Mechanical Properties of Nanomaterials (Engineering Materials) 3030746518, 9783030746513

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Engineering Materials

Joshua Pelleg

Mechanical Properties of Nanomaterials

Engineering Materials

This series provides topical information on innovative, structural and functional materials and composites with applications in optical, electrical, mechanical, civil, aeronautical, medical, bio- and nano-engineering. The individual volumes are complete, comprehensive monographs covering the structure, properties, manufacturing process and applications of these materials. This multidisciplinary series is devoted to professionals, students and all those interested in the latest developments in the Materials Science field, that look for a carefully selected collection of high quality review articles on their respective field of expertise. Indexed at Compendex (2021)

More information about this series at http://www.springer.com/series/4288

Joshua Pelleg

Mechanical Properties of Nanomaterials

Joshua Pelleg Department of Materials Engineering Ben-Gurion University Beer Sheva, Israel

ISSN 1612-1317 ISSN 1868-1212 (electronic) Engineering Materials ISBN 978-3-030-74651-3 ISBN 978-3-030-74652-0 (eBook) https://doi.org/10.1007/978-3-030-74652-0 © Springer Nature Switzerland AG 2021 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

Animals should not be abused, hurt or injured and wildlife habitat preserved. Joshua Pelleg

To my wife Ada and my children, Deenah and her late husband Gidon Barak, Ruth and Christer Kallevag, Shlomit and Asher Pelleg and to my grandchildren: Roy, Tal, Rotem and Noa Barak; Ella and Maya Kallevag; and Ofir and Ori Pelleg.

Preface

The purpose of this book is to present and test the mechanical properties of nanomaterials produced by techniques currently used for many various applications of this relatively new structural material. The production of nanomaterial objects is for various materials, such as metallic alloys and ceramics. The chapters considered in this book are outlined in the content. Accordingly, Chap. 1 defines shortly nanomaterials and characterization of the structure is presented in Chap. 2. Basic concepts for producing nanomaterials are discussed in Chap. 3. To understand deformation in general and in particular in nanomaterials, Chap. 4 is devoted to dislocations observed in specimens obtained in nanomaterials. These are observed in nanomaterials above 30 nm, but below this size partial dislocations and grain boundary sliding (GBS) mechanism are involved in the deformation process. The chapter establishes the theoretical foundations of the mechanical properties regardless if the production considers nanosize material or macrosize materials by conventional techniques. It sets the theoretical background of the experimental observations. Following the basic concept related to deformation and responsible for their occurrence under stress, namely dislocations, partial dislocations and grain boundary sliding deformation phenomena in nanomaterial specimens are discussed in Chap. 5. In Chap. 5, static deformation tests of the nanomaterial specimens are discussed, among them tension, compression and hardness. These test results are compared with similar tests but of macrosize specimens obtained by conventional fabrication methods. Dynamic deformation, time-dependent deformation (creep), cyclic deformation (fatigue) and fracture in specimens obtained in nanosize samples are presented in Chaps. 6–9, respectively. Again similar test results obtained by conventional fabrication are compared with those of the nanosized specimens. I would like to express my gratitude to all publishers and authors for permission to use and reproduce some of their illustrations and microstructures.

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Preface

Finally, without the tireless devotion, help, understanding and unlimited patience of my wife Ada, I could never have completed this book, despite my decades of teaching in this field; her encouragement was essential, and her helpful attitude was instrumental in inspiring to write this book. Beer Sheva, Israel

Joshua Pelleg

Contents

1 What Are Nanomaterials and Why the Interest in It . . . . . . . . . . . . . . .

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2 Basic Concepts for Producing Nanomaterials . . . . . . . . . . . . . . . . . . . . .

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3 Structure and Classification of Nanomaterials . . . . . . . . . . . . . . . . . . . .

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4 Imperfections in Nanomaterial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Deformation in Nanomaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Dynamic Deformation—The Effect of Strain Rate . . . . . . . . . . . . . . . . . 181 7 Time Dependent Deformation-Creep in Nanomaterials . . . . . . . . . . . . 257 8 Cyclic Deformation-Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 9 Fracture in Nano-Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519

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About the Author

Joshua Pelleg received his B.Sc. in chemical engineering at the Technion Institute of Technology, Haifa, Israel; a M.Sc. in metallurgy at the Illinois Institute of Technology, Chicago, IL; and a Ph.D. in metallurgy at the University of Wisconsin, Madison, WI. He has been in the Ben-Gurion University of the Negev (BGU) Materials Engineering Department in Beer Sheva, Israel, since 1970, was among the founders of the department and served as its second chairman. He was the recipient of the Samuel Ayrton Chair in Metallurgy. He specializes in the mechanical properties of materials and the diffusion and defects in solids. He has chaired several university committees and served four terms as Chairman of Advanced Studies at Ben-Gurion University of the Negev. Prior to his work at BGU, he acted as Assistant Professor and then Associate Professor in the Department of Materials and Metallurgy at the University of Kansas, Lawrence, KS. He was also Visiting Professor in the Department of Metallurgy at Iowa State University; at the Institute for Atomic Research, US Atomic Energy Commission, Ames, IA; at McGill University, Montreal, QC; at the Tokyo Institute of Technology, Applied Electronics Department, Yokohama, Japan; and in Curtin University, Department of Physics, Perth, Australia. His non-academic research and industrial experience includes: Chief Metallurgist in Urdan Metallurgical Works Ltd., Netanyah, Israel; Research Engineer in International Harvester Manufacturing Research, Chicago, IL; Associate Research Officer for the National Research Council of Canada,

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About the Author

Structures and Materials, National Aeronautical Establishment, Ottawa, ON; Physics Senior Research Scientist, Nuclear Research Center, Beer Sheva, Israel; Materials Science Division, Argonne National Labs, Argonne, IL; Atomic Energy of Canada, Chalk River, ON; Visiting Scientist, CSIR, National Accelerator Centre, Van de Graaf Group Faure, South Africa; Bell Laboratories, Murray Hill, NJ; and GTE Laboratories, Waltham, MA. His current research interests are mechanical properties, diffusion in solids, thin-film deposition and properties (mostly by sputtering) and the characterization of thin films, among them various silicides.

Chapter 1

What Are Nanomaterials and Why the Interest in It

Generally, nanomaterials are defined as a substance where at least one dimension is less than 100 nm (1 nm = 10–6 mm = 10–9 m) thus in a scale, comparable to that of atoms and molecules. However, there are significant differences among researchers on the more precise definition of a nanomaterial. Thus, the European Commission defines nanomaterials as “a natural, incidental or manufactured material containing particles, in an unbound state or as an aggregate or as an agglomerate and where, for 50% or more of the particles in the number size distribution, one or more external dimensions is in the size range 1 nm–100 nm". Here, the concept of classifying nanomaterials after Dr. Jha is given as: (1) (2) (3) (4)

zero-dimensional (0-D), one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D).

(1)

Materials dimensions measured in all directions are within the nanoscale, not larger than 100 nm. The most common representation of zero-dimensional nanomaterials are nanoparticles, which can be metallic, ceramic or polymeric in various shapes and forms. Further, they can be amorphous, crystalline, single crystals or polycrystals. They can exist indivdually (see Fig. 1.1) or as agglomerate (cluster) incorporated in a matrix (see Fig. 1.2).

(2)

One-dimensional nanomaterials. In this case one dimension is outside the nanoscale and two dimensions are within the nanoscale. This leads to needle like-shaped nanomaterials. Also nanotubes, nanorods, andnanowires are 1-D nanomaterials. The type of matrial can be the same as listed in (1). An example is illustrated in Fig. 1.3. A schematic illustration of a 1-D nanomaterial is seen in Fig. 1.4.

(3)

Two—D (dimensional) nanomaterials. In this case two dimensions are not confined to the nanoscale. In other word the 2-D nanomaterials exhibit platelike shapes. Nanofilms, nanolayers and nanocoatings belong to this class of

© Springer Nature Switzerland AG 2021 J. Pelleg, Mechanical Properties of Nanomaterials, Engineering Materials, https://doi.org/10.1007/978-3-030-74652-0_1

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1 What Are Nanomaterials and Why the Interest in It

Fig. 1.1 Nanoparticles where d ≤ 100 nm in all dimensions. After Dr. P. Jha. Fundamentals of nanomaterials (1918)

Fig. 1.2 An agglomerate of nanoparticles. After Dr. P. Jha. Fundamentals of nanomaterials (1918)

(4)

nanomaterials. Again all the type of materials can be the same as listed in (1). An illustration of 2-D nanomaterial is shown in Fig. 1.5. Bulk nanomaterials are materials that are not confined to the nanoscale in any dimension. These materials are thus characterized by having three arbitrarily dimensions above 100 nm. Materials possess a nanocrystalline structure or involve the presence of features at the nanoscale. In terms of nanocrystalline structure, bulk nanomaterials can be composed of a multiple arrangement of nanosize crystals, mostly in different orientations. 3-D nanomaterials can contain dispersions of nanoparticles, bundles of nanowires, and nanotubes and multinanolayers.

All dimensions of the nanosacale showwing 0-D, 1-D. 2-D and 3-D nanomaterials are shown schematically in Fig. 1.6. Thus, nanomaterials have extremely small size which having at least one dimension 100 nm or less. In other words, nanomaterial can be nanoscale in one dimension, for example surface film, two dimension fibers for example, or three dimensions, e. i.

1 What Are Nanomaterials and Why the Interest in It

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Fig. 1.3 An example of 1-D nanomaterial. After Dr. P. Jha. Fundamentals of nanomaterials (1918)

Fig. 1.4 A scematic illustration of 1-D nanoscale. The nanomaterials can be nanowires, rods and nanotubes. After Dr. P. Jha. Fundamentals of nanomaterials (1918)

particles. Common nanoscale types include nanotubes, quantum dots and fullerens. Evidence shows that the same substance behaves differently at nanoscale compared to its larger-scale counterpart. This allows the development of light-weight materials with high strength, high conductivity but also with high chemical reactivity (this reactivity makes nanomaterials metastable). The physical and chemical properties often differ from those of bulk materials, however the mechanical properties are expectedly differnt from those of macrosize bulk material because of the size effect. Small scale specimens show improved strength properties such as UTS, yield stress, hardness

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1 What Are Nanomaterials and Why the Interest in It

Fig. 1.5 An illustration for a two dimensional nano-material. a in a plate form; b another 2-D form. After Dr. P. Jha. Fundamentals of nanomaterials. (1918)

Fig. 1.6 Three-dimensional space showing the relationships among 0-D, 1-D, 2-D, and 3-D nanomaterials. After Dr. P. Jha. Fundamentals of nanomaterials (1918)

etc. and often better elongation (or as good ductility as the macro-specimens) without expense on the increased strength. The above classification of nanomaterals (in four dimensional categories) as zero-dimensional (0-D) nanoparticles or nanoclusters, one-dimensional (1-D) layer or multilayer nanostructures, two dimensional (2-D) nanograined layers, and three dimensional (3-D), equiaxed bulk solids is due to Professor R. W. Siegel. Professor H. Gleiter also classified nanomaterials according to their chemical composition and crystallite shapes composing solid structures or nanostructures. Nanomaterials are of interest because at this scale unique optical, magnetic, electrical, mechanical and other properties are differetn, usually improved or technologically (and medically) tasks can be performed which would be difficult with macroscale objects. These emergent properties have the potential for great impacts in electronics, medicine, and other fields. Thus for example, it is possible to design

1 What Are Nanomaterials and Why the Interest in It

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pharmaceuticals that can target specific organs or cells in the body such as cancer cells, and enhance the effectiveness of therapy. Understaning mechanical properties of nanomaterials is essential -one could say even crucial- for their proper use in a variaty of industrial applications, like electronic devices, sensors, thin films, composites etc. In the following sections mechanical properties such as creep, fatigue and others will be discussed in order to evaluate the behavior of nanomaterials under the influence of acting stress and to properly apply them in industry. Clearly, in research mechanical strength is a necessary property which can not be overlooked, and therefore intensive studies in the past last decades are devoted in exploring nanomaterials for a better understanding the behavior and the proper technological application. Thus, nanomaterial as nanocomposites (equivalent to its macro-scale materials) find a variety of applications in industry as well as in research. The rate controlling deformation mechanism in nanomaterials is an important concept in the understanding of the mechanical behavior of nanomaterials. It turns out that in nanomaterial above 30 nm in the range of 100 nm and above dislocations might play a significant role, however below 30 nm it is believed that grain boundary sliding and partial dislocations are the rate controlling mechanisms. A section is devoted to dislocations and imperfections considering also grain size for dislocation activity.

Chapter 2

Basic Concepts for Producing Nanomaterials

Nanocrystalline structures bridge the gap between molecular (atomic) size and macroscale objects. As mentioned in Chap. 1 the nanoscaled materials are classified as 0-D, 1-D, 2-D and 3-D depending on the spacial dimensions. They exhibit unique properties due to their high surface area to volume ratio. Assuming a spherical particle of say 100 nm, we can express the volume and surface area as follows: The volume of 100 nm particle is 3  π 100 × 10−9 π d3 4 3 = = 5.24 × 10−22 m3 V = πr = 3 6 6

(2.1)

The surface area 2  SA = 4πr 2 = π 100 × 10−9 = 3.141 × 10−14 m2

(2.2)

In this chapter the methods to produce nanomaterials are discussed. There are two approaches to fabricate nanostructures known as (2.1) Bottom-Up approach and (2.2) the Top-Down approach. 2.1.

In this approach materials or its components are reduced to an atomic (molecular) level and is followed by a self-assembly process leading to the formation of the nanostructure. Physical forces operating during the selfassembly process combine basic units into stable structures. Quantum dots formed during eptaxial growth or formation of nanoparticles formed collodial dispersion are example for the bottom-up approach. Bottom-Up approach refers to the build-up of a material from the bottom: atom-by-atom, molecule-by-molecule, or cluster-by-cluster which are of nanoscale range i.e.1 nm to 100 nm or self-assembly of atoms and molecules as in chemical and biological systems. This approach promises better opportunities to obtain nanostructures with less defects, more homogeneous chemical composition, and better short and long range ordering as compared to top-down approach (etching away material, as in building integrated circuits).

© Springer Nature Switzerland AG 2021 J. Pelleg, Mechanical Properties of Nanomaterials, Engineering Materials, https://doi.org/10.1007/978-3-030-74652-0_2

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2.2.

2 Basic Concepts for Producing Nanomaterials

Although the top-down approach has been playing a vital role in the fabrication of nanostructures, it has several limitations such as development of imperfections in processed materials, high cost (lithographic processes), requirement of high surface finished materials and longer etching time. Larger initial structures externally controlable is the technique for the nanostructure fabrication. Severe plastic deformation is an example of nanostructure formation. Ball milling is another example for the nanostructure formation. (note ball milling involves plastic deforation).

Top–Down approach corresponds to using nanofabrication tools that are controlled by external experimental parameters to create nanoscaled structures/functional devices with the desired shapes and characteristics starting from larger dimensions and reducing them to the required values. Several methods are used to fabricate nanostructures using the top-down approach such as photolithography, scanning lithography, laser machining, soft lithography, nanocontact printing, nanosphere lithography, colloidal lithography, scanning probe lithography, ion implantation and diffusion, deposition. The techniques listed below are considered briefly for nanomaterials fabrication:

2.1 Bottom-Up Approach Methods Are Listed Below as 2.1.1 The Atomic Layer Deposition (ALD) Atomic layer deposition (ALD) is a thin film deposition technique where chemical precursors are sequentially introduced to the surface of a substrate where they chemically react directly with the surface to form sub-monolayers of film. As the name implies, it is fundamentally atomic in nature and results in the precise deposition of films on the surface of a selected substrate at the atomic scale. Stated differently, ALD is a vapor-phase thin film growth technique that allows atomic scale thickness contol maintaining uniformity. The sequence of two self-liiting reactions between the gas-phase precursor molecules and a solid substrate involving their reaction until all available surface reaction sites are consumed lies at the base of the ALD process. The ALD process keeps the precursors separated from each other during the sequential deposition cycle thus preventing their reaction and allowing atomic layer-by-layer deposition with complete step coverage. Thus, the process takes place in a chamber where a substrate is placed and at a given temperature and pressure the deposition is enabled on the substrate layer-by-layer. By setting the ALD cycles the deposition thickness can conveniently be controlled. An illustration of ALD for ZnO thin film is seen in Fig. 2.1. Another example is illustrated in Fig. 2.2 to synthesize TiO2 by ALD using trimethyl aluminum (TMA) and water in the ALD reactor. The steps of a single. Cycle deposition process are:

2.1 Bottom-Up Approach Methods Are Listed Below as

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Fig. 2.1 Illustration of ALD for ZnO thin film deposition. Oviroh et al. (2019). Open access. DEZ in the figure stands for diethylzinc

Fig. 2.2 A model ALD process for depositing TiO2 on hydroxyl groups functionalized substrate using TiCl4 and H2 O as precursors. Oviroh et al. (2019). Open access

(1) (2) (3) (4) (5)

Exposure of the first precursor in the reactor chamber to form a layer on the substrate Purge the excess first precursor and the byproducts Exposure of the second precursor Purge or evacuation of the excess second precursor and by-products The process is repeated until the required film thickness is achieved.

Table 2.1 lists the advantages and diadvantages of the ALD process. Several ALD process modes are available such as the plasma enhanced ALD (PEALD). In the thermal ALD reactions occur on the surface (considered a surface driven process) which require relatively high temperatures (150–350 °C) for the reaction (therefore limited application), therfore PEALD can be used instead. ALD enables good thickness control and conformality whatever the substrate geometry

10 Table 2.1 Advantages and disadvantages of ALD. Oviroh et al. (2019). Open access

2 Basic Concepts for Producing Nanomaterials Advantages

Disadvantages

• High-quality films

• The time required for the Chemical reactions

a. Control of the film thickness

• The economic viability

b. Excellent repeatability

• Very high material waste rate

c. High film density

• Very high energy waste rate

d. Amorphous or crystalline film

• Intensive nature of the ALD process

e. Ultra-thrn films

• Nano-particle emissions

• Conformality a. Excellent 3D conformality b. Large area thickness uniformity c. Atomically flat and smooth surface coating • Challenging Substrates a. Gentle deposition process for sensitive Substrates b. Low temperature and stress c. Excellent adhesion d. Coats Teflon • Low-temperature processing • Stoichiometric control • Inherent film guality associated with self-limiting • Self-assembied nature of the ALD mechanism • Multilayer

and reactor design. Three different PEALD types are illustrated shcematically in Fig. 2.3.

2.1.2 Sol–gel Nanofabrication Several liquid phase synthesis exists for precipitating nanoparticles from a solution one of them being the sol–gel processing which is the subject of this section. Note that sol is not same as a solution because in sol, there is a very large number of small particles suspending in another major phase system for example in a liquid phase while the solution is purely one single-phase system. The sol refers to a colloidal

2.1 Bottom-Up Approach Methods Are Listed Below as

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Fig. 2.3 Schematic representation of the three different types of plasma-assisted atomic layer deposition that can be distinguished: a direct plasma b remote plasma, and c radical enhanced. For each type different hardware configurations and plasma sources. Oviroh et al. (2019). Open access

solution containing solid particles (in a liqid phase), while the gel is considered as a solid molecule in a solvent. It is a process for producing solid materials specifically oxides (among them oxides of silicon and titanium). Several stages are involved in the process. In the chemical process the sol (as stated a colodial solution) formed gradually evolves toward the formation of a gel system containing the liquid phase and solid phase particles. The removal of the liquid phase is necessary by some drying method (sedimentation with pouring off the liquid, cetnrifugation to accelerate the process, etc.) for the gel formation. The drying process is accompanied with large shrinkage and porosity formation. The liquid removal rate depends on the porosity in the gel. The microstructure is strongly influenced by the process. A firing process (i.e. heat treaatment) is required for structural stability and enhancing the mechanical properties of the product. A sintering process is often a final stage for inducing further densification which might be accompanied with grain growth. For nanoparticles only controlled grain growth is an option. Figure 2.4 presents an outline of the routes of this mechanism. In this figure xerogel refers to porous solid matrices which can be obtained by drying the gel at low temperature treatments (25–100 °C). The main benefits of sol–gel processing are the high purity and uniform nanostructure achievable at low temperatures and relatively low cost. One of the distinct advantages of using this methodology as opposed to the more traditional processing techniques is that densification is often achieved at a much lower temperature.

2.1.3 Molecular Self Assembly Self-assembly of nanostructures is a process where atoms, molecules or nanoscale building blocks spontaneously arrange themselves in ordered structures or patterns without any human intervention. It is the most promising practical low-cost and high-throughput approach for nanofabrication. The resulting structure has nanometer features. Thus the structure sponaneously forms from the basic building blocks

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Fig. 2.4 Variation steps in the sol–gel process to control the final morphology of the product. M. Niederberger and N. Pinna, in Metal Oxide Nanoparticles in Organic Solvents, Springer, p. 10. Access is enabled by Ben Gurion University,

such as atoms, molecules, or nanoparticles. Known perfect examples are the selfassembled structures in nature such as cells and living organisms. The nanostructure is formed by the spontaneous formation of ordered nanostructures from a random disordered state. One of the figures in Fig. 2.5 illustrates self-assembled metal nanostructure patter. As a matter of fact, various self-assemblies for nanostructure fabrication routine are indicated. Note that the M plane in Al2 O3 saphire is one of the six veritical planes in the hexagonal crystal structure (for example such as (1010)). In the fabrication routine presented in Fig. 2.5 three self-assembly processes are shown: (i) The spontaneous reconstruction of and Al2 O3 M plane into nanoscale facets, (ii) separation in diblock copolymer thin films and (iii) growth of metal nanostructures on chemically patterned surface of a diblock copolymer film. The approach presented in Fig. 2.5 is that the pattern formed in one self-assembly process directs the pattern formation in the following process. For additional information on the figure see Erb and al. It could be noted -as indicated above- that the self-assembly approach seems to be the most promising bottom-up technique for nanofabrication in a wide nanotechnology field enabling a broad range of applications (among them in the medical field). Further note that a diblock copolymer (indicated in the subscript of Fig. 2.5) is a polymer consisting of two types of monomers (A and B) that are grafted together to form a single copolymer.

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Fig. 2.5 Hierarchical self-assembly. Top: Sketch of the proposed nanostructure fabrication routine. Bottom: AFM topography scans of a nanostructured sample in subsequent stages. A Nanofaceted substrate obtained by high-temperature annealing of M-plane a-Al2O3. B Microphase-separated diblock copolymer template, with the lateral positioning of the chemical domains guided by the substrate topography. C Metal nanostructures formed during sputter deposition, following the chemical surface patterning presented by the diblock copolymer template. Erb et al. (2015). Open Access

2.1.4 Vapor Phase Deposition of Nanomaterials Vapor phase deposition techniques in use for the production of nanomaterials (films, particles etc.) are classified as (a) physical and (b) chemical deposition techniques. Common physical deposition techniques are: (i) plasma (PSD) and ion beam sputter deposition (IBSD) techniques, (ii) electron beam (e-beam) and molecular beam (MBE) techniques. Chemical vapor deposition (CVD) techniques are: (i) metalorganic chemical vapor deposition (MOCVD) and (ii) metal organic deposition (MOD) techniques. The vapor deposition technique has been extensively used to synthesize heterolayered structures and to produce epitaxial films. Appropriate substrate materials with proper crystal structure and lattice parameters compatible with the deposited layer are required for obtaining the desired growth and other physical properties that are likely to influence the grain size, film density etc. It is likely that substrate/deposit interfacial properties are an important controlling parameter for initiating nucleation and growth already from the incubaton stage. Thus the overall process of nucleation occurs through several stages, e.g., asorption of the arriving precursor ions or radicals, their surface diffusion on th substrate and nuclei formation and subsequent growth of the nuclei and finally their coalescence. Chemical vapor deposition (CVD) technique is one of the most common processes used to coat almost any metallic or ceramic compound, including elements, metals

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and their alloys and intermetallic compounds. The CVD process consists of depossiting a solid material from a gaseous phase, involving chemical reaction between the volatile precursors and the surface of the materials to be coated. The precursor gases passing over the heated substrate surface results in a chemical reaction forming a solid phase which is deposited on the substrate. Thus the substrate temperature is a critical parameter which migh influnce the process of different reactions occuring. Thus, we can summarize that by CVD or its derivatives indicated earlier is a process wherby a solid is deposited on or in the vicinity of a heated substrate surface. The deposited solid is either in the form of a thin film, powder or single crystal. A range of material can be grown by varying the experimental condition such as, substrate material, substrate temperature, composition of the gas mixture, pressure, gas flow etc. Basically the following steps characterize the CVD process: (1) (2) (3) (4) (5)

evaporation and transport of the precursors into the reactor gas phase reactions of precursors to produce reactive intermediate and gaseous by-products mass transport of reactants to the substrate surface adsorption of the reactants on substrate surface and surface diffusion to growth sites where nucleation and surface chemical reactions occur, leading to film formation.

CVD basically is a deposition technique to produce high quality solids among them to synthesize ceramic nanopowders in which the precursor is converted to nanoparticles. Further the process is often used in the semiconductor industry to produce thin films. Typically the wafer acting as a substrate is exposed to one or more volatile precursors, which react and/or decompose on the substrate surface to produce the desired deposit. Also, this method is mainly used for fabrication of oxide, nitride, and carbide nanopowders. Usually, volatile by-products are also produced, which have to be removed. Often the CVD process requires the deposition of a film of metallic catalyst and after the nucleation of the catalyst (thermal annealing), the precursor gas mixture is injected into the reactor. Laser-assisted CVD (LACVD) for the decomposition of a certain precursor can be used as a process for thin film deposition at relatively low temperatures making the process ideal for the growth on temperature sensitive materials. In Fig. 2.6 a general schematic of laser assisted growth for carbon nanotubes (CNT) is shown, demonstrating several variations. The laser source, providing the thermal energy necessary for CNT synthesis, can either be directed onto the substrate from the top side or the bottom side. For growth of CNT by this technique (LACVD) is influenced by catalyst and substrate, gas and thermal energy. Chemical vapor deposition by the CVD method is mainly used for the fabrication of the technologically important oxide, nitride, and carbide nano-powders.

2.1 Bottom-Up Approach Methods Are Listed Below as

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Fig. 2.6 General schematic for a laser-assisted chemical vapor deposition setup including the laser source, gas input, substrate and catalyst, stage, and sensors. Between brackets some variations or options are shown. The inset shows the two variations of CNT growth, base-growth (left) and tip-growth (right). van de Burgt (2014). Free access

2.1.5 DNA—Scaffolding for Nanoelectronics The use of DNA self-assembly using DNA as a scaffold material to attach electronic devices is adopted from the use of nano-scaffolding in the medical applications to regrow tissue, bone burned skin and other organs. Nano-scaffold is a three dimensional structure composed of polyner fibers (scale 10–9 nm) which are biodegradable. Electrospun nanofibers are prepared in the range of 100–200 nm diameter and by entangling with each other form a web which is controlled in thickness determined by the material used. The use of this scaffolding allows more effective use of stem cells and quicker regeneration. Mechanical properties are one of the most important considerations when designing scaffolds for medical use. If the mechanical properties, in particular the elastic modulus, of the scaffold do not align with those of the host tissue, the scaffold is more likely to inhibit regeneration or fail mechanically. There has been significant research in DNA self-assembly using DNA as a scaffold material for the production of electronic devices. One of the primary advantages of using emerging nanoelectronic devices is the potential for greater device density. Self-assembly is well suited to assemble large numbers of dense circuits, however, it also exhibits higher defect rates than found in the present complementary metal oxide semiconductor CMOS technologies. Bottom-up self-assembly method is used to build nanoelectronic devices. The self-assembled DNA lattice acts as a scaffolding for the nanoelectronic devices.

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Fig. 2.7 A DNA scaffolding for nanoelectronic circuits100, J. P. Patwardhan, C. Dwyer, A. R. Lebeck, and D. J. Sori, Proceedings of the International Workshop on Design and Test of Defect-Tolerant Nano-scale Architectures (NANOARCH), May 1, Palm Springs, California, p.1., Open

Figure 2.7 shows an image of a DNA lattice taken with an atomic force microscope. Using appropriate DNA segments during the construction of the lattice, the lattice can be made addressable. This addressability allows us to place active devices at specific positions in the lattice to form a circuit. (Addressability refers to the ability of a digital device to individually respond to a message sent to many similar devices). Once individual nodes have been self-assembled, they need to be linked together to form a network of nodes. This is achieved by growing DNA nanotubes between nodes, and then metallizing them to make them conductive. This second level of self-assembly gives rise to a random network of nodes. Figure 2.7 shows a schematic of a section of the network of nodes, including regions with defective or disconnected links (Fig. 2.8). For more on evaluating the connectivity of self-assembled networks of nano-scale electronic devices, and create nanoscaled structures/functional devices the reader is refered to the work of Patwardhan et al.

2.2 Top–Down Approach Main methods to produce nanomaterials are listed below: 2.2.1 Mechanical milling 2.2.2 Laser ablation synthesis and 2.2.3 Arc disharge synthesis.

2.2 Top–Down Approach

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Fig. 2.8 Schematic of self-assembled network of nodes. J. P. Patwardhan, C. Dwyer, A. R. Lebeck, and D. J. Sori, Proceedings of the International Workshop on Design and Test of Defect-Tolerant Nano-scale Architectures (NANOARCH), May 1, Palm Springs, California, p.1., Open

2.2.1 Mechanical Milling Preparation of nanomaterials by this method is a versatile and low cost process for producing many types and shaped objects and adopted for industrial application. Micro-size bulk material is ground down to the nanoscale level by the milling technique. Three types of milling devices are frequently used: (i) shaker mills, (ii) planetary ball mill and (iii) attrition mill. (i)

(ii)

(iii)

(iv)

In the shaker mill the material to be milled is placed into a vial containing milling balls (spherical) and after attaching them to the shaker, the shaker is swung back and forth for several thousans of cycles per minute. The collisions during milling (by high impact and shear forces) grinds the solid down and mixes the resulting ground particles. Vials are attached to a rotating disk and rotate around their axis in an opposing direction to the rotating disk direction. The entire system is rotated several thousands of rotation per minute (rpm) and the material consequently is ground by frictional and impact forces. Grinding by ball mills is a similar way to grind down the material. In attrition mills a vertical drum (cylinder) is attacheed with a series of propellers inside, fixed at right angles to each other. The mill is rotated at high speed with the inside impeller working producing very high shear and impact forces resulting in the ground material. In Fig. 2.9 an example of the well-known SPEX produced shaker mill is illustrated. SPEX shaker mills has been used extensively for research and small batches of powderes. One problem of milling powders is the interaction with the atmoshore, namely oxygen (to a less degree nitrogen). An other problem is a result of interaction of the powder with the surroundings; since milling by SPEX shaker is a high energy process the results of the milling

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2 Basic Concepts for Producing Nanomaterials

Fig. 2.9 SPEX 8000 mixer/mill in the assembled condition. Yadav et al. (2012). Open access

is much dependent on the mechanical behavior of the powder being milled. It is possible to reduce the interaction of the powder if the container lining and balls are made from the same (or similar) alloy as the composition of the powder being processed. (v)

Ball mill. Various ball mills are used to grind, blend and mix material to obtain nanomaterials. The priciple operations of milling in a ball mill are impact, attrition and size reduction. In the process, balls impact the material (or powder) on freely falling from near the top of the shell. The kinetics of mechanical milling or alloying depends on the impact energy. An illustration of a ball is seen in Fig. 2.10.

Another ball mill is the planetary ball mill which is mainly used in laboratories for grinding material down to very small sizes. Such a mill comsists of grinding jars attached to a sun wheel which moves in a direction opposite to the grinding Fig. 2.10 A rock tumbler Ball mill. Yadav et al. (2012). Open access

2.2 Top–Down Approach

19

Fig. 2.11 Planetary ball mill (RETSCH PM 400: department of Physics: BHU). Yadav et al. (2012). Open access

jars. The grinding balls in the grinding jars are subjected to superimposed rotational movements that of the rotating sun-wheel and those of the jars. High dynamic energy is obtained by the difference in speeds between the balls in the jars and the grinding jars, which produces an effective reduction in size in the planetary ball mill. A plenataru ball mill is illustrated in Fig. 2.11. Milling time has an effect on the final size of the particles as seen in Fig. 2.12 where SEM microstructure shows powder particles produced with different milling times of Al2 O3 and Fe48 Co52 phases (dark colors correspond to Al2 O3 and light colors to Fe48 Co52 phases). A significant reduction in Al2 O3 grain size up to 27 nm after 24 h milling is seen. Powder of Al70 Co15 Ni15 attained nanocrystalline size of ~ 90 nm already at the early milling stages of 5 h milling with further decreas in size with milling time. Lattice strain is generally introduced as a result of the milling operation as illustrated in Fig. 2.13. Note that the strain increases with decreasing crystallite size (clearly due to the increased milling time) as shown in Fig. 2.13a. Due to the process in the ball milling the mechanical energy applied lattice distortion occurs and it induces also defect formaion, namely dislocations. Annealing in vacuumm and air of the crystallites is seen in Fig. 2.13b and clearly grain size growth is expected. Beyond ~ 20 h fast increase occurs in the crystallite size. The milling time to obtain the same grain size of the nanoparticles in plenatary ball mill and attrition mill is shown in Fig. 2.14. Relations of the plenatary ball mill is presented below in the wake of Burmeister and Kwade who collected these equations from the literature (see the work of Burmeister and Kwade): In Eq. (2.3) the revolution speed of the pot (container) nP to that of the disk (on which the pot it is located) revolution speed nR is k=

nP nR

(2.3)

Depending on the motion direction k can be either positive or negative (See Fig. 2.15). The specific energy, Ei , that can be supplied to the particles at one collision

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2 Basic Concepts for Producing Nanomaterials

Fig. 2.12 SEM images of cross-sections of powder particles produced after different milling times a and b: 8 h c and d: 16 h, e and f: 24 h, g and h: 48 h. Yadav et al. (2012). Open access

is given by: n Ei =

j−1

SE j SF j mP

xt =

SN × S E mP

(2.4)

Here the total energy is related to the total mass of the powder. The total energy is determined by the frequency of the stress events SF j at interval j, the average stress energy SEj at interval j and the processing time t; mP is the mass of the powder. In

2.2 Top–Down Approach

21

Fig. 2.13 a The variation of crystallite size and lattice strain with milling time, b variation of crystallite size with annealing time. Yadav et al. (2008). With kind permission of John Wiley and Sons.

(2.4) SN is the total number of stress events and SE is the average stress energy. The stress energy SE describes the maximum energy that can be supplied to the particles at one collision and can be calculated from the relative impact velocity vj and the masses of the colliding bodies m1 and m2 and is given by

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2 Basic Concepts for Producing Nanomaterials

Fig. 2.14 Time to reach similar particle sizes during milling of TiB2 powder in a planetary ball mill and b attritor. Suryanarayana (2001)

Fig. 2.15 Scheme of planetary disks with movement in a normal and counter direction; with pot height h; pot diameter dP; revolution radius Burmeister and Kwade (2013)

2.2 Top–Down Approach

23

SE =

v 2j m 1 m 2 2(m 1 + m 2 )

(2.5)

The yield of milled product increases with milling time as a result of the consistent increase of ball collisions and as a consequence of the total amount of energy induced during the milling. However, with prolonged time decomposition of the product can occur. Therefore, a minimum revolution is required to reach the proper product quality. The speed of milling is limited by unwanted effects on the product (for example decomposition of metastable phases and additional undesirable effects depending on the material being milled) due to a significant temperature increase. Although a high temperature increase may be sometimes helpful, for example when diffusion is required in powder alloying or the reaction is promoted by high temperatures. The particle size change during the experimental grinding process can be described using an empirical equation givem as    Dt  Dt Dt = 1− exp −K p t + D0 D0 D0

(2.6)

where Dt /Dl is the normalized particle size and K p is the grinding rate. Experimental observations show that K p increases with decreasing ball diameter at high rotational speeds, but it is independent at low speeds. Also K p increases with increasing revolution speed and decreases with sample weight. Thus, it is useful to apply during the process only the required time at a moderate speed in particular in materials which are sensitive to decomposition and possible phase changes whe the materials are composites or metastable alloys. Applying shorter time (but sufficient for the desired result) and lower speed will decrease energy consumption and therefore reduce cost.

2.2.2 Laser Ablation Synthesis This is a technique to produce nano-size particles by nucleation and growth of laservaporized material in a background gas. Obtaining particles in the 10 nm size range is a consequence of the very fast quenching of laser vaporized species. Laser ablation can also be perfomed in solution, namely, water or other organic solvent. A variaty of material can be produced by this technique at very high purity. A high energy laser is focused on to a target which delivers short pulses. The energy is enough to vaporize small spots in the target which condenses as nanoparticles. The laser ablation technique is applied to produce noble metallic nanoparticles such as gold, silver and platinum, but it can be used to produce other metallic nano-particles as a matter of fact it can be used for a wide range of material.

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2 Basic Concepts for Producing Nanomaterials

Fig. 2.16 Scematic of particle generation procedure in the laser ablation process. Kim et al. (2016). Open access

A schematic illustration of nanoparticle formation process by laser ablation is shown in Fig. 2.16. The ambient media is either gas or liquid the location of the target and upon the surface of which the laser beam is focused. The temperatures of the irradiated spot rapidly increase vaporizing the target material. As a consequence of the collisions between the evaporated atoms (molecules) excitation of the electronic state which is accompanied with light emission and the generation of electrons and ions (ionization), resulting in a laser-induced plasma plume. Laser induced plume of silicon is seen in Fig. 2.17. The plasma and its size and its emission spectrum depend on the target material, the ambient media whether it is gas or liquid, ambient pressure and the state of the laser itself. Nanoparticles of various species generated by plasma ablation are illustrated by TEM electron micrographs in Fig. 2.18. In the laser ablation fabrication method the nanoparticles are nucleated and grow (difficult to measure) and is quenched very rapidly and as a consequence very high purity nanoparticles are formed. This is an advantageous consequence of the very rapid nanoparticles generation. Various kinds of nanoparticles (including semiconductor plasma dots, Fig. 2.17 Laser-induced plume of silicon in low pressure. Kim et al. (2016). Open access

2.2 Top–Down Approach

25

Fig. 2.18 Typical electron micrographsof laser ablation-generated a silicon, b carbon and c surface-oxidized nickel nanoparticles. d Aggregates of nickel nanoparticles as a result of coagulation and necking. Kim et al. (2016). Open access

carbon nanotubes, nanwires etc.) can be fabricated by laser ablation. Nanocarbon generated by lase ablation is illustrated in Fig. 2.19. Thus for fabrication by laser ablation the following is required: a suitable laser system with the desired size and

Fig. 2.19 Transmission electron micrograph of nanocarbons generated by lase ablation a Onio-like carbon, b carbon nanotubes, and c diamond-like nanoparticles. Kim et al. (2016). Open access

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2 Basic Concepts for Producing Nanomaterials

controlable critical parameters such as evaporation rate of the target material (which is controlled by laser source, wavelength, fluence, pulse width and frequency), light absorption efficiency of the target material and proper ambient media. Laser energy per unit area on the target material is defined as F=

I A

(2.7)

where F is the fluence of the laser. I (J/pulse) is the laser power and A is the area of the laser spot. The absorped photon energy of a target laser-irrediated with short laser pulses is transferred to the solid lattice as thermal energy. Following Kim -who quotes the heat transfer relations from the literature- the thermal energy in the electron and lattice subsystem can be characterized by the following equations: Ce =

∂ Q(z) ∂ Te = − γ (Te − Ti ) + S ∂t ∂z Ci

Q(z) = −ke

∂ Ti = γ (Te − Ti ) ∂t

∂ Te , S = I (t)Aα exp(−αz) ∂z

(2.8) (2.9) (2.10)

Ce and Ci are the heat capacities of the electron ans lattices subsystem, z is the perpendicular direction to the heat surface, Q(z) is the heat flux, γ is th electron– phonon coupling strength, S is the laser source term, ke is the heat conductivities of the electron and I (t) is the laser intensity. A is the absorbance of the sample and 1/α is defined as the optical penetration depth. Equations (2.8)–(2.10) can be modified for the laser pulse width. Ci

  ∂ ∂ Ti ∂T = ko + I (t)Aα exp(−αz) ∂t ∂z ∂t

(2.11)

The assumption of writing (2.11) that Te is equal to Ti that the duration of the laser pulse of a nanosecond laser is much larger than the lattice heating time. In (2.11) ko is the conventional equilibrium thermal conductivity of a substance.

2.2.3 Arc Disharge Synthesis Nanomaterial can be obtained also by arc discharge synthesis which is another top down process. In the arc discharged process bulk material is arc assisted broken down. Two electrodes kept in proximity to each other are in solution and a high voltage is

2.2 Top–Down Approach

27

applied between them while disintegration takes place. The arc discharge produces a thermal plasma discharge. A high local temperature of the plasma vaporizes the electrode surface which is in the liquid medium. The vaporized material condenses on the solvent making nanoparticles. It is clear from the above that critical parametes which determine the end product are: the condensing solvent medium, voltage and current supplied and the electrode material. Carbon nanotubes are also produced by the arc discharge process. An example of synthesizing by arc discharge Ag and Au particles is presented here. The liquid was deionized water. The experimental setup is shown in Fig. 2.20. The main parts in the system are: (i) (ii) (iii) (iv)

two Ag or Au electrodes a servo control system to maintain constant distance between the electrodes a power supply to control the DC arc discharge a glass tank for the deionized water and a Teflon electrode holder to collect the Ag or Au colloid.

Silver and gold nanoparticles obtaine by the arc discharge synthessi are shown in Figs. 2.21 and 2.22, respectively. Another interesting example of fabricating nanoparticles by arc discharge synthesis is the formation of iron nanoparticles and encapsulated in carbon for biomedical use. These particles are supermagnetic and they are important in drug delivery, magnetic resonance imaging (MRI) and in cancer treatments. TEM images of these carbon encapsulated iron nanoparticles are illustrated in Fig. 2.23. An HRTEM picture of an iron encapsulated in carbon nanoparticle is seen in Fig. 2.24. No oxygen was present as evidenced from the absence of diffraction points of iron oxides. The only phases present are α-Fe and iron carbide. The carbide is probaly

Fig. 2.20 The DC arc discharge system. Tien et al. (2010). Open access

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2 Basic Concepts for Producing Nanomaterials

Fig. 2.21 SEM image of prepared Ag nanoparticles. Tien et al. (2010). Open access

Fig. 2.22 SEM imagw of prepared Au nanopaticales. Tien et al. (2010). Open access

located between the iron core and the carbon shell. Its phase is minor compared to the α-Fe. The small image is the diffraction pattern used for structural determination. The residence time that the nucleus of the precursor iron (also the gas atoms and precursor radicals) spends inside the plasma zone depends on the gas flow rate which determines the size of the particles. Clearly, the longer they stay in the plasma zone the larger the particles grow. Along with Chaitoglou et al., we can write for the velocity u and the He flow rate, Φ, Eq. (2.12) as u=

4 π d2

(2.12)

2.2 Top–Down Approach

29

Fig. 2.23 TEM images of iron encapsaulated in carbon nanparticles by arc-discharge (40.0 + 5 A of current) using different flows and concentrations accompanied by their size distribution histograms. a 30 ml./min with a concentration of 1% w/w, b 30 ml./min with a precursor concentration of 2% w/w, and c 30 ml./min with a concentration of 4% w/w. Chaitoglou et al. (2014). Open access

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2 Basic Concepts for Producing Nanomaterials

Fig. 2.24 TEM image of a nanoparticle. In the small picture we can see the diffraction pattern from which we obtain the crystalline structure of the iron core. Here it corresponds to the α-phase. Chaitoglou et al. (2014). Open access

where d is the internal diameter of the cannula through wich the gas is targeted in the plasma zone and of ~ 3 mm. From the size of the plasma zone h ~ 5 mm, the residence time, τ, can be estimated as τ=

h u

(2.13)

See data of residence time in Table 2.2 for several values of He flow. The distribution of the nanoparticles is a lognormal function given as ⎞ ln2 D D ⎠ f (D) = √ exp⎝ 2 ln2 σg 2D ln σg ⎛

1

Table 2.2 Flow rate and resulting velocity and residence time for a precursor vapor with 1% of ferrocene concentration. Chaitoglou et al. (2014). Open access

He flow rate,  (mL/min)

Precursor vapor velocity, U (cm/s)

(2.14)

Residente time, τ (ms)

30 ± 2

7.07 ± 0.50

60 ± 2

14.13 ± 0.50

71 ± 1.5 35 ± 1.5

120 ± 2

28.28 ± 0.50

18 ± 1.5

2.2 Top–Down Approach

31

In Eq. (2.14) D is the particle diameter, D is the geometric mean, which in a lognormal distribution is equal to its median, σg is the geometric standard deviation (dimensionless) describing how spread out are the the core diameters from the geometric mean. See Fig. 2.23 for the size distribution.

References C.F. Burmeister, A. Kwade, Chem. Soc. Rev. 42, 7660 (2013) S. Chaitoglou, M.R. Sanaee, N.A. Aguayo, E. Bertran, Hindawi Publishing Corp., J. Nanomaterials, Article ID 178524 (2014) D.J. Erb, K. Schlage, R. Röhlsberger, Sci. Adv. 1, 1 (2015) M. Kim, S. Osone, T. Kim, H. Higashi, T. Seto, Kona Powder and Particle J., 30 April, 1 (2016) M. Niederberger, N. Pinna, In Metal Oxide Nanoparticles in Organic Solvents, Springer, p. 10 P.O. Oviroh, R. Akbarzadeh, D. Pan, R.A.M. Coetzee, T.-C. Jen, Sci. Technol. Adv. Mater. 20, 465 (2019) J. P. Patwardhan, C. Dwyer, A.R. Lebeck, D.J. Sori, Proceedings of the International Workshop on Design and Test of Defect-Tolerant Nano-scale Architectures (NANOARCH), May 1, Palm Springs, California, p. 1 C. Suryanarayana, Prog. Mater. Sci. 46, 1 (2001) D. C. Tien, L.-C. Chen, N.V. Thai, S. Ashraf, J. Nanomaterials, Article 67, 1 (2010). Hindawi Publishing Corp Y. van de Burgt, J. Laser Appl. 26, 032001–032011 (2014) T.P. Yadav, R.S. Tiwari, O.N. Srivastava, N.K. Mukhopadhyay, Inter. J. Appl. Cer. Tech. 5, 449 (2008) T.P. Yadav, R.M. Yadav, D.P. Singh, Nanosci. Nanotechnol. 2, 22 (2012)

Chapter 3

Structure and Classification of Nanomaterials

Rather than classify nanomaterials in terms of the seven crystal systems (fourteen Bravais lattices) as usually is done in macroscale material for structural characterization, in nanostructures (NSs) a common classification adopted is the Gleiter’s approach, who was the first to classify them. A classification has been indicated in Chap. 1 which is based on dimensionality of the NSs and repeated here as (0D), (1D), (2D) and (3D). All NSs can be built from elementary units, namely blocks having low dimensionality of (0D), (1D), and (2D). (3D), however can not be considered as elementary unit, but the bulk nanomaterials can be composed of a multiple arrangement of nanosize crystals. Thus, (3D) structures can be considered as nanostructured materials (NSMs) if they involve the (0D), (1D), (2D) NSs. In the earlier works the NSMs were categorized (Siegel) dimensionally as: (0D)—representing nanopartcles or nanoclusters, (1D)—representing layer structures, (2D)—referring to nanograined layers and (3D)—representing equiaxed bulk solids (constituent’s dimensions within the solid measured in all directions are within the nanoscale, not larger than 100 nm). Gleiter assumes as the basis of his classification scheme of NMSs that intercrystalline grain boundaries parallel with crystallites are the building blocks. The illustration representing Gleiter’s approach is seen in Fig. 3.1. The classification of nanostructured materials consisting of nanometer-sized crystallites and interfaces can be done according the chemical composition of the microstructural constituents and their dimensionality, i.e. shape. Gleiter classifies NSMs according the shape (form) of the crystallites into three categories (see Fig. 3.1): (i) layershaped crystallites, (ii) rod-shaped crystallites and (iii) NSMs composed of equiaxed nanometer-sized crystallites. These three categories can be grouped into four families depending on their chemical composition. In the first family (the simplest case) all crystallites and interfacial regions have the same chemical composition which can be examplified by semicrystalline polymers consisting of stacked crystalline lamellae separated by non crystalline regions as shown for the first category in Fig. 3.1c Note that NSM of the same chemical composition made up of equi-axed nanometer sized crystals example of which is Cu, representing the third category (Fig. 3.1). NSM of

© Springer Nature Switzerland AG 2021 J. Pelleg, Mechanical Properties of Nanomaterials, Engineering Materials, https://doi.org/10.1007/978-3-030-74652-0_3

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3 Structure and Classification of Nanomaterials

Fig. 3.1 Classification schema for NSM according to their chemical composition and the dimensionality (shape) of the crystallites (structural elements) forming the NSM. The boundary regions of the first and second family of NSM are indicated in black to emphasize the different atomic arrangements in the crystallites and in the boundaries. The chemical composition of the (black) boundary regions and the crystallites is identical in the first family. In the second family, the (black) boundaries are the regions where two crystals of different chemical composition are joined together causing a steep concentration gradient (Gleiter 1995). Gleiter (2000). With kind permission of Elsevier.

the second family consist of crystallites with different chemical compositions indicated in Fig. 3.1 by different thickness of the lines used for hatching. Well known examples are quantum well (multilayer) structures representing the first category. The third family of NSM occurs when compositional variation exists between crystallites and interfacial regions. In this case one type of atoms or molecules segregates preferentially to the interfacial regions (so that the structural modulation-namely crystals/interfaces—is coupled to the local chemical modulation). An example is Ga atoms segregated in nanometer-seized W crystals to the grain boundaries as illustrated in Fig. 3.2. The fourth NSM family is formed in nanometer-seized crystallites of either layers, rods or equiaxed crystallites dispersed in a matrix of different chemical composition. Examples are NSM of precipitation hardened alloys. The Ni–Al alloys is an example of precipitation hardened alloy used in aicraft industry where Ni3 Al precipitates from a supersaturated Ni–Al solid solution. An example is seen in Fig. 3.3. Further to the effect of the size, structure and shape of the NSM building blocks, the boundary regions between the building blocks play also an important role. The characteristics of the grain boundaries such as the chemical composition, atomic structure, thickness, etc. are crucial for the properties of the NSM even if the

3 Structure and Classification of Nanomaterials

35

Fig. 3.2 Schematic model of the structure of nanostructured Cu–Bi and W–Ga alloys. The open circles represent the Cu or W atoms, respectively, forming the nanometer-sized crystals. The black circles are the Bi or Ga atoms, respectively, incorporated in the boundaries at sites of enhanced local free volume. The atomic structure shown was deduced from EXAFS and X-ray diffraction measurements. Gleiter (2000). With kind permission of Elsevier

Fig. 3.3 Flow stress of Ni-13 at.% Ni alloys as a function of the size of the Ni3 Al precipitates. Gleiter (2000). With kind permission of Elsevier

building blocks, e.g. the crystallites of two NSM, have comparable size. An example of the immiscible Ag–Fe NSM is shown in Fig. 3.4. Thus, the interfacial layer is an integral part of nanoscale matter, fundamentally affecting all of its properties. Numerous interfaces between adjacent crystallites affect the properties of an NSM which are different from single or polycrytstals with the same average chemical composition. Their effect together with the nanometer-sized crystallites contribute to the mechanical properties which are basically structure dependent. Clearly to preserve the nano-structure, grain (crystallite) growth should be retarded. Elevated temperatures seem to affect the microstructure of NSM by inducing grain growth, but also it can change the atomic structure. Grain growth in NSM is driven by the excess energy stored in the grain or inteface boundaries and

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3 Structure and Classification of Nanomaterials

Fig. 3.4 Schematic model of nanocrystalline Ag-Fe alloys according to the data of Mos-sbauer spectroscopy. The alloys consist of a mixture of nanometer-sized Ag and Fe crystals (represented by open and full circles, respectively). In the (strained) interfacial regions between Ag and Fe crystals, solid solutions of Fe atoms in Ag crystallites, and Ag atoms in the Fe crystallites are formed although both components are immiscible in the liquid as well as in the solid state. Similar effects may occur in the grain boundaries between adjacent Fe and Ag crystals (Herr et al. 1990). Gleiter (2000). With kind permission of Elsevier

the kinetics of normal grain growth assume a linear relationship between the rate of grain growth and the inverse grain size, which in turn is proportional to the radius of curvature of the grain boundaries. The grain growth is given in Eq. (3.1) D2 − D20 = kt

(3.1)

D0 and D are the grain sizes at the beginning of an experiment and at time t, respectively, ank k is a temperature dependent constant. Since this ideal relation not always describes the experimental results, therefore a time exponent of 0.5 was incorporated in Eq. (3.1) and given as 1

D 1/n − D0n = k  t

(3.2)

or (1/n) n

D = (k  t + D0

)

(3.3)

The rate constan k (or k0 ) can be experessed by an Arrhenius type relation as k = k0 exp(−Q/RT)

(3.4)

3 Structure and Classification of Nanomaterials

37

and Q is the activation energy for isothermal grain growth. Clearly the grain size increases with time and this was also observed experimentally. It could be noted that in NSM grain growth starts at lower temperatures with smaller grain size and that grain growth is rapid above a certain temperature and becomes negligible for longer times. Since growth involves atomic transport along boundaries, often the activation energy is compared to that of grain boundary diffusion. It shoud be noted that in many nano crystalline material n differs from 0.5 of Eq. 3.2 (parabolic grain growth). In most cases, the value of n of 0.5 for grain growth of nanocrystalline materials, is different from the value indicated in Eqs. (3.1)–(3.3) describing a parabolic relationship. Grain growth can be reduced if not eliminated completely by pinning grain boundaries by a second phase inclusion. The total free energy of a segment of boundary intersecting an inclusion is reduced by the product of the cross section of the inclusion and the specific boundary free energy. Pores in the structure acts in a similar way to inclussions or impurity atoms in reducing grain growth. Thus, in a structure containing about 25% porosity the grain size was 30 nm after annealing for 20 h at 700 °C (the initial grain size is 14 nm), but after reducing the porosity to ~10%, the grain size increased to 500 nm indicating the pinning effect of pores. Further, presuure supresses grain growth as observed in sintered nano crystalline material. Regarding boundary pinning by a solute and retarding growth, three modes of motion may occur depending on the relative rates of boundary and solute cloud mobility (recall that pinning by an atom involves a solute cloud formation in many solid solutions in the vicinity of a boundary to reduce the energy of the boundary particle system. This way the boundary movement is rcestrainerd): (i) If the nigration of the boundary is slow, draging of the solute cloud with the boundary occurs, thus reducing its mobility and hence grain growth is retarded. (ii) Break away of the boundary from the solute atoms cloud occurs when the boundary migrates very fast, and consequently the solute atoms move freely. (iii) At intermediate boundary migration rates, the boundary breaks loose locally from the solute cloud and this impurity-free segment bulges out. The increase of the boundary area resulting from the bulging out, reduces the rate of motion of the imurity-free grain boundary segment and permits the impurity cloud to be formed again (it is a jerky motion). These three boundary motion modes were observed experimentally in coarse-grained polycrystals, but the first two modes are likely to occur in NSM as well (an example of pinning grain boundaries by Ni3 P precipitates in nanocrystalline Ni solid solution of a crystallized Ni–P amorphous alloy and segregation in grain boundaries has been found responsible of preventing grain growth of the nanocrystalline phase; another example is the segregaton of Si to grain boundaries in a Ni–Si solid soluton). These nanomaterial structures are generally observed directly using imaging techniques such as SEM, TEM, FIM, STM (scanning tuneling microscope), or AFM (atomic force microscope) which are principal characterization tools. In TEM,—a high-resolution instrument with resoltion of b1,2 . Since b1,2 are the shorter lattic vectors, splitting of the dislocation into smaller Burgers vector is always energetically favorable. If a dislocation would have a large Burgers vector, it would immediately split into two (or more)

4.4 Planar Defects

59

dislocations with smaller Burgers vectors. There is a decrease in the energy when the dislocation (total) splits into two partial dislocations and a stacking fault (SF). Partials form because dislocation energy is proportional to b2 . In the case of glide in a (111) plane the dissociation of the dislocation is according to the reaction

1

1 1 a 101 → a 211 + a 112 2 6 6

(4.25)

A direct method of determining the stacking fault energy (SFE) is to measure the separation width between the partials. Often in the literature instead of SFE, the letter γ is used which is defined as the energy per unir area of the fault (clearly it is thus force per unit length). The equilibrium width of the stacking fault is inversely proportional to the stacking fault energy and it may be expressed by d=

Ga 2 24π γ

(4.26)

or SFE = γ =

Ga 2 24π d

(4.27)

This expression is a consequence of γ being related to the dot product of the Burgers vectors of the partials, b1 · b2 and given as d=

G(b1 · b2 ) 2πγ

(4.28)

In the above expressions γ (SFE) is a function of the orientation of the dislocation line and b1 , b2 are the Burgers vectors of the partial dislocations and d is the equilibrium width of the SF. Recalling that the energy of an edge dislocation (Pelleg) before forming the partials is being expressed as E=

r Gb2 ln 4π (1 − v) r0

(4.29)

The meaning of the symbols is clear, but let’s indicate it again, namely, r is the radus outside around the dislocation, while r0 is the small radius inside the disloction where Hooke’s law fails. Further, the energy is evaluated per unit length of the dislocation line, which indicated that dislocations are line defects. The width of the SF is an energy balance between the repulsive forces between the partials (they have the same Burgers vectors and the same size) and the energy of SF (which is as mentioned the force per unit length) formation. When the sum of the energy of the partial dislocations +SFE is equal to the energy of the total (or also known as full) dislocation no further increas in the width of the SF can occur. The

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4 Imperfections in Nanomaterial

above statements can be expressed as the criterion for the formation of partials and SF 2Gb2p 4π (1 − ν)

ln

r r Ga 2 Gb2 ln + < r0 24π d 4π (1 − ν) r0

(4.30)

The number 2 indicates that there are two partial dislocations. Note that in the first term the Burgers vector is of the partial dislocations. Thus, the sum of the first term and the second term must be smaller than the third term representing total dislocations fo the SF formation and growth. In summary The width of stacking fault is a consequence of the balance between the repulsive force between two partial dislocations on one hand and the attractive force due to the surface tension of the stacking fault on the other hand. Stacking faults are visible under diffraction contrast mode in TEM.

