363, 367, 369–378, 380, 383–385, 391–414, 417, 419, 421, 422, 424, 436, 450, 481, 485, 486, 489, 490, 501, 510, 511, 529, 536, 537, 547, 551, 552, 555, 556, 559–561, 563, 564, 571, 581, 583, 584, 591–627, 636, 639–641 Charpy test, 616 Chemical composition, 62, 84, 134, 399, 400, 417, 423, 492, 591, 593, 636 Chemical free energy, 445, 446, 529, 530 Chemical homogeneity, 570, 571 Chemical polishing, 587 Chemical post processing, 571 Chemistry, 62, 80, 93–94, 317–320, 384, 400, 403, 503, 549, 555, 556 Circularity of powder particles, 319 Classification based on material consolidation, 7 Cobalt-chromium, 105, 127, 368, 370, 372, 373, 380, 390, 484, 522, 551, 594

Index Coefficient of thermal expansion, 344, 369, 563, 564 Cohesive strength of powder, 404 Cold spray, 202–207, 218, 219 Columnar dendritic growth, 473 Compact tension test, 617 Computational grid, 532, 533, 535 Computational methods, 228, 342 Computational models, 342–356 Computational thermodynamics, 522, 530, 540, 541, 562, 565 Computed tomography, 26, 319, 399, 641, 643 Concentration, 100, 224, 225, 299, 327, 329, 335, 375, 400, 438, 439, 444, 453–459, 470, 472–474, 486, 497, 501, 502, 515, 519, 520, 522, 528–531, 533–535, 541, 547, 550, 551, 556, 558, 563, 578, 609, 613, 615, 617 Concentration profile, 454, 533, 534, 550 Conduction, 74, 81, 185, 267, 297–299, 301, 305, 306, 343–345, 355, 433, 439, 450, 467, 475, 528, 547 Conductivity, 86, 100, 102, 185, 288, 292, 300, 324, 325, 339, 343, 345, 346, 355, 359, 369, 370, 372, 373, 377, 403, 417, 591, 592, 621, 627 Conserved concentration, 533 Constitutional undercooling, 453, 459–463 Constitution of alloys, 361–365 Contact transfer, 330 Continuous-cooling-transformation (CCT) diagrams, 495–497, 504, 505, 507–510, 544 Convection, 73, 74, 121, 185, 299, 300, 303, 304, 306, 307, 344, 348, 350, 355, 357, 450, 462, 467 Cooling curve, 439, 440, 496, 497, 505, 538–540, 547 Cooling rate, 44, 88, 102, 126, 128, 181, 182, 431, 436, 437, 439, 452, 476–478, 490–492, 495, 496, 499, 501, 503–508, 510, 524, 542, 554, 569, 571, 576, 595, 596, 642 Copper alloys, 200, 369–371, 376, 516, 592, 594 Corrosion potential, 560, 561, 563, 622 Corrosion resistance, 86, 127, 189, 367–369, 372, 377, 504, 506, 551, 592, 613, 622, 625, 627 Cost, 1, 8, 44, 45, 53, 54, 81, 84, 85, 94, 104, 105, 115, 135, 136, 171, 205, 207, 214, 221–247, 267, 278, 383, 384, 388, 389, 400, 419, 567, 580, 584, 586, 587, 641 Cost models, 235–237, 239, 241, 246

Index Cost vs. production volume, 236 Cracking, 89, 93, 100, 127, 134, 137, 224, 335–337, 369–371, 373, 374, 378, 502, 551, 555, 556, 560, 561 Cracks, 92, 134, 200, 360, 375, 556, 571, 575, 581, 612, 617, 621 Crystallographic orientation, 445, 511, 512, 514

