Recrystallization: Types, Techniques and Applications 1536167371, 9781536167375

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MATERIALS SCIENCE AND TECHNOLOGIES

RECRYSTALLIZATION TYPES, TECHNIQUES AND APPLICATIONS

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MATERIALS SCIENCE AND TECHNOLOGIES

RECRYSTALLIZATION TYPES, TECHNIQUES AND APPLICATIONS

KE HUANG EDITOR

Copyright © 2020 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions to reuse content from this publication. Simply navigate to this publication’s page on Nova’s website and locate the “Get Permission” button below the title description. This button is linked directly to the title’s permission page on copyright.com. Alternatively, you can visit copyright.com and search by title, ISBN, or ISSN. For further questions about using the service on copyright.com, please contact: Copyright Clearance Center Phone: +1-(978) 750-8400 Fax: +1-(978) 750-4470 E-mail: [email protected].

NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the Publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book.

Library of Congress Cataloging-in-Publication Data ISBN: HERRN 

Published by Nova Science Publishers, Inc. † New York

CONTENTS Preface

vii

Acknowledgments

ix

Acronyms

xi

Chapter 1

Deformation Microstructure and Recovery Tianbo Yu

Chapter 2

Applying Electron Back-Scattering Diffraction Map Segmentation to Recrystallization Azdiar A. Gazder, Ahmed A. Saleh and Elena V. Pereloma

Chapter 3

Chapter 4

Recrystallization and Grain Growth upon Annealing of Cold Worked Austenitic Stainless Steels Meysam Naghizadeh and Hamed Mirzadeh Modeling of Recrystallization of Commercial Particle Containing Al-Alloys Knut Marthinsen, Ke Huang and Ning Wang

1

45

97

117

vi Chapter 5

Chapter 6

Chapter 7

Contents Recovery and Recrystallization Process in a Commercially Pure Aluminum: The Role of Dissolved Impurities and Analysis by a New Kinetics Theory Hideo Yoshida and Mineo Asano

169

Interaction between Recrystallization and Phase Transformation in High-Strength Steels Chengwu Zheng and Dianzhong Li

261

Numerical Modeling of Recrystallization in a Level Set Finite Element Framework for Application to Industrial Processes M. Bernacki, N. Bozzolo, P. de Micheli, B. Flipon, J. Fausty, L. Maire and S. Florez

285

About the Editor

327

Index

329

Related Nova Publications

335

PREFACE This book focus on the recrystallization behavior of metallic materials. The development of the recrystallization theory has been historically linked to the production of aluminium alloys and steels, which are two types of the most used metallic materials. Further investigations related to recrystallization are now being actively carried out for other metallic materials, such as Ti alloys, Ni-based supper alloys, Mg alloys. This topic has flourished to such a degree that no author can cover all the key aspects and latest developments of recrystallization at an advanced level, a number of well-known specialists have thus been invited to write on the various principal branches. The book is aimed at those pursuing degrees in Materials Science and Engineering, but those studying Mechanical Engineering, Aerospace Engineering, will also find it useful. While principally directed for postgraduates at universities and colleges of technology, the book is also appropriate for experienced research workers who are new to recrystallization, e.g., material processing engineers previously focusing on cold deformation. The latest version of the excellent textbook on recrystallization “Recrystallization and Related Annealing Phenomena” has been recently published in 2017. In preparing this book, the reader should be aware that, in order to avoid significant overlap, it has been necessary to be selective about the content included in it. The latest development on the nature of

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Ke Huang

the deformed state and recovery, which are the precursors of recrystallization, is discussed in Chapter 2. The investigation of recrystallization relies very much on the characterization methods, an overview of the application of EBSD to investigate the mechanisms and/or kinetics of static and dynamic recrystallisation is therefore given in Chapter 3. Chapters 4 and 5 are devoted to illustrate the effect of impurities such as solute and second phase particles on recrystallization, focusing on commercial pure Al alloys and particle-containing Al alloys, respectively. The interaction between recrystallization and phase transformation, which is a relatively new topic, is introduced in Chapter 6. Finally, Chapter 7 is shifted to the numerical modelling of recrystallization in a finite element framework. Each chapter is provided with an abstract and a list of references, which will enable interested readers to skip certain unrelated topics, or delve further into a particular subject. More chapters focusing on recrystallization of more ‘recent’ metallic materials such as Ti alloys, Ni-based superalloys, Mg alloys and high entropy alloys are envisaged at the beginning of the work, but this was unfortunately not realized due to the space limitation. At the time of preparation, our contributors are unfortunately not allowed to freely reproduce classic figures from other scientists for their chapters intended for Nova Science Publishing, which inevitably direct them to use their own figures. Even if my original goals were not completely met, I am still satisfied with-and a bit proud of-the concise form of this book. Prof. Ke Huang State Key Laboratory for Manufacturing System Engineering Xi’an Jiaotong University, P.R. China 30 May 2019

ACKNOWLEDGMENTS I would like to acknowledge the contribution from all authors of the seven chapters, thanks also go to the substantial helpfulness and courtesy of the publisher’s staff. Special mention should be given to my Ph.D. student N.Y. Xi for preparing some of the files. Finally, I am pleased to acknowledge the financial support from the National Natural Science Foundation of China [51805415], Natural Science Basis Research Plan in Shaanxi Province of China [Program No. 2019JM-125], the Fundamental Research Funds for the Central Universities [xzd012019033] and Open Research Fund of State Key Laboratory of High Performance Complex Manufacturing, Central South University [Kfkt2018-04].

ACRONYMS 3D ARB ASSs BC BCC BS CA CR CR CR CT DC DIM DP DR DRX DSC EBSD EBSPs ECAP

three-dimensional Accumulative roll bonding Austenitic stainless steels Band contrast Body-centered cubic Band slope Cellular automata Cold-rolled Cold rolling Convection-reinitialization Cube-twin Direct current Deformation-induced martensite Dual-phase Direct reinitialization Dynamic recrystallisation Differential scanning calorimetry Electron backscatter diffraction Electron back-scattering patterns Equal channel angular pressing

xii ECC ECD EDS ELC FC FCC FE FEM FSP GAM GG GLS GNBs GOS HAADF HAGBs HCP HPT IA IA IDB IDB IPF IQ JMAK KAM LAGBs LEDS LEDS LS LVTM MA MC MC

Acronyms Electron channeling contrast Equivalent circular diameter Energy dispersive spectroscope Extra low carbon Furnace cooling Face-centered cubic Finite element Finite element method Friction stir processing Grain average misorientation Grain growth Global level set Geometrically necessary boundaries Grain orientation spread High-angle annular dark-field High-angle grain boundaries Hexagonal close-packed High pressure torsion Intermediate annealing Intercritical annealing Incidental dislocation boundaries Interconnecting boundary Inverse pole figure Image quality Johnson-Mehl-Kolmogorov-Avrami Kernel average misorientation Low-angle grain boundaries Low energy dislocation structure The low energy dislocation structure Level set Laguerre–Voronoï tessellation Method Mechanical alloying Monte Carlo Monte Carlo Potts

Acronyms MDF MDRX MF MGS MPF ND ODFs OI OM PDE PDRX PF PQ PSN RCSR RD ReX RVEs SADP SEM SFE SPD SPM SPP SRX STEM TBs TD TEM THAGB TRIP TWIP VHN

xiii

Multi-directional forging Metadynamic recrystallization Mean field Limiting mean grain size MultiPhase field The normal direction Orientation distribution functions Oxford Instruments Optical microscope Partial differential equation Postdynamic recrystallization Phase field Pattern quality Particle stimulated nucleation Repetitive corrugation and straightening by rolling Rolling direction Recrystallization Representative volume elements Selected area diffraction pattern Scanning electron microscope Stacking fault energy Severe plastic deformation Sphere packing methods Second phase particles Static recrystallization Scanning transmission electron microscope Twin boundaries The transverse direction Transmission electron microscope Total high-angle grain boundary Transformation induced plasticity Twinning induced plasticity Conversion of hardness

xiv VTM WQ YS

Acronyms Voronoï tessellation method Water quenching Yield strength

In: Recrystallization Editor: Ke Huang

ISBN: 978-1-53616-737-5 © 2020 Nova Science Publishers, Inc.

Chapter 1

DEFORMATION MICROSTRUCTURE AND RECOVERY Tianbo Yu* Department of Mechanical Enigneering, Technical University of Denmark, Kgs. Lyngby, Denmark

ABSTRACT This chapter is devoted to the topics of deformation microstructure and recovery. The conventional notations and understandings of recovery at low strains are briefly reviewed, followed by a presentation of materials and processing parameters controlling recovery and the microstructure-property relationship during recovery. New discoveries on deformation microstructures from the last 30 years are briefly reviewed with focus on face-centered cubic (FCC) metals with high stacking fault energy. The strong effect of microstructure on recovery is exemplified by a presentation of novel dynamic and static recovery mechanisms in ultrafine microstructures. Deformation microstructure not only determines the properties of a deformed metal but also provides the driving force for recovery and recrystallization; recovery competes with recrystallization in restoring *

Corresponding Author’s Email: [email protected].

2

Tianbo Yu microstructure and properties and at the same time facilitates nucleation of recrystallization. Therefore, such topics are important in the design, processing and understanding of novel metals with optimized properties.

Keywords: deformation microstructure, dynamic/static recovery, dislocation, geometrically necessary boundary (GNB), incidental dislocation boundary (IDB), triple junction migration

1. INTRODUCTION Metallic components are typically produced by thermomechanical processing where plastic strain and temperature are key parameters. The processing brings the metal towards an appropriate shape, produces heat, and changes the microstructure of the metal. The deformed microstructure stores a small fraction of the total deformation energy in the form of lattice defects, which greatly alter the mechanical and physical properties of the metal. In the deformed state, the metal has a high stored energy thus a driving force for the deformation microstructure to return to its undeformed soft state. Recovery is the first restoration process taking place in a deformed microstructure. In a collective review (Doherty et al. 1997), it was defined as “all annealing processes occurring in deformed materials that occur without the migration of a high angle grain boundary,” whose misorientation angle is typically larger than 15°. Recovery is a precursor of recrystallization, which is the formation of a new grain structure in a deformed material by the formation and migration of high angle grain boundaries driven by the stored energy in the microstructure. Recovery includes many processes; depending on the materials and processing parameters, such processes may also occur during plastic deformation as dynamic recovery. Dynamic recovery plays an important role during plastic deformation and, together with deformation mechanisms, determines the deformation microstructure.

Deformation Microstructure and Recovery

3

The extensive early work on deformation microstructure and recovery has been reviewed previously by a number of authors (Beck 1954; Bever 1957; Perryman 1957; Friedel 1964; Li 1966; Bever, Holt, and Titchener 1973; Gil Sevillano, van Houtte, and Aernoudt 1980; Nes 1995). Recent reviews can be found in (Niels Hansen and Barlow 2014; Raabe 2014; Humphreys, Rollett, and Rohrer 2017) and the proceedings of the 36th Risø International Symposium on Materials Science (Fæster et al. 2015). The present work starts with a review of old notations and descriptions of recovery (mainly at low strain), and then focuses on new discoveries in deformation microstructures and recovery mechanisms found in heavily deformed metals.

2. RECOVERY OF DISLOCATION STRUCTURES AT LOW STRAINS 2.1. Dislocation Accumulation Plastic deformation of metals takes place predominantly by glide of dislocations on the slip plane, causing the macroscopic strain (Friedel 1964; Hull and Bacon 2001). The stress required to deform the metal increases with increasing strain—the metal work hardened (strain hardened). This is because many generated dislocations are stored in the structure thus become immobile. Plastic deformation is therefore accompanied by an increase in the density of dislocations, which resist further dislocation glide. Annealed metals typically contains a dislocation density of 108 - 1010 m/m3, and this parameter can increase to about 1013 1014 after 10% deformation and continues to increase as the strain increases further. The dislocations represent an energy per unit length; the stored energy of the deformed material is proportional to the dislocation density. Different from slip by dislocation glide, twinning is a characteristic deformation mechanism for face-centered cubic (FCC) metals of low stacking fault energy and hexagonal close-packed (HCP) metals. However,

4

Tianbo Yu

twinning is less common than slip and twin boundaries are stable during recovery. Plastic deformation also produces point defects, i.e., vacancies and interstitials, but most of the point defects typically anneal out quickly after deformation unless the sample is deformed and subsequently stored at a very low temperature. Therefore, we shall in this section only discuss phenomena related to the dislocation structures introduced by plastic deformation.

2.2. Dislocation Annihilation During recovery, dislocation rearrangement occurs by glide, climb and cross slip of dislocations, reducing the stored energy in the metal as a result of dislocation annihilation. A number of annihilation processes have been analyzed in the literature (Friedel 1964; Li 1966) and they depend on many parameters, such as the material, strain level, strain rate, deformation temperature, and annealing temperature and time. Annihilation of dislocations may occur in a number of ways during annealing:   

Dislocations can glide to the sample surface as can be seen from slip steps; Dislocations can interact with a high angle grain boundary and get absorbed; Dislocation pairs with opposite Burgers vectors can annihilate by glide, assisted by climb (edge dislocation) and cross slip (screw dislocation) if they are not on the same slip plane.

These processes reduce the dislocation density in the deformed metal. For simple dislocation arrays, the kinetics of dislocation recovery was analyzed in detail by Li (Li 1966). For a complex dislocation structure, the recovery kinetics is typically found to be close to logarithmic, and it has been expressed as (Borelius, Berglund, and Sjoberg 1952):

Deformation Microstructure and Recovery

dP Q  P   K 0 P exp(  0 ) dt RT

5 (1)

where P is the stored energy (proportional to the dislocation density), t is the annealing time, T is the annealing temperature, R is the gas constant, Q0 is the activation energy at the end of recovery, and the three fitting parameters K0, Q0 and β are associated with the active recovery mechanisms. Similar but slightly different forms have also been suggested initially by Kuhlmann-Wilsdorf (Kuhlmann 1948). Important in these models is that the apparent activation energy (Q0-βP) increases as recovery proceeds (Kuhlmann 1948; Cottrell and Aytekin 1950; Borelius, Berglund, and Sjoberg 1952; Michalak and Paxton 1961; Friedel 1964; Nes 1995; Rath and Pande 2013). The increase of the activation energy is related to the decrease of the stored energy (driving force) during recovery, making it more difficult for recovery to proceed.

2.3. Dislocation Rearrangement There are a large fraction of dislocations in the deformed microstructure that are difficult to annihilate by the above mechanisms. During recovery, these excess dislocations have a tendency to form low energy configurations such as dislocation walls and low angle boundaries, accommodating the lattice curvature imposed by the strain. In these configurations, the dislocations mutually compensate their distortion fields and thus reduce the total elastic energy. For a low angle boundary, it is described by the Read–Shockley equation (Read and Shockley 1950) that the total energy γ increases but the energy per unit dislocation length decreases with increasing density of dislocations in the boundary, i.e., with increasing boundary misorientation angle θ:

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Tianbo Yu

       m 1  ln    ,    m  ( )    m   m   ,   m  m

(2)

where γm is the energy per unit area of a high angle boundary and θm is usually taken as 15°. These excess dislocations therefore tend to form fewer boundaries of higher misorientation angles, i.e., reducing their total energy. A simple case of forming a low angle boundary is termed glide polygonization, which was first demonstrated by Cahn (Cahn 1949), who bent and annealed a single crystal and observed that excess dislocations of one kind distributed on the slip plane will rearrange into low angle boundaries perpendicular to the slip planes upon annealing, thereby reducing the total stored energy. In the general case of deformation of polycrystalline materials, dislocations of different Burgers vectors are generated and some of them remained in the structure. During annealing, these dislocations react and arrange into three-dimensional (3D) structures, where a classic example is a cell structure with a high dislocation density in the cell walls and a low dislocation density in the cell interior. With further annealing, recovery proceeds both in the cell walls and in the cell interior. Cell walls become sharper and sharper by removing dislocation pairs of opposite Burgers vectors through mutual annihilation and rearranging the excess dislocations into low angle boundaries. Such a structure with sharp low angle boundaries and almost dislocation free interior is called a subgrain structure.

2.4. Dynamic Recovery The rearrangement and annihilation of dislocations occur not only during annealing but also in the course of deformation as dynamic recovery. Dynamic recovery is partially thermally activated and

Deformation Microstructure and Recovery

7

stress/strain assisted. It reduces both the energy storage rate and the work hardening rate. For metals of high stacking fault energy, dynamic recovery occurs readily during deformation, forming 3D cell/subgrain structures in the deformed samples (Figure 1).

Figure 1. Montage of a cell structure (in a grain of Cube texture) in the longitudinal section of Al (99.996% purity) after 10% cold rolling.

The organization of the dislocation structure in a deformed sample may be considered as a result of dynamic recovery. Alternatively, this configuration may be interpreted based on the low energy dislocation structure (LEDS) hypothesis (Kuhlmann-Wilsdorf 1989) that dislocations arrange to reduce the energy per unit length of dislocation line. The ability of dislocations to reach their lowest-energy configurations is constrained by a number of factors, including the number of available slip systems, the dislocation mobility (for both glide and climb), and the frictional stress.

2.5. Subgrain Growth The initial size of cells/subgrains depends on the materials and processing parameters, and is in the order of 1 µm. The energy stored in these cell/subgrain boundaries are the driving force for subgrain growth,

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Tianbo Yu

which reduces the stored energy by reducing the boundary area. The growth of subgrains is typically continuous (uniform coarsening, normal subgrain growth) but it can also be discontinuous (non-uniform coarsening, abnormal subgrain growth). Figure 2 shows an example of a subgrain structure in annealed Al with very few dislocations inside subgrains. Migration of subgrain boundaries (Smith and Dillamore 1970; Sandstrom 1977; Nes 1995; Humphreys, Rollett, and Rohrer 2017) is considered as the dominant mechanism for subgrain growth. The mobility of low angle subgrain boundaries is generally lower than that of high angle boundaries, and increases with increasing misorientation angle. However, dislocation boundaries with very low misorientation angles (e.g., below 1°) may have a high mobility, especially under the influence of local residual stresses. Moreover, such boundaries may disappear by continuously reducing their misorientation angle through rotation and coalescence – an alternative mechanism of subgrain growth (Jones, Ralph, and Hansen 1979; Doherty 1980). However, subgrain coalescence is not frequently observed. The kinetics of subgrain growth was commonly analyzed in analogy to grain growth, where a constant activation energy is assumed. Such an analysis neglects an important feature of recovery of a complex dislocation network structure, i.e., the increase of the activation energy during recovery (Kuhlmann 1948; Cottrell and Aytekin 1950; Borelius, Berglund, and Sjoberg 1952; Michalak and Paxton 1961; Friedel 1964; Nes 1995; Rath and Pande 2013). Consequently, many different growth exponents were reported in the literature. It should also be noted that the extent of subgrain growth is often limited due to the onset of recrystallization, thereby making it difficult for the validation of subgrain growth kinetics. A unified coarsening model for deformation microstructures was recently proposed (Yu and Hansen 2016a). The model considers the change of the activation energy as the microstructure coarsens, and was successfully applied to coarsening examples of different structural scales. One example is on subgrain growth as shown in Figure 3, where Q0 is the apparent activation energy at the end of coarsening.

Deformation Microstructure and Recovery

9

Figure 2. A well-defined subgrain structure in the longitudinal section of Al (99.9% purity) produced by 80% rolling and annealing at 255°C for 4 h.

4 Q0 = 176 ± 9 kJ/mol

D (µm)

3

300 oC 325 oC

350 oC 275 oC

2

250 oC

1 10-2

10-1

100

t (h)

101

102

Figure 3. Isothermal subgrain growth kinetics of Al-0.05% Si single crystal channel die compressed by 70% at room temperature. The data were reported in (Y. Huang and Humphreys 2000) and later fitted by the unified coarsening model (Yu and Hansen 2016a).

2.6. Materials and Processing Parameters Recovery depends on many parameters, where important ones are the stacking fault energy, solutes, second phase particles, deformation temperature, plastic strain, strain rate, and annealing temperature.

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Tianbo Yu

2.6.1. Material Properties A key material property is the stacking fault energy, which determines the extent to which a full dislocation dissociates into two partial dislocations, i.e., the width of the stacking fault between two partial dislocations. Therefore, in metals of high stacking fault energy such as Al and Fe, dislocations typically appear as full dislocations, which can easily climb and cross slip, and significant recovery may take place during deformation and annealing. By contrast, in metals of low stacking fault energy such as Cu-Zn brass and Fe-Mn austenitic steel, significant thermal activation is needed for partial dislocations to constrict into full dislocations, and the recovery of the dislocation network can be slow. The species and concentrations of solutes in the material also strongly affect recovery. Solutes may influence recovery in several ways:   

by reducing the stacking fault energy; by pinning dislocations; by pinning dislocation boundaries and thereby reducing their mobility.

Solutes retard dynamic recovery during deformation and stabilize the deformed microstructure. It leads to a higher stored energy in the deformed microstructure but also to a higher recrystallization temperature through solute drag of high angle boundaries. More significant static recovery is therefore usually observed in a solid solution than in a high purity metal. For example, there is a pronounced recovery stage in deformed arsenical Cu (Cu-0.35% As-0.05% P) but not in high purity Cu (99.98% purity) (Clareborough, Hargreaves, and West 1955). Second phase particles in the material can also stabilize the deformation microstructure by pinning dislocations and boundaries. The drag force due to the interaction between particles and boundaries is called Zener drag, which is proportional to the volume fraction of particles and inversely proportional to the particle size.

Deformation Microstructure and Recovery

11

2.6.2. Processing Parameters The deformation temperature is an important processing parameter affecting the recovery behavior. As different metals have different melting points, it is convenient to define a homologous temperature, which is the temperature divided by the melting point (Tm) in Kelvin scale. It follows that room temperature deformation may be considered as warm for Al (T/Tm = 0.49) but cold for Ni (T/Tm = 0.17). When a metal is deformed at a high homologous temperature, dislocations obtain a high 3D mobility and dynamic recovery occurs readily forming sharp subgrain boundaries (dynamic recrystallization may also occur if the temperature is high enough). As a result, subgrain growth becomes the main recovery mechanism for the subsequent static recovery. With decreasing deformation temperature, dynamic recovery is retarded and deformation stored energy is increased. This typically leads to pronounced static recovery during annealing, but recovery may be curtailed by an early onset of recrystallization. The effect of strain rate is similar to that of the deformation temperature. A low strain rate provides longer time for thermal activation during dynamic recovery, thereby facilitating dynamic recovery as in the case of a high deformation temperature. As a result, the combined effect of the strain rate (  ) and deformation temperature (T) can be expressed in the Zener-Hollomon parameter (Z): Z   exp(

Q ) RT

(3)

where Q is the activation energy and R is the gas constant. It should be also noted that a low Zener-Hollomon parameter not only promotes dynamic recovery but also facilities deformation, so that creep and hot deformation require a lower external stress. With increasing plastic strain, dislocations are continuously created, accompanied by dynamic recovery. Subgrains/cells may be formed during deformation with their size decreases continuously with increasing strain. A high stored energy, as in the case of deformation at a low homologous

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Tianbo Yu

temperature, may lead to pronounced static recovery during annealing, but may also cause early nucleation of recrystallization. In special cases where metals are only lightly deformed, the deformation microstructure may be simple and complete recovery may take place during annealing. The annealing temperature also affects the recovery process. A high annealing temperature leads to a high recovery rate. As a number of restoration processes with different activation energy occur during annealing, a change in the annealing temperature will also change the contribution of different restoration processes, including the competition between recovery and recrystallization. A low annealing temperature usually favors recovery since many recovery mechanisms operate at a lower activation energy than that required by recrystallization (Yu, Hansen, and Huang 2012).

2.6.3. Parameter Summary In summary, dynamic recovery occurs much faster than static recovery at the same temperature due to concurrent deformation, i.e., a dynamic microstructure. The parameters affecting dynamic recovery can be analyzed by characterizing the deformation microstructure. Dynamic recovery can be enhanced by increasing the mobility of dislocations and dislocation boundaries and conditions include:   

a high stacking fault energy, a low concentration of solutes and particles, a high deformation temperature.

The rate of dynamic recovery can be also enhanced by increasing the driving force (stored energy) and conditions include:  

a high strain, a high strain rate.

Deformation Microstructure and Recovery

13

Static recovery depends on the materials properties and the deformation microstructure. Static recovery may be enhanced by    

a high stacking fault energy a high stored energy a low concentration of solutes and particles a high annealing temperature

However, the last three parameters also lead to early onset of recrystallization, thereby curtailing the recovery processes. The last two parameters actually often reduce the fraction of stored energy released by recovery.

2.7. Property Change during Recovery The microstructural change during recovery is accompanied by the release of stored energy and changes in physical (e.g., density and electrical resistivity) and mechanical properties (e.g., hardness and flow stress). These changes are typically smaller compared to those taking place in recrystallization.

2.7.1. Release of Stored Energy The release of deformation stored energy during recovery can be measured directly by differential scanning calorimetry (DSC). However, the interpretation of the result is not straightforward since the energy release may take place by different recovery mechanisms, e.g.,   

annihilation of vacancies and dislocations, rearrangement of dislocations into low energy configurations, coarsening of the cell/subgrain structure.

Moreover, precipitation and other phase transformations may also occur during annealing, and a precise relationship between the stored

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Tianbo Yu

energy and the microstructure is difficult to establish. Instead, a simple estimation is often applied assuming all the remaining energy is stored in cell/subgrain boundaries, i.e., the stored energy (per unit volume) Ed can be expressed as 𝐸 = 𝛼𝛾 /𝐷

(4)

where D is the cell/subgrain size, γS is the boundary energy, which depends on the misorientation angle, and α is a geometrical constant depending on the morphology (~3 for an equiaxed 3D structure). The subgrain size can be readily determined by electron backscatter diffraction (EBSD) in a scanning electron microscope (SEM), and the boundary energy can be calculated based on the Read-Shockley equation, i.e., Equation (2), where the boundary misorientation angle is also determined by EBSD. However, it is often found that the stored energy estimated from this type of equations is lower than that measured directly by calorimetry. If a cell/subgrain structure is not formed, e.g., at a very low strain, then the stored energy may be estimated as the product of dislocation density ρ and the average energy per unit length of dislocation line as 𝐸 = 𝜌𝐺𝑏

(5)

where G is the shear modulus and b is the Burgers vector. The dislocation density may be determined by measuring (i) the projected images of dislocations in a thin foil and (ii) the foil thickness in a transmission electron microscope (TEM); alternatively, it may be measured by X-ray line profile analysis (Ungár and Borbély 1996), where certain assumptions are needed in the estimation.

2.7.2. Physical and Mechanical Properties The microstructural changes during recovery leads to a number of changes in the physical and mechanical properties, for example increase of density, decrease of electrical resistivity, decrease of flow stress, and

Deformation Microstructure and Recovery

15

increase of ductility. However, the exact relationship between these properties and the partially recovered microstructure is complex, and these properties are also affected by concurrent phase transformations. Nevertheless, recovery kinetics is commonly analyzed through measurement of the flow stress or hardness (the hardness is easier to measure and is approximately three times the flow stress). The flow stress σ is approximately related to the total dislocation density ρ (including those in cell/subgrain boundaries) as 𝜎 = 𝜎 + 𝛼 𝑀𝐺b 𝜌

(6)

where σ0 is the frictional stress, M is the Taylor factor, and α1 is a constant in the order of 0.2-0.4. An example of recovery in hardness is shown in Figure 4, where cold-rolled commercial purity Al was isothermally annealed at five different temperatures and the hardness shows a quasilogarithmic decay in the recovery range (Yu and Hansen 2016b). During annealing, the flow stress decreases with the decreasing dislocation density. However, this total dislocation density is difficult to measure accurately. An alternative way is therefore to relate the stress to the cell/subgrain size. When the interior dislocations between cell/subgrain boundaries are ignored, the flow stress σ may be expressed in terms of the subgrain size D as 𝜎 = 𝜎 + 𝑘𝐷

(7)

where σ0 is the frictional stress, k is a constant, and m was found to be between 0.5 and 1. Based on the flow stress σ, the extent of recovery R can be defined in terms of the flow stress of the deformed state σd and the flow stress of the fully recrystallized state σr as 𝑅=

(8)

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Tianbo Yu

Consequently, 1-R represents the residual hardening after recovery. By measuring either the stored energy Ed or the residual hardening 1-R during an annealing study, the recovery kinetics may be analyzed based on Equation (1) or other similar kinetics equations.

Figure 4. Hardness as a function of annealing time at the given temperatures for Al (99.5% purity) cold rolled to a true strain of 5.5. The arrow indicates recrystallized states. After (Yu and Hansen 2016b).

3. DEVELOPMENT OF DEFORMATION MICROSTRUCTURES In the last 30 year, extensive studies (Estrin and Vinogradov 2013; Niels Hansen and Barlow 2014; Cao et al. 2018) have been carried out characterizing the detailed deformation microstructure up to an ultrahigh strain. The deformation microstructure is affected by a number of materials and processing parameters, most importantly the crystal structure, the stacking fault energy, the strain, and the deformation temperature. For face-centered cubic (FCC) metals with high stacking fault energies and body-centered cubic (BCC) metals, e.g., Al, Ni and Fe, deformation is typically completely accommodated by dislocation slip (Bay et al. 1992; Niels Hansen 2001; Hughes and Hansen 2004; Niels Hansen and Barlow

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2014), whereas deformation twinning is negligible. Dislocations have a high 3D mobility and can easily cross slip, leading to wavy glide. For FCC metals with low stacking fault energies, full dislocations dissociate into partial dislocations and hence cross slip becomes difficult. As a result, plastic deformation leads to a planar Taylor lattice structure (Kuhlmann-Wilsdorf 1989; Hughes 1993). With an even lower stacking fault energy, for example in Ag and many Cu alloys, deformation twinning becomes an important deformation mechanism (Wang et al. 2010; Cao et al. 2018), supplementing dislocation slip. In this case, dynamic recovery is suppressed due to the low mobility of dislocations. For hexagonal close-packed (HCP) metals, the primary slip systems have the Burgers vectors in the basal plane. However, all of these systems put together only produce four independent slip systems and are not able to accommodate the strain along the direction. Therefore, additional slip/twinning systems are required for a homologous plastic deformation according to the Taylor model (Taylor 1938). Such slip systems can be introduced by changing materials parameters. Although there are some differences in the microstructural evolution of different groups of metals, the trend is similar when the strain in increased. Therefore, in the following, the microstructural evolution with strain will only be discussed for FCC metals with high stacking fault energies.