4.4.2 Stacking Faults in Nanocystals Stacking faults (SFs) form when a dislocation splits into partials. These partials have the same sign Burgers vector and therfore repell each other, causing a displacement of a half-unit cell where they pass. The region with the half unit cell displacement is a defected region and is faulty and the term stacking fault is used for its description. In Fig. 4.13 a SF is shown which was formed from the dissociation of a screw dislocation. The width of the SF measured by HRTEM is in the range 1.4–6.8 nm with an average of 3.5 nm. Experimental SF from a 60° dislocation in single crystal Al is reported to be only 0.55 nm, which is likely to be related to the high energy for its formation. The width of a SF is revealed by HRTEM when the two partial dislocations forming the SF are in < 110 > orientation. Difficulties in measuring SF width result from the observation which makes the SF appear wider than the real width. This can be seen in Fig. 4.13 where the real width is the line CD. Fig. 4.13 An HRTEM image of a SF ribbon (as pointed out by the black arrow) viewed from a < 110 > direction. The distance CD was measured as the SF width. Liao et al. (2004). With kind permission of Appl. Phys. Letters

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Fig. 4.14 A schematic illustration of the dislocation model for wide SF ribbon formation. Two Shockley partial dislocations (the green and red lines) are emitted consecutively from the GB AB, with their ends pinned at A and B. Liao et al. (2004). With kind permission of Appl. Phys. Letters

To understand the formation of the wide SFs, simulation results where Shokley partials are emitted from GBs are considered. In Fig. 4.14 a grain with (111) slip plane is shown. Under an applied stress a Shockley partial dislocation with a Burgers ´ is emitted from GB AB (see green lime AaBb). The ends of vector b1 = a/6[211] the partials Aa and Bb are pinned at AB. Further a trailing partial Shockley with Burgers vector b2 = a/6[1 2 1] is also emitted from the GB AB and forms the red Aa b B dislocation line. The partial dislocations lines ab and a’b’ are separated by a SF. They would form a screw dslocation of a/2 1 1 0 if collapsed together. The two partial dislocations react to form two full edge dislocation segments, Aa and Bb at grain boundaries. This mechanism of wide stacking faults should apply to other FCC metals with high SF energy. In nanocrystals however with low to medium SF energies SF may not exist inside the nanograin, because high SF energies are the main driving force for the emission of trailing partial dislocations, while lower SF energies makes it easier to emit leading partials, but more difficult to emit trailing partials. As a result, in nc metals with low to medium SF energies deformation twin formation will be preferred instead of SF ribbon formation. In Si nc HREM investigations showed that perfect dislocation with Burgers vector 1/2 < 110 > dissociateds into Shockley partials with Burgers vector 1/6 < 112 > and an SF. As in the previous case the width of the SFs has been determined from the HRTEM image, and the stacking fault energy for Si nc has been calculated to be 84 ± 9 mJm−2 . The measured width of the SF is 2.97 ± 0.33 nm. A crosssection image of the specimen is illustrated in Fig. 4.15. The size of the Si nanocrystal is ~15 nm showing that a perfect dislocation can dissociate into two Shockly partials (Fig. 4.15a) which are indicated by two arrows labeled as 30° and 90° and the dislocation line directions are along [011] direction. A clearer presentation is the enlarged HRTEM image of the rectangle enclosed region of Fig. 4.15a as shown in Fig. 4.15b. The circuit shown in the figure encloses two Shockley partials shown by the arrows and the SF is enclosed by dashed lines. The Burgrs vector determines is 1/2 < 110 >. The two major factors affecting the width of the SF are interactions between the partial dislocation and the SFE. The partials having the sane sign repel each other

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Fig. 4.15 a [011] zone-axis HRTEM image of a typical Si nanoparticle with an extended dislocation; b close-up of the extended dislocation showing two Shockley partials bounding a strip of SFs. Wang et al. (2011). Open Access

with a force f per unit length, while the SFE per unit area γ has a tendency to reduce its width, namely forces the partial dislocation lines to move closer. At equilibrium f = γ and the SF width d0 is given by Eq. 4.31 d0 = G

b1 b2 γ

(4.31)

Clearly, G is the shear modulus and b1 and b2 are the Burgers vectors of the partial dislocations.

4.4.3 Twin Boundaries 4.4.3.1

Introduction

Twins of three kinds are considered generaly in the literature, namely, deformation twins, annealing twins and growth twins. Annealing twins formation was observed in a variety of deformed and subsequently annealed FCC materials. The twin boumdary can be obtained by rotating the orientation of the parent grain 60° < 111 >. The twin boundary can be coherent or incoherent depending whether it is parallel to {111} or differs from {111}, respectively. Annealing twin boundaries affect many properties of the material, notably corrosion resistance and improved fatigue properties. Of the many theories the growth accident theory is the most accepted explanation for the annealing twin formation. The basics of this theory considers the migration of a coherent boundary due to a stacking error. The migration distance and the migration velocity are two major factors to annealing twin generation. However, no complete

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prediction of the annealing twin densiy generation during recrystallizastion exists. For recrystallized grains after deformation the annealing twin density is expressed (Jin et al. 2013) by twin density =

2 Ltb × Srg π

(4.32)

where Ltb is the total length of annealing twin boundaries and Srg is the surface area of recrystallized grains. At temperatures below those at which individual atoms are mobile, slip and twinning are the major deformation modes which enable a solid to change shape under the action of an applied stress. Deformation twins form to accommodate strains that develop during plastic deformation. Partial dislocations are involved. Contrary to slip where full {111} < 110 > dislocations are involved, in twin nucleation and propagation in FCC crystals {111} < 112 > partial dislocations and a stacking fault formation are responsible for twinning. Thus the twinning planes are the close-packed {111} planes and the twinning direcrtion is < 112 >. The energy per unit area of the fault is γI . Deformation twins form to accommodate strains that develop during plastic deformation. Twins were observed to form readily in FCC metals (even in Al alloys) at very high strain rates, e.g., shock loading. Growth twins are formed in FCC metals at low γI (for example in austanitic SS γI = 20–50 mJ m−2 , Cu 45 mJ m2 , Au 32. mJ m−2 , Ag 16 mJ m−2 and Al 160– 200 mJ m−2 ). It is believed that deformation twins formation is controlled by the SFE of the material. The lower SFE is the higher is the probability to twin formation. Thus in Al with its high SFE twin boundary formation, i.e., twinning is unlikely. A microstructure, say in thin films, is generally comprised of grain boundaries (GBs), coherent twin boundaries (CTBs) and incoherent twin boundaries (ITBs). Generally, twin and parent lattices are related by reflection in some plane (in FCC it is the {111} plane) or by rotation about some axis. Similar to grain boundaries, TBs can be obstacles to slip dislocations, giving rise to macroscopic hardening and strength. Deformation twins form by highly co-ordinated individual atom displacements contrary to slip bands which form during glide deformation.

4.4.3.2

Deformation Twins in Nanocrystals

Deformation twins are found in almost every material including some minerals. Twinning is temperature and strain rate dependent and the relative contribution to the overall strain increases with the increase of strain rate and lowering the temperature. Deformation twins form by a homogeneous shear of the parent lattice and as mentioned in the introduction this requires coordinated individual atom displacement. Considering FCC metals, the twinning tendency is determined by its SFE

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(stacking fault energy). Thus high stacking fault energy in Al or Ni deform predominently by dislocation slip whereas FCC metals with low stacking fault energy (Ag for exasmple) deform primarily by twinning. Generally, it is believed that deformation twins are formed by the glide of partial dislocations having the same Burgers vectorr on successive planes. A macroscopic strain is produced by the process to accommodate the imposed strain. The Burgers vector of the partial dislocations (Shokley partials) is b1 a/6 < 112 > as indicated in Eq. (4.25). The twin is in a mirror symmetry of atomic arrangement across a coherent twin boundary plane. In FCC metals the best viewing is along the [110] orientation (see Fig. 4.16a) that is on a coherent twin bounndary plane which is the (111) closed packed plane. Each lattice point in the two-dimensional illustration (Fig. 4.16a) represents an atom column, with the dark circles below the light circle by a distance of atomic radius, i.e. 1/4[1 1 0]. Under high-resolution electron microscope, these two types of columns give identical images, as shown in Fig. 4.16b. Low-resolution TEM is often used to identify deformation twins although atomic resolution cannot be obtained. The microstructural features of twins however can be detected as illustrated in Fig. 4.17. Fig. 4.16 a The mirror symmetry of atoms in a twin in fcc metals, when viewed from a [1 1 0] direction that is on the coherent twin boundary plane. A dark filled circle represents an atom column that is shifted for half an atomic distance below an atom column represented by a light circle. b A typical HREM image of a twin in an fcc metal. Columns represented by lighter and dark circles in (a) are not differentiated by HREM in (b). Zhu et al. (2012). With kind permission to Elsevier

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Fig. 4.17 Morphology of deformation twins in nc FCC Cu under low resolution. Twins with plate-like morphology. From the original HREM images with reduced resolutions. Zhu et al. (2012). With kind permission to Elsevier

The grain size of the nanocrystalline (nc) material has an important effect on deformation. Experimental results indicate that smaller grain size impedes deformation twinning (regardless of the crystal structure). FCC nc deforms by twinning more easily if the SF is with medium and high stacking fault energy, and it becomes difficult in very small grain sizes. In coarse-grained fcc and bcc materials, stacking faults and deformation twins usually occur in metals and alloys with low stacking faul energy, although high strain rate and low deformation temperature can significantly promote twinning. In coarse-grained hcp metals (and alloys), twinning is a common deformation mechanism because their small number of slip systems. Comparing this with nc materials: in HCP nc deformation by twinning is rarely observed, whereas in FCC nc deformation by twinning occurs more readily in particular in those FCC nc metals with medium to high SFE, but in this case also in very small grain sizes twinning becomes more difficult again. Fig. 4.18 An HREM image of nc Cu processed by high-pressure torsion (HPT), showing Shockley partial dislocations that were emitted from the lower grain boundary and stopped in the grain interior before reaching the upper grain boundary, leaving behind stacking faults. Zhu et al. (2012). With kind permission to Elsevier

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Fig. 4.19 A twin nucleus formed by overlapping of a dissociated dislocation with a stacking fault from grain boundary in nc Ni. Zhu et al. (2012). With kind permission to Elsevier

In Fig. 4.18 experimental observation of partial dislocations emitted from grain boundaries and deformation twinnig is seen. In Fig. 4.19 close to the grain boundaries a two-layer twin nucleus turned to a stacking fault which suggests that first a stacking fault was formed from the grain boundary and extented toward the grain interior. A two-layer twin nucleus is formed from the dissociated dislocation with a wide SF which slipped toward the grain boundary on an adjacent slip plane and then overlapping with the stacking fault. Deformation twins formed via the emission of partials (Shockley) from grain boundaries was predicted by moecular dynamic simulation and verified by HREM. An example in deformed nc Ni is illustrated in Fig. 4.20. Here T1 is a curved twin boundary with the matrix (Fig. 4.20a) T2 in nc Ni deformed by surface mechanical attrition treatment. The twin was formed by successive emission of partials from the grain boundary on the left. In the example of Fig. 4.20b a single twin growing from grain boundary terminated inisde the grain is seen. An additional image of deformation twin in nc Cu formed by partials having the same Burgers vector and viewed from an appropriate < 1 1 0 > orientation under HREM is illustrated in Fig. 4.21. In summary, there is an optimum grain size in nanocrystalline fcc metals at which the twinning is easiest. Twinning in nanocrystalline fcc metals occurs mainly by the emissions of Shockley partial dislocations from grain boundaries of nano-sized grains and thus they act as the source of partial dislocations in most cases. Another source for partial dislocations is the dislocation reactions at the twin boundaries (it is the primary mechanism for the formation of multiple twins). Non-equilibrium grain boundaries play an important role in the deformation twinning because they may provide ready partials for the nucleation of stacking faults and twins. Twins formed in coarse grained FCC metals have the same Burgers vector, contrary to nc FCC metals. Deformation twinning and dislocation slip usually occur simultaneously during the deformation of nanocrystalline metals. Twin boundaries are effective barriers to dislocation slip, and consequently twins can increase the strength of nanocrystalline and nanostructured

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Fig. 4.20 a A deformation twin (T 1 ) formed by successive emission of partials on adjacent slip planes from the grain boundary on the left in nc Ni deformed by surface mechanical attrition treatment. b An HREM image of a twin formed by plastically deforming electrodeposited nc Ni. The twin was formed by the emission of partials from the grain boundary on the left, and it ended in the grain interior as marked by the white asterisks. Zhu et al. (2012). With kind permission to Elsevier

Fig. 4.21 HREM micrograph of a twin in nc Cu synthesized by high-pressure torsion. The arrow indicates the twin boundary. The grain boundary has a 141° kink at its intersection with the twin boundary. This twin was formed by partials with the same Burgers vector. Note that this twin morphology is the same as that of a deformation twins in coarse-grained fcc metals. Zhu et al. (2012). With kind permission to Elsevier

materials. Twins are also found to increase the strain hardening rate and the strain rate sensitivity, which leads to increase in ductility. (i)

Twinning in High SFE FCC Metals (Al or Ni)

High SFE occuring in some metals such as Al does not favor twin formation and deformation by slip is preferable over deformation by twinning. However, molecular

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Fig. 4.22 a A deformation twin at the lower corner of a large grain with the twin boundaries marked by two white arrows, and b HRTEM image of the twin. Liao et al. (2003)

dynamic calculations predicted the formation of deformation twins in nc Al. Indeed, deformation twin formation in the high SFE Al was confirmed in nc Al film. The twins formation considered are by (a) twin nucleation from GBs and (b) twin lamelae via the dissociation and migration of GBs. In Fig. 4.22a a TEM micrographs and in (b) HRTEM image of twin is shown. The twin boundary in (a) is marked by two white arrows. It is believed that the twin shown in Fig. 4.22 was formed by the successive emisssion of partial Shockley dislocations from GBs on adjacent planes. Another type of twin is shown in Fig. 4.23a. The inset in Fig. 4.23a shows the Fourier transformation of a region that includes areas A and B. It indicates that the two areas form a crystallographic relationship with (1 1 1) as the twinning plane. The plane is wavy unlike the usual straight twinning plane. An enlarged image of the white frame in Fig. 4.23a is presented in Fig. 4.23b, indicating that the A and B areas are in twin relationship. Some straight boundary segments are coherent (1 1 1) twin boundaries marked with white arrows and are connected with nanocrystallographic segments forming a zig-zag boundary between the two twinning areas. The mechanism of this type of twin formation is associated with splitting and subsequent migration of GB segment leaving behind two coherent twin boundaries. Elongated grain with GB (outlined by dashed line) containing two twins marked by white arrows and asterisks is shown in Fig. 4.23. A HRTEM image inset in Fig. 4.24 shows twin relationship along a twin boundary near A (black). The twin boundary marked as a-a has two straight segments, which are connected by a noncrystallographic segment and formed by the mechanism outlined earlier (for Fig. 4.23). The twin boundary b-b is not entirely straight (with a slight curvature) and formed by extrinsic Frank partial dislocations as well as Shockley partials in the otherwise straight (111) twin boundaries.

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Fig. 4.23 a Areas A and B form a twinning relationship with a wavy boundary between them. The inset shows Fourier transformation of a region that encompasses areas A and B, which indicates a (1 1 1) twinning plane; b HRTEM image of a twin boundary segment from the white frame in (a). It consists of short, straight, coherent (1 1 1) twinning planes (marked by arrows) connected by incoherent, noncrystallographic segments. Liao et al. (2003)

In summary, it has been revealed that in nc Al produced by cryogenic ball milling, deformation twins could form via the dynamic overlapping of stacking fault ribbons formed by Shockley partial dislocations emitted from grain boundaries (GBs), as predicted by molecular dynamic simulation (not observed in coarse grained Al). Also curved twin boundaries caused by partial dislocations were observed. Recall that Al has very high stacking fault energy and, consequently, very narrow SF width in its coarse-grained state. Very high strain rates, e.g. in shock-loaded or explosively deformed materials, often lead to twinning, and under such conditions, twins have been observed even in f.c.c. aluminium-alloys which, according to conventional theory, should not twin because the stacking fault energy of aluminium is too high.

4.4.3.3

Growth Twins in Nanocrystals

Nanotwins (NT) have been observed in FCC metals made by electrodeposition and physical vapor deposition. The interest in them is not only scientific but technological also. These as-grown NT structures exhibit unusual and outstanding properties compared with their untwinned NC counterparts. NT metals, such as austenitic stainless steels, Cu, or Ag have been shown to exhibit very high strengths along with good ductility, thermal stability, and electrical conductivity at room temperature. As mentioned above, twin nucleation and propagation in FCC metals occurs by {111} < 112 > partial dislocations, whereas slip involves full {111} < 110 > dislocations. The fault created by {111} < 112 > partial dislocations is an intrinsic stacking fault with an energ γI. Low enegy SF (SFE) produces growth twins which were observed in FCC

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Fig. 4.24 An elongated grain (with GB marked by white dashed lines) containing two twin boundaries, marked by white arrows and asterisks. The inset shows the twinning relationship along a twin boundary near A. The twin boundary a-a is similar to that in Fig. 4.23, and the twin boundary b-b is slightly curved. Liao et al. (2003)

metals, such as austenitic stainless steels (γ I = 20–50 mJ m−2 ), Cu (45 mJ m−2 ), Au (32 mJ m−2 ), or Ag (16 mJ m−2 ). In NT materials fabricated by physical vapor deposition, {111} planes are deposited preferentially on the substrate and with increased deposition rate higher density of growth twins (or SFs) are obtained. The resulting microstructure of such fabrication is usually compprised of GBs, coherent CTBs) and incoherent twin boundaries (ITB). Twins in Al alloys until recently were considered as unexpected or even not possible to achieve, because of the very high stacking fault energy of γsf = 120 to 165 mJ m−2 . Predicted twinning in Al requires extreme conditions of deformation. Experimentally along the prediction requirements, namely high strain rates such as occurs in shock-loaded or explosively deformed metals, twin formation have been observed in Al and its alloys. The morphology and microstructure of Al electrodeposited (20 mAcm−2 ) on Ag substrate is illustrated in Fig. 4.25. The image was obtained by SEM. The wellannealed Ag substrate shows a large grain size and only few wide recrystallization twins. The coherent twin boundaries extend from the Ag substrate to the adjacent

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Fig. 4.25 Electron microscopy investigations of the electrodeposited Al layer. a SEM image of a cross section through the Al deposit, revealing micrometer-sized grains containing a high density of twins. The bright line at the bottom indicates the interface between the deposited Al film and the substrate (Ag paste). b TEM image taken from a top-view specimen, revealing a high density of twins. c This is also confirmed in the TEM image taken from a cross-sectional specimen. Rafailovi´c et al. (2019). Open Access

grain of the Al layer. Away from the substrate multiple new random grains form (because the epitaxy breaks down) which contain a high density of twins. High resolution bright field TEM images of the Al layer from both top view (Fig. 4.25b) and cross section (Fig. 4.25c). The top view image contains a high density of dislocations and twins and the cross section image is similar. The measured mean twin spacing is ~100 nm. Detailed TEM images away from the interface with the substrate are are shown in Fig. 4.26. Difraction pattern of the grain illustrated in Fig. 4.26a has a [110] zone axis orientation and contains a (111) twin boundary. A color-coded overprint of two TEM dark-field images taken with matrix and twin reflections, is shown in Fig. 4.26b indicating that the grain consists of alternating twinned lamellae. Atomically sharp twin boundaries of (111) and orientations of [110] were revealed by HRTEM and are illustrated in Fig. 4.26c. High density of growth twins in pure Al was observed which was not expected because of is high SFE. The influence of the Ag substrate is limited according to density functional theory calculations only to the layers close to the interface. The high density of twins in the case of electrodeposition of Al arises because of fast nucleation and is also promoted by a monolayer of adsorbed hydrogen originating from water impurities. Thus deposited Al coatings are reinforced by the presence of twins. For additional information on growth twins the reader can consult Beyerlein et al. (2014) and Anderoglu et al. (2008).

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Fig. 4.26 TEM investigation of the electrodeposited Al specimen (top view). a Diffraction pattern ([110] orientation) taken from a twinned grain. The mirror plane (blue line) and a twin reflection (subscript T) are marked. b Color-coded overlay of dark-field images generated using the reflections marked green (200) and red (200T ) in (A). c High-resolution TEM image showing the atomic structure of a twin boundary. Rafailovi´c et al. (2019). Open Access

4.4.3.4

Annealing Twins

Generally, the twins are deformation, growth and annealing twins. These twins in FCC alloys and pure metals are identical crystallographcally since their coherent twin boundaries are on {111} planes. Their formation occurs under different conditions: deformation twins induced by an applied stress involve partial dislocations, growth twins are formed by growth accident (also during recrystallization) during vapor deposition when vapor transforms to solid or when liquid transforms to solid and annealing twins might require grain boundary migration. Whatever type of twin might be, generally twins form to reduce the excess energy of the bulk material. For example, annealing twins formation is accompanied with reduction of the strain in a strained boundary. The distinction between deformation and annealing twins based on their shape is that deformation twins usually has a lens-like (slightly curved) shape and cold work effects can be seen within the grains, while annealing twins are parallel straight lines (also dislocation free compared to mechanical twins). Mechanical or deformation twins can form at low homologous temperatures in order to accommodate strains during deformation. The lamelae of the deformation twins (~50 nm) depends on the SFE of the material. Low to moderate SFE promote annealing twin formation after annealing of deformed material, and these low energy boundaries are created in order to decrease the overall interfacial energy of a system. In cubic metals the annealing twins usually have long parallel twin boundaries and can be of various sizes. Note that the annealing twins (errors in the stacking of close packed

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planes) are low angle grain boundaries, usually oriented single crystal. At 1% offset the yield strength of the single crystal was only ~ 0.13 GPa, about 20 times lower than that of the NC nickel. Further, it does not show any strain rate sensitivity as seen in Fig. 6.27 by the black line. The nanocrystalline nickel micropillar accommodats the plastic deformation, the single crystal pillar develops several large slip steps over the entire pillar diameter. It could be noted that testing by SEM allows the deformation observation of the specimen throughout the test. We have seen above in Eq. (6.6) the strain rate sensitivity, m, which for convenience is rewritten below m=

d log σ d log ε˙

(6.6)

The (SRJ) techniques used can thus be reliably and interchangeably used to accurately measure strain rate sensitivity in a wide variety of materials.

6.2.4 Tension in Nano 304L UFG microstructure of 304L SS can be produced by reverse transformation of deformaton induced martensite. The steps are as follows: a) First room temperature ECAP six pass processing produces a high volume fraction (∼70%) of deformation induced martensite with a mean grain size of ∼90 nm, b) annealing at 625 °C for 60 min to reversely transformed all martensite back to austenite with UFG sizes. The UFG contain high density of nanotwins which provide high strength. Effetive strain hardening is induced by dislocations and stacking faults (SF). The result of the process is a combination of high yield strength (810 MPa) and high uniform elongation (30%) in tensile tests. A TEM image of the phase reverted microstructure is show in Fig. 6.28

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Fig. 6.28 a Typical TEM micrograph showing the UFG microstructure produced by phase reversion transformation, b EBSD image. The black lines denote random GBs and the colored lines represent  coincident-site lattice boundaries, of which the 3 are represented by red lines, c distribution of twin thickness, d distribution of GB misorientation angles. C. X. Huang, W. P. Hu, Q. Y. Wang, C. Wang, G. Yang and Y. T. Zhu, Mater. Res. Lett., 3, 88 (Huang et al. 2015). Open access

with a mean grain size of ~ 660 nm. It reveals equiaxed grains with sharp grain boundaries, annealing nanotwins, and very low dislocation density. Figure 6.28b—  an electron backscattered (EBSD) image- shows a high fraction of 3 TBs (twin boundaries) outlined by red line and the average thickness of the twins is ∼110 nm, as shown in Fig. 6.28c. The GB misorientation distribution is shown in Fig. 6.28d. Figure 6.29a shows the representative true stress–strain curves of the UFG 304 L sample and compares it with a CG tensile tested specimen. In Fig. 6.29b the yield strength and uiform elongation are compared with those reported in the literature. All data of the figure indicates a decrease in yield strength with increased elongation, however the strengths uniform elongations of the UFG samples are clearly superior to those reported in literature. The UFG 304L samples are characterized after tensile testing by HRTEM illustrated in Fig. 6.30. In Fig. 6.30a the microstructure after ~ 28% tensile strain is shown at low magnification. The defect structure in the interior of a single grain is shown in Fig. 6.30b at higher magnificaton by tilting the incident beam parallel to the zone axis [011]. The formation of high density SFs

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.29 a Typical tensile true stress–strain curves for UFG and CG 304L SSs at a quasi-static strain rate of 5 × 10−4 s−1 and RT. The inset is engineering stress–strain curves. b Excellent strength–ductility combination of the current ideal UFG SS in comparison with other 304 L SSs (with Ni content of 10∼12%). C. X. Huang, W. P. Hu, Q. Y. Wang, C. Wang, G. Yang and Y. T. Zhu, Mater. Res. Lett., 3, 88 (Huang et al. 2015). Open access

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Fig. 6.30 Typical TEM micrographs showing the microstructures and defects in ultrafine austenitic grains after ∼28% tensile strain: a overview of the microstructure, b defect structure in a 520 nm grain, c a 400 × 570 nm grain with an annealing twin, (d) a 500 × 700 nm grain with two nanotwins. The corresponding SAD patterns with [011] zone axis are shown in the insets. The insets denoted by capital letters A and B are enlarged from the corresponding white frame regions, which reveal different slip planes activated in different region C. X. Huang, W. P. Hu, Q. Y. Wang, C. Wang, G. Yang and Y. T. Zhu, Mater. Res. Lett., 3, 88 (Huang et al. 2015). Open access

seen is due to to the low SF energy (SFE) of 304L SS (∼34 mJ/m2 ). The low SFE promotes dislocation dissociation during plastic deformation into partials and SFs. In low SFE materials, the SFs can be very wide, even across the entire grains, as shown in Fig. 6.30b. Annealing nanotwins are seen in Fig. 6.30c and d in two UFGs and high densities of dislocations are seen near TBs which confirms the fact that TBs are effective in blocking and storing dislocations. The nanotwins (NT) can lead to the activation of more slip-systems for dislocations/SFs. The activation of multiple slip-systems requires higher shear stress which results in high strain-hardening rate. Further contribution to strain hardening is due to to multiple slip in the dislocation entanglement. The dislocation density measured in deformed grains is ~ 1,8 × 1015 m−2 . SFs can originate from TBs via dislocation -TB reactions and were also generated in NT lamellae as seen by the straight lines indicated by arrows in Fig. 6.31. The contribution of dislocations to the plastic flow can be expressed by Taylor’s formula rewritten here for the stress as √ σ = MαGb ρ

(6.7)

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.31 High density of SFs (indicated by arrows) formed inside nanotwin lamellae. The upper-right inset is corresponding SAD pattern with the [011] zone axis. The lower-left inset is an HRTEM image showing a stacking fault formed within a nanotwin. C. X. Huang, W. P. Hu, Q. Y. Wang, C. Wang, G. Yang and Y. T. Zhu, Mater. Res. Lett., 3, 88 (Huang et al. 2015). Open access

where σ is the true flow stress, M is the Taylor factor, ρ is the dislocation density accumulated in the grain interior during plastic strain, α is a material constant, G is the shear modulus and b is the Burgers vector. In summary, the production of ideal UFG structure with high density of annealing twins and low density dislocation was achieved by phase-reversion annealing of deformation induced martensite. Superior combination of strength and ductility is the result of this technique. Contribution to strain hardening by producing SFs and partial dislocation by dislocation dissociation. High SFE is essential for the production of the ideal UFG structure. Similarly, to the reverse transformation of deformaton induced martensite described above (ECAP six pass processing), also reversion of cryorolled (CR) matensite can be processed to synthesize nanostructured 304L austenitic stainless steel. Unlike in the annealing temperature (625 °C) of the severely deformed martensite by ECAP, the reversion annealing was performed in the temperature range of 700–800 °C. Reversion of austenite (γ) from α’-martensite was analyzed during annealing at the temperatures indicated and for various times. The reversion temperature of α’-martensite to austenite was controlled as low as possible to avoid grain growth of the reversed austenite. Grain refinement in austenite occurs during SPD as a consequence of the formation of deformation twins in metastable γ-grains, which undergo stress-induced phase transition causing rapid microstructural refinement. Stacking fault energy (SFE) influences twinning and stress induced martensitic transformation. Deformation of γ occurs through dislocation glide (SFE ≈ 45 mJ m−2 ). Deformation twinning in austenitic SS occurs with SFE in the range of 18–45 mJ m−2 . Also straining promotes

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207

direct γ − α’ transformation. The following experimental steps are used: (1) Solution treatmen of long bars at 1100 °C for 1 h and water quenching. (2) Cryorolling at—153° C of the as-quenched samples. (3) Specimens acchieving 0.2 and 1,8 strain at 0.2 intervals were labeled as CR0.2, CR0.4, CR0.6, CR0.8, CR1.0, CR1.2, CR1.4, CR1.6 and CR1.8, respectively (clearly CR stands for cryorolling and the numbers represent the strain). (4) Further the CR1.8 samples were annealed at 700 °C, 750 °C and 800 °C fo 5 min and water quenched. (5) Structural investigation. Crystalline  1/2 and volume % martensite as a function of cryorolling size d, lattice strain ε2 strain -estimated from XRD peak broadening- is shown in Fig. 6.32a. XRD has also shown that the vol.% martenste in CR0.6, CR0.8 and CR1.0, namely at 0.6, 0.8 and 1.0 strains, are 95%, 98% and 100% respectively as shown in Fig. 6.32b. Various

Fig. 6.32 a Variation of crystallite size and lattice strain of austenite and martensite with CR strain. b The variations of the vol % martensite and bulk hardness with CR strain. B. Roy, R. Kumar and J. Das, Mater. Sci. and Eng., A 631, 241 (2015). With kind permission of Elsevier

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6 Dynamic Deformation—The Effect of Strain Rate

bright field (BF) and dark field (DF) TEM images and analysis of selected area electron diffraction (SAED) pattern of differently cold rolled specimens are illustrated in Fig. 6.33, showing the presence of α’ in all the CR specimens. The microstructure is

Fig. 6.33 a TEM BF image and the corresponding SAED pattern (unset) showing the presence of twins in both α’ and γ phases. b TEM BF of image CR1.0 showing α’ -laths inset, corresponding SAED pattern showing teinning. c TEM BF image of CR1.8 showing nanolamelar α’ laths. d Corresponding SAED pattern showing α’-ring and weak spots of retained-γ. e TEM bright field image and inset: SAED pattern of CR1.8–700. (f) Hystogram showing bimodal distribution of grain size in CR1.8–700. B. Roy, R. Kumar and J. Das, Mater. Sci. and Eng., A 631, 241 (2015). With kind permission of Elsevier

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lamelar as seen in Fig. 6.33a. All diffraction spots were analyzed by SAED patterns and revealed the presence of γ and α’. The estimated width of the α’-laths varies in the range of 120–200 nm in CR1.0 as seen in Fig. 6.33c. For detailed diffraction spot analysis regarding twinning seen in Fig. 6.33a, the work of Roy et al. should be consulted. True stress true strain tensile curves of the solution treated and CR samples to a strain of 1.8, i.e. CR1.8 and annealed at 700 °C, 750 °C and 800 °C are illustrated in Fig. 6.34a. The specimen CR1.8 shows a high stress of σy ~ 1590 MPa compared to the ST sample, but without any strain hardening and without ductility. All the annealed specimens have higher σy than the ST sample, the highest in CR1.8–700 at a level of 1235 MPa. The largest plastic strain, εp of ~ 0.47 is obtained at CR1.8–800. High strain hardening is observed at the higher temperatures up to the UTS, although their σy values are lower than that of CR1.8–700. The values of σmax are 1286 MPa and 1246 for CR1.8 -750 and CR1.8–800 respecitvely and are listed in Table 6.3. The strain hardening expements for CR1.8–750 and CR1.8–800 are n = 0.08 and n = 0.15, respectively and they are lower than that of the ST 304L being n = 0.34.

Fig. 6.34 a Tensile true stress-true strain plots of solution treated (ST), cryorolled up to plastic strain of 1.8 (CR1.8), and subsequently annealed at 700 °C (CR1.8–700), 750 °C (CR1.8–750), 800 °C (CR1.8–800) for 5 min, b SEM image of fractured specimen showing large necking in CR1.8–750 (εn = 0.59). c Dimples in the fracture surface of CR1.8- 750, and (d) XRD patterns from the gauge section of the specimens before and after tension test. B. Roy, R. Kumar and J. Das, Mater. Sci. and Eng., A 631, 241 (2015). With kind permission of Elsevier

CR1.8-800(5min) – 375 316

Cold 4.0 + 800 C(30min)

Cold 2.3 + 700 C(300min)

◦

◦

310

387

Cold 4.0 + 700 C(120min)

◦

Cold 4.0 + 700 C(30min)

◦

–

420±3

460±3

515±2

540±2

202±5

Bulk hardness (Hv)

Cold2.3 + 900 C(45s) + 850 C(45s)

1

10

34

100

0

%α’

Cold2.3 + 950 C(45s) + 825 C(45s)

◦

99

CR1.8-750(5min)

◦

90

CR1.8-700(5min)

◦

66

CR1.8

◦

100

0

ST

%γ

Sample

1000

670

1050

1145

711

902

850

1027

1235

1590

120

σ y (MPa)

1010

940

1160

1225

1348

1090

1246

1286

1295

1590

1212

σmax (MPa)

0.40

0.21

0.09

0.02

0.36

0.10

0.47

0.39

0.19

0.01

1.07

εp

–

–

–

–

–

–

0.48

0.59

0.21

0.05

0.52

εn

–

–

–

–

–

0.12

0.15

0.08

-

-

0.34

n

Ref. [28]

Ref. [28]

Ref. [28]

Ref. [28]

Ref. [28]

Ref. [28]

Present study

Present study

Present study

Present study

Present study

Table 6.3 EBSD volume percentage (%) of γ-austenite/α’-martensite, bulk hardness at 30 kgf load, tensile yield stress (σy ), ultimate tensile strength (σmax ), true plastic elongation (εp ), true necking strain (εn ), and strain hardening exponent (n) of austenitic SS as obtained in the present study and literature. B. Roy, R. Kumar and J. Das, Mater. Sci. and Eng., A 631, 241 (2015). With kind permission of Elsevier. Ref 28 reffers to Kumar and Raabe, Ref. 29 reffers to Shakhova et al. and 40 to Forouzan et al.

210 6 Dynamic Deformation—The Effect of Strain Rate

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211

Necking in nano austenite is observed in the broken specimen (seen in Fig. 6.34b of CR1.8–750 where the necking strain, εn is 0.59. Dimples are seen over the entire surface as shown in Fig. 6.34c, while the XRD patterns are from gage section before and after the tension test. In summary, nano-austenitic SS has been synthesized by cryorolling to transform γ-austenite → α’ → martensite and reversion annealing at a temperaturer range of 700–800 °C for 5 min. CR induces severe twinning in γ-austenite and produces 50 nm size α’-laths, which promotes the evolution of nano-crystalline γ during annealing.

6.3 Compression Test in Nanomaterials 6.3.1 Compression in Al Nanostructure The compressive properties are presented in this section. The ultrafine grains (UFG) were produced by ECAP over a wide range of temperatures in the range of 77–473 K under dynamic loading conditions. The experiments were performed at various strain rates and the results indicate the estimated temperature sensitivity and the apparent activation volume. TEM bright-field image of the UFG Al (the measured average grain size is 1 μm) shown in Fig. 6.35 indicates a homogeneous structure. EBSD micrographs before and after heat treatment are illustrated in Fig. 6.36. The true stress true strain curves of the UFG Al at the temperatures and strain rates indicated in Fig. 6.37 show higher strength as the grain size is reduced as expected from the Fig. 6.35 TEM bright-field micrographs of UFG-Al. J. Su, Z. B. Tang, C. X. Wang, T. Ye, T. Suo and Y. L. Li, Inter. J. Smart and Nano Mater., 8, 56 (Su et al. 2017). Open access

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.36 EBSD micrograph (a and b) and grain size distribution (c and d) of UFG-Al before and after heat treatment. J. Su, Z. B. Tang, C. X. Wang, T. Ye, T. Suo and Y. L. Li, Inter. J. Smart and Nano Mater., 8, 56 (Su et al. 2017). Open access

Hall—Petch relation. Strain hardening rate versus true strain for UFG Al at two strain rates and at the temperatures indicated in the curves shown in Fig. 6.38 compare quasistatic (strain rate 0.001 s−1 ) and dynamic (strain rate 3000 s−1 ) defrmation. The inset in Fig. 6.38a shows at the same rate of 0.001 s−1 the CG curves in comparison with the UFG Al. Apparent strain hardening is observed in the CG Al, however dynamic recovery of dislocations at high temperatures leads to reduction in strain hardening capacity, namely softening sets in, although some strain hardening still is observed in Fig. 6.38a, even at 473 K (Fig. 6.39). However, for the UFG Al, high strain-hardening rate is only observed at the early stage of the plastic deformation. Even in this stage, the strain-hardening rate decreases sharply with strain as seen in Fig. 6.38. The estimated dislocation for UFG is on the order of 1014 m−2 (which is close to saturation). At the beginning of plastic deformation, a large number of dislocations is generated from dislocation sources, subsequently interact with grain boundaries with the consequent high strain hardening rate. The dynamic recovery. Commonly the value of SRS is evaluated from the slope of log–log flow stress versus strain rate at a certain strain by using linear regression fit. In Fig. 8.39, m for UFG and CG Al is compared for quasi-static UFG (Q) and dynamic deformation at

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Fig. 6.37 True stress versus strain curves for UFG-Al at the strain rate of a 0.001/s, b 0.01/s, c 0.1/s, d 1000/s, e 3000/s, and f 5000/s at elevated temperatures. For comparison, the true stress versus strain curves for CG-Al tested at the strain rates g 0.001/s and h 3000/s at elevated temperatures are also shown. J. Su, Z. B. Tang, C. X. Wang, T. Ye, T. Suo and Y. L. Li, Inter. J. Smart and Nano Mater., 8, 56 (Su et al. 2017). Open access

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.38 Strain-hardening rate for UFG-Al at a quasi-static (strain rate 0.001/s) and b dynamic (strain rate 3000/s) loading rates. The inset in a is the same plot for conventional coarse-grained Al at quasi-static loading rate (strain rate 0.001/s). J. Su, Z. B. Tang, C. X. Wang, T. Ye, T. Suo and Y. L. Li, Inter. J. Smart and Nano Mater., 8, 56 (Su et al. 2017). Open access

Fig. 6.39 Temperature sensitivity factor for CG-Al and UFG-Al at different strain rates and fixed strains of 0.05, 0.10, 0.15, and 0.20. J. Su, Z. B. Tang, C. X. Wang, T. Ye, T. Suo and Y. L. Li, Inter. J. Smart and Nano Mater., 8, 56 (Su et al. 2017). Open access

different temperatures due to extremely high dislocation density, however balances fast between generation and annihilation of the dislocations. The strain hardening is observed only at 77 K, and as the temperature increases to 293 K and above, some strain softening (post-yielding strain softening) occurs when the compression is at a rate of 0.001 s−1 as seen in Fig. 6.38a. The applied stress in plastic deformation is known to depend on both strain rate and temperature, therefore the understanding of deformation of materials-and UFG

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Fig. 6.40 Strain rate-sensitivity factor at elevated temperatures. J. Su, Z. B. Tang, C. X. Wang, T. Ye, T. Suo and Y. L. Li, Inter. J. Smart and Nano Mater., 8, 56 (Su et al. 2017). Open access

systems are no exception-it is necessary to consider the temperature sensitivity (TS) and the strain rate sensitivity (SES). TS is defined as  ST =

∂σ ∂T

 (6.8) T,ε

The temperature sensitivity at fixed strain for UFG and CG Al as a function of strain rate is indicated in Fig. 6.40 and the strains of deformation are also shown. The lower experimental data at strain rates of 0.001 s−1 and 3000 s−1 represent CG Cu for comparison. The TS of UFG Al increases with decreasing grain size into the nano-regime. The flow stress dependence on the strain rate sensitivity factor (SRS) m, is expressed as  m=

∂ ln σ ∂ ln ε˙

 (6.9) T,ε

It could be noted that in CG metals and alloys plastic deformation is controlled by the nucleation and motion of dislocations. However, when the grain size is below some critical value, namely in the nanometer-range, dislocation sources and pile-ups are not expected to exist within the individual grains because of the limited grain size. In such cases the GB diffusion-mediated mechanism dominates plastic deformation. Grain boundaries are likely acting as the source of dislocations and dislocation-grain boundary interactions dominate plastic deformation involving GB sliding. In the case of CG metals, thermally activated cutting of forest dislocations is the rate controlling mechanism, and is still operating in the UFG Al with 1μm grain size, which was discussed in this section. This is more likely to occur in structures of high density dislocations.

216

6 Dynamic Deformation—The Effect of Strain Rate

6.3.2 Compression in Cu Nanostructure This section considers compression tests in ultrahigh purity nc Cu, prepared by the electrodeposition technique. The grain size of the as deposited Cu is ~ 28 nm. For comparison CG annealed OFHC Cu of ~ 30 mm was used. As usually done a Kolsky bar (minitiaturized version) which can test small samples in uniaxial compression at strain rates up tp 5 × 104 s−1 was used in the experiments. Figure 6.41 compares the compressive true stress-true strain curves of the NC-Cu and the annealed CG-Cu at a quasistatic strain rate of 4 × 104 s−1 . The strength is increased in the NC-Cu by more than 100% and also the flow stress (at a strain of 10%) increased by about 38% compared to the CG-Cu. Strain hardening occurred in both cases. The power law strain hardening given in Eq, (6.8) was used for the fitting. σ = σ0



ε ε0

n (6.10)

The flow stress σ = σ0 when ε = ε0 and it is found that for nc-Cu and cg-Cu are 0. 32 and 0.49, respectively. σ0 for nc-Cu and cg-Cu are 104.7 MPa and 52.2 MPa, respectively. Although the stress exponent of nc-Cu is somewhat lower but its high value explains the much higher flow stress of nc-Cu. The dynamic stress–strain behavior of the nc-Cu and cg-Cu at a high strain rate of 1.4 × 104 s−1 are compared in Fig. 6.42. The oscillations observed in the nc-Cu is not a material property, and they result from the nature of dynamic tests. In this high strain rate teste materials, the yield stress and the flow stress of the nc-Cu are enhanced relative to the cg-Cu. The applied strain rates for the nc-Cu spans the range of 4 × 10–4 -1.8 × 104 s−1 and the respective stress- strain curves are presented in Fig. 6.43. One can observe in

Fig. 6.41 Comparison of a typical compressive stress–strain curve for the nc-Cu with that for annealed cg-Cu at a quasistatic strain rate of 4 × 104 s−1 . D. Jia, K. I. Ramesh, E. Ma, L. Lu and K. Lu, Scripta Mater. 45, 613 (Jia et al. 2001). With kind permission of Elsevier

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217

Fig. 6.42 Comparison of a tyical compressive strss-strain curve for the nc-Cu and that for the cg-Cu at a high strain rate of 1.4 × 104 s−1 . D. Jia, K. I. Ramesh, E. Ma, L. Lu and K. Lu, Scripta Mater. 45, 613 (Jia et al. 2001). With kind permission of Elsevier

Fig. 6.43 Stress–strain curves for the nc-Cuat strain rates from 4 × 10–4 to 1.8 × 104 s−1 . D. Jia, K. I. Ramesh, E. Ma, L. Lu and K. Lu, Scripta Mater. 45, 613 (Jia et al. 2001). With kind permission of Elsevier

Fig. 6.43 that the effect of the strain rate on the strain hardening is more pronounced than on the yield stress. The strain rate sensitivity of nc-Cu and cg-Cu are compared in Fig. 6.44 where the flow stress is plotted versus the log (strain rate). In summary, the mechanical behavior of electrodeposited nc Cu compared with cg-Cu exhibits increased strengh in the quasistatic and high strain rates conditions. The strain hardening rate of the nc-Cu is strain rate dependent. The compressive behavior of the strength, strain hardening and strain rate sensitivity are different than

218

6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.44 Comparison of the rate dependence on the flow stress (at a strain of 15%) of the nc-Cu with that of the cg-Cu. A curve derived from Ref. 11 is included. D. Jia, K. I. Ramesh, E. Ma, L. Lu and K. Lu, Scripta Mater. 45, 613 (Jia et al. 2001). With kind permission of Elsevier. Ref 11 stands for Follansbea et al.

in the cg-Cu. In a comprehensive work on the properties of nanmaterials Meyers et al. in a plot in Fig. 6.45, indicate the Hall–Petch trend for grain sizes in the range micron-nanocrystalline metals, among them for Cu, as illustrated in the figure. There is a deviation from the conventional Hall–Petch relation as seen in the figure and a decrease in the slope can be seen in the the small grain sizes. Recall the Hall-Pech relation has been presented earlier in this book, but rewritten for convenience as σy = σ0 + kd−1/

(6.11)

where σ0 is the friction stress and k is a constant. Clearly σy and d are the yield stress and grain size, respectively. Stress–strain curves in tension and compression are compared in Fig. 6.46. No work hardening is observed in compression, namely dσ/dε = 0 (low tensile ductility in tension). The flat compression curve has been observed in other nanocrystalline metals also. Room temperature dynamic recovery is often observed in nanocrystalline samples while a competion exist between generation of dislocations during the plastic deformation and annihilation during recovery. The density of dislocations is determined by this competition. Grain boundaries are expected to be not only sinks, but also the locations of dislocations generation. Nevertheless, dislocations are mainly involved in the deformation and are the dominant mechanism until the grain size is in the range of ~ 10–15 nm. The strain rate sensitivity, m evaluated for nc-Cu is 0.015 in the strain rate range of 0.001–4000 s−1 shown in Fig. 6.47 where the true stress is plotted versus the true strain. Recall as indicated earlier in the book m is defined –as rewritten in Eq. (6.12)- by

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Fig. 6.45 Plots showing the trend of yield stress with grain size for Cu as compared to the conventional Hall–Petch response. M. A. Meyers, A. Mishra and D. J. Benson, Progress in Materials Sciemce, 51, 427 (Meyers et al. 2006). With kind permission of Elsevier

Fig. 6.46 Compressive and tensile stress–strain curves (tensile: engineering) for copper subjected to ECAP. M. A. Meyers, A. Mishra and D. J. Benson, Progress in Materials Sciemce, 51, 427 (Meyers et al. 2006). With kind permission of Elsevier

220

6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.47 Compressive and tensile stress–strain curves (tensile: engineering) for copper subjected to ECAP. M. A. Meyers, A. Mishra and D. J. Benson, Progress in Materials Sciemce, 51, 427 (Meyers et al. 2006). With kind permission of Elsevier

m=

∂ ln σ ∂ ln ε˙

(6.12)

There is a difference in the stress–strain curves between the strain rates at 77 K, the higher the strain rate the higher the flow stress, while at room temperature only a slight difference exists between the applied two strain rates. The proposed mechanism of plastic deformation is grain size dependent as indicated below: 1 μm > d >100 nm range namely in the UFG range; a core-and mantle-model describe the deformation. The models are based on dislocation generation at or adjacent to grain boundaries and formation of work hardened grain boundary layer layers. 100 nm > d >20 nm; in this region the dislocations encounter less and less chance of cross slip and multiplying in grains. Dislocation travel through the grains relatively unimpeded, and thus annihilate in the opposing grain boundary. The process can proceed without significant strain hardening (since density of dislocations remains constant). 20 nm > d >1 nm; in this regime grain boundary effects dominate the deformation. The separation between partial dislocations increases. Due to the increased tendency for partial dislocation emission from grain boundaries, there is a greater ease for mechanical twining. Grian boundary sliding is the principal deformation mechanism. This has been considered as the reason for the deviation in the Hall–Petch relation seen in Fig. 6.45. The mechanical twins observed in nanocrystalline metals, once a partial dislocation is emitted depends on the separation between the partials. Twinning reqires only a few partial dislocation gliding in parallel planes. Thus, the mechanical twin formation is an indication of deformation involving partial dislocations. There seems to be indications that ther is a threshold grain size at which perfect dislocations decompose into partials. In a plot of shear stress against grain size for Al (plot 104 in the work of Meyers et al.) it was shown that the stress required for emission of perfect

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221

dislocations, τ is higher than that required for the emission of partial dislocations, τp which in turn is higher than the stress for twinning, τtein .

6.3.3 Compression in Ni Nanostructure Strain-rate jump technique test and constant strain rate testing is used to explore the compression tests of NC Ni. The flow behavior is determined using compression tests with a fixed strain rate. The true stress-plastic strain data is shown in Fig. 6.48a. Fig. 6.48 a Flow behavior of NC Ni determined by constant strain-rate compression experiments and b corresponding m-values over representative plastic strains. V. Maier, K. Durst, J. Mueller, B. Backes, H. Werner and M. Göken, J. Mater. Res.,26, 1421 (Maier et al. 2011). With kind permission of Cambridge University Press

222

6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.49 SRS values for compression tests and for experimental as well as simulated nanoindentations. V. Maier, K. Durst, J. Mueller, B. Backes, H. Werner and M. Göken, J. Mater. Res., 26, 1421 (Maier et al. 2011). With kind permission of Cambridge University Press

A steady state is reached after about 5% plastic strain which is strain rate dependent as seen in the figure. As would be expected the true stress is the highest at the higher strain rate (˙ε = 10–3 s−1 ). Figure 6.48b represents the strain rate sensitivity (SRS) exponent, m determined at different plastic strains. The strain rate sensitivity exponent, m is higher at small plastic strains which decreases to a value m = 0.016 at a plastic srain of 10% for steady state deformation. Indentation tests are compared with uniaxial tests. The representarive indentation strain depends on the indenter shape. A Berkovich indenterinduces a representative strain of around 8%, whereas the representative strain of a cube-corner shaped indenter is about 22%. The stress exponent m was defined earlier in Eq. (6.10). Finite element modeling (FEM) is used for the simulation. The strain rate sensitivity as a function of the representative strain data shown in Fig. 6.49 from uniaxial compression tests show consistent results with nanoindentation experiments. The SRS measured with new nanoindentation strainrate jump tests shows a good agreement with macroscopic compression tests and the FEM simulations. Generally, it was found that FEM simulations of nanoindentation experiments with input data from uniaxial compression tests lead to consistent results (Fig. 10), although some discrepancies between the simulated and the constant strain-rate nanoindentation results are obvious. However, the SRS as measured with the new nanoindentation strain-rate jump tests shows a good agreement with macroscopic compression tests and the FEM simulations. The conventional constant strainrate nanoindentation experiments exhibit significantly higher SRS than the results obtained by using the nanoindentation strain- rate jump test (Fig. 10). As it has been shown in the FEM simulations, these differences are not an effect of the complex stress state during the nanoindentation experiment, but must be due to some experimental effects. In summary the SRS of NC Ni was determined by a nanoindentation strain rate jump test method. It was shown that the resulting m values from nanoindentation

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jump experiments are in good agreement with values determined by macroscopic compression tests.

6.3.4 Compression in 304L Nanostructure The 304L steel under consideration was additively manufactured (AM) and the postmanufacturing process was dynamically characterized in compression at various strain rates of 5 × 102 , 1.5 × 103 and 3.0 × 103 s−1 . As usually done in such cases a Kolsky bar technique -as already descried earlier- was used. For comparison, wrought 304L SS having the same composition as that of AM was also characterized at the same strain rates. It is essential to consider the microstructure for better understanding the mechanical properties. The mocrostructures of the AM and wrought 304L are illustrated in Fig. 6.50. In Fig. 6.50 the wrough and AM 304L SS are compared. In (a–c) several EBSD (recall EBSD stands for electron back scatter diffraction) views of a transverse face of the wroght 304L is seen and (a) and (b) exhibit fine equiaxed grain structure. Colors indicated orientation of the austenite grains with respect to the horizontal directin in the images which in (a–c) correspond to the billet axis (longitudinal direction). The average austenite grain size in the wrought 304L is 28 μm. The grain size of the AM is 141 μm. However, when the measurement is by EBSD area method the grain sizes of 14 microns for wrought and 37 microns for AD is produced. Further, in Fig. 6.50c a SEM with a higher magnification view of the microstructure, ferrite is observed as long stringers with red arrows. It seems that the wrought steel is fully dense without evidence of voids. The AM sample shown in Fig. 6.50d indicates that the specimen of the tested sample was nearly all austenite, grains are larger than the wrought material (Fig. 6.50a, no large voids or other defects near layer interface and no lack-of-fusion defects are observed at the layer interface. As mentioned Kolsky bar technique was used for the tests. Figure 6.51 shows a comparison of engineering stresses at both ends of the specimen. Recall that in this method incident and transmission bars are part of the bar and a striking bar applies the force, generating a compressive stress wave (incident wave) propagating in the incident bar until it arrived at the specimen. Part of the incident wave is reflected back into the incident bar and the rest transmitted through the specimen and into the transmission bar. The stress at the front face σ1 and the stress at the back face σ2 are calculated with the following respective equations: σ1 =

A0 E 0 (εi + εr ) As

(6.13)

A0 E 0 ε1 As

(6.14)

σ2 =

Here εi , εr and εt is incident, reflected and transmitted bar engineering strains, E0 is Young’s modulus of the incident/transmission bar material, A0 and As are cross

224

6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.50 Comparison of microstructures of a–c wrought and d–f AM 304L stainless steel samples. Austenite grains are colored according to their orientation, while ferrite appears black in EBSD maps a, b, d, e. The ferrite is identified with red arrows in the SEM images c, f. Oxide inclusions in the AM material are highlighted with green circles. B. Song, E. Nishida, B. Sanborn, M. Maguire, D. Adams, J. Carroll, J. Wise, B. Reedlunn, J. Bishop and T. Palmer, J. Dynamic behavior matter, 3, 412 (Song et al. 2017). Free access

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Fig. 6.51 Dynamic compressive stress equilibrium. B. Song, E. Nishida, B. Sanborn, M. Maguire, D. Adams, J. Carroll, J. Wise, B. Reedlunn, J. Bishop and T. Palmer, J. Dynamic behavior matter, 3, 412 (Song et al. 2017). Free acces

sectional areas of the bars and the specimen, respectively. The nearly overlapped stress histories at both ends of the specimen seen in Fig. 6.51 indicate that the specimen was equilibrated in stress over the nearly entire duration of dynamic compressive loading. Thus, the specimen stress can be calculated with either Eqs. (6.13) or (6.14). Then the engineering strain rate and engineering strain in the specimen is calculated by the following relations: ε˙ = − 2C0 ε=− Ls

2C0 Ls

(6.15)

t εr dt

(6.16)

0

where C0 is the elastic stress wave speed in the bar material, Ls is the gage length of the specimen. Equation (6.13) indicates that a plateau in the reflected pulse (Fig. 6.52) represents a constant strain rate in the specimen, due to the utilization of an appropriate double pulse shaping technique. Figure 6.53 shows typical stress and strain histories calculated by Eqs. (6.10) and (6.12). Further, the linear strain history in the specimen indicates a constant strain rate of roughly 5 × 102 s−1 . Compresion and tension of AM and wrought 304L were dynamically characterized. The compression tests were done at three strain rates of 5 × 102 , 1.5 × 103 and 3 × 103 s−1 , while tensile test was performed only at 3 × 103 s−1 strain rate. The mean curve of 3–5 experiments was evaluated as the representative curve. The mean curve was calculated as the representative curve at each testing condition. Figure 5.54a and b show the example results of individual compressive and tensile tests at the same conditions, respectively. Both compressive and tensile experimental results show very good repeatability at the same testing condition, respectively. As shown in Fig. 6.55, all compressive stress– strain curves exhibit very similar plastic characteristics with significant sensitivities

226

6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.52 A typical set of incident, reflected, and transmitted signals in a dynamic compression test. B. Song, E. Nishida, B. Sanborn, M. Maguire, D. Adams, J. Carroll, J. Wise, B. Reedlunn, J. Bishop and T. Palmer, J. Dynamic behavior matter, 3, 412 (Song et al. 2017). Free acces

Fig. 6.53 Engineering compressive stress and strain histories in the specimen. B. Song, E. Nishida, B. Sanborn, M. Maguire, D. Adams, J. Carroll, J. Wise, B. Reedlunn, J. Bishop and T. Palmer, J. Dynamic behavior matter, 3, 412 (Song et al. 2017). Free acces

to strain rates. In Fig. 6.55 the dynamic compressive stress–strain curves of both, -the wrought and the AM curves- the directions (locations) at various strain rates are illustrated. The transverse directions are outlined with thick lines and the longitudinal with thin lines, respectively. One can note that all compressive stress–strain curves show similar elastic–plastic characteristics. In Fig. 6.56 dynamic engineering stressengineering strain curves of AM 304L are indicated for the annealed samples along the X direction and for the as deposited specimen along the Z direction. Similar curves are illustrated in the Z dirction but at different locations in Figs. 6.57 and 6.54. In summary, AM and wrought 304L SS were presented in this section at various strain rates and dynamically characterized. The AM 304L exhibited higher yield and flow stress in compression than the wrought samples when the strain in the specimen is smaller than 30%, but as expected this is on the expense of the elongation to failure. The wrought material was included as a reference. Both, the AM and wrought 304L

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Fig. 6.54 Several engineering stress–strain curves of specimens at the same loading conditions and the corresponding mean curve. a Compressive stress–strain curves of AM material; b tensile stress–strain curves of wrought material at a higher strain rate. B. Song, E. Nishida, B. Sanborn, M. Maguire, D. Adams, J. Carroll, J. Wise, B. Reedlunn, J. Bishop and T. Palmer, J. Dynamic behavior matter, 3, 412 (Song et al. 2017). Free access

SS show significant, yet similar, strain rate sensitivity for strain rates above 5 × 102 s−1 . In this study, Kolsky compression and tension bar techniques have been applied to dynamically characterize the compressive and tensile stress–strain responses of additively manufactured 304L stainless steel with different orientations with respect

228 Fig. 6.55 Comparison of dynamic compressive stress–strain curves of wrought and AM/Z-direction 304L stainless steel. B. Song, E. Nishida, B. Sanborn, M. Maguire, D. Adams, J. Carroll, J. Wise, B. Reedlunn, J. Bishop and T. Palmer, J. Dynamic behavior matter, 3, 412 (Song et al. 2017). Free access

Fig. 6.56 Comparison of dynamic compressive stress–strain curves of AM 304L stainless steel along annealed X and as-deposited Z directions. B. Song, E. Nishida, B. Sanborn, M. Maguire, D. Adams, J. Carroll, J. Wise, B. Reedlunn, J. Bishop and T. Palmer, J. Dynamic behavior matter, 3, 412 (Song et al. 2017). Free access

Fig. 6.57 Comparison of dynamic compressive stress–strain curves of AM 304L stainless steel along Z direction but at different locations. B. Song, E. Nishida, B. Sanborn, M. Maguire, D. Adams, J. Carroll, J. Wise, B. Reedlunn, J. Bishop and T. Palmer, J. Dynamic behavior matter, 3, 412 (Song et al. 2017). Free access

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to the AM processes. As a reference, wrought 304L stainless steel with similar chemical composition was also characterized at the same strain rates. The experimental results showed that the AM 304L stainless steel exhibited higher yield and flow stresses than the wrought material when the strain magnitude was less than 30%, in both compression and tension in dynamic deformation, the as-deposited AM material showed about 35% less elongation to failure than the wrought material. Both AM and wrought 304L stainless steel show significant, yet similar, strain-rate sensitivity for strain rate magnitudes above 500 s−1 .