D Data representation, 14–32 Debinding, 167, 176, 186, 189, 190, 192, 414, 567, 569, 575–580, 608–611 Defects, 6, 42, 76, 91, 107, 122, 125, 131, 134, 148, 157, 244, 312, 325, 335, 336, 360, 366, 378, 391, 517, 524, 567, 572, 581, 591, 592, 597, 605, 609, 613–618, 627, 638, 641 Deformation based AM, 195–219 Delamination, 134, 206 Densification, 53, 70, 72, 152, 165, 166, 187, 321–322, 578, 579 Density of powder particles, 396–399, 424 Denudation, 76, 322–324 Design, 1, 7–9, 13, 14, 22, 39, 44, 45, 51, 53, 55–57, 61, 63, 68, 114, 118, 120, 125, 141, 142, 156, 157, 167, 174, 180, 186, 187, 190, 200, 203, 212, 221–247, 255, 261, 269, 360–362, 374, 376, 385, 396, 412, 421, 497, 498, 522, 546, 567, 571, 576, 581, 582, 584, 587, 591, 592, 597, 608, 612, 616, 617, 622, 627, 633–640, 645 Design and process definition, 635, 637 Design for AM (DfAM), 223–227 Design requirements, 584, 591, 636 Design specifications, 567 Destructive testing, 637 Diffusional reactions, 482, 485–501, 504, 506, 507, 537, 538, 540, 542, 546, 547 Diffusivity, 339, 450, 488 Dilution, 121, 122, 440, 441, 549–553, 555–557 Dimensionless numbers, 159 Dimensions, 3, 8, 14, 25, 37, 40, 49, 71, 104, 134, 135, 137, 140, 143, 144, 159, 167, 173, 184, 188, 190, 199, 212, 222, 226, 227, 231, 372, 373, 393, 436, 549, 551, 552, 567–569, 580, 581, 587, 617, 637 Directed energy deposition (DED), 2–6, 111–148, 212–214, 267, 283, 307, 313, 317, 325–329, 348, 373, 374, 378, 379,

653 383, 404, 408, 411, 415, 417, 419, 423, 424, 427–431, 434, 436–437, 440, 450, 463–469, 473, 475–479, 482, 483, 498–500, 506, 508, 509, 511, 516, 517, 522, 534, 535, 541–543, 545, 548, 549, 551–553, 556, 558, 559, 562–564, 567, 596, 605, 606, 608, 615, 622–627, 645 Direct laser melting system (DMLS), 59 Direct slicing, 42–43 Discretization, 238, 532, 533, 538, 540, 542, 546 Dislocations, 366, 367, 470, 486, 487, 497, 498 Distortion, 43, 44, 53–56, 61, 68, 93, 134, 137, 147, 200, 245, 335–337, 348, 349, 353–356, 366, 367, 507, 510, 552, 635, 639, 640, 643, 644 Drag finishing, 582–586 Drilling, 1, 581 Driving force for solidification, 441–445, 460, 478 Droplet formation, 158–160, 162–164, 174 Droplet on demand, 155–157, 161 Droplet substrate interaction, 158–164 Ductility, 146, 336, 367–370, 373, 503, 507, 561, 570, 571, 591, 592, 596, 597, 605, 608, 609, 615, 616

E Eager and Tsai, 342 Early AM patents, 195 Ebeam DED, 139, 148 Economic justification, 219 Effective activation energy, 495 Electric arc, 2, 3, 111, 135, 141, 278–283, 301, 303, 313, 314, 318, 348, 384, 400 Electro chemical post processing, 498, 501, 571 Electrochemical response, 335–337, 344–345, 622 Electron beam, 3, 4, 59–107, 120, 135, 138–141, 147, 249, 269–279, 282, 283, 285, 293–296, 299, 301, 305, 313, 314, 318, 324, 330, 331, 348, 350, 373, 378, 400, 415, 428, 450, 465, 467, 476–478, 512, 513, 516, 517, 553, 598, 599, 602, 606, 607, 615, 640 Electron beam propagation, 274–277 Electro polishing, 624 Element activation, 346 Ellingham diagrams, 518, 519 Elongation, 133, 319, 422, 592, 596–599, 601, 603, 605, 606, 609, 610

654 Energy density, 63, 72, 76, 78, 79, 82, 92, 102, 122–124, 126, 128, 129, 133, 140, 250, 252, 282, 378, 431–433, 463–465, 475–478, 517, 529–533, 552, 555, 595, 596, 615, 626 Energy-dispersive x-ray (EDX), 319, 399, 401, 473, 474, 497 Energy-dispersive x-ray spectroscopy (EDS), 399, 400, 402, 493, 497 Energy propagation, 249–283 Energy transport, 10, 428, 450 Enthalpy, 300, 440–442, 444, 451 Equiaxed growth, 463 Equilibrium composition, 439, 456 Equilibrium constant, 515, 518 Equilibrium fraction, 539 Errors in STL files, 22–27 Eutectic, 363, 369, 444, 455, 458, 473, 530 Extrusion based AM, 151–192, 608

