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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Digital materials are integral to the modern design methods for industrial components and structures, allowing mechanical properties to be predicted from a description of the microstructure and behavior laws of the constituent parts.
This book examines a wide range of material properties, from transport phenomena to the mechanics of materials and microstructure changes in physical metallurgy. The fundamental mechanisms of deformation, annealing and damage to materials involve complex atomic processes; these have been explored and studied by numerical simulations, such as molecular dynamics.
In contrast to this minutely detailed approach, Digital Materials explores how these mechanisms can instead be integrated into an approach that considers the continuum of the physics and mechanics of materials at the mesoscopic scale. The book thus focuses on the mechanics of continuous media and the continuum thermodynamics of irreversible processes. The models displayed take the myriad properties of different materials into account, in particular their polycrystalline and/or composite natures; this becomes an intermediate step toward establishing effective laws for engineers in the processes of structure calculation and manufacturing.
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Seitenzahl: 518
Veröffentlichungsjahr: 2024
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Table of Contents
Cover
Table of Contents
Title Page
Copyright Page
Preface
1 Dislocation-based Mechanics: The Various Contributions of Dislocation Dynamics Simulations
1.1. Introduction
1.2. Overview of discrete dislocation dynamics
1.3. Mesoscale plasticity
1.4. Conclusion and future work
1.5. Acknowledgments
1.6. References
2 Statistical Approach to the Representative Volume Element Size of Random Composites
2.1. Introduction
2.2. Elements of numerical homogenization of heterogeneous media
2.3. Statistical definition of the RVE
2.4. Examples of application
2.5. Conclusion
2.6. References
3 Analytical Micromechanical Methods for Elasto-Viscoplastic Composites and Polycrystals
3.1. Introduction
3.2. Translated field method
3.3. The
β
-model dynasty for multiphase elastoviscoplastic polycrystals
3.4. Applications of the analytical micromechanical methods
3.5. Concluding remarks
3.6. References
4 Vertex and Front-Tracking Methods for the Modeling of Microstructure Evolution at the Solid State
4.1. Introduction
4.2. Vertex frameworks
4.3. From Vertex to front-tracking then to enriched Vertex frameworks
4.4. Enrichment of the Vertex approach
4.5. Other front-tracking frameworks for the modeling of microstructure evolution
4.6. Conclusion
4.7. References
5 Phase Field: Theory, Numerical Implementation and Applications
5.1. Introduction
5.2. The soliton solution of a propagating wave front
5.3. Thermodynamically consistent derivation of the phase-field equations
5.4. The multi-phase fields approach
5.5. Multi-component alloy transformation
5.6. Multi-phase field with elasticity
5.7. Numerical treatment and applications
5.8. Examples
5.9. References
6 Level-Set Method for the Modeling of Microstructure Evolution
6.1. Introduction
6.2. Kinetics equations of microstructure evolution at the mesoscopic scale
6.3. Level-set function, description of polycrystal and meshing adaptation
6.4. Isotropic framework for LS modeling of ReX and GG
6.5. Anisotropy of GB properties and CDRX modeling
6.6. Static/evolutive SPPs
6.7. Modeling of diffusive solid-state phase transformation
6.8. Solute drag aspect
6.9. Conclusion
6.10. References
7 Resolution Methods for Digital Materials – Recent Developments of Cellular Automaton Method
7.1. Introduction
7.2. Cellular automaton and applications
7.3. CA front tracking model within the static recrystallization case study
7.4. Calculation times and perspectives
7.5. References
List of Authors
Index
End User License Agreement
List of Tables
Chapter 3
Table 3.1. Material parameters for simulations of two-phase fiber-reinforced o...
Table 3.2. Material parameters for uniaxial tension simulations with “SC-TF-SE...
List of Illustrations
Chapter 1
Figure 1.1. (a and b) Compact core structure obtained by ab initio and by an E...
Figure 1.2. (a) Strain energy integrated in a cylinder around an edge dislocat...
Figure 1.3. Illustration of hybrid method solver from Queyreau et al. (2014). ...
Figure 1.4. (a) Schematic illustration of the modeling of an interface separat...
Figure 1.5. (a–d) A thinfoil of 0.5 μm is extracted from sequenc...
Figure 1.6. Top panel: two dislocations from secant slip systems (a) collide a...
Figure 1.7. (a) Schematic representation of a glissile junction formed in fcc,...
Figure 1.8. Top left: distribution of junction lengths lj under stress and at ...
Figure 1.9. (a) Simulated strain curves for Cu single crystals by DDD for thre...
Figure 1.10. Top panel: (a–d) pair correlations ζ
(α1α1)
...
Figure 1.11. Evolution of the simulated dislocation microstructures with tempe...
Figure 1.12. (a) Dislocation microstructure obtained for a tricrystal oriented...
Figure 1.13. Negative dislocation interacting with colinear GB edge dislocatio...
Figure 1.14. Cross view of dislocation accumulation at impenetrable GB in a fc...
Figure 1.15. Top left: stress strain curves and traces of slip activity corres...
Figure 1.16. (a) Simulated persistent slip bands simulated in Déprés et al. (2...
Figure 1.17. Strong tension-compression asymmetry in the plastic deformation o...