6.3.5 Compression in Nano Alumia Alumina is mainly used as a reinforcing agent for various elements or compounds, and therefore it should not be surprising that very limited information is found in the literature, despite the extemsive work on alumina composites. Sandial National Laboraties has published some information on deformation of alumina particles at room temperature. The essential data relevant to this section is presented below: Areosol deposition (AD) enables integration of the submicron particles to be consolidated in the form of a film. The submicron particles of the film microstructure undergo plastic deformation and break up into small nano crystallites of 20–75 nm. Particle compressive deformation in situ and molecular dynamic (MD) was performed and the submicron particles served as building blocks for AD coatings. The deformation behavior is influenced by the number of internal defects, temperature and crystal orientation and its size. Pre-existing immobile defects exist which scale with size. Particles of quasi-static deformation at room temperature shown in Fig. 6.58 illustrate in (a) and (b) highly defective 3.0 μm alumina particles and in (c) an 0.3 μm nearly defect free particle. In situ micro compression of ultra pure single crystal 0.3 and 3.0 μm particles of Al2 O3 were performed. The in situ TEM micro-compression of the 0.3 μm at a strain

Fig. 6.58 Deformation behavior influence by the number of internal defect. P. Sarobol, M. Chandross, W. M. Mook, P. G. Kotula, D. C. Bufford, K. Hattar, B. L. Boyce, J. D. Carroll, T. D. Holmes, A. S. Miller and A. C. Hall, International Thermal Spray Conference. May 11, 2015. Long Beach, CA. Free access

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6 Dynamic Deformation—The Effect of Strain Rate

rate of 5 × 10–3 s−1 is illustrated in Fig. 6.59b showing a plot of load against depth. In (a) the result of the compression is indicated. In Fig. 6.60b the load is against depth at a rate of 9.0 × 10–3 , while in (a) the result of the micro-compression is shown. Table 6.4 summerizes the micro-compression of alumina. Frther results of the microcompression of the particles is illustrated in Fig. 6.61 comparing the particles before and after the deformation at the loadig rates of 8 nn s−1 and 15 nm s−1 , respectively. The various stages indicated by the letters in Fig. 6.59 is illustrated in Fig. 6.62. In Fig. 6.62a is the particle shape before deformation, (b) represent the yield strength,

Fig. 6.59 In situ TEM micro-compression at a rate 5 × 10–3 s−1 . P. Sarobol, M. Chandross, W. M. Mook, P. G. Kotula, D. C. Bufford, K. Hattar, B. L. Boyce, J. D. Carroll, T. D. Holmes, A. S. Miller and A. C. Hall, Intenational Thermal Spray Conference. May 11, 2015. Long Beach, CA. Free access

Fig. 6.60 In situ TEM micro-compression at a rate 9. 0 × 10–3 . P. Sarobol, M. Chandross, W. M. Mook, P. G. Kotula, D. C. Bufford, K. Hattar, B. L. Boyce, J. D. Carroll, T. D. Holmes, A. S. Miller and A. C. Hall, International Thermal Spray Conference. May 11, 2015. Long Beach, CA. Free access

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Table 6.4 Micro compression summary. P. Sarobol, M. Chandross, W. M. Mook, P. G. Kotula, D. C. Bufford, K. Hattar, B. L. Boyce, J. D. Carroll, T. D. Holmes, A. S. Miller and A. C. Hall, International Thermal Spray Conference. May 11, 2015. Long Beach, CA. Free access Particle identifier

Diameter (μm)

Nominal strain rate (s−1 )

Strain Energy density before displacement excursion (MJ/m3 )

Strain at displacement excursion (%)

Large Particles SEM-LP1

2.9

0.03

47

5

SEM-LP2

2.6

0.006

106

5

SEM-LP4

2.9

0.005

70

5

SEM-LP5

2.9

0.003

203

Avg Large Particles

2.8

–

SEM-SP2

0.17

0.09

494

11

SEM-SP3

0.29

0.05

366

12

SEM-SP4

0.28

0.05

607

13

SEM-SP5

0.29

0.05

675

16

*TEM-SA2

0.38

*0.005

573

32

*TEM-SB1

0.24

*0.009

1066

27

Avg Small Particles

0.26

630 ± 238

±9

7 5.5 ± 1

Small Particles

–

(c) and (d) re shapes before burst and post burst respectively and after crack formation in the alumina the shapes are seen in Fig. 6.62e and f. The starting particle (particle A) size is 100 nm. The pre-burst plasticity is characterized by large regime with high dislocation activity involving nucleation and moving through the particle. The crack nucleation and propagation leads to through-particle fracture. Similar stages of the particle B deformation are not presented here, but interested readers can consult the Sandia pulication. In summary of this section type and number of pre-existing defects influence the deformation behavior of alumina and the observations of the in situ microcompression experiments agree with the simulated results (not indicated in this section). Brittle fracture occurs in compression of defective micron seized Al2 O3 . Nearly defect-free submicron Al2 O2 particles deform plastically and fracture after higher accumulated strain. Dislocation are nucleatd and mobile dislocations are induced by ball milling of the sub-micron particles. In the wake of dislocation mobility slip occurs by shear deformation causing significant shape changes before crack formation and final fracture.

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6 Dynamic Deformation—The Effect of Strain Rate

8 nm/s

15 nm/s

Fig. 6.61 Particle before and after compression. a and b before compression, and after deformation at c and d at the indicted loading rate. P. Sarobol, M. Chandross, W. M. Mook, P. G. Kotula, D. C. Bufford, K. Hattar, B. L. Boyce, J. D. Carroll, T. D. Holmes, A. S. Miller and A. C. Hall, International Thermal Spray Conference. May 11, 2015. Long Beach, CA. Free access

6.4 Hardness-Indentation Test in Nanomaterials 6.4.1 Hardness in Nano Al It has been observed that the strain rate sensitivity increases at grain sizes below a critical value, which is illustrated in Fig. 6.63 for Cu. Such behacior is expected in other metals among them also for nano Al. Enhanced strain sensitivity has been measured also by nanoindentation hardness tests. The plot of the strain sensitivity m, versus the size, d. and is shown in Fig. 6.64a for Al. Ultra fine grain sized Al has an m value (namely the slope) of 0.027 and is shown in Fig. 6.64. Comparison is with conventional grain size Al where m is only 0.007. The increased strain rate sensitivity in metals is often related to a change in the plastic deformation. As we have seen earlier m is given by m=

∂σ ∂ ln ε˙

Another expression in terms of the activation volume, m is

(6.17)

6.4 Hardness-Indentation Test in Nanomaterials Fig. 6.62 Various stages indicated by the red letters in Fig. 6.59. P. Sarobol, M. Chandross, W. M. Mook, P. G. Kotula, D. C. Bufford, K. Hattar, B. L. Boyce, J. D. Carroll, T. D. Holmes, A. S. Miller and A. C. Hall, International Thermal Spray Conference. May 11, 2015. Long Beach, CA. Free access

Fig. 6.63 Strain rate sensitivity plot for Cu as a function of grain size. M. A. Meyers, A. Mishra, D. J. Benson, Prog. Mater. Sci., 51, 427 (Meyers et al. 2006). With kind permission of Elsevier

Zone axis near [2532]

233

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.64 Comparison of strain rate sensitivity (from hardness measurements) for conventional and ultrafine grain sized aluminum. M. A. Meyers, A. Mishra, D. J. Benson, Prog. Mater. Sci., 51, 427 (2006). With kind permission of Elsevier

m=

31/2 kT V σy

(6.18)

where V is the activation volume for plastic deformation which is related to the mechanism of deformation and σy is the yeald stress. The increased strain rate sensitivity is directly related, to a change in the rate controlling mechanism for plastic deformation. It can be seen through Eq. (6.18) that m is proportional to V−1 meaning that m is inversely proportional to the activation energy. FCC metals commonly have a large activation volume of   V ∼ 102 − 103 b3 for dislocations cutting through forest dislocations compared to grain boundary processes (controlled by GB diffusion) with much lower atomic volume of V ∼ (1 − 10)b3 Equation 6.17 can als be expressed in terms of hardness as m indent. =

d(ln H ) d(ln ε˙ indent. )

(6.19)

The strain rate is proportiona to the rate of displacement h˙ as ε˙ =

h˙ h

(6.20)

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the strain rate can be given also as 1 ε˙ = 2

 ˙  P 1 P˙ H˙ ≈ − P H 2P

(6.21)

and (6.18) can be written in terms of hardness H and can be written as √ 3 3kT 31/2 kT = m= V.σf V.H

(6.22)

As can be seen the hardness, H is related to the flow stress using a factor of 3.

6.4.2 Hardness in Nano Cu The specimens were produced by pulsed electrodeposition. It has been observed in the past years that grain refinement in the nanometer range induces substantial strengthening due to the large number of grain boundaries which act as obstacles to dislocation motion. Observations also indicated, that in nanostructured metals (such as Cu, Ni, ect.) -smaller than 100 nm (~ 40 nm)—the deformation characteristics is highly load rate dependent and an increase in the loading rate greatly increases the resistance to plastic flow. There are indications, that in some metals (Ni for example) indentation in nanocrystalline samples are strain rate dependent, but microcrystalline (average grain size > 1μm) are relatively not strain rate sensitive. Hoever, in Cu of ~ 200 nm, produced by ECAP (high intial defect density) a strong rate sensitivity of the plastic flow was observed. In uniaxial deformation the strain rate sensitivity, m was given in Eq. (6.12) and in terms of hardness in Eq. (6.19). The activation volume V of Eq. (6.22) can be expressed as V =

  √ ∂ ln ε˙ 3kT ∂σ

(6.23)

It was indicated in the earlier section that V −1 is proportional to m, namely the strain rate sensitivity is contolling the plastic deformation, which means that m is inversely proportional to the activation energy for deformation. Similarly, to GBs twin boundaries (TB) also hinder dislocation motion and thus strengthen the metal. As a matter of fact, significant strengthening in polycrystalline Cu was observed by nano-scale twins introduced by pulsed electro-deposition. The concentration of twins can be varied systematically by the processing parameters. Cu specimens (three types) after nanoindentation test were prepared for structural characterization by TEM observation. The same grain size specimens for the nanoindentation are different in their twin concentration and are classified as ultra fine crystalline (UFC) Cu with an average twin width of 20 nm, lower twin density UFC Cu with

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6 Dynamic Deformation—The Effect of Strain Rate

average twin width of 90 nm and the control UFC Cu without twins. For experimental details the work of Lu et al. can be consulted. The TEM images of the three Cu specimens are illustrated in Fig. 6.65. The TEM images show that the grains of the Cu saples are about equiaxed, each grain containing a large number of growth twins with thickness up to tens of nms and a difraction pattern in Fig. 6.65a. The average grain size is almost the same for all samples about 400–500 nm. The hardness of the copper samples as a function of loading rate is shown in Fig. 6.66. The experiments were performed at constant loading rates of 1 × 10–1 , 1 × 100 , 1 × 102 and 1 × 103 mN s−1 . The strain rate sensitivity m is shown in the plot on the right ordinate. The strengthening effect of the twins is clearly seen in the figure, as indicated by the higher hardness (2.0 to 2.6 GPa) for the higher twin density specimen, compared the UFC Cu without twins, having an average grain size < 300 nm. The assumption that m of σ ∝ ε˙ m is that the indentation hardness and loading rate are equivalent to stress and strain rate respectively. Thus, the strain rates, ε˙ in thre stress–strain curves are 6 × 10–4 s−1 , 6 × 10–3 s−1 , 6 × 10–2 s−1 and 6 × 10–1 s−1 , respectively. Indented microstructure of a specimen with high density twins is shown in Fig. 6.67. Due to high local strains the TBs are displaced and inside the twins and at the TBs a high density of dislocations is observed. Also the twin width is altered by the severe plastic deformation as a result of the interaction of slip bands with twins. Contrary to the undeformed specimens in the post-indented TEM images illustrated in Fig. 6.68, large density of dislocation debris is revealed in the vicinity of coherent twin boundaries (CTBs). The CTBs in the deformed specimens are not straight as they are in the undeformed samples. Note in this figure that the TBs marked as A, B, C and D are parallel straight lines. During deformation some twins disappeard as seen in Fig. 6.68b. Displaced TBs of the nanoindented Cu is shown in more details in Fig. 6.69.

Fig. 6.65 TEM images of the as-processed microstructure of a Cu with a higher twin density, b Cu with a lower twin density, and c control UFC Cu essentially without twins. L. Lu, R. Schwaiger, Z. W. Shan, M. Dao, K. Lu and S. Suresh, Acta Materalia 53, 2169 (2005). With kind permission of Elsevier

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Fig. 6.66 Hardness from nanoindentation experiments plotted as a function of loading rate for the UFC Cu with different twin densities. The rate sensitivity exponent m was determined using the relation σ ∝ ε˙ m (with the stress σ and the strain rate ε˙ ) under the assumption that indentation hardness and loading rate are equivalent to stress and strain rate, respectively. L. Lu, R. Schwaiger, Z. W. Shan, M. Dao, K. Lu and S. Suresh, Acta Materalia 53, 2169 (2005). With kind permission of Elsevier

Fig. 6.67 TEM image of an indented Cu sample with high twin density. L. Lu, R. Schwaiger, Z. W. Shan, M. Dao, K. Lu and S. Suresh, Acta Materalia 53, 2169 (2005). With kind permission of Elsevier

In summary, it was shown above, that the loading rate of UFG Cu having high density of CTBs is significantly higher than that of UFG Cu without twins. With a decrease of the CTB density the hardness and the strain rate sensitivity also decrease. CTBs play an important role in plastic deformation. The high hardness of UFC Cu with nano-scale twins results from the effective hindering of dislocation motion by the many CTBs.

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.68 Post-indentation TEM images of dislocation sources from displaced CTBs in Cu sample with higher twin density. L. Lu, R. Schwaiger, Z. W. Shan, M. Dao, K. Lu and S. Suresh, Acta Materalia 53, 2169 (2005). With kind permission of Elsevier

Fig. 6.69 Displacement of CTBs resulting in steps and jogs in the boundary, as shown by the downward pointing arrows in this postindentation TEM image of UFC Cu with high twin density. The upward pointing arrow shows a dislocation loop apparently emitted from the twin boundary in the vicinity of the step. L. Lu, R. Schwaiger, Z. W. Shan, M. Dao, K. Lu and S. Suresh, Acta Materalia 53, 2169 (2005). With kind permission of Elsevier

6.4.3 Hardness in Nano Ni Hardness measurements is an important method to get information on the strength of a material. Of the methods used for the measurement, a new method the nanoindentation strain-rate jump technique has been developed for determining the local strain rate sensitivity (SRS) of nanocrystalline and UFG materials. In Fig. 6.70 the hardness results of a SRS jump test are shown which indicate that the hardness of NC-Ni changes with the strain rate and its value is smaller at lower identation strain rates (the Young’s modulus is included in the figure). The hardness variation with

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Fig. 6.70 Resulting hardness and Young’s modulus of NC Ni in a nanoindentation strain-rate jump experiment with reversible strain-rate jumps. V. Maier, K. Durst, J. Mueller, B. Backes, H. W. Höppel and M. Göken, Mater. Res., 26, 1421 (2011). With kind permission of Cambridge University Press

the indentation depth is shown in Fig. 6.71, and the strain rates are also indicated. The strain rates, ε˙ applied are in the range from 5 × 10–4 s−1 to 5 × 10–2 s−1 , more specifically 5 × 10–4 s−1 , 1.5 × 10–3 s−1 , 2.5 × 10–3 s−1 , 5 × 10–3 s−1 , 1.5 × 10–2 s−1 , 2.5 × 10–2 and 5 × 10–2 s−1 . As seen from Fig. 6.71 the hardness at indentation strain rates in the range from 5 × 10–2 s−1 to 2.5 10–3 s−1 are almost constant at an indentation depth >500 nm. At slow indentation strain rates < 1.5 × 10–3 an increase in hardness is seen with increasing indentation depth. Generally, the hardness decreases with decreasing strain rate. The hardness values for NC-Ni spans the range of 5.4–4.7 GPa at an indentation strain rate of from 5 × 10–2 to 1.5 × 10–3 , respectively. Note that the hardness of SX Ni at 5 × 10–3 is constant at a much lower value than the NC-Ni. SRS data for the nanoindentation is shown in Fig. 6.72, and the exponent m of Eq. 6.17 was obtained from the slope of the ln (H) versus ln ε˙ curve of this figure. Each hardness value in the figure is the average of six indentations (Fig. 6.73). Fig. 6.71 The hardness values at indentation strain rates from 5 × 10–4 s−1 to 5 × 10–2 s−1 are constant at an indentation depth of more than 500 nm. Strain rate of a SC at at a strain rate of 5 × 103 is included. V. Maier, K. Durst, J. Mueller, B. Backes, H. W. Höppel and M. Göken, Mater. Res., 26, 1421 (2011). With kind permission of Cambridge University Press

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.72 Strain-rate sensitivity (SRS) exponent m of NC-Ni measured by nanoindentation strain-rate jump tests and conventional constant strain rate nanoindentation tests. V. Maier, K. Durst, J. Mueller, B. Backes, H. W. Höppel and M. Göken, Mater. Res., 26, 1421 (2011). With kind permission of Cambridge University Press

Fig. 6.73 Evaluation of the SRS for an ideally plastic material for a Berkovich and cube-corner indentation tip. V. Maier, K. Durst, J. Mueller, B. Backes, H. W. Höppel and M. Göken, Mater. Res., 26, 1421 (2011). With kind permission of Cambridge University Press

In Fig. 6.72 the constant strain rate tests are compared with the strain rate jup tests. It is probable that the difference is a consequence of the different depth region between the two kind of tests. The difference is not great and is at the 5 × 10–4 strain rate not more than ~ 0.8 MPa. Further, notice that the difference between the two tests decreases greatly as the strain rate increases. Clealy it is expected that the m values (shown in the graph) will be different since the lines and thus the slopes are different of the two tests. Hardness as a function of strain rate by two different indeters, that of the Berkovch and cube-corner, are shown in Fig. 6.73 and are compared with finite element modeling (FEM) results. The FEM hardness for Berkovich and cube-corner indentations are about the same. The evaluation of the slope of the hardness strain rate data leads to a nearly similar m-value ranging from 0.014 to 0.02. Summarizing this section, of NC-Ni, SRS was determined by a newly developed nanoindentation strain-rate jump test method. However, the SRS obtained conventionally by using constant strain-rate indentation experiments leads to significantly

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higher m-values. The higher SRS values in conventional indentation could be the result of the long identation times required for tests at low indentation strain rates compared to the srain rate jump test technique which offers the possibility of determining SRS at low strain rates with a much reduced testig time. Recall that the strain rate jump technique is associated with abrupt strain-rate changes which are implemented in a single indentation experiment for the the hardness evaluation.

6.4.4 Hardness in Nano 304L SS Nanocryatalline structures of about 100 nm in austenitic stainless steels were obtained by cold rolling which is considered a severe plastic deformation. As expected the nanocrystalline structure induced significant strengthening. Cold rolling to total strain above 2 produced nanocrystalline structure with the transverse grain sizes of about 100 nm and the grain size strengthening is along the concept of Hall–Petch. The rapid grain refinement is promoted by the development of deformation twins and martensitic transformation. The significant reduction in the transverse grain size is illustrated in Fig. 6.74. The transevers austenite grain size in the 304L SS decreases to 70 nm (see Fig. 6.74) after straining to 2 and further decreases at a strain of 4 to 60 nm. The grain size of the strain induced ferrite present in the steel is ~200 nm, then it decreases in transverse ferrite to 100 nm after straining to 1.2. Further rolling almost does not vary the structure. The hardness change with strain is shown in Fig. 6.75. Included in the graph is the 316L steel (recall that 316L has almost

Fig. 6.74 The strain effect on the transverse austenite/ferrite grain size in 316L and 304L steels. A. Belyakov. M. Odnobokova, A. Kipelova, K. Tsuzaki, R. Kaibyshev, Mater. Sci. Eng., 63, 012,156 (2014). Open access

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.75 The strain effect on the hardness of 316L and 304L steels. A. Belyakov. M. Odnobokova, A. Kipelova, K. Tsuzaki, R. Kaibyshev, Mater. Sci. Eng., 63, 012,156 (2014). Open access

the same composition as that of 304L and the difference in properties is regarding corrosion resistance). The initial microstructure of the 304L steel is illustrated in Figs. 6.76 and 6.77. The initial annealed grain size in the 304L steel was 24 μm. The 304L specimen undergoes during rolling twinning and martensitic transformation. Fig. 6.76 Initial microstructures of 304L stainless steel. A. Belyakov. M. Odnobokova, A. Kipelova, K. Tsuzaki, R. Kaibyshev, Mater. Sci. Eng., 63, 012,156 (2014). Open access

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Fig. 6.77 Deformation microstructures a, c) and the corresponding phase maps b, d of the 304L stainless steel subjected to cold rolling to total equivalent strain of 0.4 a, b and 4 c, d. The inverse pole figures in (a, c) are shown for the rolling axis (RA). A. Belyakov. M. Odnobokova, A. Kipelova, K. Tsuzaki, R. Kaibyshev, Mater. Sci. Eng., 63, 012,156 (2014). Open access

Strain induced ferrite shown in the figure indicates BCC martensite, the fraction of which increases fast upon further cold rolling. TEM micrograph of cold rolled 304L to a strain of 4 is seen in Fig. 6.78. The strain effect on the structural changes in 304L steel is quantitatively presented in Figs. 6.79. The austenite fraction rapidly decreases to about 0.17 during cold rolling to a strain of 2 and then slightly decreases to 0.16 upon further processing to a strain of 4 as seen in Fig. 6.79. In this section on 304L SS the development of nanocrystalline strcture of 304L SS during cold roling to large strain was considered. Reduction of the grain size of astenite after cold roling to 70 nm, occurs on strainning to a strain of 2, and with a further decrease to 60 nm on straining to a strain of 4 as seen in Fig. 6.74. Rapid grain refinement was promoted by the development of deformation twinning and

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.78 TEM micrograph of the fine structures evolved in 304L steel subjected to cold rolling to total equivalent strain of 4. A. Belyakov. M. Odnobokova, A. Kipelova, K. Tsuzaki, R. Kaibyshev, Mater. Sci. Eng., 63, 012,156 (2014). Open access

Fig. 6.79 The strain effect on the austenite fraction in 304L steel. A. Belyakov. M. Odnobokova, A. Kipelova, K. Tsuzaki, R. Kaibyshev, Mater. Sci. Eng., 63, 012,156 (2014). Open access

martensitic transformation. Significant strengthening of nanocrystalline structures as indicated by the hardness data is considered to be the result of the grain size strengthening (Hall–Petch relationship) and the development of internal stresses, which were attributed to the large internal distortions involved by severe deformation.

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6.5 Torsion Test in Nanomaterials 6.5.1 Torsion Test in Nano Al Torsion testing involves the twisting of a sample along an axis and is a useful test for acquiring information like torsional shear stress, maximum torque, shear modulus, and breaking angle of a material or the interface between two materials. In this test generally a longitudinal sample is placed in a torsion tester and one end of the sample is twisted around the long axis until failure. The force applied is known as the torque and the displacement -an angular displacement- are recorded. The shear strength is measured during the torsion test. High-pressure tube twisting (HPTT) is a new SPD method and within this process of severe plastic deformation technique also thin wall tubes or cylinders can be obtained as net shaped components. By this process ultra-fine grained (UFG) microstructures can be obtained with grain sizes of 300 nm. It has also been used to deform commercial pure (CP) Al tubes up to shears of 24. As a result of HPTT enhanced mechanical properties are obtained (due to the UFG) such as high strength at ambient temperature and superplastic deformation at elevated temperatres. Experimental description of high pressure twisting (HPT) is described by the evolution of the stress as a function of the average shear strain and the torque was monitored as a function of twist angle. The hydrostatic pressure was kept nearly constant throughout the process. The applied shear rate was 0.1 s−1 . All tests were performed with a crosshead speed of 0.5 mm min1 , producing an initial strain rate of 1.3 × 103 s1 . Before the test, the tubes were heat-treated at 400 °C for 20 min and then water quenched, resulting in equiaxed grains with an average size of 24 as seen in the grain structure in Fig. 6.80. Stress–strain curves obtained by HPTT in CP Al is shown in Fig. 6.81. The calculated average shear stress is plotted in this figure as a functon of the average shear. Figure 6.81 shows the strain-hardening curve up to a shear of 24, during which there was unloading three times (after 60 rotations each time due to equimental limitation in the rotation angle). Its oscillating nature is due to the manual control of the axial force. The average shear stress is calculated by Eq. (6.24) and the average shear by Eq. (6.25). In this equations a and b are the internal and external radii of

Fig. 6.80 Inverse pole figure map of the grain structure before HPTT obtained by EBSD. The projected direction is the axial direction of the tube. Arzaghi, J. J. Fundenberger, L. S. Toth, R. Arruffat, L. Faure, B. Beausir and X. Sauvage, Acta Materialia, 60, 4393 (2012). With kind permission of Elsevier

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.81 Stress–strain curves obtained by HPTT for CP Al in three consecutive loadings up to a shear of 24; the upper dashed line envelopes three curves. The strain-hardening curve obtained by free end torsion is superposed for comparison. M. Arzaghi, J. J. Fundenberger, L. S. Toth, R. Arruffat, L. Faure, B. Beausir and X. Sauvage, Acta Materialia, 60, 4393 (Arzaghi et al. 2012). With kind permission of Elsevier

P[GPa]

Torsion

the tube, θ is the rotation angle, T is the external torque and h is the height of the tube. The micrographs after shear from three locations, the internal middle and outer sections of the tube are shown in Fig. 6.81 (a), (b) and (c) respectively. The T ln(b/a)  τ= 2 b − a2 π h γ =

θ ln(b/a)

(6.24) (6.25)

grain structure in the internal section is more deformed than the middle and that at the outer section. Figure 6.82d, a strain analysis, shows that the shear is largest at a value of 6 near the internal surface, and much lower in the outer. Figure 6.83 displays quantitative measurements of the evolution of the grain size and the fraction of largeangle grain boundaries as a function of strain. The grain sizes were obtained by the linear intercept method in two directions: parallel (“length”) and perpendicular to the shear direction (“width”) section. Figures 6.84 and 6.85 show TEM micrographs of the tube deformed to a mean shear strain of 20. The observations were made on two perpendicular planes: on the plane with normal axial direction (AD) shown in Fig. 6.84a–c and on the plane with normal shear direction (SD) in Fig. 6.85 a–d. On the AD plane a fairly uniformly spaced, parallel and nearly planar dense dislocation wall substructure can be seen. Note the low dislocation density inside nanoscaled grains and their smooth and straight boundaries. The microstructure on the SD plane consists of ultrafine equiaxed grains, as seen in Fig. 6.84a–d.

6.5 Torsion Test in Nanomaterials

247

(a)

(b)

10µm

8

(c)

6

(d)

4

2

10µm

10μm

0 0.0

0.2

0.4

0.6

0.8

1.0

distance from inner surface

Fig. 6.82 Micrographs obtained by EBSD after an average shear of 4 imposed on the tube near the inner surface a, in the middle b and near the outer surface c. The shear values measured form the three micrographs are displayed in c as a function of the distance from the inner surface, d shows the result of strain analysis carried out on the three micrographs a, b and c and d, a strain analysis, that shows that the shear is largest at a value of 6 near the internal surface, and much lower in the outer section. M. Arzaghi, J. J. Fundenberger, L. S. Toth, R. Arruffat, L. Faure, B. Beausir and X. Sauvage, Acta Materialia, 60, 4393 (2012). With kind permission of Elsevier

In summary a new HPTT process is a severe plastic deformation technique which was successfully applied to deform CP Al tubes up to shears of 24. Ultra-finegrained microstructures were obtained with grain sizes of 300 nm.

6.5.2 Torsion Test in Nano Cu Experimental investigations in single crystals Cu has indicated that deformationtwinning occurs at very low temperature of 4.2 K and 77.3 K, but in CG Cu it does not take place under normal deformation conditions such as tension, compression or torsion at room temperature (RT) and low strain rates < 100 s−1 . The absence of deformation -twinning in CG FCC metals at RT and low strain rate is mainly due to two reasons: (a) the existence of many independent slip systems making slip a very sufficient deformation mode and (b) much higher critical twinning stress, more

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.83 Evolution of the grain length and width and proportion of HAGB during HPTT of CP Al at room temperature. The grain sizes were obtained by the linear intercept method in two directions: parallel (“length”) and perpendicular to the shear direction (“width”). M. Arzaghi, J. J. Fundenberger, L. S. Toth, R. Arruffat, L. Faure, B. Beausir and X. Sauvage, Acta Materialia, 60, 4393 (2012). With kind permission of Elsevier

Fig. 6.84 Bright-field TEM images obtained in the AD plane (electron beam parallel to the tube axis) and showing the typical microstructure of the Al alloy processed by HPTT up to a shear strain of 20. The three images do correspond to different regions of the tube: outer part a, center part b and inner part c. M. Arzaghi, J. J. Fundenberger, L. S. Toth, R. Arruffat, L. Faure, B. Beausir and X. Sauvage, Acta Materialia, 60, 4393 (2012). With kind permission of Elsevier

than several times higher than the slip stress. This observation is related to CG FCC metals having medium to high stacking fault energy (SFE). However, deformationtwins were widely observed in polycrystalline Cu with grain sizes varying from micrometers to nanometers during the process of equal channel angular pressing at room temperature and low strain rate ~ 10–2 s−1 . It was also found that deformationtwinning in coarse-grained Cu occurred mainly in shear bands and their intersections as a result of the very high local stress resulted from the severe plastic deformation with a decrease in the grain size down to submicrometer. Further, the experimental

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Fig. 6.85 TEM images obtained in the SD plane (electron beam parallel to the shear direction) and showing the typical microstructure of the Al alloy processed by HPTT up to a shear strain of 20. Images correspond to two different regions of the tube: the inner part (a and b) and the outer part (c and d). Images (a) and (c) are bright-field images with the electron diffraction pattern (insert); images (b) and (d) are the corresponding dark-field images obtained with an aperture selecting part of the two first Debye–Scherrer rings of the SAED. M. Arzaghi, J. J. Fundenberger, L. S. Toth, R. Arruffat, L. Faure, B. Beausir and X. Sauvage, Acta Materialia, 60, 4393 (2012). With kind permission of Elsevier

observations have also demonstrated that deformation-twinning in CG-Cu or Ni took place only after sufficient strain hardening has occurred. It was indicated that a certain critical amount of dislocation density is required for the nucleation of deformationtwins. For those materials with relatively high SFE, these deformation conditions can be obtained under a very low temperature and/or a high strain rate ~ 103 s −1 , where dislocation-slip processes are suppressed. SEM -electron channeling contrast micrograph of the initial undeformed CG Cu is seen in Fig. 6.86. Deformation have been performed by ECAP at several passes. TEM bright field micrographs and the corresponding SAD patterns of Cu after ECAP deformation for (a) 1 pass, (b) 8 passes and 24 passes are shown in Fig. 6.87. A change in size and shape of the grains occurs after each pass of ECAP from parallel subgrain bands to the shear direction (a) to UFGs with mean grain size of 300 nm in the Y plane (b) (after 8 passes) and 270 nm in the X plane after 24 passes. The ultrafine grains are formed via the processes of grain subdivision evolving dislocation accumulation, tangling and rearrangement. The SAD pattern with discontinuous rings obtained indicates that a number of different orientations exist within the selected area. TEM observations indicate as illustrated in Fig. 6.88 that the deformation-twins are located in shear bands, which is a location undergoing SPD. Also it is shown in the SAD patterns in regions A and C in the micrograph that dislocation slip dominates the plastic

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.86 SEM-electron channeling contrast micrograph of the initial CG Cu rod. C. X. Huang, K. Wang, S. D. Wu, Z. F. Zhang, G. Y. Li and S. X. Li, Acta Materialia, 54, 655 (2006). With kind permission of Elsevier

Fig. 6.87 Bright-field TEM micrographs of deformation microstructures of CG-Cu after ECA pressing for: a one pass in the Y plane; b eight and c 24 passes in the X plane. C. X. Huang, K. Wang, S. D. Wu, Z. F. Zhang, G. Y. Li and S. X. Li, Acta Materialia, 54, 655 (2006). With kind permission of Elsevier

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251

Fig. 6.88 TEM micrographs of deformation twins formed in a shear band. The SAD patterns with zone axis [011] taken from the regions marked with white letters A, Band c Cin micrograph, respectively. C. X. Huang, K. Wang, S. D. Wu, Z. F. Zhang, G. Y. Li and S. X. Li, Acta Materialia, 54, 655 (2006). With kind permission of Elsevier

deformation, but in the region B deformation-twinning is activated. The twin lamellae are narrow and are limited to the shear bands. The UFGs obtained with the increase of pressing passes and the deformation-twins in these grains are nucleated at GBs and GB junctions and extend into the grain interior as indicated by the arrows in Fig. 6.89a and b. It is likely that the deformation twins in the Cu are formed UFGs via partial dislocation emission from GBs and their junctions. The deformation-twins transect regions as seen in Fig. 6.90 at A and B (grain sizes in the cross sect. 20 nm), while in region B and C the propagation of the twins is very small up to a few tens of nanometers. Their propagation is terminated by subgrain boundaries. The nanocystallite at D is completely twinned. The narrowest width of the subgrains is > 100 nm. In Fig. 6.91 the grain size dependence of the shear stresses τs and τp is indicated. With decreasing grain size, τp will be smaller than τs and deformation twinning should occur via partial dislocation emission from GBs. The critical grain size, dc , at which deformation modes transform from slip to twinning, can be obtained from Eqs. (6.26) and (6.27) shown below: τs =

2αμ b d

(6.26)

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6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.89 Bright-field TEM micrographs of deformation twins in ultrafine grains in Cu ECAPed for: a 16; b 20 passes in the X planes and c 24 passes in the Y plane. C. X. Huang, K. Wang, S. D. Wu, Z. F. Zhang, G. Y. Li and S. X. Li, Acta Materialia, 54, 655 (2006). With kind permission of Elsevier

Fig. 6.90 Bright-field TEM micrographs of deformation twins: a in an ultrafine grain and a nanocrystallite; b in subgrains of an ultrafine grain. C. X. Huang, K. Wang, S. D. Wu, Z. F. Zhang, G. Y. Li and S. X. Li, Acta Materialia, 54, 655 (2006). With kind permission of Elsevier

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Fig. 6.91 Grain size dependence of the shear stress required for dislocation emission from GB of UFG- and NC-Cu. C. X. Huang, K. Wang, S. D. Wu, Z. F. Zhang, G. Y. Li and S. X. Li, Acta Materialia, 54, 655 (2006). With kind permission of Elsevier

τp =

γ 2αμbl + d bl

(6.27)

A model suggested by Chen et al. is based on computer simulation which predicted that with decreasing grain size, the dislocation nucleation at GB transform from full dislocation emission to partial dislocation emission. In his model it is proposed that the shear stresses required to initiate a full dislocation (of type ½[110]) and Shockley partial (of type 1/6[112]) dislocation from GBs is according to relations (6.24) and (6.25).

6.5.3 Torsion Test in Nano 304L Shear stress shear strain data show a dependence on test temperature and strain rate. The plots obtained from torsion tests are presented in Fig. 6.92 at two strain rates, at temperature range 20–600 °C at (a) and is known as warm working data, and in the range 800–1200 °C at (b) and referred to as hot working data. The strain rates of the curves are ε˙ = 1 × 10−3 s−1 and ε˙ = 1 × 101 s−1 , respectively. The cold and warm curves show a significant temperature effect inducing softening and decreasing the shear stress, in particular at temperatures > 750 °C. The strain rate effect is less significant at temperatures < 750° C but quite pronounced in the temperature range > 750 °C. The torsion data indicated refer to thin walled tube geometry.

254

6 Dynamic Deformation—The Effect of Strain Rate

Fig. 6.92 Flow curves from torsion test a cold and warm working temperatures and b hot working temperatures, S. L. Semiatin and J. H Holbrook, Metal. Trans., A 14, 1681(1983). Free access

References

255

References M. Wang, A. Shan, J. Alloys Compounds 455, L10 (2008) Y. Jiang, J. Hu, Z. Jianga, J. Lian, C. Wen, Mater. Sci. Eng., A 712, 341 (2018) L. Lu, S.X. Li, K. Lu, Scripta. Materialia 45, 1163 (2001) F. Dalla Torre, H. van Swygenhoven, M. Victoria, Acta Mater. 50, 3957 (2002) R. Schwaiger, B. Moser, M. Dao, N. Chollacoop, S. Suresh, Acta Mater. 51, 5159 (2003) C.X. Huang, W.P. Hu, Q.Y. Wang, C. Wang, G. Yang, Y.T. Zhu, Mater. Res. Lett. 3, 88 (2015) B. Roy, R. Kumar, J. Das, Mater. Sci. and Eng., A 631, 241 (2015) B.R. Kumar, D. Raabe, Scrip. Mater. 66, 634 (2012) I. Shakhova, V. Dudko, A. Belyakov, K. Tsuzaki, R. Kaibyshev, Mater. Sci. Eng., A 545, 176 (2012) F. Forouzan, A. Kermanpur, A. Najafizadeh, A. Hedayati, Int. j. Mod. Phys. 5, 383 (2012) J. Su, Z.B. Tang, C.X. Wang, T. Ye, T. Suo, Y.L. Li, Inter. j. Smart Nano- Mater. 8, 56 (2017) J. May, H.W. Höppel, M. Göken, Scripta Mater. 53, 189 (2005) J. Chiddister, L. Malvern, Exp. Mech 3, 81 (1963) D. Jia, K.I. Ramesh, E. Ma, L. Lu, K. Lu, Scripta Mater. 45, 613 (2001) P.S. Follansbea, G. Regazzoni, U.F. Kocks, Inst. Phys. Conf. 70, 71 (1984) M.A. Meyers, A. Mishra, D.J. Benson, Prog. Mater Sci. 51, 427 (2006) V. Maier, K. Durst, J. Mueller, B. Backes, H. Werner, M. Göken, J. Mater. Res. 26, 1421 (2011) B. Song, E. Nishida, B. Sanborn, M. Maguire, D. Adams, J. Carroll, J. Wise, B. Reedlunn, J. Bishop, T. Palmer, J. Dyn. Behav. Matter 3, 412 (2017) P. Sarobol, M. Chandross, W.M. Mook, P. G. Kotula, D.C. Bufford, K. Hattar, B.L. Boyce, J.D. Carroll, T.D. Holmes, A.S. Miller, A.C. Hall, International Thermal Spray Conference. May 11, 2015. Long Beach, CA Alemnis Application Note, Nicholas Randall for Alemnis (2015) L. Lu, M.L. Sui, K. Lu, Science Magazine 287, 1463 (2000) L. Lu, R. Schwaiger, Z.W. Shan, M. Dao, K. Lu, S. Suresh, Acta Mater. 53, 2169 (2005) V. Maier, K. Durst, J. Mueller, B. Backes, H.W. Höppel, M. Göken, Mater. Res. 26, 1421 (2011) A. Belyakov. M. Odnobokova, A. Kipelova, K. Tsuzaki, R. Kaibyshev, Mater. Sci. Eng. 63, 012156 (2014) M. Arzaghi, J.J. Fundenberger, L.S. Toth, R. Arruffat, L. Faure, B. Beausir, X. Sauvage, Acta Mater. 60, 4393 (2012) C.X. Huang, K. Wang, S.D. Wu, Z.F. Zhang, G.Y. Li, S.X. Li, Acta Mater. 54, 655 (2006) M.W. Chen, E. Ma, K.J. Hemker, Y.M. Wang, X. Cheng, Science 300, 1275 (2003) S.L. Semiatin, J.H. Holbrook, Metal. Trans., A 14, 1681 (1983)

Chapter 7

Time Dependent Deformation-Creep in Nanomaterials

7.1 Introduction Time dependent deformation occurs not only at high temperatures but often is observed close to ambient temperature. Creep close to ambient temperature clearly is associated with the melting point of the material, typically lead is an example of low temperature time dependent deformation. Further a decisive factor in time dependent deformation is the grain size of the material; it decreases with increasing grain size and at its limit, namely single crystal, creep rate is the least. In polycrystalline material grain boundary diffusion plays an important role in the process together with grain boundary sliding and dislocation (climb) activity. Dislocation motion is hindered at grain boundaries and are blocked in their advance. The process of time dependent deformation in nanostructures is a more complex situation than in CG material due to the presence of a very large number of grain boundaries. As an example one can indicate the experimental observations that the Hall–Petch concept which relates some mechanical property (hardness, yield or flow stress) to the grain size does not hold anymore below a critical grain size. A so-called negative Hall–Petch effect is observed in its relation, namely the property drops after a maximum is reached, and thus the slope changes and becomes negative. Note that the grain size dependence where the negative Hall–Petch effect sets in is at about ~ 10 nm as observed in several metals among them Cu. This negative Hall–Petch relationship is attributed to a combination of inhibited lattice dislocations motion and the enhanced grain boundary sliding. Investigations indicate that the activity of lattice dislocations almost cease below the critical grain size while diffusion creep, grain boundary sliding and triple junction contribution dominate the overall time dependent deformation. (i)

Basic Concepts: It might be useful to consider here before further discussing creep in nano structures the essential concepts of time dependent deformation in bulk material. Homologous temperature (in absolute temperature) can be considered as the demarcation point for creep separating low-temperature creep from high-temperature creep and is defined relative to the melting point, Tm as

© Springer Nature Switzerland AG 2021 J. Pelleg, Mechanical Properties of Nanomaterials, Engineering Materials, https://doi.org/10.1007/978-3-030-74652-0_7

257

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7 Time Dependent Deformation-Creep in Nanomaterials

homologous temperature =

T Tm

(7.1)

Low temperature creep at or < 0.5 Tm is controlled by non diffusion mechanisms unlike creep > 0.5 Tn which is diffusion controlled. The factors generally acting simultaneously in creep are stress, time and T which may be expressed in terms of the strain rate as ε˙ = f (σ, t, T )

(7.2)

It is clear that for safe use at high temperatures (even for ceramics) over a long period—during their life time-high melting point material is essential to resist creep and often ceramics are considered as candidates for such application. To eliminate the contribution of grain boundary sliding which is a significant contributor to creep, it is essential to investigate it in single crystals. It is customary to divide creep as: (a) primary (transient), secondary (steady state) and tertiary (accelerated); the instantaneous elongation upon applying the force is not considered creep. A test is usual plotted in terms of strain against time as indicated in Fig. 7.1a. In this figure at (b) the strain rate, ε˙ is shown against time. Andrade should be considered ‘the father of creep’, since it was he who first suggested a unified creep relation. All the many equations describing creep given in Fig. 7.1 a A schematic creep curve showing three stages of creep and an instantaneous elongation on application of load; b schematic strain rate plot versus time. Pelleg (2017)

7.1 Introduction

259

the literature follow in the wake of Andrade’s concept of his empirical relation. One may express the variation of strain over time as:   ε = ε0 1 + β t1/3 exp(κ t)

(7.3)

where β and κ describe beta or kappa creep. When κ = 0, the constant β creep is obtained:   ε = ε0 1 + β t1/3

(7.4)

Equation 7.4 represents transient creep, since the creep rate is a decreasing function of time. Differentiating Eq. (7.4) gives the strain rate 1 dε = ε˙ = ε0 βt −2/3 dt 3

(7.5)

However, when β = 0 in Eq. (7.4) κ creep is obtained which describes the stationary creep and is given as ε = ε0 exp(κ t)

(7.6)

and again to obtain the strain rate Eq. (7.6) has to be differentiated, resulting in ε˙ = κε0 exp(κt) = κε

(7.7)

Andrade postulated that β creep is related to dislocation glide within the grain, while κ flow is related to slip along grain boundaries. Ascribing κ flow to gran boundary sliding is considered presently to be an error. Clearly there is an interest to avoid all forms of creep. Therefore, it is of utmost importance to evaluate a threshold stress and temperature—the additional factors of time-below which creep will not occur. Norton attempted to determine this threshold by suggesting a relation based on the observation that a constant stress produces a constant secondary creep rate as ε˙ = Aσ n

(7.8)

A and n are constants determined experimentally that are functions of temperature only. The effect of temperature on the shape of the creep curve at constant stress is illustrated in Fig. 7.2a. Only at some temperature level the standard creep curve shown in Fig. 7.1a is obtained experimentally. At high and low temperatures only segments of the curve can be observed. As can be seen line B is similar to the conventional creep curve often shown in many text books. Many empirical relations were suggested in the wake of Andrade’s formula. McLean suggested for the minimum secondary creep an Arrhenius type relation

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.2 Strain–time creep curves: a the shape of creep curves; (A) a creep curve at low temperature and stress and; (B) the standard creep curve (see 7.1a); (C) a high temperature and high stress curve; b Schematic creep curves at a constant temperature with variable stress. Note that σ 3 represents the standard creep curve with all three stages. Pelleg (2017)

as   Q 0 − ασ dε = ε˙ = A exp − dt kT

(7.9)

Here A and α are constants and Q0 is the activation energy for creep. A is the ‘pre-exponential’ or ‘frequency factor’. An additional expression for the creep rate, where the stress and temperature terms are separated, is given as:   Q ε˙ = Bσ exp − kT n

(7.10)

Cottrell and Cottrell and Aytekin suggested either Eq. (7.11) or Eq. (7.12) given as dγ = γ˙ = At −n dt

(7.11)

dε = ε˙ = Bt −n dt

(7.12)

or

A, B and the exponent, n are constants, with 0 ≤ n ≤ 1. Equation (7.11) is expressed in a logarithmic form, and when n = 1 the logarithmic creep is obtained which often is observed experimentally γ = α lnt (t > 1)

(7.13)

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261

Very frequently the observed experimental value is n = 2/3, and thus Eq. (7.11) can be rewritten as dγ = γ˙ = At −2/3 dt

(7.14)

Integrating (7.14) gives the equation for strain as γ = β t1/3

(7.15)

Equation (7.15) represent transient creep and called as Andrade or β creep, while Eq. (7.14) is often called α creep (also logarithmic creep). Uchic et al. taking into account the non creep instantaneous strain on loading the specimen, suggest an equation of the form: γ = γ0 + α ln(βt + 1)

(7.16)

where γ0 is the instantaneous strain, α and β are constants. Schematic logarithmic creep curves are shown in Fig. 7.3 where the plot is of γ versus lnt. The lines indicate stresses and all emanate from the origin and they are linear just like the second stage (steady state) creep curve. A function combining the instantaneous strain, γ0 and the linear contribution of second stage creep κt (Cottrell and Aytekin) well describes many creep experiments and can be written as and illustrated in Fig. 7.4. γ = γ0 + βt1/3 + κ t

(7.17)

In tertiary creep, the strain and strain rate increase until fracture occurs. In metals, entering stage III occurs when there is a reduction in the cross-sectional area due to necking or internal void formation, but in ceramic tertiary is usually not recorded, Fig. 7.3 Logarithmic creep. The lines are shown for different stresses. Pelleg (2017)

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.4 A graphic presentation of Eq. (7.17) without γ0 , obtained from the combination of transient (γI = βt1/3 ) and steady-state (γII = κt) creeps. Pelleg (2017)

unless the test is continued long enough time. In ceramics, it is void formation, in the form of pores or flaws, which effectively causes a reduction in area. Generally, in ceramics, tertiary creep is relatively short and sometimes even absent. The onset of tertiary creep occurs at the end of steady-state creep. Several investigators have shown that the starting time of tertiary creep and rupture life are related according the relation of Garofalo et al. given as t2 = Atαr

(7.18)

where tr is the rupture life, t2 is the starting time of the tertiary creep, A and α (often ~ 1) are constants. Equation 7.18 is a creep relation in particular for tertiary creep for high temperature applications. Other expressions for tertiary creep are given below as: ε I I I = ε˙ min t + At g

(7.19)

εIII = θ3 (exp[θ4 t] − 1)

(7.20)

ε I I I = −(ln[1 − C ε˙ min t])/C

(7.21)

In these Eqs., for tertiary creep without a primary stage, min in ε˙ min refers to the minimum creep rate, and A, g, θ 3 , θ 4 and C are parameters. Values of g are ~ 7–10 (Dobeš) and 3 (Graham and Walles). (ii)

Nano structure: A nanostructured material may be regarded as an intrinsic composite material consisting of grains and inter crystalline components since the grain boundary fraction is relatively large. In coarse-grained materials, the portion of the intercrystalline components is so small that its effect on timedependent deformation at ambient temperature is negligible. On the contrary, in nano-structured materials, the intercrystalline components have a large volume fraction and do play a significant role in deformation. Therefore, the total plastic

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263

deformation in nanostructured materials may be conveniently divided into two contributing components: dislocation glide and volume diffusion in the grain interior, and grain boundary migration known as grain boundary sliding. Creep testing in nanocrystalline structures, say grain size < 100 nm and UFG materials (grain size < 1 μm) may require different technics for characterizing their creep properties compared to CG material. The accepted method to produce materials in the nanometer or the UFG ranges is the equal-channel angular pressing (ECAP) technique which is a severe plastic deformation (SPD) processing method. The change in microstructure is expected to improve mechanical properties based on the concept that small size grains induce higher strength levels in the bulk material having similar composition to the small-size counterpart. Generally, in bulk material with conventional grain sizes increase in strength runs opposite to ductility which decreases. In creep, strength and ductility are key features for creep resistant material but these both are rarely achieved. It turns out that high strength and good ductility are some of the beneficial properties of nanostructures material. In the following sections of this chapter creep in nanostructures of selected materials is discussed.

7.2 Creep in Nano Al 7.2.1 Tensile Creep The Al specimens used for the creep evaluation was produced by ECAP at room temperature from commercial CG rods. Figure 7.5 shows the microstructure in cross section normal to the pressing direction after four passes ECAP. Two routes of ECAP processing are shown for changing the slip system. In route A no rotation of the sample takes place during consecutive passes, while route BA involves rotation by 90° after each consecutive pass in alternate directions between passes. Specims BC

Fig. 7.5 TEM micrographs of aluminum after four subsequent ECAP passes on route a A and b B. Sklenick et al. (2012). Open access

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7 Time Dependent Deformation-Creep in Nanomaterials

are rotated at the same sence after 90° rotation between each pass. In specimen C the sample is rotated by 180° between passes. The microstructure in Fig. 7.6 is an illustration after four and eight subsequent ECAP passes, the structure obtained by route Bc and C, respectively. ECAP undergoing severe deformation is designated as EBSD. EBSD grain maps is shown in Fig. 7.7 after 4 and 8 passes by route BC . Table 7.1 lists the grain sizes and Vicker hardnesses after heat treatment at a constant temperature (473 K) for varying times indicated in the Table for ECAP 4 passes by routes A and B. Grain size growth occurred and the hardness also changes. Softening is expected as indeed observed. During creep test no appreciable grain coarsening occurred in the specimens crept at 473 K for the times of the experiment duration as seen from Table 7.2. TEM micrographs shown in Fig. 7.8 illustrate dislocations inside the larger grains (a) which evolved during creep. They are wavy and occasionally tangled. The grains smaller than a certain size are dislocation free. In this figure the effect of the number of the ECAP passes is shown on the dislocation evolution. The

Fig. 7.6 Typical microstructure and associated SAED patterns after passage through the die for a 4 pressings, route B and b 8 pressings, route C. Sklenick et al. (2012). Open access

Fig. 7.7 Grain maps for ECAPDed Al after: a 4 passes, and b 8 passes by route B (EBSD). Sklenick et al. (2012). Open access

7.2 Creep in Nano Al

265

Table 7.1 Thermal stability and Vickers microhardness of the ECAP aluminium. Sklenick et al. (2012). Open access Annealing conditions

ECAP 4 passes route A

ECAP 4 passes route B

Grain size (μm)

Microhardness HV5

Grain size (μm)

Microhardness HV5

No annealing 473 K/0.5 h 473 K/1 h 473 K/2 h 473 K/5 h 473 K/24 h 473 K/168 h

0.9 6.6 7.9 7.3 7.3 12.2 13.4

37 27 23 23 21 19 18

0.9 4.5 4.8 4.8 5.3 5.0 10.4

38 32 32 27 27 23 21

Table 7.2 Grain size of the ECAP materials after crept at 473 K and 15 MPa. Sklenick et al. (2012). Open access

Specimen

ECAP conditions

Grain size (μm)

Time to fracture (h)

A4

Route A, 4 passes

6.4

79

A8

Route A, 8 passes

7.0

26

A12

Route A, 12 passes

6.7

17

B4

Route B, 4 passes

8.7

62

B8

Route B, 8 passes

7.2

60

B12

Route B, 12 passes

8.8

39

Fig. 7.8 TEM micrographs from the longitudinal section of an aluminum processed by ECAP route BC a after 1 ECAP pass and creep, b after 8 ECAP passes and creep. Creep at 473 K and 15 MPa. Sklenick et al. (2012). Open access

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.9 Influence of different ECAP routes and different number of ECAP passes on a creep rate, and b time to fracture. Sklenick et al. (2012). Open access

effect of EPAC passes on creep in UFG aluminum is considered below which might be different than the EPAC processed CG counterpart. Specifically, the important creep rate parameter in design for life time is of great interest. In particular, the mechanism of strengthening or softening compared to CG is of concern due to the interest of adopting nanomaterial (including Al) for technological applications. The minimum creep rate and the time to fracture of ultra high pure Al versus the number ECAP passes is shown in Fig. 7.9. All ECAP routes and the number of passes are illustrated for the minimum creep rate (a) and time to fracture (b) with no dramatic difference between the routes. Strain versus time and creep rate versus strain are illustrated in Fig. 7.10. Significant difference is observed in the creep behavior of the ECAP Al compared to the CG as seen in Fig. 7.10a. The difference is: (1) ECAP Al exhibits longer creep life than the CG counterpart. (2) The minimum creep rate for the ECAP material is 1–2 orders of magnitude less than the CG one. (3) The shape of creep curves of the high number ECAP passes differs from those performed at smaller ECAP numbers by the extent of their stages of creep. The activation energy for minimum creep rate in the temperature range 423–523 K and at two applied stresses of 15 and 20 MPa is calculated according to relation. 