3.1. Microstructural Evolution Dislocation cells and cell boundaries have been studied for many decades but detailed microstructural characterization in the last 30 years (Bay et al. 1992; Q. Liu, Juul Jensen, and Hansen 1998; Hughes and Hansen 2000; Niels Hansen 2001; Wert, Liu, and Hansen 1997) showed that cell boundaries coexist with planar dislocation boundaries. These extended planar boundaries delineate regions that are further subdivided by cell boundaries (Figure 5). Extended boundaries have their origin in a different range of active slip systems in neighboring regions called cell blocks. Each cell block has been assumed (Kuhlmann-Wilsdorf and

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Hansen 1991; Bay et al. 1992) to deform by four or fewer active slip systems, i.e., falling short of the five required for homologous deformation according to the Taylor model (Taylor 1938). However, a group of cell blocks may collectively fulfill the Taylor criterion. In such a cell block structure (Figure 5), boundaries are therefore classified into two types based on their formation mechanisms (Kuhlmann-Wilsdorf and Hansen 1991; Bay et al. 1992): 



geometrically necessary boundaries (GNBs), which are extended cell block boundaries delineating regions of different slip activities; incidental dislocation boundaries (IDBs), which are cell boundaries formed by mutual trapping of glide dislocations.

The structural morphology changes as the strain increases. After deformation to a high strain, for example by cold rolling, the structure is characterized by extended lamellar boundaries, with interconnecting boundaries and loose dislocations in the region between extended lamellar boundaries. Lamellar boundaries are categorized as GNBs and typically of medium to high angle; interconnecting boundaries are categorized as IDBs and are of low angle. An example of such a microstructure is shown in Figure 6 for heavily cold rolled Al (Yu, Hansen, and Huang 2011). The tracing clearly shows that lamellar boundaries are not perfectly parallel or infinite. Instead, they form triple junctions, which are not in equilibrium conditions. Detailed microstructural observations (Yu, Hansen, and Huang 2011) showed that there are three types of triple junctions in the lamellar structure (Figure 7):   

Y-junctions, each formed by three lamellar boundaries; H-junction pairs, each formed by two lamellar boundaries and an interconnecting boundary between them; r-junctions, each formed by three interconnecting boundaries.

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At an ultrahigh strain, the structural refinement by deformation is counter-balanced by dynamic recovery. The structural morphology generally follows the shape change of the bulk material, for example forming a lamellar structure in rolling and a fibrous structure in wire drawing. For monotonic deformation, elongated structural morphology can be found in the longitudinal section with the aspect ratio depending on materials and processing parameters.

Figure 5. A cell block structure in 5% cold-rolled Al (99.99% purity) viewed in the longitudinal plane. Both GNBs and IDBs are illustrated. Courtesy of Xiaoxu Huang.

Figure 6. A lamellar structure in Al (99.5% purity) cold rolled to a true strain of 5.5. (a) TEM image viewed in the longitudinal plane; (b) tracinging of lamellar boundaries (black) and interconnection boundaries (gray). After (Yu, Hansen, and Huang 2011).

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Figure 7. Illustrations and examples of three types of triple junctions in lamellar structures. (a) A Y-junction formed by three lamellar boundaries (GNBs); (b) two Hjunctions (an H-junction pair) formed by two lamellar boundaries and an interconnecting boundary (IDB) between them; and (c) a r-junction formed by three interconnecting boundaries. Triple junctions are highlighted in bold lines with dihedral angles 2θ indicated. Both Y-junctions and H-junctions are lying close to the rolling plane, whereas r-junctions are oriented almost parallel to the normal direction (ND). After (Yu, Hansen, and Huang 2011).

3.2. Microstructural Parameters Both cell block boundaries at low strains and lamellar boundaries at high strains are GNBs delineating regions with different slip activities, whereas both cell boundaries at low strains and interconnecting boundaries at high strains are IDBs formed by mutual trapping of glide dislocations (Kuhlmann-Wilsdorf and Hansen 1991; Niels Hansen 2001). For both GNBs and IDBs, the average boundary spacing decreases and the average misorientation angle across the boundary increases when the strain is increased (Figure 8). The GNB spacings and misorientation angles evolve much faster than those of the IDBs, indicating different mechanisms controlling their evolution.

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Figure 8. Boundary spacing and misorientation angle in Ni (99.5% purity) deformed by high pressure torsion (HPT) to an ultrahigh strain. (a) Boundary spacing; (b) misorientation angle. Based on data reported in (H. W. Zhang, Huang, and Hansen 2008).

When an ultrahigh strain is achieved, saturation is approached in both boundary spacing and misorientation angle. It has been showed that when Ni (99.5% purity) was deformed by high pressure torsion at room temperature, the GNB spacing reaches about 60 nm and the GNB misorientation angle reaches about 40° (H. W. Zhang, Huang, and Hansen 2008), see Figure 8. During structural refinement, there is a continuous increase in the fraction of high angle boundaries, which at large strain can approach about 60–80%. The evolution in boundary spacing is related to the dynamic recovery processes, whereas the causes behind the evolution of misorientation angle are not only dynamic recovery but also crystal symmetry and creation of new low angle boundaries. Besides the average values of the microstructural parameters, their distributions have been studied extensively by applying a scaling hypothesis (Hughes et al. 1997; Hughes et al. 1998; Godfrey and Hughes 2000). This hypothesis is based on the assumption that similar underlying mechanisms control the formation of deformation microstructures. The scaling hypothesis reduces the amount of tasks in microstructural characterization and provides a general tool for analysis of structural parameters as demonstrated in analyses of the evolution in boundary spacing and angles with increasing strain. The distributions of these parameters at a given state depend on strain, but the scaling hypothesis

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demonstrates that the distributions may be represented by a strainindependent distribution using a scaling parameter either the average boundary spacing or the average misorientation angle at each strain. The distribution functions used when applying the scaling hypothesis have been analyzed theoretically for the misorientation angle distributions (Pantleon and Hansen 2001). It should also be noted that the scaling of GNB misorientation angle breaks down at very high strains when the distribution becomes bimodal as it contains both low and high angle boundaries.

3.3. Orientation Dependence Microstructural subdivision during plastic strain can be significantly affected by the crystallographic orientation of the grain. This has been demonstrated in many single crystal and polycrystal studies (Driver, Juul Jensen, and Hansen 1994; Q. Liu and Hansen 1995; X. Huang and Winther 2007). The cause of this orientation dependence of microstructure has been related to the orientation dependence of slip systems (Winther and Huang 2007). Three different structural types have been identified (X. Huang and Winther 2007; X. Huang and Hansen 1997) relating to the grain orientation (Figure 9): 

 

The type 1 structure is a cell block structure with cell block boundaries (GNBs) aligned approximately with the {111} slip planes (within 10°). The type 2 structure is a cell structure without GNBs. The type 3 structure is also a cell block structure similar to type 1, but the GNBs deviate substantially from the {111} slip planes (>10°).

The orientation dependence of microstructural subdivision leads to different stored energy depending on the local texture. In a study of deforming Al single crystals of three typical rolling texture orientations to a true strain of 1.5 (Godfrey, Hansen, and Jensen 2007), it was found that

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different cell block structures formed in crystals of different orientations and also showed that the stored energy is higher in {112} Copper and {123} S orientations than in {110} Brass orientation. The difference in stored energy is expected to play an important role when the samples are annealed. When the strain is increased during rolling, the three types of microstructures transform to a finely spaced lamellar structure, where most of the cell blocks rotate to various variants of the rolling texture components (Copper, S and Brass) separated by lamellar boundaries on a very fine scale. It was shown that rolling texture components often form wider bands than other texture components (Q. Liu et al. 2002), leading to a texture dependence of the spatial distribution of high angle boundaries. Detailed observations (Xing, Huang, and Hansen 2006) also showed that both the average GNB and IDB misorientation angles are smaller in bands of rolling texture components than in bands of other texture components. This difference in the microstructure leads to a higher stored energy in bands of other texture components. As a result, during subsequent annealing much higher recovery rate was found in bands of other texture components (Xing, Huang, and Hansen 2006). Similar orientation dependence of deformation microstructure and recovery was reported in a study of channel die deformed Al–0.1% Mn crystals (Albou et al. 2011).

Figure 9. Crystallographic orientation of the tensile axis for three types of deformation microstructures.

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4. RECOVERY OF LAMELLAR STRUCTURES AT HIGH STRAINS Classical analyses of recovery are largely based on the activities of dislocations and evolution of cells and subgrains. However, the deformation microstructure after a high monotonic strain (e.g., by rolling or compression) is commonly characterized by a finely spaced lamellar structure with a high fraction of high angle boundaries. The deformation stored energy is stored in these lamellar and interconnecting boundaries, and the recovery of this boundary network is important. Annihilation and rearrangement of dislocations still occur at high strain (Yu, Hansen, and Huang 2012). Due to the small boundary spacings at high strain, however, there are increased dislocation-boundary interactions and decreased dislocation-dislocation interactions. In this section, focus is on novel recovery mechanisms in lamellar deformation microstructures. Recovery is favored in Al in the competition between recovery and recrystallization, and therefore commercial purity Al (99.5% purity) has been chosen as a model material to demonstrate important recovery mechanisms.

4.1. Microstructural Coarsening during Deformation 4.1.1. Removal of Lamellar Boundaries The decrease of the lamellar boundary spacing with increasing strain was found to be much slower than the externally imposed shape change at large strains (Langford and Cohen 1969; Godfrey and Hughes 2000), see the sketch (Figure 10). It follows that there must be a dynamic recovery mechanism removing lamellar boundaries during deformation, counteracting the structural refinement. Such a mechanism has been recently observed experimentally during cold rolling of commercial purity Al (Yu et al. 2014).

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Figure 10. Illustration of the evolution of the boundary spacing measured along the ND. At low strains, the spacing decreases faster than geometrical reduction but at high strains it is slower.

4.1.2. Dynamic Y-Junction Migration As shown in Figure 7a, a Y-junction is a special type of triple junctions connecting three lamellar boundaries. Consequently in a 3D structure, all lamellae are bounded by Y-junctions. In a longitudinal viewing plane, all lamellae are terminated at two Y-junctions as shown in the orientation maps (Figure 11) obtained from electron backscatter diffraction (EBSD) experiments, and the density of Y-junctions can be related to the average lamella length and spacing (Yu, Hansen, and Huang 2011). It can be further seen from Figure 11 that there are many pairs of separated lamellae with similar orientations (similar color in the EBSD orientation map). These configurations are considered as a result of break-up of lamellae followed by Y-junction migration in the bulk interior during deformation (Yu et al. 2014). Direct evidence of Y-junction migration has also been observed during an ex situ study (Yu et al. 2014). In that study, heavily cold rolled Al was initially characterized by EBSD and electron channeling contrast (ECC) imaging in a scanning electron microscope, and then the samples were additionally cold rolled by a small amount of reduction and characterized by EBSD and ECC again. These processes were repeated a few times to follow the microstructural change in the longitudinal/transverse section during further deformation of the lamellar structure. Figure 12a shows the

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evolution of the microstructure in a selected area in the longitudinal section before and after additional rolling with thickness reductions of 5% and 20%. The Y-junction indicated by red arrows migrated along the RD during additional rolling, leading to a decrease of the length of the middle lamella (indicated by black arrows) and an increase of the thickness of the original neighboring lamellae. After 5% additional rolling, parts of two boundaries of misorientation angle ~20° were replaced by a single boundary of misorientation angle 4°. Figure 12b shows another example of Y-junction migration (red arrow) and also an example of break-up of a lamella (yellow arrow). The break-up of the lamella may be caused by localized shear so that two neighboring lamellar boundaries meet each other. This creates a pair of triple junctions, and is typically followed by migration of the triple junction pair away from each other as can be seen in Figure 11.

Figure 11. EBSD orientation maps showing deformation microstructures in an Al (99.5% purity) sample cold rolled to a true strain of 5.5. The maps are colored according to the crystallographic orientation of the transverse direction (TD). Separated pairs of lamellae are marked. (a) In the longitudinal section; (b) in the transverse section. After (Yu et al. 2014).

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Figure 12. EBSD orientation maps showing Y-junction migration observed in the longitudinal section of cold rolled Al (99.5% purity) samples during additional cold rolling. The amounts of additional rolling are indicated within the maps. The two migrating Y-junctions are marked by red arrows, and the corresponding shortening lamellae are marked by black arrows. Boundaries with misorientation angles larger than 2° are shown by white lines, and the misorientation angles of lamellar boundaries forming the migrating Y-junctions are indicated in the sketches. (a) Initial strain 5.5; (b) initial strain 4, where the yellow arrow indicates break-up of the lamella by local shear during deformation. After (Yu et al. 2014).

Dynamic Y-junction migration counteracting the structural refinement during deformation:   

it replaces two lamellar boundaries by one, increasing the lamellar boundary spacing; it removes interconnecting boundaries and dislocations in swept regions, reducing the dislocation density; it may create low angle boundaries due to a texture effect (Figure 12a), reducing the fraction of high angle boundaries.

Dynamic Y-junction migration modifies the microstructure in a continuous manner and its directional feature leads to the retaining of the lamellar morphology. Dynamic Y-junction migration can be enhanced by thermal activation and is stress/strain assisted. Examination of large areas in heavily deformed Al revealed that this mechanism preferentially removes thin lamellae and strongly cancels out the microstructural

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refinement by rolling. It rationalizes many typical features of high strain deformation, for example:    

the average lamellar boundary spacing is reduced but only to a small extent; the average length of lamellae decreases; the fraction of high angle boundaries reaches 60% ~ 80%; the work hardening rate is low.

The configurations shown in Figure 11 are common in deformed lamellar structures, and dynamic Y-junction migration has been observed, e.g., in tantalum deformed by high pressure torsion (Renk, Ghosh, and Pippan 2017) and Ni deformed by accumulative roll bonding (F. Liu et al. 2018). At ultrahigh strains, the lamellar structure often has a tendency to gradually reduce its aspect ratio and become more equiaxed, due to either inhomogeneous shear deformation or enhanced boundary mobility. In this case, dynamic boundary migration loses the directional feature and becomes normal boundary migration (Legros, Gianola, and Hemker 2008; Renk et al. 2014).

4.2. Microstructural Coarsening during Annealing 4.2.1. Microstructural Changes The heavily deformed microstructure contains a high stored energy, serving as the driving force for recovery and recrystallization during annealing. Such a deformation microstructure can be seen in Figure 13a, showing a typical lamellar morphology (Yu, Hansen, and Huang 2013). After annealing below the recrystallization temperature, dislocation annihilation and microstructural coarsening occurred. As shown in Figure 13b, there is an increase in the lamellar boundary spacing and a decrease in the dislocation density, but the lamellar morphology was largely maintained. An important recovery mechanism has been identified

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accounting for this pattern of microstructural change (Yu, Hansen, and Huang 2011).

Figure 13. TEM micrographs showing microstructures in the longitudinal section of Al (99.5% purity) samples. (a) Deformed to a true strain of 5.5; (b) after annealing at 180°C for 1 h. After (Yu, Hansen, and Huang 2013).

4.2.2. Uniform Coarsening by Y-Junction Migration Direct in situ and ex situ TEM observations of thin foils during annealing revealed that the uniform microstructural coarsening is due to thermally activated Y-junction migration. One example is shown in Figure 14, where a Y-junction terminating the middle lamella migrated up during annealing, leading to local increase of the lamellar boundary spacing but maintaining the lamellar morphology. During migration of a Y-junction, there is a strong interaction between attached interconnecting boundaries (i.e., IDBs) and the Y-junction. Figure 15 shows such an example (Yu et al. 2015). The Y-junction in the center of the micrograph (arrowed in Figure 15a) was initially pinned by a neighboring interconnecting dislocation boundary, which was attached to one of the receding lamellar boundaries on the left side of the Y-junction.

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As the Y-junction migrated downwards (Figure 15b), this interconnecting boundary was forced to extend and bow, exerting a large pinning force on the connected lamellar boundary. Four dislocations are visible in this interconnecting boundary, which is sketched in Figure 15j. With further annealing, these four dislocations were unpinned successively from the moving Y-junction (Figure 15b-i). For de-pinning of each dislocation, the incubation time is much longer than the time used for glide. After all of the four dislocations in the interconnecting boundary had been unpinned, the Y-junction migrated further before it stopped near the next set of interconnecting boundaries. Thermally activated Y-junction migration was found to be the key recovery mechanism in heavily deformed Al (Yu, Hansen, and Huang 2011; Yu, Hansen, and Huang 2013), leading to   

an increase of the lamellar boundary spacing, a decrease of the stored energy, a gradual transition from a lamellar to an equiaxed structure.

Uniform coarsening by Y-junction migration is followed by nucleation of recrystallization and growth of nuclei, and therefore it is considered as a recovery mechanism (a high strain counterpart of subgrain growth). This new recovery mechanism involves migration of deformation induced high angle boundaries and is therefore different from recovery taking place in lightly deformed microstructures. The geometry of a Y-junction is important in determining its stability, in particular the spacing D and the dihedral angle 2θ associated with the middle lamella (Figure 7a). Thin lamellae delineated by high angle boundaries have a high tendency to be removed by Y-junction migration due to a high driving force from the grain boundary surface energy. Consequently, thin lamellae of other texture component imbedded in rolling texture components are preferentially removed, leading to sharpening of the rolling texture when a dominant texture variant is present (Mishin et al. 2013). The preferential removal of thin lamellae results in a uniform coarsening and a more symmetric distribution of the lamellar

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boundary spacing, i.e., the skewness of distribution decreases slightly (Yu, Hansen, and Huang 2011).

Figure 14. An example of triple junction migration observed in the longitudinal section of Al (99.5% purity) cold rolled to a true strain of 5.5 and annealed at 120°C for different time intervals, as marked.

Figure 15. Migration of a Y-junction and its lengthy interaction with an attached interconnecting boundary in Al (99.5% purity) cold rolled to a true strain of 4 during annealing at 180°C. The time sequence from 0 to 145.0 s is shown in each micrograph. The arrows in (a) and (b) point to the Y-junction, whose migration was retarded by the attached interconnecting boundary; each small arrow in (c)–(i) points to an interconnecting boundary dislocation which was unpinned after bowing. In the corresponding sketch in (j), lamellar boundaries are shown in bold lines, and the interconnecting boundary is composed of four dislocations, which are shown by thin lines. In the sketch, the big arrow indicates the direction of Y-junction migration, whereas the small arrow indicates the direction of dislocation glide during de-pinning. After (Yu et al. 2015).

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Thermally activated Y-junction migration causes uniform coarsening of deformed lamellar structures in many systems, for example pure and impure Al (T. Huang et al. 2014; Sun, Li, and Hsu 2016), Cu-Ni alloy (Tian et al. 2013), and pure and impure Ni (Y. B. Zhang, Yu, and Mishin 2017; Yu and Hughes 2018). The progress of uniform coarsening leads to the onset of recrystallization. Solutes can increase the recrystallization temperature and thereby enlarge the window for uniform coarsening by Yjunction migration (Yu and Hughes 2018).

4.2.3. Model of Coarsening Kinetics The driving force for recovery coarsening results from the stored energy in the deformed materials, mainly stored in the form of deformation induced boundaries as expressed in Equation (4). The coarsening kinetics may be analyzed by combining this equation with the recovery kinetics equation, i.e., Equation (1). Such a combination leads to (Yu and Hansen 2016a): dD k  k1D exp( 2 ) dt DT

(9)

where k1 is temperature dependent and k2 is a constant, written as

k1  K0 exp(

k2 

 R

Q0 ) RT

(10)

(11)

where D is the boundary spacing, t is the annealing time, T is the annealing temperature, R is the gas constant, γ is the boundary energy, and Q0 is the apparent activation energy at the end of recovery. The three fitting parameters K0, Q0 and β are associated with active recovery mechanisms.

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Equation (9) can be solved with the aid of exponential integrals (Vandermeer and Rath 1990), resulting in the following relationship (D=D0 at t=0) Ei ( 

k2 k )  Ei (  2 )  k1t DT D0T

(12)

where Ei( ) is the exponential integral of the quantity inside the bracket. Equation (12) describes the continuous coarsening of a deformation structure during isothermal annealing. To estimate the model parameters k1 and k2 at one annealing temperature, coarsening data, i.e., (t, D) pairs, are inserted into Equation (12) and a curve of k1 vs k2 is calculated for each (t, D) pair. A maximum convergence point (k2, k1) is then determined manually by superimposing k1 vs k2 curves of all annealing times at that temperature. The model thus gives a fitting of the isothermal coarsening kinetics. When such a procedure is carried out for other temperatures, different convergence points (k2, k1) can be obtained, but the estimated temperature independent constant k2 may vary slightly. Therefore an important subsequent procedure is to use a single average k2 for all temperatures to re-fit the coarsening data. Such a collective fitting can reduce the fitting error significantly, especially for estimating the activation energy Q0 based on Equation (11). Subsequently, the apparent activation energy (Qapp) at any stage of coarsening can be obtained as Qapp  Q0 

k2 R D

(13)

The above coarsening model is considered to be universal for uniform coarsening of deformation microstructures (Yu and Hansen 2016a). It can be applied to both coarse structures, e.g., subgrain growth during annealing of metals deformed to low/medium strains (Figure 3), and fine structures, e.g., grain coarsening in nanocrystalline metals produced by plastic deformation to ultrahigh strains. To ensure a satisfactory accuracy,

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typically three to four annealing temperatures are required, in combination with four to five annealing periods at each temperature.

4.2.4. Kinetics of Y-Junction Migration The kinetics of uniform coarsening via Y-junction migration can also be analyzed based on the above model. For example, it was shown that the coarsening kinetics of heavily deformed Al follows this model (Yu and Hansen 2016a). Based on Equation (12), an average value of k2 = 1.87×10-3 m·K can be obtained and the corresponding coarsening curves by collective fittings are drawn in Figure 16a, showing a good agreement with the experimental data over a time span over four orders of magnitude. The temperature dependence of k1 can be determined by a collective fitting according to Equation (10), and it follows that Q0 = 214±12 kJ/mol. Based on Equation (13), the dependence of the apparent activation energy on the boundary spacing can also be calculated, for example Qapp = 149 kJ/mol at D0 = 0.24 µm. The apparent activation energy increases rapidly at the beginning but slowly at later stages. By combining Equations (12) and (13), one can also derive the time dependence of the apparent activation energy during annealing at different temperatures (Figure 16b). The apparent activation energy increases approximately logarithmically with the annealing time, and at a given annealing time the apparent activation energy increases with increasing annealing temperature. The estimated apparent activation energy Q0 is consistent with the diffusion of Fe in Al, suggesting solute drag as an important rate controlling mechanism. Lower activation energies at early stages of coarsening are related to the heavily deformed microstructure, which provides a high driving force and short-circuit diffusion paths. The model has also been successfully applied to the uniform coarsening of the deformed lamellar structure in commercial purity Ni (Yu and Hughes 2019), showing the apparent activation energy increases during annealing. The increase of the activation energy makes coarsening of deformation microstructure significantly different from grain growth in a fully recrystallized coarse microstructure, where the apparent activation energy is considered to be a constant.

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Figure 16. Recovery kinetics in Al (99.5% purity) cold rolled to a true strain of 5.5. (a) EBSD (solid symbols) and ECC (open symbols) data for the average lamellar boundary spacing during isothermal annealing at 5 different temperatures; (b) the apparent activation energy during recovery coarsening at different temperatures. After (Yu and Hansen 2016a).

4.2.5. Y-Junction Migration and Recrystallization

Figure 17. Sketch showing a continuous increase in the apparent activation energy and a gradual transition in the structural morphology during annealing of a deformed lamellar structure. An example of Y-junction migration is shown in the inset. After (Yu, Hansen, and Huang 2013).

Y-junction migration and recrystallization are both driven by the deformation stored energy and are competing processes during annealing. However, uniform coarsening by Y-junction migration also provides the nuclei for recrystallization. The sketch and example shown in Figure 17 indicate how Y-junction migration gradually transforms the finely spaced lamellar structure to be more equiaxed. At later stages of Y-junction

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migration, the activation energy was found to be similar to that for recrystallization, pointing to a continuous microstructural evolution and a strong effect of solute drag on recovery and recrystallization (Yu, Hansen, and Huang 2013).

CONCLUSION AND OUTLOOK In the last 30 years, detailed microstructural characterization has led to new understandings of the deformation microstructure and recovery processes, especially for metals and alloys deformed to high strains. Quantification and analysis of structural parameters have shown for a variety of metals and processes that the microstructural evolution follows a universal and hierarchical pattern of grain subdivision on multiple length scales by the formation of GNBs and IDBs. The deformation microstructure is free of long range stresses and can be analyzed by the low energy dislocation structure (LEDS) hypothesis. During annealing, recovery shows a quasi-logarithmic kinetics with an increasing apparent activation energy. Recovery mechanisms directly relate to the deformation microstructure, leading to a strong orientation (texture) dependence of recovery; at high strains a finely spaced lamellar deformation structure leads to uniform coarsening by Y-junction migration during deformation and annealing. The new discoveries and understandings of deformation microstructures and recovery processes have been closely linked to the invention and development of advanced microscopic techniques, which enable structural parameters to be quantified with a high accuracy and a high speed. Novel techniques such as those based on high energy X-rays allow nondestructive characterization of bulk samples, allowing 3D in situ observations during deformation and annealing. New techniques have also been developed for chemical analysis and correlating transmission electron microscopy and atom probe tomography. An application of such techniques may lead to break-through in the understanding of the effect of solutes on recovery mechanisms and kinetics. In parallel, modeling and

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simulation techniques have advanced significantly and can now cover several length scales reaching towards the possibility of coupling models over multiple length scales. Further development of in situ characterization techniques provides the possibility for validation and improvement of numerical modelling, and together they are expected to bring new knowledge on deformation and annealing, so that dynamic and static recovery mechanisms and kinetics are better controlled and stronger and thermally more stable metals and alloys can be produced with less energy.

ACKNOWLEDGMENTS This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 788567). The author is grateful to Dr. Niels Hansen for his critical comments.

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Borelius, G, S Berglund, and S Sjoberg. 1952. “Measurements on the Evolution of Heat during the Recovery of Cold-Worked Metals.” Arkiv for Fysik 6 (2): 143–49. Cahn, R W. 1949. “Recrystallization of Single Crystals after Plastic Bending.” J. Inst. Metals 76: 121–43. Cao, Yang, Song Ni, Xiaozhou Liao, Min Song, and Yuntian Zhu. 2018. “Structural Evolutions of Metallic Materials Processed by Severe Plastic Deformation.” Materials Science and Engineering R: Reports 133: 1–59. Clareborough, L, M Hargreaves, and G West. 1955. “The Release of Energy during Annealing of Deformed Metals.” Proceedings of the Royal Society of London Series A-Mathematical and Physical Sciences 232 (1189): 252–70. Cottrell, A H, and V Aytekin. 1950. “The Flow of Zinc Under Constant Stress.” Journal of the Institute of Metals 77 (5): 389–422. Doherty, R.D. 1980. “Nucleation of Recrystallization in Single Phase and Dispersion Hardened Polycrystalline Materials.” In Proceedings of the 1st Risø International Symposium on Metallurgy and Materials Science, edited by N. Hansen, A. R. Jones, and T. Leffers, 57–69. Roskilde, Denmark: Risø National Laboratory. Doherty, R D, D A Hughes, F J Humphreys, J J Jonas, D. Juul Jensen, M E Kassner, W E King, T R McNelley, H J McQueen, and A D Rollett. 1997. “Current Issues in Recrystallization: A Review.” Materials Science and Engineering A 238 (2): 219–74. Driver, J. H., D. Juul Jensen, and N. Hansen. 1994. “Large Strain Deformation Structures in Aluminium Crystals with Rolling Texture Orientations.” Acta Metallurgica Et Materialia 42 (9): 3105–14. Estrin, Y., and A. Vinogradov. 2013. “Extreme Grain Refinement by Severe Plastic Deformation: A Wealth of Challenging Science.” Acta Materialia 61 (3): 782–817. Fæster, S, N Hansen, C Hong, X Huang, D Juul Jensen, O V Mishin, J Sun, T Yu, and Y B Zhang. 2015. 36th Risø International Symposium on Materials Science. IOP Conference Series: Materials Science and

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Engineering. Vol. 89. Roskilde, Denmark: Technical University of Denmark. Friedel, J. 1964. Dislocations. Oxford: Pergamon. Gil Sevillano, J., P. van Houtte, and E. Aernoudt. 1980. “Large Strain Work Hardening and Textures.” Progress in Materials Science 25 (2– 4): 69–134. Godfrey, A, N Hansen, and D J Jensen. 2007. “Microstructural-Based Measurement of Local Stored Energy Variations in Deformed Metals.” Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science 38A (13): 2329–39. Godfrey, A, and D A Hughes. 2000. “Scaling of the Spacing of Deformation Induced Dislocation Boundaries.” Acta Materialia 48 (8): 1897–1905. Hansen, Niels. 2001. “New Discoveries in Deformed Metals.” Metallurgical and Materials Transactions A 32 (12): 2917–35. Hansen, Niels, and Claire Barlow. 2014. “Plastic Deformation of Metals and Alloys.” In Physical Metallurgy, edited by D E Laughlin and K Hono, 5th ed., 1681–1764. Amsterdam: Elsevier. Huang, Tianlin, Chao Li, Guilin Wu, Tianbo Yu, Qing Liu, Niels Hansen, and Xiaoxu Huang. 2014. “Particle Stabilization of Plastic Flow in Nanostructured Al-1 %Si Alloy.” Journal of Materials Science 49 (19): 6667–73. Huang, X., and N. Hansen. 1997. “Grain Orientation Dependence of Microstructure in Aluminium Deformed in Tension.” Scripta Materialia 37 (1): 1–7. Huang, X, and G Winther. 2007. “Dislocation Structures. Part I. Grain Orientation Dependence.” Philosophical Magazine 87: 5189–5214. Huang, Y., and F. J. Humphreys. 2000. “Subgrain Growth and Low Angle Boundary Mobility in Aluminium Crystals of Orientation {110}.” Acta Materialia 48 (8): 2017–30. Hughes, D. A. 1993. “Microstructural Evolution in a Non-Cell Forming Metal - Al-Mg.” Acta Metallurgica Et Materialia 41 (5): 1421–30.