F Fatigue, 375, 376, 422, 581, 583, 584, 586, 592, 609–618, 627 Fatigue endurance limit, 376, 613 Fatigue limit, 376, 613, 614 Fatigue strength, 76, 92, 374, 376, 613, 614, 616, 627 Fatigue testing, 375, 376, 612, 615 Feedback control, 330, 640 Feed-forward control, 640 Feedstock, 1, 4, 7, 10, 44, 59, 61, 62, 72, 76, 84, 89, 92, 102, 105, 111, 120–123, 128, 130, 131, 133, 135, 141, 164, 165, 176, 179–182, 184–186, 189, 190, 196, 207–209, 211, 236, 240–244, 249, 282, 314, 317–332, 371, 373, 374, 383–424, 428, 549–557, 564, 575, 591, 597, 606, 608, 622, 623, 635, 636, 639, 640 Feedstock delivery, 249, 317–332 Ferrite, 485, 501–505 Filament, 97, 176–179, 182, 183, 186, 189–190, 270, 272, 273, 278, 413, 415, 424, 575, 587, 608, 610, 611 Flaws, 375, 621, 638, 644, 645 Flowability, 84, 85, 102, 115, 130, 163, 165, 320, 331, 391, 405–409, 412, 418, 424, 425, 636 Flow function, 407, 424 Fluence, 429–432, 436, 437, 463, 465, 475, 476, 478, 551, 552, 555, 558, 595–597, 627 Fraction of solid, 364, 438, 439, 453, 457

Index Fracture toughness, 375, 376, 422, 571, 591, 617–621 Free energy, 441–449, 451, 479, 514, 515, 518–522, 529–533, 541, 547 Free energy density, 529–533 Free-flight transfer, 330 Functionally graded materials, 121, 135, 214 Furnace atmosphere, 572, 578 G Galvanic corrosion, 556, 560, 561, 565 Gas atomization, 84, 102, 318, 384, 385, 388, 389, 398, 424 Gas flow, 14, 50–52, 60, 62–63, 69, 76, 107, 117, 119, 120, 142, 281, 303, 304, 322–324, 327, 329 Gas pycnometry, 320, 398, 399 Gaussian heat source, 342 Ginsberg-Landau equation, 529 Gradient energy, 528 Grading, 186, 527, 549, 555–565 Grain boundary strengthening, 366, 367, 377, 484, 485, 605 Green part, 151–153, 164, 166, 170, 171, 173, 176, 186, 567, 575 Grinding, 213, 319, 377, 389, 581–583 Growth, 2, 7–9, 71, 88, 128, 143, 146, 209, 364–366, 375, 445, 449–459, 461–464, 467–469, 473, 475, 476, 478, 482, 486–490, 492, 493, 495, 497, 499, 503, 507, 511, 512, 515, 528, 533–538, 541–547, 570, 571, 608, 609, 612, 617, 621 Growth rate, 88, 462–464, 467, 475, 490, 534 H Hall flow meter, 408–410 Hardness, 76, 143, 189, 200, 205, 367, 368, 373, 374, 377, 412, 490, 491, 498, 499, 504, 522–524, 551–554, 563–565, 570, 584, 586, 591, 592 Hatch spacing, 46, 49, 77, 78, 80, 102, 122–126, 130, 204, 206, 342, 432–435 Heating, 5, 53, 62, 70, 71, 76, 87, 88, 93, 97, 100, 102, 120, 128, 137, 142, 143, 156, 167, 173, 180, 187, 196, 205, 208, 218, 242, 249, 270, 273, 280, 282, 285, 294, 296–314, 322, 325, 326, 328, 329, 335, 336, 341, 342, 365, 366, 403, 414, 418, 419, 428–430, 436, 437, 439, 440, 475, 481, 482, 490, 491, 493–495, 515, 527, 536, 538, 543, 545, 546, 570, 572, 575, 576, 578, 579, 644

Index Heat source, 1, 4, 5, 7, 111, 122, 123, 126, 128, 170, 285, 293, 299, 300, 304, 331, 335, 339–342, 346, 348, 350, 353, 404, 415, 419, 421, 427–434, 436, 450, 464, 468, 475, 481, 549, 559 Heat treatment, 14, 53, 88, 89, 188, 209, 211, 225, 366, 367, 484, 500, 501, 504, 535, 552, 567, 570–574, 603, 605, 608, 614, 623, 624, 626 Helix, 330 Heterogeneous nucleation, 364, 445–449, 451, 494, 507, 512 History of AM, 2–4 Homogenization, 74, 228, 486, 493, 501, 570, 571 Hot isostatic pressing (HIP), 53, 169–171, 188, 225, 567, 570–572, 600, 614–616, 627 Hybrid AM, 195–219 Hybrid element activation, 346 Hydrides, 522 Hygroscopy, 412