∂ ln ε˙ min QC = ∂(1 − /kT)

 (7.22) σ

From the slope of Fig. 7.11b, namely of the logdε/dt versus 1/T, the stress dependent activation energy can be determined as 129.7 ± 16 and 110.9 kJ/mol for the stresses 20 and 15 MPa, respectively. Creep strain generally depends on dislocation glide, climb and grain boundary sliding (GBS). Further, stress assisted vacancies contribution (via diffusion) and intergranular void nucleation and growth have to be

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Fig. 7.10 Standard creep and creep rate versus strain for unpressed state and various number of ECAP passes via route BC (creep in tension up to fracture). Sklenick et al. (2012). Open access

Fig. 7.11 Dependence of minimum creep rate for unpressed state and 8 ECAP passes on: a applied stress, b testing temperature at two levels of stress. Sklenick et al. (2012). Open access

taken into account also. The observed intensive GBS in UFG materials is believed to be a consequence of the more rapid diffusion in ECAP processed material (apparently because GBs might be not in equilibrium). SEM measurements (Fig. 7.12) show the longitudinal marker lines, u and the fraction of boundaries, κS with observable GBS. GBS was measured on the surface of tensile specimens crept to a predetermined strain ε ≈ 0.15. The grain boundary strain component is given by. εgb = (1 + ε) μ · κ S /L

(7.23)

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.12 Example of grain boundary sliding in the ECAP aluminum (route BC , 8 passes) after creep testing at 473 K and 15 MPa. Tensile stress axis is horizontal. Sklenick et al. (2012). Open access

Table 7.3 Summary of GBS measurements (ε ∼ = 0.15). Sklenick et al. (2012). Open access No of passes

u¯ (μm)

κs

L ¯ (μm)

εgb.102

εgb/ε.102

1

0.51

0.80

14.9

3.15

21.0

2

0.48

0.83

12.7

3.60

24.0

4

0.55

0.93

12.2

4.80

32.0

8

0.49

0.91

10.8

4.70

31.0

12

0.52

0.92

11.0

5.00

33.0

The mean grain size, L was determined by the linear intercept method and the creep strain is given by γ = εgb /ε. The summary of the GBS measurements is presented in Table 7.3. A relation similar to Eq. (7.6) is shown below for the creep rate but taking into account the contribution of the grain size also as ε˙ m = Aσ n (1/d) p exp(−Q C /T T )

(7.24)

n, p and QC are stress, temperature and grain size dependent activation energy and it is assumed that they are associated with different creep mechanisms. The minimum creep rate ε˙ m is plotted against the applied stress for pure aluminum based on the data of Fig. 7.11, and displayed in Fig. 7.13. The figure shows that the minimum creep rate of the UFG material at high stresses is about two orders of magnitude lower than the unpressed material, but this difference decreases with decreasing stress and at ~ 10 MPa almost no difference exist. The dashed lines in Fig. 7.13 indicate the predictions of the theoretical creep according various models such as the NabarroHerring’s model for superplastic flow, Coble’s diffusion creep and the power law by dislocation glide and climb. The theoretical models based on Eq. (7.24) are listed in Table 7.4. The observed values of the stress exponents according to relation (7.25)

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Fig. 7.13 Experimentally determined and theoretical predicted stress dependence of the minimum creep rates for various creep mechanisms in aluminum. Sklenick et al. (2012). Open access

Table 7.4 Creep mechanisms and material data. Sklenick et al. (2012). Open access Al (473 K) dECAP = 1 μm dCREEP = 12 μm [27] Number of Creep mechanism n curve

p

A

D (m2 s−1 )

(1), (1*)

Superplastic flow

2

2

10

DGB

(2), (2*)

Nabarro–Herring creep

1

2

28

(3), (3*)

Coble creep

1

3

(4)

dislocation climb and glide

5

0

Q (kJ mol−1 )

Source

5.9 × 10–14

86

[66]

DL

2.72 × 10–20

143.4

[66]

62

DGB

5.9 × 10–14

86

[66] [67]

103

D*

1.9 × 10–14

124

[66]

are ~ 4.5 for the ECAPed aluminum and ~ 3 of the ECAPed material. The stress exponent is expressed as n = ∂ln ε˙ /∂ln T

(7.25)

The value of n ~ 4.5 in the CG Al alloy is characteristic for a dislocation climbbypass mechanism, and the lower value of n ~ 3 in the UFG material might indicate a GBS mechanism. Creep ductility in tension can be expressed by the strain to fracture, εf given as

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.14 Standard creep and creep rate versus strain curves for unpressed state and various number ECAP passes via rout BC (creep in compression ~ 0.35). Sklenick et al. (2012). Open access t f (σ,T,S)

ε f (σ, T, S) =

ε˙ (σ, T, S, t)dt

(7.26)

0

S is a structure characterizing parameter and tf is the time to fracture. This can be expressed after integrating as ε f (σ, T, S) = t f (σ, T, S)˙ε(σ, T, S)

(7.27)

ε˙ (σ, T, S) is a strain rate in the interval from 0 to tf . In summary, the number of RCAP passes determines the microstructure. Already between 1 and 4 ECAP passes equiaxed array of UFG grains evolve to d < 1 μm. By increasing the pass number from 4 to 12 passes, no substantial change in the average grain size occurs. The creep resistance to creep of pure Al in comparison to unpressed CG Al considerably increases already after the first ECAP pass. However, successive ECAP pressing lead to a noticeable decrease in the creep properties. A possible explanation for this observation (softening) in terms of indirect effect of GBS, namely, it influences the evolution of dislocations by affecting the rate of their generation and annihilation at GBs. Grain boundary sliding contribution to the overall creep is progressively increasing along high angle grain boundaries with the increase of pass number. It has been observed that creep occurs in pure aluminum after ECAP processing by the same mechanism as in conventional CG materials with intragranular dislocation glide and climb as the dominant rate-controlling deformation process. Thus. The faster creep rate is associated with the smaller grain size after ECAP inducing intensive GBS, but another reason strongly influences intragranular deformation, namely the high dislocation density resulting from the intense straining during the pressing.

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Fig. 7.15 Stress dependence of minimum creep rate for pure aluminum and its alloys in the unpressed and ECAPed conditions. Sklenick et al. (2012). Open access

7.2.2 Compression Creep Representative creep curves under compression at 473 K (which is ~ 0.5 Tm ) and an initial stress of 15 MPa is shown in Fig. 7.14. The creep test was run at a true strain of ~ 0.35 with interruptions. The observed stress exponents are for the unpressed specimen ~ 6.6 while for the ECAP Al in compression it is ~ 4.8. Compare this value with that of tension of 5.7 indicated in the previous section. The minimum creep rate as a function of stress is shown in Fig. 7.15. Al is compared with some of its alloys. The plot compares ECAP Al (and some alloys) with those of unpressed. The stress exponents by compression for the ECAP 8 passes Al and that of the unpressed one are n = 5 and n = 6.5, respectively. It is seen that the minimum creep rate of the ECAP Al is lower by about one order of magnitude than the respective unpressed Al, but this difference decrease at lower stress and at about 10 MPa is small if not negligible. Surprisingly, this observation does not hold for the Al alloys and their levels are higher than those of the unpressed ones.

7.2.3 Double Shear Test Double shear test is used to determine the shear strength, which can be performed in a universal testing machine (UTM). In direct shear test, the shearing stress is considered as uniformly distributed over the entire cross section. The shear force is applied by a suitable test rig, two different cases of shearing may arise; i.e., single shear and double shear. In single shear, shearing occurs across a single surface, and

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7 Time Dependent Deformation-Creep in Nanomaterials

in double shear shearing occurs across two surfaces. Knowledge of shear failure is important while designing any structures or machine components. Shear force causes the surface to go out of the alignment with each other and thus the material fails. Double shear creep specimen, for example made of Al, can be loaded directly on its slip systems, i.e. the applied shear stress is along the slip direction on the slip plane, so that it can be used to evaluate slip systems in creep. Based on the experiments of the double shear creep specimens in different orientations the creep and damage behavior of the double shear creep specimens can be investigated systematically with the help of a creep damage crystallographic constitutive relationship and the finite element method. Results show that there is a near uniform stress state in the shear zone and the uniform stress is almost independent of the creep time. In the center part of shear zone, only one slip system is activated. The creep damage crystallographic constitutive relationship can be used to model the creep behavior of say Al. Low temperature creep behavior of ECAPed Al 5083 (Al–4.4 Mg–0.7Mn–0.15Cr; compared with 6061 with only Al-0.8–1.2 Mg, 0.0–0.15 Mn, 0.04–0.35 Cr) alloy with grain sizes of approximately 300 nm was investigated at temperatures of 498, 523 and 548 K. As indicated earlier ECAP is a method to produce material in the UFG and nano scale ranges. The alloy was annealed at 773 K for 2 h. The ECAP of 8 passes was carried out at 473 K on the annealed alloy. Double-shear specimens from the ECAPed rods with a diameter of 10 mm was used for the creep tests. The creep tests were conducted in air in a three-zone furnace and the strain during creep was measured with a linear variable differential transformer (LVDT), accurate to 1.7 × 10–3 mm. The illustrations are presented as normal stress, σ and normal strain, ε after converting the shear stress, τ and the shear strain, γ using the expressions σ = 2τ and ε = 2/3γ

(7.28)

The tests were performed at constant stress and constant temperature in the range of 498–548 K corresponding 0.58–0.65 Tm thus highest than the common 0.5 Tm . The stress range of the creep test was conducted at 10–100 MPa. Figure 7.16a shows strain versus time curves at the temperatures indicated and other pertinent information is also presented, while Fig. 7.16b illustrates a typical well defined stage II (steady state) creep (creep rate is constant) following the primary creep as was illustrated earlier in Fig. 7.1b. Clearly during the primary creep indicated in Fig. 7.16, the creep rate continuously decreases with increasing time. Figure 7.16b is a plot of logarithmic strain rate, ε˙ with the total strain, ε under the same stress of 20 MPa. The stress dependence of the steady state is plotted on a logarithmic scale in Fig. 6.17. In this figure an unECAPed line is also included, i.e. a CG Al for comparison, in order to show the effect of the grain size on the creep strain rate. The mean grain size of the unECAPed sample is 48 μ m. A significant variation is in the stress exponent with stress, but is independent of temperature. The low value is 3.5 (at low stress level) and the high value is 5 (at the high stress level). The threshold stress was obtained by plotting the true (strain rate)1/n , ε˙ 1/n against the true stress as illustrated in Fig. 7.18. The threshold stress, σth for the ECAPed and unECAPed specimens is 2.2 and 5.5 MPA respectively. The threshold stress is related to the initiation of

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Fig. 7.16 Creep curves for 8 pass ECAPed 5083 Al alloy at 20 MPa: a strain against time, and b creep rate against strain. Kim (2010). With kind permission of Springer Nature

dislocation glide at triple junctions, ledges or particles at grain boundaries. As the temperature increases thermal vibration enhances their motion by unpinning them. This way they can overcome obstacles and initiate glide. Since smaller grain sizes have more grains, more particles per unit volume are lying on grain boundaries and consequently more glide sources are activated in fine grain metals. This results in a greater creep strain in comparison with coarse grain metals and leads to lower threshold stress in the UFG 5083 Al alloy (Fig. 7.17). Fig. 7.17 Steady-state strain rate against stress for specimens tested from 498 to 548 K. Kim (2010). With kind permission of Springer Nature

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.18 Determination of the threshold stress by plotting ε˙ 1/n against σ on a ECAPed UFG alloy and b unECAPed CG alloy. Kim (2010). With kind permission of Springer Nature

Similar equations to (7.9) and (7.10) for the activation energy for creep a powerlaw creep equation is suggested, taking into account the threshold stress, σth given in Eq. (7.29). The equation is for steady state creep rate.   Q ε˙ = A(σ − σth )n exp − RT

(7.29)

In Eq. (7.29) σth is the threshold stress, A is a material constant and the other symbols are known parameters. The analysis of the creep data according to Fig. 7.19 provides for the activation energy 72.6 kJ/mol for the low stress level (30 MPa) and 96.1 for the high stress level (80 MPa), respectively. It seems on the basis of the 72.6 activation energy the stress exponent of 3.5 that creep deformation is controlled by dislocation climb and the rate controlling mechanism might be dislocation pipe diffusion of the Mg atom in Al alloy rather than grain boundary diffusion since the exponent of 3.5 is not consistent with that of grain boundary diffusion. The value of Q = 72.6 is smaller than Qgb of Al = 86 kJ/mole, where Qgb refers to the grain boundary activation energy. The activation energy for lattice diffusion is Q = 142 kJ/mol far away from the 72.6 or even from 96.1 kJ/mol at high stress levels. Further, the activation energy of 96.1 at high stress level is close to the activation energy for grain boundary diffusion Qgb of Al indicated above as Qgb = 86.1 kJ/mol, and it agrees with the value of dislocation pipe diffusion of Al atom in Al (Q/QL = 0.68) rather than grain boundary diffusion since the stress exponents of 5 is not consistent with the occurrence of grain boundary diffusion. Summarizing shortly this section of step by double shear test, resulting from the observation and interpretation of the results as: (1) Creep behavior of well annealed UFG (~ 300 nm) and CG 5083 Al alloy is considered at three temperatures (498 K, 523 K, and 548 K). (2) CG (unECAPed) samples show a lower creep rate than those

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275

Fig. 7.19 Determination of the activation energy for creep in ECAPed UFG 5083 Al alloy a at low stress and b at high stress by plotting ε & Gn − 1 T against 1000/T. Kim (2010). With kind permission of Springer Nature

of the UFG (ECAPed) specimens. (3) The stress exponent values are at low stress 3.5 ± 0.2 and increase to 5 ± 0.2 at high stress level. (4) At low stress level steady state creep is observed in the ECAP processed samples. (5) The activation energies are 72.6 and 96.1 at low and high stress, respectively. (6) On the basis of the activation energies and the stress exponents the mechanisms are dislocation glide and the rate controlling is pipe diffusion of Mg in Al alloy (the alloy contains 4.4 wt% Mg) at low stress, while at high stress he mechanism and rate controlling step are dislocation climb and Al atom pipe diffusion in the Al alloy. (7) At low stress level, the creep curve exhibits typical class II behavior (i.e. steady state).

7.2.4 Indentation (Hardness) Despite of some controversy reports regarding the improvement of the mechanical properties of nc and UFG materials the general concept is that these material, especially the nc material, show exceptionally improved strength properties and sufficiently good ductility. The well known Hall–Petch relation relates the decrease in grain size with the enhanced strength, while the simultaneous good ductility is explained by the increased strain rate sensitivity. The large number of grain boundaries in nc directly influences creep or other time dependent deformation by (i) grain boundary sliding and grain boundary migration and (ii) the evolution of a dislocation structure (glide) and thermally activated processes (climb). Because the size limitations of nc grains, it is more convenient to perform mechanical properties test by nanoindentation, rather than performing uniaxial macroscoping testing. There

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7 Time Dependent Deformation-Creep in Nanomaterials

are many empirical relationships that convert indentation tests to yield or tensile strength. Further, uniaxial macroscopic tensile or yield test is the result of averaging over many grains, while nanoindentation is a method to understand deformation on a local scale allowing an insight to the localized deformation. The median grain size of the UFG Al is around 370 nm. The nanoindentation for the creep experiments were performed with a Berkovich indenter with testing temperature by a commercial heating stage. Contrary to the usually performed indentation tests of short duration, at around room temperature, and a preset time between 1 min and 1 h, the current test was performed at room temperature and at 200 °C, of long duration and constant load up to 10 h dwell time. The load is held constant while the dynamic indentation is monitord as a function of time. Fused Silica, the most commonly used reference material for indentation experiments, was used also in the experiments. The UFG aluminum samples were prepared by ECAP up to 8 passes. For long term creep by nanoindentation tests the equations below are of interest. The method was introduced by Weighs and Pethica which is a dynamic indentation technique with corrections for thermal drift influences. The contact stiffness, S is continuously recorded during the indentation, but the indentation depth, h is much influenced by the thermal drift, whereas the contact stiffness not. Therefore, the true contact area Ac can be determined by Eq. (7.30) if the reduced modulus, ER is known 2β S = √ · E R · Ac = SC S M π

(7.30)

expressing Ac Ac =

π S2 · 4β 2 E 2R

(7.31)

Ac is a function of the contact depth hc , namely, where f the function of the known tip area Ac = f(hc )

(7.32)

Expand f(hc ) in terms of mh as 1/4 2 f (h c ) = m 0 h 2c + m 1 h c + m 2 h 1/2 c + m3hc + . . . + mn hc

1−n

=

n

m i h 2c

1−i

i=0

(7.33)  1−n to solve the polynomial equation (calculating the eigenSubstitute h ∗c = h 2c values) to calculate at the end, h from the contact depth hc taking into account the elastic sink-in around the indenter as

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277

h = hc + ε ·

P SC S M

(7.34)

ε is a geometrical constant which depends on the shape of the indenter and which was determined for a Berkovich-pyramid as 0.75. The derivative with respect of time of h is ∂h h˙ = ∂t

(7.35)

∂h c h˙ c = ∂t

(7.36)

and the contact depth is

Equations (7.35) and (7.36) are used to calculate the indentation creep rates as ε˙ c =

h˙ ε˙ c S˙ and ε˙ = ∼ hc S h

(7.37)

The true hardness, H based on the contact stiffness is given as H=

P 4β 2 E 2R · 2 =P· Ac π S

(7.38)

Here Eq. (7.31) was substituted for Ac . H is directly related to the flow stress, σ f at a representative strain using the constrain c* . For Berkovich indenter the representative strain ε rep-Berko = 8% and for the cube corner it is ε rep-CC = 20%. The flow stress at the representative strain (called further equivalent stress is used to compare the indentation data to stress from macroscopic compression experiments as   H = c∗ · σ f εr ep−Ber ko = 8 %

(7.39)

Analyzing the nanoindentation with the assumption that creep data is in the steady state its creep rate can be described as dependent on stress given as ε˙ = K σ n = K σ 1/m

(7.40)

K is a constant n has been defined earlier as the stress exponent and m is the strain rate sensitivity. Now substituting flow stress, i.e., the equivalent stress with hardness, and recalling the definitions of m and n which can be determined from the slope of the logarithmic plot of the hardness versus the strain rate one can write Eq. (7.41) as m=

∂ln H 1 ∂lnσ ∼ = ∂ln ε˙ ∂ln ε˙ n

(7.41)

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7 Time Dependent Deformation-Creep in Nanomaterials

The activation volume A given in Eq. 7.41, is calculated from the stress exponent and this volume is associated with the thermally activated dislocation glide. √ A = 3. 3 · kT ·



∂ln ε˙ ∂H

 (7.42)

Long term nanoindentation for the creep experiments of UFG Al is shown in Fig. 7.20. It is composed of two parts the top and the bottom are plots of load and indentation depth versus indentation time, respectively. For the indentation experiment the load was increased until a preset maximum indentation depth (e.g., 1000 nm) was reached as shown in the top part of Fig. 7.20. The load was kept constant and the changes in time (1, 2, 5 and 10 h) was recorded for the variation of the displacement. The contact stiffness was calculated and the dynamic correction procedure was applied for the corrected area, Ac by Eq. (7.31) which requires the knowledge of the reduced modulus ER . The corrected contact depth, hc was derived by solving for the tip area the relation given in Eq. (7.33). It is composed of two parts the top and the bottom are plots of load and indentation depth versus indentation time, respectively. For the

Fig. 7.20 UFG-Al—Illustration of the indentation method used for long-term nanoindentation creep experiments. The upper curve represents the raw load (with reference to the surface), which is kept constant during the creep segment. The large effect of the thermal drift on the measured displacement of the indenter can be corrected by the proposed analysis. For room temperature (RT), the required value of the reduced modulus Er is measured during the loading segment as the hardness and modulus data carried out continuously during the loading segment). Maier et al. (2013a). With kind permission of Cambridge University Press

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279

indentation experiment the load was increased until a preset maximum indentation depth (e.g., 1000 nm) was reached as shown in the top part of Fig. 7.20. The load was kept constant and the changes in time (1, 2, 5 and 10 h) was recorded for the variation of the displacement. The contact stiffness was calculated and the dynamic correction procedure was applied for the corrected area, Ac by numerically using linear interpolation. The displacement data recorded by the nanoindenter, seen in the lower section of Fig. 7.20 as a blue curve differs from the calculated contact stiffness data seen as the black curve. The corrected, true hardness shown as a gray curve (also in the bottom portion of Fig. 7.20 is derived from Eq. (7.39) and the corresponding stresses were determined by Eq. 7.38. The material-dependent constrain for the use of Eq. (7.39) for Al is 2.8 (taken from Table 1 of Maier et al., and not reproduced here). The resulting true contact and the true indentation depth of Eq. (7.34) and the hardness were fitted with a three-parameter power law function. UFG and CG Al are illustrated in Fig. 7.21, which include jump tests also. The nanoindentation creep tests are in good agreement with the strain-rate jump test marked with crossed symbols. The creep rate tests are by about three of magnitude lower than the strain rates applied during nanoindentation strain rate jump tests. The creep rate was calculated by Eq. (7.37). The effect of temperature on the creep rate of UFG Al in a plot of the creep rate versus equivalent stress is illustrate in Fig. 7.22. The mechanical behavior is strongly affected by the testing temperature. With increasing temperature, the hardness of the UFG Al decreases from 0.72 GPA to 0.40 GPA, thus softening sets in and the strain sensitivity increases as seen in Fig. 7.23. In Fig. 7.22 also is seen (May et al.) the macroscopic compression tests on ECAP processed UFG Al indicating a similar behavior at both temperatures, RT and 200 °C (T/Tm = 0.5). Strain rate sensitivity data at RT and 200 °C are shown in Fig. 7.23, and Fig. 7.21 Nanoindentation creep tests results in a Norton-Plot of a Al in an ufg- and cg-state. The results from some nanoindentation strain-rate jump tests are shown (crossed symbols) in comparison. Maier et al. (2013a). With kind permission of Cambridge University Press

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.22 Time- and temperature-dependent deformation behavior results of nanoindentation creep tests for 2 h at RT and 200 °C; equivalent stresses are directly derived from the hardness according to Eq. (7.37), b ufg-Al. Maier et al. (2013a). With kind permission of Cambridge University Press

Fig. 7.23 All investigated materials—evaluation of strain-rate sensitivity m and stress exponent n regarding the equivalent stress for RT experiments (small, filled symbols), nonambient temperatures (200 °C) (red, open symbols), nanoindentation strain-rate jump tests (black crosses), and macroscopic compression tests (big circles). Maier et al. (2013a). With kind permission of Cambridge University Press

included are also those of Ni. The results of the indentation tests at RT and 200 °C after constant strain rate experiment are shown in Fig. 7.24 as SEM micrographs. Close to the indentation, GBS with pile-up formation is seen showing that some grains have slided out of the flat surface associated with strong roughness. The grain sizes seem to be quite stable and no stress driven grain coarsening occurred for indentations performed at room temperature. Strong GBS is seen along the indenter edges, where single grains individually have sheared out of the surface. SEM images

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281

Fig. 7.24 SEM-micrographs of ufg-Al—a resultant impression of a room temperature (RT) constant strain-rate experiment with magnification of GBS close to the indenter edge, b post impression of a high-temperature (200 °C) long-term (2 h) experiment with obvious grain-boundary sliding behavior close to the surface but less pile-up formation, and c corresponding FIB-cross-section with special magnifications of the areas showing near-surface GBS, but homogeneously deformed areas in the deeper regions of the indentation. FIB stands for focused ion beam. Maier et al. (2013a). With kind permission of Cambridge University Press

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7 Time Dependent Deformation-Creep in Nanomaterials

Table 7.5 Activation volume A and strain-rate sensitivity m; values taken at the very end of a 2 h nanoindentation creep experiment (basic data also see Figs. 2 and 3). It should be noted that the interpretation and the meaning of the values for the activation volume is questionable, since dislocation glide is not the rate controlling mechanism. Maier et al. (2013a). With kind permission of Cambridge University Press Material Temperature T °C Activation volume A Strain-rate sensitivity Stress exponent n b3 m ufg-Al

22

22

0.069

14.5

ufg-Al

200

34

0.271

3.7

cg-Al

22

209

0.013

77

of the impressions after 2 h creep at 200 °C is seen in (b) indicating coarsening within and around the impression. The median grain size now is 520 nm. Note that the shape of the residual pile-up in the plastic zone at 200 °C differs from that of RT. Table 7.5 lists the activation volume, the strain rate sensitivity and the stress exponent ogf UFG Al. It can be seen that the activation volume of the UFG Al in both temperatures are less than in the CG Al. The activation volume is usually considered as useful in the indication of dislocation glide mechanism. However, during indentation creep local relaxation takes place and there is a dislocation rearrangement leading to dislocation annihilation near GBs. Thus around the indentation of UFG Al extensive GBS and pile-up is observed. Increasing the temperature decreases the pile-up followed by an increase in GBS. Long term creep tests at RT with initial indentation depth of 1000 nm for various duration up to 10 h are shown in Fig. 7.26a. The temperature fluctuation between 23.2 and 23.6 within the 10 h test is included. Based on contact stiffness measurements the h data were corrected as seen in (b). The result of measurement of h˙ over the applied creep time is shown in (c) the UFG Al and the hardness variation with creep rate is shown in (d). SEM images of the indentations for various times are illustrated in Fig. 7.26. Magnification of grains along the indenter edges does not indicate grain coarsening during the long term indentation tests (Figs. 7.27 and 7.28). Summarizing the effect of long term indentation of UFG Al (370 nm), the main points are: (1) Time and temperature (200 °C) dependent behavior was recorded to consider creep by dynamic nanoindentation method. (2) The strain rate from the nanoindentation creep experiments is several orders of magnitude lower than that from jump tests. (3) Increasing the creep experiment testing time of UFG and nc materials increases the strain rate sensitivity compared to CG components. (4) Extensive grain boundary sliding and pile-up is observed at RT. At increased temperature GBS increases but the pile-up is reduced.

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283

Fig. 7.25 ufg-Al-Creep data carried out during nanoindentation long-term creep tests at 1000 nm indentation depth and tested at room temperature (RT) with variation of the applied creep time (1 h, 2 h, 5 h, and 10 h); a Indentation depth data from the indentation system and exemplarily corresponding ambient temperature during 10 h experiment, b corrected indentation depth data ˙ over creep time (with fused silica as a reference according to Eqs. (7.31) and (7.34), c resultant h, material), and d hardness over resulting creep-rate. Maier et al. (2013a). With kind permission of Cambridge University Press.

Fig. 7.26 SEM images of different indentations in ufg-Al varying the applied creep time (according to Fig. 7.25). Maier et al. (2013a). With kind permission of Cambridge University Press

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.27 Creep curve of nano-grained pure Cu at 40 °C and 142 MPa. Csai et al. (2000). With kind permission of Elsevier

Fig. 7.28 Strain–time relation of the primary creep of nano-grained pure Cu. (1) At 40 °C and 142 MPa; (2) at 50 °C and 125 MPa. Cai et al. (2000). With kind permission of Elsevier

7.3 Creep in Nano Cu 7.3.1 Tensile Creep Nanocrystalline pure Cu having a grain size of 30 nm and produced by electrodeposition technique underwent tensile creep experiments at quite low temperatures of 20–50 °C (0.22–0.24 Tm ), basically in the vicinity of RT. The obvious reason for such low temperature creep tests is clearly to avoid grain growth (which was observed to occur already at 100 °C annealing). It is expected that at such low temperatures, interface controlled diffusional creep is the dominant contributor, which is characteristic to Coble creep. Within such creep experiments it is of interest to evaluate the steady state creep, the effective and threshold stress and also the activation energy

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for the low temperature creep. It should be emphasized that creep exist at such low temperature (even at RT) provided very long time exposure of load prevails. High purity Cu (99.995%) of thickness 1.7 mm (sheets) deposited on Ti substrate was prepared by spark erosion, mechanically and chemically polished. The dimension of the creep strain is plotted against t1/3 at two conditions, namely at 142 MPa/40 °C and 125 MPa/50 °C. The strain can be expressed as ε = ε0 t 1/3

(7.43)

ε0 is the instantaneous strain. The steady state creep rate (SSCR) tested at the temperatures indicated (20, 30, 40 and 50 °C) in Fig. 7.29 were obtained by jump tests after sufficient time has elapsed under the applied stress. The strain rate increases with the applied stress linearly, and that a threshold stress, σ 0 exists. Its value decreases with increasing temperature (see Fig. 7.29). The extrapolated threshold stress values are 137, 134, 129, and 124 MPa, respectively. Accordingly, the effective stress is given as σe = σ − σ0

(7.44)

Equation (7.10) can be rewritten for the steady state in the form of ε˙ =

  Aσe Q exp − kT kT

(7.10a)

The equation can be rearranged for plotting kT˙ε /σe versus 1/T illustrated in Fig. 7.30 for the evaluation of the activation energy from the slope as Q = 0.72 eV and A is = 1.07 × 10−22 m3 s−1 . Threshold stress, σ0 is expressed as a function of temperature in Fig. 7.31 and is given as Fig. 7.29 Steady state creep rate as a function of applied stress s for nano-grained pure Cu at different temperatures. Cai et al. (2000). With kind permission of Elsevier

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.30 The parameters kT˙ε /σe as a function of 1/T for nano-grained pure Cu. Cai et al. (2000). With kind permission of Elsevier

Fig. 7.31 The threshold stress σ0 as a function of temperature T. B. Cai et al. (2000). With kind permission of Elsevier

  T σ0 = B 0 1 − Tc

(7.45)

where Tc is a critical temperature, and B0 is a constant. The critical temperature obtained from Fig. 7.31 is Tc = 617 K and B0 = 262 MPa. Considering the value of the activation energy, it is much smaller than that of the lattice diffusion of 2.0 eV or that of the GB diffusion of 1.08 eV in CG Cu. However, it is close to the grain boundary diffusion of 0.69 eV in NC Cu. It is thus likely that creep is associated with grain boundary diffusion. The experimental SSRC (Fig. 7.29) is found to be of the same order of magnitude as the calculated from the equation of Coble creep given by

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ε˙ =

148Db δ Q π d 3 kT

(7.46)

(see also Pelleg, 2017, p. 37) with Db, the grain boundary diffusion coefficient given as   Qb (7.47) Db = Db0 exp − kT Db0 is the preexponential factor. Numerical calculations of Eqs. 7.46 and 7.47 by substituting also complemented data from literature indicate that the calculated values of SSCR are larger than the measured values by a factor of ~ 5 but both are in the same order of magnitude. The creep rates are found to be of the same order of magnitude as those calculated from the equations for Coble creep. The existence of threshold stress implies that the grain boundaries do not act as perfect sources and sinks of atoms or vacancies. The results suggest that the creep can be attributed to the interface controlled diffusional creep. In other words, more exactly, the interface controlled Coble creep is responsible for the low temperature creep in Cu.

7.3.2 Compressive Creep Creep tests over a range of temperature and stress were conducted in compression in the axial direction with the specimens between heated flat platens of hardened steel, using static weights to generate the load. The specimens were cylindrical of 4 mm diameter and of 5 mm in height. Displacements were measured using a scanning laser extensometer and tests were carried out at 4 temperatures and the stresses in the range 83–182 MPa. Conventional creep strain versus time, similar to the transient part of Fig. 7.1 and according to Eq. 7.10, is shown for copper at the stresses shown in the inset of Fig. 7.32. Also modelled strain rate data of stage II, namely steady state, are included as dotted lines. The fitting values for Cu using Eq. (7.10) of A (3.79 108 MPa), n (1.47) and Q (13.4 kJ mol−1 ) were obtained from Fig. 7.33 which is a plot of (a) ln (dσ/dt) versus ln (σ) and (b) ln (dε/dt) versus 1/T. For creep curves that illustrates both the primary and secondary creep, the relation of Miller-Norton can be used given as εcr eep

  Q Cσ n t m+1 exp − = m+1 RT

(7.48)

where C is a constant (units of MPa−n s−(m+1) )) and m is a dimensionless constant. Figure 7.35 shows the creep curves obtained by compression testing, together with predictions from Eq. (7.48) for a best fit set of parameter values—these are given in

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Fig. 7.32 Experimental creep strain data from conventional compression testing, at temperatures of a 298 K, b 348 K, c 423 K and d 473 K. Also shown are corresponding modelled stage II strain rates, obtained using Eq. (2) with parameter values of A = 3.79 108 MPan s1 , n = 1.47 and Q = 13.4 kJ mol1 . Dean et al. (2013). With kind permission of Elsevier

the caption. It can be seen that there is good agreement over the complete range of temperature and stress levels.

7.3.3 Creep by Twins and Stress-Jump Tests Experimental creep behavior and atomistic simulations of nanotwinned (nt) and nanograined (ng) Cu performed at a range of temperatures of 22, 40, 50, 60 and

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Fig. 7.33 Plots of the natural logarithm of the strain rate in stage II, as measured in conventional creep tests, against a the log of the applied stress (in MPa) and b the reciprocal of the absolute temperature, showing how estimates of the stress exponent and the activation energy were obtained. Dean et al. (2013). With kind permission of Elsevier

70 °C are presented in this section. The experimental data, the deformation parameters, the microscopic observations and the activation parameters indicate that the transition of creep mechanism variation with stress from Coble creep to twin boundary (TB) migration and dislocation nucleation and activation occurs during the process. The experimental and simulation data imply that nanotwinning effectively enhances creep resistance of twin free ng Cu. In CG, creep is mainly caused by lattice diffusion as exemplified by Nabaro-Herring creep or by GB diffusion in Coble creep under relatively low stress and dislocation activity involvement (moving dislocations interacting with forest dislocations). However, in ng crystal dislocation multiplication and motion is much suppressed due to space limitation of the very small grains and due to the constraint of the GBs. Thus Coble creep occurs because of the GB diffusion and due to GBS and GB migration and rotation. Consequently, in ng material the dominant creep mechanism occurs under low and medium stress levels, but under high stress levels, GBs related dislocation activity governs the creep deformation. The rate of diffusion-governing creep increases with decreasing grain size, therefore-as known—the smaller the grain size, the higher the creep rate will be. Creep deformation behavior has been expressed by Eq. (7.10) with the relevant creep deformation parameters (Q ≡ G, A ≡ B) (Fig. 7.34). The nt and ng Cu was prepared by electro-deposition technique as sheets with 500 μm thickness, and the creep specimens (dog-bone shaped) were cut with electrodischarge machine. Uniaxial tensile creep tests were applied at a strain rate of 102 s−1 at the initial loading to a sustained stress level, and then the creep strain was recorded with creep time. Stress-jump-creep test (stress level was increased gradually and continuously repeated) was performed isothermally until creep fracture occurred. The grain size of the twin-free ng-Cu is 70 nm, that of the nt-Cu the mean grain size is 65 nm and the twin lamellar thickness is 50 nm. In Fig. 7.35 RT stress–strain curves are compared with—stress-jump-test-creep. Figure 7.35a indicates the nt Cu enhances the UTS from 450 to 650 MPa and the ductility from 4.5 to 11.5% compared

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Fig. 7.34 Experimental creep strain data from conventional compression testing, at temperatures of a 298 K, b 348 K, c 423 K and d 473 K. Also shown are corresponding modelled creep histories, obtained using Eq. (7.48) with parameter values of C = 1.5 10–6 MPan s(m+1) , m = 0.5, n = 1.47 and Q = 13.4 kJ mol1 . (The modelled curves are offset along the creep strain axis, for clarity). Dean et al. (2013). With kind permission of Elsevier

to the ng Cu, while in (b) the stress-jump-creep curves are shown indicating that the creep strains in the ng Cu are higher than the corresponding strains in nt Cu. In Fig. 7.35c the stress-jump-creep test is seen and in (d) the SSCR as a function of stress is shown. Note in Fig. 7.35d that the strain rate is considerably higher in the ng Cu. Stress-jump creep curves of nt Cu are shown in Fig. 7.36. The temperatures and the stress levels are indicated in this figure. The stress jumps from 100 MPa to fracture at 450 MPa are shown in some of the figures, but in Fig. 7.36f the SSCR is shown for the temperatures tested at high stress region (HSR), medium stress region (MSR) and low stress region (LSR). As seen in Fig. 7.36f the creep behavior is temperature and stress dependent. In the LSR of Fig. 7.36f a linear region of SSCR

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Fig. 7.35 a The tensile stress–strain curves of the ng- and nt-Cu at room temperature (RT), showing that nanotwins enhance simultaneously the strength and ductility of the ng-Cu. b The developed stress-jump-creep tests on the ng-Cu and nt-Cu specimens under sustained stresses of 100 MPa, 150 MPa, 200 MPa and 250 MPa at temperature of 40 °C. The creep fracture occurs in the ng-Cu specimen under sustained stress 250 MPa. c Creep strain versus time and associated strain rate versus time from the creep test on the nt-Cu specimen under 100 MPa at 40 °C, which shows that the secondary creep stage, i.e., steady state creep stage, with nearly constant creep strain rate has been reached after around eight-hours creep. d Steady state strain rates (SSCRs) of the ng-Cu and nt-Cu specimens crept at temperature of 40 °C under sustained stresses 100–250 MPa, showing that the nt-Cu possess a higher creep deformation resistance than the ng-Cu. Yang et al. (2016). With kind permission of Elsevier

is seen between 100 and ~ 250 MPa at all temperatures. Another linear region in the MSR is seen between 275 MPa and varying upper stress limit depending on temperature. The linear part in HSR starts at a higher stress at ~ 300 MPA (70 °C) than that the LSR and the MSR. The strain rate, ε˙ Eq. (7.10) can be rewritten for the SSCR as

√   n   σ G 0 − σ V / 3 G(σ ) = ε˙ SS0 exp − ε˙ SS (σ, T ) = ε˙ SS0 (σ ) exp − kB T σ0 kB T (7.49)

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.36 a–e Creep strain–time curves of the stress-jump-creep tests on the nt-Cu at temperatures of a RT, b 40 °C, c 50 °C, d 60 °C and e 70 °C, respectively. f The logarithmic SSCR versus applied sustained stress at temperatures of RT, 40, 50, 60 and 70 °C, showing the low stress region (LSR), medium stress region (MSR) and high stress region (HSR). Yang et al. (2016). With kind permission of Elsevier

Here ε˙ SS0 and  G (σ) are the temperature independent creep rate and the stress dependent activation energy, respectively.  G0 is the intrinsic activation energy at zero stress, V is the activation volume and ε˙ SS0 , σ 0 and n are respectively the stress independent parameter, reference stress and the stress exponent. Using the experimental data of Fig. 7.36f a plot and linear fitting of the logarithmic SSCR can be plotted versus 1/T under the applied stress to obtain an Arrhenius type plot as illustrated in Fig. 7.37a, b. From the linear fitting at all stresses, the plot allows the determination of an activation energy in both cases, i. e., the LSR and MSR. The average values so obtained are G1 = 0.276 ± 0.003 eV (LSR) and G2 = 0.412 ± 0.007 (MSR). The plots indicate that the Arrhenius relation given by Eq. 7.9 holds over the entire creep deformation at the temperature range of the tests. G (σ) and ε˙ SS0 are determined from the slope and intercept of the linear fitting then the determined value of G (σ) is plotted against the stress in Fig. 7.37d to obtain G0 3 and V. For the LSR G0I = 0.282 eV and VI =  0.65  b , while for MSR G0II = 0.487 1 3 and VII = 3.67b ; b = 2.56 Å of a perfect 2 110 {111}dislocation in Cu(FCC). The stress exponents for LSR and MSR are n = 0.877 and n = 1.72 which are obtained from Figs. 7.37e, f by fitting of the straight lines. A change in creep mechanism with temperature is likely as seen in Fig. 7.37c where a change in slope is seen. The values of G (σ) derived for the two lines are respectively, 0.344 eV below 40 °C and 0.99 eV above 40 °C. Figure 7.38 is a plot of the logarithm SSCR against the logarithmic stress at various temperatures for three regions of LSR, MSR and HSR and indicating the corresponding strain rate sensitivity values of mL = 0.846–0.982, mM = 0.197–0.242 and mH = 0.076–0.094, respectively. The reciprocal value of m,

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Fig. 7.37 a–c Arrhenius plots of logarithmic SSCR against the reciprocal temperature in the a LSR, b MSR and c HSR to determine the stress-dependent activation energy and the stress-dependent plastic deformation rate. d The stress-dependent activation energy versus stress with linear fitting to determine the stress-independent activation energy and the activation volume in the LSR and MSR. e, f Yang (2016). With kind permission of Elsevier

is given as 1 =n+ m



σV √ 3k B T

 (7.50) T

Table 7.6 lists the relevant parameters for creep at LSR and MSR. In Fig. 7.38b, c plots of 1/m versus √3kσ T are presented for LSR and MSR, respectively to evaluate B the activation volume, V and the stress exponent, n for nt Cu. The values are for LSR V = 0.55 b3 and n − 0.891, while for MSR these are V = 4.45 b3 and n = 1.186, respectively. The logarithmic SSRC of ng Cu at 40 °C is plotted against stress in 7.38d indicating for the lines the respective m values as mngI = 0.465 (100–200 MPa range) and mngII = 0.102 (200–250 MPa range). Based on the experimental results a map is suggested for the nrt Cu for the which outlines in LSR, MSR and HSR the creep mechanisms showing the stress variation and the respective temperature range for the likely acting mechanisms. This is illustrated in Fig. 7.39. The creep map with the deformation strain rate contours shown by dashed lined is constructed for nt Cu based on Eq. 7.49 and the experimentally determined activation parameters in the LSR, MSR and HSR regions. The activation energy is evaluated by Eq. (7.10) (recall that A is written instead of B). As seen in Fig. 7.39 the suggested mechanisms of the time, stress and temperature dependent creep are: (1) Coble Creep diffusion in LSR, (2) Twin boundary (TB) migration in MSR, (3) dislocation mediated plasticity plus TB migration mechanisms in HSR,

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Fig. 7.38 a, d Logarithmic SSCR versus logarithmic stress at temperatures of RT, 40, 50, 60 and 70 °C to determine the strain rate sensitivity parameter m in the a nt-Cu and d ng-Cu. b, c The reciprocal of strain rate sensitivity parameter versus the term of ∂ kBT at various temperatures in the b LSR and c MSR for the nt-Cu. Yang et al. (2016). With kind permission of Elsevier

and 4) mixed mechanism in the stress transition region between LSR and MSR. The creep map indicates that under high stress and low temperature dislocation mediated plasticity dominates creep and yield high strain rates, whereas low stress and high temperature favor TB and Coble diffusion creep mechanisms. It might be of interest to show the microstructural aspect of creep in nt and ng Cu. SEM images of creep fracture surfaces are shown in Fig. 7.40. In (a) creep by stress-jump-test from 100 to 250 MPa at 40 °C is shown (the inset is of low magnification) indicating a “void like” structure with low density and small size dimples. The fracture surface morphology implies that in ng Cu GB diffusion/sliding and dislocation activity confined by GBs takes place which are locations of stress concentration inducing voids and the reason for intergranular fracture. In contrast, the TB-mediated dislocation nucleation and slip transfer reaction promote effectively dislocation-mediated plasticity in the nt-Cu. TBs resistance to dislocation motion is more moderate in comparison to GB dislocation interaction and lattice dislocations can be readily trapped and absorbed by TBs. The dislocation-TB interaction in nt metals may result in glissile dislocations along TBs, sessile dislocations at TBs and SFs in neighboring twin planes. Those dislocations/faults accumulated on TBs remain mobile. In Fig. 7.40b high density of dimples are seen across most of the

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Table 7.6 The determined reciprocal strain rate sensitivity 1/m, stress exponent n, and the term σ˜V 3 kBT in the LSR and the MSR in the nt-Cu at temperatures of RT, 40, 50, 60 and 70 °C, where the average stress σ˜ is taken from the stress range in Fig. 7.38. Yang et al. (2016). With kind permission of Elsevier. 250–300 MPa, which might imply a change in the creep mechanism. Linear fitting the data of  (G σ ) versus stress in each region of LSR and MSR gives the values of G0 and V to be G0I = 0.282 eV and V I = 0.65 b3 in the LSR, and G0II = 0.487 eV and V II = 3.67 b3 in the MSR RT

40°C

50°C

60°C

70°C

1/m

1.112

1.183

1.018

1.096

1.118

n

0.877

0.877

0.877

0.877

0.877

∼ √σ V 3k BT

0.267

0.252

0.244

0.237

0.230

σ ˜(MPa)

175

175

175

175

175

1/m

5.082

4.532

4.371

4.141

4.150

n

1.716

1.716

1.716

1.716

1.716

∼ √σ V 3k BT

3.072

2.895

2.677

2.501

2.335

σ ˜(MPa)

353.6

353.6

337.5

325

312.5

Low stress region (LSR)

Medium stress region (MSR)

Fig. 7.39 A creep map is constructed for the nt-Cu specimens in the LSR, MSR and HSR regions. Yang et al. (2016). With kind permission of Elsevier

cross section. In situ HRTEM has indicated that in the nt specimens, partial and perfect dislocations can easily be emitted from the TB–GB intersections and other locations with high stress concentrations. Although nanotwins greatly suppress the GB movement, nanotwins promote the dislocation-mediated plasticity and thus delay

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Fig. 7.40 Typical SEM images of the fracture surfaces, where the insets are of lower magnitude, of a the ng-Cu specimen stress-jump-creep fractured under 250 MPa at 40 °C and b the nt-Cu specimen stress-jump-creep fractured under 400 MPa at 70 °C. Yang et al. (2016). With kind permission of Elsevier

the creep fracture. Figure 7.41a, b shows respectively the bright-field TEM and its associated HRTEM images of the nt-Cu which was stress-jump-crept at temperature 70 °C under the stress of 300 MPa for 8 h, i.e., in the MSR. The TEM images in Fig. 7.41a and its inset show that a large amount of defects debris accumulates near the TBs, making the TBs severely strained. The Burgers circuit in Fig. 7.41b shows that the defect is a Shockley partial dislocation with Burgers vector of b = a/6 [121],

Fig. 7.41 HRTEM and atomistic configurations from MD simulations about TBs migration and dislocation activities-mediated mechanisms of creep. a, b) and d, e Bright-field TEM and associated HRTEM images of the nt-Cu specimen stress-jump-crept at 70 °C under a, b 300 MPa and d, e 400 MPa. c, f Atomistic configurations from MD simulations of (c) parallel and (f) inclined dislocation nucleation with respect to the TB (111) planes. The former leads to TB migration, while the latter induces full dislocation slip if the twin spacing is wide enough. Defective atoms are recognized by the centrosymmetric parameter. Yang et al. (2016). With kind permission of Elsevier

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moving along the TB. Figure 7.41d, e shows respectively the bright-field TEM and the associated HRTEM images of the nt-Cu stress-jump-crept at 70 °C temperature under a stress of 400 MPa for ~ 8 h, i.e., in the HSR. The high stress creep generates high densities of tangles and networks of dislocations inside the nt-Cu, as illustrated in Fig. 7.41d which pile up at twin lamellae. Figure 7.41e shows the Fourier filtered HRTEM image of the rectangle shown in Fig. 7.41d. Two sets of perfect dislocations with Burgers vectors of b1 = ½[101] on (111) planes and b2 = a/2[101] on (111) planes are shown respectively in Fig. 7.41e. MD snap shots of stress dependent creep mechanism are shown in Fig. 7.41c, f. In Fig. 7.41c at relatively low stress the dominant creep mechanism is the partial dislocation nucleation from the intersection line between GB and TB and the propagation of the partial dislocation on planes (111) parallel or within the twin plane. At high applied stress inclined dislocation nucleation governs the deformation mode as shown in Fig. 7.41f. In summary, the experiments performed consider atomistic simulations and highresolution electron microscopy to understand the creep behavior of the nanotwinned and nanograined copper at temperatures in the range of 22 °C (RT)—70 °C. Several mechanisms of the time-, stress-, and temperature-dependent creep deformation in the nt-Cu are suggested which are (1) Coble creep, (2) TB migration in the MSR, (3) Dislocation mediated plasticity and TB migration in HSR and (4) a mixed mechanism on stress change between LSR and MSR. Further, the relationship between the activation volume, stress exponent and strain rate sensitivity is given. The results demonstrate that nanotwins make the ng Cu more thermally stable and greatly improves its creep resistance.

7.3.4 Indentation-Hardness Indentation information to be considered in this section has been a part of the research investigation concerned with compression in nano Cu during creep. Nano indentation is used in the procedure to consider primary and secondary creep regimes. The material is the same as that employed in the compression considered in an earlier section of this chapter, namely OFHC extruded copper rod, in as-received form was cut and prepared for the indentation tests. The indentation was carried out using a pendulum based nanoindenter housed in a vacuum chamber to be able testing under vacuum. The indenter was a spherical diamond indenter of 10 μm radius and the indentation direction was parallel to the extrusion direction of the copper bar at temperatures of 25, 50, 100 and 150 °C. The loading rates of the test were 0.1, 0.5, 3.0. 10.0 and 20.0 mN s−1 . Three indents were made at each loading until a depth of 2 μm has been attained. Once this indentation depth had been reached the load was held constant at this point for 3600 s, known as the creep dwell time. At this stage unloading took place at a rate of 20 mN s−1 . Indentation information is seen in Fig. 7.42 where a plot of load against displacement is shown in (a), while in (b) creep displacement is plotted against time. The indentation was performed at 298 K for several loading rates. The creep displacement (Fig. 7.42b) is greater with

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.42 Experimental indentation data obtained at ambient temperature (T = 298 K), showing a load–displacement plots during both the buildup of the load and the dwell, and b displacement histories during the dwell, for five different loading rates during the build-up. Dean et al. (2013). With kind permission of Elsevier

increased loading rate for a specific time. It would be on place to remind that in CG metals plastic deformation occurs by nucleation and movement of intragranular dislocations. Interactions of dislocations on intersecting slip planes form a dislocation network which hinders their further motion thus strengthening (hardening) materials. Such dislocation activity is not possible in NC materials and instead emission of dislocation from GB sources and their propagation across the grains and absorption in the opposite GBs occur. Instead GB mediated processes take place such as GB sliding (GBS) and GB diffusion concurrently with dislocation activity. The average grain size of the Cu used is ~ 25 nm. TEM bright field image shows the NC Cu in Fig. 7.43a and the distribution of the grain size is illustrated in Fig. 7.43 b. The nano-indentation was performed with a Berkovich diamond indenter at room temperature on polished surface to a mirror-like finish. Nano-indentation creep tests

Fig. 7.43 The TEM bright-field image of the NC Cu a and the grain size distributions b. Sun et al. (2019). With kind permission of Elsevier

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˙ from 0.05 mN/s to 500 mN/s to were performed at a wide range of loading rates (P) a. peak load of 300 mN with a holding time of 1000 s. The indenter was unloaded to 10% of the maximum load and held for 500 s for thermal drift correction to minimize its negative influence on the displacement measurement. The nano-indentations were repeated at least ten times under the same conditions. Figure 7.44a shows the plot of load versus displacement, (P–h) curves at various loading rate, P from 0.05 mN/s to 500 mN/s. It can be seen that with the decreasing load rate, P˙ at a given load, P the displacement h increases. Note that in the holding regime the P versus h curves exhibit wide load plateaus, namely, large creep displacement, hcreep . In Fig. 7.44 the corresponding creep displacement versus holding time. (hcreep -tH ) curves for various creep rates is shown. In this regime the h − t data of holding time can be fitted with and empirical equation given as  h = p + qln

r −1 t −s

 (7.51)

p, q, r and are the fitting parameters. Experimental and fitting curves are shown in Fig. 7.44c–e. here the curves (h − t) are at the strain rates P˙ = 500 mN/s, 5 mN/s and 0.05 mN/s. Experimental and fitting curve are in good agreement. The creep strain rate, ε˙ H is given by ε˙ H =

1 ∂h h ∂t

(7.52)

The creep strain rate curves versus holding time (˙ε H − t H ) obtained from the (h − t) curves is seen in Fig. 7.44f. Here ε˙ H drops rapidly with increasing tH and decreases slowly in the subsequent steady state creep. The strain rate ε˙ H is seen to increase ˙ Load versus with P˙ for a given th which means that creep strongly depends on P. displacement (P–h) and the corresponding stiffness versus displacement are shown in Figs. 7.45a, b respectively at the loading strain rates of 0.5, 0.05 and 0.005 s−1 , respectively. Creep stress versus (σH − tH ) is plotted in Fig. 7.46 in the holding regime obtained by relation σH =

P 3Ac

(7.53)

where Ac is the contact area which can be expressed as + C3 h 1/4 Ac = C0 h 2c + C1 h c + C2 h 1/w c c

(7.54)

where C0 , C1 , C2 , C3 are fitting parameters which were obtained by area calibration procedure and hc is the contact depth expressed as

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.44 The load versus displacement (P − h) curves a obtained at a maximum load of 300 mN ˙ The corresponding creep displacement versus holding and holding time of 1000 s at different P. time (h t creep − H) curves b, the experimental displacement versus time (h − t) curve and the fitted curve obtained at P˙ = 500 mN/s (c), P˙ = 5 mN/s (d) and P˙ = 0.05 mN/s (e) and the creep ˙ − H) curves (f) in the holding regime. Sun et al. (2019). With strain rate versus holding time (ε t H kind permission of Elsevier

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Fig. 7.45 The load versus displacement (P − h) curves a and the corresponding contact stiffness versus displacement (S-h) curves b obtained by CSM technology at the loading strain rates of 0.5, 0.05 and 0.005 s−1 . Sun et al. (2019). With kind permission of Elsevier. CSM stands for continuous stiffness measurement

Fig. 7.46 The creep stress versus holding time (σH − tH ) curves in the holding regime. Sun et al. (2019). With kind permission of Elsevier

hc = h −

εP S

(7.55)

Figure 7.45b is used to determine hc and Ac . One can see in Fig. 7.46 that σH decreases rapidly with increasing tH . The dropping rate of σH is larger at higher P˙ ˙ ε˙ H and σH at the same tH can be determined from Figs. 7.44, 7.45, than at lower P. and 7.46 for different P˙ and the resulting ε˙ H versus σH curve is seen in Fig. 7.47a. Based on the ε˙ H versus σH curves the true activation volume V* can be expressed as V ∗ = MkT



∂ln ε˙ δσ ∗

 (7.56)

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Fig. 7.47 Creep strain rate versus creep stress (˙ε H − σ H ) curves (a), activation volume versus creep stress (V − σ*H ) curves (b) and strain rate sensitivity versus creep stress (m-σH ) curves (c) in the holding regime. Sun et al. (2019). With kind permission of Elsevier

where M is Taylor factor and σ∗ is the effective stress which can be expressed as σ∗ = (σH − σi ); σi usually is assumed to be constant. Substituting this expression into Eq. (7.56) and remembering that σi is considered a constant one gets for V* 

∂ln ε˙ V = MkT ∂σ H ∗

 (7.57)

Taking M = 31/2 , k = 1.38 × 10–23 J/K and T = 298 and using the plot ε˙ H versus σH data from Fig. 7.47a, the variation of V* with σH can be illustrated in Fig. 7.47b. Recalling the definition of the strain rate sensitivity, m in earlier sections, for example Eq. (5.25), for the current presentation it is modified in terms of σH and ε˙ H as m=

∂lnσ H ∂ln ε˙ H

(7.58)

and the results are illustrated in Fig. 7.47c. It can be seen that there are two regions quite as in (b). It is shown that in region I, m decreases with the increase of σH from

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1.04 to a minimum of 0.8 at 530 MPa. In region II, m increases with the increase of σH from the minimum to 1.2. This relation between m and σH is contrary to the relationship between V* and σH in (b). Duhamel et al. have proposed a model for the relation between V* and σ∗ accordingly a critical stress σ H∗ can be expressed as σ H∗ =

MβGb d

(7.59)

where β is a material constant and clearly G is the shear modulus. When σ∗ ≤ σ0∗ the plastic deformation is controlled by GB activities and the corresponding V* may be written as V∗ = VGB

(7.60)

where VGB = 1b3 the activation volume is controlled by GBs. When σ∗ ≥ σ0∗ the contribution of dislocation and GB activity to V* control the deformation and V* is given by

∗

V = VG B

 2 −1 δC σ0∗ σ ∗ − σ0∗ + + 2MkT B b σ ∗ − σ0∗

(7.61)

where δ = 2b is the thickness of GB and B and C are fitting parameters. On the right side in the parenthesis the first term represents dislocation activity and the second term represent GB activities to V* respectively. B and C can be expressed as B =1+

δ ∂νG B >1 bd 2 νe ∂ρ

C=

νG B Bνe

(7.62) (7.63)

Here, νe is the frequency of dislocation emission from GB, νGB is the frequency of an elementary shear at GB and ρ is the dislocation density. B and C can be regarded as constants and C can be determined by a condition in which deformation is controlled only by GB activities. Accordingly, (σ ∗ − σ0∗ )/B in Eq. (7.61) is smaller than the 2 σ∗ term δC ( 0 ) and Eq. (7.61) can be rewritten as b σ ∗ −σ0∗

V ∗ ≈ VG B +

 2MkT b  ∗ ∗  ∗ 2 σ − σ0 δC σ0

(7.64)

Reckoning (7.64) indicates that C can be determined from the slope of the experimental versus σH data when the relation of (σ∗ − (σ∗ − σ0∗ ) to σH is determined. According to σ∗ = σH − σi and σi = σ0 − σ0∗ one has σ∗ − σ0∗ = σH − σ0 where

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7 Time Dependent Deformation-Creep in Nanomaterials

σ0 is the value of σH at which V* = 1b3 . Thus, σ0 can be determines by finding the crossover point of the tangent of V* versus σH curve in region I with the σH axis as seen in Fig. 6.47b. The determined σ0 = 450 MPa by taking β = 0.5 and d = 25 nm, σ0∗ = 374 MPa. Inserting σ∗ = σH − 76 MPa, σ0∗ = 374 MPa and the values of other parameters into Eq. (7.64) and comparing with the slope value of the experimental V* versus σH curve in region I (0.07b3 MPa) the C value can be determined to be 0.02. Furthermore, inserting σ∗ = σH − 76 MPa, σ0∗ = 374 MPa, C = 0.02 and the values of other parameters, the V* versus σH curve calculated for different values of B and compared with the experimental curve. The comparison result in Fig. 7.49a. It shows, that with the values of B = 2.5, the V* versus σH curves exhibits the best agreement with the experimental curve. With the value of   m = MkT/ σH V∗

(7.65)

and the expression for V* [Eqs. (7.60) and (7.61)] m can be written as m=

MkT (σH < σ0 ) σ H VG B

(7.66)

or then  m=

 −1 −1 σ H VG B σ H −σ0 δC σ02 + 2σ H + σH > σ0 MkT B b σ H − σ0

(7.67)

Inserting the values of σ0 = 450 MPa and C = 0.02 and values of other parameters, the m versus σH curves were calculated for different B values and compared with experimental curves. The results are shown in Fig. 7.48b and the calculated m versus σH with B = 2.5 curve exhibits the best agreement with experimental curve. In summary, theoretical and experimental creep deformation by indentation was presented in this section. Nano indentation tests were carried out to investigate the creep behaviors of NC Cu with a grain size of 25 nm after deforming under a wide range of loading rate at room temperature. Based on the relationship between the creep strain rate and creep stress obtained at different loading rates, the activation volume and strain rate sensitivity versus creep stress data were determined by cooperating CSM technique (continuous stiffness measurement). The results show that the activation volume increases and then decreases, and the strain rate sensitivity decreases and then increases with the increasing creep stress. Activation volume and strain rate sensitivity analysis shows that at lower stress grain boundary activities dominate and lead to lower creep strain rate, while at higher stress dislocation activities dominate and lead to higher creep strain rates. For NC metals, dislocation activities, including the nucleation from GB sources, their propagation across the grains and eventual absorption in the opposite GBs occurs when a critical stress is

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Fig. 7.48 Comparison of the activation volume versus creep stress (V* − σH ) curves obtained by experiment and Duhamel et al.’s model (a), and comparison of the strain rate sensitivity versus creep stress (m − σH ) curves obtained by experiment and Champion’s model with different B (b). Sun et al. (2019). With kind permission of Elsevier

Fig. 7.49 Primary creep of nanocrystalline nickel at room temperature. Yin et al. (2001). With kind permission of Elsevier

reached. At low stress, this critical stress cannot be satisfied, so the deformation must be mediated by GB activities. The creep mechanisms over a wide range of the creep stress from the initial to steady stage was presented. The analysis based on the data of the nano-indentation test also reveal that the continuous creep strain rate versus creep stress data used allows to reveal the mechanism over a wide range of the creep, from initial to steady state creep. The experimental activation volume and strain rate sensitivity versus the creep stress data are in good agreements with the theoretical values calculated by the model.