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Hughes, D. A., D. Chrzan, Q. Liu, and N. Hansen. 1998. “Scaling of Misorientation Angle Distributions.” Physical Review Letters 81 (21): 4664–67. Hughes, D. A., and N Hansen. 2000. “Microstructure and Stength of Nickel at Large Strains.” Acta Materialia 48: 2985–3004. Hughes, D. A., Q. Liu, D. C. Chrzan, and N. Hansen. 1997. “Scaling of Microstructural Parameters: Misorientations of Deformation Induced Boundaries.” Acta Materialia 45 (I): 105–12. Hughes, D A, and N Hansen. 2004. “Plastic Deformation Structures.” In ASM Handbook. Hull, D., and D. J. Bacon. 2001. Introduction to Dislocations, Fourth Edition. Oxford: Butterworth-Heinemann. Humphreys, F. J., Anthony D. Rollett, and Gregory S. Rohrer. 2017. Recrystallization and Related Annealing Phenomena. 3th ed. Amsterdam: Elsevier. Jones, A. R., B. Ralph, and N. Hansen. 1979. “Subgrain Coalescence and the Nucleation of Recrystallization at Grain Boundaries in Aluminium.” Proceedings of the Royal Society of London Series AMathematical Physical and Engineering Sciences 368 (1734): 345–57. Kuhlmann-Wilsdorf, D. 1989. “Theory of Plastic Deformation: - Properties of Low Energy Dislocation Structures.” Materials Science and Engineering A 113: 1–41. Kuhlmann-Wilsdorf, D., and Niels Hansen. 1991. “Geometrically Necessary, Incidental and Subgrain Boundaries.” Scripta Metallurgica et Materiala 25 (7): 1557–62. Kuhlmann, Doris. 1948. “Zur Theorie Der Nachwirkungserscheinungen.” Z. Fur Phys. 124 (7–12): 468–81. Langford, G, and M Cohen. 1969. “Strain Hardening of Iron by Severe Plastic Deformation.” Asm Transactions Quarterly 62 (3): 623–38. Legros, Marc, Daniel S. Gianola, and Kevin J. Hemker. 2008. “In Situ TEM Observations of Fast Grain-Boundary Motion in Stressed Nanocrystalline Aluminum Films.” Acta Materialia 56 (14): 3380–93.

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Rath, B. B., and C. S. Pande. 2013. “Recovery of Low-Temperature Flow Stress in Zone-Refined Aluminum Single Crystals.” Acta Materialia 61 (10): 3735–43. Read, W T, and W Shockley. 1950. “Dislocation Models of Crystal Grain Boundaries.” Physical Review 78 (3): 275–89. Renk, O., P. Ghosh, and R. Pippan. 2017. “Generation of Extreme Grain Aspect Ratios in Severely Deformed Tantalum at Elevated Temperatures.” Scripta Materialia 137: 60–63. Renk, O, A Hohenwarter, S Wurster, and R Pippan. 2014. “Direct Evidence for Grain Boundary Motion as the Dominant Restoration Mechanism in the Steady-State Regime of Extremely Cold-Rolled Copper.” Acta Materialia 77 (100): 401–10. Sandstrom, Rolf. 1977. “Subgrain Growth Occurring by Boundary Migration.” Acta Metallurgica 25 (8): 905–11. Smith, C J E, and I L Dillamore. 1970. “Subgrain Growth in High-Purity Iron.” Metal Science 4 (1): 161–67. Sun, Pei Ling, Wan Ju Li, and Wei Chih Hsu. 2016. “Formation of a Dominant Dillamore Orientation in a Multilayered Aluminum by Accumulative Roll Bonding.” Journal of Materials Science 51 (7): 3607–18. Taylor, G I. 1938. “Plastic Strain in Metals.” Journal of the Institute of Metals 62: 307–24. Tian, Hui, H L Suo, O V Mishin, Y B Zhang, D Juul Jensen, and J-C Grivel. 2013. “Annealing Behaviour of a Nanostructured Cu–45 at.% Ni Alloy.” Journal of Materials Science 48 (12). Springer: 4183–90. Ungár, T., and A. Borbély. 1996. “The Effect of Dislocation Contrast on X-Ray Line Broadening: A New Approach to Line Profile Analysis.” Applied Physics Letters 69 (21): 3173–75. Vandermeer, R A, and B B Rath. 1990. “Interface Migration during Recrystallization - the Role of Recovery and Stored Energy Gradients.” Metallurgical Transactions A-Physical Metallurgy and Materials Science 21 (5): 1143–49. Wang, Y. B., X. Z. Liao, Y. H. Zhao, E. J. Lavernia, S. P. Ringer, Z. Horita, T. G. Langdon, and Y. T. Zhu. 2010. “The Role of Stacking

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Faults and Twin Boundaries in Grain Refinement of a Cu-Zn Alloy Processed by High-Pressure Torsion.” Materials Science and Engineering A 527 (18–19): 4959–66. Wert, J. A., Q. Liu, and N. Hansen. 1997. “Dislocation Boundary Formation in a Cold-Rolled Cube-Oriented Al Single Crystal.” Acta Materialia 45 (6): 2565–76. Winther, G., and X. Huang. 2007. “Dislocation Structures. Part II. Slip System Dependence.” Philosophical Magazine 87 (33): 5215–35. Xing, Q, X Huang, and N Hansen. 2006. “Recovery of Heavily ColdRolled Aluminum: Effect of Local Texture.” Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science 37A (4): 1311–22. Yu, Tianbo, and Niels Hansen. 2016a. “Coarsening Kinetics of Fine-Scale Microstructures in Deformed Materials.” Acta Materialia 120: 40–45. ———. 2016b. “Recovery Kinetics in Commercial Purity Aluminum Deformed to Ultrahigh Strain: Model and Experiment.” Metallurgical and Materials Transactions A 47 (8): 4189–96. Yu, Tianbo, Niels Hansen, and Xiaoxu Huang. 2011. “Recovery by Triple Junction Motion in Aluminium Deformed to Ultrahigh Strains.” Proceedings of the Royal Society A 467 (2135): 3039–65. ———. 2012. “Recovery Mechanisms in Nanostructured Aluminium.” Philosophical Magazine 92 (33): 4056–74. ———. 2013. “Linking Recovery and Recrystallization through Triple Junction Motion in Aluminum Cold Rolled to a Large Strain.” Acta Materialia 61 (17): 6577–86. Yu, Tianbo, Niels Hansen, Xiaoxu Huang, and Andy Godfrey. 2014. “Observation of a New Mechanism Balancing Hardening and Softening in Metals.” Materials Research Letters 2: 37–41. Yu, Tianbo, and Darcy A Hughes. 2019. “Strong Pinning of Triple Junction Migration for Robust High Strain Nanostructures.” Philosophical Magazine 99: 869–886. Yu, Tianbo, Darcy A Hughes, Niels Hansen, and Xiaoxu Huang. 2015. “In Situ Observation of Triple Junction Motion during Recovery of Heavily Deformed Aluminum.” Acta Materialia 86: 269–78.

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Zhang, H W, X Huang, and N Hansen. 2008. “Evolution of Microstructural Parameters and Flow Stresses toward Limits in Nickel Deformed to Ultra-High Strains.” Acta Materialia 56 (19): 5451–65. Zhang, Y. B., T. Yu, and O. V. Mishin. 2017. “An Electron Microscopy Study of Microstructural Evolution during In-Situ Annealing of Heavily Deformed Nickel.” Materials Letters 186: 102–4.

In: Recrystallization Editor: Ke Huang

ISBN: 978-1-53616-737-5 © 2020 Nova Science Publishers, Inc.

Chapter 2

APPLYING ELECTRON BACK-SCATTERING DIFFRACTION MAP SEGMENTATION TO RECRYSTALLIZATION Azdiar A. Gazder1,*, Ahmed A. Saleh2 and Elena V. Pereloma1,2 1

Electron Microscopy Centre, University of Wollongong, New South Wales, Australia 2 School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, New South Wales, Australia

ABSTRACT The development and application of new data analysis techniques opens pathways to a more in-depth understanding of the mechanisms underlying recrystallization. This chapter presents an overview of the application of electron back-scattering diffraction to investigate the *

Corresponding Author’s E-mail: [email protected].

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Azdiar A. Gazder, Ahmed A. Saleh and Elena V. Pereloma mechanisms and/or kinetics of static and dynamic recrystallization. Microstructure and micro-texture evolution during recrystallization is detailed by segmenting partially recrystallized EBSD maps into unrecrystallized and recrystallized grain fractions based on the grain orientation spread and other morphological (size/shape) criteria via case studies of low carbon steel, twinning-induced plasticity steel, and Ni-FeNb-C alloy.

Keywords: electron back-scattering diffraction, grain orientation spread, recrystallization, segmentation, threshold

1. INTRODUCTION Cold, warm or hot deformation induces strain incompatibilities between grains that are accommodated by increases in their internal stored energies via the generation of defects such as dislocation tangles, clusters, loops, cells, shear bands and/or stacking faults and deformation twins. This is also accompanied by subgrain formation and leads to the development of boundary bulges, corrugations or serrations (Sakai et al. 2014). The protuberance of serrated grain boundaries is followed by grain rotation of the bulged portion, grain shape changes and/or further slip and deformation twinning effects (Wusatowska-Sarnek, Miura, and Sakai 2002). The driving force for subsequent recrystallization is provided by the stored energy via the elimination of these deformation-induced defects and thereafter, a reduction in the grain boundary area. Thus, the overall magnitude of the driving force for recrystallization is dictated by the dislocation density, (sub)grain size and boundary energy of the deformed microstructure (Doherty et al. 1997). Recrystallization may be defined as the process by which deformed grains are consumed and replaced by the nucleation and/or growth of a new set of defect-free grains and can be broadly classified as discontinuous and continuous types (Humphreys and Hatherly 2004). Discontinuous recrystallization involves the creation of nuclei that subsequently grow into new grains. On the other hand, continuous recrystallization comprises

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recovery (where the defect substructures within deformed grains are eliminated) followed by grain growth. Although nucleation is generally a stochastic process, dislocation clusters, shear bands, precipitates, special boundary types, twins, and/or triple/quadruple junctions within the deformed microstructure serve as preferential local sites for the heterogeneous formation of a new, thermodynamically stable and defect-free structure (Humphreys and Hatherly 2004). Here nucleation is regarded as site-saturated or constant rate types depending on whether it is observed early-on only or it continues throughout the annealing process, respectively. The growth of nuclei into stable grains that consume the deformation microstructure and undergo subsequent polygonization occurs by grain boundary migration and is driven by the material need to reduce its overall boundary area. It follows that boundary mobility dictates the rate of boundary migration and is based on the difference in stored energy as well as the grain orientations on either side of a boundary interface that define its character. Alternatively, recovery competes with the process of nucleation and grain growth as it only involves an internal clean-up of defect substructures without boundary migration (Humphreys and Humphreys 1994, Zaefferer, Baudin, and Penelle 2001, Hutchinson 2012). Recrystallization is also classified as static or dynamic types. The former takes place either during the isothermal or isochronal annealing of previously cold or warm deformed alloys. Its study is based on tracking microstructure evolution as a function of time (isothermal) or temperature (isochronal) increments during annealing. In a similar vein, dynamic recrystallization (DRX) studies involve a sample series subjected to different deformation increments at high temperature, whereas post-dynamic recrystallization studies relate to the processes following high temperature deformation (for example – different holding times after deformation or inter-pass times during hot-rolling). During deformation at high temperature, work hardening and work softening are concurrent. The first results in an increase in dislocation density and stored energy via dislocation generation whereas the second has the opposite effect. Work softening takes place during either: (i) the

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discontinuous dynamic recrystallization of low to medium stacking fault energy (SFE) materials; where new dislocation-free grains nucleate from deformed grains and subsequently grow or, (ii) the continuous dynamic recrystallization (also known as dynamic recovery) of high SFE materials; where new grains appear by subgrain formation and growth (Sellars and McTegart 1966, Humphreys and Haterly 2004). Here the SFE level influences the motion of dislocations and thus the softening phenomena, such that dislocation climb and cross-slip are widely prevalent in high SFE materials but are relatively limited in low SFE materials (Dillamore 1970). Since its inception, electron back-scattering diffraction (EBSD) has been routinely applied to characterize the static and dynamic recrystallization behaviors of a variety of alloys. EBSD is a quantitative/ statistical near-surface scanning electron microscopy technique for orientation measurement and phase analysis of microstructures on a macroscopic to sub-micron or nanometer scale. The basis of the technique involves an incident electron beam rastering over a region of interest at a pre-defined step size and interacting with a sample tilted at 70° to generate electron back-scattering patterns (EBSPs); images of which are collected using an off-axis EBSD detector setup. The EBSPs comprise gnomonic projections of multiple diffracted Kossel cones, also referred to as characteristic Kikuchi bands of primary, secondary and other orders; each of which denote a family of planes. The widths of the Kikuchi bands are proportional to the lattice plane 𝑑-spacing and are related to the lattice parameters of the unit cell. The angles between Kikuchi bands correspond to angles between lattice planes. The intersections of various Kikuchi bands are lattice plane intersections and are equivalent to zone axes (or the common crystal direction shared by two or more lattice planes). It follows that the position of the Kikuchi bands is directly linked to the exact orientation of the diffracting crystal located at a particular point on the sample surface from which it is generated. On the other hand, the width and sharpness of the individual Kikuchi bands denotes the deformed, recovered or recrystallized state of the material. The exact orientation contained in the EBSP is solved by autoindexing the Kikuchi bands via Hough transformation and application of a

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butterfly mask; after which the experimental EBSP is fitted to a simulated EBSP based on the unit cell parameters of the material under observation. Correspondingly, materials in their fully recrystallized state return closer fits to the simulated EBSP whereas deformed materials return higher angles of deviation between the experimental and simulated EBSPs. The samples subjected to isothermal or isochronal annealing at the beginning and end of a series denote deformed and fully recrystallized/ grain growth microstructures, respectively. The samples in-between these extrema comprise partially recrystallized microstructures with unrecrystallised and recrystallized grain fractions. Partially recrystallized microstructures can therefore be thought of as time or temperature –based incremental “snapshots” quantifying the progress of recrystallization such that all their constituent features are subject to changes in size, shape, misorientation and micro-texture via the softening processes operating throughout annealing. Since the sample is titled at 70° during EBSD, the projected electron beam on the sample surface is elliptical with an aspect ratio of ∼2.92 (Schwartz et al. 2009). The beam spread along its major axis reduces the spatial resolution of the EBSD map in the vertical direction. The above coupled with other electron beam-sample interaction issues and hardware limitations means that the characterization of nanometer-sized structures, such as initial nuclei or stacking faults that lead to the formation of annealing twins during the early stages of recrystallization, remain outside the capability of conventional EBSD (Schwartz et al. 2009). It follows that in place of nuclei, recently recrystallized grains can be tracked using the partially recrystallized sample series. In order to study the unrecrystallised and recrystallized fractions individually, partially recrystallized microstructures require segmentation using various statistical methods during the post-processing of EBSD maps. However, the lack of a comprehensive method that consistently distinguishes between the above fractions poses a significant hurdle to furthering our understanding of the complex interplay between them during recrystallization. Consequently, the segmentation of partially

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recrystallized microstructures has only been applied in a limited number of studies to-date as follows. While initial procedures involved single-condition segmentation using image quality (IQ, also known as the pattern quality (PQ) or band contrast (BC)), the band slope (BS) (Tarasiuk, Gerber, and Bacroix 2002) and confidence indices (Alvi, El-Dasher, and Rollett 2003) of the acquired EBSP after Hough transformation, later advances applied various internal misorientation criteria in order to distinguish the residual strain/stored energy content of (sub)grains (Wright, Nowell, and Field 2011). In subsequent studies, multi-condition segmentation (Wu and Juul-Jensen 2008) such as IQ/PQ/BC, internal misorientation, size, shape and boundary criteria have been introduced for partially recrystallized Cu (Field et al. 2007b, Tarasiuk, Gerber, and Bacroix 2002), brass (Tarasiuk, Gerber, and Bacroix 2002), and a variety of Al alloys (Alvi et al. 2003, Alvi, ElDasher, and Rollett 2003, Alvi et al. 2004, Cheong and Weiland 2007, Wu and Juul-Jensen 2008). The IQ/PQ/BC define the average intensity of the Hough peaks (Wright and Nowell 2006, Wright, Nowell, and Field 2011) whereas the BS denotes the average slope of the intensity change between the Hough peaks and their surrounding background (Ryde 2006). In practice, the IQ/PQ/BC and BS are greyscaled and binned to a byte range between 0 (black) to 255 (white). The IQ/PQ/BC is correlated to the work hardening state of the indexed pixels (Tarasiuk, Gerber, and Bacroix 2002) such that structures with elastically distorted lattices, higher density of crystalline defects or residual stresses (typical of deformed or unrecrystallized microstructures) present with blurred Kikuchi band edges, diffused Hough peaks and appear darker with lower IQ/PQ/BC and BS values (Maitland and Sitzman 2007). Conversely, recrystallized grains exhibit sharper Kikuchi band edges, more intense Hough peaks and have higher IQ/PQ/BC and BS values. Consequently, the IQ/PQ/BC are the most commonly used parameters to distinguish between features with varying dislocation density by thresholding the distribution between areas of low and high contrast. In order to accomplish this semi-quantitatively, the thresholding procedure relies on the presence of a clear and specific inversion point

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between individual peaks of the IQ/PQ/BC distribution. For example, in the case of a bimodal distribution, the threshold is conventionally defined as the lowest value between the two distinct peaks. However, it is also more often the case that the IQ/PQ/BC or BS return asymmetric distributions with a single peak; such that the segmentation of unrecrystallized and recovered/recrystallized fractions becomes significantly more difficult. Moreover, the above procedure is heavily dependent on the ability of the EBSD software to correctly index a diffraction pattern and assumes that surface preparation and mapping parameters are consistent over all samples (Choi and Jin 2004, Randle 2009, Kim, Lee, et al. 2013). Another issue with the IQ/PQ/BC and BS parameters is that they are affected by the crystal orientation itself (Kim, Park, et al. 2013) and the pixels at grain boundary interfaces nominally return smaller values as a result of the combined EBSP from a diffracting volume containing contributions from neighboring but differently oriented substructures (Wright, Nowell, and Field 2011). In order to reduce grain boundary effects, the IQ/PQ/BC and BS values of (sub)grains can be averaged such that variations within individual (sub)grains are lost but the ability to compare between (sub)grains is enhanced (Wu et al. 2005, Wright, Nowell, and Field 2011). A crucial parameter that requires definition before the application of any internal misorientation criteria is the critical (sub)grain boundary misorientation angle which in turn, is necessary for computing the pixel based size/area of individual contiguous structures. In general, it signifies that boundary misorientation angle beyond which a dislocation cannot glide through. The critical angle delineates subgrain and grain boundaries such that values below and above it are classified as low and high angle boundaries, respectively. Consequently, a grain denotes a contiguous crystalline area of approximately similar crystallographic orientation bound by high-angle grain boundaries. Alternatively, a subgrain is defined as a localized area within grains whose orientation differs from that of the average grain and is bound by low-angle geometrically necessary boundaries. In the literature, the critical grain boundary misorientation

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angle varies from 7° to 15° such that the exact value used directly affects the result of the internal misorientation criteria. The internal misorientation criteria encompass short or long –range variations in (sub)grain lattice orientation (Kim, Oh, and Lee 2002, Wright and Nowell 2006, Dziaszyk et al. 2010, Wright, Nowell, and Field 2011). Short-range variations comprise in-grain orientation gradients such as the grain average misorientation (GAM) or the kernel average misorientation (KAM) criteria. The GAM is measured as the average misorientation between neighboring pixel pairs in a contiguous subgrain/grain (Alvi et al. 2004). The KAM is the misorientation between the pixel at the centre of a user-defined kernel (whose size is defined by its nth nearest neighbor) and its immediate neighbor pixels at the perimeter of the kernel; all of which must belong to the same (sub)grain (Lehockey, Lin, and Lepik 2000). Both GAM and KAM criteria return values lower than the user-defined critical (sub)grain boundary angle; signifying the localized misorientation gradients within single (sub)grains. The GAM is highly dependent on the step size since its calculation is based on averaging point-to-point misorientations and other studies have found the KAM unsuitable for segmenting unrecrystallized and recrystallized fractions on account of the kernel neighborhood (Wright, Nowell, and Field 2011, Kim, Park, et al. 2013). Alternatively, long-range variations can be represented by the grain orientation spread (GOS) which is calculated as the average misorientation between all pixel pairs in a subgrain/grain (Alvi et al. 2003, Alvi et al. 2004, Cheong and Weiland 2007, Field et al. 2007b). To-date, numerous studies on different material types have shown that the GOS criterion provides the most effective segmentation of unrecrystallized and recrystallized fractions (Mitsche, Poelt, and Sommitsch 2007, Gazder, Saleh, and Pereloma 2011, Wright, Nowell, and Field 2011, Primig et al. 2012, Gazder et al. 2015, Haase et al. 2015, Jedrychowski et al. 2015, Mannan et al. 2016, Chauve et al. 2017, Cross et al. 2017, Athreya et al. 2018).

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The GOS criterion delineates various substructure types as it assigns a single value to all pixels of a particular (sub)grain and enables utilization of the inherent variation in intragranular orientation spread between unrecrystallized and recrystallized fractions. Consequently, grains with higher geometrically necessary dislocation content record larger GOS values within their boundaries and are classified as the deformation substructure (Alvi et al. 2003, Alvi et al. 2004, Cheong and Weiland 2007). By correlating the fraction recrystallized in the EBSD maps to (micro)hardness –based softening estimates and/or JMAK curves (in the case of isothermal annealing (Alvi et al. 2003)), threshold values of GOS = 3° and 6° have been adopted to define the maximum intragranular misorientation cut-off angles for the recrystallized and recovered fractions, respectively (Alvi et al. 2003, Alvi et al. 2004, Cheong and Weiland 2007). The application of EBSD-based segmentation methods typically tend to divide the microstructure into unrecrystallized and recrystallized fractions only. For example, while a threshold value of GOS = 6° was calculated for the recovered substructures in (Cheong and Weiland 2007), further segmentation of the unrecrystallized microstructure into deformed and recovered fractions is usually not undertaken. Although conditional algorithms that delineate between unrecrystallized and recrystallized microstructures by grain morphology -based criteria (Wu and Juul-Jensen 2008) have been developed, they are also not commonly applied. The recrystallized microstructure is usually considered as a whole, with only a few studies applying grain size and morphology –based criteria to delineate it into recently recrystallized and growing grain fractions (for example, Refs. (Gazder et al. 2011, Primig et al. 2012, Gazder et al. 2014)). Furthermore, criteria that distinguish continuous and discontinuous recrystallization are also required. With the above in mind, this chapter presents recrystallization case studies of a body-centered-cubic (bcc) extra low carbon (ELC) steel, a face-centered-cubic (fcc) twinning induced plasticity (TWIP) steel and an fcc Ni-30Fe alloy. The ELC and TWIP steels were statically recrystallized via isothermal and isochronal annealing treatments, respectively, whereas the Ni-30Fe alloy was subjected to dynamic recrystallization.

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2. EBSD MAPPING PARAMETERS AND INITIAL MAP POST-PROCESSING Experimental details on sample processing and conditions of the Fe0.78Cr-0.02C wt.% ELC steel, the Fe-24Mn–3Al–2Si–1Ni–0.06C wt.% TWIP steel and the 69.7Ni-29.8Fe-0.33Nb-0.04C wt.% Ni-30Fe alloy can be found in Refs. (Gazder et al. 2011, Saleh, Gazder, and Pereloma 2011, Mannan et al. 2016). Normal/compression direction–rolling direction (ND/CD–RD) cross-section samples were cut from the middle of all three alloys and mapped using a JEOL JSM-7001F field emission gun–scanning electron microscope fitted with an Oxford Instruments (OI) Nordlys-II(S) EBSD detector operating at 20 kV (ELC steel) or 15 kV (TWIP and Ni30Fe), ~5 nA and 15 mm working distance. In the case of ELC steel, a step size of 0.3 µm was used throughout. For TWIP steel, step sizes of 0.05 µm and 0.4 µm (cold-rolled, CR), 0.125 µm (600°C) and 0.2 µm (all other conditions) were utilized. For the Ni-30Fe alloy, step sizes of 1 μm (ε = 0.23, 0.35, 0.68 and 0.85) and 0.5 μm (ε = 1.2) were used. The initial post-processing of all EBSD maps was undertaken using the OI Channel-5 software suite. The EBSD maps were cleaned by removing wild orientation spikes, filling in zero solutions via cyclic extrapolation up to 6 neighbors. In the case of ELC steel, pseudo-symmetry errors caused by the unusual incidence of Σ13b (27.8°〈111〉) and Σ3 (60°〈111〉) coincidence-site-lattice boundaries were reduced. Any remaining pixelations denoted by negative or zero slopes of the major axis of the fitted equivalent circle ellipsoid were removed based on a shape criterion. Subgrain/grain reconstruction was undertaken using 2° as the minimum misorientation in order to fix the angular resolution limit, reduce orientation noise and retain orientation contrast/texture information. A minimum spatial resolution of 3 times the nominal step size was maintained constant in order to remove map artefacts. In all EBSD maps, subgrain/grain structures are defined by misorientations θ ≥ 2°. Low-angle grain boundaries (LAGBs) are defined as 2° ≤ θ < 15° misorientations whereas high-angle grain boundaries (HAGBs) comprise θ ≥ 15°

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misorientations. In the case of the fcc materials, first order annealing twin boundaries (TBs) are defined as Σ3 = 60° 〈111〉 while second order TBs are defined as Σ9 = 38.9° 〈110〉. The maximum tolerance of the misorientation angle (Δθ) from the exact axis-angle relationship was identified by the Palumbo–Aust criterion (i.e., Δθ ≤ 15° Σ−5/6) (Palumbo and Aust 1990) yielding a tolerance limit of 6° for Σ3 and 2.4° for Σ9 boundaries. All orientation distribution functions (ODFs) (ϕ2 = 0° and 45° sections (ELC steel) and ϕ2 = 0°, 45° and 65° sections (TWIP steel and Ni30Fe alloy)) are depicted using Bunge’s notation.

3. THE EARLY STAGES OF RECRYSTALLIZATION The mechanisms of both static and dynamic recrystallization are discussed and surveyed in greater detail in Refs. (Sakai and Jonas 1984, Doherty et al. 1997, Humphreys and Hatherly 2004, Sakai et al. 2014). Numerous EBSD studies have: (i) confirmed the initiation of discontinuous recrystallization via bulging at grain boundaries in both low (10-30 mJ/m2) and medium stacking fault energy (40-60 mJ/m2) materials, and (ii) correlated the orientations of the recently recrystallized grains with the deformed matrix. Consequently, this section provides two examples of the same for static and dynamic recrystallization. During the static recrystallization of 42% cold-rolled TWIP steel, recent recrystallization events in the form of twins bulging at grain boundaries (Figure 1a, top inset) or within deformed grain interiors (Figure 1a, bottom inset) were detected after annealing at 600°C for 300s when recovery is dominant. The recently recrystallized grain in Figure 1a, top inset exhibits a Σ3 (60° 〈111〉) relation with the top grain and a ~Σ3 (59° 〈323〉) with the bottom grain. Since the latter boundary is incoherent and mobile, it can migrate and contribute significantly to the recrystallization process. Similar observations of twins bulging at grain boundaries were seen during the recovery of 20% and 50% cold-rolled AISI310 and 20% cold-rolled Nb-stabilised austenitic stainless steels (Jones 1981). The recently recrystallized grains marked 1 and 2 in Figure 1a, bottom inset

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exhibit ~Σ9 (37.3° 〈101〉) and ~Σ3 (58.5° 〈233〉) relationships, respectively, with the deformed matrix. This indicates the evolution of an equiaxed island grain due to a lamellar annealing twin penetrating the deformed matrix as demonstrated by Bystrzycki et al. (Bystrzycki, Przetakiewicz, and Kurzydłowski 1993). Alternatively, based on the in-situ EBSD observations of two types of nuclei with orientations either close to or twin related to the deformed matrix (Field et al. 2007a), it was suggested that twin-related nuclei initially nucleate close to the orientation of the deformed matrix and then the twins proliferate in order to form HAGBs with the matrix. In addition to the nucleation events described above, other cases emphasizing the role of annealing twins were observed after annealing at 700C (Figure 1b, top inset), where grain 1 has an orientation close to the deformed matrix and a Σ3 relation with grain 2 which in turn, possesses a ~ Σ9 (mobile) boundary with the matrix. This is similar to Peters (Peters 1973), where the formation of the first nuclei was suggested to occur by polygonisation with orientations close to the deformed matrix, followed by first and second order twinning upon recrystallization of a 97% cold-rolled Cu-10Sn bronze. During the DRX of Ni-30Fe alloy, the dominant nucleation mechanism at low strains is associated with grain boundary bulging (Figure 2a) and is accompanied by the formation of either dislocation networks, cells and sub-boundaries or annealing twins. The strain accumulation at pre-existing grain boundaries is evident by the concentration of relatively higher intragranular local misorientations along them (Figure 2b). Such local misorientation gradients at grain boundaries create differential pressure across their interfaces resulting in boundary corrugation/serration and bulge formation. The bulging phenomenon is in agreement with the common theory of recrystallization initiating by strain-induced boundary migration (Beck and Sperry 1950, Bailey and Hirsch 1962). The appearance of recently recrystallized grains at higher strains (≥ 0.68) was simultaneous at pre-existing boundaries (see smaller DRX grains

(a)

(b)

Figure 1. Grain boundary maps of TWIP steel isochronally annealed for 300 s at (a) 600°C and (b) 700°C. In (a), the top and bottom insets are magnifications of recently recrystallized grains. The top inset in (b) is a magnification of the recrystallized grain indicated by the dashed arrow. LAGBs = grey, HAGBs = black, Σ3 TBs = red, Σ9 TBs = blue, RD = horizontal. Reprinted with permission from Elsevier, copyright 2011.