I Imaging, 53, 86, 132, 158, 162, 306, 307, 313, 328, 391, 392, 394, 395, 398, 419, 641–643 Inactive element activation, 346 Inductively coupled plasma-mass spectroscopy (ICP-MS), 319, 399, 400, 402 Infill, 46–49, 80, 81, 83, 93, 104, 186–188 Inkjet droplet, 154–158 In-situ sensing, 641, 647 Interface stability, 459–463, 534 Introduction to AM, 1–11 Inverse bremsstrahlung, 301, 311, 312 Izod test, 616

J Johnson-Mehl-Avrami-Kolmogorav (JMAK) relationship, 495, 537, 538, 540, 541, 547

K Keyhole/key hole, 75, 80, 92, 134, 299–302, 305–307, 314, 517 Kinetics, 99, 100, 105, 140, 161, 182, 202, 272, 279, 282, 293, 294, 365, 398, 399, 428, 449, 488, 489, 491, 493–495, 501, 520, 528, 536–538, 540–547, 578–580

655 L Lack of fusion, 80, 92–93, 125, 131, 134, 325, 336, 517, 524, 597, 605, 616 Laser, 2, 37, 59, 111, 151, 214, 243, 247, 285, 318, 348, 396, 428, 481, 534, 551, 583, 598, 640 Laser beam propagation, 257–265 Laser delivery systems, 64, 107 Laser diffraction, 396, 397, 420 Laser focusing, 66 Laser polishing, 586 Laser powder bed fusion, 3, 103, 308, 616, 618, 621, 638 Laser powder feed DED, 135 Laser scanning, 59, 322 Laser shock peening, 586 Latent heat of fusion, 300, 440, 442 Lattice structures, 45, 94, 104, 106, 221, 230–234, 247, 486, 492, 513, 514, 569 Layer-wise, 239, 240, 353–357, 643 Lever rule, 440, 441 Liquidus temperature, 128, 366, 438–440, 459, 460, 468, 483, 526, 530 Logging, 641

M Machine learning (ML), 641, 643, 647 Machining, 8, 14, 53, 111, 135, 137, 147, 149, 199, 200, 202, 211–218, 234, 377, 412, 568, 569, 572, 581, 583–586, 614 Magnetic deflection, 273, 275–277, 283 Magnetic focusing, 273, 276, 283 Marangoni convention, 121, 300, 302, 306–308, 528 Martensite, 367, 368, 389, 475, 476, 484, 503–505 Mass flow rate, 116, 122, 124, 125, 130, 131, 182, 326, 327, 329, 411, 549, 558 Mass transport, 70, 528, 576 Master Sintering Curve (MSC), 578, 580 Material addition, 1, 373 Material extrusion, 5, 6, 176, 383, 413, 415, 424, 587 Material interactions, 285–314, 634, 641 Material jetting, 5, 6, 172–175, 192, 413, 414, 427, 486, 567, 575, 608 Material properties, 10, 28, 56, 72, 79, 84, 122, 128–130, 180, 189, 196, 213, 225, 227, 249, 299, 313, 339, 340, 342, 354, 365, 379, 380, 422, 424, 427, 536, 561, 569, 592, 596, 599, 641 Material qualification, 638, 647

656 Material response, 10, 87, 128, 342, 428, 430, 436, 438, 439, 484, 486, 490, 536, 542, 592, 607 Mechanical post processing, 571 Mechanical properties, 9, 10, 44, 62, 72, 76, 88, 92, 121, 129, 134, 140, 143, 146, 211, 317, 342, 360, 361, 369, 371, 419, 422, 427, 483, 486, 501, 503, 511, 536, 547, 564, 569, 571, 572, 584, 586, 587, 591–627 Media blasting, 582, 583 Melt flow, 304, 306, 314, 318 Melting, 1, 37, 59, 115, 151, 195, 244, 282, 285, 325, 335, 362, 384, 427, 481, 528, 551, 569, 595, 646 Melt Pool Evolution, 74–76 Metallic systems, 6, 10, 359, 360, 366–370, 373, 377, 380, 384, 403, 439, 483–485, 497, 501, 510, 514, 515, 569, 570, 592 Metal matrix composites (MMCs), 117, 377–380, 389, 411, 559 Metal transfer, 330–332 Method of images, 340–342 Microsegregation, 470–475 Microstructural analysis, 342, 522, 637 Microstructure formation, 88, 102, 122 Micro structures, 10, 43, 76, 122, 152, 207, 317, 361, 389, 427, 481, 527, 561, 567, 593 Milling, 1, 214, 216–218, 317, 389, 581 Modeling, 5, 13, 19, 42, 56, 74, 88, 257, 298, 303, 308, 328, 343, 345, 346, 356, 391, 463, 494, 495, 527–548, 584, 608 Moisture content, 85, 373, 405, 412, 418 Monitoring system output, 640–643 Morphology, 72, 76, 84, 85, 88, 101, 102, 121, 128, 146, 163, 165, 190, 319, 320, 342, 364, 365, 379, 385, 388, 393, 437, 449, 450, 452, 453, 459, 461–470, 472, 473, 475, 479, 485, 501, 503, 507, 511, 524, 528, 533, 534, 595, 605, 616 Multiaxis DED systems, 214–216 Multi-material, 549 Multi material parts, 202, 214, 217