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7 Time Dependent Deformation-Creep in Nanomaterials

7.4 Creep in Nano-Ni 7.4.1 Tensile Creep Pure nanocrystalline nickel of 0.3 mm thickness was prepared by pulse electrodeposition for creep investigation. Tensile tests, at strain rates of 4 × 10–5 and 8 × 10–4 , were carried out also for comparison. Displacement was measured with a high sensitivity extensometer attached to the gage section of the specimens. The uniaxial creep tests were performed at RT and 373 K in the load range of 500–1050 MPa. The step-load method was used to reveal the strain rate change and instantaneous behavior during loading and unloading. TEM (foils) bright and dark field images from the as received sheets and deformed (post-creep) samples were inspected for the microstructural changes and for its characterization. In Fig. 7.49 primary creep is shown at 600–1050 MPa in the conventional way as a plot of strain versus time. After prolonged primary creep, the creep rate at 600 MPa decreased to 9 × 10−10 s−1 which is the measurable minimum. Note that the primary creep lasted more than 200 h at 600 and 700 MPa, but it decreased to 130 h at 900 MPa (Fig. 7.49). The applied stress was close to the yield stress (see Fig. 7.50 for comparison), the creep in nanocrystalline Ni was very small at room temperature. Therefore, the creep test at room temperature was interrupted at low load and adjusted to higher loads for achieving the minimum strain rate. The reduction of the load from 1050 MPa resulted in a prolonged incubation period greater than 60 h as shown in Fig. 7.50a. The nanocrystalline Ni exhibited accelerated creep. The creep rate at 373 K and at 700 MPa reached a minimum value at 8.8 × 10−8 s−1 , larger than the one at RT (1.1 × 10–9 s−1 ). The decrease of load from 600 to 500 MPa did not show incubation period. The microstructure of the as received material was equiaxed as seen in Fig. 7.52. TEM did not show grain growth at RT, but the post-creep specimen at 373 K showed slight increase in grain size. The stress dependence of creep could be observed from the plot of strain rate versus stress. Constant load and step load tests are shown in Fig. 7.53. The stress exponent for creep is ~ 1 at 290 K and increases

Fig. 7.50 Tensile behavior at room temperature and 373 K, a strain rate dependence, b temperature dependence. Yin et al. (2001). With kind permission of Elsevier

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to the value of 6.5 at 373 K. Up to 353 K the grains were stable while abnormal grain growth took place at 393 K but no evidence to this was observed up to 373 K. The diffusional Nabarro–Herring or Coble creep exhibit linear dependence of the creep rate on stress. Dislocation dominated creep rate is basically independent of grain size, while diffusional creep is inversely proportional to the second power of the mean grain size and diffusion occurs by the lattice and to the third power of the mean grain diameter when it occurs through grain boundaries. Coble creep rate for spherical grains is given by (Fig. 7.51)   Qb 148 Db0 δb σ b exp ε˙ = π d 3 kT RT

(7.68)

Fig. 7.51 Tensile creep curves of nanocrystalline nickel, a 700 MPa, b Step-load. Yin et al. (2001). With kind permission of Elsevier

Fig. 7.52 Microstructure of as received nanocrystalline nickel. Yin et al. (2001). With kind permission of Elsevier

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Fig. 7.53 Minimum strain rate dependent on stress. Yin et al. (2001). With kind permission of Elsevier

In Eq. (7.68) Db0 is the grain boundary diffusion coefficient, db is the effective grain boundary width and  is the atomic volume. Since Db0 for nanocrystalline is not available the use of δb Db0 4 × 10–15 m3 s−1 and Qb = 108 kJ mol−1 were used for nanocrystalline Ni. Given  = 8 × 10–3 nm3 , 30 nm, the creep rate is ε˙ =

  4x103 σ 12996 exp − T T

(7.69)

The calculated strain rate value at RT and 700 MPa is 3.3 × 10–10 s−1 which is of the order as the experimental value of 11 × 10–10 s−1 . Since the stress exponent is 6.5 obtained at 373 K and since the calculated strain rate value according to Eq. (7.68) was much smaller than the experimental value at 373 K the creep mechanism may no longer be dominated by the Coble mechanism, but rather by dislocation mechanism. Nevertheless, the creep mechanism might change from a diffusion controlled process at room temperature to a multiple mechanism at 373 K, meaning that above ambient temperature lattice dislocation gliding and grain boundary sliding may play an important role in tensile-uniaxial deformation.

7.4.2 Creep by Nano Twins in Ni Superior mechanical properties are observed in NC and nanotwinned (NT) materials below 100 nm compared to CG or even to UFG metals because of the large volume fraction of GBs. Unlike the high strength of NC on the expense of ductility, NT material have an improved strength-ductility combination. The ductility encountered in NT metals is not on the expense of the strength. Due to the large volume faction of grain boundaries in NT materials the twin boundaries (TBs) serve as strong obstacles to dislocation motion and can also serve as effective sources and/or sinks of dislocations. As a matter of fact, introducing numerous NTs into UFG metals (for example Cu) the twin thickness, λ effects the strength and improves it in a similar manner to the size, d in NC material. It has been reported that reducing λ (meaning increasing

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the density) of NTs, increases their strength and the strain rate sensitivity (SRS), m of nanostructured pure metals and alloys in particular their creep behavior. Creep deformation by tensile tests in the < 50 nm in NC pure metals exhibit enhancement of creep rates compared to the CG counterparts. Creep deformation in NC pure metals in this nano-range is ascribed to the GB-mediated creep mechanism with GBS becoming the major deformation mechanism at high stress levels, whereas the diffusion creep mechanism could be significant for smaller grain-sized samples. High purity NT-Ni on a stainless steel substrate were prepared by electrodeposition from a nickel sulphate bath. A series of samples with different initial grain sizes of d ~ 84, 120 and 300 nm, but similar twin thickness of λ ~ 38 ± 2 nm was obtained. Free standing Ni foils could be readily peeled off from the substrate. The microstructural features of the free-standing NT-Ni foils before and after creep deformation were characterized by HRTEM and the elemental composition was identified by energy dispersive X-ray (EDX). The NT Ni free-standing foils were loaded at three different loading rates, i.e., ~ 0.5, 5 and 50 mN s−1 and then held at constant applied stress between 400–900 MPa for a given period of time. On the basis of creep strain-creep time curve the creep strain rate, ε˙ c (=dε/dt) where ε is expressed by the empirical function as ε = ε 0 + x(1 − t0 )y + zt, with ε0 the initial creep strain, t0 is the starting time of the creep process, t is the creep time and x, y, z are fitting constants. TEM plan view images of the three as-deposited foils, are shown with growth twins prevalent, either terminated in at GBs or ended in grain interiors. These features are seen in the TEM images before creep in Fig. 7.54a–c. The three d NT-Ni foils at the loading rates of ~ 50 mN s−1 with the applied stress a = 700 MPa seen in Fig. 5.74d–f are post-mortem TEM observations of the deformed microstructure. In the vicinity of GBs/TBs dislocation debris are seen marked by white arrows. Table 9. 7 lists the statistical results of the three different NT-Ni samples before and after creep of the as deposited samples at the loading rate of ~ 50 mN s−1. under different stress levels (d is grain size, f is the fraction of twinned and λ is the average twin thickness). TEM images and statistical size, d and fraction,f results are shown after creep in Fig. 7.55. The figure indicates that the stress level can significantly influence the microstructural evolution. One can observe a considerable increase in grain size from Table 7.7 and Fig. 7.55. Tensile strain rate jump experiments by changing the strain rate from 1 × 10–5 to 8 × 10–5 s−1 at a constant strain to find m the SRS assuming that the microstructure remains identical. The grain size, d ~ 300 nm NTNi foil exhibits higher stress level than samples with lower d, which is attributed to the dislocation-nucleation-governed softening mechanism with TB migration. The grain size, d, the twin thickness and its fraction, f significantly strengthen the NTNi samples. From the slope SRS (m) is obtained by linear fitting of the jump tests presented in Fig. 7.56b. It is seen that SRS decreases from  m√ = 0.25 to m = 0.15 BT increases with with grain size decrease, while the activation volume V* = 3k mσ decreasing grain size (Fig. 7.56c). This implies that the emission of dislocations from boundaries (GBs an TBs) should be the predominant plastic deformation mechanism. Figure 7.56d indicates the considerably increased SRS at a similar grain size. Representative creep figures are shown for the case of 84 nm NT-Ni in Fig. 7.57.

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.54 TEM bright-field micrographs of three different d-NT-Ni foils before creep are respectively shown in (a–c), showing prevalent growth twins. The corresponding typical post-deformed TEM micrographs of the three d-NT-Ni foils at the loading rate of ~ 50 mN s−1 with the applied stress σ a = 700 MPa are respectively presented in (d–f). a, d 84 nm, b, e 120 nm, c, f 300 nm. In the vicinity of GBs/TBs, a high population of dislocation debris can be found (indicated by white arrows). Li et al. (2016). By kind permission of Taylor & Francis

In Fig. 7.57a creep rate versus creep time is shown at a loading rate of 50 mN s−1 and applied stress of σ a = 600 MPa. The figure shows the steady state creep also. In (b) the creep strain versus creep time is plotted at the stresses indicated (400–700 MPa) for the creep rate of mN s−1 . At these lines at all stresses applied, both stages of the creep, namely primary and secondary (steady state) creep still are present at the 50 mN/s loading rate. The variation of the creep strain rate with creep time (holding time) at the stresses indicated and at a loading rate of 50 mN/s is shown in Fig. 7.57c and in (d) it is for various loading rates at σ a = 500 MPa. The creep resistance as a function of grain size is seen in Fig. 7.58a and as expected it increases with a decrease in the grain size at all stresses, while in (b) the creep strain rate, ε˙ CS increases with grain size contrary to the reported in the literature. The increase in creep strain rate with increasing applied stress is illustrated in Fig. 7.58c, where (d) the applied stress variation with creep strain rate is shown for the three sized NT-Ni and including in the figure the respective values of m (strain rate sensitivity). To understand the creep mechanism the loading behavior the variation of the primary strain rate, ε˙ PC and that of the secondary creep rate, ε˙ SC with loading rate for different grain sized NT-Ni is required. This is seen in Fig. 7.59. It is seen that ε˙ SC increases with a decrease in

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Fig. 7.55 Typical TEM images of 84 nm NT-Ni (a) and 300 nm NT-Ni (c) after creep at the loading rate of ~ 50 mN s−1 under the high stress level of ~ 900 MPa. Twins (Twin1, Twin2 and Twin3) and secondary twin (i.e. Twin4) in (a) are indicated. The corresponding statistical results of d and f are shown in (b) and (d), respectively. Li et al. (2016). By kind permission of Taylor & Francis

loading rate, while ε˙ PC is lower with slower loading rate, but the steady state creep rate, increases. It is accepted that when deformation occurs in nanometer regime, the mechanism changes from forest dislocation cutting to dislocation emission from GBs and TBs. It is associated in the former case with a lower SRS, m and a larger V* , while in the latter case a higher SRS, m, and a smaller V* are induced. In the current experiments, the NT-Ni foils show greater SRS (as indicated earlier, m ~ 0.14–028) and smaller V* an indication of the dislocation-based mechanism in creep at RT rather than GB-associated such as GB diffusion and/or GBS. In particular, with λ ~ 38 nm the boundary emits partial dislocations governing creep at RT instead of bulk source activation mechanism. The variation of λc —the critical lamellae sizewith the grain size (seen in Fig. 7.60) shows that it decreases with reduced grain size, d. The maximum strength occurs when d equals the dc the critical value in the

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Table 7.7 Statistical results of the internal features of three different NT-Ni samples before and after creep at the loading rate of ~ 50 mN s−1 under different stress levels. Li et al. (2016). By kind permission of Taylor & Francis Sample d/nm

f /%

λ/nm

120 nm NT-Ni

300 nm NT-Ni

as-deposited

84 nm NT-Ni 84 ± 15

120 ± 18

300 ± 25

900 MPa

50 ± 12

–

294 ± 25

700 MPa

221 ± 20

209 ± 20

290 ± 23

400 MPa

235 ± 20

216 ± 25

305 ± 28

as-deposited

60 ± 4

67 ± 4

70 ± 4

900 MPa

77 ± 4

–

83 ± 4

700 MPa

80 ± 4

83 ± 4

88 ± 4

400 MPa

85 ± 4

86 ± 4

86 ± 4

as-deposited

35 ± 2

40 ± 2

39 ± 2

900 MPa

7±2

–

29 ± 2

700 MPa

32 ± 3

30 ± 2

37 ± 3

400 MPa

35 ± 2

31 ± 3

38 ± 2

range of ~ 500–4400 nm. When d < d c , a strength softening mechanism dominates and the detwinning process can occur and the strength decreases. φ p and φ TB are geometrical factors (~ 0.5–1.5). Twinning mechanism leads to twin assisted grain growth which is evidenced by HRTEM in Fig. 7.61. The NT would form in one grain, and then propagates into the neighboring grain. Further, twinning partial often hit on GB, resulting in GB dissociation (marked by red asterisks) and local change of misorientation from high-angle to low-angle GBs. The two nearby grains eventually coalesce into one grain with twins. Schematically the process is shown in Fig. 7.62a, b. The shrinkage of twins after creep implies also that an additional detwinning mechanism is operating in the grain growth, a glide involving multiple twinning (detwinning) dislocations. HRTEM images of Figs. 7.63b–d indicate the twin steps at TBs in the deformed NT-Ni. The figures also show twinning partials or SFs formed at (incoherent) TBs. Figure 7.63 provides the typical TEM images of twin steps at TBs (indicated by arrows) in the deformed NT-Ni foils, indicating that the first stage of detwinning is the movement of steps at TBs, which further facilitates a decrease in λ. Figure 7.63 (b–d) also shows twinning partials or SFs formed at (incoherent) TBs. Under the external stress, multiple twinning partials successively nucleate at GBs and glide along the twinning plane, which causes the pile-up stress concentration to trigger local relaxation of GBs and atomic rearrangement, resulting in grain growth, see Fig. 7.62c, d. It has been suggested that interactions between dislocations and GBs leads to twinning/detwinning assisted grain growth, during uniaxial tension at RT. It was observed in creep tests that incoming dislocations can also transmit across a GB either directly or indirectly and release a residual dislocation. The residual dislocation

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Fig. 7.56 a True stress–strain curves of three different d-NT-Ni foils under RT strain rate jump experiments with the strain rates varying from 1 × 10−5 to 8 × 10−5 s−1 ; b double logarithmic plots of flow stress versus˙ drawn from the jump tests in (a), and the SRS m is acquired from the slope of the linear fitting; c effect of d on the SRS m and activation volume V* in jump tests and creep experiments at the loading rate ~ 50 mN s−1 ; d comparisons of SRS m in the present study with the literature (tensile) data of non-twinned Ni. Li et al. (2016). By kind permission of Taylor & Francis. [30] stands Gray et al., [31 for Dalla et al., [32] for Gu et al., [33] for Pan et al., [34] for Schwaiger et al. and [35] for Wang et al.

can lower the GB misorientation and facilitate GB motion and thus promoting grain growth. Regarding grain refinement at high stress levels in NT-Ni foils, it can also be ascribed to the detwinning process via secondary twinning. In the NT-Ni foil it is observed that increasing loading rate, increases the primary creep strain rate,˙PC while the steady-state creep strain rate˙SC decreases. This has been interpreted by the effect of dislocation stress fields on dislocation activities; the initial imposed loading effect on the stored dislocation density and this in turn affects the subsequent˙PC and˙SC . The strain rate˙PC , is a function of the mobile dislocation density, ρm and can be given according to the Orowan equation by. ε˙ PC = ρm bυ =

 m σa ε PC bυ0 bl σ

(7.70)

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Fig. 7.57 Summarized typical results of creep behaviour of 84 nm NT-Ni foils: a variations in˙SC and creep strain with creep time under σa = 600 MPa at the loading rate of ~ 50 mN s−1 ; b creep stain versus creep time and c ˙SC versus creep time at the loading rate of ~ 50 mN s−1 with different σa , respectively; and d ˙SC versus creep time at σ a = 500 MPa with different loading rates. Li et al. (2016). By kind permission of Taylor & Francis

where υ is the average dislocation velocity, εPC is the primary creep strain, υ0 is the unit velocity, l is the obstacle spacing, m is a fitting parameter and σ0 is a material constant. Normalization of primary creep strain rate ε˙ PC , defined as ε˙ PC at different stress levels with respect to ε˙ PC , say at ~ 400 MPa to estimate the influence of the initial stored dislocation density during the loading stage on the subsequent ε˙ PC . Thus, Eq. (7.70) can be rewritten as  x 400 m ε˙ PC = ε˙ xPC /˙ε400 ˙ xPC /˙ε400 PC = ε PC σ /σ

(7.71)

It is found from Fig. 7.64 that both ε PC and ε˙ PC monotonically increase with the increase of σ a and that ε˙ PC can be fitted using Eq. (7.71) with reasonable m of ~ 0.1–1.1. Using other loading rates can be used for the NT-Ni, which is an indication that indeed ε PC and also the steady state creep rate,˙SC are strongly affected by the initial dislocation density.

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Fig. 7.58 a Creep resistance of NT-Ni foils versus d−1/2 at different σa ;˙SC as a function of (b) d and c σa , respectively; d double logarithmic relation of σa and˙SC to estimate the SRM m. Li et al. (2016). By kind permission of Taylor & Francis

In summary, NT Ni (Ni exhibiting a high SFE) free standing foil with different grain sizes but with nearly the same twin lamellae thickness was crept at RT resulting: (1) Grain growth occur under low stresses by a twinning/detwinning process via dislocation-GB interaction. (2) Grain refinement under high stresses occurs by a detwinning process. (3) Creep damage is relieved by the twinning/detwinning grain growth and also reduces creep strain rate. (4) The grain refinement process accelerates creep strain rate. (5) The creep rate is significantly influenced by the loading history; decreasing load rate reduces primary creep rate while the steady state creep is enhanced.

7.4.3 Compression in Nano-Ni Compression creep tests were carried out in nanocrystalline nickel at constant load at 373 K under stresses in the range of 1000–2000 MPa. The creep experiments of the

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Fig. 7.59 Effect of loading rate on ε˙ SC and the primary creep strain rate ε˙ PC under σ a = 400 and 500 MPa for three different d-NT-Ni: a 84 nm, b 120 nm and c 300 nm. Li et al. (2016). By kind permission of Taylor & Francis Fig. 7.60 The critical twin thickness λc as a function of grain size d in the present NT-Ni and reported NT-Cu materials. Li et al. (2016). By kind permission of Taylor & Francis

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Fig. 7.61 HRTEM image of the red boxed region in the top right corner, showing GB dissociation induced by twinning to facilitate grain growth. The red asterisks indicate GB, and the red lines indicate the twin relationship, G1 and G2 are the two neighboring grains. Li et al. (2016). By kind permission of Taylor & Francis

electrodeposited nanocrystalline Ni was carried out al low temperatures; no barreling occurred during the compressional creep. A few experiments were performed at 353 and 393 K in order to evaluate the activation energy. Clearly the removal of load was required when the temperature was altered and stabilization of the system is necessary during this time. Progressive grain growth through the thickness of the sample and the variation of the texture (defined as the relative ratio of I(111) /I(200) peaks) are illustrated in Fig. 7.65a, while in (b) the influence on grain growth and texture of annealing and creep deformation at σ = 2 GPa and ε ~ 28%. The opened and closed bars correspond to the opposite sides of the electrodeposited plate. The as processed sample is also shown. Creep is often characterized by a relation which includes the diffusion coefficient, D in an equation of the form as presented. ε˙ ∼ Dd − p σ n

(7.72)

Here ε˙ refers to the steady state creep rare and d is the grain size, p and n are constants termed as inverse grain size and stress exponent, respectively. The variation of creep strain with time at Fig. 7.66a and that of the creep rate with strain indicate the usual creep behavior as seen earlier when analyzing Andrade’s illustrations. Only transient creep is seen in Fig. 7.66a and steady state creep was not attained yet despite the seemingly almost linear appearance at about 373 K and 1000 MPa. From the variation of strain rate with stress, shown in Fig. 7.67a the stress exponent at

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Fig. 7.62 Schematic figures of twinning/detwinning-mediated grain growth during creep. A, c show the microstructural parameters such as d and λ before creep, b, d are the corresponding schematic illustrations of twinning and detwinning mediated grain growth during creep, respectively. The evolution of microstructural parameters is also shown, and several dislocations are indicated by ‘⊥’ at GBs/TBs. Li et al. (2016). By kind permission of Taylor & Francis

strains 1%, 2%, 3% and 4% was evaluated respectively, as n ~ 8. 10, 12 and 13. The creep rates decrease with strain as seen in Fig. 7.67b. Typically, the values of p and n of Eq. (7.72) for intragranular dislocation creep processes involve p = 0 and n > 3, whereas grain boundary sliding and diffusion creep processes involve n ≤ 3 and p = 1. However, constant load compressive creep experiments on electrodeposited Ni with a grain size of 40 nm revealed extensive primary regions, and no evidence for steady state deformation. The lack of any change in texture coupled with grain growth suggests that grain boundary sliding/rotation/migration accompanies intragranular dislocation creep. It may be noted, that ~ 1 is attributed to Coble creep grain boundary diffusion, whereas n > 5 has been attributed to some form of dislocation creep, but as shown in Fig. 7.67 Coble creep is not in line with the ε˙ − σ plot, and the statement in the earlier sentence indicating the creep mechanism should prevail. The indentation test for measuring creep at high temperature in Ni single crystal is performed by a flat punch indenter with a diameter of only 20 s μm. The test was carried out at 650 °C at stress levels in the range 85–400 MPa. The punch indenter used is a cylindrical flat punch indenter, instead the conical or pyramidal indenters, which provides a constant contact area. So that the load test can be performed to achieve steady state conditions. The samples for the indentation creep tests were polished. Since the sample and the tip are both encapsulated in the furnace during the experiment, they have the same temperature and a separate tip heating system is not

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Fig. 7.63 a Typical TEM images of twin steps formation at TBs (as shown by arrows with different directions) in deformed 84 nm NT-Ni foils at the loading rate of ~ 0.5 mN s−1 with σa = 400 MPa. Several steps are indicated by arrows located at TBs. b–d are the corresponding HRTEM image of twin steps marked in (a), respectively, showing the detwinning process. The twin relationships were indicated by red lines, and several dislocations are marked by ‘⊥’ in the vicinity of TBs. The inset in d is the inverse FFT HRTEM image of incoherent TBs (ITBs) of red boxed regions showing the SF structures. Li et al. (2016). By kind permission of Taylor & Francis

necessary. The force on the sample is generated electromagnetically and is continuously measured and the displacement is determined by an inductive displacement transducer. The temperature was kept constant for 150 min to equilibrate the temperature for the test. The indentation of the creep test is shown in Fig. 7.68a as a plot of depth against time at 650 °C at different loads. They are similar in shape to uniaxial strain–time creep tests. In the transient creep region, the slope of the curve decreases then reaching a constant level at the minimum creep rate in the steady state creep. From the indentation depth-tine data the indentation velocity, h˙ has been calculated and seen in Fig. 7.68b.

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Fig. 7.64 Effect of σ a on the primary creep behavior of NT-Ni foils with different d at the loading rate of ~ 5 mN s−1 . a Primary creep strain versus σ a ; b normalised primary creep rate (˙εPC = ˙x PC /˙400 PC ) versus σ a . Li et al. (2016). By kind permission of Taylor & Francis

Fig. 7.65 a Variation of grain size and texture across the thickness of electrodeposited plate. b Comparison of grain size in the as processed, annealed (44 h at 373 K) and deformed (at 373 K, at 2 GPa for 28%, for 42 h) specimens. Kottada and Chokshi (2005). With kind permission of Elsevier

The gray dashed lines in these figures (Fig. 7.68; load 0.125 N) indicate repeated tests to test reproducibility. The finite element (FE) model reproduces the deformation in single crystalline Ni at different loads very well as seen in Fig. 7.69. By using this FE model a plot the normalized minimum indentation velocity n ˙ log(hmin/C 1 ) as a function of stress exponent n, keeping all other material properties constant is seen in Fig. 7.71. The measured indentation depth or velocity and indentation stress can be converted quite easily into equivalent uniaxial values of

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Fig. 7.66 a Creep curves at 300 and 373 K. b Strain rate versus strain curves for 300 and 373 K. Kottada and Chokshi (2005). With kind permission of Elsevier

Fig. 7.67 a Variation of strain rate with stress. b Data from a temperature jump experiment. Kottada and Chokshi (2005). With kind permission of Elsevier

stress σ and strain rate ε˙ . Often, values of C1 = 1/3 and C2 = 1 are used with the relations given in Eq. (7.73 and 7.74), σ = C1 · σind

(7.73)

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.68 Results of the indentation creep tests performed on pure Ni at a temperature of 650 °C and different loads. a Experimentally determined indentation depth versus time curves. b Indentation velocity as a function of time. For the load of 0.125 N three curves are shown, which illustrates the good reproducibility of the tests. (D. Matschkal-Amberger et al. Materials and Design 183 1,080,905 (2019). With kind permission of Elsevier

Fig. 7.69 Comparison of the indentation depth as a function of time between experiment and simulation for the load of 0.125 and 0.088 N. Matschkal-Amberger et al. (2019). With kind permission of Elsevier

and ε˙ =

h˙ C2· D

(7.74)

7.4 Creep in Nano-Ni

323

Fig. 7.70 Indentation creep tests on pure Ni at a temperature between 650 °C and 750 °C at a constant load of 0.044 N a Indentation depth versus time curves. b Indentation velocity as a function of time. Matschkal-Amberger et al. (2019). With kind permission of Elsevier

Fig. 7.71 a Normalized minimum indentation velocity as a function of the stress exponent for different reference stress parameters C1 at 650 °C under punch load of 0.125 N, b minimum strain rate as a function of minimum indentation velocity divided by the diameter of indenter for different loads at 650 °C. The reference stress parameter C1 is equal to 0.5. Matschkal-Amberger et al. (2019). With kind permission of Elsevier

but in Fig. 7.71, 0.5 is used for C1 . Figure 7.72 a shows the calculated orientation dependence of three orientations normal to the surface, those of [001], [011] and [111] indicating almost no influence of indentation depth in the creep depth, but lead to a large difference in the creep strain as seen in (b). However, due to the anisotropy of single crystals C2 is orientation dependent, and the values used are 0.564, 0.697 and 1628 for the orientations [001], [011] and [111], respectively. The indentation creep test conversion to the equivalent uniaxial stress and strain rate, σ and ε˙ of the single crystals, the values of C1 = 0.5 and C2 = 0,564 were used. The results are shown in Fig. 7.73.

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.72 Calculated indentation depths as a function of time for different crystallographic orientations under punch load of 0.125 N at 650 °C in the flat punch test. b Corresponding strain versus time curves obtained from simulations of uniaxial creep tests for different crystallographic orientations at 650 °C. Matschkal-Amberger et al. (2019). With kind permission of Elsevier

Fig. 7.73 a Norton plot of the indentation creep data showing the calculated minimum strain rate as a function of the applied stress for pure Ni measured at a temperature of 650 °C. b Temperature normalized Norton plot for Ni. The indentation creep data from this work are compared with conventional compression tests and uniaxial creep tests. Matschkal-Amberger et al. (2019). With kind permission of Elsevier

Nanocrystalline Ni is compared with CG Ni in Fig. 7.74 obtained by nanoindentation at RT creep to evaluate the equivalent stress. In the figure strain rate plots against equivalent stress are seen. Figure 7.75 shows the time- and the temperature dependent behavior of nc-Ni at RT and 200 °C. Literature data are also included for comparison. At this experiment, at higher temperatures, the curve is shifted to slightly lower stress values, with little change in the curvature. The creep behavior

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Fig. 7.74 Nanoindentation creep tests results in a Norton-Plot of Ni in a ncand cg-state. b The results from some nanoindentation strain-rate jump tests are shown (crossed symbols) in comparison. Maier et al. (2013b). With kind permission of Cambridge University Press

Fig. 7.75 Time- and temperature-dependent deformation behavior-results of nanoindentation creep tests for 2 h at RT and 200 °C; equivalent stresses are directly derived from the hardness according to Eq. (7.75), c nc-Ni. Maier et al. (2013b). With kind permission of Cambridge University Press

is therefore nearly unaffected by increasing the temperature up to 200 °C.   H = c∗ σf εrep−Berko = 85

(7.75)

In Table 7.8 the activation volume at the end of the long term indentation creep test is shown for nc Ni. The activation volume at RT of the UFG and NC metal is much smaller than the CG counterpart. By increasing the temperature to the value of the

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Table 7.8 Activation volume A and strain-rate sensitivity m; values taken at the very end of a 2 h nanoindentation creep experiment (basic data also see Figs. 7.74 and 7.75). It should be noted that the interpretation and the meaning of the values for the activation volume is questionable, since dislocation glide is not the rate controlling mechanism Material Temperature T °C Activation volume A Strain-rate sensitivity Stress exponent n b3 m nc-Ni

RT

5.6

0.047

21.3

nc-Ni

200 °C

5.4

0.128

7.8

cg-Ni

RT

52

0.014

71.4

current experiment of the NC-Ni it was observed that the activation volume remains almost unchanged around 5.5b3 . The activation volume is useful, generally, by its indication of the dominant dislocation glide mechanism. In indentation creep tests, however, local relaxation may lead to local dislocation rearrangement accompanied by dislocation annihilation near the grain boundaries. In summary the dynamic indentation method allows measuring indentation creep rate at RT and 200 °C of Ni with NC microstructure to obtain the strain rate variation with equivalent stress regarding time and temperature effect on the creep behavior. Increasing time increases the strain rate sensitivity and in the NC material the strain rate sensitivity is more pronounced compared to the CG one and also more pronounced softening occurs during creep, which much increases at 200 °C. Further, indentations induce extensive grain boundary sliding and pile-up is observed. Increasing the temperature is associated with a reduction of pile-up followed by an increased GBS (Table 7.8).

7.5 Creep in Nano 316L SS 7.5.1 Tension in Nano 316L In view of the lack of pure unalloyed 304L for creep studies, in the following 316L is considered. However, for fast nuclear fission and fusion power plant (in India) 316L austenitic steel is used as structural material. It is N containing to enhance the various properties of the material and is designated as 316LN. Nitrogen at a level of 0.14 wt% is added and as a consequence the creep strength increases which in turn increases the life of a fast reactor. Sodium cooled fast reactors (SFRs) is largely dependent on the performance of core structural materials, i.e., clad and wrapper materials of the fuel subassembly, which are subjected to intense neutron irradiation at high temperature during service. Consequent to irradiation, void swelling and helium embrittlement occur. The 316 SS in 20% cold work condition is used as clad and wrapper in the Fast Breeder Test Reactor (FBTR). Void formation is seen in Fig. 7.76. 316 SS is designed to improve the void swelling resistance.

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Fig. 7.76 Void formation in 20% cold worked 316 austenitic stainless steel neutron irradiated at 40 dpa and 771 K. Jayakuma et al. (2013). Open access. dpa stands for (displacement per atom in solid)

Austenitic SS of type 316 and the related 316LN are the preferred candidates for high temperatures structural components of SFRs due to their high temperature tensile and creep strength compatibility with the sodium coolant, ease of fabrication, weldability and commercial availability. Despite of these qualities pronounced heatto-heat variation in the long term application creep rupture might occur. This can be seen in Fig. 7.77 where heat-to-heat variation in creep rupture strength is illustrated. The improved creep resistance of heat-A is associated with its finer grain size and to the relatively higher percentage of interstitials C, B, and N within the specified

Fig. 7.77 Heat to heat variations in creep rupture strength of 316 SS at 823 K. Jayakuma et al. (2013). Open access

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.78 Precipitation of chromium-rich M23C6 type of carbides on a grain boundaries (873 K/22100 h) and b on dislocations in the intragranular regions (823 K/8300 h). Jayakuma et al. (2013). Open access

range. The 316 SS displayed microstructural stability over long periods as depicted by linear variation in stress dependence of creep rupture life plots as seen in Fig. 7.77. This is attributed to the fine scale precipitation of chromium-rich M23 C6 type of carbides on grain boundaries as seen in Fig. 7.78a as well as on dislocations in the intragranular regions illustrated in Fig. 7.78b. The fine precipitates on dislocations prevented the recovery in substructure. While fine carbides on grain boundaries reduce grain boundary sliding, the intragranular precipitation of carbides strengthen the matrix by retarding the glide and climb of dislocations. The addition of N to 316 SS is to improve its resistance against intergranular stress-corrosion cracking in caustic and chloride environment. Rupture life increased significantly with N additions seen in Fig. 7.79. Creep rupture strength increased substantially with increase in nitrogen content as seen in Fig. 7.80. After the creep test the dislocation have been rearranged in the form of subgrains at a N content of 0.07 wt% as seen in Fig. 7.81a. The tendency to form subgrains decreases with increased N content and in the metal containing 0.22 wt% no evidence for cell/subgrain formation. Instead dislocations were distributed uniformly in the matrix as illustrated in Fig. 7.81b. In summary, 316LN SS with N content of ~ 0.14 wt% have a higher creep strength and increased life in the use of fast reactors. The major structural materials chosen as fuel clad and wrapper material for PFBR (Prototype Fast Breeder Reactor) components and piping is 316LN. Creep strength and void swelling resistance are the most important properties for fast neutron reactor core structural materials for which appropriate components are required for life increase to the planned one by design.

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Fig. 7.79 Influence of nitrogen on creep properties of 316L (N) SS steel. Jayakuma et al. (2013). Open access

Fig. 7.80 Influence of nitrogen on creep properties of 316LN 923 K. Jayakuma et al. (2013). Open access

7.5.2 304L for Reactors: Tension and Hardness One of the important applications of 304L SS is in extreme radiation environments to reduce void swelling accompanied by precipitation and neutron irradiation damage

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Fig. 7.81 Transmission electron micrograph of creep tested 316LN SS at 923 K (stress = 175 MPa). Jayakuma et al. (2013). Open access

at high temperatures. It was reported by Sun et al. that UFG 304L SS with an average grain size of ~ 100 nm can withstand Fe ion irradiation at 500 °C to 80 displacements per atom (dpa) with moderate grain coarsening. Under neutron irradiation, the microstructural damage in metals includes point defects, dislocation loops, voids, precipitates, etc. With high dose of > 10 dpa, neutron irradiation at elevated temperatures in the range 300–700 °C, formation of voids and precipitates (M23 C6 ) are the major microstructural changes. Voids nucleated (from supersaturated vacancies for example) can cause volumetric swelling which jeopardizes the use of austenitic SS in reactors (as fuel cladding). Internal defect trapping sinks redistribute the concentration of irradiation-induced point defects and their clusters, and thus have a significant impact on the formation of voids and phase stability under irradiation. High angle grain boundaries (HAGBs), twin boundaries, phase boundaries and free surfaces can effectively absorb the radiation-induced defect clusters. However, for nuclear reactor applications, these defect sinks need to be thermally stable against high temperature irradiations, ~ 500 °C. It has been experimentally observed that UFG 304L SS has excellent thermal stability up to 600 °C and high strength as tested at 500 °C. Substantial reduction of swelling and swelling rate occurs by the stable defect sinks. The UFG 304L was produced by ECAP technique to an average grain size of ~ 100 nm. The microstructure and the corresponding indentation hardness results are illustrated in Fig. 7.82 comparing the micron size and ECAP reduced 100 nm samples, in (a) and (b) respectively. Enhanced void swelling resistance of UFG 304 l SS is seen in Fig. 7.83d; the image was obtained by TEM, compared to the CG cross-sectional TEM micrograph seen in Fig. 7.83a where a large number of voids are shown. Magnified micrographs taken from the surface region at A seen in Fig. 7.83b and region B at a depth of 600 nm from surface seen in Fig. 7.83c indicate a high density of voids. Contrary to this in irradiated Fig. 7.83d showing sporadic distribution of voids. A magnified view of the irradiated surface region C seen in Fig. 7.83e shows voids near free surface. In UFG 304L the void density is much lower than in CG SS sample. It would be of interest to show that in UFG 304L specimens the maximum void density occurred near the surface region and the overall density was much less than in that

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Fig. 7.82 Microstructure, thermal stability and high temperature mechanical properties of ultrafine grained (UFG) 304L stainless steel (SS). a Optical micrograph of coarse grained (CG) 304L stainless steel showing an average grain size of 35 μm. b TEM micrograph of UFG 304 SS shows the average grain size is, 100 nm, and the inserted selected area diffraction (SAD) pattern shows austenite is the dominant phase. c Thermal stability of as processed UFG 304L SS without radiation. The indentation hardness of the annealed specimens (one hour) measured at room temperature remained unchanged up to 600 °C, followed by softening thereafter. d Engineering stress–strain curves of CG and UFG 304L SS under tension tests at 500 °C. The 0.2% off-set yield strength is 630 MPa for UFG 304L SS, and 85 MPa for CG specimen. Sun et al. (2015). Open access

of CG sample throughout the entire irradiated specimen. Statistic show that UFG 304L SS has significantly lower void swelling than CG 304L SS due to reduced void density and size. In Fig. 7.84a a statistic analysis shows that void density along the projected radiation depth reached a maximum both near surface and at 700–800 nm in irradiated CG specimen. In UFG specimens, the maximum void density occurred near surface region, and the overall void density in UFG SS was much less than that of CG counterpart throughout the entire irradiated specimens. SRIM (stopping range of ions in matter) simulated depth dependent radiation damage (in unit of dpa) was superimposed on the same plot in Fig. 7.84a. In summary, nano 327G-grains of 304L SS can drastically reduce the magnitude of void swelling of irradiated 304L SS. UFG grains also effectively alleviate the

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.83 Extraordinary void swelling resistance of UFG 304L SS subjected to Fe ion irradiation at ion energy of 3.5 meV and a total fluence of 6 3 1020/m2 at 500 °C by defocusing the ion beam. a Panoramic cross-section TEM micrograph of Fe ion irradiated CG 304L SS showing a large number of voids. b The magnified TEM image of region A in Fig. 2a shows high-density small voids near the surface of irradiated CG 304L SS. c In region B of the same specimen, at a depth of ~ 500 nm from surface, high-density large voids were observed. d Cross-section TEM overview of irradiated UFG 304L SS showing much less voids. e The magnified TEM image of surface region (e) in irradiated UFG 304L SS shows numerous faceted voids distributed primarily along grain boundaries. f Magnified TEM micrograph of region (f) at ~ 500 nm from surface shows much lower void density compared to that in irradiated CG counterpart. Sun et al. (2015). Open access

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333

Fig. 7.84 Statistic studies show that UFG 304L SS has significantly lower void swelling than CG 304L SS due to reduced void density and size. a Statistic analysis shows that void density along the projected radiation depth reached a maximum both near surface and at 700–800 nm in irradiated CG specimen. In UFG specimens, the maximum void density occurred near surface region, and the overall void density in UFG SS was much less than that of CG counterpart throughout the entire irradiated specimens. SRIM simulated depth dependent radiation damage (in unit of dpa) was superimposed on the same plot. Sun et al. (2015). Open access

formation of carbide precipitates. The UFG grains in 304L SS also have exceptional thermal stability against radiation at elevated temperature and enable a combination of high strength and good ductility. The present study implies that UFG austenitic SSs have promising applications in extreme radiation environments.

7.6 Creep in Nano Alumina Nanoceramics-have been studied in the past decades extensively. Interest in the subject is associated with the many important properties in nano materials in general and in nanoceramics in particular. Such an important property is associated with superplasticity which is exhibited by many of the nano materials which is probably associated with the very small grain size, in the submicron size-often in the 50 nm range. The consolidation techniques of the raw materials and the production methods generally determine the mechanical, physical and other properties of a ceramic. This is particularly true in the case of nanoscale ceramics, since the distribution of the phases in composite ceramics, for example, and their location relative to the commonly-found micro cracks are decisive factors in obtaining strong, tough, fracture-resistant substances. Nanoceramics show excellent physical, chemical and

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7 Time Dependent Deformation-Creep in Nanomaterials

mechanical properties which generally are much desired properties for various technological applications. Thus regarding mechanical properties, our interest is in creep studies, nanoceramics are known to possess outstanding strength, superior hardness and good fatigue resistance. Since the properties of solids—and nanoceramics are no exemption-depend on their chemical composition, atomic structure and microstructure, nanomaterials may exhibit properties that are very different from conventional polycrystalline material. These properties among them creep depend on the production method. Glassy phases are often observed in nanocrystalline structures and their occurrence depends on the production method. Improved creep resistance can be obtained by eliminating the glassy phases from the nanoceramics. By using an appropriate production method to eliminate glassy phases at grain boundaries, a strong, significantly-improved, creep-resistant nanoceramics can be obtained. The formation of the glassy phase is associated with the presence of oxygen. The amount of oxygen its distribution determines the amount of the glassy phase. Often the oxygen is not distributed homogeneously in the grain-boundary regions, some having more than others. In the past decades much effort was devoted to the production of nanoceramics, because they are expected to exhibit advanced mechanical properties usable for functional applications. The prerequisite to obtain such nanoceramics rests in the production of structures without pores, cracks and other flaws. Modern production techniques have been developed which might provide the hope for achieving such flawless structures. Furthermore, another interest in producing sound nanoceramics is associated with the expectations that some nanoceramics might exhibit ductile properties alongside with high strength which is absent in bulk ceramics. This expectation is a consequence of the fact that the fundamental behavior of nanostructures is quite different from that of bulk, since in very small size structures surface and atomistic properties dictate their performance. In general, all test results are dependent on the grain size. The strength of materials—including ceramics-increases with a decrease in grain size and also when the structure is small, namely in nanometric crystals. The strengthening in small sized structures is associated with the restriction of dislocation motion. (Note that when no dislocations are involved in deformation, high strength at a level approaching the theoretical strength is required to induce strain in the test specimen). Unlike conventionally-sized test specimens, in which ductility usually decreases with increased strength, some nanocrystalline-sized specimens show high strength combined with good elongation. Moreover, such nano-specimens may reach high values of plasticity, which, in some ceramics, may lead to superplastic behavior before fracture. Generally, the creep behavior is tested by compression rather than tensile stress to avoid cavitation by crack formation. Thus, studies of nanoscale ceramics are an inevitable step for the understanding the experimental observations. It should be noted that in order to facilitate densification of the nanoceramics and other production problems additives are usually incorporated in the nanostructure. In the following creep-tests in nanoceramics will be discussed and exemplified by alumina. Alumina acts usually with other components, either as a strengthening

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335

agent or as the major constituent with other material. Seldom is found in the literature if at all, nano alumina by itself as the only phase. Below alumina containing SiC as an additive is considered which is a major alumina composite.

7.6.1 Creep in Alumina/SiC Alumina (Al2 O3 ) and silicon carbide (SiC) powders at different volume fractions (3, 5, 10, 15, and 20 vol%) were mixed and then hot-pressed for 1 h at 1740 °C in Ar atmosphere under a pressure of 30 MPa. Creep experiments were performed up to 1350 °C and load up to 200 MPa and the results were compared with monolithic Al2 O3 as reference. Table 7.9 characterizes the starting powders. The volume fraction of SiC significantly influences the microstructure and the average grain size of the alumina matrix as can be seen from Table 7.10. As can be seen 20 vol% SiC changes the grain size of the matrix to 0.6 μ m (600 nm). The green bodies were prepared by homogenization, drying, sieving, and consolidation. They were hot pressed at a temperature of 1350 °C under a pressure of 30 MPa for 1 h in vacuum, using the BN protective bed. Dense Al2 O3 /SiC microcomposites were fabricated by hot pressing in a rectangular graphite die for 1 h under 30 MPa uniaxial pressure at 1740 °C and Ar protective atmosphere. The basic characteristics of all prepared materials are summarized in Table 7.10. The mean size of the Al2 O3 matrix grains in the composites decreased with increasing SiC content. The fraction of SiC significantly affected the microstructure and the creep behavior of the Table 7.9 Basic characteristics of the starting powders as provided by the producers. Parchovianskýa et al. (2014). With kind permission of Elsevier Powder

Density (g/cm3 )

Specific surface area (g/m2 )

Average particle size (nm)

Purity (%)

α-Al2 O3

3.98

14.5

170

99.995

β-SiC

3.21

13.5–18.5

200

97–99

Table 7.10 Basic characteristics of the studied materials. Parchovianskýa et al. (2014). With kind permission of Elsevier Samples SiC content (vol%) Relative density (%) Average size of the Al2 O3 matrix grains (μm) A

0

98.3

1.4 ± 0.4

AS3

3

99.6

14.2 ± 1.1

AS5

5

99.4

10.9 ± 0.2

AS10

10

99.4

1.8 ± 0.2

AS15

15

99.4

1.1 ± 0.2

AS20

20

99.3

0.6 ± 0.1

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7 Time Dependent Deformation-Creep in Nanomaterials

Al2 O3 /SiC microcomposite and the average size of the alumina matrix. Compared to monolithic Al2 O3 the creep resistance of Al2 O3 /SiC was markedly improved. Long loading time before mechanical failure suggested grain boundary sliding and cavitation controlled creep behavior. The enhanced creep resistance was attributed to grain boundary pinning by the intergranular SiC nanoparticles. The pre-crept microstructures of the monolithic Al2 O3 and the composites are compared in Fig. 7.85. The grain boundaries tended to be pinned more efficiently by larger SiC particles, which were dragged along as the grain boundaries moved. The high temperature creep rate can be expressed in an equation similar to Eq. (7.10) and given as   DGb b p  σ n ε˙ = A kT d G

(7.76)

The symbols—described earlier-is rewritten for convenience. Clearly, D is the appropriate diffusion coefficient, G is the shear modulus, b is the Burger’s vector, p is an exponent related to grain size and n is the stress exponent. Creep deformation can be induced either by lattice or grain boundary mechanisms. Creep deformation controlled by dislocation glide, dislocation creep, i.e., Nabarro-Herring is lattice dominated, while diffusion creep, namely, Cobble creep, grain boundary sliding are governed by grain boundary diffusion. In the boundary mechanism the exponent p is ≥ 1, contrary to lattice controlled mechanism affecting the grain interior, independently of the grain size with p = 0. The value of the stress exponent also depends on the mechanism that controls creep; For the lattice diffusion of the Nabarro-Hering creep n = 1, while for the Coble creep n = 2 and for the dislocation mechanism n = 3–5. Strain versus time plots for all the materials listed in Table 7.10 are assembled in Fig. 7.86 obtained by a step-wise method, with a gradual increase of the applied stress from 75 to 200 MPa, and at a temperature of 1350 °C. Primary and secondary creeps are seen, but no tertiary. Increasing the volume fraction of SiC increases the creep resistance, however the best performance of strain resistance was when the composite contained 10 vol% SiC. It endures 200 MPa at 1350 °C and did not fail after 150 h. It failed when the applied stress was 200 MPa at 1450 °C. In comparison the monolithic alumina and the other composites failed after 75 MPa and 150 MPa, respectively. Due to the good creep resistance of the 10 vol% SiC composite, creep tests performed at higher temperatures up to 1450 °C (but failed at 200 MPa) is seen in Fig. 7.87. From the slope of Fig. 7.88, which is a plot of the log ε˙ (of the steady state rate) versus log σ, the stress exponent was evaluated by linear fitting as n = 3.4 ad n = 3.5 at 1350 °C and 1400 °C, respectively, while at 1450 °C the value was smaller as n = 2.6. Such high n values of the composite are characteristic of dislocation controlled creep, either by dislocation glide or climb. However, there are claims (by the authors) that creep mechanism in composites and multiphase material, the stress exponent index is not the only concept for evaluating the deformation mechanism. Thus, a claim is made, that grain boundary sliding and cavitation control the creep behavior. Indeed, cavitation was observed after creep as illustrated in the microstructure after creep in Fig. 7.89. In Fig. 7.89a the alumina grains are elongated (compare with 7.85a before

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Fig. 7.85 Microstructure of monolithic Al2 O3 /SiC nanocomposites prior to creep tests: a Al2 O3 . b AS3, c AS5, d AS10, e AS15 and AS20. Parchovianskýa et al. (2014). With kind permission of Elsevier

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Fig. 7.86 Creep curves (strain–time plots) of the monolithic Al2 O3 and of the Al2 O3 /SiC composites obtained at 1350 °C, under the applied stress ranging from 75 to 200 MPa. Parchovianskýa et al. (2014). With kind permission of Elsevier

Fig. 7.87 Creep curves (strain–time plots) of the composite AS10 measured at 1350, 1400, and 1450 °C, under the applied stress ranging from 75 to 200 MPa. Parchovianskýa et al. (2014). With kind permission of Elsevier

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Fig. 7.88 Steady-state creep rate versus stress plot of the AS10 composite measured in the temperature range between 1350 and 1450 °C, under applied stresses from 75 to 200 MPa. Parchovianskýa et al. (2014). With kind permission of Elsevier

creep) with irregular grain boundaries, which suggest grain boundary sliding as the main deformation mechanism. It is expected that in the Al2 O3 /SiC composite similar creep deformation mechanism occurs. Besides, in ceramics one of the principal creep mechanisms is grain boundary sliding. Thus, at low stresses grain boundary sliding, while at high stresses cavitation and microcraking caused by stress concentration are the responsible mechanisms for creep. Grain boundary separation was also observed in some cases which is seen in Fig. 7.90. In summary, grain boundary sliding and cavitation control the creep behavior. The minimum creep rate of the Al2 O3 /SiC nanocomposite is about three orders of magnitude lower and the creep life ten times longer than that of the monolithic Al2 O3 . The improvement of the creep resistance is attributed to the pinning effect of the SiC particles located at the grain boundaries. These inhibited grain boundary sliding and reduced the creep strain rate. A strong interface bonding between Al2 O3 and SiC particles develops, and as a consequence, the intergranular SiC particles inhibit grain boundary diffusion. Additional factors such as the volume fraction of SiC, microstructure, and the mean size of the alumina matrix grains have to be also considered.

7.6.2 Compressive Creep in Alumina Creep in alumina with a fine grain size of 0.5 and 0.42 μm (500 and 420 nm), respectively has been performed by spark plasma sintering (SPS) and the steady state stage

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Fig. 7.89 Microstructures of monolithic Al2 O3 and Al2 O3 /SiC nanocomposites after creep tests obtained at 1350 °C, under applied stresses ranging from 75 to 200 MPa; cavities at grain boundaries and in the triple grain boundary junctions are marked with white arrows. a Al2 O3 , b AS3, c AS5, d AS10, e AS15, and f AS20. Parchovianskýa et al. (2014). With kind permission of Elsevier

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Fig. 7.90 Microstructures of Al2 O3 /SiC nanocomposites after creep tests obtained at 1350 °C, under applied stresses ranging from 75 to 200 MPa; grain boundary separations are marked with white arrows. a AS15 and b AS20. Parchovianskýa et al. (2014). With kind permission of Elsevier

deformation was investigated under continuous load or stress and controlled temperature. The relative punch displacement (RPD) is monitored with an accuracy of ~ 1 μm and can be converted to strain which allows determination of the corresponding creep rate, the creep test itself is performed in a relatively simple manner, by setting the designated temperature and load (pressure is calculated according to sample cross-section) and tracking RPD. An example of AlSi10 Mg samples before and after creep test (~34% strain) at 225 °C under an initial applied pressure of 130 MPa is illustrated to show the results of a test by SPS. Thus, the strain rate, ε˙ during compressive creep tests can be summarized as the following equation which has been given earlier, but rewritten for convenience.      Q F (7.77) ε˙ = A 2 exp(εt ) exp − RT a0 This equation is equivalent to Eq. 7.29 where the term of σth has been replaced by the relation σt =

F a20

(7.78)

where F is the applied load and a02 is the initial sample cross-section area as seen in Fig. 7.91. Clearly the strain in Eq. (7.77) is given by εT (T ) = ln

lt l0

(7.79)

It was found that Q, the activation energy of Eq. (7.77) decreases with increased applied stress. The creep curves of the fine grained alumina under an applied stress

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Fig. 7.91 Example of AlSi10 Mg samples before and after creep test (~34% strain) at 225 °C under an initial applied pressure of 130 MPa. Ratzker et al. (2020). Open access

of 100 MPa and in the temperature range 1125–1250 °C are shown in Fig. 7.92a, while the corresponding strain rate versus time plots at the temperatures indicated are illustrated in Fig. 7.92b. Strain rate (creep rate) versus stress is shown in Fig. 7.92c comparing current results with those from the literature. From the slope the stress exponent, n was evaluated for fine-grained alumina, resulting in ~ 1.8 which is close to 2 (Ratzker et al. 2017). In the case of insulating ceramics, a graphite die must be used. In summary, An SPS apparatus can be used for studying high temperature mechanical properties, particularly compressive creep of metals and ceramics. A wide range of temperatures and pressures can be applied, and all the necessary data for creep tests can be easily acquired. However, the SPS apparatus, as a tool for mechanical testing, has some technical limitations, among them the lack of the possibility for tensile testing and that only a constant load regime can be applied.