(a)

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Figure 2. (a) Band contrast and (b) intragranular local misorientation maps of Ni-30Fe alloy deformed to 0.23 strain at 1075°C. In (a), LAGBs = blue, HAGBs = black, Σ3 TBs = red, white arrows indicate recently recrystallized grains. In (b), green = areas with relatively higher local misorientation. CD = vertical. Reprinted with permission from Elsevier, copyright 2016.

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Figure 3. Magnified band contrast maps of selected regions of interest of Ni-30Fe alloy deformed to true strains of (a) 0.68 and (b) 0.85 at 1075°C. (c-e) Misorientation axis distributions in the crystal coordinate system of the boundaries between the recently recrystallized grains and the unrecrystallized matrix demarcated by white arrows in (a, b) such that (c) corresponds to the rightmost recently recrystallized grain in (a), while (d and e) correspond to the left and right recently recrystallized grains in (b), respectively. In (a, b), LAGBs = blue, HAGBs = black, 60° 〈111〉 Σ3 TBs = red.

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at coarser grains/matrix interfaces in Figures 3a and 3b) as well as within elongated, deformed grains with well-developed interior subgrain structures. At this stage, the 2-3 necklace-like layers of DRX grains form at pre-existing boundaries. Thereafter, contiguous recently recrystallized grains are seen at recrystallized-unrecrystallized grain interfaces when the original nucleation sites are fully occupied (Roberts, Boden, and Ahlblom 1979). The leftmost, second and third arrows in Figure 3a are examples of recently recrystallized grains forming by subgrain rotation; whereby lowangle subgrain boundaries absorb dislocations originating at subgrain interiors and gradually evolve into high-angle boundaries. These three recently recrystallized grains are at an intermediate stage of development compared to the rightmost one; such that the former are partially surrounded by HAGBs whereas the latter is fully enclosed by HAGBs. The boundary of the recently recrystallized grain demarcated by the rightmost white arrow in Figure 3a exhibits a misorientation angle/axis with the unrecrystallized matrix of ~ 38-41° 〈221〉 (Figure 3c) whereas the boundaries of the left and right grains in Figure 3b are ~ 39-45° 〈332〉 (Figure 3d) and ~ 30-34° 〈221〉 (Figure 3e), respectively. The above spread of misorientation angles/axes is close to the commonly reported 30-40° 〈111〉 relationship that favors the growth of Cube-oriented (C, {001}〈100〉) grains during static recrystallization (Hutchinson 2012).

4. MICROSTRUCTURE AND MICRO-TEXTURE EVOLUTION DURING RECRYSTALLISATION 4.1. Static Recrystallization during the Annealing of Warm and Cold –Rolled ELC Steel This case study applies the GOS criterion to track microstructure and micro-texture evolution of (i) 27%, 56%, 73% and, (ii) 26%, 48%, 66% partially recrystallized, warm and cold –rolled ELC steel, respectively

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(Gazder et al. 2011). Thresholding via the GOS criterion was undertaken by tracking the changes in the slope of its normalized cumulative distribution. In most studies, a fixed misorientation threshold is used (which includes the TWIP and Ni-30Fe examples shown here) whereas a constant cut-off criterion is applied to ELC steel. The latter is defined as the value of internal misorientation at which the change in the slope of the normalized cumulative distribution with respect to the origin tends to 1. For example, applying the above cut-off criterion to the 26% partially recrystallized cold-rolled map results in a critical internal misorientation angle  = 0.91°, which is close to the conventionally used 1° denoting a fully recrystallized structure. By employing the above threshold angle, the microstructure is segmented into structures with internal misorientations: (i) above  , (ii) below  but surrounded by substructures whose internal misorientations are above it and (iii) below  . While (i) and (iii) belong to the unrecrystallised and recrystallised fractions respectively, (ii) still contains possibly recrystallized structures surrounded by a highly unrecrystallized matrix. To account for this, a threshold was applied to (ii) via an aspect ratio criterion with a maximum equal to the arithmetic mean plus the standard deviation of the grains of the recrystallized subset. Following this, the average internal misorientation criterion was re-applied to all the subgrains of this fraction with a maximum limit equal to  . The substructures that fulfil both of the above criteria are added to the recrystallized fraction while the remainder belongs to the unrecrystallized fraction. Re-applying the cut-off criterion to the normalized cumulative distribution of the unrecrystallized fraction, subdivides it into recovered (slope < 1) and deformed (slope = 1) grains. Consequently, recovered grains are morphologically similar to deformed grains in terms of their sizes and aspect ratios but possess lower internal misorientation angles. The distinction between extended recovery and continuous recrystallization is based on the character and mobility of the boundaries (Humphreys and Hatherly 2004) such that the former corresponds to softening accompanied by immobile HAGBs whereas the latter involves HAGB migration (Doherty et al. 1997).

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The recrystallized fraction is subdivided into: (i) a recently recrystallized grain fraction with a size range between the map minimum (3×step size in the present case) and the arithmetic mean of the frequency distribution, and (ii) a growing grain fraction with sizes between the mean and the maximum of the frequency distribution. In following this approach, grains with a size advantage over their smaller counterparts at any instance of partial recrystallization are automatically segmented. On further annealing, repeating the above differentiation on a coarsening grain size frequency distribution provides statistical information on the morphology and micro-texture changes between the two grain sets. The inverse pole figure (IPF) maps of partially recrystallized, warm and cold -rolled ELC steel are shown in Figure 4 with the lamellar grains expectedly thinner after cold-rolling due to the extra strip thickness reduction (Figures 4a and 4b). As a result of its higher total dislocation density, the cold-rolled sample contains greater area fractions of in-grain shear bands (typically inclined at 15-35° to RD) that are of greater thickness and intensity compared to the warm-rolled samples. To serve as an example, the 26% partially recrystallized cold-rolled map in Figure 4b was segmented into deformed, recovered, recently recrystallized and growing grain fractions, as shown in Figures 5a-5d. One of the benefits of microstructure segmentation is defining the interface between any two neighboring fractions via double-dilation of the individual subsets. Figure 5e depicts the interface between the unrecrystallized and recrystallized fractions which can then be used to estimate various microstructural parameters as shown below. While the specific interfacial area per unit volume (𝑆 ) is usually estimated from the equivalent circle diameter (𝑆 ~ 3⁄𝑑 ), it can be better calculated from EBSD map data using double-dilation of the map fractions, as mentioned above. For this purpose, the following expression was derived: 𝑆 =

=

∙

(1)

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where 𝐿 is the total interface length, A is the total map area and 𝑓 is the pixel fraction making up the interface. The standard error is calculated for each map by summing the 𝑓 values of the four fractions against the pixel percentage of the recrystallised and unrecrystallised fractions.

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Figure 4. IPF maps of the (a, c, e) warm and (b, d, f) cold -rolled ELC steel partially recrystallized to (a) 27%, (b) 26%, (c) 56%, (d) 48%, (e) 74% and (f) 66%. LAGBs = grey, HAGBs = black and RD = horizontal. Reprinted with permission from Elsevier, copyright 2011.

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(a)

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(e) Figure 5. IPF maps of the 26% partially recrystallized, cold-rolled ELC steel segmented into: (a) deformed, (b) recovered, (c) recently recrystallized and, (d) growing grain fractions. (e) Double-dilation of the recrystallized and unrecrystallised fractions. Reprinted with permission from Elsevier, copyright 2011.

The obvious advantage of double-dilation (Figure 5e) and Eq. (1) to calculate specific 𝑆 is that only the boundary segments at the interface between various grain fractions are taken into account. As seen in Figs. 6a and 6b, the values of 𝑆 decline monotonically due to uniform coarsening in the warm-rolled samples whereas new interfaces form up to 48% recrystallization in the cold-rolled sample. If a qualitative check for the three-dimensional spheroidal growth of the recrystallizing grains is utilized, linearity and non-linearity are observed in the warm and cold rolled samples, respectively (Figures 6(c, d)) (Rios and Padilha 2003, Vandermeer and Juul-Jensen 2003a, b). The non-linearity in Figure 6d qualitatively suggests three-dimensional spheroidal growth during

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discontinuous recrystallization in the cold-rolled samples (Gazder et al. 2011). On the other hand, the continuous decrease in interfacial area (compare Figures 6a and 6b), linear changes in 𝑆 ⁄(1 − 𝑋) versus −𝑙𝑛(1 − 𝑋) (Figures 6c and 6d) and the much higher growth rates (Figures 6e and 6f) provide supporting evidence that continuous recrystallization occurs during the later stages of annealing in the warm-rolled samples. Since the annealing of ELC steel was performed under non-isothermal conditions, a true growth rate cannot be calculated. Nevertheless, apparent growth rates (G) applicable to the various interfaces can be estimated (Bocos et al. 2003) by using the above specific 𝑆 values and adapting the extended Cahn-Hagel approach (Juul-Jensen 1992, 1995): 𝐺=

=

∙

(2)

where, 𝑑𝑋⁄𝑑𝑇 ≃ 0.04 is the slope of the linear second stage of the typical sigmoidal recrystallized fraction versus temperature plot and 𝑑𝑇⁄𝑑𝑡 = 4 × 10 °C ∙ s is the heating rate during annealing. The differences between the apparent growth rates of the various fractions of the warm and coldrolled samples are presented in Figures 6e and 6f. The growth rates of the deformed/recently recrystallized grains interfaces are the highest throughout annealing and accelerates dramatically during the recrystallization of warm-rolled samples. The growth rates of the deformed/growing grains and recovered/growing grains interfaces are also consistently higher in the warm-rolled samples compared to their coldrolled counterparts. The faster growth rates are indicative of HAGBs encountering fewer barriers to their migration across particular recrystallization fronts. While double-dilation enables a better understanding of the processes occurring during recrystallization, three aspects deserve mention. Firstly, when the microstructural features are not approximately parallel to either the local horizontal or vertical axes of the EBSD map, the average inclination angle should be accounted for before computing the total length of the boundary interface. In the present case, since the unrecrystallized

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Figure 6. Evolution of (a, b) specific interfacial area, (c, d) in 𝑆 ⁄(1 − 𝑋) on −𝑙𝑛(1 − 𝑋) and, (e, f) apparent growth rates during recrystallization of (a, c, e) warm and (b, d, f) cold -rolled ELC steel. Reprinted with permission from Elsevier, copyright 2011.

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grains are aligned with the RD = horizontal, this angle has been ignored. Secondly, the specific 𝑆 returned by double-dilation is a strictly localised estimate that only accounts for the pixels between two dissimilar grain fractions. Given that the specific 𝑆 value depends on the percentage of pixels making up the interface in question (Figures 6a and 6b), it follows that further subdivision of the unrecrystallized fraction into deformed and recovered subsets and the recrystallized fraction into recently recrystallized and growing grain subsets results in lower specific 𝑆 values as the percentage of pixels making up those interfaces decreases. Lastly, the choice of the ‘correct’ step size to use with respect to a partially recrystallized map is a critical parameter. Excessively fine step sizes lead to orientation noise in the vicinity of the boundary due to curvature effects whereas too coarse a step size results in inaccurate boundary interface estimates. Figure 7a is a schematic of the ϕ2 = 45° ODF section for rolled and recrystallized bcc steel. To serve as an example, the ODFs of the 26% partially recrystallized cold-rolled map Figure 7b is included along with the deformed, recovered, recently recrystallized and growing grain fractions in Figures 7c-7f. While the micro-texture of the full map comprises the typical α (〈110〉 ||RD) and γ (〈111〉 ||ND) fibres, the differences in the relative strength of the α and γ fibres in the deformed and recovered fractions are of interest. The deformed grain orientations belong mostly to the α-fibre with an intense peak around 112 〈110〉 (Figure 7c), whereas more recovered grain orientations belong to the γ-fibre (Figure 7d) as the stored energies associated with these orientations are higher than those of the α-fibre (i.e., - the γ-fibre orientations more readily undergo recovery). As seen in Figure 7e, during the initial stages of annealing, the recently recrystallized grains are oriented along the γ-fibre and clustered mainly around the 111 〈112〉 orientations. Weaker intensities near the (112) 110 and (001) 110 orientations are also visible. Concurrently, the growing grain fractions resemble their recently recrystallized counterparts as the sharpest intensities remain centered around 111 〈112〉 (Figure 7(f)).

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Figure 7. ϕ2 = 45° ODF sections of the (a) ideal bcc rolling and recrystallization fibres, (b) cold-rolled ELC steel partially recrystallized to 26% along with its (c) deformed, (d) recovered, (e) recently recrystallized and (f) growing grain fractions. Contour levels: 1×. Reprinted with permission from Elsevier, copyright 2011.

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The presence of 111 〈112〉 orientations in the recently recrystallized fraction resembles the recrystallization textures of a Ti-stabilized IF steel. Barnett (Barnett 1998) compared the recrystallization textures of a Ti-IF steel and a 0.22 wt.% Mn-containing LC steel warm-rolled to 65% thickness reduction. In the case of the Ti-IF steel, the recrystallization textures were dominated by the 111 〈112〉 orientation; a feature attributed to the increased density and severity of in-grain shear bands. Conversely, the lack of in-grain shear banding in the Mn-containing LC steel resulted in the absence of the 〈111〉 || ND recrystallization components. It is highlighted that only a limited number of recently recrystallized grains were noted at the shear bands in the ELC steel samples. Thus, shear bands alone cannot account for the 111 〈112〉 orientations of the recently recrystallised grains. The more plausible explanation for the appearance of these orientations is based on an annealing study conducted by Barnett and Kestens (Barnett and Kestens 1999) on a Ti-IF steel cold-rolled to 65% thickness reduction. They reported that the presence of “soft” ℎ𝑘𝑙 〈110〉 orientations adjacent to “hard” 111 〈𝑢𝑣𝑤〉 grains favoring the formation of near 111 〈112〉 recently recrystallized grains.

4.2. Static Recrystallization during the Isochronal Annealing of Cold-Rolled TWIP Steel This case study highlights the advantages of using the GOS-based segmentation approach in understanding recrystallization texture evolution in a 42% cold-rolled TWIP steel isochronally annealed at 600, 700, 750, 775 and 850°C for 300s (Saleh, Gazder, and Pereloma 2011). The partially recrystallized maps were segmented into unrecrystallized (deformed and recovered) and recrystallized (recently recrystallized and growing grains) fractions. In brief, the unrecrystallized and recrystallized fractions were first segmented with a fixed  = 1.5°. Then the unrecrystallized fraction was further sub-divided into deformed and recovered fractions by applying a threshold of  = 7°; which is close to the threshold value of 6°

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previously reported for recovered substructures (Humphreys and Humphreys 1994). Lastly, the recrystallized fraction was sub-divided into recently recrystallized and growing grain fractions by applying a threshold based on the arithmetic mean of the frequency distribution of the recrystallized grain size. The latter accounts for increases in grain size with higher isochronal annealing temperature.

Figure 8. The softened and recrystallized fractions of TWIP steel estimated by microhardness and EBSD. Reprinted with permission from Elsevier, copyright 2011.

The fraction recrystallized (X) is estimated from the map area fraction (via the  criterion used to segment the maps) as well as the total highangle grain boundary fraction (THAGB) of the full map such that (Jazaeri and Humphreys 2004):

𝑋=

THAGB − THAGB THAGB − THAGB

(3)

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where, THAGBCR and THAGBX are the total HAGB fractions (HAGBs + TBs) of the cold-rolled and fully recrystallized maps, respectively. As seen in Figure 8, the fraction recrystallized estimated from EBSD (both segmented maps area fraction and %THAGB) generally corroborate the microhardness results. The disparity at 600°C can be ascribed to the dominance of recovery at this stage of annealing. Representative IPF maps of the cold-rolled and partially recrystallized microstructures are shown in Figure 9. The 42% cold-rolled microstructure expectedly comprises elongated grains, with many of them containing deformation twins, either as parallel primary twins or as intersecting arrangements of primary and secondary twins (Figure 9a). As pointed out earlier, annealing at 600C led to recovery as well as twin bulging at preexisting grain boundaries and the appearance of recently recrystallized grains at them (Figure 9b). Annealing at 850°C results in an ~ 96% recrystallization fraction (Figure 8) along with a corresponding increase in the average recrystallized grain size (Figures 9c-f and Table 1). Recently recrystallized grains and their subsequent growth within the 600-775C temperature range also led to increases in the Σ3 and Σ9 area fractions (Table 1). Here the relatively low fraction of Σ9 boundaries compared to Σ3 is attributed to the limited impingement of Σ3 boundaries leading to Σ9 formation via the twinning reaction (Randle 1999): Σ3+Σ3→Σ9. Thereafter, further decreases in the Σ9 boundary area fraction at 775 and 850°C is ascribed to the twinning reaction: Σ3+Σ9→Σ3, as postulated in the Σ3 regeneration model proposed by Randle (Randle 1999). The unrecrystallized (deformed and recovered) and recrystallized (recently recrystallized and growing grains) fractions of the partially recrystallized 700C sample are shown in Figures 10a-10d with their corresponding disorientation distributions given in Figure 10e. While the unrecrystallised fraction is dominated by LAGBs, the recovered grains have an expectedly lower fraction of LAGBs compared to their deformed counterparts (Figure 10e).

Table 1. Change in the average recrystallized grain size, average misorientation (θAVG°), grain boundary area fraction and recently recrystallized grain density in TWIP steel with isochronal annealing temperature

CR 600°C 700°C 750°C 775°C 850°C

Recrystallized grain size (μm) w/o with TBs TBs 3.6 ± 2.7 2.1 ± 1.4 4.9 ± 3.7 2.7 ± 1.8 4.9 ± 3.7 2.7 ± 2.0 7.9 ± 5.5 4.4 ± 3.0

Grain boundary area fraction (%)

Average misorientation (θAVG°)

LAGB

HAGB

Σ9 TB

Σ3 TB

14.15 15.97 36.79 48.87 48.97 48.49

79.1 ± 1.6 74.1 ± 0.6 30.3 ± 1.4 9.4 ± 0.8 5.3 ± 0.2 4.4 ± 0.6

9.4 ± 0.2 11.4 ± 1.1 34.9 ± 0.3 48.1 ± 0.5 47.0 ± 0.7 50.2 ± 0.6

0.4 ± 0.4 0.6 ± 0.7 5.6 ± 0.1 10.7 ± 0.1 7.4 ± 0.1 7. 1 ± 0.2

11.5 ± 2.2 14.6 ± 2.5 34.8 ± 2.4 42.5 ± 2.1 47.7 ± 1.7 45.4 ± 0.9

Recently recrystallized grain density (10³ mm-2) w/o with TBs TBs 194 1075 136 705 105 554 50 241

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Figure 9. IPF maps of (a) 42% cold-rolled, (b) 600°C recovered and, (c) 700°C, (d) 750°C, (e) 775°C, and (f) 850°C partially recrystallized TWIP steel.

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Figure 10. IPF maps of 700°C TWIP steel segmented into: (a) deformed, (b) recovered, (c) recently recrystallized and (d) growing grain fractions. (e) The misorientation distribution of the various fractions and (f) at the interface between the recently recrystallized and unrecrystallized fractions of the 700, 750 and 775°C samples. The ϕ2 = 0° ODF section at the interface for the 700°C sample is inset. RD = horizontal. Reprinted with permission from Elsevier, copyright 2011.

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The fraction of Σ3 TBs is the lowest in the deformed grains, is higher in the recovered grains, is highest in the recently recrystallized grains and then reduces in the growing grains fraction (Figure 10e). On the other hand, the fraction of Σ9 TBs is more pronounced in the recrystallized fractions than the unrecrystallized fractions (Figure 10e). The lower TB population in the growing grains fraction as opposed to their recently recrystallized counterparts follows Gindraux and Form (Gindraux and Form 1973), where annealing twins form to reorient the grain boundaries in order to facilitate dislocation absorption and mobility during the initial stages of recrystallization. Here, twinning contributes significantly to the overall reduction in stored energy when recently recrystallized grains begin appearing. Thereafter, during the grain growth stage, the previously formed twins are annihilated and a relatively limited evolution of newer twins occurs. Utilizing the segmentation approach provides insight into the recrystallized grains growth kinetics by examining the character of boundary segments at the interface between recently recrystallized and unrecrystallized fractions via double-dilation (Gazder et al. 2011) for the 700, 750 and 775°C samples (Figure 10f). The low-mobility LAGBs and TBs together constitute ~ 59%, 41% and 47% of the total interface boundary population at 700, 750 and 775°C, respectively (Figure 10f). This suggests that orientation-dependent, stored energy considerations have a dominant role in dictating microstructure evolution during recrystallization (Gazder, Saleh, and Pereloma 2011). Thus, recently recrystallized grains with orientations that inherently possess locally higher stored energies carried over from cold-rolling will have a growth advantage in order to maximize their stored energy release (Sebald and Gottstein 2002). The segmentation approach also facilitates an understanding of texture development during recrystallization. While the micro-texture of the partially recrystallized 700°C sample (Figure 11a) generally resembles the cold-rolled one (Saleh, Pereloma, and Gazder 2011), the developed α-fibre (typically extending from the Goss (G, 110 〈001〉) to the Brass (B, 110 〈112〉) orientations) extends further through to the P ( 110 〈122〉)

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orientation. The micro-textures of the deformed, recovered, recently recrystallized and growing grain fractions are shown in Figures 11b-11e. Here the intense peak around the B orientation in the deformed fraction (Figure 11b) as opposed to the G and P orientations in the recovered fraction (Figure 11c) is indicative of the higher internal misorientation and stored energy associated with the B orientation. This observation contradicts Taylor factor –based predictions of stored energy (E) under plane-strain deformation along the α-fibre wherein E(Goss) < E(Brass) < E(P). The discrepancy is ascribed to the inability of the Taylor model to capture deformation inhomogeneities and that the Taylor factor is only a measure of the material’s current state without considering its prior deformation history. In agreement with Ref. (Saleh, Pereloma, and Gazder 2011), the recrystallization textures also comprised orientations similar to the original cold-rolling texture and their evolution is ascribed to: (i) the recently recrystallized grains (observed predominantly at grain boundaries) with orientations close to that of the deformed matrix (Figure 11d), (ii) followed by annealing twinning to crystallographically identical variants. The relatively homogeneous deformation microstructure led to a uniform distribution of nucleation sites and nearly site-saturated nucleation as depicted by the initially high and subsequently declining recently recrystallized grain density (Table 1). This behavior is expected in TWIP steels as their low stacking fault energy limits recovery due to restricted dislocation climb and provides a higher driving force for recrystallization. While the texture of the recently recrystallized grains (Figure 11d) does not display any predominant orientation, a gradual strengthening of B at the expense of the G and P orientations is seen in the growing grain fraction (Figure 11e) and the end-texture after annealing at 850°C (Figure 11f). This strengthening of the B orientation is ascribed to the orientationdependent, stored energy considerations discussed above, leading to a growth advantage in order to maximize the energy release. Lastly, the development of the 112 〈131〉 orientation was also detected upon the completion of recrystallisation at 850°C (Figure 11(f)). This orientation is linked to the G orientation with the 30° 〈111〉 favoured

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growth relationship (Humphreys and Hatherly 2004) and to orientations near the α-fibre (between G and B, at 032 〈13 2 3〉) with a second order twinning relationship (Σ9 = 38.9° 〈101〉). Since no size advantage was observed for the 112 〈131〉 grains, oriented growth contribution can be negated and the importance of Σ9 twinning during recrystallization is further re-emphasized (Saleh, Pereloma, and Gazder 2011).

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Figure 11. ϕ2 = 0° and 45° ODF sections of the (a) 700 °C partially recrystallized TWIP steel segmented into: (b) deformed, (c) recovered, (d) recently recrystallized and (e) growing grain fractions, and (f) the 850 °C recrystallized sample. Contour levels = 0.5×. Reprinted with permission from Elsevier, copyright 2011.

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4.3. Dynamic Recrystallization during the Plain Strain Compression of Ni-30Fe Alloy This case study utilizes the segmentation approach to track the evolution of dynamic recrystallization texture in a Ni-30Fe alloy subjected to plain strain compression to true strains (ε) of 0, 0.23, 0.35, 0.68, 0.85 and 1.2 at 1075°C (Mannan et al. 2016). The partially recrystallized maps were segmented into recrystallized and unrecrystallized fractions using the GOS criterion such that (sub)grains with a fixed  ≤ 2° were classified as the recrystallized fraction, whereas (sub)grains with  > 2° were considered part of the unrecrystallized fraction. The band contrast maps in Figure 12 track the evolution of the DRX microstructure as a function of strain, while the IPF maps in Figure 13 depict the same areas segmented into recrystallized and unrecrystallized fractions. Due to the nature of DRX, the recrystallized fraction strictly comprises a set of grains that are recrystallized at any given strain while the unrecrystallized fraction contains a mixture of originally deformed, recovered and secondary deformed grains. It follows that the sub-fractions of unrecrystallized grains changes with increasing strain and that segmenting these unrecrystallized sub-fractions requires tracking the same set of grains throughout the strain range. This is not possible using the present experimental data set as different samples were used for each strain level. The initial microstructure (ε = 0) comprises nearly equiaxed grains with a high fraction of Σ3 (Figure 12a) annealing twin boundaries. At ε = 0.23 (Figures 12b, 13a and 13b), the grains begin to elongate and a few recrystallized grains are readily observed along the original grain boundaries (Figures 13a and 13b). At ε = 0.35 (Figures 12c, 13c and 13d), a clear necklace layer of recrystallized grains decorate the original grain boundaries. With increasing strain at ε = 0.68, 0.85 and 1.2, the microstructure comprises a significant fraction of recrystallized grains (Figures 12d-12f, 13e, 13g and 13i).

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Figure 12. Band contrast maps of Ni-30Fe alloy at ε = (a) 0, (b) 0.23, (c) 0.35, (d) 0.68, (e) 0.85, and (f) 1.2 at 1075°C.

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Figure 13. (Continued).

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(j) Figure 13. IPF maps of Ni-30Fe alloy segmented into: (a, c, e, g, i) recrystallized and (b, d, f, h, j) unrecrystallized fractions at ε = (a, b) 0.23, (c, d) 0.35, (e, f) 0.68, (g, h) 0.85 and (i, j) 1.2. Reprinted with permission from Elsevier, copyright 2016.

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The mean intragranular local misorientation (𝜃 ) of the full map and the recrystallised and unrecrystallised fractions as a function of true strain is depicted in Figure 14. 𝜃 -values initially exhibit a sharp increase up to ε = 0.35 in the recrystallized and unrecrystallized fractions. Thereafter, 𝜃 values continue to rise rapidly in the unrecrystallized fraction up to ε = 0.85, while only a slight increase is observed in the recrystallized fraction. At ε = 1.2, 𝜃 plummets in both subsets as the fraction of recrystallized grains exceeds 0.65. Additionally, the unrecrystallized fraction also contains a noticeable amount of secondary deformed grains (recrystallized grains undergone secondary deformation), which in turn exhibit lower values of 𝜃 .

Figure 14. Mean intragranular local misorientation of Ni-30Fe alloy for the full map, recrystallized and unrecrystallized fractions as a function of true strain. Reprinted with permission from Elsevier, copyright 2016.

As stated before, one of the main benefits of segmenting partially recrystallized microstructures is a better understanding of micro-texture evolution during recrystallization. The micro-texture of the full map at ε = 0.23 and 0.35 comprises a weak spread between the Cube, Cube-RD ({013}〈100〉) and Cube-ND ({001}〈310〉) orientations, along with B and

ϕ2 = 0° ϕ2 = 45° ϕ2 = 65°

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Figure 15. ϕ2 = 0°, 45° and 65° ODF sections of the full maps of Ni-30Fe alloy at ε = (a) 0.23, (b) 0.35, (c) 0.68, (d) 0.85 and (e) 1.2. Contour levels = 2×. Reprinted with permission from Elsevier, copyright 2016.

ϕ2 = 0° ϕ2 = 45° ϕ2 = 65°

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Figure 16. ϕ2 = 0°, 45° and 65° ODF sections of the unrecrystallized fractions in Ni-30Fe alloy at ε = (a) 0.23, (b) 0.35, (c) 0.68, (d) 0.85 and (e) 1.2. Contour levels = 2×. Reprinted with permission from Elsevier, copyright 2016.

ϕ2 = 0° ϕ2 = 45° ϕ2 = 65°

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Figure 17. ϕ2 = 0°, 45° and 65° ODF sections of the recrystallized fractions in Ni-30Fe alloy at ε = (a) 0.23, (b) 0.35, (c) 0.68, (d) 0.85 and (e) 1.2. Contour levels = 2×. Reprinted with permission from Elsevier, copyright 2016.

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Cu orientations and an intensity spread near Rt-G as seen in Figures 15a and 15b, respectively. At ε ≥ 0.68, the C orientation becomes dominant and intensifies with increasing strain. This is accompanied by weaker intensities for the α-fibre and the Cu and ~S ({123}〈634〉) orientations (Figures 15c-15e). The unrecrystallized texture at ε = 0.23 is characterized by intensity spreads along Φ near the B and Cu orientations and an intensity split around Rotated Goss (Rt-G, {011}〈011〉) (Figure 16a). At ε = 0.35, increasing deformation leads to stronger intensities along the α-fibre accompanied by orientation splitting at ~ ϕ1 = 45°, Φ = 45°, ϕ2 = 0° (Figure 16b). At ε ⩾ 0.68, the orientations of the unrecrystallized textures (Figures 16c-16e) mirror those of the full map (Figures 15c-15e) with a dominant and intensifying C orientation along with weaker intensities for the α-fibre and the Cu and ~S orientations. From the onset of strain, the recrystallized texture demonstrates continuous strengthening of the C orientation such that it dominates the final DRX texture at ε = 1.2 (Figure 17). A weak intensity spread is also seen along the α-fibre and near the ~S and Cube-Twin (CT, {122}〈212〉) orientations (Figures 17c-17e). To sum up, the ODFs in Figures 16 and 17 show that by ε = 0.68, the original deformation texture (Figures 16a and 16b) is replaced by C orientations that originated via recrystallization and thereafter underwent subsequent secondary deformation (Figures 17a-17c). As a consequence, at ε ⩾ 0.68 the unrecrystallized and recrystallized ODFs are similar and denote the recent recrystallization, growth and secondary deformation of mostly C orientations. One of the common explanations related to the formation of Cube texture is based on its low stored energy (when estimated based on the Taylor factor calculated using octahedral slip systems for fcc materials) and its orientation stability during secondary deformation (Mannan et al. 2016). However, more recent experimental investigations (microhardness combined with EBSD measurements) and self-consistent modelling work (using an intermediate grain–matrix interaction scheme between the Taylor and Sachs models) (Saleh et al. 2018) have revealed that the Cube orientation is not necessarily a low

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stored energy orientation as generally viewed in the literature. The dominance of the Cube orientation in the DRX texture in (Saleh et al. 2018) was ascribed to its: (i) higher stored energy (when calculated using an intermediate grain–matrix interaction scheme) and subsequently higher probability of nucleation and, (ii) stabilization via non–octahedral {011}〈110〉 slip at high temperatures.