N Neural networks, 643 Nickel alloys, 86, 308, 359, 371, 378, 380, 593 Nitrides, 367, 379, 380, 389, 390, 392, 516, 519–523, 559 Non-destructive inspection, 637 Non-isothermal reactions, 536, 539, 540, 543

Index Nucleation, 364–366, 445–449, 451, 468, 478, 479, 482, 486–490, 492, 494, 495, 497, 499, 507, 512, 515, 528, 537, 538, 543, 545, 546, 570 Nucleation rate, 449, 488, 490 Numerical models, 328, 391

O Ohnesorge number, 159, 161 Optical coherent tomography, 643 Optical emission spectroscopy (OES), 399, 400, 402 Optical image analysis, 394 Optics, 2, 63, 64, 66, 94, 114, 115, 133, 214, 260, 262, 266, 267, 269, 270, 278, 283, 289, 328, 640, 641 Orientation, 13, 27–29, 39, 43–46, 51, 55–57, 81, 88, 89, 134, 140, 143, 146, 167, 224, 225, 233, 239–241, 247, 361, 379, 445, 473, 475, 511–514, 596–303, 599, 601, 605, 606, 608–610, 614, 616, 618–621, 627, 639, 640 Over-aged condition, 487, 488 Overhangs, 43–45, 81, 152, 170, 172, 176, 187, 216, 226, 233, 635 Oxidation, 60, 62, 113, 174, 187, 202, 205, 214, 278, 281, 368, 373, 376–378, 388, 419, 569, 572, 573, 622 Oxides, 62, 80, 99, 119, 141, 196, 200–201, 205, 244, 274, 291, 324, 378, 388, 390, 403, 412, 417, 516–522, 577, 578, 626

P Packing density, 61, 84, 102, 154, 165, 166, 247, 396, 405, 406, 576, 636 Packing efficiency, 409 Particle microstructure, 319 Partitioning of solute, 452–459, 470 PBF, see Powder bed fusion (PBF) Performance requirements, 359, 360, 374, 633, 634, 637 Phase diagram, 362–365, 380, 438–440, 444, 453, 454, 458, 470, 485–487, 501, 502, 530, 540, 541, 562–565 Phase field (PF) modeling, 528, 533, 536 Phase field parameters, 528–531, 533 Photodetectors, 642, 643 Photodiodes, 642, 643 Physical characteristics of powder, 391–403, 417, 419, 424 Pitting corrosion, 626