7.6.3 Hardness in Alumina—Creep, Radiation Effect Due to lack of suitable materials for advanced nuclear systems, requiring simultaneous long life resistance against radiation damage, corrosive environment and the action of high temperature, the attention was shifted to oxide nanoceramics thin films such as alumina and extensive research was conducted in this direction. Contrary to the as-deposited films, irradiation induces in the initially homogeneous dispersion of nanocrystals in an amorphous matrix crystallization, grain growth with the consequent enhancement of the hardness. The grain growth induces softening, namely, since a change in grain size occurs the process of softening occurs according to the Hall–Petch relation. The main energy of the irradiation impact is by twin formation. Radiation damage induces in addition, irradiation creep, void swelling and high temperature helium embrittlement. Coolants, like liquid metals such as sodium at ~

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Fig. 7.92 a Example of alumina creep tests strain under an applied stress of 100 MPa at the 1125– 1250 °C temperature range and b corresponding strain rates; c comparison of creep rates (at 1200 °C and varying stress) measured for alumina by an SPS apparatus in compression (black squares) and conventional compression testing equipment (blue circles). Ratzker et al. (2020). Open access

400 to 1000 °C are of high concern regarding corrosion. In order not to affect the basic structure the deposition of ceramic coatings on metallic structural materials can provide corrosion resistance without affecting structural requirements. This way ceramics who represent a promising class of materials due to their high temperature strength, and due to their chemical inertness in several corrosive environments became an option to avoid catastrophic failure. Thin films of Al2 O3 1.3 μm thick are grown by Pulsed Laser Deposition (PLD) at room temperature on substrates of austenitic steel. Samples were irradiated with heavy ions as a substitute technique of neutron irradiation. The Bright-Field (BF) TEM micrographs shown in Fig. 7.93 display the nanostructure of the as-deposited Al2 O3 thin films. The dark contrast spots correspond to randomly-oriented ultra-fine nanocrystalline γ-Al2 O3 domains (6 ± 4 nm), whereas the bright contrast results from the presence of the amorphous phase of Al2 O3 . The rings of the diffraction pattern (DP) (relatively sharp) and the diffused intensity halo confirm that the sample consists of two phase structure, that of the amorphous γ-Al2 O3 and γ-Al2 O3 nanocrystalline regions in very low proportion (~1%). ADF-STEM (annular dark field scanning TEM) micrographs, shown in Fig. 7.94, illustrate the structural features of the as-

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Fig. 7.93 BF-TEM micrograph, and high-resolution (HR) close-up (inset) of the nanostructure of the as-deposited Al2 O3 thin films showing a homogeneous dispersion of a low volume fraction of randomly-oriented nanocrystalline Al2 O3 domains in an amorphous Al2 O3 matrix. Ferré et al. (2016). Open access

Fig. 7.94 ADF-STEM micrographs and DPs showing as-deposited (a) and irradiated Al2 O3 thin films after 20 dpa (b), 40 dpa (c) and 150 dpa (d) at 600 °C. The coarsening induced by irradiation releases excess free energy due to the interaction between point defects and GBs. Ferré et al. (2016). Open access

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deposited and the irradiated thin films. These images indicate that a fully nanocrystalline structure is realized upon irradiation, and that extended irradiations induce grain growth as the dpa (displaced per atom) levels are increased. The average grain size increases from 6 ± 4 nm to 101 ± 56 nm at 20 dpa, 153 ± 62 nm at 40 dpa and 293 ± 85 nm at 150 dpa (Fig. 7.94b–d). Note the diffraction pattern changes from the diffused intensity halo to DP rings and isolated spots. The plot in Fig. 7.95a shows the dependence of grain growth both on the total amount of energy injected into the material and on displacive radiation damage (displacements per atom). In the irradiated material, grain growth is accompanied by the formation of planar defects, which has been identified as twins and shown in Fig. 7.95b. Confirmation that the defects observed are indeed twins is indicated in Fig. 7.95c. Structural changes, such as crystallization and grain growth induced by irradiation and this in turn causes changes in the mechanical properties of the material. These changes are plotted in Fig. 7.96 as a function of the average grain size. Also the reduced Young’s modulus Er increases monotonically with grain size as seen in Fig. 7.96a. The formation of twins in nanocrystalline solids can be understood in terms of mechanisms such as stacking fault formation led by Shockley partial dislocations. Compared to the as deposited hardness of ~ 10 GPa, seen in Fig. 7.96,

Fig. 7.95 Grain growth in the Al2 O3 thin films as a function of total energy injection and displacive radiation damage (a). The grain coarsening is accompanied by the formation of twin boundaries (b), which release accumulated mechanical energy. The presence of a mirror plane in both the HR-TEM micrograph (c) (indicated by arrows), and in the DP inset confirms the twin relationship of the adjacent grains. Ferré et al. (2016). Open access

Fig. 7.96 Effect of radiation-induced grain growth on the mechanical properties of Al2 O3 nanoceramic thin films, namely the Young’s modulus E (a), the hardness H (b) and the hardness to Young’s modulus ratio H/E (c). The trend of hardness is well-described by the Hall–Petch effect, due to the increase of grain size with increasing damage exposures. Ferré et al. (2016). Open access

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irradiation at moderate damage exposures increases the hardness as a function of grain size to 17.8 GPa at H20 dpa, 17.2 GPa at H40 dpa and 15.9 GPa at H150 dpa. The overall variation in hardness with grain size can be described by the Hall–Petch relation, namely Hv = H0 + kD−1/2

(7.80)

H0 is the intrinsic hardness (depends on frictional lattice resistance to dislocation motion), k as known is the strength coefficient and D is the average grain size. The linear fit of Hv versus grain size D−1/2 yields H0 = 13.26 GPa and k = 46.64 GPa nm1/2 . Basically the inverse Hall–Petch effect is observed in the hardness data (decreasing grain size) of the irradiated material. Figure 7.97 shows cross-sectional TEM micrographs of representative nanoimpact imprints on the Al2 O3 nanoceramic thin films before (a) and after irradiation up to 20 dpa (b) and 150 dpa (c). No major structural rearrangements are induced by impact loading in the unirradiated samples, as confirmed by the identical SADPs gathered distant from and below the impact imprint (d). The appearance of arcs and rings in imprints for as-deposited and irradiated samples are seen. In the unirradiated samples (a), impact energy is dissipated through shear banding, and no major structural rearrangements are induced by the impact loading. Figure 7.97b, c show the cross-section of nanoimpact imprints in samples exposed to 20 dpa and 150 dpa, respectively. The SADPs (selected area diffraction pattern) distant from and within the impact imprint appear identical as shown in (d). Beneath the impact zones arcs and rings appear in the SADPs indicating that plastic strain is the main energy dissipation mechanism and also by localized amorphization. Amorphization from crystalline phase transformation is considered also as an energy dissipation mechanism and is described as a toughening mechanism. The localized amorphization is seen by HRTEM in Fig. 7.97e, f and is indicated by arrows in (b) and (c), respectively. Summarizing the effect of irradiation with heavy ions at 600 °C on the nano alumina, it has been observed that initially irradiation induces an amorphous to crystalline transformation of nanograined structure, while extended irradiation induces grain growth and softening in accordance of the Hall–Petch relationship. There is an initial increase of H/E, the hardness ratio to the Young’s modulus, upon crystallization and decrease thereafter. The initial increase of the H/E ratio suggests a potential improvement in the fracture toughness of the irradiated thin films, which manifests itself by twin formation associated with energy dissipation mechanism and also in localized crystalline-to-amorphous transformation under impact loading. The overall findings in this work encourage the use of nanoceramics (thus nano-alumina also) in radiation environments well beyond the traditional limiting range for standard nuclear materials. The fracture toughness is given by Eq. (7.81).  1/2 E F x 3/2 KI = 0.016 H C

(7.81)

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347

Fig. 7.97 Displays the cross-sectional images of representative nanoimpact in the SADPs beneath the impact zones in the irradiated samples is due to energy dissipation through bending of the lattice planes. Another energy dissipation mode present is localized amorphization, which is indicated by arrows in (b, c), and shown in high-resolution in (e, f). The FFT insets in (e, f) confirm that the bright contrast corresponds to the amorphous phase, and that the dark contrast corresponds to the crystalline phase. Ferré et al. (2016). Open access

where F is the load in Newtons, C is the crack length from the center of the indent to the crack tip in meters, E is the Young’s modulus in GPa and H is the Vickers hardness in GPa. The amorphous matrix precludes grain sliding, enables plastic deformation and inhibits crack nucleation.

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7 Time Dependent Deformation-Creep in Nanomaterials

7.6.4 Tensile Creep in Alumina Tensile data in pure nano alumina is not really available in the open literature. As alumina/SiC composite is considered below. In any event, generally, two-phase mixtures exhibit less grain growth than single-phase materials and tend to be more microstructurally stable. However, the mechanism by which multiphase ceramic oxide fibers resist creep rupture is not completely understood. It is thought that the grain morphology plays a key role in creep retardation. SiC nanoparticles enhance creep strength of alumina, particularly when the particles are preferentially located along the alumina grain boundaries. The postulate put forward is that the SiC particles inhibit grain boundary sliding inducing a “back stress” that resist creep. Also it was inferred from sintering studies, that SiC particles decrease the overall grain boundary diffusion rate and thus creep is inhibited by the slow diffusion. But as mentioned the exact mechanism is still obscure. Calculations have implied that grain elongation along the fiber axis can enhance creep strength, when diffusion mechanisms dominate creep rate as illustrated in Fig. 7.98. The tensile creep rate in a specimen containing 5 vol% SiC is shown in Fig. 7.99. Compare the strain rates of alumina and the one with the 5 vol% SiC composite. The strengthening effect is obvious and the creep rate is reduced by ~ 2 orders of magnitude. Addition of proper dopants further increases the creep resistance; yttrium is such a dopant. The addition of yttrium and other oversized isovalent cations to alumina has also been shown to enhance creep strength. The steady state tensile creep for yttria doped and undoped alumina is shown in Fig. 7.100. The oversized ions segregate to the alumina grain boundaries and inhibit creep (see Fig. 7.100), but a comprehensive understanding of the mechanism of retardation remains elusive (Fig. 7.101). Fig. 7.98 Predicted creep rates for alumina fibers as a function of aspect ratio using a two-dimensional model. The National Academic Press (1998). Open access

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Fig. 7.99 Tensile creep rate of Al2 O3 -SiC nanocomposite containing 5 volume percent of 0.15 μm (0.006 mils) SiC particles and undoped Al2 O3 of the same grain size. The hatched band represents flexural strain rate data for SiC whisker-reinforced alumina. The National Academic Press (1998). Open access

Fig. 7.100 The steady-state tensile creep rate for undoped alumina and alumina doped with 1000 ppm Y2 O3 . Note that yttria doping dramatically reduces the creep rate The National Academic Press (1998). Open access

In summary, the recent experimental findings described above highlights and indicate the opportunity for developing polycrystalline materials that combine high tensile strength with excellent creep resistance. There are limitations of the material choice for use for creep in general and tensile creep in particular, alumina and SiC are among the usable material. Therefore, tensile creep enhancement can be achieved

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7 Time Dependent Deformation-Creep in Nanomaterials

Fig. 7.101 High resolution secondary ion mass spectroscopy compositional maps showing dopant segregation in yttrium and lanthanum doped alumina. The National Academic Press (1998). Open access

by a combination of these constituents in the proper proportion. Single-crystals have certain creep performance advantages, but their cost is prohibitive.

References A.N. da C. Andrade, Proc. Royal Soc. London A 84, 1 (1910) A.N. da C. Andrade, Proc. Royal Soc. London A 90, 329 (1914) B. Cai, Q.P. Kong, L. Lub, K. Lub, Mater. Sci. Eng. A 286, 188 (2000) A.H. Cottrell, J. Mech. Phys. Solids 1, 58 (1952) H. Cottrell, V. Aytekin, J. Inst. Met. 77, 389 (1950) J. Dean, A. Bradbury, G. Aldrich-Smith, T.W. Clyne, Mech. Mater. 65, 124 (2013) F. Dobeš, J. Mater. Sci. 33, 2457 (1998) C. Duhamel, Y. Brechet, Y. Champion, Int. j. Plast. 26, 747 (2010) F.G. Ferré, A. Mairov, L. Ceseracciu, Y. Serruys, P. Trocellier, C. Baumier, O. Kaïtasov, R. Brescia, D. Gastaldi, P. Vena, M.G. Beghi, L. Beck, K. Sridharan, F. Di Fonzo, Sci Rep. 6, 33478 (2016) F. Garofalo, Fundamentals of Creep and Creep-Rupture in Metals (The Macmillan Company, New York, 1965). A. Graham, K.F.A. Walles, J. Iron Steel Inst. 179, 105 (1955) G.T. Gray III., T.C. Lowe, C.M. Cady, R.Z. Valiev, I.V. Aleksandrov, Nanostruct. Mater. 9, 477 (1997) C.D. Gu, J.S. Lian, Z.H. Jian, Q. Jiang, Scr. Mater. 54, 579 (2006) J. Ho-Kyung Kim, Mech. Sci. Tech. 24, 2075 (2010) T. Jayakuma, M.D. Mathew, K. Laha, Procedia Eng. 55, 259 (2013) R.S. Kottada, A.H. Chokshi, Scripta Mater. 53, 887 (2005) X.Y. Li, Y.J. Wei, L. Lu, K. Lu, H.J. Gao, Nature 464, 877 (2010)

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J. Li, J.Y. Zhang, P. Zhang, K. Wu, G. Liu, J. Sun, Phil. Mag. 96, 3016 (2016) V. Maier, B. Merle, M. Göken, K. Durst, J. Mater. Res. 28, 1777 (2013) W. Maier, B. Merle, M. Göken, K. Durst, J. Mater. Res. 28, 1177 (2013) D. Matschkal-Amberger, M. Kolb, S. Neumeier, S. Gao, A. Hartmaier, K. Durst, M. Göken, Mater. Des. 183, 108090 (2019) J. May, H.W. Höppel, M. Göken, Scr. Mater. 53, 189 (2005) D. McLean, Mechanical Properties of Metals (Wiley, 1962) F.H. Norton, The Creep of Steels at High Temperatures (McGraw-Hill, New York, 1929). D. Pan, T.G. Nieh, M.W. Chen, Appl. Phys. Lett. 88, 161922–161931 (2006) M. Parchovianskýa, D. Galusek, M. Michálek, P. Švanˇcárek, M. Kašiarová, J. Dusza, M. Hnatko, Ceram. Int. 40, 1807 (2014) J. Pelleg, Mechanical Properties of Materials (Springer, Berlin, 2013) J. Pelleg, Creep in Ceramics (Springer, 2017) The National Academic Press, Ceramic Fibers and Coatings Advanced Materials for the Twenty-first Century, Chapter 5, Materials and Microstructures (1998), p. 49 B. Ratzker, M. Sokol, S. Kalabukhov, N. Frage, Ceram. Int. 43, 9369 (2017) B. Ratzker, S. Kalabukhov, N. Frage, Materials (basel) 13, 396 (2020) R. Schwaiger, B. Moser, M. Dao, N. Chollacoop, S. Suresh, Acta Mater. 51, 5159 (2003) V. Sklenick, J. Dvoˇrak, M. Svoboda, P. Kral, M. Kvapilova, Equal-Channel Angular Pressing and Creep in Ultrafine-Grained Aluminium and its Alloys (IntechOpen, 5th December, 2012) C. Sun, S. Zheng, C.C. Wei, Y. Wu, L. Shao, Y. Yang, K.T. Hartwig, S.A. Maloy, S.J. Zinkle, T.R. Allen, H. Wang, X. Zhang, Sci. Rep. 5, 7801 (2015) W. Sun, Y. Jiang, G. Sun, J. Hu, T. Zhou, Z. Jiang, J. Lian, Mater. Sci. Eng., A 751, 35 (2019) F.D. Torre, P. Spätig, R. Schäublin, M. Victoria, Acta Mater. 53, 2337 (2005) M.D. Uchic, D.C. Chrzan, W.D. Nix Intermetallics 9, 963 (2001) Y.M. Wang, A.V. Hamza, E. Ma, Acta Mater. 54, 2715 (2006) T.P. Weihs, J.B. Pethica, Monitoring time-dependent deformation in small volumes, in ThinFilms: Stresses and Mechanical Properties III, ed. by W.D. Nix, J.C. Bravman, E. Arzt, L. B. Freund (Mater. Res. Soc. Symp. Proc. 239, Pittsburgh, PA, 1992), p. 325. X.-S. Yang, Y.-J. Wang, H.-R. Zhai, G.-Y. Wang, Y.-J. Su, L. H. Dai, S. Ogata, T.-Y. Zhang, J. Mech. Phys. Solids 94,191 (2016) W.M. Yin, S.H. Whang, R. Mirshams, C.H. Xiao, Mater. Sci. Eng., A 301, 18 (2001)

Chapter 8

Cyclic Deformation-Fatigue

8.1 Tensile Test in Nano-Al Ultrafine grained Al 6061 processed by high-pressure torsion (HPT) at room temperature was tested for the fatigue properties. The HPT processing leads to the formation of a microstructure with an average grain size of 170 nm. The fatigue behavior of the UFG material and the fracture surface is considered in terms of low and high cycle fatigue. The microstructure consists of a very homogeneous grain structure and thus in turn it is expected to show a homogeneous resistance to crack nucleation. It is suggested that the very homogeneous grain structure so obtained can be an approach for the improvement of the low cycle fatigue (LCF) and the high cycle fatigue (HCF) properties of Al alloys. It might be noted that as a rule, severe plastic deformation (SPD) processing can provide formation of microstructures with a grain sizes in the range of 50 nm–1 μm in bulk Al. Contrary to the current findings, it is claimed in reports in the literature that the HCF mechanical properties are not enhanced significantly in UFG Al alloys, and the insignificant improvement in its fatigue life is related to the low resistance to crack nucleation. In the case of LCF, the behavior of Al alloys is complex and the UFG grains have a low ability to sustain cyclic loads in this regime, which is related to the low ductility on deformation promoting early crack initiation. Also the higher fraction of grain boundaries is favorable for crack propagation. UFG Al alloys show low cyclic strain hardening and often during deformation at constant strain even cyclic softening occurs. Nevertheless, proper design in the UFG Al alloys can significantly improve their HCF and LCF behavior. An Instron was used to carry out fatigue testing of solution treated and HPT processed samples with a frequency of 30 Hz under repeated tension conditions with a constant cycle stress of σmin = 100 MPa. Fatigue fracture surfaces were observed by SEM equipped for analysis with EDX (electron dispersive X-ray). HPT processing of the solution-treated Al 6061 alloy resulted in the formation of a very homogeneous UFG microstructure consisting mainly of equiaxed grains having an average size of 170 nm (Fig. 8.1c, d). Included in the figure are also conventionally treated 6061 © Springer Nature Switzerland AG 2021 J. Pelleg, Mechanical Properties of Nanomaterials, Engineering Materials, https://doi.org/10.1007/978-3-030-74652-0_8

353

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Fig. 8.1 Microstructure of the Al 6061 alloy after conventional T6 treatment (a, b) and highpressure torsion (HPT) processing at RT (c, d). The arrow indicates the pressing direction and the orientation of the bands formed by primary phase particles. Murashkin et al. (2015). Open access

T6 Al before and after HPT in Fig. 8.1a and b. Second phase precipitates having a needle shape are also present in the microstructure as seen in Fig. 8.1b. The structure is confirmed by SAED patterns shown in Fig. 8.1d. The HPT processing has doubled the endurance limit, σf at about 107 cycles compared to the CG Al T6. The increase is from 100 MPa of the CG T6 Al to 200 MPa after HPT processing is shown in Fig. 8.2. It could be noted that the UFG Al 6061 to which the HTP processed material is compared was also in the nano range, but at a level of 500 nm (or 0.5 μm). This is an indication not only to different processing method, but also showing the wellknown size effect on the strength of material. The endurance limit of the UFG HPT is plotted vs. the ultimate tensile strength in Fig. 8.3. CG Al 6061 alloy processed by conventional thermal treatments (O, T4, T6) and by thermo-mechanical treatment (T91) are included for comparison. The analysis of the data shows that the ratio of the fatigue limit to the ultimate tensile strength (σf /σUTS ) for the given material decreases from ~0.50 to 0.25 with increasing σUTS . The UTS values and the (σf /σUTS ) ratio of the alloys indicated in Fig. 8.3 are listed in Table 8.1. Mechanical properties of the Al

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Fig. 8.2 Fatigue curves for the studied Al 6061 alloy. Murashkin et al. (2015). Open access

Fig. 8.3 Ultimate tensile strength versus endurance limit for the Al 6061 alloy subjected to various processing treatments. Murashkin et al. (2015). Open access. [34] stands for Hatch

6061 alloy in the present microstructure in Fig. 8.4a and extends into the specimen by ~150 μm. This is known as stage I (or the short crack growth propagation stage). Slip close to the crack tip develop at different planes initiating stage II. As a consequence of the crack growth K, the stress intensity factor increases. The stage of stable crack growth is seen in Fig. 8.4b. Surface ripples characterize stage II, which are better known as striations and observed more clearly in Fig. 8.4c. The average width of the striations is ~3 μm. Cyclic loading is blamed to be the reason for the striations when blunting and re-sharpening of the crack tip occurs during loading. Stage III is related to unstable crack growth as K approaches KIc associated with Fig. 8.4e. The fatigue crack propagation is shown by the arrows in (f), but dimples are also seen a sign of ductility. The ductile fracture with spherical dimples observed in Fig. 8.6g indicating the fracture pattern transition from a fatigue fracture to the final breakdown. Similar stages of fatigue crack initiation and propagation can be defined on the fatigue fracture surface of the HPT-processed Al alloy, which is seen in Fig. 8.5.

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Table 8.1 Images of the fatigue fracture surface of the CG T6 treated Al and the HPT processed Al 6061 are presented as SEM images of Figs. 8.4 and 8.5. In the CG T6 Al at the fracture surface crack initiation starts at the surface indicated in the top of the work is compared with the mechanical properties reported in earlier studies. ECAP, equal-channel angular pressing; AA, artificial aging; CR, cold rolling; UFG, ultrafine grained; CG, coarse grained. Murashkin et al. (2015). Open access Processing

State

σ0.2 (MPa)

σUTS (MPa)

δ (%)

σf (MPa)

σf /σUTS

Reference

T6

CG

276

365

14

100

0.27

Present work

HPT for 10 turns at RT

UFG

605

675

5.5

200

0.30

T6

CG

275

310

12

97

0.31

[34]

ECAPat UFG 125 °C for 1 pass

310

375

20

80

0.21

Tabor (1951)

ECAPat 100 °C, 4 passes

UFG

386

434

11

–

–

ECAP + AA(130 °C for 24 h)

UFG

434

470

10

–

–

ECAP + CR (15%)

UFG

470

500

8

–

–

[33]

The area of the fatigue initiation is smaller also located at the surface of the specimen (Fig. 8.5a). Brittle striations are observed in the area of stable crack propagation in the UFG material (7.85 (b)). Unlike in the fatigue-tested CG T6 specimens, crack propagation is accompanied by formation and growth of micro-cracks of 50–100 μm length, and due to energy dissipation the growth of the main fatigue crack is delayed. The final fracture of the specimen occurs on dimpled ductile fracture surface as seen in Fig. 8.5d–g. The size of the dimples is smaller compared to the CG T6 samples. It is assumed contrary to CG Al T8 specimens, that unaccommodated grain boundary sliding might result in local micro-cracking or nano-void formation at grain boundaries. It is further suggested that both transgranular and intragranular fatigue crack growth can take place in Stage II in this case of UFG material. In Stage III, nano-voids which are significantly larger than the individual grains can grow and partially relieve the constraints on a grain, but also act as sites for nucleation of the dimples in the UFG alloy. In summary, UFG of 170 nm can be obtained by HTP of the Al 6061 alloy, having a homogeneous microstructure. The alloy exhibits improved mechanical properties (Yield strength, and UTS) compared to the CG counterpart processed by conventional T6 heat treatment. The endurance limit is higher by a factor of two compared to CG T6 Al and the resistance to fatigue crack initiation in HCF is improved. In LCF regime the UFG shows somewhat lower fatigue resistance due to its lower strain hardening and the consequent softening taking place. Three stages of fatigue crack initiation occur in both, the UFG and CG Al alloys. An important difference between CG and UFG Al alloys is that striations in the former are ductile, while in the latter (the

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Fig. 8.4 SEM images of the fatigue fracture surface of the CG T6 Al 6061 alloy tested under a stress amplitude of 150 MPa to 2.2 × 105 cycles) (the arrows indicate the direction of fatigue crack propagation). Murashkin et al. (2015). Open access

UFG alloy) brittle striations seem to dominate the fatigue fracture surface. Dimpled fracture surface is observed in both alloys at the final stage of crack propagation (smaller dimple size in the UGG Al).

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Fig. 8.5 SEM images of the fatigue fracture surface of the UFG Al 6061 alloy: a, b, e, f tested under a stress amplitude of 225 MPa to 4.4 × 105 cycles; c, d tested under a stress amplitude of 200 MPa to 4.35 × 104 cycles (the arrows indicate the direction of fatigue crack propagation). Murashkin et al. (2015). Open access

8.2 Tensile Test in Nano-Cu In this section gradient nano-grained (GNG) Cu is shortly discussed since, in general this type of structures-characterized spatially with increasing grain from the nanoscale range at the surface to CG in the core- attracted considerable interest because the combination of high strength and good ductility in tension tests. For Engineering applications not only static, time dependent properties are important but cyclic (fatigue) behavior is critical. Fatigue failure accounts for more than 80%

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Fig. 8.6 Typical cross-sectional SEM images of GNG Cu (a) in the as-SMGTed state and (d) after annealing treatment. TEM images of GNG Cu at positions B and C indicated in (a) are shown in (b, c) and those of annealed GNG Cu at positions E–F indicated in (d) are shown in (e, f). The insets in (b, c) and (e, f) are SAED patterns. Long et al. (2018). Open access. SMGT stands for surface mechanical grinding treatment

of all structural breakdowns, but of more concern is the fact that it occurs suddenly without any warning. SEM observations (Fig. 8.6a) describes the above indicted grain gradient as follows: (i) Almost equiaxed grains of 80 ± 10 nm) on the average are formed in the top 20 μm thick surface layer Fig. 8.6b, (ii) in the depth interval 20–220 μm UFGs are observed with an average grain size of 218 ± 75 nm at a depth of 50 mm as seen in Fig. 8.6c. Electron diffraction seen in the insetreveal that the NG s and UFGs remain randomly oriented after annealing, indicating that slight microstructural recovery might have occurred, but no grain growth occurred in the GNG layer after low temperature heat treatment. However, annealing of the GNG Cu had a relatively lower defect density compared to the as SMGTed state. Cyclic stress in tension of the GNG and annealed Cu are illustrated in Fig. 8.7 at a strain amplitude εt /2 of 12%. In the figure maximum stress, σmax in tension and minimum stress, |σmin | in compression of GNG Cu and annealed GNG Cu cyclically deformed at the strain amplitude indicated is shown. Note that the NG Cu exhibits a longer fatigue to failure life Nf , (8.3 × 105 cycle) than the CG Cu (2.2 × 105 cycle), which is consistent with results reported under stress control. An asymmetry in tension compression is seen in the figure |σmin | > σmax in GNG Cu. Thus at 3000 cycles |σmin | is 117 MPa showing a decrease with increasing cycles while σmax is 96 MPa and showing an increase with increasing cycles. The stress gap of (|σmin | − σmax ) is large at a value of 21 MPa, but it decreases to 3 MPa with increasing cycles. The asymmetry tends to disappear with increasing cycles. Further, both σmax and |σmin | during all the fatigue life test are larger than that of CG Cu (~88 MPa). Stress–strain hysteresis loops of the GNG Cu (Fig. 8.8a), the annealed Cu (Fig. 8.8b) and the CG Cu are compared in Fig. 8.8 at εt/2 12%. As can be seen

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Fig. 8.7 Cyclic stress tensile maximum stress, σmax and compressive minimum, σmin responses of GNG Cu, annealed GNG Cu and CG Cu cyclically deformed at the total strain amplitude εt/2 of 12%. Long et al. (2018). Open access

Fig. 8.8 Variations of hysteresis loops of a GNG Cu, b annealed GNG Cu and c CG Cu cyclically deformed at εt/2 = 0.12%. Long et al. (2018). Open access

the loops are asymmetric, but it decreases with increase in cycles. It is suggested that the tension–compression asymmetry is an inherent phenomenon of nano structured metals during fatigue. It is accepted that the residual stress, associated with high-density defects, is readily developed in metals when straining, as a result of inhomogeneous plastic deformation in grains and/or between grains. The compressive residual stress varies with depth from the surface as illustrated in Fig. 8.9. Its value at the surface layer of GNG Cu at the depth of 120 μm is 33 MPa and gradually increases at regions closer to the surface because the larger strain imposed by the SMGT process. The residual stress reaches the maximum value of 123 MPa at a depth of 40 μm, but it decreases to 89 MPa at the top of the surface due to relaxation at the free surface. Partial release of the residual stress in annealed GNG Cu to a smaller value is seen in Fig. 8.9a, and the maximum compressive stress decreases to 72 MPa at a depth of 40 μm. The recovered microstructure is seen in Fig. 8.6e, f. The asymmetry (larger σmin than σmax ) observed by the experimental results is mainly

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Fig. 8.9 a In-depth residual stress distributions in GNG and annealed GNG Cu before, during (40% Nf ) and after fatigue-to-failure (100%Nf ). Typical cross-sectional SEM images of microstructure of b GNG Cu and c annealed GNG Cu after fatigue-to-failure, showing that abnormal grain coarsening phenomenon is observed in both samples. Long et al. (2018). Open access

induced by compressive residual stress in the fatigued GNG Cu. A higher residual stress in the GNG layer contributes more to the cyclic asymmetry (Fig. 8.7). Summarizing this section on two kinds of GNG Cu samples (one as-SMGTed and a second annealed) it was found that the residual stresses are different. Consequently, tension–compression asymmetry is observed with compressive minimum stress higher than the tensile maximum stress in the cyclically deformed GNG Cu at εt/2 = 0.12%. Either with increasing cycles or annealing at low temperature the mentioned asymmetry gradually diminishes and almost vanishes. Further it should be recalled as mention in this sction, that the asymmetry is caused mainly by the residual compressive stress in the GNG-Cu layer during SMGT processing. However, on the other hand the presence of the residual compressive stress contributes to the higher high-cycle fatigue-life of the GNG Cu.

8.2.1 Microcrack Initiation UFG Cu produced by ECAP technique was tested in fatigue deformation in the range of lives from 5 × 103 to 2 × 1010 cycles. The samples in general exhibit in comparison to conventional CG size metals (alloys) higher tensile strength without substantial loss in ductility. For exapmple a tensile strength of 387 ± 4 MPa, yield stress of σ0.1 = 349 ± 4 MPa, σ0.2 = 375 ± 4 MPa and a modulus of elasticity E = 115 ± 11 GPa are reported for a grain size of 0.3 μm (300 nm). By one of the same authors in a

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8 Cyclic Deformation-Fatigue

different publication the tensile properties are shown and to be compared later with the fatigue behavior of Cu. The tensile stress–strain relation is seen in Fig. 8.10 and compared to CG Cu in Fig. 8.11. These data are listed in Table 8.2. The fatigue curves were evaluated in three regions: (i) Low cycle fatigue (LCF); in this region hysteresis loops were recorded and the frequency of cycles were either 1 Hz, or 5 Hz or 10 Hz. The plastic strain was taken as the half width of the hysteresis loop. (ii) High cycle fatigue (HCF) region; the long-life tests (from ~106 to 108 ) were performed at a frequency of 124 or 213 Hz and no hysteresis loops were taken. (iii) Very high cycle Fig. 8.10 Tensile diagrams of UFG Cu prepared by ECAP, route Bc . Kunz and Collini (2012). Open access

Fig. 8.11 Comparison of tensile diagrams of UFG and CG Cu. Kunz and Collini (2012). Open access

8.2 Tensile Test in Nano-Cu Table 8.2 Tensile properties of UFG Cu prepared by ECAP, route Bc, 8 passes Kunz and Collini (2012). Open access

363 Ultimate tensile Yield stress strength σ UTS σ 0.1

Yield stress σ 0.2

Modulus of elasticity E

[MPa]

[MPa]

[MPa]

[GPa]

387 ± 5

349 ± 4

375 ± 4

115 ± 11

Fig. 8.12 S–N curves of UFG and CG copper specimens. Lukáš et al. (2012). Open access

fatigue (VHCF) region testing at 20 kHz and long-life tests from 108 to 2 × 1010 . In Fig. 8.12 the stress amplitude variation with the number of cycles to failure is plotted. The top curve of UFG samples covers the range of cycles from LCF up to VHCF. It illustrates that the fatigue strength of UFG Cu is by about a factor of 2 higher than that of CG Cu in the whole range of fatigue lives including VHCF. The fatigue strength as a function of grain size is illustrated in Fig. 8.13. The fatigue strength in terms of the stress amplitude at the chosen numbers of cycles to failure is presented for two CG coppers with different grain sizes (1200 and 70 μm, respectively) and are compared with one UFG Cu of 300 nm. It is of interest to note that the grain size has an exponent pf −1/2 thus in the format of the Hall–Petch relation (stresss versus inverse square root). Thus, one is wondering if the Hall–Petch relation is useful for fatigue strength also in the light that the original Hall–Petch relation which was applied for the yield stress variation with the variation of the inverse square root grain size. It may be noted that for a certain grain size the stress amplitude increases with decreasing the number of cycles. Hardening/softening curves of UFG Cu is seen in the plot of the plastic strain amplitude against the ratio N/Nf , where clearly, Nf is the number of cycles to failure (see Fig. 8.14). The stress amplitude and the number of cycles to failureare shown on the right next to the curves. It might be of interest to show a few SEM microstructures of HCF and VHCF indicating slip bands

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Fig. 8.13 Fatigue strength of copper in dependence on grain size. Lukáš et al. (2012). Open access

Fig. 8.14 Hardening/softening curves of UFG copper. Lukáš et al. (2012). Open access

formation, which are the location where microcracks are nucleated leading to fatigue failure. In Fig. 8.15 cyclic slip bans are shown in specimens cycled in HCF region. The surface relief is developed after on electro-polished specimen after cycling in HCF region (σa = 170 MPa). Pronounce slip localization is seen. The cyclic slip bands are parallel exceeding substantially the grain size of the UFG Cu (300 nm). Topography of extrusions (hill) and intrusions (valley) of the slip bands can be well

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365

Fig. 8.15 SEM micrograph of cyclic slip bands in specimen cycled in HCF region. Lukáš et al. (2012). Open access

seen. Another example of surface relief in VHCF region is seen in Fig. 8.16. The fatigue slip bands seen is close vicinity to cracks and again and again hill valley topography is seen. The slip activity on parallel slip planes within individual grains can be seen in Fig. 8.17. The essence of this section is the finding that fatigue microcracks nucleate in cyclic slip bands, which run across many grains in regions of nearby oriented grains. The first or the beginning of fatigue damage in HCF and VHCF regions occurs in the formation of cavities and elongated voids consisting of the crack nuclei and their formation is attributed to the dislocation interactions (both within the grain interiors and grain boundaries), producing vacancies which migrate and cluster together in the form of cavities. Thus microcracks in nanostructured Cu of commercial purity— formed by ECAP—initiate in cyclic slip bands. Further, no grain coarsening was Fig. 8.16 SEM micrograph of surface slip bands in specimen cycled in VHCF region. Lukáš et al. (2012). Open access

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Fig. 8.17 High magnification SEM micrograph showing slip activity on parallel slip planes within the individual grains (marked by arrows). Lukáš, et al. (2012). Open access

observed (thus not a prerequisite for crack initiation). Finally fatigue in UFG Cu cycled in the VHCF is a highly localized phenomenon. There is a similarity in the concept of static tensile stress and fatigue strength and frequent comparison s made between them. For example, in Fig. 8.18 a relation Fig. 8.18 Relation of tensile and fatigue strength for fatigue limit based on 108 cycles for cold worked Cu and UFG Cu. Kunz and Collini (2012). Open access. (Recall UFG Cu is produced by ECAP)

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367

Fig. 8.19 a Microstructure of Cu after ECAP as observed in TEM, longitudinal section, b microstructure of Cu after ECAP as observed in TEM, transverse section. Kunz and Collini (2012). Open access

between them is shown. The microstructure after ECAP at two sections is illustrated in Fig. 8.19. A known expression for the applied tensile stress, σa in terms of the number of cycles to failure, Nf (originally suggested by Murphy) is given as σa = kN −b f

(8.1)

where the k and b parameters are 388 MPa and 0.107, respectively. Similarly, to static deformation the UTS and the fatigue strength are improved with smaller grain size and thus fine grained material exhibit improved resistance to damage also against fatigue crack growth. The relation between crack propagation rate, da/dN and stress intensity factor K is given by   da m = A K am − K ath dn

(8.2)

Experimentally evaluated crack propagation is illustrated for CG and fine grained Cu (although in the micron and not nano range) in Fig. 8.20. The√ values derived from the curves in this figure are: A = 1.1 × 10–10 (mm/cycle)(MPa m)-m and m = 70 √ for fine grained Cu and A = 5. × 10–11 (mm/cycle)(MPa m)-m and m = 7.1 for CG Cu. The threshold value of the stress intensity √ factor, below which the long cracks do not propagate, is Kath = 2.1 and 2.7 MPa m for fine-grained and coarse grained Cu, respectively. From this data it is evident that from the point of view of crack propagation the fine-grained Cu is worse than the coarse-grained one. However, the data does not reflect what is happening in the nano range grain size, which might be different for different reasons according to my opinion. In coarse grained and micron sized material dislocations are involved in the deformation. Examples are

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Fig. 8.20 Comparison of crack propagation curves for fine grained and coarse grained Cu. Kunz and Collini (2012). Open access

shown in Figs. 8.21, 8.22 and 8.23. In the nanoscaled material, however dislocation activity might be involved when the grain size is > 100 nm, but in samples < 100 nm, specifically in the 50 nm range, there is no space to accommodate dislocations and therefore the dominant deformation mechanism is grain boundary sliding (GBS). In stage II which is represented by propagation of cracks, Paris’ law seems to apply given as da = C(K )m dn Fig. 8.21 Dislocation cell structure adjacent to fracture surface in conventionally grained Cu. Kunz and Collini (2012). Open access

(8.3)

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369

Fig. 8.22 Bi-modal dislocation structure after constant plastic strain amplitude loading. Kunz and Collini (2012). Open access

Fig. 8.23 Dislocation structure after constant stress amplitude loading, σa = 340 MPa. Kunz and Collini (2012). Open access

Here C and m are coefficients which depend on R, the ratio defined as R = Kmin /Kmax

(8.4)

where for fatigue crack growth for UFG Cu and CG Cu, R = 0.25, 0.5, 0.5 and 0.7 for grain sizes dg = 270, 300 and 300 nm and CG Cu are given as C = 7.72 × 10–10 , 3.75 × 10–8 , 1.10 × 10–7 , 4 × 10–7 and m = 3.54, 2.32, 1.90 and 1.36. In conclusion, regarding fatigue, SPD can improve the fatigue strength. Stress controlled deformation can increase the number of cycles of UFG Cu provided that the microstructure remains stable. However, if the fatigue loading is performed in the plastic strain-controlled regime the UFG structure is prone to grain growth (coarsening) and the fatigue life for the same plastic strain amplitude is shorter than that

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of CG Cu. In UFG structure fatigue crack initiates at cyclic slip bands in all loading cycles from LCF up to GHCF. The preferable concept is that the mechanism of crack initiation involves GBS. Nevertheless, contrary data are still available regarding the mechanism of the resistance to fatigue propagation, in particular to the microstructure and its changes in the wake of fatigue deformation.

8.2.2 In Ultra Thin Film It is expected that the fatigue behavior in nanoscale films will be different from similar CG or bulk material having similar overall characteristics. Thus, Cu thin films even ultrathin films with nanometer grains should respond to fatigue failure differently than micrometer thick large grain Cu films. In the following fatigue strength as a function of film thickness measured under constant total strain range at a frequency of 10 Hz is considered. The experimental results indicate that strength and fatigue life time are film thickness dependent. But this should not surprise the reader, since such a dependence just reflects the well-known size dependent strength observed in the static strength properties of material. It was observed and reported in the literature that when the film thickness approaches 200 nm (still in the nano regime) fatigue damage becomes more prevalent. This topic is the subject of his section considered below. For the start we should characterize in a few words the method of production and the specimens themselves. The Cu films were deposited onto a dog-bone-shaped substrate (polyimide) by magnetron sputtering in vacuum when the base pressure is 1 due to 0 < PL < 1) and (III) In this region the dislocations are completely stored inside the grains (ρL > 0 due to PL = 0). Further, in region III, ρL increases as d decreases (Fig. 8.54c), but is not affected by G (Fig. 8.54d), implying that ρL is controlled only by dislocation emission because dislocation absorption does not occur in this region (PL = 0). In summary, it has been emphasized that plastic deformation occurs in NC-Co on unloading and that it strongly depends on loading and unloading rates under compressive cyclic tests at room temperature. The plastic deformation dependence on loading and unloading rates arises from the fast absorption of the accumulated dislocations on loading by GBs ad their emission from GB ledges. There is a critical loading strain rate, below which GB processes (for example sliding) switch on, while above this strain rate dislocation activity dominates the plastic deformation. At higher loading strain rates grain refinement occurs.

8.3.2 Compression Test in Nano-Ni NC-Ni in the form of pillars prepared by electron beam lithography and electroplating process, were tested for fatigue properties. It is known that cyclic loading leads to considerable hardening of the material which s attributed to the dislocation source exhaustion at GBs. In the experiments cyclic tests of the specimen were subsequently compression tested to evaluate hardening. It was observed that both the yield strength and flow stress significantly increase because of prior cyclic loading. A TEM image of the representative microstructure of as-fabricated pillars is displayed in Fig. 8.55. The inset displays a representative micrograph of the pillar. The top surfaces of the pillars are flat while the side-surfaces are almost taper-free. The nominal outer diameter, D, of the pillars is ~580 nm and the height-to-diameter aspect ratio is ~1.5. The Fig. 8.55 Representative TEM image showing the grain structure of as-fabricated nc Ni pillars (with inset of SEM image for pillar morphology). Lee et al. (2017). With kind permission of Elsevier

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TEM image of the microstructure indicates an average grain size of ~12 ± 3 nm. The pillars were compression-compression cyclically loaded with a sawtooth shape wave form shown in Fig. 8.56a. The entire cycling was done below the yield point, thus entirely in the elastic region and in Fig. 8.56b engineering stress–strain is seen which were obtained: the stress P/A0 (where P is the load and A0 the initial cross section of the pillar), and the strain e = h/L0 (where L0 is the initial pillar height and h is the height). The stress–strain shown in (b) is after 200 cycles. For clarity only the data for every 20 cycles are shown in Fig. 8.56b. The inset of Fig. 8.56b represent the area of the hysteresis loop observed during early cycles, and as known the area of the loop,  , is a measure of the strain energy dissipated during the cycle (It is evaluated and plotted as a function of the number of the cycles). The width loop reaches a steady state at 30 cycles. In Fig. 8.56c stress–strain curve and representative SEM images of a pillar before and after in situ cyclic test is shown and as seen tit remains unchanged and without noticeable plastic deformation (or localized failure) after N = 200 cycles. Figure 8.57 indicates the hardening effect of the cyclic deformation on the σ-ε monotonic (static) curves mentioned earlier, obtained by post-cyclic loading the pillars which were subjected to quasi-static compression tests. Volume conservation was assumed on determining the σ-ε relation. In Fig. 8.57a the effect of increasing the number of cycles on σ-ε curves are indicated, while in (b) the increase in yield strength and flow stress are shown with increasing N. The variation of the strain rate sensitivity, m and the activation volume (see inset) are shown in Fig. 8.58. The sensitivity factor decreases from ~0.037 to ~0.017 with increased N, the number of cycles, while the activation volume increases. Recall that determination of m at a given strain and temperature is done by  m=

∂lnσ f ∂ln ε˙

 (8.20) ε,T

To obtain further understanding on the post-cycle plastic deformation, the activation volume V* —shown in the inset of Fig. 8.58—can provide information. Its value is indicative whether grain boundary sliding or dislocation dominated mechanism are operative. Earlier in this book, V* was given as V∗ =

  √ ∂ln ε˙ 3kT ∂σ f

(8.21)

V* varies by orders of magnitude for different rate-limiting processes. Thus, V* in the range from 1 to 10 b3 is either for lattice or GB diffusion, ~10 b3 is for GB sliding and 100–1000b3 for dislocation glide. V* is determined from the slope by linear fitting ln ε˙ against σf (see Fig. 8.48). As seen in Fig. 8.48 V* increases from 3.0 to 11.4 b3 with increasing the number of cycles. (Contrary to m which decreases from ~0.037 to ~0.017). From these values it seems that the dominant deformation is not significantly affected by prior cyclic loading, since the change is not by orders of magnitude.

8.3 Compression in Nanostructures

397

Fig. 8.56 Results of cyclic tests: a load versus time and displacement versus time obtained during cyclic loading; b converted engineering stress–strain responses with inset of hysteresis loop area as a function of N; c the curve from in-situ SEM experiments and the SEM images taken before and after cyclic loading. Lee et al. (2017). With kind permission of Elsevier

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Fig. 8.57 Results of monotonic compression tests: a true stress-true strain curves and b changes in yield strength and flow stress as a function of Lee et al. (2017). With kind permission of Elsevier. Lee et al. (2017). With kind permission of Elsevier

This section on cyclic compression in NC-Ni indicates the influence of prior cycling on the strengthening. NC-Ni pillars subjected to compression test after cyclic deformation undergo significant strengthening already within the first 20 cycles. Such strengthening may be caused by GB relaxation, surface reconfiguration and residual strain change, all of which can lead to enhanced resistance to plastic deformation. The strength and flow stress significantly increase because of prior-cyclic loading. The origins for the observed hardening are discussed in terms of strain-rate sensitivity, and activation volume for deformation.

8.4 Indentation-Hardness

399

Fig. 8.58 Estimation of strain-rate sensitivity and activation volume (in inset) of as-fabricated and cyclic-loaded pillars. Lee et al. (2017). With kind permission of Elsevier

8.4 Indentation-Hardness 8.4.1 General Concept For a detailed discussion on hardness obtained by indentation measurement reference could be made to an earlier Springer publication on Mechanical Properties of Materials (Pelleg). Historically, Brinnel suggested the widely used and well-known relation of. HB =

2P 

π D D − D2 − d2

(8.22)

where clearly P is the load, D is the diameter of the ball indenter and d is the residual area of impression. A closely related hardness test was followed by Myers relation. His hardness, H is calculated from the load P divided by the projected area A, and is given as H=

4P P = A π d2

(8.23)

Vickers applied a square-based pyramid diamond indenter with 136° semi-angle instead of ball indenter. The Vickers hardness, HV is defined as the load divided by the surface area of the impression and written as HV =

P 136 2P P = 2 sin = 1.8544 2 A 2 dV dV

(8.24)

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8 Cyclic Deformation-Fatigue

dV is the length of diagonal of the surface area. Further, Meyer has suggested an empirical relationship between the applied load and the diameter of the residual area of the impression after unloading as P = Cdn

(8.25)

C is a constant and n the exponent is Meyer index with d being the diameter of the residual area of the impression after unloading. In nano-indentation the area is to small be directly measured from the residual impression area, and therefore the contact area is determined from the penetration depth. Instead the relation given in Eq. (8.25) the expression is P = C  hn

(8.26)

C is a constant and h is the indentation depth. It could be noted here, that Tabor has proven that the hardness could be related to the yield stress, σ, (based on the theory that indentation hardness is related to the yield stress of a perfectly-plastic solid) as. H = Cσ

(8.27)

8.4.2 Indentation-Hardness in Nano-Al In Fig. 8.59 the hardness variation from the sample surface is illustrated. The specimen has been treated by “ultrasonic nano-crystal surface modification” (UNSM) which is a treatment to provide good fatigue properties to improve the corrosion resistance of high specific strength metals such as aluminum. A 40% increase in the Vickers hardness was recorded after the UNSM treatment. The surface roughness also decreased 3.4–8.7 times with the treatment. At a depth of 80–120 μm from the surface the hardness reaches a constant value of HV ~120. The microstructure of the surface for the hardness measurement, which is also the fatigue specimen is illustrated in Fig. 8.60. The UNSM treatment increased the fatigue strength about 50%. As in bulk specimens, in common nano-indentation experiments also the indenter makes contact with the material surface and then penetrates to a certain depth. It may be worthwhile to illustrate a typical penetration curve obtained by nanoindentation as a function of displacement showing the loading and unloading profile on thin film materials. The penetration represents the displacement into the sample, and the quantities that can be calculated are the maximum depth of penetration, hmax, the peal load, Pmax , the final depth after unloading, hr and the contact stiffness, S, which is the slope of the upper portion of the unloading curve. Any inconsistency in the curve indicate cracking or another failure in the coating or the thin film. Recall that the indentation hardness has been given and rewritten here as

8.4 Indentation-Hardness

401

Fig. 8.59 Distribution of hardness before and after UNSM treatment. The Univ. of Tokushima, Advanced Material Lab. in Kyungpook National University, Lee et al. (2010), free access The Univ. of Tokushima, Advanced Material Lab. in Kyungpook National University. Lee et al. Free access. UNSM stands for Ultrasonic Nano-crystal Surface Modification. Free access. Also in Lee et al. (2010)

H=

Pmax A

(8.28)

The indentation modulus, E* (usually determined from the slope of the unloading curve at maximum load) expressed as dP/dh and the area of contact is given in Eq. (8.29). √ 1 π dP E = √ 2 A dh ∗

(8.29)

The displacement at the peak load, ht in terms of the contact stiffness allows to calculate the contact depth, hc as hc = ht − ε

Pmax S

(8.30)

For the Berkovich indenter ε = 0.75. The projected contact area is calculated from the empirically determined indenter area as

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Fig. 8.60 The variation of surface treatments between before and after UNSM. The Univ. of Tokushima, Advanced Material Lab. in Kyungpook National University. Lee et al. (2010), Free access

Ac = 24.56 h 2c

(8.31)

Permanent deformation to a depth of ~850 nm in the 2 μm thick Al layer is illustrated in Fig. 8.62 obtained from multicycle loading–unloading versus penetration depth at a load of 10 mN. Plastic behavior is seen. When the samples are subjected to multiple cycles of loading–unloading, it is observed that the stiffness (see Fig. 8.61 for stiffness definition) of Aluminum layer increases. A decrease in hardness at the end of each cycle is observed on aluminum and is shown in Fig. 8.63. The linear fit yielded the relation y = −0.837x + 1073 (correlation coefficient r2 = 0.9908. The sudden discontinuity after the 15th cycle is due to creep. In summary, permanent deformation is observed in aluminum film under the applied load of 10mN. The depth is ~850 nm derived from the loading–unloading curve. The sample was subjected to multiple cycles of loading–unloading (see Fig. 8.62) and it is observed that the hardness decreases, while the stiffness in the aluminum layer increases. The rapid decrease in hardness after 15 cycles is due to creep.

8.4.3 Indentation-Hardness in Nano-Cu Commercial purity copper consisting of equiaxed coarse grains was treated to introduce a thin superficial layer of nanostructure over a coarse-grained core to suppress

8.4 Indentation-Hardness

403

Fig. 8.61 Typical load–displacement curve measured on nano-indenter tester. P.M. Bodhankar, C. Gurada, S. Shinde, H. Muthurajan, V. Kumar, J. Mater. Sci. Surface Eng. 3, 227 (2015). Open access

Fig. 8.62 Experimental curve of load versus penetration depth for aluminum. P. M. Bodhankar, C. Gurada, S. Shinde, H. Muthurajan, V. Kumar, J. Mater. Sci. Surf. Eng. 3, 227 (2015). Open access

strain localization and surface roughening. This way an unusual resistance to LCF and HCF can be achieved and without the expense of the ductility. Progressive homogenization of the surface graded copper is shown to be superior in fatigue properties compared to any homogeneous copper sample with micron-, submicron or nanograined structures. The nanograined surface layer is produced by subjecting the CG samples to surface mechanical grinding treatment (SMGT) at cryogenic temperatures of ~173 K. The specimens are designated as GNG/CG Cu. The section concentrates on the hardness of a copper treated as indicated above. Cross sections of GNG/CG, GUFG/CG (specimens were polished to obtain ultrafine grained Cu) and CG Cu before and after cyclic deformation were characterized

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Fig. 8.63 Hardness as a function of contact depth for aluminum. P.M. Bodhankar, C. Gurada, S. Shinde, H. Muthurajan, V. Kumar, J. Mater. Sci. Surf. Eng. 3, 227 (2015). Open access

by SEM and are compared in Fig. 8.64. Fatigue induced microstructure is illustrated in Fig. 8.65. An almost entirely homogeneous grain structure is seen in the fatigue induced microstructure on the left part of Fig. 8.65a, negligible intra-crystalline dislocations are seen in (b), (c) and (d), separated by GBs, which are re-illustrated in Fig. 8.66. Also, the crystalline microstructure shows equiaxed grains as seen in (b) and (c). The hardly detectable dislocation structure by EBSD, HRTEM observations indicate well developed dislocation cells after cyclic deformation as seen in Fig. 8.66a. As shown, the high density of randomly distributed dislocations are detected in the CG core fatigued at εt /2 of 0.5% after 4% of fatigue life cycle (Nf ). With increasing fatigue cycles, formation of dislocations and their arrangement results in the formation of cells at N = Nf (Fig. 8.66b). Vickers micro-hardness variation vs. depth from the surface is shown in Fig. 8.67, for the first cycle (N = 1 cycle), after 4%, 40% and 100% of the fatigue life cycles, N = Nf . The hardness decreases steeply with depth from the GNG layer (white region) and remains constant in the CG core (blue region). The NG layer at the surface begins to yield at N = Nf . The graded nanostructure progressively yields plastically through the thickness during fatigue straining with structural evolution. The NG and UFG surface layers are capable to accommodate plastic strain through grain coarsening from fatigue, the CG core accommodates plasticity by the generation and rearrangement of dislocations into cell structure. The surface of GNG/CG remains smooth even after 2500 cycles with only few damage as seen in Fig. 8.68a. As usually occurs in fatigue, the GNG layer after failure also shows that the micro-cracks nucleated from the surface (presence of extrusions/intrusions) as seen in Fig. 8.68b. The major conclusion from the above presentation is, that a significant improvement in fatigue resistance can be achieved by coating CG material with a thin graded nanostructure that produces a combination of cyclic properties in both LCF life and HCF limit, compared to its homogenous CG counterparts. The variation of hardness with depth from the surface (Fig. 8.67)

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405

Fig. 8.64 Graded surface nanostructure a Cross-sectional EBSD image of GNG/CG Cu produced via surface mechanical grinding treatment. The corresponding higher-magnification bright-field TEM and SEM images in regions marked (b), (c), (d) and (e) in Fig. 8.64a are shown in (b–e), respectively. Top surface of the sample is outlined by a dashed line in (a). Insets in (b–d) show selected area electron diffraction patterns (SAED). J. Long, Q. Pan, N. Tao, M. Dao, S. Suresh, L. Lu, Acta Materialia, 166, 56 (2019). With kind permission of Elsevier. EBSD stands for electron backscatter diffraction

is an indication of the fatigue cycles effect on going from the surface layer (NG) to the CG core of the sample. Good surface preparations are required for good fatigue properties, since every flaw or scratch at the surface acts a stress riser.

8.4.4 Indentation-Hardness in Nano-Ni As known the strength of materials is significantly influenced by the grain size. Materials with nanocrystalline structure exhibit superior yield stress, fracture strength, wear resistance and often even superplasticity at relatively low temperatures and high strain rates compared to microcrystalline alloys. Therefore, attention to the potential industrial application of nanostructured material is directed to the investigationamong other tributes-of the mechanical properties in both the static and dynamic conditions. Advanced nanoindentation techniques are often used to evaluate the

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Fig. 8.65 Fatigue-induced microstructure homogenization. a Cross-sectional EBSD image of GNG/CG Cu after repeated loading until failure over 2600 cycles at εt/2 of 0.5%. The bright-field TEM images corresponding to the regions marked (b), (c), (d) and (e) in Fig. 8.64a for the specimen prior to fatigue are shown here in (b–e), respectively, after fatigue straining until failure. Top surface of the sample is indicated by a dashed line. Insets in (b–e) are SAED patterns. f Variation of the average grain and/or cell size along the distance from the top surface to interior for GNG/CG Cu before and after cyclic failure at εt /2 of 0.5%. J. Long, Q. Pan, N. Tao, M. Dao, S. Suresh, L. Lu, Acta Materialia, 166, 56 (2019). With kind permission of Elsevier

mechanical properties instead the more expensive tests for strength, since it is possible to calculate yield strength, hardness, and other characteristics of the material. Indentation fatigue behavior can be related to conventional fatigue and crack evolution tests. The hardness of electrodeposited Ni is considered in this section. In Fig. 8.69 the microstructures of the electrodeposited pure nickel are shown for 10 and 100 nm (refereed to UFG) Ni. The hardness variation with indentation depth is shown in Fig. 8.70. Multi-step indentations, were performed between 5 and 40 mN by increasing the indentation load by 5 mN per step. The indentations were performed with constant load at 5, 10, 20, 30 and 40 mN. The measured hardness value varies with the maximum indentation load. In Fig. 8.70b the hardness against maximum load of the UFG Ni is the same regardless if the measurements were performed by single or multiple steps. The indentation depth as a function of indentation cycles is illustrated in Fig. 8.71 for 5 and 10 mN, respectively. In Fig. 8.72 some examples of indentation

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Fig. 8.66 TEM images of microstructures at CG core of GNG/CG Cu after different fatigue cycles (N) at εt /2 of 0.5%. a N ¼ 4% Nf, and b N = Nf , showing that dislocation cells are gradually formed during cyclic deformation. J. Long, Q. Pan, N. Tao, M. Dao, S. Suresh, L. Lu, Acta Materialia, 166, 56 (2019). With kind permission of Elsevier

Fig. 8.67 Variations of hardness (a), plastic strain amplitude (εpl /2). The area with the white background in (a) indicates top GNG surface layer while the area with the light blue background indicates the CG core. J. Long, Q. Pan, N. Tao, M. Dao, S. Suresh and L. Lu, Acta Materialia, 166, 56 (2019). With kind permission of Elsevier

step for different number of cycles at 10 mN can be observed. Again UFG is included, but recall that UFG refers to 270 nm. The TEM micrographs of the electrodeposited Ni showed mean grain size dimensions of 20 nm for the nanocrystalline Ni while 270 nm for the UFG material. In summary, nanoindentaion fatigue experiments can provide important and useful information on plastic zone propagation, cyclic hardening, crack nucleation and growth in nanostructured material. Like in static loading, crack tip either blunts by the surrounding plasticity or shields crack tip from applied stress. In dynamic loading plastic deformation during cyclic indentation leads to nucleation and growth of crack by increasing the number of cycles. The variation of Ni hardness varies

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8 Cyclic Deformation-Fatigue

Fig. 8.68 Side surface view (a) and cross-sectional (b) SEM images of GNG/CG Cu after failure at εt /2 of 0.5%, showing fatigue cracks are formed at the sample surface, owing to cyclic deformation induced surface roughening. J. Long, Q. Pan, N. Tao, M. Dao, S. Suresh, L. Lu, Acta Materialia, 166, 56 (2019). With kind permission of Elsevier

Fig. 8.69 a 10 nm nc Ni, b 100 nm. P. Cavaliere, Procedia Eng. 2, 213 (2010). With kind permission of Elsevier

Fig. 8.70 Hardness variation as a function of the indentation load. P. Cavaliere, Procedia Eng. 2, 213 (2010). With kind permission of Elsevier

8.4 Indentation-Hardness

409

Fig. 8.71 a Indentation depth as a function of indentation cycles at 5 mN; b Indentation depth as a function of indentation cycles at 10 mN. UFG Ni is also included to the right of nc Ni. P. Cavaliere, Procedia Eng. 2, 213 (2010). With kind permission of Elsevier

Fig. 8.72 Indentation depth as a function of indentation cycles for electrodeposited Ni. P. Cavaliere, Procedia Eng. 2, 213 (2010). With kind permission of Elsevier

with maximum indentation load which is a function of the indentation cycles. The variation of the indentation depth in nc and UFG Ni is a function of indentation cycles as indicated in Fig. 8.72.