CONCLUSION Through case studies on ELC and TWIP steel and Ni-30Fe alloy, the present chapter showcases how EBSD provides insights into the recrystallization mechanisms starting from identifying the nucleation sites during the early stages of recrystallization and the subsequent evolution of microstructures and micro-textures. The GOS criterion provides a robust means of segmenting the partially recrystallized EBSD maps of a variety of materials subjected to different thermo-mechanical processing regimes and annealing treatments. In addition to this, the use of multi-condition segmentation methodologies involving the thresholding of (sub)grain sizes, shapes and boundary criteria, sub-divides the microstructure into deformed, recovered, recently recrystallized and growing grain fractions which in turn, provides further insights into recrystallization kinetics. The accurate determination of the specific interfacial area via doubledilation between the unrecrystallized (deformed/recovered) and recrystallized (recently recrystallized/growing) grain fractions, qualitatively differentiates discontinuous and continuous recrystallization. Here checking for the three-dimensional spheroidal growth of the recrystallized grains in the ELC steel indicated continuous and discontinuous recrystallization in the warm and cold -rolled samples, respectively. Inspecting the recently recrystallized grain density provides insights into the distribution of nucleation sites and discriminates site-saturated and constant rate type nucleation events. For example, the initially high and

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subsequently declining recently recrystallized grain density in the present TWIP steel alludes to a nearly site-saturated nucleation. As seen in all case studies, tracking the micro-textures of the various map fractions enables a better understanding of the orientation-dependent, stored energy effects on the end recrystallization texture. Combined with the available segmentation-based microstructural information (such as the nucleation type and the spheroidal growth of the recrystallized grains), the associated micro-textures can be further linked to the operative nucleation (site-saturated or constant rate) and recrystallization (discontinuous or continuous) mechanisms. The EBSD map segmentation can also be effectively combined with other experimental and modelling investigations to understand the preference and/or dominance of particular orientations during static and dynamic recrystallization.

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In: Recrystallization Editor: Ke Huang

ISBN: 978-1-53616-737-5 © 2020 Nova Science Publishers, Inc.

Chapter 3

RECRYSTALLIZATION AND GRAIN GROWTH UPON ANNEALING OF COLD WORKED AUSTENITIC STAINLESS STEELS Meysam Naghizadeh and Hamed Mirzadeh* School of Metallurgy and Materials Engineering, College of Engineering, University of Tehran, Tehran, Iran

ABSTRACT Microstructural evolutions during annealing of cold rolled AISI 304 and AISI 316 metastable austenitic stainless steel sheets are an interesting subject. The reversion of deformation-induced martensite to austenite, the primary recrystallization of the retained austenite, and grain growth have been characterized as the distinct phenomena that happen during annealing. The need for recrystallization postpones the formation of an equiaxed microstructure, which coincides with the coarsening of very fine reversed grains. The differences between the annealing behaviors of these alloys can be related to the presence of molybdenum in AISI 316 stainless *

Corresponding Author’s E-mail: [email protected].

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Keywords: stainless steels, deformation-induced martensitic transformation, reversion annealing, recrystallization, grain growth

1. GRAIN REFINEMENT OF AUSTENITIC STAINLESS STEELS Based on their excellent corrosion resistance, good toughness and acceptable weldability, austenitic stainless steels (ASSs) have attracted a considerable attention in various industrial applications. However, the strength of these steels is relatively low in the annealed state, which is a drawback for many potential applications. As a result, various methods such as grain refinement (Mirzadeh et al. 2012, Naghizadeh and Mirzadeh 2018a), solid solution strengthening (Korzhavyi and Sandström 2015), and work hardening (Mirzaie et al. 2018, Spencer et al. 2004) have been practiced so far. Among these mechanisms, grain refinement can be exploited to improve strength as well as toughness. Since these steels do not have any notable phase transformations during cooling, the severe plastic deformation (SPD) techniques and recrystallization processes should be used for structural refinement. SPD techniques impose large accumulated plastic strains and can be used to produce ultrafine grained stainless steels (Song et al. 2006). SPD

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techniques like high pressure torsion (Mine et al. 2016), equal channel angular pressing (Karavaeva et al. 2016), multi-directional forging (Nakao and Miura 2011), accumulative roll bonding (Mohammad Nejad Fard et al. 2017), mechanical alloying (Garcia-Cabezon et al. 2017), friction stir processing (Liu and Nelson 2016), and shot peening (Bagherifard et al. 2016) have been successfully used for extreme grain refinement of ASSs. Recrystallization processes for grain refinement of ASSs are based on deformation and annealing, and hence, processes like static recrystallization (Di Schino et al. 2002) and dynamic recrystallization (Aashranth et al. 2018, Mallick et al. 2018, Mandal et al. 2011, Mirzadeh et al. 2012) have been widely studied. Hot deformation of austenitic stainless steels, which have low stacking fault energies, may be accompanied by discontinuous dynamic recrystallization, which affects the evolution of grains and can thus be utilized to achieve grain refinement by the necklace mechanism (Mirzadeh et al. 2016). DRX by necklace mechanism is based on the nucleation along existing grain boundaries, where the growth of each grain stops by the concurrent deformation. This behavior can be mainly ascribed to the increase in dislocation density of the new DRX grains and reducing the driving force for their further growth. Nucleation of further grains at the migrating boundaries seems to be an additional growth inhibition factor (Humphreys et al. 2017, Mirzadeh et al. 2016). The DRX process continues until the completion of the first layer of necklace structure to cover the entire grain boundary. Afterwards, the subsequent layers form at the recrystallization front between the recrystallized and unrecrystallized portions until the completion of the recrystallization process. The conventional recrystallization processes are not very effective compared with severe plastic deformation techniques. As a result, an advanced thermomechanical processing route has been developed, which is based on the formation of deformation-induced martensite in metastable ASSs and its subsequent reversion to fine-grained austenite (Kisko et al. 2016, Lee et al. 2014, Lei et al. 2018, Mirzadeh and Najafizadeh 2008, Momeni and Abbasi 2011, Naghizadeh and Mirzadeh 2016a, Qin et al. 2019, Souza Filho et al. 2019, Sun et al. 2018, Sun et al. 2019, Tomimura

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et al. 1991, Zha et al. 2019). A schematic representation of the processing routes employed in this study is shown in Figure 1. It has been reported that for obtaining a marked grain refinement, the availability of great amounts of martensite before reversion is required (Lo et al. 2009). The amount of martensite can be monitored by magnetic methods (Shirdel et al. 2015), X-ray diffraction by consideration of Equation 1 (Kheiri et al. 2019), microstructural techniques (Mohammad Nejad Fard et al. 2017, Naghizadeh and Mirzadeh 2018b), and other methods. Austenite stability (chemical composition and the initial grain size) and cold working variables (temperature, strain, strain rate, and stress state) play critical roles on the formation of martensite and its amount (Celada-Casero et al. 2019, Mirzadeh and Najafizadeh 2008). The martensite phase is not stable at elevated temperatures and its reversion to fine grained austenite can occur by annealing at elevated temperatures (Kheiri et al. 2019). f  

I (211)  I (211)   0.65(I (311)  I (220) )

(1)

Figure 1. Schematic representation of the thermomechanical processing of formation and reversion of deformation-induced martensite for grain refining of ASSs.

Recrystallization and Grain Growth upon Annealing of Cold … 101

2. MARTENSITE FORMATION DURING COLD WORKING For AISI 304 stainless steel, the XRD patterns of the as-received and 70% deformed sheets are shown in Figure 2. It can be seen that both γ and α'-martensite peaks are present. By increasing the amount of plastic deformation, the intensities of γ(220) and γ(311) austenite peaks generally decrease while that of α'(211) increases. As a result, based on Equation 1, the amount of martensite increases with increasing the reduction in thickness. The same discussion can be applied in the case of XRD patterns of the AISI 316 stainless steel shown in Figure 3a. The microstructures shown in Figure 2 also show that the prior austenite grains become progressively more pancaked by imposing the cold rolling strain. However, the formation of martensite cannot be followed from these microstructures that are revealed by the grain boundary etch (Table 1). For this purpose, both grain boundary etch and martensite etch (Table 1) can be applied to the cold rolled sheets. An example is shown in Figure 3c, where it can be clearly seen that the formation of martensite phase is related to the shear bands and their intersections (Das et al. 2008, Talonen and Hanninen 2007). As the deformation proceeds, the shear bands intersect one another, where these intersections act as nucleation sites for martensite embryos that coalesce and grow parallel to the shear bands (Li et al. 2018, Murr et al. 1982). Table 1. Common polishing and etching methods for revealing the microstructural features Usage

Solution

Surface Polishing

Electrolytic polishing in a mixture of 1:1 H3PO4 and H2SO4 solution at 40 V (Naghizadeh and Mirzadeh 2018a)

Grain Boundary Etch

Electrolytic etching in a 60% HNO3 solution at 2 V (Mirzadeh 2015)

Martensite Etch

0.1 g Na2S2O5 – 10 ml HCl – 150 ml distilled water (Naghizadeh and Mirzadeh 2018a)

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Figure 2. AISI 304 stainless steel: XRD patterns and the corresponding microstructures (grain boundary etch) of the as-received and cold rolled sheets.

Figure 3. AISI 316 stainless steel: (a) XRD patterns, (b) as-received microstructure (grain boundary etch), and (c) a cold rolled microstructure (martensite etch followed by grain boundary etch).

Recrystallization and Grain Growth upon Annealing of Cold … 103 The summary of the phase calculations based on Equation 1 is shown in Figure 4. For both materials, it can be seen that the formation of martensite follows the usual sigmoidal kinetics seen in phase transformations (Naghizadeh and Mirzadeh 2018b, Zecevic et al. 2019) but the kinetics of transformation for the AISI 304 alloy is faster. It seems that there is a saturation for the volume fraction of obtainable strain-induced martensite at room temperature, which is ~ 87% and ~ 80% for AISI 304 and AISI 316, respectively. Therefore, it can be surmised that the austenite phase in the AISI 316 stainless steel is more stable against the martensitic transformation. This can be verified based on the calculation of the Md30/50 temperature (Naghizadeh and Mirzadeh 2018c, Nohara et al. 1977) as shown in Equation 2, where Md30/50 is the deformation temperature (expressed in degree Celsius) at which 50 vol% strain-induced martensite forms by true tensile strain of 0.3 (30%), Gs is the ASTM grain size number, and all the elements are expressed in weight percent. In fact, the Md30/50 temperature of the present AISI 316 and AISI 304 alloys can be calculated as - 60°C and - 7°C (Naghizadeh and Mirzadeh 2018a), where the lower Md30/50 temperature for AISI 316 implies the higher stability of austenite. This saturation has been achieved at cold rolling reduction of 70%. It has been reported that this saturation strongly depends on deformation temperature; and by rolling at lower temperatures, it is possible to achieve more than 90% martensite. In fact, some amount of retained austenite presents in the microstructure but usually it is neglected in discussing the results and reporting the obtained grain sizes. One of the main aims of the present chapter is to discuss the effect of retained austenite during annealing of plastically deformed austenitic stainless steels. M d 30 /50 = 551 - 462(C + N ) - 9.2 Si - 8.1Mn - 13.7Cr - 29( Ni + Cu ) 18.5 Mo - 68 Nb - 1.42(Gs - 8)

(2)

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Figure 4. The effect of cold rolling reduction on the amount of strain-induced martensite.

3. REVERSION, RECRYSTALLIZATION, AND GRAIN GROWTH DURING ANNEALING While the reversion process has received considerable attentions in recent years for enhancement of mechanical properties (Kheiri et al. 2019, Naghizadeh and Mirzadeh 2019), the different stages of microstructural evolution were identified recently (Naghizadeh and Mirzadeh 2018a, Kheiri et al. 2019), which enable microstructural control during thermomechanical processing. During reversion annealing, the reversion of strain-induced martensite to austenite, the primary recrystallization of the retained austenite (if it is present), and the grain growth process are important phenomena (Kheiri et al. 2019, Kisko et al. 2016, Naghizadeh and Mirzadeh 2018a, Sun et al. 2018), which significantly affect the resultant microstructure and mechanical properties. XRD patterns of the 70% cold rolled AISI 304 and AISI 316 stainless steel sheets after annealing at 750°C are shown in Figure 5. It can be seen

Recrystallization and Grain Growth upon Annealing of Cold … 105 that by increasing the annealing time, the intensities of γ(220) and γ(311) austenite peaks generally increase while that of α'(211) decreases. Therefore, the amount of martensite decreases during annealing, which along with the measured hardness values is summarized in Figure 6. Both hardness and martensite content decline with continued annealing. However, some distinct stages can be identified. In Stage I, the reversion of martensite to austenite takes place up to 45 min for both steels. As can be seen in Figure 7, very fine reversed austenite grains start to consume the microstructure with the consequent decrease in hardness. However, even at 45 min, where the reversion process becomes completed (Figure 6), some deformed austenite grains remain (large and pancaked bright areas). The latter is related to the retained austenite after the cold rolling step.

Figure 5. XRD patterns of the 70% cold rolled sheets after annealing at 750°C.

Figure 6. Effect of annealing time at 750°C on the amount of martensite and hardness of the cold rolled sheets: (a) AISI 304 and (b) AISI 316.

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Figure 7. Microstructural evolutions during annealing at 750°C (Stage I).

In Stage II, from 45 min to 90 min for AISI 304 stainless steel, the amount of martensite remains essentially unchanged but the value of hardness significantly declines. Comparing microstructures at 45 min and 90 min in Figure 8 reveals that the main differences are the recrystallization of the retained austenite (bright areas) and somewhat coarsening of reverted grains. These might be responsible for the observed decrease in hardness. Therefore, an equiaxed microstructure is obtained,

Recrystallization and Grain Growth upon Annealing of Cold … 107 which is composed of finer reversed grains (See the magnified rectangular area) along with the larger recrystallized grains (See the elliptical area). This marks the end of the microstructural evolutions resulted from plastic deformation. While at 45 min annealing, the reversion process has been completed, the equiaxed microstructure only forms after annealing for 90 min to provide enough time for the recrystallization process. Afterward, by continued annealing in Stage III, hardness does not change considerably (Figure 6) and the microstructure coarsens slowly as can be seen in the microstructure of 900 min annealed sheet (Figure 8). This sluggish grain growth is related to the fact that 750°C is a low temperature for grain growth of AISI 304 stainless steel. It has been shown that significant grain growth happens in this alloy at temperatures higher that ~ 800°C (Naghizadeh and Mirzadeh 2016b). The significant decline of hardness beyond 45 min is absent for AISI 316 stainless steel and the deformed retained austenite grains can be identified even after 900 min annealing. In fact, the kinetics of recrystallization and grain growth in this alloy is very slow. This is related to the presence of molybdenum in AISI 316 alloy, which effectively pins the grain boundaries and results in slower kinetics of recrystallization and grain growth (Naghizadeh and Mirzadeh 2016b). In fact, Mo effectively increases the grain growth activation energy from that of AISI 304, i.e., the lattice diffusion activation energy: 280 kJ/mol (Mirzadeh et al. 2011), to 568 kJ/mol due to an interaction energy of 288 kJ/mol between Mo and grain boundaries (Naghizadeh and Mirzadeh 2016b). Figure 8 reveals that at reversion temperature of 750°C, the recrystallization of the retained austenite in AISI 316 alloy is very slow. It should be noted that there is an interaction energy between Mo and grain boundaries (U) based on the relation of c  exp( U / RT ) (Gottstein and Shvindlerman 2010, Naghizadeh and Mirzadeh 2016b), where c is the concentration of alloying element (here Mo) in the boundary, R is the gas constant, and T is the absolute temperature. This relation predicts that the concentration of the solute atoms (e.g., Mo) in the boundaries decreases by increasing temperature. A point might be reached where the segregated impurities (e.g., Mo) no longer able to keep up with the boundaries and the

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boundaries can move freely (Gottstein and Shvindlerman 2010). As a result, a higher annealing temperature might be favorable for the occurrence of recrystallization process. Therefore, higher annealing temperature of 1000°C was also considered for AISI 316 alloy (Figure 1) and the resultant microstructures are shown in Figure 9.

Figure 8. Microstructural evolutions during annealing at 750°C (Stage II and III).

Recrystallization and Grain Growth upon Annealing of Cold … 109

Figure 9. Microstructural evolutions of cold-rolled AISI 316 stainless steel during annealing at 1000°C.

Based on Figure 9, 1 min annealing at 1000°C is enough for the onset of recrystallization and a completely recrystallized and equiaxed microstructure can be seen in a very short period of 2 min. In the microstructure of 2 min annealed sample, a significant grain coarsening of reversed grains can be identified. Therefore, at high annealing temperature of 1000°C, the retardation effect of Mo is weak. As a result, at 1000°C, the processes of recrystallization and grain growth occur easily and an equiaxed microstructure can be quickly achieved. Greater annealing times results in the fast grain growth, which implies that the inhibition effect of Mo is ineffective.

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CONCLUSION Microstructural evolutions during annealing of cold rolled AISI 304 and AISI 316 metastable austenitic stainless steel sheets are an interesting subject. The reversion of deformation-induced martensite to austenite, the primary recrystallization of the retained austenite, and grain growth have been characterized as the distinct phenomena that happen during annealing. The need for recrystallization postpones the formation of an equiaxed microstructure, which coincides with the coarsening of very fine reversed grains. The differences between the annealing behaviors of these alloys can be related to the presence of molybdenum in AISI 316 stainless steel, which segregates to the boundaries and effectively pins the grain boundaries by solute drag mechanism at low annealing temperatures and severely retards the occurrence of recrystallization. At high annealing temperatures, however, at a short period of time, the recrystallization of AISI 316 stainless steel becomes completed and significant grain growth occurs as the annealing time goes on. These observations can be related to the temperature dependency of the retardation effect of Mo. Therefore, it can be deduced that both alloying elements and annealing temperature play critical roles during recrystallization annealing of austenitic stainless steels. In summary, the present chapter unraveled the important microstructural evolution stages during reversion annealing and can shed light on the requirements and limitations of the thermomechanical treatment based on the formation and reversion of deformation-induced martensite.

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Recrystallization and Grain Growth upon Annealing of Cold … 113 Mirzadeh, H. (2015). “A Simplified Approach for Developing Constitutive Equations for Modeling and Prediction of Hot Deformation Flow Stress.” Metallurgical and Materials Transactions A, 46, 4027-37. Mirzadeh, H. & Najafizadeh, A. (2008). “Correlation between processing parameters and strain-induced martensitic transformation in cold worked AISI 301 stainless steel.” Materials Characterization, 59, 1650-4. Mirzadeh, H., Cabrera, J. M. & Najafizadeh, A. (2011). “Constitutive Relationships for Hot Deformation of Austenite.” Acta Materialia, 59, 6441-8. Mirzadeh, H., Cabrera, J. M., Najafizadeh, A. & Calvillo, P. R. (2012). “EBSD Study of a Hot Deformed Austenitic Stainless Steel.” Materials Science and Engineering A, 538, 236-45. Mirzadeh, H., Roostaei, M., Parsa, M. H. & Mahmudi, R. (2016). “Dynamic Recrystallization Kinetics in Mg-3Gd-1Zn Magnesium Alloy during Hot Deformation.” International Journal of Materials Research, 107, 277-9. Mirzaie, T., Mirzadeh, H. & Naghizadeh, M. (2018). “Contribution of Different Hardening Mechanisms during Cold Working of AISI 304L Austenitic Stainless Steel.” Archives of Metallurgy and Materials, 63, 1317-20. Mohammad Nejad Fard, N., Mirzadeh, H., Rezayat, M. & Cabrera, J. M. (2017). “Accumulative Roll Bonding of Aluminum/Stainless Steel Sheets.” Journal of Ultrafine Grained and Nanostructured Materials, 50, 1-5. Momeni, A. & Abbasi, S. M. (2011). “Repetitive thermomechanical processing towards ultra fine grain structure in 301, 304 and 304L stainless steels.” Journal of Materials Science and Technology, 27, 338-43. Murr, L. E., Staudhammer, K. P. & Hecker, S. S. (1982). “Effects of Strain State and Strain Rate on Deformation-Induced Transformation in 304 Stainless Steel: Part II. Microstructural Study.” Metallurgical Transactions A, 13, 627-35.

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Naghizadeh, M. & Mirzadeh, H. (2016a). “Microstructural Evolutions during Annealing of Plastically Deformed AISI 304 Austenitic Stainless Steel: Martensite Reversion, Grain Refinement, Recrystallization, and Grain Growth.” Metallurgical and Materials Transactions A, 47, 4210-6. Naghizadeh, M. & Mirzadeh, H. (2016b). “Elucidating the Effect of Alloying Elements on the Behavior of Austenitic Stainless Steels at Elevated Temperatures.” Metallurgical and Materials Transactions A, 47, 5698-703. Naghizadeh, M. & Mirzadeh, H. (2018a). “Microstructural Evolutions during Reversion Annealing of Cold-Rolled AISI 316 Austenitic Stainless Steel.” Metallurgical and Materials Transactions A, 49, 2248-56. Naghizadeh, M. & Mirzadeh, H. (2018b). “Microstructural Modeling the Kinetics of Deformation-Induced Martensitic Transformation in AISI 316 Metastable Austenitic Stainless Steel.” Vacuum, 157, 243-8. Naghizadeh, M. & Mirzadeh, H. (2018c). “Processing of Fine Grained AISI 304L Austenitic Stainless Steel by Cold Rolling and HighTemperature Short-Term Annealing.” Materials Research Express, 5, 056529. Naghizadeh, M. & Mirzadeh, H. (2019). “Microstructural Effects of Grain Size on Mechanical Properties and Work-Hardening Behavior of AISI 304 Austenitic Stainless Steel.” Steel Research International, 90, 1900153. Nakao, Y. & Miura, H. (2011). Nano-Grain Evolution in Austenitic Stainless Steel during Multi-Directional Forging.” Materials Science and Engineering A, 528, 1310-17. Nohara, K., Ono, Y. & Ohashi, N. (1977). “Composition and grain-size dependencies of strain-induced martensitic transformation in metastable austenitic stainless steels.” Journal of Iron and Steel Institute of Japan, 63, 212-22. Qin, W., Li, J., Liu. Y., Kang, J., Zhu, L., Shu, D., Peng, P., She, D., Meng, D. & Li, Y. (2019). “Effects of Grain Size on Tensile Property

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Reversion from Deformation Induced Martensite.” ISIJ International, 31, 721-7. Zecevic, M., Upadhyay, M. V., Polatidis, E., Panzner, T., Van Swygenhoven, H. & Knezevic, M. (2019). “A Crystallographic Extension to the Olson-Cohen Model for Predicting Strain Path Dependence of Martensitic Transformation.” Acta Materialia, 166, 386-401. Zha, X., Xiong, Y., Gao, L., Zhang, X., Ren, F., Wang, G. X. & Cao, W. (2019). “Effect of Annealing on Microstructure and Mechanical Properties of Cryo-Rolled 316LN Austenite Stainless Steel.” Materials Research Express, 6, 096506.

In: Recrystallization Editor: Ke Huang

ISBN: 978-1-53616-737-5 © 2020 Nova Science Publishers, Inc.

Chapter 4

MODELING OF RECRYSTALLIZATION OF COMMERCIAL PARTICLE CONTAINING AL-ALLOYS Knut Marthinsen1,, Ke Huang2 and Ning Wang3,† 1

Department of Materials Science and Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway 2 State Key Laboratory for Manufacturing System Engineering, Xi’an Jiaotong University, P.R. China 3 Gränges Technology AB, Finspång, Sweden

ABSTRACT In order to describe and discuss the recrystallization behavior of commercial particle containing Al-alloys, the physical basis and a mathematical formulation of a softening model nicknamed ALSOFT, accounting for the combined effect of recovery and recrystallization behavior during annealing of heavily deformed aluminum alloys have  †

Corresponding Author’s Email: [email protected]. Corresponding Author’s Email: [email protected].

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Knut Marthinsen, Ke Huang and Ning Wang been reviewed. The prediction power of the model is discussed using two different Al-Mn-Fe-Si-alloys experiencing different processing conditions, giving very different microchemistries in terms of solute and second-phase particle structures. The experiments clearly demonstrate the strong influence of microchemistries and in particular the strong dispersoid effects that may be experienced during back-annealing, either from pre-existing dispersoids or concurrent precipitation. It is demonstrated that good model predictions may be obtained for alloys and conditions which are not or to a limited extent influenced by particle drag effects and concurrent precipitation while conditions strongly affected by these effects are increasingly difficult to model and in the most extreme cases impossible with reasonable input model parameters. Possible causes for these difficulties are discussed and potential improvements of the model are suggested.

Keywords: recovery, recrystallization, concurrent precipitation, Zener drag, modeling

1. INTRODUCTION Thermo-mechanical processing of aluminum alloys is commonly characterized by a complex sequence of deformation (hot/cold) and annealing steps, to achieve the final microstructure, which largely determines the properties and performance of the final material and/or product e.g., during sheet rolling the material is first hot-rolled, and then cold rolled before final annealing. When the cold deformed material is annealed at a sufficient high temperature, recrystallization will take place, driven by the stored energy (mainly in the form of line defects, i.e., dislocations) introduced during deformation. Recrystallization refers the formation (“nucleation”) of new dislocation-free grains and the gradual consumption of the cold worked matrix by growth of these grains (by migration of high-angle grain boundaries). The process of recrystallization of plastically deformed metals and alloys is of central importance during thermomechanical processing for two main reasons. The first is to soften and restore the ductility of material hardened by deformation. The second is to control the grain structure and texture (grain orientation distribution)

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of the final product. For aluminum alloys, recrystallization after deformation is the only method for producing a completely new grain structure with a modified grain size, shape, and, in particular, a desired grain orientation distribution (texture), all aspects of which are crucial for the properties of the semi-finished material (rolled sheet). In some cases, a partly back-annealed (softened/recrystallized) condition is desired, to balance hardness and ductility. In such cases, it is crucial being able to control the softening kinetics. Most commercial aluminum alloys have a complex microchemistry in the form of solid solution levels of alloying elements, volume fraction and size of constituents and dispersoids, and, which may be strongly modified during thermomechanical processing. Although the type and amount of solutes may play a role (through solute drag effects), the most significant effects are related to the second phase particles, which may strongly affect both nucleation and growth of recrystallized grains, and thus both the kinetics and the final grain structure and texture. In which way the second phase particles will affect the recrystallization behavior of a given alloy, as compared to a single-phase alloy, will depend on whether they are present prior to deformation or are precipitated during/after recrystallization. If present before the deformation stage, to which extent and how the recrystallization process will be influenced, will depend on the type, size and spatial distribution of the particles, through their influence on the deformed state, and the subsequent nucleation and growth behavior. Large particles will generally accelerate the reaction, through particle stimulated nucleation (PSN) of recrystallization and strongly influence the final grain size and texture (Nes and Embury 1975, Daaland and Nes 1996). On the other hand, a high density of small particles (dispersoids) will generally give rise to a significant drag force (Zener pinning), acting on moving subgrain and grain boundaries (of growing recrystallization grains) and may strongly retard, and in some cases completely suppress recrystallization and strongly modify the final grain structure and texture. This influence may be even more pronounced in case of precipitation simultaneous with the recrystallization reaction (i.e., concurrent precipitation) (Nes and Embury 1975, Daaland and Nes 1996, Vatne, Engler et al. 1997,

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Humphreys and Hatherly 2004, Sjolstad, Marthinsen et al. 2004, Tangen, Sjolstad et al. 2010). In the present chapter all these aspects will be covered, i.e., the effects of solute and in particular the effects of second phase particles on the nucleation and growth kinetics of recrystallization as well as the effects on final grain structure. The different phenomena and reactions will be described and discussed in terms of classical theories and simple models (when available), and exemplified by experiments and numerical simulations. A special attention will be given to recent findings in AlMnalloys, which perfectly illustrate the potential strong effects of secondphase particles on the softening behavior, in particular the influence of preexisting dispersoids and/or concurrent precipitation, leading to strongly suppressed nucleation, sluggish growth and a recrystallized grain structure of coarse elongated grains and partly unconventional textures. As basis for describing and illustrating the influence of different microchemistries, in terms of solute levels, constituents and dispersoids will make use of the so-called ALSOFT mode. The ALSOFT model is a statistical mean field model for the simulation of the softening behavior of deformed Al-alloys that was developed within the Norwegian aluminum community in the nineties (Vatne, Furu et al. 1996, Vatne, Marthinsen et al. 1996, Saeter 1998). The model accounts for the combined effect of static recovery and recrystallization during annealing of the deformed state and incorporates the effects of solutes (solute drag), constituents (PSN) and dispersoids (Zener drag), by the use of classical models for these phenomena. Although not the most sophisticated model that exists, it still mainly reflects our current understanding and model descriptions for these phenomena, and is well suited to illustrate the effects of solute and in particular second phase particles on the recovery and recrystallization behavior. The model has successfully been applied to predict the softening behavior of various Al-alloys, in particular after hot deformation and conditions of mainly isothermal annealing [(Vatne, Furu et al. 1996, Vatne, Marthinsen et al. 1996, Saeter 1998, Marthinsen, Abtahi et al. 2004, Engler, Lochte et al. 2007, Marthinsen, Friis et al. 2012).