Index Plasma, 4, 111, 124, 135, 141, 142, 149, 279–283, 285, 296–298, 300, 303, 306, 309–314, 318, 319, 329, 372, 374, 383, 388–390, 399, 400, 424, 587 Plasma arc DED, 111, 141, 142, 149 Plasma electrolytic polishing, 587 Plasma rotating electrode process (PREP), 124, 318, 388–390, 424 Plastic deformation, 195, 196, 200, 202, 205, 207, 335, 366, 375, 406, 586, 597 Point source, 339, 340 Pole figure diagrams, 512–514 Polishing, 213, 268, 319, 582, 583, 586, 587, 615, 616, 624, 625 Porosity, 10, 53, 89–93, 102, 134, 165, 168, 169, 171, 188, 190, 205, 206, 230, 306, 319, 373, 389, 396, 398, 399, 403, 514–517, 524, 567, 575, 587, 597, 605, 609, 616, 626 Post-processing, 1, 9, 53, 57, 188, 192, 213, 223, 225, 236, 241, 245, 246, 501, 567–587, 591, 592, 597, 598, 605, 608, 614–616, 626, 627, 635 Powder, 2, 14, 59, 111, 151, 202, 225, 267, 291, 317, 350, 371, 383, 427, 482, 551, 567, 596, 636 Powder aggregate, 403–414, 424 Powder attributes, 396, 410, 412 Powder bed fusion (PBF), 2, 3, 5, 6, 46, 48, 49, 52, 59–107, 111, 113, 115, 117, 118, 120, 122, 134, 139, 140, 148, 152, 154, 171, 190, 211, 213, 216, 217, 239–241, 244–246, 267, 269, 278, 283, 308, 309, 312, 317, 318, 321–325, 350–356, 378, 379, 383, 386, 404, 411–414, 417, 419–424, 427, 428, 433–437, 440, 449, 450, 452, 464, 466, 475–479, 493, 497–499, 506, 508, 509, 512, 513, 524, 587, 596–599, 601, 603, 605, 613–616, 618, 619, 621, 624–628, 638, 640–643 Powder blown, 325, 329, 331, 332 Powder characteristics, 84, 132, 133, 163, 167, 317–321, 331, 385, 391–413, 421, 422, 636 Powder compaction, 154, 155, 320, 391 Powder delivery, 60–62, 90–92, 116, 154, 641 Powder delivery systems, 115–117 Powder feed parameters, 204 Powder flowability, 84, 85, 165, 320, 405, 409, 424 Powder layer defects, 91 Powder packing, 93, 391, 405, 409, 410

657 Powder packing density, 405 Powder properties, 85, 120, 167, 317–321, 332, 411, 421 Powder rheometer, 406, 410, 411 Powder shape, 385, 392–394, 404, 413 Powder size, 84, 165, 190, 326, 385, 386, 390, 395–398, 414, 422, 559, 577, 578 Powder spreading, 91, 93, 94, 100–102, 152, 154, 155, 165, 166, 327 Powder spreading systems, 60–62, 154 Powder storage and handling, 245, 417–424 Power density, 65, 66, 77, 93, 102, 115, 120, 293, 586 Power of heat source, 5, 464 Precipitation strengthening, 365–367, 369, 370, 483, 484, 488, 493, 498, 499, 504, 556, 570, 596, 605, 608 PREP, see Plasma rotating electrode process (PREP) Process behavior, 634, 639, 641–645 Process conditions qualification, 637 Process monitoring, 139, 140, 638, 640 Process parameter, 14, 42, 48, 55, 69, 76–84, 87, 92, 93, 107, 121–126, 128, 140, 141, 143, 144, 148, 164–167, 175, 181, 186–188, 199–200, 202, 204–207, 240, 241, 342, 354, 434, 465, 467, 637 Process performance qualification, 634–638, 647 Process qualification record, 637 Process system qualification, 636–637 Properties, 4, 32, 62, 115, 145, 213, 227, 317, 346, 371, 385, 427, 440, 490, 536, 598

Q Quasi-steady state, 433, 434, 436, 478, 534 Quiet element activation, 346

R Radiation, 63, 73–76, 115, 250, 251, 280, 294–299, 312, 314, 343, 348, 350, 396, 399, 400, 450, 467 Rate constant, 494, 537, 538, 541, 579 Rate of reaction, 491 Recycling of powder, 103, 417–424 Reduction reaction, 376, 578 Reflection, 72, 74, 121, 255, 266, 268, 272, 286, 289–293, 301, 312, 328, 498, 512 Refractory metals, 281, 359, 377, 378, 389 Regular solution, 529, 530

658 Residual stress, 44, 46, 47, 53, 61, 82, 89, 93, 94, 100, 102, 134, 137, 140, 143, 147, 148, 182, 185, 195, 196, 205, 208, 224, 245, 335, 336, 352, 486, 567, 570–572, 586, 616, 640 Resistance heating based DED, 142–143 Reynolds number, 159 Rheology, 406 Rosenthal, 339–340, 342 Roundness of powder particles, 394 Run-out, 612