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8 Cyclic Deformation-Fatigue

8.4.5 Indentation-Hardness in Nano-301L It is quite difficult to find in the literature work which is discussing simultaneously the type of a material, its grain size and its mechanical properties. In the present consideration hardness is the subject. Thus, instead 304L, a very similar SS alloy, the 301L is presented. The two alloys have almost the same composition, except that the 304 SS alloy has more Cr and Ni than the 301, which makes the 304 alloy more expensive than the 301 one. Generally speaking, grade 301 tends to be a little less corrosion resistant than grade 304 because the 301 alloy has a lower chromium. Hardness versus the cycle number is illustrated in Fig. 8.73. In (a) the test was performed under loading while in (b) it was evaluated under displacement control mode. Loading and unloading curves, for cyclic indentation namely, P–h curves, was performed with normal direction and close to the orientation is illustrated in Fig. 8.74 and is labeled as 1 and 2. Inverse pole figure (IPF) determined by means of electron backscatter diffraction (EBSD) for mechanical and structural characterization before indentation is illustrated in Fig. 8.75a. The displacement and loading modes, labeled in (b) as (1) and (2), respectively are used to perform the cyclic indentation tests. High density of pre-existing twins generated during the annealing process are also seen in Fig. 8.75a. The microstructures extracted by focused ion beam (FIB) and further imaged by TEM provide information on the plastic deformation induced by the mentioned testing conditions, is shown in Fig. 8.76. Dislocation forest surrounding the deformed region is seen in Fig. 8.76a in the bright field BF-TEM image. Electron diffraction pattern in (c) reveales that no phase transformation has occurred, but in addition to the forest dislocations shear bands are also seen. Further, the dark field DF-TEM image shown in Fig. 8.76b reveals a shear band underneath the residual imprint. In conclusion, the hardness decreases as the number of cycles increases as seen in Fig. 8.73. Under displacement control the hardness decrease is much more pronounced than under loading controlled. Nanoindentation under displacement

Fig. 8.73 Hardness (H) and elastic modulus (E) evolution against the cycle, determined under loading control mode (a) or under displacement control mode (b). Roa et al. (2018). With kind permission of Elsevier

8.4 Indentation-Hardness

411

Fig. 8.74 Fifty cyclic indentation loading–unloading curves (or P–h curves) performed under displacement and loading control mode and labelled as (1) and (2), respectively. P–h curves for the experiments performed under displacement control mode have been shifted 50 nm, to clearly discern the shape of the cycles. Insets present in the right hand side exhibit a magnification of the cyclic region. Roa et al. (2018). With kind permission of Elsevier

Fig. 8.75 a Local crystallographic orientation map (or Inverse Pole Figure map, IPF) determined by EBSD prior to the nanoindentation process. The dash white square exhibits the regions where the different indentation tests were performed. Step size was held constant and equals to 100 nm, and b field emission scanning electron microscopy (FESEM) image of the residual cyclic imprints. The label (1) and (2) denote the indentation mode used to perform the test, displacement and loading control modes, respectively. Roa et al. (2018). With kind permission of Elsevier

control mode illustrated in Fig. 8.76 reveals the presence of dislocation forest and shear band in cyclically deformed samples. The deformation generated under loading control mode is much higher than that produced under displacement control mode.

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8 Cyclic Deformation-Fatigue

Fig. 8.76 TEM imaging of a thin foil obtained by FIB of a region at the center of the cyclic nanoindentation imprint tested under displacement control mode. a Bright field BF-TEM image showing the deformed microstructure generated during the cyclic process, b Darkfield DF-TEM image illustrating a shear band activated during the cyclic indentation process, and c SAED pattern obtained from the region delimited by a white dash rectangle in (a). Roa et al. (2018). With kind permission of Elsevier

8.4.5.1

Indentation-Hardness in Nano-316L

As mentioned already through this book the composition of 304L and 316 L is almost the same except to the 2–3% Mo in the latter case. Rewritten here for convenient comparison, 304L contains 18–20% Cr and 8–12% Ni, while in 316L these elements are 16–18% and 10–14%, respectively. All the other constituents are exactly the same. It was felt of interest to add the variation of hardness with the number of cycles, not only for the sake of complementing available information, but also because the additional data provide information in the solution annealed (SA) and cold worked (CW) conditions. The hardness variation with cycles in very HCF test is shown in 8.77. The hardness is presented in terms of universal hardness which is defined as the quotient of the test load and the surface area of the indentation under an applied test load, which is obtained by Hu =

Pmax 2 26.43Dmax

(8.32)

where Dmax is the maximum depth and Pmax is the maximum load. As seen in Fig. 8.77 the universal hardness in the case of SA shows an increase with the number of cycles, which is known by the familiar term of cyclic hardening. Contrary to this the 10% CW alloy shows a decrease up to 106 cycles known as a so called cyclic softening, but thereafter cyclic hardening sets in. However, note that in the 20% CW case hardening sets in after ~107 cycles and up to that point softening occurs. This clearly

8.4 Indentation-Hardness

413

Fig. 8.77 Relationship between hardness and the number of cycles. Xiong et al. (2015). With kind permission of Elsevier

is understood by the known concept, that work hardening occurs on soft metals and its degree depends on the softness of the material. The softer the metal is there is more room to increase the hardening up to a degree when failure might set in which is commonly avoided. The strengthening -here indicated as hardening- depend on the density of dislocations which generally increases with strain (work) hardening irrespective if the deformation is static or cyclic (fatigue). The relation between hardness and dislocation density is given by √

ρ=

H−A B

(8.33)

A and B are constants and in the case of 316L for Vickers hardness measurement they are 157 and 3.03 × 10–6 , respectively.

References P.M. Bodhankar, C. Gurada, S. Shinde, H. Muthurajan, V. Kumar, J. Mater. Sci. Surf. References T. Hanlon, E.D. Tabachnikova, S. Suresh, Int. J. Fatigue 27, 1147 (2005) J.E. Hatch, Aluminium: Properties and Physical Metallurgy, (ASM International, Materials Park, OH, USA, 1984a), p. 636 J.E. Hatch, Aluminum: Properties and Physical Metallurgy, (ASM International, Materials Park, OH, USA, 1984b), p. 636 J. Hua, J. Zhang, Z. Jianga, X. Ding, Y. Zhang, S. Hana, J. Sun, J. Lian, Mater. Sci. Eng. A 651, 999 (2016) O. Kraft, P. Wellner, M. Hommel, R. Schwaiger, E. Arzt, Z. Metalkd. 93, 392 (2002) L. Kunz, L. Collini, Frattura Ed Integrità Strutturale 19, 61 (2012) J.-A. Lee, D.-H. Lee, M.-Y. Seok, I.-C. Choi, H.-N. Han, T.-Y. Tsui, U. Ramamurty, J.-I. Jang, Scripta Mater. 140, 31 (2017)

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C.J. Lee, R. Murakami, C.M. Suh, Fatigue properties of aluminum alloy (A6061–T6) with ultrasonic nanocrystal surface modification. Int. J. Modern Phys. B 24, 2512 (2010) S.-P. Liu, K. Ando, J. Chinese Ins. Eng. 27, 395 (2004) J. Long, Q. Pan, N. Tao, L. Lu, Mater. Res. Let. 6, 456 (2018) P. Lukáš, L. Kunz, L. Navrátilová, Kovove Mater. 50, 407 (2012) R. Murakami, The University of Tokushima, Advanced Material Laboratory in Kyungpook National University M. Murashkin, I. Sabirov, D. Prosvirnin, I. Ovid’ko, V. Terentiev, R. Valiev, S. Dobatkin, Metals 5, 578 (2015) M.C. Murphy, Fatigue Eng. Mater. Struct. 4, 199 (1981) K. Niihara, J. Cer. Soc. Japan 99, 974 (1991) J. Pelleg, Mechanical Properties of Materials (Springer, 2013), p. 37 A. Pineau, A.A. Benzerga, T. Pardoen, Acta Mater. 107, 508 (2016) J.J. Roa, I. Sapezanskaia, G. Fargas, . R. Kouitat, A. Redjaïmia, A. Mateo, Mater. Sci. Eng. A 713, 287 (2018) T. Sumigawa, T. Kitamura, The Transmission Electron Microscope, ed. by Maaz Khan, (2012), p. 355 D. Tabor, Hardness of Metals (Clarendon Press, Oxford, 1951). H. Ueno, K. Kakihata, Y. Kaneko, S. Hashimoto, A. Vinogradov, Acta Mater. 59, 7060 (2011) Z. Xiong, T. Naoe, T. Wan, M. Futakawa, K. Maekawa, Procedia Eng. 101, 552 (2015) G.P. Zhang, K.H. Sun, B. Zhang, J. Gong, C. Sun, Z.G. Wang, Mater. Sci. Eng. A 483–484, 387 (2008)

Chapter 9

Fracture in Nano-Structures

9.1 General Concept Detailed description of the basic concept of fracture in bulk material can be found in earlier works of the author (Pelleg 2013, 2014). Following this section comprehensive consideration to nanomaterial is presented, discussing the various fracture types including those of static, time dependent and fatigue related observations. Grosso modo, fracture is the separation of a material into two or more pieces under the action of stress at temperatures below the melting point. Clearly, regardless of the kind of fracture (static, cyclic or creep), most types of failure by fracture are either brittle or ductile. Brittle fractures occur with no apparent deformation before fracture and ductile fractures occur when visible deformation does occur before separation. Terminology considers fracture strength or breaking strength as the stress when a specimen fails or fractures. Crack initiation (nucleation) often precedes total failure and its propagation is leading to complete fracture. A detailed understanding of how fracture occurs in materials will be considered next. Figure 9.1 illustrates the various types of fractures encountered in materials, some of which appear only in very ductile materials, especially in metals such as steel or aluminum and in very ductile and soft specimens, e. g., Pb, Au etc. Ceramic material such as alumina might contain pores or microcracks in the as grown condition even without the application of stress. The theoretical strength of a ductile material such as metals has been indicated (Pelleg 2013, 2014) in terms of shear stress as τmax = τ0 ∼

G Ga ∼ 2π h 6

(9.1)

(since a = ~h) where τ0 is the critical shear stress (~4.5–13 GPa) for lattice instability. Experimental τ0 ~0.0069 GPa (is 2–3 orders of magnitude smaller) than the theoretical value with the inevitable conclusion that real crystals must contain defects, which reduce their mechanical strength. © Springer Nature Switzerland AG 2021 J. Pelleg, Mechanical Properties of Nanomaterials, Engineering Materials, https://doi.org/10.1007/978-3-030-74652-0_9

415

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9 Fracture in Nano-Structures

Fig. 9.1 A schematic illustration of some types of fractures observed in metals, such as steel or aluminum: a brittle fracture; b ductile fracture; c shear fracture; and d complete ductile fracture, also known as ‘chisel point fracture’. Pelleg (2013)

For non-ductile materials, the normal stress, σ, rather than the shear stress, τ, is applicable. Applying a tensile stress normal to the planes, which separates two atomic planes, the theoretical cleavage stress may be evaluated in the same way as described for the shear stress, but instead a normal stress is considered. A similar equation can be derived in terms of the theoretical cleavage stress as E ∼ E σmax = σ0 ∼ = = 2π 6

(9.2)

Fracture occurs when the applied force is larger than the cohesive force. Various theories have been suggested and special attention has been given for brittle fracture. Derivation of the appropriate relations were indicated in earlier publications (Pelleg 2013, 2014) and here only the final expressions are presented. The following theories were suggested for analyzing fracture.

9.1.1 Griffith’s Theory on Fracture The existence of flaws in the form of microcracks explains why the actual strength is lower than the theoretical strength. For constant load and plane strain conditions the suggested relation is  σL =

2γ E πc

(9.3)

9.1 General Concept

417

c is half the major axis of an elliptical crack and γ is the surface energy per unit area of the crack. For constant load and plane strain conditions the above can be written as  2γ E  σL =  (9.4) 1 − υ2 Griffith approach is regarded for brittle materials, such as glass entirely satisfactory (amorphous materials), but cannot, in principle, be extended to metals or ductile materials, due to the different nature of plastic deformation in ductile materials.

9.1.2 Orowan’s Fracture Theory Orowan has arrived to a similar relation as Griffith’s. He writes after replacing σmax  with the stress concentration factor, Kt = σσmax a  σa =

E a c 20

(9.5)

a and are half of the elliptical crack. In Eq. (9.5) a is the atomic distance.

9.1.3 The Stroh Model of Fracture The theory of fracture based on the concept of cracks initiated by the stress concentration of a dislocation pile-up. Stroh has calculated that the condition for crack initiation may be given as  τ=

3π Gγ 8(1 − υ)L

(9.6)

γ is the surface energy of the cleavage plane and L is the distance of the dislocation pile-up. Another expression for shear stress, τs is given as:  τs≈ τi +

2γs nb

(9.7)

τI is the lattice friction in the slip plane and n is the number of dislocations in the pile up as illustrated in Fig. 9.2.

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9 Fracture in Nano-Structures

Fig. 9.2 Nucleation of a wedge crack due to piled-up dislocations on a slip plane (Stroh’s model). Sarfarazi and Ghosh (1987). With kind permission of Elsevier

9.2 Tensile Fracture in Nano-Al 9.2.1 Molecular-Dynamic (MD) Simulations Al is a soft metal and therefore it is strengthened by various additives among them alumina, SiC etc. The reinforced Al composite is of technical interest and therefore in focus of investigations reported in the literature. However, molecular-dynamics studies of the mechanical deformation in nano-crystalline aluminum were performed. In the following molecular-dynamic (MD) simulations of tensile loading of nanocrystalline Al modeled by an embedded-atom method (EAM) potential is presented, the results of which are to provide the experimental expectations of real specimen’s behavior. Nano-crystalline metals exhibit properties different than common polycrystalline material, an important example is the Hall–Petch relation. The Hall–Petch relation predicts that as the grain size decreases the yield strength increases. However, for grain sizes below a critical value, the hardness decreases with decreasing grain size, i.e., an inverse Hall-Petch effect. Experiments on many nano-crystalline materials demonstrated that if the grains reached a small enough size,—the critical grain size which is typically around 10 nm—the yield strength would either remain constant or decrease with decreasing grains size. This phenomenon has been termed the reverse or inverse Hall–Petch relation. In the MD simulation of nano-crystalline Al it is found that intergrain fracture can occur, which is identified by a sudden drop in the stress– strain plot. The nano-crystalline initial sample configuration is shown in Fig. 9.3 (for details Kadau et al. should be consulted). As seen in Table 9.1 the resulting density is close to ideal and the grain boundary structure is indepeendent of grain size, even down to the nanometer region as illustrated in Fig. 9.4 which is confirmed by experimental observations. The tensile simulation shown in Fig. 9.5 indicates a decrease in flow stress with decreasing grain size, which means an inverse Hall–Petch

9.2 Tensile Fracture in Nano-Al

419

Fig. 9.3 A nano-crystalline sample (190,785 atoms) containing 32 grains, with an average grain size d = 4.73 nm. Grain boundary atoms are yellow; bulk atoms are red. Kadau et al. (2004). With kind permission of Springer Nature

Table 9.1 Average grain size d, density as compared to the bulk value (before loading), Number of atoms, and measured flow stresses for different strain rates ε˙ for the two different preparation methods. Kadau et al. (2004). With kind permission of Springer Nature Method

d (nm)

Density (Pct bulk)

Number of atoms

Flow stress ε˙ = 5 Flow stress ε˙ = l × 10−8 /s × 10−8 /s

Voronoi

3.15

97.03

55,210

1.68 GPa

Voronoi

4.73

97.69

190,785

–

1.54 GPa

Voronoi

6.31

98.15

457,422

1.87 GPa

1.62 GPa

Voronoi

1.38 GPa

9.56

98.72

1,561,466

–

1.66 GPa

Sinter pressure 2 4.14 GPa

97.12

129,256

1.82 GPa

–

Sinter pressure 1 3.33 GPa

95.75

66,452

1.79 GPa

–

Sinter pressure 1 4.22 GPa

91.00

129,256

1.37 GPa

–

Sinter pressure 1 7.25 GPa

83.59

600,728

0.87 GPa

–

behavior. It is seen in the figure that the flow stress increases with grain size, also a sudden drop in the flow stress for larger grain sizes is observed, which means that fracture has set in. Samples with larger grain sizes tend to fracture at smaller strains than those with smaller grains. The inverse Hall–Petch behavior in the simulations for small grain sizes shown in Fig. 9.6 indicates softening with decreasing grain size. In Table 9.1 the sintered samples are also indicated, having a larger porosity than the Voronoi samples which could be improved by increasing the sintering pressure or the

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9 Fracture in Nano-Structures

Fig. 9.4 Fraction of grain boundary atoms as a function of inverse grain size. The linear behavior demonstrates the independence of the grain boundary thickness from the grain size. Kadau et al. (2004). With kind permission of Springer Nature

Fig. 9.5 Stress–strain response for tensile loading of nano-crystalline Al. Intergrain fracture can occur, identified by the sudden drop in the stress strain curves (particularly the red dashed curve). Kadau et al. (2004). With kind permission of Springer Nature

sintering time. The increase in flow stress with increasing the pressure is illustrated in Fig. 9.7. Intergranular fracture was observed for the larger Al grain sizes. Samples sintered at 2 GPa show a larger flow stress (dashed line in Fig. 9.7), suggesting that grain boundaries formed by sintering process might be more stable. The sintered samples also show an intergrain fracture at larger strains (Fig. 9.7). Further, the more porosity the sample has, the more pronounced is the growth of pores and the less pronounced are the grain boundary sliding processes which eventually the growth of pores leads to fracture starting at pores and propagating along the grain boundaries. Summarizing the simulation results, the following can be noted. (a) At very small grain sizes an inverse Hall–Petch relation is observed (substantiating experimental results). (b) At large strains during the plastic flow process fracture occurs along the

9.2 Tensile Fracture in Nano-Al

421

Fig. 9.6 The inverse Hall–Petch relation for Al, i.e., softening with decreasing grain size. The flow stress as a function of 1/d (d = average grain size) for nano-crystalline Al shows a linear behavior, suggesting that the deformation mechanism for small grain sizes is related to the surface-to-volume ratio of the grains, indicating the dominance of intergrain activity. The insets show the Hall–Petch plot (diamonds) and the raw data (squares) that might suggest the cross over between the inverse Hall–Petch and the normal Hall–Petch regime at larger grain sizes (d = 10 nm). Kadau et al. (2004). With kind permission of Springer Nature Fig. 9.7 Stress–strain response for tensile loading of sintered nano-crystalline Al. The flow stress for the lower density sample is significantly smaller than for the higher density sample, underlining the importance of sample quality. Kadau et al. (2004). With kind permission of Springer Nature

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9 Fracture in Nano-Structures

grain boundaries. (c) pore growth should be reduced by applying higher sintering pressure or sintering time. (d) The flow stress strongly depends on sample quality, namely higher density and lower porosity.

9.2.2 Al 7075 Of the three most used Al, the 6061, and the 2024, the choice was to consider below Al 7075. Although one has to mention that the major compositional constituents is almost the same apart the difference in the Zn, Cu and Mg which are higher in 7075, while 6061 has a higher Si content. Aluminum 6061 is cost effective of medium strength and easy to work with, while 7075 is exceptionally strong with typically smoother finishes and is used extensively by the aircraft industry, almost immediately to its discovery. 6061 alloys provide superior welding abilities and workability over other alloys, good corrosion resistance, but it does not have the same high strength and stress resistance as 7075. Microstructural and mechanical properties of nano/UFG structured 7075 aluminum alloy obtained by accumulative roll-bonding (ARB) process id considered in this section. The fully annealed microstructure of the starting material, showing eqiaxed grains, is illustrated in Fig. 9.8. Figure 9.8 (a) is a field emission scanning electron microscope micrograph (FESEM), while (b) is back scattered electron micrograph of the starting material. The micrographs observed at TD plane of the ARB processed sheets after six cycles is shown in Fig. 9.9. The microstructure by ARB is a consequence of severe deformation. The elongated ultrafine grains along the rolling direction (RD) are homogeneous through a large area of the thin foil used for the TEM specimens. The average grain size of the UFG after six cycles is 130 nm. Tensile engineering stress–strain curves of 7075 Al alloy sheets after various cycles

Fig. 9.8 a Secondary electron; b back scattered electron micrograph of starting material. Alvandia and Farmanesh (2015). With kind permission of Elsevier

9.2 Tensile Fracture in Nano-Al

423

Fig. 9.9 TEM microstructures observed at the TD plane of the specimen ARBed by six cycles. Alvandia and Farmanesh (2015). With kind permission of Elsevier

of ARB at room temperature are shown in Fig. 9.10. The stress–strain curves show the effect of the rolling cycles, and as can be seen increasing the number of cycles increases the stress–strain curves. The increase in work hardening can be attributed to an increase in dislocation density, the grain refinement and the precipitates. The fracture of the annealed specimens—as seen in Fig. 9.11 at different strains—is a typical ductile fracture showing deep equiaxed dimples, which become smaller and finer in size and shallower with increased number of the ARB process cycles as seen in (b)–(d). Thus, increasing the number of cycles, decreases the plastic deformation until fracture sets in. Al 7075 was chosen to represent the various Al alloys because the subject of this book is mechanical properties and this Al alloy is exceptionally strong, which makes it of specific interest in various technological applications, mainly in the aircraft industry.

Fig. 9.10 Engineering stress–strain curves for 7075 aluminium sheet ARB processed. Alvandia and Farmanesh (2015). With kind permission of Elsevier

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9 Fracture in Nano-Structures

Fig. 9.11 Tensile fracture surface morphology of annealed condition and accumulative rolled bonding (ARB) Al 7075 alloy samples at different strains (ε); a Starting material; b ε = 0.8; c ε = 2.4 and d ε = 4.8. Alvandia and Farmanesh (2015). With kind permission of Elsevier

9.3 Tensile Fracture in Nano-Cu If in the previous section Al a typical soft metal was present, in this section the tensile fracture of a typical metal, i.e., Cu is evaluated. The nc copper sheets with a thickness of ~300 nm was obtained by electrodeposition from a copper containing solution. Almost a theoretical density nc pure Cu (~99.6% of 8.92 ± 0.02 g cm−3 ) was obtained by this process.

9.3 Tensile Fracture in Nano-Cu

425

Tensile dog-bone-shaped specimens were machined from the as deposited-sheet and the uniaxial tensile tests were performed on the polished specimens at the strain rate range 1 × 10–5 − 0.1 s−1 . Sheets of nc Cu with a thickness of about 300 nm were electrodeposited from an appropriate solution. Uniaxial tensile tests were performed with a strain rate in the range 1 × 10–5 –0.1 s−1 . The grains are mostly equiaxed and their distribution is shown in Fig. 9.12b. The grain size distribution is broad. In the range 10–290 nm, but the mean grain size by TEM images indicate 47 nm. Twins and dislocation structures can also be detected in some grains. Engineering stress– strain curve at a strain rate of 10–4 s−1 at room temperature and true stress–strain curves are illustrated in Fig. 9.12. From the engineering stress–strain curve the UTS was evaluated as 620 MPa for the nc Cu. The effect of the strain rates is seen in Fig. 9.13a. The UTS increases from 630 to 1040 MPa with increasing strain rates, while as expected the elongation drops from 20 to 4.7%, which is seen in the plot of the true stress versus true strain. The strain sensitivity index was determined from the slope of the plot of ln(stress) against ln(strain rate) shown in Fig. 9.13b. Recall that the relations for the strain sensitivity and the activation volume were given earlier, but for convenience they are rewritten here as Eqs. (9.8) and (9.9). m=

∂lnσ f ∂ln ε˙

(9.8)

and

Fig. 9.12 a Bright-field TEM image and b grain size distribution plot of the nc Cu showing a broad grain size distribution. Wang et al. (2008). With kind permission of Cambridge University Press

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Fig. 9.13 a Tensile engineering and b true stress–strain curves of the nc Cu at strain rate of 1 × 10−4 s−1 and room temperature. The inset in (a) is typical tensile specimens before and after deformation at this strain rate. The inset in (b) is corresponding normalized  work  hardening rate plotted versus true strain. The normalized work hardening grate: = σ1 ∂σ ∂ε ε , where σ is true stress and ε true strain. Wang et al. (2008). With kind permission of Cambridge University Press

υ=

√ ∂ln ε˙ 3kT ∂σ f

(9.9)

Clearly, σf is the flow stress. Also recall that the strain sensitivity index is related to the activation volume as (Fig. 9.14)

9.3 Tensile Fracture in Nano-Cu

427

Fig. 9.14 a True stress–strain curves of nc Cu at different strain rates. b logarithm plots of flow stress at 1% plastic strain (σ1% ) as a function of strain rate (˙ε ) for nc Cu. The strain rate sensitivity (m value) is estimated from the slope of the linear fit. c Plots of ln ε˙ versus σ1% transformed from (b). The activation volume (υ) was estimated from the slope of linear fit using Eq. (9.9). Wang et al. (2008). With kind permission of Cambridge University Press

√ m=

3kT σfυ

(9.10)

The fracture surfaces of the nc Cu deformed at two different strain rates, ε˙ = 0.1 s−1 and ε˙ = 1 × 10–4 s−1 are illustrated in Fig. 9.15a, c, respectively. Both samples show ductile fracture with dimpled structures.

9.4 Tensile Fracture in Nano-Ni Nanocrystalline materials have attractive properties and as a result many potential applications in areas—such as magnetic, structural wear and corrosion—are considered. The most common preparation techniques for nanocrystalline metals and alloys are inert gas condensation (ICG), ball milling (BM) and pulsed electrodeposition (PED). Because of some disadvantages of ICG (cost) and BN (introduction of impurities and elastic lattice distortion), PED became an attractive production method.

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9 Fracture in Nano-Structures

Fig. 9.15 Fracture surfaces of the nc Cu specimen tested at strain rate of a 1 × 10−1 s−1 and c 1 × 10−4 s−1 . b High-magnification image of (a), and d high-magnification image of (c). Wang et al. (2008). With kind permission of Cambridge University Press

Pure nickel and its alloys produced by PED have controlled grain size, high density and free of pores. The strength of nanocrystalline Ni and its alloys produced by PED much exceeds the strength of conventional Ni with large grains and can be obtained with grain sizes in the range 10–100 nm. Because they exhibit excellent mechanical properties they are considered for structural applications. Commonly it is known that the strength, σ of crystalline materials is controlled by grain size as formulated by Hall–Petch in Eq. 7.80 for hardness and rewritten here Hv = H0 + kd−1/2

(9.11)

H0 is the intrinsic hardness (depends on frictional lattice resistance to dislocation motion), k as known is the strength coefficient and d is the average grain size. This relation is also expressed in terms of strength as σy = σ0 + kd−1/2

(9.12)

9.4 Tensile Fracture in Nano-Ni

429

However, in very small nano-size crystals this relation does not hold and we talk about the inverse Hall–Petch relation. As the scale reduces to the nanometer range the properties may also change, which will be considered below. The basic tensile properties were determined by uniaxial testing using dogbone shaped tensile specimens and the resulting loads versus crack mouth opening behavior are given in Fig. 9.16. Carbon doped nano nickel is included in the figure. All specimens initially show linear elastic behavior as observed in the figure, which became non-linear when the load drops. This occurs with increasing load when the non-linearity is an of “crack-tip” plastic flow and stable crack growth. Crack extension resistance, KR was calculated from the crack length (+ correction for plastic flow) as seen in Fig. 9.17. After fracture toughness testing, all specimens necked through the thickness in varying extent. An example is shown in Fig. 9.18. The modes of fracture were a shear-dominant mode and there was not a significant change as a function of various heat treatments. Ductile fracture in pure nanocrystalline Ni (PRNi) is shown in Fig. 9.19 for as received, 100 and 200 °C annealed cases. In all of them a transgranular-tearing mode fractograph is seen. The dimples become coarser and shallower (200 °C) with increasing annealing temperature. The dimples are coarser in carbon doped Ni (CDNi) than in pure nickel and non-uniform (see Fig. 9.20), but after annealing at 200 °C the dimple shape changes to spherical and unifom. The crack growth resistance of nanocrystalline nickel is reduced with increasing annealing temperature. It is thought that the reason is the large concentration of non-equilibrium vacancies formed inside the grains during the process of recrystallization of nc material including Ni. The reason proposed for the high supersaturation of vacancies is the athermal emission of vacancies from grain boundaries

Fig. 9.16 Load* —crack mouth-opening curves (*: load normalized by specimen thickness). Mirshams et al. (2001). With kind permission of Elsevier

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9 Fracture in Nano-Structures

Fig. 9.17 KR -resistance curves. Mirshams et al. (2001). With kind permission of Elsevier

Fig. 9.18 A typical SEM fractograph of cross section over view in a fracture surface for as received nanocrystalline Ni. The figure shows a shear dominant mode of fracture. Mirshams et al. (2001). With kind permission of Elsevier

dislocation during boundary migration. Clearly the driving force is the reduction of the total free energy of the system due to grain growth. Condensed microvacancies clusters increase during annealing and preferentially segregate along grain boundaries. With further increase in the annealing temperature, these clusters accumulate and can grow to pores along grain boundaries and weaken them significantly, and at a micron level, the fracture is totally intergranular at 500 o C , as it is seen in Fig. 9.21b leading to separation at grain boundaries. At a lower annealing temperature, say at 300 °C the fracture is a mixture of ductile transgranular and intergranular fracture as seen in Fig. 9.21a. The emission of non-equilibrium vacancies is much stronger in nanocrystalline material than in conventional grain polycrystalline material since

9.4 Tensile Fracture in Nano-Ni

431

Fig. 9.19 SEM fractographs of PRNi: a as-received; b 100 °C annealed; c 200 °C annealed. Mirshams et al. (2001). With kind permission of Elsevier

Fig. 9.20 SEM fractographs of CDNi: a as-received; b 200 °C annealed. Mirshams et al. (2001). With kind permission of Elsevier

the initial large volume of grain boundaries and therefore, conventional nickel is not sensitive to annealing to a significant degree. The thermal stability of Ni was improved by doping it by 500 ppm carbon. Carbon segregates preferentially at grain boundaries at thermal equilibrium, which reduces

432

9 Fracture in Nano-Structures

Fig. 9.21 SEM fractographs of PRNi after annealed at: a 300 °C; b 500 °C. Mirshams et al. (2001). With kind permission of Elsevier

grain growth. Furthermore, the carbon at grain boundaries might prevent or reduce the segregation rate of vacancies and also reduce the sensitivity of nickel to annealing temperature. In summary, (i) pure nc Ni is more crack growth resistant when annealed at 100 °C than polycrystalline nickel but which decreases on annealing at higher temperatures. At 200 °C crack growth is unstable and shows lower crack growth resistance than polyctystalline nickel. (ii) Carbon doping greatly reduced crack growth resistance of nanocrystalline nickel. However, the crack growth resistance of carbon-doped nanocrystalline Ni could be improved through annealing processing. Crack growth resistance can be explained by vacancy cluster segregation at grain boundaries.

9.4.1 Strain Rate and Grain Size Effect As mentioned in the previous section nc material smaller than 100 nm possess high yield and fracture strength and some even exhibit superplasticity at relatively low temperatures, compared to microcrystalline components with grain sizes of ~1 μm or larger. Also limited experimental reports indicate that nc material exhibit strainrate mechanical properties. This has been observed in nc Ni also and the strain to failure was observed to increase with strain rate compared to samples with larger or conventional grain size. High purity fully dense nickel sheets produced by electrodeposition with grain sizes of 20 and 200 nm and referred to as nc and ufg Ni. The surface grain structure after polishing is shown in Fig. 9.22a, b for nc and ufc Ni, respectively. The nc Ni has a narrow grain size distribution with a mean grain size of approximately 40 nm. Growth twins were also observed. No dislocations were observed in the grain interior and no evidence existed of second phase particles in the boundaries. Some of the grain sizes were larger than the average grain size of 320 nm, nevertheless the surface grain structure after polishing was more uniform in the case of the nc foil. Tensile test curves for the different Ni samples of different

9.4 Tensile Fracture in Nano-Ni

433

Fig. 9.22 FIB images showing the grain structure on the surface of the a nc and b ufc electrodeposited Ni foils after polishing. Due to ion channeling contrast in the FIB, the grain structure is visible. Schwaiger et al. (2003). With the kind permission of Elsevier. FIB stands for focused ion beam

grain sizes are shown in Fig. 9.23a and at three strain rates in yield strength as well as tensile strength (TS) increase with decreasing grain size as seen in this figure. In Fig. 9.23b the nc Ni deformed at three different strain rates are seen and the flow stress increases with increasing strain rate. Tensile fracture surfaces are seen in Fig. 9.24 for different nickels. In the mc specimens necking is seen, in both directions, in plane and perpendicular to the foil. Dimples are formed on the fracture surface, the smallest of which is for the nc Ni. It also has the more uniform size distribution. In summary-as stated several times in this book: (i) strengthening is associated with grain size reduction (see for example Fig. 9.23a). Of the 3 nickel materials the nc ones has the smallest grain size and consequently with the general concept, significant improvement in strength properties is expected and as indeed observed experimentally. It might be of interest to cite the strength values and the significant

Fig. 9.23 Stress versus strain a for nc, ufc, and mc Ni at a strain rate ε˙ = 3 × 10–1 s−1 and b for nc Ni at three different strain rates. Schwaiger et al. (2003). With the kind permission of Elsevier

434

9 Fracture in Nano-Structures

Fig. 9.24 FIB micrographs of the fracture surfaces for different grain sizes and strain rates. a nc Ni, ε˙ = 3 × 10–1 s−1 ; b nc Ni, ε˙ = 3 × 10–4 s−1 ; c ufc Ni, ε˙ = 3 × 10–1 s−1 ; d ufc Ni, ε˙ = 3 × 10–4 s−1 ; e mc Ni, ε˙ = 3 × 10–1 s−1 ; f mc Ni, ε˙ = 3 × 10–4 s−1 . Schwaiger et al. (2003). With the kind permission of Elsevier

9.4 Tensile Fracture in Nano-Ni

435

change in the samples illustrated in Fig. 9.23a. Thus, the values are 450 MPa, 920 and 1600 MPa for mc (grain size 10 μm), ufc (grain size 320 nm) and nc (grain size 40 nm), respectively. (ii) And also as indicated many times, the strength improvement is on the expense of ductility. The strain at TS is reduced from 30% for the mc Ni to only of 2–3% for the nc and ufc Ni foils. (iii) The grains are essentially free of dislocations, but dislocation activity in grains >100 nm has been observed by in situ straining in TEM. (iv) Pure nc-Ni exhibits strain rate sensitivity, which is related to the grain size an (v) Dimples are found on the fracture surface, the average size varies, being the smallest in nc—Ni and largest for the mc—Ni. Nm grain clusters are surrounded by many small nanograins of 10–20 nm, while the grains in the cluster are 30–80 nm. The grain size distribution in Fig. 9.25c is 5–80 nm. Tensile tests performed at different strain rates at room temperature are shown in Fig. 9.26b.

Fig. 9.25 TEM micrographs: a lower magnification, b higher magnification and c grain size distribution of the electrodeposited nc Ni. Gu et al. (2006). With kind permission of Elsevier

436

9 Fracture in Nano-Structures

Fig. 9.26 a Typical tensile specimens before testing and after deformation at a strain rate of 1.04 × 10–3 s−1 ; b nominal engineering stress–strain curves of nc Ni performed at different strain rates and RT and c logarithmic plot of flow stress (at 1% plastic strain) versus strain rate. Gu et al. (2006). With kind permission of Elsevier

Contrary to the low strain of nc-Ni mentioned earlier (2–3%), an elongation of 7.5–8.3% was reported in a somewhat more recent work produced by the same method (electrodeposition) and also of having about the same average grain size of 40 nm. A strong preferred orientation of {200} was obtained. TEM image of the nc-Ni is shown in Fig. 9.25. Selected area diffraction (SAD) pattern is also seen in Fig. 9.25a. As shown in this figure there are many gtain clusters within sizes of about 150–300 nm. The thickness surface morphology of the broken specimens tested at a strain rate of 1.04 × 10–3 s−1 is presented in Fig. 9.27. Necking is seen of ~400 μm in length and the deformation at various strains is seen in Fig. 9.28. The difference in ductility between the reports of nc Ni produced by electrodeposition and of about the same grain size is explained by the author of this book, as a result of the difference in the tensile stress in particular the UTS. The low ductility nc sample have a stress of 1600 MPa, while the high ductility sample (in the later work) has an UTS of 1200 MPa. As one can recall these two mechanical property values are in inverse relation, namely, high strength is associated with lower ductility, while the lower stress is compensated by

9.4 Tensile Fracture in Nano-Ni

437

Fig. 9.27 Thickness surface morphologies of the broken specimen tested at a strain rate of 1.04 × 10–3 s−1 and RT. Gu et al. (2006). With kind permission of Elsevier

higher ductility. Another suggestion for the higher elongation is the assumption that dislocation activity in the strain hardening stage and collective grains rotation after instability sets in are responsible for the enhanced ductility.

9.5 Tensile Fracture in Nano-304L The alloys 304L and 316L represent the iron group metals and belong to the stainless steel family and the difference between them is that the 316L steel contains ~2% Mo. 304L for example, is the most versatile and widely used material one of the reasons being its excellent corrosion resistance, ease of fabrication and very good formability. Further, it is the most weldable of the high-alloy steels. One of the accepted production methods of nanostructured 304L SS is by cryorolling (CR) and reversion annealing in the temperature range of 700–800 °C. Recall that the reversion annealing related to re-transform martensite formed dung the fabrication back to austenite. CR which is performed at sub-zero temperature promotes twinning in the γ-austenite which transforms into α -martensite with lath thickness 50–100 nm. On reversion annealing 50–300 nm size γ-grains recrystallize in nano-twinned α . As in other structures, grain refinement in the austenitic SS improves its strength which can be obtained by severe plastic deformation (SPD). From XRD peak broadening the evolution of crystallite size (d), lattice strain  2 1/2 ), and the vol% of martensite formed on CR were estimated. The estimated (ε

438

9 Fracture in Nano-Structures

Fig. 9.28 Sheet surface morphologies of the broken specimen tested at a strain rate of 1.04 × 10–3 s−1 with different strains: a ε = 0.0%; b ε = εU = 5.5%; c ε = 1–15% and d ε = 30–35%. Gu et al. (2006). With kind permission of Elsevier

values of d and (ε21/2 ) are plotted against the strain of CR as shown in Fig. 9.29; in (a) the grain size and in (b) the martensite volume fraction against the CR strain are seen. All CR specimens have a lamellar microstructure and the presence of α in all of them was revealed by TEM bright field (BF), dark field (DF) and selected area diffraction The SAED patterns revealed γ diffraction spots and α

(SAED)

patterns.  along 121 and 113 zone axes, respectively. Twin diffraction spots (recognized by         double diffraction spots) from 101 α  , 202 α  , 303 α  , 024 γ of both structures have been indexed and marked by arrows in Fig. 9.30a. In Fig. 9.30b α -lath is shown in CR for 1.0 strain. SAED pattern indicates that the microstructure is predominantly α at CR1.8 as seen in Fig. 9.30d, but weak spots of (111)γ and (200) γ were identified with the α rings. This observation occurs after a large CR strain of 1.8. TEM BF

9.5 Tensile Fracture in Nano-304L

439

Fig. 9.29 a Variation of crystallite size and lattice strain of austenite and martensite with CR strain. b The variations of the vol% martensite and bulk hardness with CR strain. Roy et al. (2015). With kind permission of Elsevier

image and the corresponding SAED patterns of CR1.8 annealed at 750 °C, is shown in Fig. 9.30e and the inset were indexed as (111) γ, (200) γ and (220)γ, meaning that a well recrystallized austentite structure has developed on annealing. The γ grain size distribution, which varies between 50 and 300 nm is shown in Fig. 9.30f. The distribution is a bimodal grain size distribution since there is the presence of 200–300 nm size UFG in the nanocrystalline matrix of 50–100 nm. Twin boundaries (TB) in prior γ grains marked by arrows are shown in EBSD image in Fig. 9.31a. CR1.8–700 image in Fig. 9.31b shows the presence of larger size grains (200–300 nm) in a nanocrystalline matrix by EBSD image. Phase fraction is indicated by EBSD image in Fig. 9.31c shows the presence of α in CR1.8–700 (indicating incomplete α -γ transformation; α -red color), however a complete α -γ transformation upon annealing is revealed by XRD. True tensile stress–strain curves of solution treated (ST) specimens are illustrated in Fig. 9.32. Low yield strength

440

9 Fracture in Nano-Structures

Fig. 9.30 a TEM BF image of CR0.2 and the corresponding SAED pattern (inset) showing the presence of twins in both α and γ phases. b TEM BF image of CR1.0 showing α -laths, inset: corresponding SAED pattern showing twinning. c TEM BF image of CR1.8 showing nanolamellar α -laths, d corresponding SAED patterns showing α -ring and weak spots of retained-γ. e TEM bright field image and inset: SAED pattern of CR1.8–700. f Histogram showing bimodal distribution of grain size in CR1.8–700. Roy et al. (2015). With kind permission of Elsevier. Note the numbers following CR are strain and temperature

9.5 Tensile Fracture in Nano-304L

441

Fig. 9.31 Section EBSD image of a CR1.0, b CR1.8–700. c phase mapping image of CR1.8–700. d grain-boundary image of CR1.8–800 showing presence of ultrafine γ-grains in nanocrystalline matrix. e grain misorientation plot of CR1.8–700 and CR1.8–800. Roy et al. (2015). With kind permission of Elsevier

and large plastic strain is seen in ST specimens (σy = 120 MPa a strain of 1.07 as seen in Fig. 9.32a. CR specimens show higher yield strength, but low ductility, while unannealed CR1.8 have nil ductility. Necking is observed in the broken specimen shown Fig. 6.32b and the strain hardening exponent, n of the nano-austenitic steel is lower than those of the CR and ST samples. Pertinent experimental results from the work on martensitic reversion in nano-austenitic SS are listed in Table 9.2. In summary, nano austenitic 304L SS has been fabricated by CR where transformation of γ-austenite- α -martensite and reversion annealing at a temperature range

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9 Fracture in Nano-Structures

Fig. 9.32 a Tensile true stress-true strain plots of solution treated (ST), cryorolled up to plastic strain of 1.8 (CR1.8), and subsequently annealed at 700 °C (CR1.8–700), 750 °C (CR1.8–750), 800 °C (CR1.8–800) for 5 min, b SEM image of fractured specimen showing large necking in CR1.8–750 (εn = 0.59). c dimples in the fracture surface of CR1.8–750, and d XRD patterns from the gauge section of the specimens before and after tension test. Roy et al. (2015). With kind permission of Elsevier

of 700–800 °C for 5 min was considered. Severe twinning is induced in γ-austenite by CR and produces 50 nm size α -laths, which promotes the evolution of nanocrystalline γ during annealing. The γ-α transformation during tensile deformation confirms the restoration of ductility in nano-austenitic SS upon martensitic reversion annealing.

9.6 Compressive Fracture in Nano-Structures 9.6.1 Compressive Fracture in Nano-Al/Al2 O3 Surprisingly enough and despite the wide us of Al, no information on fracture of pure nano Al is available, and what is generally considered is reinforced Al, namely its composites. In the opinion of the author of this book, that because Al being a soft metal, and technological applications require strength, it must be reinforced by proper additives. The additives might be in various shape and size (mostly as small particles),

375 316 310

Cold4.0 + 700 °C (120 min)

Cold4.0 + 800 °C (30 min)

Cold2.3 + 700 °C (300 min)

850

420 ± 3

1000

670

1050

1145

711

902

1027

460 ± 3

387

1

1235

515 ± + 2

Cold4.0 + 700 °C (30 min)

CR1.8–800 (5 min)

10

34

–

99

CR1.8–750 (5 min)

120 1590

202 ± 5 540 ± 2

–

90

CR1.8–700 (5 min)

100

0

σ y (MPa)

Bulk hardness (Hv)

Cold2.3 + 900 °C (45 s) + 850 °C (45 s)

66

CR1.8

%a 

Cold2.3 + 950 °C (45 s) + 825 °C (45 s)

100 0

ST

%γ

Sample

1010

940

1160

1225

1348

1090

1246

1286

1295

1590

1212

σmax (MPa)

0.40

0.21

0.09

0.02

0.36

0.10

0.47

0.39

0.19

0.01

1.07

εp

–

–

–

–

–

–

0.48

0.59

0.21

0.05

0.52

εn

–

–

–

–

0.12

0.015

0.15

0.08

–

–

0.34

n

Ref. [40]

Ref. [29]

Ref. [29]

Ref. [29]

Ref. [28]

Ref. [28]

Present study

Present study

Present study

Present study

Present study

Table 9.2 EBSD volume percentage (%) of γ-austenite/α-martensite, bulk hardness at 30 kgf load, tensile yield stress (σy ), ultimate tensile strength (σmax ), true plastic elongation (εp ), true necking strain (εn ), and strain hardening exponent (n) of austenitic SS as obtained in the present study and literature. Roy et al. (2015). With kind permission of Elsevier

9.6 Compressive Fracture in Nano-Structures 443

444

9 Fracture in Nano-Structures

but one has to keep in mind that the increase in strength by the reinforcement is on the expense of its ductility. Most popular reinforcement additives are Al2 O3 and SiC, therefore short discussion on these Al based composites will be considered below, despite the original intent not to consider alloys.

9.6.1.1

Al/Al2 O3 Composite

The nanocomposite Al-Al2 O3 was produced from Al powder of size 60

>60

>60

Failure strain (%)

139 ± 8

118 ± 5

110 ± 11

105 ± 2

TYS (MPa)

154 ± 6

141 ± 5

126 ± 7

116 ± 4

UTS (MPa)

Tensile properties

Table 9.3 Mechanical properties of pure Al and Al-Al2 O3 composites. Reddy et al. (2017). With kind permission of Elsevier

7.2 ± 0.7

9.4 ± 0.5

11.2 ± 0.6

13.6 ± 0.3

Elongation (%)

448 9 Fracture in Nano-Structures

9.6 Compressive Fracture in Nano-Structures

449

Fig. 9.39 Fractography of compression tested specimens a pure Al and b Al-15 vol% Al2 O3 composites. Reddy et al. (2017). With kind permission of Elsevier

Fig. 9.40 SEM micrographs of microwave-hot extruded of a pure Al, b Al-0.5 vol% SiC and c Al-1.0 vol% SiC nanocomposites. Reddy et al. (2017). With kind permission of Elsevier

where G is the shear modulus for Al 68 GPa, b the Burgers vecot 0.32 nm for Al and r is the respective radius of the nanoparticles. The interparticulate distance, λ within the Al matrix is given by λ=

4(1 − f)r 3f

(9.14)

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Fig. 9.41 Compression engineering stress–strain curves (a) and yield strengths (b) of microwavehot extruded Al-SiC nanocomposites with different volume fraction of SiC particles. Reddy et al. (2017). With kind permission of Elsevier

and f is the volume fraction of the reinforcement particles. Increasing the fraction of SiC reduces the spacing between the SiC particles, requires a higher compressive (or tensile) stress, T0 for the inducing movement of dislocations between the particles according Eq. (9.15), resulting in an increase of the material strength. T0 =

Gb λ

(9.15)

G in the relation is the elastic modulus (of matrix and reinforcing particle). Further, mismatch in the thermal expansion coefficients (CTE) between particle and matrix increases the dislocation density and subsequent strengthening of the composite. Even small temperature changes can generate thermal stresses due to the large difference in CTE. These stresses can be relieved by generation of dislocations in the vicinity of the interface. The generated dislocation density has been given by Taya and Arsenault as ρ=

BεVr bd(1 − Vr )

(9.16)

Here B is a geometric constant, ε is the thermal mismatch, Vr is the volume fraction and d is grain diameter of the reinforcing particle. SEM fractographs of pure Al and Al-1.5% Al2 O3 under compressive loading are illustrated in Fig. 9.42. In summary, addition of SiC strengthen the Al/SiC composite, which was fabricated through microwave sintering process followed by extrusion. Under compression testing, the CYS and the UCS values increased significantly and with 1.5 vol% the CYS and the UCS have increase by ~80% and ~25% respectively compared to the pure Al matrix. Thus reinforcing aluminum provides a technologically and more effectively usable material for versatile application.

9.6 Compressive Fracture in Nano-Structures

451

Fig. 9.42 SEM fractographs of a Pure Al and b Al-1.5 vol% SiC under compressive loading. Reddy et al. (2017). With kind permission of Elsevier

9.6.2 Compressive Fracture in Nano-Cu On many occasions twinning has been included in this book. However, one should not be surprised since twinning occurs in many metals at high strain rate cryogenic deformation in which dislocation recovery is basically suppressed while twining is the dominant dynamic plastic deformation (DPD). Copper is one of those metals which deforms by twinning at high strain rate in what is known as dynamic deformation. In the following quasi static compressive (QSC) deformation is compared with DPD (processed at liquid nitrogen temperature at a strain rate of 103 s−1 ) observations in high purity monocrystalline copper. An annealed coarse grained (CG) copper cylinder served for the DPD process where the strain is defined by ε = ln(hi /hf )

(9.17)

where hi and hf are the initial and final height of the treated sample, respectively. From the same UFG sample the QSC specimens with the same strain and a strain rate of 10–1 s−1 was prepared for the comparison. The QSC is a SPD and the specimens prepared were at ambient temperature, at the same true strain of 2.0. The microstructure, including the morphology, boundary misorientation, dislocation density as well as the saturated grain size of the QSC Cu sample, are analogous to those of the ECAP Cu reported in the literature. Transverse TEM microstructures of DPD and QSC Cu are illustrated in Fig. 9.43. Severely refined region to the nanometer scale is seen at A and magnified in Fig. 9.43b including selected area electron diffraction (SAED) pattern. The average grain size of the matrix is 66 nm, smaller than the QSC Cu shown in (d). The lamellar spacing of the twin is about 46 nm seen in Fig. 9.43c. Region B of (a) is a high density deformation twinning embedded in the nanoscale matrix. A high density of dislocations is observed in or in the vicinity of twin boundaries (TB). It could be noted that the DPD Cu is of randomly oriented nanoscale grains characterized by a composite structure

452 Fig. 9.43 Typical transverse TEM microstructures of a as-prepared DPD Cu and (d) QSC Cu; b magnified TEM image with a SAED pattern of nanoscale grains (region A); c detailed observation of the nanoscale deformation twin bundles (region B) with SAED pattern. Qin et al. (2009). With kind permission of Elsevier

9 Fracture in Nano-Structures

9.6 Compressive Fracture in Nano-Structures

453

Fig. 9.44 Typical load–displacement curves in the 3 PB tests of the DPD Cu, QSC Cu and CG Cu samples. Qin et al. (2009). With kind permission of Elsevier

with a bundle of nanotwins, while the QSC Cu consists of monolithic elongated grains (short axis ~300 nm). Load displacement curves are shown in Fig. 9.44. Note as indicated earlier, the QSC refers to quasi-static compression at ambient temperature with a strain rate level of 10−1 s−1 , thus in Fig. 9.44, the stress–strain relations—a compressive curve (QSC)—is compared with DPD and CG coppers. Softening after the peak load (load drop in the load–displacement curve) is observed in the DPD Cu, but not in n the QSC or CG copper. This is related to dislocation pinning by the nanoscale twins and creating a storage of mobile dislocations. The fracture toughness Kq is calculated by Kq =

PL f(α/W) BW3/2

(9.18)

where P is the load when the crack propagates for 0.2% which is obtained in the load–displacement curve of three-point-bending (3 PB) tests; L, W, B, α are the span length, width, thickness and the total crack length of the single edge notch (SEN) sample, respectively. f is a dimension factor which depends on the ratio α/W. The plane-strain fracture toughness, KIc is estimated by  δ f E B0 1/2 Kq 1+ KIc 24σ y B

(9.19)

According to Eq. (9.19) Kq of DPD Cu is 31 ± 1MPam1/2 and higher than that of the QSC which is 24 ± 1 MPam1/2 and CG which is 9 ± 1 MPam1/2 (indicated in Fig. 9.44 for DPD and QSC). KIc of DPD Cu and QSC Cu is somewhat smaller but close to Kq . To get an insight to the high fracture toughness the fracture surface of the 3 PB tested Cu one should look at the SEM and CLSM microstructures presented in Fig. 9.45. The dimples of the QSC Cu are more homogeneous, quite shallow and

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9 Fracture in Nano-Structures

Fig. 9.45 SEM observations of the fracture surface of a DPD Cu and e QSC Cu. The specific fine and deep dimples in the fracture surface of DPD Cu are shown in b and c, respectively; d 3-D topography of a deep dimple from CLSM observation. Qin et al. (2009). With kind permission of Elsevier. Note CLSM stands for confocal laser scanning microscope. Diverse dimpled fracture surface is seen in the DPD Cu sample. The dimples are deep indicating sufficient plasticity as seen in Fig. 9.35a, b

simple over the entire fracture surface as seen in Fig. 9.45e. These fine and shallow dimpled structure indicate very local plasticity and explains the limited ductility and toughness often observed in nc metals. The deep dimples of the DPD Cu consume much higher fracture energy and provide a much larger local plasticity than the shallow ones. Deep dimples were detected only in DPD Cu containing nanoscale twin bundles. It is assumed that the inhomogeneous deep dimples are the result of the high density twin bundles. In summary, the improved fracture toughness in DPD Cu compared with UFG structure of the QSC Cu is attributed to the twin bundles which help to form deep dimples during fracture and resist effectively the initiation and propagation of cracking.

9.6 Compressive Fracture in Nano-Structures

9.6.2.1

455

Cu/Al2 O3 Composite

Nano-composites of Cu/Al2 O3 were produced by powder metallurgy technique and sintering. The composite contained 1, 3, 5 and 7 vol% Al2 O3 of average size σ cA = σ Cc as seen in Fig. 6.62. Unlike in the case of the tensile deformation (see Fig. 9.65) the compressive stress–strain test did not continue to fracture. Therefore, no fracture morphology in specimens after compression test is shown.

9.6 Compressive Fracture in Nano-Structures

469

Fig. 9.65 Full compression of two alumina nano-particles: a initial state, b and c images during compression process, and d after unloading. No crack is observed during compression. Calvié et al. (2012). With kind permission of Elsevier

9.6.5 Compressive Fracture in Nano-Al2 O3 Very limited information is available on pure alumina, where all three ingredients of interest in this book, namely, compression, fracture and microstructural morphology coexist. In situ compression of alumina nanoparticles is investigated in TEM, where small particles 40 nm in diameter has undergone SPD without failure. However, 120 nm seized nanoparticles failed by brittle fracture. The great attention attracted by nano seized polycrystalline ceramics (such as alumina) is due to their specific mechanical properties such as high hardness and crack propagation resistance. Further, some bulk ceramics composed of nano seized grains could undergo ductile deformation under pressure at low temperature of 180 °C. The compression results of the two cases, i.e., 40 nm and 120 nm, where no fracture and brittle fracture has occurred are illustrated in Fig. 9.65a–d and 9.66a–d, respectively. Full compression experiment of two alumina particles of 40 nm each, at applied force of 40 mN was used. The irreversible deformation of the particles is characteristic to

470

9 Fracture in Nano-Structures

Fig. 9.66 Compression experiment of a 125 nm diameter alumina nanoparticle. a Initial state, b during compression, c after unloading, and d corresponding load–displacement curve, with emphasis on the detection of the fracture. Calvié, et al. (2012). With kind permission of Elsevier

plastic deformation and as mentioned it occurred without failure. The effect of the nanoparticle size in the 120 nm range on the deformation can be seen in Fig. 9.66a–d. The nanoparticles exhibited elastic behavior up to the maximum load tested or up to failure in a few cases. The figure shows TEM pictures of load–displacement curve recorded during the compression. Fracture occurred at an applied displacement of 30 nm with a correspomding load of 50 mN. Finite elements simulations were performed to estimate the maximum tensile stress that the 120 nm particle could sustain for a load of 50 mN. For details of the experimental procedure and the finite element simulations one is referred to the work of Calvié et al. In another publication, in situ TEM micro-compression of 0.3 μm (300 nm) alumina particles was performed and the results were compared with 3μm sized particles to evaluate the mechanical behavior, specifically whether plastic deformation occurs before fracture. The submicron particles had a diameter of 0.24 μm and the compression was performed at a strain rate of 9 × 10–3 s−1 . Two alumina particles, denoted A and B. Particle A is illustrated before and after compression as TEM bright field images in Fig. 9.67a, b. Steps of the compression at all stages is illustrated in Fig. 9.68a. Note in Fig. 9.68b, the regions denoted c and d are the location before and post burst (fracture) of the alumina particcle. In an other publication by the same authors the location c is clearly indicated as the fracture as shown in Fig. 9.69.