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The structure of the chapter will be as follows. Firstly, a rather detailed presentation of the ALSOFT model will be given, including some recent modifications, which are assumed to be relevant for commercial Al-alloys with a complex microchemistry. Generic model predictions will then be presented, which illustrate how the recovery and recrystallization behavior depend on processing conditions and alloy microchemistry. These generic model results will then be followed by a case study where the ALSOFT model is applied and its prediction power discussed in relation to a recent comprehensive experimental study for the back-annealing behavior of selected Al-Mn-Fe-Si–alloys with various microchemistries presented in a series of papers by the present authors (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Huang, Li et al. 2015, Huang, Li et al. 2015, Huang and Marthinsen 2015, Huang, Loge et al. 2016, Wang, Huang et al. 2016, Huang, Zhang et al. 2017). These experimental studies have clearly shown that the softening behavior during back annealing of cold rolled Al-Mn(Fe-Si) alloys is the result of a critical balance between the processing conditions and microchemistry and its associated changes during processing, in terms of size and number of constituents, solute level of alloying elements and in particular the presence of dispersoids. In particular, it has been shown that finely dispersed dispersoids, whether preexisting or precipitated concurrently with the recovery and recrystallization reaction, may strongly retard the softening kinetics and give a coarse and uneven grain structure. In view of the ability of the ALSOFT model to capture these phenomena and to reproduce the characteristics of these experiments, the chapter will end with a critical review and discussion of our current understanding, and models for the recovery and recrystallization behaviour in commercial Al-alloys, and suggest some ideas for modifications that might be adequate and necessary to handle cases/conditions where current model(s) are not satisfactory.

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2. MODELING RECOVERY AND RECRYSTALLIZATION IN PARTICLE CONTAINING AL-ALLOYS 2.1. The ALSOFT Model The main concepts and mathematical implementation of the ALSOFT model is well documented in the literature (Vatne, Furu et al. 1996, Vatne, Marthinsen et al. 1996, Saeter 1998, Engler, Lochte et al. 2007); however for completeness and as basis for discussing already implemented and possible further extensions of the model, the main ingredients will be also be presented here. The ALSOFT model is based on a two-parameter description of the asdeformed sub-structure after cold/hot deformation where the microstructure is characterized by an average sub-grain size, , and a dislocation density, i, inside the sub-grains. The average sub-grain size after deformation can be obtained from experiments or from adequate models, like the ALFLOW model, e.g., (Nes 1997, Marthinsen and Nes 2001, Nes and Marthinsen 2002). For hot deformation, the following empirical relationship between the subgrain size and the Zener-Hollomon parameter has been found to be adequate (Nes 1995): =

⇌ 𝑙𝑛

(1)

where A and B are alloy-dependent constants, and Z is the Zener-Hollomon 

parameter, Z =  exp[Q/RT]. Here Q is an activation energy and R is the universal gas constant. The sub-grain size  and the dislocation density i

   , where

are in this case linked through the scaling relationship  i  C

2

C is a constant ~2. During annealing of the as-deformed state recovery will take place through sub-grain growth and by annihilation of the sub-grain interior dislocations. In the original version of the ALSOFT model, recovery

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kinetics is assumed to be controlled by solute drag, where the rate controlling mechanism is assumed to be thermal activation of solute atoms away from climbing jogs. Based on this assumption the following explicit evolution equations with time for sub-grain size and dislocation density, respectively, have been derived (Nes 1995, Saeter 1998, Engler, Lochte et al. 2007):  A Gb 4  i (t )   Ua  d  i (t ) 2 sinh   vD bA B  i (t ) 3/ 2 exp        dt kT (t )  RT (t )    A  w  csseff



(2)

e

 A Gb4 1   U  d (t ) eff  e (3)  vDbA B exp   a  2sinh    ; A  w  css  dt  RT (t )   kT (t )  (t ) 

Here G is the shear modulus, b is Burgers vector (b = 0.286 nm in aluminum), SB is the sub-boundary energy, vD is the Debye frequency, k is Boltzmann’s constant, w , and e , are model parameters, and B , eff

alloy specific fitting constants. css is an effective level of solute (at%) derived from a summation of the solute concentration of the individual alloy elements, weighted with their activation energy for diffusion. Ua is an activation energy, which in the case of solute drag equals that of diffusion of the relevant solutes. The instantaneous stored energy/driving pressure for recrystallization due to cell interior dislocations and sub-grains is calculated according to the following equation:

PD (t )  

 SB 1 2  Gb i (t ) 2  (t ) 2

(4)

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In this equation the subgrain boundary energy can be approximated by the Read-Shockley relation as follows (Read 1953, Humphreys and Hatherly 2004):

 SB 

Gb    ln  e c  4 1      



is the Poisson ratio,

where and

(5)

 is the average subgrain misorientation

c is the critical value at which a sub-boundary becomes a high-angle

boundary (typically taken to be ~15o). is a constant of the order of three. In the presence of finely dispersed dispersoids a dragging pressure, i.e., a Zener pressure PZ(t) will result. With dispersoids of average size, rp(t), and a volume fraction of, fp(t), (both which may change with time due to precipitation) the classical Zener pressure expression is given by (Nes, Ryum et al. 1985, Humphreys and Hatherly 2004):

PZ (t ) =

3 f p (t ) gGB 2 rp (t )

(6)

and the driving pressure for recrystallization has to be modified eff

accordingly, i.e., giving an effective driving pressure PD (t ) :

PDeff (t )  PD (t )  PZ (t )

(7)

In this case, with a Zener pressure from dispersoids, the equation for sub-grain growth has in the present work also been modified accordingly, i.e., in analogy with normal grain growth, the driving pressure resulting from curvature is reduced by the Zener drag and the following equation is obtained:

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 A  Gb4  Ug  d b3     DbA B  exp    PZ (t )     2sinh   4 (t )   dt  RT (t )   kT (t )   (t )

125 (8)

the consequences of which will be discussed later in this paper. The recrystallization module of ALSOFT is an extension of the classical Johnson-Mehl-Kolmogorov-Avrami (JMAK) approach, treating recrystallization as a nucleation and growth process (Kolmogorov 1937, Avrami 1939, Johnson 1939, Avrami 1940, Avrami 1941). Nucleation of recrystallization is assumed to take place from sub-grains, which fulfill the general nucleation criteria for recrystallization, i.e., sub-grains that fulfil the Gibb’s Thomson relationship:

 * (t ) 

4 GB PD (t )  PZ (t )

(9)

and which moreover are surrounded by high-angle boundaries, i.e., at deformation heterogeneities in the material where this is the case. In the current version of ALSOFT, three types of nucleation sites are considered, i.e., nucleation from deformation zones around large particles (PSN), nucleation from old grain boundaries and nucleation from retained cube bands (Daaland and Nes 1996, Vatne, Furu et al. 1996). The total density of nucleation sites is given by

NTot =NC +NGB +NPSN

(10)

The density of PSN sites, NPSN, is determined by an integration of the particle size distribution f ( ) : 

N PSN  CPSN  f ( )d *

(11)

where the particle size distribution is characterized through the distribution parameters N0 and L, i.e.,

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f ( )  N0 L exp( L )

(12)

where CPSN is a constant which determines the number of recrystallized grains nucleated at each particle that is larger than *. * is a critical particle size for a successful nucleation of a grain (assumed to scale with Eq. 9) that can be derived from the Gibbs-Thompson equation, i.e., *=4GB/(PD-PZ), where GB is the specific grain boundary energy between the nucleus and the deformation matrix. The following relationship results for the nucleation of PSN nuclei:

 4 L  N PSN  C PSN N 0 exp   GB   PD  PZ 

(13)

The density of cube sites, Nc, is given by

NC  CC C A( )(1  RC ) RS SC* (14)

(14)

Here  C is the average size of the cube subgrains, with  C  1.3   matrix , A() is the surface area per unit volume of cube grains that have undergone a deformation of an effective strain , RS is the fraction of cube bands surrounded by the S deformation texture component and Sc* is the density of over-critically large subgrains within the cube bands. A() is given by the initial grain size D0 and the instantaneous volume fraction of cube in the material, Rc= f(,Z). The factor (1-RC) is included because a cube band with another cube grain as neighbor will not provide nuclei and CC is a constant (Vatne, Furu et al. 1996). In analogy with Eq. (14) the density of grain boundary nuclei becomes: * NGB =2CGB  matrix (1- RC ) SGB A( )

(15)

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where the different terms have the same/corresponding meaning as above and CGB is a (fitting) constant. The recrystallization kinetics is calculated by applying the standard assumptions of site saturation nucleation kinetics and a random distribution of nucleation sites, i.e., the following transformation kinetics equation is obtained:

dX (t ) 2  1  X (t )  NTot 4   r (t )   G (t ) dt

(16)

Here X(t) is the fraction recrystallized after an annealing time t, r(t) is the size and G(t) the growth rate of the recrystallized nuclei/grain. These two quantities are linked through the following relationship:

dr  G (t ) dt

(17)

where growth rate is generally given by

G (t )  M (t )   PD (t )  PZ (t ) 

(18)

Here M(t) is the boundary mobility (assumed to be orientation independent) which depend on the temperature through the following Arrhenius type relation:

M (t ) 

M0  U  exp   RX  c kT  RT  eff ss

(19)

Here URX is an activation energy for migration of high-angle grain boundaries, most likely determined by slow diffusing elements like Mn. The effect of solute drag is included through the inverse proportionality to

csseff , a dependency consistent with the high solute limit of the classical

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Cahn-Lücke-Stüwe approach (Cahn 1962, Lucke and Stuwe 1971). In the case of a multicomponent alloy, the total concentration of solutes, csseff , is derived from summation of the solute concentration of the individual alloy elements, weighted by their activation energy for diffusion of the solutes (Vatne 1999). Once the fraction recrystallized is determined, the grain size in the transformed regions can then easily be calculated as:

D  ( X / NTot )1/3

(20)

where NTot is the total number of nuclei (Eq. 10), while the fractions of the different recrystallization texture components are given as fi = Ni /NTot. The assumption of site-saturation nucleation kinetics has partly been introduced for mathematical convenience, but it has also been shown to be an adequate assumption for aluminum for recrystallization following hot deformation (Daaland and Nes 1996, Alvi 2005, Alvi, Cheong et al. 2008). However, it is a question whether this assumption still holds for recrystallization following cold deformation and more specifically during non-isothermal annealing conditions. This aspect will be discussed later in the chapter. Because of the combined reactions of recovery and recrystallization, the associated yield stress (YS) during back-annealing is then given by the following relationship (Saeter 1998, Marthinsen, Abtahi et al. 2004, Engler, Lochte et al. 2007):



 y (t )   0 (t )  1MGb i (t )   2 MGb 

1  1  X (t )   (t ) 

(21)

where 1 and 2 are constants, with typically values of 0.3 and 2.5, respectively. 0 is the yield stress of the fully soft condition and may be expressed through

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 o (t )   i   ss (t )   p (t ) where

129 (22)

 ss (t ) is the strength contribution from atoms in solid solution:

css (t )  k  css0  csseff (t )    1/ 2

0

Here css is a base level of solute due to impurity atoms (and/or minority solute atoms not for accounted by

 ss (t ) and  p (t ) is the

strength contribution from non-shearable particles (primary particles and/or dispersoids), i.e.:

 p (t ) 

AGbM 1.24  2

    1      ln ;  0.8 2    rp      fp   b    

(24)

k is a constant that has to be fitted to the actual alloy, and A is a constant of the order of one.  is the particle spacing (surface to surface) in the slip plane (Brown 1971, Nes and Marthinsen 2002).

2.2. Generic Model Predictions The present work is based on a MATLAB-implementation of ALSOFT where the time-temperature schedule during annealing can be explicitly specified on input, together with the corresponding time evolution of the effective solute level (Eq. 23) and the Zener drag (Eq. 6). In order to illustrate how the model responds to different processing parameters during deformation and back-annealing as well as material parameters depending on alloy composition, initial microstructure (grain structure and texture) and microchemistry state (i.e., solid solution level, volume fraction/number density and size/size distribution of constituents

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particles and dispersoids, as determined by the casting and homogenization procedure), a set of generic model simulations has been carried out with representative variations in these parameters relevant for this work and AA3xxx-alloys in general (Marthinsen, Abtahi et al. 2004, Sjolstad, Marthinsen et al. 2004). The generic model calculations also include modeling results showing how the model responds to some key model parameters that generally have to be fitted to/determined from experiments. This has been done to illustrate the sensitivity of the model to these parameters and also as a basis for discussing the actual model predictions presented in the next section where the model is used in relation to the experimental results presented in previous work (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Wang, Huang et al. 2016). The effect of dispersoids, through the Zener drag effect (cf. Eq. 6), on softening kinetics and final grain size (through the effect on nucleation (Eq. 9)) is considered in some detail, including the consequences of the new recovery model which also accounts for a possible Zener drag effect during recovery. As a reference for the model calculations given in this part, input parameters corresponding to the as cast condition of an AlMnFeSi-alloy (1wt% Mn, 0.5 wt% Fe, 0.15wt% Si; denoted C2 (cf. Table 1 below)), cold rolled to a strain of  = 3, and isothermally annealed at T = 300oC, is used (for details see (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Wang, Huang et al. 2016)). This is also the processing condition used if not explicitly stated differently. A complete list of input parameters is given in Appendix (cf. the case study chapter for some more details on the choice of relevant material parameters). A large number of these parameters are kept fixed throughout the calculations presented here, partly for convenience but also since most of them is supposed to be adequate for this work as they come from previous work/applications of the ALSOFT-model on similar alloys and conditions, including a set of activation energies relating to boundary migration and diffusion in AlMn-alloys (Marthinsen, Abtahi et al. 2004, Sjolstad, Marthinsen et al. 2004, Engler, Lochte et al. 2007)]. The first simulation example refers to the effect of varying (isothermal) annealing temperature. Temperature affects both recovery kinetics (cf. Eqs. 2-3), as well as recrystallization kinetics (growth rate of

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recrystallized grains; Eqs. 18 and 19) as illustrated in Figure 1. At high enough temperature recrystallization takes place within a very short time and the recovery stage is almost completely suppressed. The shift in time to reach the fully soft (recrystallized) condition is primarily determined by the activation energy in Eq. 19. It should be noted though that in the present version of ALSOFT, with site saturation nucleation, the final grain size is not influenced by the annealing temperature, as the density of nucleation sites is determined by the as deformed condition alone (Eqs. 915 & 20). The effect of deformation conditions (temperature, strain and strain rate) will manifest itself in terms of a different as deformed condition, i.e., a different mean sub-grain size and a different sub-grain interior dislocation density, which again determines the stored energy and driving force for the recovery kinetics and recrystallization during subsequent annealing (Eq. 4), as well as the as deformed yield strength (Eq. 21). The effect of stored energy on the recrystallization kinetics and final grain size is illustrated in Figure 2 for a limited range of sub-grain sizes relevant to this work ( ~ 0.45 – 0.65 m). As noted, the most pronounced effect is on the initial yield stress and initial recovery rate as well as on the final grain size (60% increase). Decreasing stored energy increases the critical subgrain size for nucleation, and makes nucleation more “difficult,” i.e., the density of all three nucleation sites decreases and the final grain size becomes larger. For a given set of processing conditions, the alloy composition and microchemistry state may also have a significant influence on the softening behavior. Figure 3 illustrates the effect of variations in effective solute content (corresponding to the range of effective solute level of Mn (at%) obtained by the different homogenizations used in paper (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Huang, Li et al. 2015, Huang, Li et al. 2015, Huang and Marthinsen 2015, Huang, Loge et al. 2016, Wang, Huang et al. 2016, Huang, Zhang et al. 2017). Decreasing the effective solute level strongly influences the recovery kinetics, consistent with Eq. 2 and 3 for which solute drag is assumed to be the rate controlling mechanism. Also the recrystallization kinetics is slowed down in accordance with the

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inverse proportionality of the mobility to the (effective) solute level in Eq. 19.

Figure 1. Generic model calculations showing the effect of different annealing temperatures on the softening behaviour of an Al-Mn-Fe-Si-alloy cold-rolled to a strain of  = 3.

Figure 2. Generic model calculations showing the effect of differences in initial stored energy/driving force for recrystallization on the softening behavior of an Al-Mn-Fe-Sialloy cold-rolled to a strain of  = 3. (a) Kinetics. (b) Evolution in recrystallized grain size.

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Figure 3. Generic model calculations showing the effect of different (effective) solid solution levels on the recovery and recrystallization behavior Al-Mn-Fe-Si-alloy coldrolled to a strain of  = 3.

Figure 4. Generic model calculations showing the effect of differences in the mobility pre-factor M0 on the softening behavior of an Al-Mn-Fe-Si-alloy cold-rolled to a strain of  = 3.

The latter dependency is closely related to the mobility pre-factor factor M0 (Eq. 19). This parameter is generally difficult to obtain, both theoretically and from experiments, and it is commonly taken as a fitting parameter using an initial value obtained from one or more reference experiments (for a given alloy and processing condition). As we can see

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from Figure 4, when M0 changes with several orders of magnitude, the kinetics (time in seconds to recrystallized fraction) changes accordingly. As demonstrated in (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Huang, Li et al. 2015, Huang, Li et al. 2015, Huang and Marthinsen 2015, Huang, Loge et al. 2016, Wang, Huang et al. 2016, Huang, Zhang et al. 2017) the actual homogenization procedure may have a strong influence on the microchemistry state, both in terms of number density and size/size distribution of constituent particles and dispersoids where both types of particles may have a strong effect on the softening behavior.

Figure 5. Generic model calculations showing the effect of differences in size distribution of constituent particles (potential PSN activity) on the softening behavior of an Al-Mn-Fe-Si-alloy cold-rolled to a strain of  = 3. (a) Kinetics. (b) Evolution in recrystallized grain size.

The effect of varying particle structures, again referring to the C2 alloy and the range of particle structures observed for this alloy, is illustrated in Figure 5. With the rather limited variations present for these alloys, the difference in kinetics is limited (through Ntot and NPSN and its effect on the recrystallization kinetics Eq. 11). The most noticeable effect, although still limited is on the final grain size (Figure 5b). Much more considerable effects may be obtained in the presence of dispersoids, present in the form of high number density and small size. The effect of different scenarios, partially artificially, corresponding to the Zener drag variations given in Figure 6, goes far beyond what has been observed for the relevant C2-alloy. However, some extreme variants are

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included as they still have relevance for some of the experimental observations made in (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Huang, Li et al. 2015, Huang, Li et al. 2015, Huang and Marthinsen 2015, Huang, Loge et al. 2016, Wang, Huang et al. 2016, Huang, Zhang et al. 2017), in terms of kinetics and final grain structures (slow kinetics and very coarse grains). Referring to Figure 6, the first 3 variants refer to cases with an increasing Zener drag resulting from pre-existing dispersoids affecting both nucleation of recrystallization and softening kinetics. A case with PZ = 0 is included for reference (dotted line). For the first three cases the effect is most noticeable on the kinetics, and for the third case with PZ = 0.2 MPa recrystallization stops before 100% completion because

PD (t )  PZ as a result of significant recovery, and the final stage of softening takes place by “extended” recovery (sub-grain growth and dislocation annihilation) of the remaining deformation structure. In the latter two cases, an even higher Zener drag, acting only during nucleation, has been introduced, the main effect being that nucleation of recrystallization is strongly suppressed and the final grain size can become very large (cf. Eq. 9 and the critical particle size for nucleation

*   * 

that goes into Eq. 11).

Figure 6. Generic model calculations showing the effect of differences in Zener drag (Eq. 6), both pre-existing and during annealing, on the softening behavior of an AlMn-Fe-Si-alloy cold-rolled to a strain of  = 3. (a) Kinetics. (b) Evolution in recrystallized grain size. (Note: Zener drag values in legends is given in units of Pa).

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Figure 7. Generic model calculations using a modified sub-grain growth expression (Eq. 8) including Zener-drag effects and its effect, as function of different Zener drag (pre-existing and during annealing), on recovery and its resulting effect on the overall softening behaviour of an Al-Mn-Fe-Si-alloy cold-rolled to a strain of  = 3. (a) Kinetics, Tanneal = 300oC; (b) Kinetics, Tanneal = 400oC; (c) Evolution in recrystallized grain size, Tanneal = 300oC c) Evolution in recrystallized grain size, Tanneal = 400oC; (e) Sub-grain size evolution during annealing, Tanneal = 300oC; (f) Sub-grain size evolution during annealing, Tanneal = 400oC.

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As mentioned in the previous section, as the alloys considered in this work are assumed to be strongly influenced by dispersoids and Zener drag effects, a modified recovery expression for sub-grain growth has been derived (Eq. 8) which also include a possible Zener drag effect on the migration of sub-grain boundaries. Different scenarios are illustrated in Figure 7, referring to two different annealing temperatures and different increasing values of the Zener drag acting both during nucleation of recrystallization and during recovery and recrystallization (i.e., pre-existing dispersoids). The general trend with increasing Zener drag is that recovery is reduced/slowed down and onset of recrystallization delayed, the latter follows from lower nucleation density (suppressed nucleation) as discussed above, which is also indicated by the increasing grain size as shown in Figures 7c and d. The reduced recovery rate is explicitly illustrated by the sub-grain growth curves in Figures 7e. For annealing at 400 oC we also see that at the highest Zener-drag, sub-grain growth completely stops after a certain time, indicating that the driving force for further sub-grain growth is balanced by the Zener drag, an effect analogous to the Zener-limiting grain size experienced during normal (curvature driven) grain growth in the presence of particles. It is interesting to note that such a Zener-limited sub-grain growth in the context of the ALSOFT model has also recently been considered in (Myhr, Furu et al. 2012), however, in their work it was just set as cut-off given by the Zener-limiting sub-grain/grain size (Humphreys and Hatherly 2004). The above discussion show that recrystallization kinetics is difficult to model for conditions with strong particle drag, it is actually even more challenging if the grain structure after recrystallization needs to be considered, this is illustrated below in Figure 8. The Al-Mn-Fe-Si samples in as-cast states (C1-0) were homogenized at two different conditions to achieve two desired levels of Mn in solid solution (C1-2 and C1-3) and, in turn, different densities of dispersoid particles. It is enough to state that C13 has the least Mn in the solid solution while C1-0 has the highest, leading to different precipitation potential. The interested readers are referred to (Huang, Engler et al. 2015) for more details. These three variants were subjected to the same cold rolling process before annealing at different

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conditions. The fact that both annealing conditions and microchemistry of the samples have great influence on the recrystallization kinetics and final grain structure can be easily seen in Figure 8. When non-isothermally annealed to 300oC for 105s, recrystallization has completed in C1-3 (see Figure 8g) while it has not initiated for the sample of C1-0 (see Figure 8a). The big difference in grain structure is also obvious when comparing the samples of C1-0 (Figure 8c) and C1-3 (Figure 8i) annealed to 500 oC.

Figure 8. EBSD micrographs showing the effect of microchemistry on the final recrystallized microstructure non-isothermally annealed to different temperatures and hold for 105 s, samples were cold rolled to a strain of 3.0. (a) C1-0, 300 °C@105 s; (b) C1-0, 400 °C@105 s; (c) C1-0, 500 °C@105 s; (d) C1-2, 300 °C@105 s; (e) C1-2, 400 °C@105 s; (f) C1-2, 500 °C@105 s; (g) C1-3, 300 °C@105 s; (h) C1-3, 400 °C@105 s; (i) C1-3, 500 °C@105 s.]. (Huang, Engler et al. 2015).

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2.3. Recrystallization Kinetics and the Influence of Non-Random Spatial Distribution of Nucleation As explained above, the ALSOFT model is based on the classical Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation (Humphreys and Hatherly 2004), and thus the assumption that the nucleation sites are randomly distributed in space (Kolmogorov 1937, Avrami 1939, Johnson 1939, Avrami 1940, Avrami 1941), i.e., X V (t )  1  exp(kt ) (referred n

to as the JMAK equation), where XV(t) is the volume fraction of transformed material at the annealing time t, k is a function of growth rate and nucleation rate/density of viable recrystallization nuclei and n the socalled Avrami exponent. In the special case of constant growth rate and a random spatial distribution of nucleation sites, the JMAK equation (1) is exact with n = 4 when also the nucleation rate is constant (Johnson-Mehl nucleation kinetics) and n = 3 when the nucleation rate decreases so rapidly that all nucleation events effectively occur at the start of recrystallization (site saturated nucleation). The latter is consistent with what is used in the ALSOFT model. However, in many cases Avrami exponents of 3 or 4 are not observed, and in general the Avrami exponent varies with time (fraction recrystallized) and typically found to be less than 3 and in some cases even below 2. It is well known that nucleation of recrystallization is a highly heterogeneous process which typically takes place at deformation heterogeneities like shear bands, transition bands and in deformation zones around large particles (Humphreys 1977). Nevertheless, the assumption of a random spatial distribution of nucleation sites (a prerequisite for the JMAK-equation is often a good assumption, and for an Al-Mg-Mn alloy (AA3004) it has actually been confirmed experimentally that this is an adequate assumption (Daaland and Nes 1996). At the same time computer simulations have shown that both the spatial distribution of nucleation sites and the nucleation rate may influence the transformation kinetics and the recrystallized grain structure in a significant way (Srolovitz, Grest et al. 1988, Furu, Marthinsen et al. 1990, Novikov and Gavrikov 1995,

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Marthinsen 1996, Marthinsen and Ryum 1997, Marthinsen, Fridy et al. 1998). A 3D computer simulation procedure originally developed by Mahin et al. (Mahin, Hanson et al. 1980) and later modified to include more general growth rate variations and nucleation models (Marthinsen, Lohne et al. 1989, Saetre, Hunderi et al. 1989) have been used to analyze the influence of various non-random spatial distributions of nucleation sites (Furu, Marthinsen et al. 1990, Marthinsen, Fridy et al. 1998). This is a three-dimensional model in which nuclei are spatially distributed within a cubic volume with periodic boundary conditions start to grow according to a specified nucleation model, and where nucleated grains grow according to a given growth law and the transformation is complete when the grains impinge on one another. The resulting microstructure is analyzed in a twodimensional section through the cube (similar to most experimental observations), and the model can handle thousands of grains, allowing the kinetics as well as the microstructure evolution (i.e., size distribution of recrystallized grains) to be followed. Using this 3D simulation procedure, e.g., it was found that with different degrees of spatial clustering of nucleation sites and site saturation nucleation kinetics, that clustering may have a profound effect on both the Avrami exponent n and on the resulting sectioned grain size distributions (Marthinsen, Fridy et al. 1998). Assuming site-saturation nucleation kinetics, the Avrami exponent decreased rapidly from the expected value of 3 with the degree of clustering, and a value of less than 1.5 was observed with a strongly clustered distribution of nucleation sites. Moreover, the size distributions of sectioned grain areas were considerably broadened with clustering as compared to that resulting from randomly distributed nucleation sites. These results illustrate that spatially inhomogeneity of nucleation sites is an important factor that needs to be accounted for when considering recrystallization kinetics and microstructure, and is one factor (amongst several others) which may explain the low (and non-constant) Avrami exponent often observed experimentally.

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In heavily deformed commercial aluminum alloys containing large second phase particles, particle stimulated nucleation (PSN) of recrystallization is often the most important and dominating nucleation mechanism (Humphreys 1977), and the spatial distribution of the large constituent particles is therefore important for the recrystallization behavior. Although the assumption of a near random distribution of particles is fulfilled (Marthinsen, Fridy et al. 1998), exceptions do exist. Marthinsen et al. (Marthinsen, Daaland et al. 2003) investigated the spatial distribution of nucleation sites and its effect on the recrystallization kinetics in two commercial Al alloys (commercial purity AA1145, and an Al-Mg-Mn alloy (AA3004) during cold rolling. They documented a transition from a rather non-uniform spatial distribution of particles at low rolling strains, towards a more or less random distribution at high strains. An important point in this connection is that with a non-random distribution of nucleation sites one of the basic assumptions of the classical JMAK approach (Kolmogorov 1937, Avrami 1939, Johnson 1939, Avrami 1940, Avrami 1941) is no longer valid, and (semi-)analytical modelling based on the JMAK approach of recrystallization (like the ALSOFT model) is in general no longer possible. In this case one has to resort to spatially discrete computer simulations, like Potts Monte Carlo models or Cellular Automata models (e.g., (Srolovitz, Grest et al. 1988, Marx, Reher et al. 1999)).

3. RECOVERY AND RECRYSTALLIZATION BEHAVIOR OF ALMNFESI ALLOYS - A CASE STUDY In the following, the ALSOFT model in its current state and as presented in the modeling section is applied to the experimental results presented in (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Wang, Huang et al. 2016). As far as possible experimentally measured relevant material parameters (e.g., alloy composition, as cast grain size) and microstructure parameters (size and number density of primary particles

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and dispersoids) have been used as input. Comparisons with experiments and modeling results are made in terms of the softening behavior (yield stress versus time) and final recrystallized grain size. The relevant material parameters for the two different alloys considered, i.e., alloy 1 (0.4wt%Mn, 0.5 wt%Fe, 0.15wt%Si) and alloy 2 (1wt% Mn, 0.5 wt% Fe, 0.15wt% Si), only differing in the amount of Mn, as well as the relevant microstructure parameters resulting from the different homogenization treatments (cf. Table 1 below) are given in Table 2 in Appendix. After homogenization both alloys were cold rolled to a strain of  = 1.6 and  = 3. In the following these two alloys are denoted C1 and C2, respectively, being consistent with previous literature about these alloys (e.g., (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Wang, Huang et al. 2016)). Here the numerical values for the stored energy, PD, and Zener drag, PZ, refer to the initial as-deformed state (or after just a few seconds of initial annealing (5–10 s) for the conditions where the Zener drag mainly originate from concurrent precipitation (cf. (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Wang, Huang et al. 2016)). The actual model parameters used (those that have changed from condition to condition) are given in Table 3 in Appendix. It is noted that for some conditions the as deformed structure in terms of sub-grain size and subgrain interior dislocation density have been adjusted to fit the as deformed yield stress. Table 1. Four homogenization procedures (including the as-cast condition) and resulting different concentration levels of Mn in solid solution for alloy C2 Sample C2-0 C2-1 C2-2 C2-3

Mnss [wt%] 0.69 0.35 0.23 0.21

Dispersoids

Homogenization procedure

Low Low Medium High

As-cast condition 50oC/h up to 600oC + 24h@600oC + quenching 50oC/h up to 450oC + 24h@450oC + quenching 50oC/h up to 600oC + 4h@600oC + 25oC/h down to 500oC + 4h@500oC + quenching

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For the conversion of hardness (VHN), as measured experimentally in the previous papers ((Huang, Wang et al. 2014, Huang, Engler et al. 2015, Wang, Huang et al. 2016)) to yield strength (YS) (provided by ALSOFT) the following simple relationship has been used:

YS ( MPa)  4.5*VHN  85

(25)

This relationship is consistent with the ones found independently by (Sjølstad, Marthinsen et al. 2004) and (Sande 2011) for similar alloys and conditions. The resulting experimental yield strength for the different conditions of the C2 alloy (Cf. Table 1 in Appendix) is used as basis to estimate the individual contributions of solid solution strengthening and particle strengthening in Eq. 22. The intrinsic yield stress of the fully soft condition, i, in Eq. 22 is taken to be 10 MPa, a typical value for high purity aluminum alloys. In order to calculate the particle contribution to the yield stress (Eq. 24) the volume number density NV is required while the area density NA is what one obtained from experiments (SEM BSE micrographs) (Wang, Flatoy et al. 2012, Wang, Huang et al. 2016). For the conversion the following formula has been used (Li 2010):

NV 

NA t t kd part  t

(26)

Here dpart is the mean particle diameter measured from 2D sections in SEM-BSE images and t is the penetration/information depth taken to be 30 nm at a typically used acceleration voltage of 10 kV. The volume fraction of particles (fp) is then easily calculated, and also the inter-particle spacing,  (Eq. 24). When calculating p from Eq. 24 a value of A = 0.7 is used and the Taylor factor is set to M = 3.06 (the value of random texture) (Brown

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1971). Finally best-fit values of k and css in Eq. 23 are found to be 0

k = 1.95e9 and css = 0.0012.