S Sanding, 583 Scanning Electron Microscopy (SEM), 89, 167, 169, 319, 390, 393, 398, 399, 416, 419, 420, 452, 512 Scanning strategies, 47, 80 Scheil relationship, 457, 458 Secondary Ion Mass Spectroscopy (SIMS), 403 Selective laser melting (SLM), 2, 3, 37, 59, 167, 583 Sensing, 134, 638, 641–643, 647 Sensor-based quality assurance, 638–647 Sensors, 8, 53, 100, 119, 180, 202, 217, 634, 641–647 Shape reference for powders, 393 Shot peening, 586 Sievert’s law, 515 Sieves, 319, 386, 395 Sieve size, 386, 395 Simulation, 10, 13, 53–55, 74, 118, 232, 240, 278, 295, 308, 309, 339, 345, 346, 348, 350, 352–357, 428, 429, 434, 436, 527, 533–536, 543, 544, 546, 547, 584, 635, 640 Sintering, 2, 5, 59, 65, 69–72, 100, 102, 151, 152, 164–171, 173, 176, 182, 186–190, 256, 323, 335, 379, 389, 414, 415, 427, 486, 567, 569, 575–580, 587, 608–611, 627 Size distribution, 71, 80, 84, 92, 186, 291, 318–320, 324, 385, 386, 389, 392, 395–397, 405, 414, 421, 422, 424, 578 Size histogram, 395 Slicing, 15, 22, 24, 26, 32–44, 46, 56, 78 S-N curve, 376, 612 Solidification, 1, 5, 6, 10, 71, 73, 74, 87, 88, 93, 102, 119, 120, 126–128, 134, 140, 146, 182, 195, 249, 362, 364, 365, 369, 371, 374, 378, 379, 384, 400, 403,

Index 427–478, 481, 485, 487, 499, 502, 510, 511, 516, 528–548, 555, 595, 605, 609 Solidification front, 439, 449, 450, 453, 458, 459, 461, 468, 528, 534 Solidification interface, 453, 456, 460 Solidification morphology, 128, 146, 364, 437, 449, 450, 452, 453, 464–470, 485, 534, 605 Solid solution, 363, 365–370, 373, 377, 421, 483, 486, 489, 501, 502, 507 Solid solution strengthening, 366–370, 373, 377, 421, 483, 484, 507 Solid state AM, 195 Solid state transformations, 10, 128, 365, 437, 473, 475, 481–524, 536–547 Solidus temperature, 71, 73, 364, 365, 428, 437, 438, 462, 530, 579 Solubility, 363, 366, 486, 499, 503, 514–516, 524 Solute, 362, 363, 366, 368, 438, 452–460, 463, 470–474, 486, 488, 528, 534 Solute partitioning, 458 Solute redistribution, 455–457, 459, 472 Solute rejection, 458 Solution anneal, 571–574 Solution heat treatment, 500, 504, 535, 570–572 Solutionizing, 484, 486, 487, 491, 492, 498, 499, 501, 535, 605, 624, 625 Source interactions, 328, 331 Sources, 4, 5, 15, 93, 111, 131–139, 141, 170, 179, 234, 249–283, 285, 286, 299, 301, 312, 325, 328–331, 340–342, 516, 517, 638 Spatter, 63, 76, 91, 93, 114, 121, 312, 323–325, 329, 640, 642 Specific properties, 318–320, 359, 370, 376, 569 Spheroidization, 390 Spot size of heat source, 342 Spreadability, 331, 421 Stainless steels, 75, 85, 119, 127, 170, 189, 302, 309, 367, 368, 372, 373, 379, 380, 388, 401, 423, 424, 478, 483–485, 503–505, 516, 522–524, 560, 561, 563, 565, 592, 622, 624–627 Stimulated emissions, 63, 250–257, 266, 282 STL file format, 15–27 Strength, 5, 43, 46, 76, 92, 134, 143, 146, 152, 166, 167, 173, 187, 189, 190, 205, 211, 230, 256, 272, 276, 288, 289, 335, 359, 361, 362, 366–370, 373–378, 404–407, 411–414, 490, 503, 504, 506, 507, 522, 552, 571, 592, 605, 608, 613, 627

Index Strengthening, 10, 365–370, 373, 377–380, 421, 483–486, 491–493, 496–499, 501–514, 543, 544, 592, 596, 605, 608 Strengthening mechanisms, 366, 367, 380, 483–485, 524, 592 Stress ratio, 612 Stress relief, 245, 246, 482, 486, 569–574, 614–616, 619 Supersaturated solutions, 366, 486, 489, 570 Support structures, 13, 38, 40, 41, 43–45, 53–55, 81, 93, 94, 100, 135, 152, 170, 172, 176, 180, 187, 224, 225, 233, 236, 238, 239, 241–245, 247, 336–337, 342, 567, 569, 581 Surface chemical characteristics of powders, 391 Surface finishing, 40, 43, 44, 48, 49, 53, 71, 89, 104, 132, 143, 173, 212, 225, 247, 569, 580, 581, 583–587, 614, 637 Surface modification, 383, 559, 565, 569 Surface roughness, 40, 41, 44, 71, 76, 137, 147, 160, 188, 199, 212, 241, 291, 319, 404, 581–584, 586, 613, 614, 616 Surface tension, 72–76, 85, 121, 147, 156, 159–161, 164, 166, 300, 302, 306–308, 324, 330, 390, 434, 446, 447, 449