9.6 Compressive Fracture in Nano-Structures

471

Fig. 9.67 TEM bright field images of particle A, a before and b after compression. The arrow indicates fracture line. Sarobol et al. 2014, Unlimited public release

Fig. 9.68 In situ TEM micro-compression-0.3 μm. Sarobol et al. 2015. Unlimited public release

Compare the behavior of the 0.3 μm Al2 O3 particle (nano-size) of Fig. 9.68 with the micron size one of size 3 μm in Fig. 9.70. The sub-micron sized particles exhibited ductile deformation whereas micron sized particles exhibited brittle fracture in compression. TEM has indicated that the 0.3 μm (300 nm) particles were single crystals and relatively free of defects, whereas the 3 μm particles were highly defective single crystals (with low angle grain boundaries). The presence of defects plays a significant role in the different deformation by compression between the nano- and micron scale alumina particles.

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9 Fracture in Nano-Structures

Fig. 9.69 Forces as a function of displacement collected during two open-loop nanoindentations on a single, 0.3 μm, Al2 O3 particle “A”. Indent 1 (block curve), particle was loaded elastically and rolled with peak load of 180 μN. Indent 2 (red curve), particle was loaded elastically and plastically before fracturing at the peak load of 435 μN. Sarobol et al. 2014, Unlimited public release

Fig. 9.70 Top view SEM images of two AA-3 (3 μm) particles before (left column) and after compression (middle and right columns). Large particles fractured into pieces. Sarobol et al. 2014, Unlimited public release

In summary, pre-existing defects in alumina influence very much the deformation behavior. Nearly defect free, sub-micron (nanoscale) Al2 O3 particles exhibit plastic deformation before fracture, while defective micron seized particles show brittle fracture in compression.

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473

9.7 Time Dependent (Creep) Fracture in Nano Structures 9.7.1 Introducrion Historically, the observation of the inverse Hall–Petch relation in many metals initiated an extensive investigation of nano-materials. Recall that the inverse-Hall Petch relation in many materials such as Ni, Cu, Fe and many more, is reserved to the observation indicating that yield strength decreases instead of increasing when grain size becomes smaller than a critical size. It is also referred to as a negative Hall– Petch relation. Almost all dislocation activity would cease below the critical grain size while the intercrystalline components play a more active role in the plastic deformation. One of these intercrystalline components playing an important role in the plastic deformation is grain boundary sliding. Thus, the negative Hall–Petch relationship is attributed to a combination of inhibited lattice dislocations and enhanced grain boundary sliding. Creep is also termed as time dependent deformation, because fracture does not occur suddenly on the application of stress, but rather as a long term applied stress as a consequence of which strain accumulates until fracture sets in if the load is maintained for sufficient time. But not only fracture accompanying plastic flow, but also changing shape and dimensions of a component are of concern which clearly cannot be tolerated in actual application of any part of a structure. Grain boundary diffusion plays an important role in the creep process. Creep generally occurs below the yield strength as a result of relatively long exposure time to high levels of stress, but in nanostructures it can occur at ambient temperature. The mechanical properties including creep are very sensitive to grain size and their distribution, presence of defects and their types and impurity content. Therefore, the properties obtained—even of the same material processed in a similar way—may vary from one laboratory to another. In the following sections, fracture induced by creep in some of the materials relevant to this book will be considered.

9.7.2 Creep Fracture in Nano-Cu The creep behavior and the fracture properties of nanograin (ng) and nanotwin (nt) Cu are presented in this section. HREM was used at temperatures of 22, 40, 50, 60 and 70 °C to evaluate the creep behavior in the nanosized copper. It was indicated in this book several times that creep is a plastic deformation under sustained stress usually at elevated temperatures, but not only. It can occur at ambient temperature also at stresses below the yield strength. The steady state creep rate (SSCR) ˙εss has been given before as Eqs. (7.10) or (7.18) and is rewritten here as Eq. (9.27) 

ε˙ SS

G = Aσ ex p − kB T n

(9.27)

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9 Fracture in Nano-Structures

where A is a nanostructure dependent constant, σ is the applied sustained stress, and

G is the activation energy. Clearly, n, kB and T are the stress exponent, Boltzmann’s constant and the temperature, respectively. The grain size of the twin free ng-Cu is ~70 nm, of the nt ~65 nm and the twin lamellae thickness ~50 nm. Figure 9.71 (a) shows room temperature stress–strain curves indicating that the nt Cu enhances the UTS (from 450 to 650 MPa) and significantly the ductility (from 4.5% to 11.5). In (b) experimental stress-jump-creep strain versus time under sustained stress are shown for 100 MPa, 150 MPa, 200 MPa and 250 MPa, respectively. The fluctuations in (c) are the result of the SEM-servohydraulic testing machine, thus not associated with the creep itself, and the smoothing line is the relevant creep line for the nt-Cu in the strain versus time curve under a sustained stress of 100 MPa at 40 °C.

Fig. 9.71 a The tensile stress–strain curves of the ng- and nt-Cu at room temperature (RT), showing that nanotwins enhance simultaneously the strength and ductility of the ng-Cu. b The developed stress-jump-creep tests on the ng-Cu and nt-Cu specimens under sustained stresses of 100 MPa, 150, 200 and 250 at temperature of 40 °C. The creep fracture occurs in the ng-Cu specimen under sustained stress 250 MPa. c Creep strain versus time and associated strain rate versus time from the creep test on the nt-Cu specimen under 100 MPa at 40 °C, which shows that the secondary creep stage, i.e., steady state creep stage, with nearly constant creep strain rate has been reached after around eight-hours creep. d Steady state strain rates (SSCRs) of the ng-Cu and nt-Cu specimens crept at temperature of 40 °C under sustained stresses 100–250 MPa, showing that the nt-Cu possess a higher creep deformation resistance than the ng-Cu. Yang et al. (2016). With kind permission of Elsevier

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Fig. 9.72 Typical SEM images of the fracture surfaces, where the insets are of lower magnitude, of a the ng-Cu specimen stress-jump-creep fractured under 250 MPa at 40 °C and b the nt-Cu specimen stress-jump-creep fractured under 400 MPa at 70 °C. Yang et al. (2016). With kind permission of Elsevier

Note in Fig. 9.71b that in the ng-Cu failure occurs earlier than in the nt-Cu at the same stress level (250 MPa) and with lower ductility (4.5%). The strain is lower ~3.5%, much smaller than that of ng-Cu (also less than the RT ultimate tensile ductility). The creep strains in the ng-Cu are always higher than the corresponding strains in the nt-Cu. SEM images show the creep fracture surface of the ng-Cu stressjump-crept from 100 to 250 MPa at temperature of 40 °C in Fig. 9.72. Also, the nt-Cu is presented in Fig. 9.72. Thus, the creep behavior is highly structure dependent of the specimen and nano twins increase the creep resistance of the nanostructured metals. The nanotwins make the ng-Cu more thermally stable and greatly improve the creep behavior of ng-Cu.

9.7.3 Creep Fracture in Nano-Ni It was seen in previous sections that nano-materials often exhibit in their structure nanotwins (NT) which show exceptional combination of high strength, good ductility, large fracture toughness, fatigue resistance and creep stability. (Although contrary reports also exist considering the high strength and good ductility in nanostructures where no nanotwins are present, or where detwinning occurs). To make a point as an example, nanotwinning in Cu and Ag can be illustrated as seen in Fig. 9.73. It is also of interest to indicate fracture in twinned microstructure although as mentioned it occurred in twinned structures other than Ni. Among the many attributes of nanocrystalline metals, the ultra-high yield and fracture strength should be indicted. Also enhanced superplastic formability at lower temperatures and faster strain rates should be added to their characteristics compared say with their microcrystalline counterpart. These qualities in metallic systems with nanometer scale grains generated considerable interest for possible structural applications (Figs. 9.74 and 9.75).

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9 Fracture in Nano-Structures

Fig. 9.73 Typical microstructures of nanotwinned (NT) metals. a A bright-field transmission electron microscope (TEM) image of NT bulk Cu with equiaxed grains. b Cross-sectional TEM image of NT Ag film with columnar grains. Li et al. (2016). With kind permission of Cambridge University Press

As received electrodeposited pure nc Ni was crept and the fractured surface was observed by bright field TEM. The as received pure Ni is shown in Fig. 9.76. The creep data also include in addition to pure Ni a nanocomposite reinforced by nano SiO2 . The plots were obtained at room temperature, 373 and 473 K. In Fig. 9.76 (a) the variation of the minimum creep rate, ε˙ min with stress and in (b) the variation of the time to fracture, tf with stress are shown. Clearly the composite-which is not the scope of this book-shows a better creep resistance than nickel and longer time to fracture (b) at temperatures other than the room temperature. In the composite, at room temperature this is not conclusive for a general statement. slopes of  Since the ·

and for the minimum creep rate the apparent stress exponent n = ∂ln ε/∂lnσ T   the time to fracture m = ∂lnt f /∂lnσ T for both electrodeposits are the same. Also the values of the exponents decrease with increasing testing temperature. The creep fracture surface of the nickel is seen in Fig. 9.77. Dimples are seen on the fracture surface which is an indication of ductile fracture. In nanoindentation creep experiments, a comparison betweeen the long term creep data and the strain rate jump data of Ni in UFG and CG state at room temperature were compared as illustrated in Fig. 9.78. The time and temperature dependent behavior of nc-Ni at R.T. Figure 9.79 shows the time and the temperature dependent creep behavior of nc-Ni at RT and at 200 °C. Since nanoindentation was used for the creep experiments, which was introduced by Weighs and Pethica for long term creep experiments, the relevant relations are of interest, and are presented below.

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477

Fig. 9.74 Fracture of nanotwinned (NT) metals. a Directional anisotropy in brittle-ductile responses of a coherent twin boundary (CTB). Dark blue atoms have face-centered-cubic symmetry, light blue atoms have hexagonal close-packed symmetry, and atoms with other colors are disordered. b Scanning electron microscope image of the fracture surface of NT Cu prepared by dynamic plastic deformation. Coarse/deep dimples are indicated by the solid circles, while fine/shallow dimples are highlighted by the dashed circle. c Transmission electron microscope (TEM) image of crack bridging by nanoscale twins. Main crack is indicated by an arrow, and interfacial cracks (ICs) are marked. d TEM image showing the region ahead of a growing crack tip and TBs that appear highly dislocated. Dislocation walls are highlighted by the circle (c, d). Li et al. (2016). With kind permission of Cambridge University Press

The contact stiffness, S is continuously recorded during the indentation tests  2β S = √ E R Ac = SC S M π

(9.28)

Ac and ER are the true constant area and the reduced modulus. Equation (9.24) can be expressed as

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9 Fracture in Nano-Structures

Fig. 9.75 TEM bright field micrographs and the corresponding SAD patterns for the as received electrodepossited pure nickel. Sklenicka et al. (2005). Open access

Ac =

π S2 4β 2 E @ R

(9.29)

Knowing, Ac the contact area, the contact depth hc is determined by solving the equaton Ac = f (hc ), where f is the known tip area function 1/4 2 f (h c ) = m 0 h 2c + m 1 h c + m 2 h 1/2 c + m3hc + · · · + mn hc

1−n

=

n 

m i h 2c

1−i

i=0

(9.30) After appropriate substitution h ∗c = h 2c it is possible to calculate the indentation depth, h from the contact depth hc accounting for the elastic sink-in around the indenter: 1−n

9.7 Time Dependent (Creep) Fracture in Nano Structures

479

Fig. 9.76 Stress depeendence of a minimum creep rates, and b times to fracture for eletrodeposited pure nickel (nc-Ni) and its composite. The experimental data for pure electrodeposited nickel with grain size of 30 nm are plotted in (a). Sklenicka et al. (2005). Open access

Fig. 9.77 SEM micrograph of creep fracture surface of electrodeposited pure nickel crept at 473 K and 400 MPa. Sklenicka et al. (2005). Open access

h = hc + ε

P SC S M

(9.31)

where ε is a geometrical constant which depends on the shape of the indenter. For Berkovich indenter it is 0.75. The time derivatives for the indentation and contact depth are ∂h ∂h c and h˙ c = h˙ = ∂t ∂t

(9.32)

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9 Fracture in Nano-Structures

Fig. 9.78 Nanoindentation creep tests results in a Norton-Plot of Ni in a ncand cg-state. The results from some nanoindentation strain-rate jump tests are shown (crossed symbols) in comparison. Maier et al. (2013). With kind permission of Cambridge University Press

Fig. 9.79 Time-and temperature-dependent deformation behavior—results of nanoindentation creep tests for 2 h at RTand 200 °C; equivalent stresses are directly derived from the hardness; nc-Ni. Maier et al. (2013). With kind permission of Cambridge University Press

The creep indentation rates are ·

εc =

· h˙ εc S˙ and ε = ∼ hc S h

(9.33)

The true hardness based on the contact stiffness is given as H=

P 4β 2 E @ R =P Ac π S2

(9.34)

The hardness H is directly related to the flow stress σf at a so-called representative strain using the constraint factor c*. The representetive strain by Berkovich indenter is εrep-Berko = 8%. The flow stress at this strain called in the following equivalent stress is now used for comparing indentation data with macroscopic compression experiments:

9.7 Time Dependent (Creep) Fracture in Nano Structures

  H = c∗ σ f εrep-Berko = 8%

481

(9.35)

The steady state creep rate is applied stress dependent as ε˙ = K σ n = K σ 1/m

(9.36)

where n is the stress exponent, m the strain-rate sensitivity and K is a constant. Substituting the flow stress with hardness of Eq. 9.35, one obtains ∂ln H 1 ∂lnσ ∼ = ∂ln ε˙ ∂ln ε˙ n  √ ∂ln ε˙ A = 3 3kT ∂H

m=

(9.37) (9.38)

Thus, the local strain-rate sensitivity m and stress exponent n, respectively, can be determined from the slope of the logarithmic plot of the hardness versus the strain-rate as seen in Eq. (9.37). In summary, in the dynamic nanoindentation mehod the contact stiffness and thus the contact area are continuously recorded which allows measuring the indentation creep. It was performed at RT and 200 °C. The time and temperature dependent behavior of UFG- and nc microstructure Ni were determined.

9.7.4 Creep Fracture in Nano-304L In many situations where the evaluation of the mechanical behavior of material (specially new alloys) is limited to small size specimens, development of design and test methods is necessary. This is particularly essential for the determination of the creep behavior of a sample material. The small punch creep test (SPCT) has the potential to characterize the full uniaxial creep curve (as the specimen is taken to fracture). It is for this reason that the small punch creep test has attracted much interest. For example, small punch creep test (SPCT) has great advantages in practice compared with traditional uniaxial creep test because a small sheet specimen (10 × 10 × 0.5 mm) can be obtained from in-service facilities or mechanical components without damage. SPCT plots for the 316L austenitic SS at 650, 675 and 700 °C are shown in Fig. 9.80. The plots are similar to the conventional uniaxial creep test and the three creep stages are observed. The third stage creep-known as the tertiary-stage-marks the final fracture at rupture time tr . It is seen in the figure that the applied load changes the shape of the curves in a similar manner as the uniaxial creep test. Also it can be observed that the length of the secondary-creep stage and rupture time tr decrease as the testing load increases. The morphology of SP is shown in Fig. 9.80a, b for

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9 Fracture in Nano-Structures

Fig. 9.80 Curves of SP creep test for steel tested at: a 650, b 675 and c 700 °C. Saucedo-Muñoza et al. (2015). Open access

the specimens tested with a load of 234 N at 650 and 700 °C, respectively. The fracture occurred along the circumference of the hemispherical specimen surface where the equivalent strain is the largest. The failure morphology for the tested steel, corresponding to Fig. 9.81a, b, is shown in Fig. 9.82a, b, respectively. The photographs represent SP creep test ruptured specimens. The failure is intergranular

Fig. 9.81 SEM photographs of SP creep test specimens after testing at: a 650 and b 700 °C with a load of 234 N. Saucedo-Muñoza et al. (2015). Open access

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483

Fig. 9.82 SEM photographs of the failure morphology of small punch creep after testing at: a 650 and b 700 °C with a load of 234 N. Saucedo-Muñoza et al. (2015). Open access

and occurred through the grain boundaries. The small reduction in thickness suggest a low ductility of the specimen tested at 650 °C, while the specimen tested at 700 °C at 234 N (b), occurred in a ductile intergranular manner. This type of failure mode was observed also at 675 °C, irrespective to the load applied. The creep rate, δ versus time is shown in Fig. 9.83 (a). The minimum SP creep rate decreases with decrease in load as seen in (b). The microstructures of the as-received 316 SS and after the creep test are illustrated in Fig. 9.84. The precipitates mainly in the grain boundaries are carbides (Cr23 C6 carbide) resulting from aging at the test temperatures. From the slope of Fig. 9.85 (a) the exponent can be determined (the plot is the SP creep rate δ˙ against stress; in the plot it is the testing load, F). The value of n obtained is ~4.7. Clearly in conventional creep test it is the strain rate, ε˙ and the stress σ which are used for the determination of n. Thus. instead the conventional (the power law) creep rate given as,  Q ε˙ = A0 σ n ex p − RT

(9.39)

we write

Fig. 9.83 Plots of the: a SP creep rate and b testing load versus time for steel tested at 650 °C. Saucedo-Muñoza et al. (2015). Open access

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Fig. 9.84 SEM micrographs of a the as-received steel; the specimens after testing at b 650 and c 700 °C with a load of 234 N. Saucedo-Muñoza et al. (2015). Open access

δ˙ = A S P F 4.7

(9.40)

As known n values in the range 3–5 indicate creep deformation by grain boundary sliding. It is thus SP creep rupture in 316 type SS is controlled by grain boundary sliding. In Fig. 9.85 (b) a log–log plot of the SP creep rate and the time to rupture is shown; it is linear and given as log tr + C log ε· = K

(9.41)

C and K are constants. The temperature dependence of the SP creep tests at loads of 199 and 234 N is shown in Fig. 9.85c and from the slope an apparent activation energy is determoned as ~175–205 kJ mol−1 . The lattice and grain boundary diffusion reported are 250 and 160–200 kJ mol−1 , respectively. It seems thus, that the activation energy for SP creep (tests at 650, 675 and 700 °C) is grain boundary sliding controlled because of the similarity to the GB diffusion value. This is also supported by the n value of SP creep which is close to 5 (namely 4.7).

9.7 Time Dependent (Creep) Fracture in Nano Structures

485

Fig. 9.85 Plots of the SP creep rate versus a testing load, b time to rupture and c inverse of temperature. Saucedo-Muñoza et al. (2015). Open access

9.7.5 Creep Fracture in Nano-Alumina/SiC Often pure substances of interest like here, is not readily available and it is even doubtful if they ever have been in the focus of interest. Nano alumina is one of theses materials. The reason must be because its importance in industry either as a reinforcing agent in metals, or the need to improve its properties by adding reinforcing agents to form composites. One such reinforcing agent of alumina to enhance its properties is SiC; Al2 O3 /SiC nanocomposites have been investigated, and it was reported that small amounts of SiC significantly enhance the mechanical properties— such as hardness, fracture toughness and fracture strength—of the Al2 O3 matrix at room temperature. The high temperature properties are also affected by SiC addition. In particular, the interest in this section is the effect of SiC on the microstructure and the creep behavior of this composite. Al2 O3 /SiC composites containing 3, 5, 10, 15, and 20 vol% SiC were prepared by mixing alumina and silicon carbide powders, followed by hot pressing at 1740 °C. The mean size of the SiC particles was 200 nm. The microstructure of the reference alumina and the Al2 O3 /SiC composite before the creep test are shown in Fig. 9.86. The creep tests were performed at grains and irregular grain boundaries, which suggests grain boundary sliding as the main deformation mechanism (Figs. 9.87 and 9.88). The creep deformation mechanisms in the Al2 O3 /SiC nanocomposites is expected to be similar to that in the monolithic

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Fig. 9.86 Microstructures of monolithic Al2 O3 and Al2 O3 /SiC nanocomposites prior to the creep tests: a Al2 O3 , b AS3, c AS5, d AS10, e AS15, and f AS20. Parchovianský et al. (2014). With kind permission of Elsevier. Note the numbers following AS are the amounts of the SiC. 75, 150 and 200 MPa as illustrated in Fig. 9.87 in the strain versus time plots of the composites with various SiC and of the reference monolithic alumina. Creep curves of AS10 (10 vol% SiC) at the temperature

9.7 Time Dependent (Creep) Fracture in Nano Structures

487

Fig. 9.87 Creep curves (strain–time plots) of the monolithic Al2 O3 and of the Al2 O3 /SiC composites obtained at 1350 °C, under the applied stress ranging from 75 to 200 MPa. Parchovianský et al. (2014). With kind permission of Elsevier

Fig. 9.88 Creep curves (strain–time plots) of the composite AS10 measured at 1350, 1400, and 1450 °C, under the applied stress ranging from 75 to 200 MPa. Parchovianský et al. (2014). With kind permission of Elsevier

Al2 O3 because grain boundary sliding is one of the principal creep mechanisms of all ceramic materials. Two stress mechanisms seem to control creep in the composite: (a) at low stress grain boundary sliding and (b) at high stress creep is controlled by cavitation and microcracking caused by stress concentration. SEM micrographs of Fig. 9.89 (d) revealed extensive intergranular void formation and cavitation when the SiC content increased from 10 to 20 vol%. In some cases, grain boundary separation was observed as illustrated in Fig. 9.90, and as the consequence of which, premature failure or fracture sets in. The stress exponent n for the nanocomposite Al2 O3 was determined from the slope of the linear fit of the log ε˙ v is logσ plot shown in Fig. 9.91. From the linear fit the values obtained for n are n = 3.4 and n = 3.5 at 1350 °C and 1400 °C, respectively, while at 1450 °C n = 2.6. Values of n = 3 or n = 5 are characteristic for dislocation controlled creep mechanism; the actual values depend if it is dislocation glide or dislocation climb. The SiC particles at grain boundaries

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Fig. 9.89 Microstructures of monolithic Al2 O3 and Al2 O3 /SiC nanocomposites after creep tests obtained at 1350 °C, under applied stresses ranging from 75 to 200 MPa; cavities at grain boundaries and in the triple grain boundary junctions are marked with white arrows. a Al2 O3 , b AS3, c AS5, d AS10, e AS15, and f AS20. Parchovianský et al. (2014). With kind permission of Elsevier

9.7 Time Dependent (Creep) Fracture in Nano Structures

489

Fig. 9.90 Microstructures of Al2 O3 /SiC nanocomposites after creep tests obtained at 1350 °C, under applied stresses ranging from 75 to 200 MPa; grain boundary separations are marked with white arrows. a AS15 and b AS20. Parchovianský et al. (2014). With kind permission of Elsevier

Fig. 9.91 Steady-state creep rate versus stress plot of the AS10 composite measured in the temperature range between 1350 and 1450 °C, under applied stresses from 75 to 200 MPa. Parchovianský et al. (2014). With kind permission of Elsevier

impede the motion of grain boundary dislocations—which often is associated with grain boundary sliding—by pinning. In conclusion, increasing the volume fraction of SiC in the composite up to 10% increases the creep resistance, but above it the SiC inpairs the creep resistance. The improvement of the creep resistance is attributrd to the pinning of the SiC particles at the grain boundaries and thus inhibiting grain boundary sliding. The consequence is that the strain rate is reduced, but also SiC refines the grain size of the microstructure of the matrix. Altogether the strain size of the composite is reduced with the result of enhanced mechanical properties. It would be of interest to add some observations from an earlier publication on the effect of nano SiC on the alumina matrix. Explicitly, the variation of the fracture strength with the SiC content in the Al2 O3 /SiC nanocomposite is seen in Fig. 9.92. At 5% SiC addition the fracture strength is ~3 times higher than that of the Al2 O3

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Fig. 9.92 The improvement of fracture strength by the nano-size SiC dispersion for the Al2 O3 /SiC nanocomposites. Niihara (1991). Open access

as indicted in Fig. 9.92. The dispersion of SiC in Al2 O3 changed the fracture mode from the transgranular-intergranular to complete transgranular fracture. Further, subgrain boundaries were formed (Fig. 9.93) due to pinning and pile up of dislocation by intragranular SiC particles generating them in the Al2 O3 matrix during cooling down from the sintering temperature by the thermal stresses resulting from the mismatch between alumina and SiC. It seems that the observed refinement of the matrix Al2 O3 grains by SiC dispersion is associated with the sub-grain boundary formation in the matrix grains, which were more extensive after annealing as seen in Fig. 9.94. A summary of the improvement of the composite is listed in Table 9.5. Fig. 9.93 The sub-grain boundaries observed within the Al2 O3 grains for the Al2 O3 /SiC nanocomposite. Niihara (1991). Open access

9.8 Fatigue Fracture in Nano-Structure

491

Fig. 9.94 The further development of sub-grain boundaries by an nealing at 1300 °C for 1 h in air atmosphere for the Al2 O3 /SiC nanocomposite. Niihara (1991). Open access

Table 9.5 Improvement of the mechanical properties observed for the Al2 O3 /SiC nanocomposite. Niihara (1991), Open access Composite systems Toughness (MPam1/2 ) Strength (MPa) Max. operating temperature (°C) Al2 O3 /SiC

3.5 → 4.8

350 → 1520

800 → 1200

9.8 Fatigue Fracture in Nano-Structure 9.8.1 Introduction The static mechanical properties (excluding creep) is strongly grain size dependent. Fatigue is one of the most damaging mechanism in structural materials and as stated earlier about 90% of all fractures occurs by fatigue. Nano scale material is characterized by exceptionally small grain size, and the damage phenomena investigation should be almost at atomic scale. Based on experimental results, the resistance of metals to fatigue crack initiation and propagation is influenced significantly by grain size. Further, it is known form experimental results of microcrystalline metals (>1 μm) that the fatigue endurance limit is reduced by increasing the grain size. On the other hand, a coarser structure can lead to an increased fatigue threshold stress intensity factor range, as well as a decrease in the rate of fatigue crack propagation. The resistance to fatigue is often described by the endurance limit stress (a term used in S–N curves) at or below which fatigue fracture does not occur, while above it samples fracture at or after a certain cycles (if the endurance limit does not exhibit a horizontal line, 106 –107 cycles define it by convention). Surface energy becomes an important part of the total energy because of the high specific surface area of nanomaterials and one has to recall that fatigue fracture is very often if not always surface initiated. Small specimens impose considerable experimental difficulties in

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performing a reliable test, and therefore several specimens must be tested to obtain an acceptable average value.

9.8.2 Fatigue Fracture in Nano-Al/Al2 O3 The set goal of this book as stated in the preface is to consider only pure unalloyed constituents is not achievable practically and albeit undesirable compromises has to be made. As done in some cases in earlier chapters, appropriate alloying agent was added. As is known soft metals such as Al are intentionally alloyed to improve some physical properties, often for advancing the mechanical properties for industrial applications. In the present section reinforcement of Al is via addition of Al2 O3 . The excellent fatigue resistance and other mechanical properties of the Al/Al2 O3 composite made it a potential candidate for various applications on industrial scale. The Al metal matrix nanocomposite (MMNC) was prepared using powder metallurgy technique and extrusion at 600 °C. Various nanocomposites samples with 4, 6 and 8 wt% of Al2 O3 nanoparticles were prepared and pure aluminum was used as reference for comparison. From Figs. 9.95 and 9.96, the relative density and the strength properties versus the wt% Al2 O3 , respectively is apparent that strengthening occurs up to 6% Al2 O3 . Table 9.6 summarized the mechanical properties for the Al/Al2 O3 alloys with different amounts of the reinforcing Al2 O3 including the fatigue strength at 107 cycles. Pure Al data are also included. The stress amplitude versus the number of cycles to failure in the nanocomposite is seen in Fig. 9.97. The fractured surfaces are shown in Fig. 9.98. The amount of dimples—a sign of ductile elongation—decreases with the increase of Al2 O3 beyond 6%, which means

Fig. 9.95 Relative density of various Al/Al2 O3 prepared nanocomposites. Vaghari et al. (2019). Open access

9.8 Fatigue Fracture in Nano-Structure

493

Fig. 9.96 The changes of strength and Vickers micro-hardness of Al/Al2 O3 prepared nanocomposites as a function of wt% of Al2 O3 as reinforcement. Vaghari et al. (2019). Open access

Table 9.6 Mechanical properties of prepared composites. Vaghari et al. (2019). Open access Sample

Yield strength (MPa)

Tensile strength (MPa)

% elongation

σa (MPa)

Fatigue strength at 107 cycles (MPa)

Al-0 wt% Al2 O3

85

120

35

80

32

Al-4 wt% Al2 O3

110

200

31

130

48

Al-6 wt% Al2 O3

155

250

28

165

72

Al-8 wt% Al2 O3

140

220

25

145

67

that embrittlement or rather a decrease in ductile behavior sets in. Micro-cracks are seen in 8 wt% Al2 O3 as in Fig. 9.98d. The voids seen are the obvious locations for the crack development. It is most probable that the reduced strength properties are a consequence of the void formation which eventually leads to crack formation its propagation and the final fracture in the cyclically deformed Al/Al2 O3 nanocomposite. Thus in summary, the results of this experiment indicate that the presence of Al2 O3 nanoparticles up to 6 wt%, enhances the fatigue life of the composite, while higher amounts of Al2 O3 nanoparticles at an 8 wt% level has an adverse effect on the fracture strength of this nanocomposite.

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Fig. 9.97 S–N curves for a Al, b Al-4 wt% Al2 O3 , c Al-6 wt% Al2 O3 and d Al-8 wt% Al2 O3 . Vaghari et al. (2019). Open access

9.8.3 Fatigue Fracture in Nano-Cu Fatigue crack propagation experiments in freestanding Cu films of ~500 nm in thickness was investigated in ambient air and inside a vacuum chamber of a field emission scanning electron microscope (FESEM) and the results are presented below. As generally observed in macro-size materials, here in nano-scale materials also, preceding intrusions/extrusions were formed ahead of the fatigue crack tip and the fatigue crack propagated preferentially through these intrusions/extrusions in the lower stress intensity factor range K. The Cu film was deposited by electron beam evaporation. The crystal orientation map of the as-deposited film is shown in Fig. 9.99. The black lines are grain boundaries. 3 twin boundaries were observed inside the grains. A single side edge notch with a length of roughly 100 μm was introduced to the gage section of the film specimen. Cyclic stress with a sinusoidal wave form was applied at a frequency, f of 10 Hz and the maximum stress, σmax was held at 130 MPa. In situ FESEM images of fatigue crack propagation in vacuum at a stress intensity factor range K ≈ 2.4 MPa m1/2 is illustrated in Fig. 9.100. Before applying the cyclic load, a slip is observed ahead of the notch as seen in Fig. 9.100 (a). When the number of cycles is N = 20 × 103 ,

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Fig. 9.98 Fracture surface of the specimens: a Al, b Al-4 wt% Al2 O3 , c Al-6 wt% Al2 O3 and d Al-8 wt% Al2 O3 . Vaghari et al. (2019). Open access

Fig. 9.99 Crystal orientation map of approximately 500 nm thick Cu film. Kondo et al. (2014). Open access

damage in the form of intrusions/extrusions are observed ahead of the notch root as seen in Fig. 9.100 (b). With increasing number of cycles the damage increases and the intrusions/extrusions growth larger as seen in Fig. 9.100 (c). At a later stage at 9.0 × 103 new intrusions/extrusions are formed ahead of the crack tip as seen in (d). The process repeats at the same scheme, namely formation of intrusions/extrusions ahead of the fatigue crack tip, crack propagation through these intrusions/extrusions as seen in (e) and (f). This fatigue crack propagation behavior is similar to that in the

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Fig. 9.100 Sequential FESEM snapshotsof fatigue crack propagation at K ≈ 2.4 MPa m1/2 . Kondo et al. (2014). Open access

low-Kmax region in air. As K increased to ≈ 4.1 MPa m1/2 , no intrusions/extrusions were observed near the crack tip and instead slip limes formed ahead of the crack tip indicating that this region is plastically strained. This is seen in Fig. 9.101 (a) at N = 2.03 × 105 . Necking occurs in the thickness direction and thus the fatigue crack propagates in tensile fracture mode. The crack length as a function of N, the number of cycles is shown in Fig. 9.102 for both tests, in air and in vacuum under the same condition. (σmax = 130 MPa, R = 0.1, f = 10 Hz and the initial notch length of ~100 μm). Recall the ratio, refers to the minimum stress to the maximum stress. The crack propagates stably in both environments. In both environments, the fatigue crack stably propagated, accelerating slowly and finally fracturing in an unstable manner. The fatigue crack propagation rate, da/dn versus stress intensity factor range, K in both environment is shown in Fig. 9.103. The figure indicates that in vacuum environment the fatigue crack propagation in the low K region is reduced. The fracture surface in vacuum and air is illustrated in Fig. 9.104.

Fig. 9.101 Sequential FESEM sbapshots of fatigue crack propagation in vacuum at K ≈ 4.1– 4.5 MPa m1/2 . Kondo et al. (2014). Open access

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Fig. 9.102 Effects of vacuum environment on a versus N relationship under the same condition. Kondo et al. (2014). Open access. Note B is the thickness

Fig. 9.103 Comparison of da/dN versus K relationship between in air and vacuum. Kondo et al. (2014). Open access

In summary, fatigue crack propagation in free standing film under vacuum is reduced compared with that occurring in air. Intrusions/extrusions are formed ahead of the crack tip, and the fatigue crack then propagates preferentially through these intrusions/extrusions. At large cycles (N = 2.04 × 105 ) slip lines are observed, while the intrusions/extrusions fade out and disappear. The fatigue crack propagation gradually is accelerated and then the specimens finally fractures unstably.

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Fig. 9.104 Fracture surface in air and vacuum. Kondo et al. (2014). Open access

9.8.4 Fatigue Fracture in Nano-Ni 9.8.4.1

Nano-Films

Discussion on electrodeposited nanocrystalline Ni films exposed to cyclic deformation (fatigue) is presented below. The electrodeposited Ni is shown in Fig. 9.105. In this figure the nano microstructure is compared with wrought Ni (CG). The mean grain size of the CG Ni is ~50 μm while that of the NC Ni is 40 nm. Since normalization of the max. stress by the UTS in Fig. 9.106 (b) and the yield stress in Fig. 9.106 (c), it was felt that it might be of interest to illustrate also the static mechanical properties, namely, the UTS and the yield stress as done in Fig. 9.107. The fractured surfaces of the CG and NC samples are illustrated in Figs. 9.108 and 9.109, respectively. In the CG sample the crack initiated at the top growing downward and at each

Fig. 9.105 2 Microstructures a SEM image of wrought nickel, and b TEM image of electrodeposited nickel. Baek and Lee (2011). Open access

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Fig. 9.106 Stresses versus cycles to failure of nanocrystalline nickel and coarse grain nickel under 17 Hz and, R = 0.2; a maximum stress, b normalized by ultimate tensile strength, and c normalized by yield strength. Baek and Lee (2011). Open access Fig. 9.107 Load displacement curves under different loading rate for coarse grain nickel and nanocrystalline nickel. Baek and Lee (2011). Open access

Fig. 9.108 Fractured surface of coarse grain nickel after 2.8 × 105 cycles under 17 Hz, max. stress of 350 MPa and load ratio, R = 0.2. a crack initiation at top and growth; b magnification of B mark in Fig. 5(a). Baek and Lee (2011). Open access

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Fig. 9.109 Fractured surface of nanocrystalline nickel after 3.0 × 105 cycles under 131 Hz, max. stress of 940 MPa and load ratio, R = 0.2. a Total fractured surface; b magnification of B mark and c magnification of C mark in (a) respectively. Baek and Lee (2011). Open access

cycle a striation is formed. In the NC Ni no striation are seen, but crack initiation, growth and final rupture (fracture) is seen in Fig. 9.109 (a). Although the grain size of the crack initiation zone in NC is large so to enable the formation of extrusion and intrusion by persistent slip bands but they are suppressed due to the nanograins. The parallel lines in crack initiation zone Fig. 9.109 (b), look like slip bands formed by dislocation activity as typical in CG metals. Striation is not seen in this NC figure but brittle-like facture surface along the grain boundary is apparent. The stress amplitude versus the number of cycles in high cycle fatigue tests with two different load ratios are seen in Fig. 9.110. It seems in (a) that maximum stress is not a proper parameter for fatigue life of the NC-Ni. The scatter is large. The stress amplitude on the other hand correlates fatigue life well with the cycles to failure. The effect of frequency on fatigue life in NC is shown in Fig. 9.110 (c), which indicates a longer fatigue life at higher frequency. Fatigue strength of NC film can be improved by suppressing fatigue assisted grain growth (Fig. 9.109c) of the NC at the crack initiation stage.

Fig. 9.110 Stress amplitude versus cycles to failure of nanocrystalline nickel. Baek and Lee (2011). Open access

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9.8.4.2

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Grain Size Effect in Nano-Ni

The stress-life fatigue behavior and fatigue crack growth characteristics of pure Ni is presented here as a function of grain size from the nanometer scale to the micron range. The grain structure of the samples is shown in Fig. 9.111. The grain size effect on the resistance to the total fatigue life time in terms of S–N plot is shown in Fig. 9.112. It can be seen the nc-Ni with ~30 nm has a somewhat greater resistance to fatigue than the ufc with 300 nm. The fatigue resistance plot is stress—controlled. The endurance limit of mc-Ni is much below of those of nc and ufc. The variation of the crack length as a function of the number of the fatigue cycles is shown in Fig. 9.113. The variation of the crack growth rate with K, the stress intensity factor range is illustrated in Fig. 9.114. Surprisingly, the micron size Ni shows a slower crack growth rate at a given K than both the ufc Ni or the nc Ni. The variation in fatigue crack growth rate at various ratios with respect to K of nc and ufc Ni is

Fig. 9.111 Micrographs showing the grain structure of a nc Ni, b ufc Ni, and c mc Ni. Hanlon et al. (2003). With kind permission of Elsevier

Fig. 9.112 A comparison of the S–N fatigue response showing the stress range versus number of cycles to failure for the nc, ufc and mc pure Ni. Hanlon et al. (2003). With kind permission of Elsevier

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Fig. 9.113 A comparison of the variation of fatigue crack length as a function of the number of fatigue cycles for mc, ufc, and nc pure Ni subjected to an initial stress intensity factor range of 11.5 MPa m1/2 at R = 0.3 at a fatigue frequency of 10 Hz at room temperature. Hanlon et al. (2003). With kind permission of Elsevier

Fig. 9.114 Variation of fatigue crack growth rate, da/dN, as a function of the stress intensity factor range,

K, for mc pure Ni and for electrodeposited ufc and nc pure Ni at R = 0.3 at a fatigue frequency of 10 Hz at room temperature. Hanlon et al. (2003). With kind permission of Elsevier

shown in Fig. 9.115. The effect of load ratio on the fatigue crack growth in nc and ufc Ni is plotted in Fig. 9.116. Increase in R leads to faster crack growth in both materials over the entire range of K examined. Decreasing the grain size from the mc to the ufc to the nc regime leads to reduction in the extent of crack path tortuosity and fracture surface roughness. The crack paths is shown in Fig. 9.117. The extent of the crack face roughness is significantly reduced in the nano-size regime. It is also seen that the fatigue fracture path is significantly straighter in the nc Ni (~30 nm) compared even to the ufc Ni (recall that the grain size of ufc is ~300 nm). In summary, despite the substantially higher stress controlled fatigue resistance of the electrodeposited nc Ni than the conventional mc Ni, the fatigue crack growth rate is inferior. The meaning of these results is that grain refinement in the nc regime might have a deleterious effect to the resistance of fatigue fracture. But on the other

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Fig. 9.115 Variation of the fatigue crack growth rate, da/dN, as a function of K for pure electrodeposited ufc, and nc Ni at load ratios a R = 0.1, b R = 0.3, and c R = 0.7, at a fatigue frequency of 10 Hz at room temperature. Hanlon et al. (2005). With kind permission of Elsevier

Fig. 9.116 Fatigue crack growth rate as a function of K at different load ratios for nc Ni (upper figure) and ufc Ni (lower figure). Hanlon et al. (2005). With kind permission of Elsevier

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Fig. 9.117 Scanning electron micrographs of mc, ufc, and nc Ni subjected to sinusoidal fatigue loading at initial K values of 10, 6.2, and 8.5 MPa m1/2 , respectively. A cyclic frequency of 10 Hz and load ratio, R = 0.3 were used in all cases. Crack path tortuosity clearly decreases with grain refinement. Images (d) through (f) are higher magnification images of (a) through (c), respectively, and the magnification of (f) is 10 times that of (d) and (e). Hanlon et al. (2005). With kind permission of Elsevier

hand, a beneficial effect of grain size reduction was observed with respect to the total life under stress-controlled fatigue.

9.8.5 Fatigue Fracture in Nano-316L 9.8.5.1

Strain Controlled Fatigue Experiments

Because the lack or limited availability of pure nanosized 304L material, specifically discussing fatigue fracture, a very similar alloy that of 316L was chosen for the subject under consideration. The fatigue experiments were performed by strain controlled tension–compression cyclic deformation. The samples were prepared by surface mechanical rolling treatment (SMRT) to provide a gradient nanostructured surface layer range from 30 to 300 nm. The microstructural features induced by SMRT is shown in Fig. 9.118. The SMRT affected layer is ~500 μm since below this thickness nearly equiaxed austenitic grains are seen. The top region, region I, extending to ~50 μm is composed mainly of nano structure, more specifically of gradient nano structure (GNS) with a high amount of martensitic volume fraction in Fig. 9.118 (b). A sharp decrease in martensite (froom 55% to 17%) and an increase in grain size from ~120 nm to ~260 nm occurs as shown in (c)–(d). The average grain size is ~260 nm and a gradualte decrease in martensite fraction from 17 to 4% occurs in this region (region II). CG areas are formed in Fig. 9.118 (e), region III, and martensite volume

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Fig. 9.118 Cross-sectional EBSD images of the SMRT sample. a Band contrast (BC) image showing the SMRT affected layer. b–d High-resolution IPF maps of the respective areas in (a). e High resolution BC of the outlined area in (a) with arrows indicating slip lines within the austenitic grains. Bottom images show the distribution of BCC—martensite and FCC—austenite. Carneiro et al. (2020). With kind permission of Elsevier

remains low in the CG area. The band contrast (BC) image in (e) shows slip bands (white arrows) formed as a result of high dislocation concentration in the CG grains. The variation of the mean stress during the strain controlled fatigue experiments on the SMRT specimens is shown in Fig. 9.119. The mean stress is compressive and relaxation is also observed. The strain-life fatigue (strain controlled fatigue) curves of the SMRT 316L is compared with the CG (above was indicated that region III contains CG area) ones in Fig. 9.120. The solid line fitting to the experimental data is expressed by the relation 

ε − ε0 N f (9.42) C= 2

ε 2

is the strain amplitude, Nf is the number of cycles to failure and ε0 , ξ and C are fitting constants. Clearly the arrows represent the run-out tests. The stress amplitude as a function of the number of cycles for the SMRT and CG 316 samples is illustrated in Fig. 9.121. The endurance limit of the of the SMRT is ~350 MPa, while that of the CG 316 is lower at a 250 MPa. Also at identical stress amplitude, the SMRT 316

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Fig. 9.119 Variation of mean stress with loading cycles for the strain-controlled fatigue experiments on SMRT 316L SS at selected strain amplitudes. Carneiro et al. (2020). With kind permission of Elsevier

Fig. 9.120 Strain-life fatigue curves for the SMRT and CG 316L SS. Carneiro et al. (2020). With kind permission of Elsevier

SS exhibits a higher fatigue life than than the CG. Fatigue crack—as in almost all cases—is initiared at the surface of the specimen and gradually propagates inward until final fracture, in 316 SS as ductile fracture. An example of such fracture is seen in Figs. 9.122 and 9.123 at two strain amplitudes, respectively. In the figure, extrusion, tangential and radial directions are indicated by ED, TD and RD, respectively. Many

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Fig. 9.121 Stress-life fatigue curves obtained from strain-controlled fatigue experiments on the SMRT and CG 316L SS. Carneiro et al. (2020). With kind permission of Elsevier

Fig. 9.122 Fracture profile of SMRT 316L SS subjected to ε 2 = 0.7%, a 3D optical image of the ε/2 = 0.7% fractured surface showing crack initiation, early crack growth, and final fracture zones. b SEM image near the crack initiation and early crack growth area. Carneiro et al. (2020). With kind permission of Elsevier

initiations sites of cracks at the surface, an early fatigue crack growth are associated with the coalescence of these cracks which lead to fracture. The process of SMRT resulted in enhanced fatigue strength often attributed to the high compressive residual stresses induced by the process. From textbook knowledge, it is evident that compressive stress improves fatigue resistance and even a healing process of cracks sets in. However, the compressive residual stresses are not the only

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Fig. 9.123 Fracture profile of SMRT 316L SS specimen subjected to ε 2 = 0.28%, a 3D optical

ε/2 = 0.28% image of the fracture surface evidencing the crack initiation, crack growth, and final fracture zones. b SEM image of the crack initiation and early propagation areas

contributors to the fatigue resistance improvement. The formation of the nano layer in the SMRT process, more precisely the gradient nano structured surface (GNS), is naturally related to the improved fatigue performance.

9.8.5.2

Stress Controlled Fatigue Experiments

The surface modification by SMRT produces—as indicated in the previous section— a topmost surface with grain sizes in the nanometer scale. The mean grain size of the topmost surface is 30 nm and increases with depth gradually to grain sizes on micrometer scale. The SMRT technique modification of the structure occurs up to a few hundres micrometers. As already noted the fatigue strength of a sample is significantly emhanced compared to the CG sample in both the low- and highcycling fatigue regimes. The improvement of the fatigue behavior (enhancement of the fattigue property) is a consequence of suppressing the initiation of cracks and accommodating plasticity in the location where crack is supposed to form. Austenitic 316L SS—a widely used engineering material in various industries-is used to obtain relevant information on mechanical properties among them that of fatigue fracture. The tests were performed at room temperature under the stress control mode at a frequency of 5 Hz. Plastic deformation and microstructure refinement are clearly revealed in the SMRT surface depth of 500 μm. At 300 μm below the surface, nanoscaled twins (25 nm thickness) with a large number of doslocations are formed as seen in (c). Layer of 800 μm thickness in Fig. 9.124. The grains in the matrix, >400 mm from the surface, remain equiaxed and a large number of dislocations are visible. In Fig. 9.124 (b) a high density of dislocations and tangles are observed in the austenitic region at TEM micrographs characterize in (b)–(g) the microstructure evolution induced by SMRT. S–N curves of SMRT and CG samples are compared in

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Fig. 9.124 a A typical cross-sectional SEM image of the SMRT sample. b–g Bright-field crosssectional TEM observations at different depths as marked in (a). Inserts in (c), (d), and (g) show the corresponding SAED patterns. Twin relationship among the lamellae in (c) is indicated by the inserted SAED patterns. Huang et al. (2015). With kind permission of Elsevier

Fig. 9.125. In this figure S–N SMRT curves are compared with a CG sample and it is obvious that the fatigue strength of the 316L stainless steel is increased significantly by the SMRT treatment concerning the lifetime relative to LCF and HCF regimes. The surface morphologies of the CG and the SMRT samples are compared in Figs. 9.126 and 9.127, respectively. In this illustrations the crack intiation and propFig. 9.125 a S–N curves of different samples. T-SMRT-6 and T-CG denote SMRT-6 and CG samples after a uniaxial tensile strain of 3%, respectively. Solid symbols denote tests continuing to fatigue failure and open symbols for tests terminated without failure after 2 × 106 cycles. Huang et al. (2015). With kind permission of Elsevier

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Fig. 9.126 Surface morphologies of the CG sample tested after different cycles at constant σ/2 = 190 MPa: a 0, b 2 × 104 , c 8 × 104 and d 1.6 × 105 cycles (after fracture). Arrow LD shows the fatigue loading direction. PSB and cracks are marked by open and solid arrows, respectively. Huang et al. (2015). With kind permission of Elsevier

Fig. 9.127 Surface morphologies of the SMRT sample tested after different cycles at constant σ/2 = 330 MPa: a 0, b 1.8 × 105 and c 1.95 × 105 cycles (after fracture). Arrow LD shows the fatigue loading direction. Cracks are marked by solid arrows. Huang et al. (2015). With kind permission of Elsevier

agation are seen at various fatigue stages. Localized persistent slip bands (PSB) seen on the initially smooth surface after 2 × 104 cycles as seen in Fig. 9.126 (b). Increasing the fatigue cycles to 8 × 104 induces microcracks on the surface illustrated at (c), which grow and combine to a large crack which might lead finally to fatigue fracture. The microcracks grow in length along direction perpendicular to the loading direction and coallescence to realize the fracture as shown in the illustration of Fig. 9.126 (d). On the other hand, any PSB or cracks on the SMRT sample surface during cyclic deformation are unchanged even after 1.8 × 105 cycles under constant σ/2

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330 MPa as seen in Fig. 9.127 (a) and (b). But however, after 1.95 × 105 cycles, a large number of macrocracks together with microcracks and slip bands are seen on the surface after fatigue fracture as shown in (c). The slip bands accommodate most of the plastic deformation and provide crack nucleation sites. Whereas it is difficult to detect marteensite in CG samples after fatigue tests, in the SMRT samples deformation induced martensitic grains are detected in the interior after secondary hardening as confirmed by SEM and TEM observations in Fig. 9.128. Clearly, the deformation induced martensite strengthens the matrix of the SMRT sample. Residual compressive stresses were indiuced in the surface layer in the SMRT processed samples as seen in Fig. 9.129. In the figure α and γ refer to martensites and austenite at the topmost samples they reach the maximum values of 1230 MPa and 1520 MPa, respectively which decrease gradually with increasing depth. The values are rather high compared with values obtained by other surface treatments such as shot peening or deep rolling. In conclusion tension–compression fatigue tests performed on GNG (gradient nano grain) surface layer (obtained by SMRT) under the stress-controlled mode show significantly enhanced fatigue strength in both the LCF and th HCF regimes. The gradient nanosurface (GNS) surface layer suppresses the initiation of cracks

Fig. 9.128 a A typical cross-sectional SEM image of the SMRT sample after fatigue at σ/2 = 325 MPa. b Bright- and c dark-field TEM images of the matrix in (a). Inserts in (b) and (c) show the corresponding SAED patterns. Huang et al. (2015). With kind permission of Elsevier

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Fig. 9.129 In-depth residual stress distributions in martensitic and austenitic phases in the as-SMRT sample and the SMRT sample after a uniaxial tension strain of 3% (T-SMRT). Huang et al. (2015). With kind permission of Elsevier

Residual stress (MPa)

512

by accommodating plastic strain amplitude during fatigue resulting in the improved fatigue behavior. Deformation induced martensite also contribute to the better fatigue resistance to fracture.

9.8.5.3

Twinning in Fatigue Experiments—316L

The cyclic (fatigue) and the monotonic strength of 316L SS can considerably be improved by introducing in the nanostuture intensive twinning. The austenitic 316L SS has been subjected to severe plastic deformation by EPAC (equal channel angular pressing) at 423 K up to four passes. After one EPAC pass the microstructure is inhomogeneous as seen in Fig. 9.130 (a) containing mechanical twin bundels within severly deformed matrix. A fragment of the untwinned matrix is shown in Fig. 9.130 (b), wheres in (c) magnified TEM image of nanotwin bundels are seen. In Fig. 9.130 (e) SAD micrograph reveals the split of the diffraction spots, which usually   indicates the presence of twins. The reflections are mirror image with respect of 111 plane   indicating that the band constitue of 111 twin relationship. The twin bundels with nanometer scale twin layer thickness comprises ~60 vol% of the structure. After EPAC with three passes the structure is more uniform as seen in Fig. 9.131 (a). Intersecting elongated twins are seen in (b) having nanometer dimensions in width but in length also. S–N curves of ECAP 316L compared with literature data are shown in Fig. 9.132. With additional ECAP pressing (three pass) the S–N curve shifts upward reaching a value of ~570 MPa, which is much higher than the value of conventionally processed steel. Surface relief on specimens after HCF at σ/2 = 600 and 700 MPa, is seen in Fig. 9.133. The surface markings have the same appearance as the twin bundles shown in Fig. 9.130. Hence it is likely that the fatigue cracks initiate and propagate along the twin boundaries oriented favorably in the plane of the maximum shear stress at 45° to the loading axis and ED of ECAP. Finally, fracture occurs after formation of many disconnected microcracks. The fatigue markings are

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Fig. 9.130 TEM micrographs of the deformation microstructure of 316L steel after 1 ECAP pass at 423 K: a bright field image of a large area composed of a deformed matrix and multiple deformation twin bundles; b enlarged fragment of an untwinned area and c a twinned area; d, e corresponding SAD patterns with zone axes [1 1 2] and [0 1 1]. Ueno et al. (2011). With kind permission of Elsevier

highlighted by SEM on the surface of EPAC samples at σ/2 = 600 MPa in Fig. 9.134 (a) and (b) and at 700 MPa in (c) and (d). Fine slip markings indicate dislocation induced plasticity during cyclic deformation. The interaction between dislocations and twin boundaries may be the reason of twin boundary cracking, the mechanism of which is still obscure. Summarizing the observed result obtained by severe plastic deformation induced by EPAC either by one or three pass application one can state: (a) After one pass the microstructure is nonuniform and bundeles of twins are embedded in the secerely deformed matrix. (b) Much more ubiform structure is obtained and the structure is equiaxed and the grain size formed is 10–40 nm in size. Distinct improvement is

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Fig. 9.131 TEM micrographs of the deformation microstructure of 316L steel after 3 ECAP passes at 423 K: a bright field image of large area showing a reasonably uniform deformation flow pattern aligned with the SD direction on the TD plane; b enlarged fragment showing intersecting twin layers and the formation of equiaxed nanostructure; c twinned area with inserted SAD pattern, which was obtained with a small size aperture, indicated by the circle, showing twinning at nanoscale width; d a fragment of the deformation structure with nanoscale grains and SAD patterns showing diffraction rings typical of polycrystals dominated by large angles of misorientations. Ueno et al. (2011). With kind permission of Elsevier

obtained, and the fatigue strength of the nanostructured 316L is significantly higher than the values acieved in conventional processing methods.

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Fig. 9.132 S–N curves showing the high cycle fatigue properties of SUS 316L stainless steel after ECAP. Reference data are plotted for comparison. Ueno et al. (2011). With kind permission of Elsevier

Fig. 9.133 SEM images showing fatigue markings and microcracks on the surface of SUS 316L stainless steel after 1 ECAP pass and an HCF test at constant Ds/2 = 600 MPa. Microcracks initiate and propagate along twin boundaries. Arrow LA shows the loading axis, which is aligned with ED (extrusion direction). The other ECAP coordinates are also indicated. (SD is shear direction). Ueno et al. (2011). With kind permission of Elsevier

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Fig. 9.134 SEM images showing fatigue markings on the surface of SUS 316L stainless steel after 3 ECAP passes and an HCF test at constant Ds/2 = 600 MPa (a) and (b) and 700 MPa (c) and (d). Arrow LA shows the loading axis, which is aligned with ED. The other ECAP coordinates are also indicated. Ueno et al. (2011). With kind permission of Elsevier

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Index

A Activation energy, 37 Al, 232 α -martensite, 437 Alumina, 229 Al/Al2 O3 , 442 Austenite, 437 Austenitic 316L, 508

F Fatigue, 353 Fatigue fracture, 491 Fatigue fracture in nano-Ni, 498 Flow stress, 420 Fracture, 496 Fracture in nano-Al, 418 Fracture toughness, 453

B Bend test, 171 Bottom-up, 7 Brittle fracture, 416

G Grain boundary sliding, 83, 184, 190, 257, 258, 266, 268, 270, 281, 282, 308, 318, 326, 328, 336, 339, 348, 368, 371, 396, 420, 473, 484–486 Grain size, 432 Grain size effect, 432 Griffith’s theory on fracture, 416 Growth twins in nanocrystals, 69

C Compression, 211 Creep, 257 Compression - 304L, 223 Compression - Cu, 216 Compression in nanostructures, 385 Compression-Ni, 221 Compression test in Nano-Cu, 385 Compressive fracture, 442, 469 Cryorolling, 437 Cu/Al2 O3 composite, 455 Cyclic deformation, 353

D Dimensions, 372 Dimensional specification, 1 Dimples, 453 Dynamic deformation, 181

H Hall-Petch, 418 Hardness, 128 Hardness -nano-Al, 129, 400 Hardness -nano-Cu, 402 Hardness -nano-Ni, 405

I Indentation, 128 Indentation fatigue, 406 Indentation–Hardness, 128, 399 Indentation-Hardness, Nano-Al, 400 Inverse Hall-Petch, 418

© Springer Nature Switzerland AG 2021 J. Pelleg, Mechanical Properties of Nanomaterials, Engineering Materials, https://doi.org/10.1007/978-3-030-74652-0

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520 M Martensite, 437 Molecular-dynamic simulations, 418

N Nano-Al, 129, 232, 400 Nano-Al/Al2 O3 , 442 Nano alumina, 229, 415, 469 Nano-Cu, 402 Nanoindentation, 405 Nano-304L, 437 Nano-Ni, 498 Nanostructure, 221 Nanotwins, 452 Ni nanostructure, 221

O Orowan’s fracture theory, 417

P Planar defect, 58 Partial dislocations, 221

R Reversion annealing, 206, 211, 436, 440, 442

Index S Stainless steel, 509 Static properties, 83 Strain-life fatigue, 506 Strain rate effect, 432 Strain Rate Sensitivity (SRS), 222 Stress controlled fatigue, 508 Stress-strain relation, 84 Stroh model of fracture, 417

T Tensile fracture in nano-Al, 418 Tensile fracture in nano-304L, 437 Tensile fracture in nano-Ni, 427 Tensile stress-strain, 422 Tensile test in Nano-316L, 381 Tension, 202 Tension in nano 304L, 202 Top-down, 7, 8, 16 Twinning, 383, 437, 451 Twinning in fatigue, 512

V Vickers, 130 Vickers hardness, 399