Figure 9. Experimental softening curves and corresponding model predictions for the C1-3 alloy for different annealing temperatures during annealing after cold rolling to a strain of  = 3.

During softening the value of in Eq. 21 is kept constant. In reality due to possible concurrent precipitation, the individual contributions from solid solution (decreasing) and from dispersoids (increasing) may change. However, the two contributions may most probably (at least partly) counterbalance each other, and the effect is therefore for convenience neglected in the present work. The model predictions of the softening behavior of the C1 alloy, together with the corresponding experimental results (corresponding to strain of  = 3), for homogenization No. 3 (50oC/h to 600oC + 4h@600oC + 25oC/h to 500oC + 4h@500oC + quenching; (Wang, Huang et al. 2016)) is shown in Figure 9 (named C1-33; first figure: alloy; second figure: homogenization; third figure: strain ( = 1.6(2);  = 3(3)). This homogenization variant is designed to give considerable precipitation (little Mn left in solid solution after homogenization) and few and fairly large dispersoids, i.e., relatively low Zener drag. Relevant input parameters are given in Table 3 in Appendix. In lack of experimental data for as-deformed sub-grain size and the particle

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size distribution of constituents (for this particular alloy), similar values as for the C2 alloy for the same homogenization conditions are used. In view of the generic simulations in the previous section with different values of these parameters, this is not believed to represent any significant cause of “error.” Although the experimental results are scarce and somewhat scattered the calculated softening curves seems to compare well with the experimental results. The final recrystallized grain size (for all temperatures) is predicted by ALSOFT to be D = 14 m as compared to an experimental value of D = 12 m. Changing now to homogenization variant No 2 (50 oC/h to 450 oC + 4h@450oC + quenching) of the C1-alloy after strain of = 3 (C1-2-3). Also for this variant most of the Mn precipitate during homogenization (i.e., limited amount of Mn remains in solid solution and thus also limited potential for concurrent precipitation), however in this case a relatively large amount of relatively small pre-existing dispersoids results, giving a static Zener-drag during back-annealing of PZ = 3x104 Pa. The corresponding softening curves are shown in Figure 10.

Figure 10. Experimental softening curves and corresponding model predictions for the C1-2 alloy (incl. pre-existing dispersoids) for different annealing temperatures during annealing after cold rolling to a strain of  = 3.

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In this case as well the modeling predictions reproduce the experimental results quite well, except for the lowest temperature where a considerable discrepancy is observed for larger times, where the experimental results show very slow kinetics and a fully soft condition is not reached even after 105 s of annealing. However, by a combination of a (un-physical?) much lower mobility pre-factor M0 (1/10) and a tripled PZ value a somewhat better agreement may be obtained (dashed line). The predicted grain size is higher than for the first case, i.e., D = 26 m, however, which also compares reasonably well with experiments, D = 22 m (cf. Table 2). We then move to the C2-alloy with the higher amount of Mn (1 wt%). We also start here with homogenization variant No. 3, i.e., the condition with a fairly coarse dispersoid structure and very limited concurrent precipitation. Except for changing the initial sub-grain sizes, in accordance with the experimentally measured values for this alloy at strain of = 1.6 and  = 3 (named C2-3-2 and C2-3-3, respectively), and the Zener drag resulting from the pre-existing dispersoid structure, mainly the same model parameters as for the C1 alloys are used. In addition, two other parameters have been changed, i.e.,  = 4 and CPSN = 0.1. The modeling results together with the relevant experimental results are shown in Figure 11. Again ignoring a considerable scatter in the experimental results, the model predictions seem for most of the cases quite good. Only at the lower rolling strain (Figure 11a) and the lowest annealing temperature for long annealing times there are some discrepancies. The experimental and modeled grain sizes are given in Table 2. For the conditions of the largest recrystallized grain size, the grains are quite elongated in the rolling direction. Grain shape is not accounted by the ALSOFT model (i.e., only isotropic growth is considered), so the experimental grain sizes given in Table 2, are for comparison the calculated circular area equivalent diameter (ECD). Except for the lowest annealing temperature, the agreement is quite good. At this annealing temperature (T = 300oC) a better agreement is obtained both for the kinetics and the grain size with a higher pre-existing Zener drag (4x) and lower mobility (0.5x).

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Figure 11. Experimental softening curves and corresponding model predictions for the C2-3 alloy for different annealing temperatures during annealing after cold rolling to (a) strain of  = 1.6 and (b) strain of  = 3.

Table 2. Calculated and experimental measured (circle area equivalent diameter) of fully recrystallize grain structures Alloy/condition

Annealing temperature

C1-3-3 C1-2-3 C2-3-3 C2-3-2 C2-3-2 C2-2-3 C2-2-3 C2-2-3 C2-1-2 C2-1-2 C2-1-3 C2-1-3

All All 450/400/350 450/400/350 300 450 400 350 450/400 350 450/400 350

Experiment [m] 12 22 24/19/23 25/23/26 39 83 77 Na 22/20 32 19/23 52

Model [m] 14 26 19 28 28 88 45 na 19 22 18 21

Alt model [m]

45

We now turning to homogenization condition No. 1 (50oC/h to 600oC + 24h@600oC + quenching). In this alloy condition (C2-1) some precipitation has taken place (fairly coarse dispersoid structure), but significant Mn is still left in solution for potential concurrent precipitation during annealing (temperature dependent, see (Huang, Wang et al. 2014) for details). The corresponding modeling results together with relevant

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experimental results are shown in Figure 12. As shown, again a fairly good agreement is obtained for all conditions. In addition, the experimental and modeled grain sizes correlate quite well, although they are clearly underestimated at the lowest temperature considered (T = 350oC), i.e., the condition mostly affected by concurrent precipitation. It should be noted however, that to achieve this generally good agreement some modeling parameters needed to be changed (cf. Table 2&3 in Appendix), and some are also changed from condition to condition. Even more difficulties in reproducing the experimental results are experienced for homogenization condition No. 2 (i.e., C2-2; same as for C1-2 alloy), with a large amount of fairly small pre-existing dispersoids (considerable Zener drag acting during both nucleation and growth). Because of this, only a very few selected conditions are shown in Figure 13. The relevant material and model input parameters are given in Tables 1-3 in the Appendix. In particular, it is noted that a considerably higher initial Zener drag (acting during nucleation) need to be included to give reasonable kinetics and grain size, and consistent results were not obtained with the same parameters for all conditions. The annealing behavior at the lower temperatures and for the lower strain was not possible to model with reasonable input parameters and reasonable results.

Figure 12. Experimental softening curves and corresponding model predictions for the C2-1 alloy for different annealing temperatures during annealing after cold rolling to (a) strain of  = 1.6 and (b) strain of  = 3.

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Figure 13. Experimental softening curves and corresponding model predictions for the C2-2 alloy for different annealing temperatures during annealing after cold rolling to a strain of  = 3.

Attempts to model the softening behavior of the as cast variant C2-0 has not been successful at all. This variant is most strongly influenced by concurrent precipitation and neither the recovery behavior at temperatures and strains where recrystallization is completely supressed nor conditions which do recrystallize but very slowly and with a very coarse fine grain structure, have been possible to model, even with extreme and unphysical values of some of the model parameters.

4. DISCUSSION The generic model simulations presented in the first modeling section have clearly shown how and to which extent different material and model parameters influence the softening behavior and final grain structure. Most of the effects are quite easy to understand and in line with what one would expect. However, for certain quantities and model parameters the model dependency are more involved and their influence is not so easy to predict. For example, the effective solute level (Figure 3) has a quite significant effect on the recovery behavior while the effect on the recrystallization

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kinetics is less pronounced. Here a lower solute level considerably speeds up the recovery kinetics, which also means that the driving force for recrystallization decreases quite fast, at the same time as the mobility of grain boundaries of actual recrystallized grain increases, with the effects demonstrated in Figure 3. It should be commented that the solute dependency of the mobility (Eq. 19) used here is valid for conditions where solute drag is the rate controlling mechanism for boundary migration and in the limit of a “fully loaded” boundary (Lucke and Stuwe 1971, Hersent, Marthinsen et al. 2013). When the solute concentration,

csseff , decreases Eq. 19 will eventually break down. In such a case a more sophisticated solute drag model has to be used, which is also valid in the limit of very small solute concentrations, e.g., like the model recently presented by .(Hersent, Marthinsen et al. 2013). In the present work, the problem of a very (too) low effective solute level, is partly avoided by the 0

base level solute parameter css in Eq. 23. As already mentioned the effective solute concentration is also closely linked to the mobility pre-factor M0, which has a significant effect on the recrystallization kinetics (Figure 4). In principle this factor, once fitted to one relevant condition, should be kept constant for all conditions and alloys considered (within a certain class of alloys and similar processing conditions). As demonstrated in the previous section (Cf. Table 3 in Appendix) this was not possible in order to get reasonable fit between experiments and model predictions for all conditions in the present work. In particular, for conditions strongly affected by concurrent precipitation, significant changes in the M0 seemed necessary. This indicates a weakness of the model with possible changes in solute/dispersoid-boundary interaction mechanisms that is not properly accounted for by the model in its present state. In this connection, it should be mentioned that the value of in Eq. 21 was kept constant for all simulations in the present work. In reality, especially during conditions of concurrent precipitation, the individual contributions from solid solution (decreasing) and from dispersoids (increase) may change. However, the two contributions may

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most probably (at least partly) counterbalance, and the effect is therefore for simplicity neglected in the present work.  The generic model simulations show that several input parameters affect the final grain size, mainly those related to differences in processing conditions (deformation conditions) and the microchemistry state in terms of the size distribution of large constituent particles (potential PSN sites) and the size and volume fraction of dispersoids which determines the possible Zener drag operating. A Zener drag resulting from pre-existing dispersoids will, in accordance with general accepted theory (e.g., Humphreys and Hatherly 2004), affect the recrystallization kinetics in two ways, through a reduced effective driving force for recrystallization (Cf. Eq. 18) and through suppressed nucleation due the fact that the critical size for nucleation (Eq. 9) will be increased which again will decrease the density of all three types of nucleation sites (Eq. 13, 14 and 15), see Figure 6. When the Zener drag is large compared with the stored energy PD, even from the start of annealing, a very coarse grain structure may result, and if it becomes equal to the driving force PD (continuously decreasing during annealing) recrystallization will stop before completion (cf. Figure 6b). However, if the Zener drag is not acting during nucleation, but results from concurrent precipitation during annealing, the final recrystallized grain size will (according to the model) not be affected, only the kinetics. This is not consistent with most experimental observations in the present and previous work where conditions of strong concurrent precipitation tends to give very coarse-grained structures (Sjolstad, Marthinsen et al. 2004, Tangen, Sjolstad et al. 2010, Huang, Wang et al. 2014, Huang, Engler et al. 2015, Wang, Huang et al. 2016). This observation indicates another weakness of the model, especially for these conditions, which may indicate that the assumption of site saturation nucleation kinetics used presently is not adequate and needs to be relaxed to handle these cases. Attempts to modify the nucleation assumptions of ALSOFT, allowing for time-dependent nucleation have recently been reported and promising generic results were shown which were qualitatively in line with typical experimental behaviour (Marthinsen, Friis et al. 2013). It is based on the assumption that nucleation of recrystallization occurs by a kind of abnormal sub-grain

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growth mechanism during coarsening of the sub-grain structure during initial stages of annealing, consistent with previous ideas (Holm, Miodownik et al. 2003, Humphreys and Hatherly 2004) and also supported by some recent studies of sub-grain growth in similar alloys (Bunkholt, Marthinsen et al. 2013). Recent detailed experimental investigations of the initial stages of the microstructure evolution in the same alloys as studied here have also indicated time-dependent nucleation of recrystallization (or some kind of incubation time) (Huang, Zhang et al. 2017). The EBSD characterization of early stage of static recrystallization is detailed in Chapter 2 of this book. Since dispersoids and Zener drag effects is quite prominent in the alloys and condition considered, it is also reasonable to assume that Zener drag effects may act during sub-grain growth. Since sub-grain growth is treated analogous to normal grain growth (Furu, Orsund et al. 1995) it is assumed that a Zener drag will act on sub-grain boundaries in a similar way, reducing the effective driving pressure for growth, resulting in the modified sub-grain growth expression in Eq. 8. Its effect on the softening behavior is demonstrated in Figure 7, at two different annealing temperatures. As shown there, the effect is considerable both on the recovery stage and the recrystallization stage, both being increasingly retarded with increasing Zener drag. An important (modeling) effect of this reduced recovery behavior is that the stored energy decreases more slowly, and more seldom PD becomes less than PZ and recrystallization stops, which seems to be more consistent with general experimental observations than previous modelling results have indicated, without accounting for the Zener drag effect also during recovery. The recrystallized grain size evolution is shown in Figures 7c and d, and although not related to the different recovery behaviors, the curves illustrate what was also discussed above that a large initial Zener drag (from pre-existing dispersoids) may have a very strong effect on the grain size. The actual sub-grain growth behavior is shown in Figures 7e and f, where Figure 7f illustrates cases where growth is completely stopped when the Zener drag becomes large enough. In all application examples presented in the previous section, the Zener drag modified sub-grain growth equation (Eq. 8) with the

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appropriate Zener drag values obtained from experiments (cf. Tables 2&3 in Appendix) have been used with good model predictions indicating this modification to be appropriate. However, to reproduce both the kinetics and the final grain structure in conditions of significant Zener drag effects it has been necessary to increase the Zener drag acting during nucleation of recrystallization by 2-5 times of its nominal value (cf. Table 3 in Appendix), based on the experimentally measured mean size and number densities of dispersoids and the classical Zener drag expression in Eq. 6. Using more sophisticated expressions for the Zener drag taking into account, e.g., shape factors (Nes, Hunderi et al. 1985) and/or the whole size distribution of dispersoids (Furu and Vatne 2000) change the numerical values of the Zener drag, but is not expected to give changes of the order used in the calculations. Actually using the whole size distribution of dispersoids typically gives lower values for the Zener drag (Furu and Vatne 2000). An aspect which may influence the value of the Zener drag is subgrain/grain boundary –particle correlations (Humphreys and Hatherly 2004). Experiments indicate that the precipitation of dispersoids preferentially takes place on grain boundaries and sub-grain boundaries (the latter only relevant for concurrent precipitation). Such correlations may lead to an increased effective Zener drag. By assuming that the subgrains have a cubic shape with an edge length of , and that most of/all the dispersoids (of volume density NV, radius r and volume fraction fV) are located at sub grain boundaries, a new equation can be deduced to calculate the Zener drag force (Daaland and Nes 1996, Vatne, Engler et al. 1997). The Zener drag force due to sub-grain boundary dispersoids (where nA is the number of dispersoids per unit area of boundary) can be calculated by

PZSB  nA r   rNV

3



(27)

Using fV  4  r 3 N V to replace NV, the following expression results 3

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PZ 

 fV 

(28)

4r r

Comparing with the Zener drag force contributed by randomly distributed dispersoids (Eq. 6),

PZSB  PZrandom

 6r

So depending on the ratio 

(29)

the effective Zener drag value may be 6r increased considerably. However, for the present alloys and conditions, the values of the sub-grain and dispersoid sizes are such that this ratio is of the order of 1 for all conditions except the as-cast variant and thus not able to account for the artificially increased model values of PZ referred to above. If this still were the case, and the cause of suppressed nucleation, this also imply that nucleation of recrystallization cannot be site saturated but takes place after a certain incubation time giving time for (concurrent) precipitation to occur and pin the sub-structure (i.e., some kind of timedependent nucleation). On the other hand whether and to which extent classical Zener drag effects operates during recrystallization (i.e., retard boundary migration of a growing recrystallization grain) has recently been questioned (Humphreys and Hatherly 2004, Rollett 2013, Huang, Zhang et al. 2017) in contrast to what most classical literature presents (e.g., Humphreys and Hatherly 2004). The experimental results for the two highest annealing temperatures of the C1 alloy with (C1-2) and without (C1-3) pre-existing dispersoids (Figures 9 and 10) may be in support of such a view as limited or no effects of the pre-existing dispersoids on softening kinetics (although still some effect on the grain structure in terms of shape and size (Huang, Wang et al. 2014) are observed for the C1-2 condition (Figure 8) for these temperatures. On the other hand for the lowest annealing temperature (T = 300oC) the effect is quite obvious where the condition with pre-existing dispersoids is not even fully recrystallized at 105s. Partly recrystallized

Modeling of Recrystallization of Commercial Particle …

155

grain structures caused by dispersoids is also a well-known phenomenon which supports the classical view. The apparently contradictory observations above for the C1-alloy may indicate a temperature dependent particle drag effect that is not accounted for by the classical temperature independent Zener drag expression. From the very strong dispersoid effect for this alloy and also for several of the other conditions at lower temperatures (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Wang, Huang et al. 2016, Huang, Zhang et al. 2017) one can speculate about a boundary-particle interaction mechanism which involve some kind of thermal activation which give the strong “low temperature” effect while the particle drag effect weakens accordingly at higher temperature. The significant changes of the mobility prefactor M0 that was needed for a good fit in some of the simulation cases considered above, especially those strongly affected by concurrent precipitation, may be consistent with such an effect, and acted here as a “compensation” for the possible inadequate Zener drag expression for these conditions, or it may possibly be the mobility itself that is actually affected through a shift in migration mechanism. In the current version of ALSOFT, the Zener drag are included by explicitly specifying PZ(t) on input (i.e., through a weak coupling) where the relevant PZ(t) evolution may be obtained from experiments or an independent precipitation model. Ideally a fully coupled precipitation and recover/recrystallization model should be used (strong coupling) which in principle account for the effect on precipitation on recovery/ recrystallization (including changes in solid solution level (ignored in the present work) and the possible opposite effect of recovery/recrystallization on the precipitation behavior. Such a coupled model has recently been implemented (Hersent, Huang et al. 2013), based on a recently developed dedicated precipitation model for Al-Mn-Fe-Si-alloys. However, preliminary model predictions by this model indicates a too abrupt precipitation behavior, and a corresponding variation of the Zener drag which gives poor fit to experimental observations, an apparent deficiency which is not unique for this precipitation model.

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Thus further work is needed to provide a more adequate precipitation model which may be used in a fully coupled softening model, attempts towards this direction have been recently summarized in a review paper focusing on the interaction between recrystallization and second-phase particles (Huang, Marthinsen et al. 2018). [https://linkinghub.elsevier.com/ retrieve/pii/S0079642517301287]. It may also need a more sophisticated particle-boundary interaction model capable of predicting the complex behavior discussed in this and related work (Huang, Wang et al. 2014, Huang, Engler et al. 2015, Wang, Huang et al. 2016, Huang, Zhang et al. 2017).

CONCLUSION In order to describe the influence of microchemistry (solute and second-phase particles in particular) of commercial aluminum alloys on the softening behavior of particle containing alloys, the physical basis and mathematical formulation of the ALSOFT model accounting for the combined effect of recovery and recrystallization during back-annealing of heavily deformed aluminium alloys has been reviewed. A modified subgrain size evolution expression accounting also for a possible Zener drag effect during recovery has been introduced and has proved useful and adequate in model predictions of softening behaviors subjected to particle drag effects. To demonstrate the different phenomena of recovery and recrystallization and microchemistry interactions, generic model simulations relevant for Al-Mn-Fe-Si-alloys have been performed, which clearly illustrated how and to which extent key material and process parameters affect the softening behavior and the final grain structure. The actual microstructure evolution and associated softening behavior may be significantly affected by a number of material and specific process parameters. However, it is also clearly demonstrated that one of the most pronounced effects is obtained when a strong Zener drag is present already at the onset of recrystallization (i.e., from pre-existing dispersoids and/or

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157

dispersoids formed before nucleation of recrystallization take place) causing strongly suppressed nucleation of recrystallization giving heavily retarded softening kinetics and a very coarse grain structure. To further illustrate and exemplify the recovery and recrystallization behavior of particle containing commercial aluminum alloys, a set of available softening results for two different Al-Mn-Fe-Si-alloys and processing conditions, giving very different microchemistries in terms of solute and second-phase particle structure have been presented. The experiments clearly demonstrate the strong influence of different microchemistries and in particular the strong dispersoid effects that may be experienced during back-annealing, either from pre-existing dispersoids or concurrent precipitation. The experiments have been accompanied by corresponding model predictions by the ALSOFT model, and it has been demonstrated that the model provide quite good predictions, with consistent model parameters, of material and process conditions which experience no or limited influence of pre-existing dispersoids and/or concurrent precipitation. However, providing reasonable model predictions becomes increasingly challenging with increasing influence of dispersoid effects and concurrent precipitation, and for some conditions satisfactory agreement is only obtained with significant and apparently unphysical changes of some model parameters. For the most strongly affected conditions reasonable model predictions were not possible even with extreme changes in the model parameters. The latter observations emphasize that the ALSOFT model, and thus also mainly our current understanding of these phenomena and their complex interactions are not fully satisfactory, especially for alloys and conditions strongly affected by dispersoids, either pre-existing and/or as a result of concurrent precipitation. It is clearly needs for more work and further to improve our understanding and quantitative description (modeling) of these complex phenomena and interactions. An obvious limitation of ALSOFT model is the current assumption of site saturated nucleation kinetics, which is not consistent with certain experimental results, and consequently needs to be relaxed. This has been handled by other more recent models (Zurob,

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Brechet et al. 2006, Dunlop, Brechet et al. 2007, Buken and Kozeschnik 2017), however, although an interesting approach, it is not directly transferrable to the ALSOFT model. The present results and their analysis also seem to indicate that a classical temperature independent Zener drag is not satisfactory to account for the effects observed and that a more sophisticated particle-boundary interaction mechanism may be needed.

APPENDIX Table 1. Generic ALSOFT input (appropriate for C2-0 alloy) Bitflag for mode selection, currently unused... Initial dislocation density (#/m^2) Initial subgrain size (m) Initial recrystallised grain size (m) Friction stress (MPa) Constant in evolution eq. for dislocation density Constant in evolution eq. for dislocation density Constant in evolution eq. for subgrain size Constant in evolution eq. for subgrain size Constant in expr. for density of particle stimulated Constant in particle size distribution (1/m) Prefactor for mobility (m^4/s) Initial (as-cast) grain size (m) Constant in evolution eq. for subgrain size Constant in evolution eq. for dislocation density Constant in strength model Constant in strength model Taylor factor Burgers vector (m) Debye frequency (1/s) Grain boundary energy (J/m^2) Constant in expr. for density of particle stimulated Prefactor for density of particle stimulated nucleat Constant in expr. for density of grain boundary nucl Geometric constant in driving pressure for recrystal Missorientation (Deg.) Constant for missorientation (Deg.)

as_mode rho_i delta r R_FLP B_rho w_rho B_delta w_delta N0 L M0 D0 e_delta e_rho alpha1 alpha2 Mtaylor b nu_D gamma_GB CPE C_PSN C_GB alpha theta theta_c

0 1.98E+13 4.50E-07 0 5.30E+01 8.00E+04 0.5 2 5 2.67E+17 3.14E+06 1.00E+05 1.00E-04 0.6667 0.6667 0.3 2.5 3 2.86E-10 1.00E+13 0.3 1.2 0.2 0.12 2.5 4 15

Modeling of Recrystallization of Commercial Particle … Poisson number Initial volume fraction of cube grains Constant in expr. for density of cube nucleation sit Scale factor for mean cube grain size Constant in expr. for volume fraction cube grains Constant in expr. for volume fraction cube grains Constant in expr. for volume fraction cube grains Constant in expr. for volume fraction cube grains Constant in expr. for volume fraction cube grains Constant in expr. for volume fraction cube grains Constant in expr. for volume fraction cube grains Constant in expr. for fraction S deformation texture Constant in expr. for fraction S deformation texture Constant in expr. for fraction S deformation texture Eff. activation energy for solute diffusion (J/mol) Activation energy for recrystallisation (J/mol) Prefactor in expr. for shear modulus (Pa) [2.99e10] Exp. factor in expr. for shear modulus (K^-1) [5.4eTemperature during initial deformation (C) Zener drag during initial deformation (Pa) True strain after initial deformation Zener-Holomon parameter (1/s) Particle radius [m] Volume fraction particles

nu R_c0 C_Cube fCube R_cA R_cB R_cC R_cD R_cE R_cF R_cG R_sA R_sB R_sC U_a U_rex G0 G1 T_def PZ_def strain_def Z rp fr

159

0.33 0.04 0.4 1.3 2.6 1 0.3 -2 0.1 -1.4 -1.8 0.04 0.173 2 2.00E+05 2.00E+05 2.65E+10 0 20 0 3 4.00E+21 1 0.001

Table 2. Experimental material for data for input to ALSOFT

Strain  Css (Mn) at% Css_eff at%

C2-1 3.0 0.0014

C2-3 3.0

C2-0 1.6

0.0014

0.0034 0.0046 53

ss-eff (MPa) N0 (#/m3) L (m) m d_part (m) NA (#/m2) NV Fv 

5.4e-8 1.3e12 1.6e19 2.51e3 1.08e-6

1.27e-7 5.5e10 2.9e17 5.9e4 5..4e-6

p (MPa) VHN VHN (fully soft) YS (MPa) (as def) YS (MPa) (fully soft) ~ PD (MPa) ~ PZ (MPa)

55.5 29 165 40 0.75 0.03

51.4 25 146 30 0.75 0.003

3.0

C2-1 1.6

3.0

0.0017 0.0029 39

C2-2 1.6

3.0

0.0011 0.0023 34

C2-3 1.6

3.0

0.0010 0.0022 33

3.24e17 3.37

2.67e17 3.14

4.55e16 1.78

5.64e16 1.87

2.21e17 3.19

1.12e17 2.78

4.97e16 2.04

5.0e16 2.02

0.69

0.41

0.98

0.65

0.58

0.46

0.56

0.48

1.05e-7 2.8e12 2.07e19 1.26e-2 5.8e-7

0.53 0.14

74.1 33 248 63.5 0.92 0.14

0.38 0.03

64 30 203 50 0.57 0.03

0.64 0.12

1.56e-7 9.0e11 4.84e18 9.62e-3 1e-6

16.5

10.2

56.1 33 167 63.5 0.81 0.12

57.6 30 174 50 0.78 0.075

0.67 0.075

Table 3. Actual material and model parameters used in the ALSOFT calculations

T(oC)

csseff

C1-3-3 All 0.0012

C1-2-3 All 0.0014

C1-2-3 300 0.0014

C2-3-2 300 0.0021

C2-3-2 >= 350 0.0021

C2-3-3 All 0.0021

C2-1-2 350 0.0035

C2-1-2 400 0.0035

C2-1-2 450 0.0035

C2-1-3 350 0.0035

C2-1-3 400 0.0035

C2-1-3 450 0.0035

C2-2-3 350 0.0023

C2-2-3 400 0.0023

C2-2-3 450 0.0023

i

1.6e+13 1.6e+13 1.6e+13

1.5e+13 1.5e+13 1.7e+13 1.6e+13 1.6e+13 1.6e+13 1.6e+13 1.6e+13 1.6e+13 1.6e+13 1.6e+13 1.6e+13

m

5.0e-07 5.0e-07 5.0e-07

5.5e-07 5.5e-07 4.8e-07 5.0e-07 5.0e-07 5.0e-07 5.0e-07 5.0e-07 5.0e-07 5.0e-07 5.0e-07 5.0e-07

0

3.0e+01 4.0e+01 4.0e+01

5.0e+01 5.0e+01 5.0e+01 5.0e+01 5.0e+01 5.0e+01 5.0e+01 5.0e+01 5.0e+01 6.3e+01 6.3e+01 6.e+01

B

8.0e+04 8.0e+04 8.0e+04

8.0e+04 8.0e+04 8.0e+04 8.0e+04 8.0e+04 8.0e+04 8.0e+04 8.0e+04 8.0e+04 8.0e+04 8.0e+04 8.0e+04



0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

B

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2.5

2.5

2.5

4

4

4

3

4

4

4

5

5

5

5

5

 N0(#/m3) L (1/m) M0 D0 CPE CPSN CGB PZ (Pa) 

5.0e+16 1.12e+17 1.12e+17 2.02e+06 2.78e+06 2.78e+06 1.0e+05 1.0e+05 1.0e+05 1.0e-04 1.0e-04 1.0e-04 1.2 1.2 1.2 0.2 0.2 0.2 0.12 0.12 0.12 3.0e+00 3.0e+04 3.0e+04 3.0 3.0 3.0

4.97e+16 4.97e+16 5.0e+16 4.55e+16 4.55e+16 4.55e+16 5.64e+16 5.64e+16 5.64e+16 1.12e+17 1.12e+17 1.12e+17 2.04e+06 2.04e+06 2.02e+06 1.78e+06 1.78e+06 1.78e+06 1.87e+06 1.87e+06 1.78e+06 2.78e+06 2.78e+06 2.78e+06 5.0e+04 1.0e+05 1.0e+05 3.0e+04 1.0e+05 1.0e+05 3.0e+04 3.0e+04 3.0e+04 4.0e+04 2.0e+04 4.0e+04 1.0e-04 1.0e-04 1.0e-04 1.0e-04 1.0e-04 1.0e-04 1.0e-04 1.0e-04 1.0e-04 1.0e-04 1.0e-04 1.0e-04 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 2.5e+05 7.5e+04 7.5e+04 1.0e+05 3.0e+04 3.0e+04 1.0e+05 3.0e+04 3.0e+04 5.0e05 5.0e+05 5.0e+05 1.6 1.6 3.0 1.6 1.6 1.6 3.0 3.0 3.0 3.0 3.0 3.0

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alloys. Proceedings of the 6th International Conference on Aluminum Alloys (ICAA6), Japan, Japanese Institute of Light Metals (JILM). Saetre, T. O., O. Hunderi and N. Ryum (1989). “Modeling grain-growth in 2 dimensions.” Acta Metallurgica 37(5): 1381-1387. Sande, G. (2011). Numerical modeling of recrystallization in aluminum alloys. Trondheim, Norway, Norwegian University of Science and Technology. Sjolstad, A., K. Marthinsen and E. Nes (2004). Modeling the softening behavior of commercial AlMn-alloys. Recrystallization and Grain Growth, Pts 1 and 2. B. Bacroix, J. H. Driver, R. LeGall et al. 467-470: 677-682. Srolovitz, D. J., G. S. Grest, M. P. Anderson and A. D. Rollett (1988). “Computer-simulation of recrystallization. 2. Heterogeneous nucleation and growth.” Acta Metallurgica 36(8): 2115-2128. Tangen, S., K. Sjolstad, T. Furu and E. Nes (2010). “Effect of Concurrent Precipitation on Recrystallization and Evolution of the P-Texture Component in a Commercial Al-Mn Alloy.” Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science 41A(11): 2970-2983. Vatne, H. E. (1999). Modelling of Metal Rolling Processes 3. London, IOM Communications. Vatne, H. E., O. Engler and E. Nes (1997). “Influence of particles on recrystallisation textures and microstructures of aluminum alloy 3103.” Materials Science and Technology 13(2): 93-102. Vatne, H. E., T. Furu, R. Orsund and E. Nes (1996). “Modeling recrystallization after hot deformation of aluminum.” Acta Materialia 44(11): 4463-4473. Vatne, H. E., K. Marthinsen, R. Orsund and E. Nes (1996). “Modeling recrystallization kinetics, grain sizes, and textures during multi-pass hot rolling.” Metallurgical and Materials Transactions a-Physical Metallurgy and Materials Science 27(12): 4133-4144. Wang, N., J. E. Flatoy, Y. J. Li and K. Marthinsen (2012). “Evolution in microchemistry and its effects on deformation and annealing behaviour

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of an AlMnFeSi alloy.” Proceedings of the 13th International Conference on Aluminum Alloys (Icaa13): 1837-1842. Wang, N., K. Huang, Y. J. Li and K. Marthinsen (2016). “The Influence of Processing Conditions on Microchemistry and the Softening Behavior of Cold Rolled Al-Mn-Fe-Si Alloys.” Metals 6(3). Zurob, H. S., Y. Brechet and J. Dunlop (2006). “Quantitative criterion for recrystallization nucleation in single-phase alloys: Prediction of critical strains and incubation times.” Acta Materialia 54(15): 3983-3990.