T Temperature history, 342 Temperature prediction, 640 Tempering, 484, 486, 570, 571, 573, 605 Tensile test, 146, 422, 592, 597–599, 601, 603, 606, 610, 616 Texture, 15, 27, 28, 34, 198, 199, 511–513, 605 Thermal cycles, 87, 128, 146, 355, 428, 433–437, 481, 482, 493, 495, 508–511, 527, 538, 542, 546, 547, 578 Thermal fields, 87, 428, 436, 437 Thermal gradient, 44, 88, 128, 185, 434, 449, 450, 460–465, 467–469, 475, 476, 512, 528, 642 Thermal post processing, 569–575, 627 Thermal processing, 567, 572, 578, 580 Thermal response, 10, 79, 87, 122, 427–437, 450, 481–483, 485, 510, 524, 536, 542, 544, 546, 548 Thermodynamic analysis, 520, 522, 530, 541, 562 Thermodynamic equilibrium, 280, 441 Thermo mechanical post processing, 569–575 Three bar analogy, 335–337, 355 3MF file format, 32

659 Time-temperature transformation (TTT) diagrams, 490, 492, 493, 495, 496 Titanium alloys, 4, 105, 119, 127, 141, 167, 318, 336, 359, 368–371, 373, 376, 378, 384, 416, 421, 483, 484, 506, 507, 510, 516, 543, 570, 572, 592, 596, 627 Tomography, 398, 399, 643 Tool path generation, 37, 42, 46–51 Tool steels, 103, 127, 167, 189, 371, 372, 484, 504, 505, 570, 592, 593, 605, 627 Topology optimization, 8, 45, 56, 94, 221, 224, 227–230, 247 Toughness, 359, 360, 367, 368, 374–376, 378, 422, 486, 503, 552, 570, 571, 573, 591, 595, 616–621, 627 Transformation rate, 489, 494, 495 Transformations, 10, 16, 73, 74, 88, 128, 203, 363, 365–369, 427, 437, 442, 444, 445, 473, 475, 481–524, 527, 536–548, 554, 570, 595, 605 Transpassive region, 622 Tumble finishing, 583 Turning, 1, 581 2D and 3D nesting, 51–52 U Ultimate tensile strength (UTS), 133, 146, 359, 374, 375, 571, 592, 596, 597, 599, 601, 603, 606, 610, 627 Ultrasonic additive manufacturing (UAM), 195–202 Undercooling, 443–445, 447, 449–452, 461–463, 478, 535 Unified numbering system (UNS), 86, 127, 370–372 Unit cost of production, 234 V Vacuum atomization, 384, 389 Value proposition, 221–222, 638 Vaporization, 63, 74, 76, 134, 300, 301, 304–306, 312, 313, 324, 377, 575 Velocity of heat source, 430, 468, 549 Vibratory finishing, 583 Virgin powder, 241, 244, 418, 421–423 Virtual heat source, 340–342 W Water atomization, 84, 317, 384, 385, 388 Wear resistance, 127, 367, 372–374, 377–379, 504, 506, 522, 551–553, 565, 587, 591, 592

660 Weber number, 159, 166 Widmanstatten, 146, 507 Wire, 111, 130, 135, 137–145, 147–149, 174, 207, 215, 226, 245, 246, 281, 282, 297, 303, 317, 329–332, 371, 374, 380, 383, 386, 415–417, 428, 473, 474, 555, 556, 559, 606, 607, 620, 628 Wire feed DED, 135–148 Wire feed parameters, 143–145 Wire feedstock, 282, 317, 329–331, 383, 415–417, 551, 552, 622, 623 Workflow for AM, 13–57, 246

Index X X-ray florescence spectroscopy (XRD), 510, 512 X-ray photoelectron spectroscopy (XPS), 403

Y Yield strength (YS), 134, 146, 211, 230, 335, 366, 374, 375, 407, 411, 592, 597, 599, 601, 603, 606, 610