In: Recrystallization Editor: Ke Huang

ISBN: 978-1-53616-737-5 © 2020 Nova Science Publishers, Inc.

Chapter 5

RECOVERY AND RECRYSTALLIZATION PROCESS IN A COMMERCIALLY PURE ALUMINUM: THE ROLE OF DISSOLVED IMPURITIES AND ANALYSIS BY A NEW KINETICS THEORY Hideo Yoshida1, and Mineo Asano2,† 1

ESD Laboratory, Nagoya, Japan (Former UACJ Corporation, Research and Development Division) 2 UACJ Corporation, Flat Rolled Products Division, Nagoya Works, Nagoya, Japan

ABSTRACT The purpose of this chapter is first to clarify the influence of impurities, i.e., iron and silicon on the recovery and recrystallization of commercially pure aluminums, 1050 and 1200, by isochronal or  †

Corresponding Author’s Email: [email protected]. Corresponding Author’s Email: [email protected].

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Hideo Yoshida and Mineo Asano isothermal annealing based on the mechanical properties and the microstructure observation and consider the mechanism of recovery and recrystallization. As a result, it was found that the dissolved solute atoms of the impurities segregate, precipitate and coagulate on the boundaries of the dislocation cell, subgrain and recrystallized grain during annealing, which process control the grain growth, and these microstructural changes affect the mechanical properties. Second, we analyze the recovery and recrystallization rate of a 1050 hot-rolled aluminum sheet with a new rate equation, and verify the mechanism of recovery and recrystallization by this equation. This new equation is an extension of the Johnson-Mehl-Avrami equation containing the term of the particle number that exponentially changes. It was found that the entire reaction was divided into two reactions, i.e., the recovery and recrystallization and expressed by superimposing the two processes. The rate of the recovery and recrystallization is controlled by segregation, precipitation and coagulation of the dissolved solute atoms of the impurities on the boundaries of the cell, subgrain and recrystallized grain. From the viewpoint of precipitation of the dissolved impurities, there have been few studies that examined the recovery and recrystallization rate. It is considered that our study is meaningful because it provides a new viewpoint approach to the research of the recovery and recrystallization.

Keywords: recovery and recrystallization, commercially pure aluminum, new rate equation, dissolved impurities, precipitation, dislocation cell, subgrain boundary

1. GENERAL INTRODUCTION Commercially pure aluminums are widely used for utensils, building panels, litho sheets, fin stocks for air conditioners, electrical wires, household foils and electrolytic capacitor foils due to having a high performance for formability, corrosion resistance, surface treatment, thermal conductivity, electrical conductivity etc. Commercially pure aluminums contain impurities, mainly iron and silicon, which are originally contained in the bauxite. These impurities cannot be removed by the Hall-Héroult electrolytic smelting process and remain in the ingots. The Hall-Héroult process can produce aluminum ingots with up to 99.8 or

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99.9% purity. The refining processes of a three-layers electrolytic or segregation one can produce higher purity ingots of 99.99%. Recently, the high strength and high formability foil of Al-Fe alloys with more than 1 mass % iron has been developed by adding iron as an additional element. The aluminum alloy with dissolved iron atoms has high work hardenability as a result of the reaction with dislocations, but the solid solubility of iron in the aluminum is very low (about 0.04 mass % in phase diagram (Mondolfo 1976)). Therefore, it cannot be expected to achieve a significant increase in strength unless it is manufactured by the rapid solidification method. On the other hand, when aluminum alloys contain more than the solid solubility of iron, Al3Fe compounds are formed as second phase particles during solidification or soaking (homogenizing) of an ingot, and contribute to the dynamic recovery during hot or cold working. The strength and formability depend on the content of the dissolved impurities, therefore, it is important to control it for commercial production (Yoshida 2013, 62-105). Even if the impurity levels are very low, the behavior of the recovery and recrystallization significantly changes depending on whether the impurities are dissolved in the matrix. Recrystallization of high purity aluminum over 99.99% occurs at room temperature, which depends on the production conditions. Ohno et al. cast the Al- 0.5% Fe alloy into a mold with 99.998% aluminum and 99.9% iron base metal. They then hot-rolled the ingot after pre-heating at 520ºC, followed by intermediate annealing (IA) at 260ºC for 16h and finally coldrolled the plate with 50% and 85% reductions. The 50% rolled sheet did not soften at room temperature, while the 85% one began to immediately soften and finished in 24 h. The recrystallization of the 85% rolled sheet occurred at room temperature (Yoshida 2013, 62-105). Such a softening phenomenon by cold working is a kind of dynamic recovery and has been known as work softening. Ohno et al. also studied the work softening of the Al-2.0% Fe alloy. They reported that work softening began at a 50% reduction in the Al-2.0% Fe alloy without silicon, but work softening is difficult to occur in the alloy with 0.02% Si shown in Figure 1. (Ohno et al. 1977, 539-542).

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Figure 1. Effect of cold rolling reduction on Vickers hardness of Al-2.0% Fe sheets containing different amounts of Si (Ohno et al. 1977, 539-542).

Yamamoto et al. also studied the effect of the IA temperature on work softening of the Al-1.7% Fe alloy soaked at 400ºC for 24 h followed by hot rolling, IA and cold rolling (CR). They reported that work softening began at the reduction of 40% CR at 400ºC IA, but it did not begin until the reduction of 90% CR at 600ºC IA as shown in Figure 2 (Yamamoto, Mizuno, and Kirihata 1992, 142-147, Yamamoto, Kirihata and Mizuno 1992, 757-763). This is related to the dissolved iron content in the matrix. It is necessary for the work softening that the iron sufficiently precipitates as Al3Fe. According to the experimental results of Ohno and Yamamoto, a very small amount of dissolved iron and silicon delays the recovery and recrystallization. Figure 3 shows the relation between the recrystallization temperature and the process conditions of the 95% cold-rolled Al and Al2% Fe alloy sheet made with 99.999% high purity aluminum (Yamamoto, Kirihata and Mizuno 1992, 757-763, Yamamoto 2005). It was found that the recrystallization temperature changes at the IA temperature before cold rolling and that the recrystallization temperature decreases to near room temperature when dissolved iron atoms are sufficiently precipitated during annealing at 400°C.

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Figure 2. Effect of annealing conditions on Vickers hardness of Al-1.7% Fe (Yamamoto, Mizuno, and Kirihata 1992, 142-147).

Figure 3. Recrystallization temperature of 99.6, 99.99% and 99.999% Al and Al-2.0 mass% Fe alloy hot-rolled at 400°C and annealed at 400 or 600°C (Yamamoto, Kirihata and Mizuno 1992).

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The behavior of such impurities is the same for commercially pure aluminum. Impurities are precipitated by homogenization of the ingot and IA to improve the drawability by controlling the earing ratio. In general, cold-rolled sheets are inferior in formability, so a final annealing may be carried out to achieve both strength and formability. Since this final annealing temperature also depends on the amount of the impurities, in particular, dissolved solute atoms in this manufacturing process, therefore, a slight change of their amount causes fluctuations in the strength and elongation. The study of the behavior of these impurities leads to the stability of the final product’s quality. The purpose of this chapter is first to clarify the influence of impurities on the recovery and recrystallization of commercially pure aluminum by isochronal or isothermal annealing based on the mechanical properties and the microstructural observation and consider the mechanism of recovery and recrystallization in the first two sections. Second, we analyze the recovery and recrystallization rate of aluminum with a new rate equation, and verify the mechanism of recovery and recrystallization by this equation. This chapter consists of two parts; one is “Effect of impurities on mechanical properties and microstructures during recovery and recrystallization” and the other is “Analysis of the recovery and recrystallization rate by a new rate equation.” In the former part, two subjects are discussed, one is the relationship between the microstructures and tensile property during the isochronal annealing of 1050 aluminum and the other is the cause of the curious change in the tensile properties, in particular, the elongation during the isothermal annealing of 1200 aluminum. Based on the change in the microstructures during annealing, the concept of microstructural change during recovery and recrystallization was proposed. In the latter part, the rate of recovery and recrystallization of 1050 aluminum hot-rolled sheets was analyzed by a new rate equation and the role of dissolved impurities on the recovery and recrystallization rate was clarified. Finally the concept of microstructural change in the recovery and recrystallization proposed in the first part of this chapter was confirmed by these analyses. From the viewpoint of precipitation of the

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dissolved impurities, there have been few studies that examined the recovery and recrystallization rate. We consider that our study is meaningful because it provides a new viewpoint approach to the research of the recovery and recrystallization.

2. EFFECT OF IMPURITIES ON MECHANICAL PROPERTIES AND MICROSTRUCTURES DURING RECOVERY AND RECRYSTALLIZATION (PART 1): PRECIPITATION BEHAVIOR OF IMPURITIES AND MICROSTRUCTURAL CHANGE DURING ISOCHRONAL ANNEALING OF A 1050 COLD-ROLLED ALUMINUM SHEET1 2.1. Introduction In recent years, along with the development of analytical techniques by electron microscopy, the crystallization and precipitation behavior of Fe and Si during casing and heat treatment have been studied in detail. (Kosuge 1988, 292-308; Asami and Doko 1988, 319-327; Matsuo et al. 1988, 400-406; Matsuo et al. 1987, 134-140; Westengen 1982, 360-368; Dons 1984, 170-174; Skjerpe 1987, 189-200). However, there are few studies about ductility from the precipitation behavior of Fe and Si. In this study, the annealing properties of the cold-rolled sheet of a commercially pure aluminum 1050 were investigated and the effect of the annealing temperature on the ductility was investigated. In particular, a curious phenomenon that the elongation of the annealed sheets at 250 to 300°C is maximized has been found in the past (Göler and Sachs 1927, 9093; Koda 1942 32; Kawashima and Nakamura 1951, 11-15, 1951, 195199; Ikeno, Yokomoto and Nohara 1953, 292-296), but a detailed investigation has not been done. Therefore, the reproducibility of the 1

This section is a revision of the paper published in the Journal of The Japan Institute of Light Metals, (Moriyama, Yoshida and Tsuchida 1989, 184-189).

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occurrence of the elongation peak at 250 to 300 °C was initially investigated, then the cause of the occurrence of the peak was considered from the viewpoint of the precipitation of the impurities.

2.2. Experimental The chemical compositions of the DC ingot of the 1050 aluminum and the 99.99% high purity aluminum are shown in Table 1. The DC ingot of the 1050 aluminum was commercially homogenized at 540°C for 3 hours, heated at 525°C and hot-rolled to 4.8 mm. The cold-rolled sheets were then produced in the following two processes in order to investigate the influence of intermediate annealing (IA). In process (I), the IA at 380°C for l h was performed after cold rolling to 2.4 mm at 50% reduction, then cold rolling to 0.115 mm. In process (II), cold rolling was carried out to 0.115 mm without the IA. The DC ingot of the 99.99% high purity aluminum was also hot-rolled to 4.8 mm and cold-rolled to 0.115 mm without IA. The final annealing condition was an isochronal annealing at an interval of 25°C from 150 to 350°C for l h in each process. The heating rate for annealing is 50°C/h and the cooling rate is 25°C/h. Furthermore, in order to investigate the change in isothermal annealing at 200°C, it was heated in an air furnace at the heating rate of about 40°C/h. Table 1. Chemical compositions of 1050 (mass%) and 4N (99.99%) aluminum Alloy 1050 (mass %) 4N-Al (ppm)

Si 0.11 4

Fe 0.28 6

Cu 0.02 48

Mn 0.00 2

Mg 0.00 0

Cr 0.00 1

Zn 0.00 0

Ti 0.01 0

Al bal. bal.

From these annealed sheets, tensile specimens were obtained by cutting along the rolling direction. The shape of the specimen is the type JIS No. 5 (Gauge Length: 50 mm, Width:12.5 mm). A tensile test was then performed at a tension speed of 2 mm/min to obtain the tensile, yield

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strength and elongation to create an annealing curve. The precipitation of the compound was observed using an optical microscope (OM), JSM-50A scanning electron microscope (SEM) and JEM-200CX transmission electron microscope (TEM). The TEM specimens were prepared by a window frame method with an electrolytic bath of perchloric acid ethanol. Identification of the compound was carried out by an energy dispersive spectroscope (EDS) and structural analysis by a selected area diffraction pattern (SADP). In addition, in order to know the degree of the dissolved solute atoms or precipitation of the compound, the electrical resistivity was measured in liquid nitrogen by a four-terminal method by spot welding.

2.3. Results

200

TS

20

YS 150

TS

15

YS

100

10

50

5

Elongation (%)

Tensile and Yield Strength (MPa)

2.3.1. Annealing Curve Figure 4 shows the final annealing curve of a 1050 aluminum coldrolled sheet. Regardless of the IA, a peak of elongation at 275°C was observed.

0

Annealing Temperature (°C / 1 h)

Figure 4. Effect of final annealing temperature on the tensile properties of a 1050 aluminum cold-rolled sheet.

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However, the elongation increased and the strength decreased with the IA. Figure 5 shows the annealing curve of a 99.99% high purity aluminum cold-rolled sheet. The noticeable peak of elongation like 1050 was not observed. This figure shows the results of process (II) without the IA, and nearly the same result was obtained for process (I) with the IA. Based on these results, it seems that the occurrence of the peak of elongation was related to the precipitation behavior of the impurities during the final annealing. Figure 6 shows the norminal stress - elongation curve when it was isothermally annealed at 200°C in an air furnace (Moriyama, Yoshida and Tsuchida 1987, 61-62). Table 2 shows the values of the tensile strength and elongation obtained from the curve shown in Figure 6. The elongation decreased the most at 100 to 1000 min. Also, when annealing for 5000 to 10000 minutes, the stress was constant with respect to elongation, and it was understood that work hardening did not occur. This change in elongation during isothermal annealing will be described and discussed in the next section.

Tensile Strength (MPa)

E 15

150

100

TS

10

Elongation (%)

20

200

5

50

0

Annealing Temperature (°C / 1 h)

Figure 5. Effect of final annealing temperature on the tensile properties of a 99.99% high purity aluminum cold-rolled sheet.

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Figure 6. Effect of final annealing time at 200°C on nominal stress and elongation curve of the 1050 aluminum cold-rolled sheet (Moriyama, Yoshida and Tsuchida 1987, 61-62).

Table 2. Tensile strength and elongation of 1050 aluminum cold-rolled sheet isothermally annealed at 200°C

2.3.2. Microstructures The microstructures during the recovery and recrystallization process were investigated of the 1050 aluminum cold-rolled sheet of process (I) with the IA. Figure 7 shows the grain structure using a polarization microscope. Recrystallized grains were partially formed at 275°C and fully formed with diameters of 20 to 30 μm at 300 to 350°C. Figure 8 shows a large number of fine particles that precipitated at 275°C. The distribution densities of the fine particles (about 1 μm or less) measured from the microstructures are shown in Figure 9. It can be seen that in the 275°C annealed sheet, where the peak of elongation is obtained, fine particles are more distributed than in the as-rolled, 300 and 350°C annealed sheets.

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(a) As Cold Rolled

(c) 300°C

(b) 275°C

(d) 350°C

100µm

Figure 7. Grain structures of the 1050 aluminum cold-rolled sheet followed by final annealing (Process (I): HR-CR-IA-CR).

(a) As Cold Rolled

(b) 275°C

(c) 300°C

(d) 350°C

10µm

Figure 8. Microstructures of the 1050 aluminum cold-rolled sheet followed by final annealing (Process (I): HR-CR-IA-CR).

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Density of Fine Particles (x 103 / mm2)

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Annealing Temperature (°C / 1 h)

Figure 9. Effect of final annealing temperature on the density of fine particles with less than 1μm of the 1050 aluminum sheet (Process (I): HR-CR-IA-CR).

Furthermore, Figure 10 shows the TEM structures. The as cold-rolled sheet had a high number of dislocations and dislocation cells within the subgrains that occurs during cold rolling. At 275°C, a mixed grain structure of subgrains and recrystallized grains, and a ring in which many fine particles were linked in a ring shape within the grain were observed. At 350°C, the rings completely disappeared. The size of the dislocation cells, subgrains and recrystallized grains by annealing are shown in Figure 11. In order to find out what the size of the ring depends on, TEM structures of the annealed sheet below 200°C are shown in Figure 12. Comparing the 150°C annealed sheet with the as cold-rolled one, it was found that the diameter of 0.5 to 1 μm of the ring is the same as the size of the dislocation cells. The SEM image of the fine particles in the 275°C annealed sheet and EDS analysis are shown in Figure 13. The ring having a diameter of 0.5 to 1 μm was linked with the fine particles and the presence of Si in the particles was confirmed. Furthermore, in order to clarify its composition and structure, the TEM image of the ring and structural analysis by SADP are shown in Figure 14. It is understood that many single crystals of Si (fcc, a = 0.542 nm) (Westengen 1982, 360-368) having a diameter of 0.1 to 0.2 μm formed the Si-ring.

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(a) As Cold Rolled

(c) 300°C

(b) 275°C

(d) 350°C

1µm

Figure 10. TEM structures of the 1050 aluminum cold-rolled sheets followed by final annealing (Process (I): HR-CR-IA-CR).

Figure 11. Effect of final annealing temperature on the size of cell, subgrain and recrystallized grain of the 1050 aluminum sheet (Process (I): HR-CR-IA-CR).

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As Rolled

150°C /1 h

200°C /1 h Figure 12. Formation process of Si-ring during annealing.

(a) SEM Image

1µm

(b) EDS Analysis of Particles

Figure 13. SEM image and EDS analysis of Si-ring in the 1050 aluminum cold-rolled sheet annealed at 275°C.

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(a) BF Image of Particles 0.2µm

(b) SADP of Si

Figure 14. TEM image and selected area diffraction pattern of Si-ring in the 1050 aluminum cold-rolled sheet annealed at 275°C.

5µm

(a) As Cold Rolled

(b) Intermediate Annealing at 380°C

Figure 15. Microstructures of the 1050 aluminum cold-rolled sheet followed by intermediate annealing.

(a) BF Image of Particles 0.2µm

(b) SADP of α'-AlFeSi

Figure 16. TEM image and selected area diffraction pattern of α’-AlFeSi compounds formed during annealing at 380°C.

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Figure 15 shows the microstructure before and after the IA. Fine particles are observed within the grain after the IA. Figure 16 shows the TEM image of this fine particle and structural analysis by SADP. It was revealed that this particle was α'-AlFeSi (hexagonal, a = 1.230 nm, c = 2.620 nm, P 63 / mmc) (Kosuge 1988. 292-308; Skjerpe 1987, 189-200). with a diameter of about 0.2 μm.

Change of Electrical Resistivity (µΩ・mm)

2.3.3. Electrical Resistivity Figure 17 shows the change in the electrical resistivity of the final annealed sheet. The electrical resistivity of as-rolled sheet without the IA was set to 0, and it is indicated by the difference from it. Regardless of the IA, the electrical resistivity becomes a minimum at 275°C, and the electrical resistivity increases at a temperature higher than 275°C. The electrical resistivity of the intermediate annealed sheet is reduced by about 0.2 μΩmm. Based on the electrical resistivity and the TEM structures, it is

Annealing Temperature (°C / 1 h)

Figure 17. Effect of final annealing temperature on the electrical resistivity of a 1050 aluminum cold-rolled sheet.

considered that the Si rings precipitated up to 275°C and dissolved at a temperature higher than that. It is also considered that the electrical resistivity of the sheet with the IA became low since α'-AlFeSi precipitated during the IA. Based on these results, the peak of elongation at 275°C is

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related to the precipitation of Si, and the improvement of elongation by the IA is considered to be related to the precipitation of α'-AlFeSi.

2.4. Discussion Based on the above results, Si-rings were observed within the grains of the annealed sheet. Furthermore, the value of about 0.5 to 1 μm in diameter of the ring was almost the same as the diameter of the dislocation cell. The electrical resistivity at 275°C was minimal. Based on these results, the precipitation of silicon atoms during the annealing was considered as follows. As the annealing temperature increased, dissolved silicon atoms in the matrix or silicon atoms trapped in the dislocations in the as-rolled sheet segregated and precipitated on the dislocation cell boundary, then coagulated on the cell boundary. In addition, during annealing up to 275°C, the coagulated silicons were linked in a ring shape on the cell boundary. As a result of the coagulation of silicon, it is considered that the silicon atoms or precipitates on the cell boundaries decrease and these boundaries migrate and disappear. Therefore the Si-rings remained within the subgrains and the concentration of the dissolved silicon atoms in the matrix also decreased. The improvement of elongation at 275°C will be discussed in the next section. Furthermore, it is considered that the dissolved solute atoms of iron and silicon segregate on the subgrain boundaries and inhibit the growth of the subgrains. However, the segregated atoms of iron and silicon combine to form AlFeSi precipitates, which coagulate on the subgain boundaries. Thus the subgrain boundaries can easily migrate from these coagulated AlFeSi precipitates. As a result, the subgrains grow or coalesce into recrystallized grains. The Si-rings almost disappear and dissolve in the matrix during 300 to 350°C annealing. As already mentioned, the dissolved solute atoms of impurities segregate, precipitate and coagulate on the boundaries of the dislocation cell, subgrain and recrystallized grain. Through these processes the grain growth occurs. Therefore, it is considered that the rate of the recovery and recrystallization is controlled

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by segregation, precipitation and coagulation of the dissolved solute atoms of the impurities. For the 300°C and 350°C annealed sheets, the elongation slightly decreased compared to the 275°C annealed one. It seems that the decrease in elongation is related to the increase in the dissolved silicon atoms in the matrix. Although the elongation slightly increased and the strength decreased due to the IA, it is considered that the strength decreases due to a decrease in the amount of dissolved iron and silicon atoms which precipitate as α'-AlFeSi compounds during the IA while the elongation increases.

2.5. Conclusion 1) It was found that the tensile properties of a 1050 cold-rolled aluminum sheet during isochronally heating to 350°C change as follows. The higher the heating temperature, the lower the strength. However, interestingly, the elongation once decreases at 150°C and increases, then shows the maximum value at 275°C. However, it decreases at 300°C and becomes a constant value during heating to 350°C. During 275°C annealing, it was confirmed that a peak of elongation occurred regardless of the IA, but a peak of elongation did not occur in the 99.99% high purity aluminum. The elongation of the 1050 annealed sheet with the IA is greater and its strength is lower than that without the IA. 2) The as cold-rolled sheet had a high number of the dislocations and dislocation cells within the subgrains which were formed during the cold rolling. As the annealing temperature increased, dissolved silicon atoms in the matrix or silicon atoms interacted with the dislocations in an as-rolled sheet segregated and precipitated on the dislocation cell boundary, then coagulated on the cell boundary. Silicon particles having a diameter of 0.1 to 0.2 μm precipitated and linked in a ring shape (Si-ring) having a diameter of about 1

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Hideo Yoshida and Mineo Asano μm on the dislocation cell. Therefore, the diameter of this ring is the same as the diameter of the dislocation cell. 3) The Si-rings remained within the subgrains after disappearance of the cell grain boundaries at a higher annealing temperature. During 275°C annealing, Si-rings were mostly distributed within the grain and the electrical resistivity was minimal. Recrystallized grains were partially formed at this temperature. However, the Si-rings almost disappeared and dissolved in the matrix during 300 to 350°C annealing and the electrical resistivity increased. It is considered that the peak of elongation during the 275°C annealing is related to the decrease in dissolved silicon atoms in the grain and the partial recrystallization. 4) During the intermediate annealing, the precipitation of α'-AlFeSi with a diameter of about 0.2 μm is observed within the recrystallized grain. The formation mechanism of the α'-AlFeSi is considered as follows. The dissolved solute atoms of iron and silicon segregate on the subgrain boundaries and inhibit the growth of subgrains. These segregated atoms of iron and silicon combine to form AlFeSi precipitates and these precipitates coagulate on the subgain boundaries. Thus the subgrain boundaries easily migrate from these coagulated AlFeSi precipitates. As a result, the subgrains grow or coalesce into recrystallized grains. The higher elongation obtained by the intermediate annealing is considered to be due to the decrease in the amount of dissolved iron and silicon atoms since α'-AlFeSi precipitates are formed. 5) The dissolved solute atoms of the impurities segregate, precipitate and coagulate on the boundaries of the dislocation cell, subgrain and recrystallized grain. Through these processes, the grain growth occurs. Therefore, it is considered that the rate of the recovery and recrystallization is controlled by the segregation, precipitation and coagulation of the dissolved solute atoms of the impurities.

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3. EFFECT OF IMPURITIES ON MECHANICAL PROPERTIES AND MICROSTRUCTURES DURING RECOVERY AND RECRYSTALLIZATION (PART 2): EFFECT OF MICROSTRUCTURES ON THE ELONGATION DURING ISOTHERMAL ANNEALING IN A 1200 COLD-ROLLED ALUMINUM SHEET2 3.1. Introduction Commercially pure aluminum, 1000 series aluminum sheets, have an excellent thermal conductivity, so applications to heat exchangers or heat sinks are progressing. When applied to such various products, a balance between the strength and ductility is required since press forming is generally performed. Therefore, it is often used in the H2n temper. The final annealing for temper, H22 to H26, is often performed at a relatively low temperature of 300°C or less. Dover et al. (Dover and Westengen 1984, E668-E671) investigated the tensile properties of the 1100-H2n sheet that had a final anneal at 200°C, and the elongation of the H26 temper (annealing at 200°C for 60 to 120 min) was about 1% and lower than that of the H18 temper (as cold-rolled). Similarly, as shown in Figure 6 in the previous section 2, we also investigated the tensile properties of the 1050 - H2n sheet which was final annealed at 200°C, and the elongation of the H26 temper (annealing at 200°C for 100 min) was below 2% and lower than that of H18 temper (Moriyama, Yoshida and Tsuchida 1987, 61-62). This decrease in elongation was related to the segregation and precipitation of silicon on the dislocation cell boundary. However, the role of silicon in the decrease in elongation is not well understood. Therefore, in this study, the influence of annealing time on the ductility was investigated using a 1200 aluminum sheet annealed at 250°C where a 2

This section is a revision of the paper published in the Journal of The Japan Institute of Light Metals, (Asano, Nakamura and Yoshida 2014, 279-284).

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decrease in elongation was seen in the H26 temper. We discussed the cause of the decrease in elongation based on the change in the optical microscope (OM) and transmission electron microscope (TEM) structures before and after tensile deformation.

3.2. Experimental Table 3 shows the chemical compositions of the test materials. In order to clarify the effect of iron on the elongation, 1200 aluminum with an iron content more than 1050 aluminum was chosen as the test material in this research. Table 3. Chemical composition of 1200 aluminum (mass%) Alloy 1200 (mass %)

Si 0.06

Fe 0.85

Cu 0.02

Mn