Chapter 2
Figure 2.1. Realization of a two-components Voronoi mosaic, with the FE mesh (...
Figure 2.2. Apparent bulk modulus K and interval of variation estimated from F...
Figure 2.3. Apparent shear modulus G and interval of variation estimated from ...
Figure 2.4. 3D simulation of Poisson fibers (radius 1 in a cube with edge 60) ...
Figure 2.5. Variance scaling of the apparent bulk modulus K
app
with the volume...
Figure 2.6. Apparent shear modulus for isotropic bulk polycrystalline copper a...
Figure 2.7. Apparent shear modulus of polycrystalline thin films: (a) example ...
Figure 2.8. 3D simulation of a Boolean model of spheres.
Figure 2.9. Integral range of σm, for porous and rigid Boolean models of spher...
Figure 2.10. Example of simulation (800 × 800) of a 2D Cox Boolean model of di...
Figure 2.11. Simulation of an autodual RS: Symmetric dead leaves of discs (non...
Figure 2.12. Hard core model of non-intersecting spherical holes in a matrix f...
Figure 2.13. Comparison of the limit asymptotic von Mises equivalent stress (l...
Figure 2.14. First cyclic overall stress–strain loop for textured polycrystall...
Figure 2.15. Crystallographic texture of the copper thin films (top left pole ...
Chapter 3
Figure 3.1. Overall and phase average stress responses of two-phase linear and...
Figure 3.2. Overall and phase average stress responses of two-phase linear and...
Figure 3.3. Simulation of the effective behavior of a two-phase nonlinear elas...
Figure 3.4. Simulation of the effective behavior of a two-phase nonlinear elas...
Figure 3.5. The estimates of the overall asymptotic stresses , given by “TF-S...
Figure 3.6. Case of an f.c.c. polycrystal made up of 200 isotropic grain orien...
Figure 3.7. Case of an f.c.c. polycrystal made up of 200 isotropic grain orien...
Figure 3.8. Case of an f.c.c. polycrystal made of 2016 isotropic grain orienta...
Figure 3.9. Case of an f.c.c. polycrystal made of 200 isotropic grain orientat...
Figure 3.10. Case of an f.c.c. polycrystal made of 200 isotropic grain orienta...
Figure 3.11. Cauchy stress components for a BCC single crystal under prescribe...
Figure 3.12. Rolling texture after 100% logarithmic strain: in the case of (a)...
Chapter 4
Figure 4.1. Successive stages in the growth of a 2D grain structure with the n...
Figure 4.2. 2D Topological transformations: (a) recombination (T1), (b) annihi...
Figure 4.3. Schematic illustration of simulation techniques for modeling bound...
Figure 4.4. Grain structure obtained by Weygand et al. (1998a) by considering ...
Figure 4.5. Left side: Three-dimensional elementary processes: (a) recombinati...
Figure 4.6. First 3D representative simulations realized with the Vertex metho...
Figure 4.7. The equilibrium shape of the grain boundaries as a function of the...
Figure 4.8. Top: elementary process for unpinning process as proposed by Weyga...
Figure 4.9. Top: new TA topological transformation proposed by Piȩkos et al. (...
Figure 4.10. (Top) Time evolution in 3D of one grain boundary evolving in a cl...
Figure 4.11. From top to bottom and left to right: time evolution of a 3D pure...
Figure 4.12. This figure illustrates the use of TRM code in the context of the...
Chapter 5
Figure 5.1. Three contributions to the phase-field functional. The phase-field...
Figure 5.2. Cutout of a multi-grain structure (left) and a single grain with t...
Figure 5.3. Double-well versus double obstacle potential in dimensionless unit...
Figure 5.4. The chemical bulk free energy f
bulk
as a mixture of two convex (i...
Figure 5.5. Simulated martensite microstructure in low alloyed steel for diffe...
Figure 5.6. Comparison of flow stress evolution between experiment and simulat...
Figure 5.7. Hot compression test of a multi-grain structure in MS-W 120 steel ...
Figure 5.8. Phase-field simulation results obtained for a solidification proce...
Figure 5.9. Concentration distribution of all solute elements of CMSX-4 at the...
Chapter 6
Figure 6.1. LS description of a polyhedral grain (blue interface) in an unstru...
Figure 6.2. (a) 2D micrograph obtained by EBSD (each grain being plotted with ...
Figure 6.3. Scheme depicting one GB and its parameters. Image available online...
Figure 6.4. (a) 2D Inconel 718 microstructure example where local anisotropic ...
Figure 6.5. Illustration of (a) overlapping of level sets at a triple junction...
Figure 6.6. Complex thermomechanical path for a 304 L stainless steel. From le...
Figure 6.7. Initial microstructure (a) with 5,000 grains and the grain size di...
Figure 6.8. Comparison of GB distribution properties: (a) DDF and (b) GBED. Ad...
Figure 6.9. Initial crystallographic characteristics. Adapted from Murgas et a...
Figure 6.10. Time evolution for the different formulations for the Random conf...
Figure 6.11. Time evolution for the different formulations for the Uniform con...
Figure 6.12. Creation and evolution of sub-grains in Zircaloy-4 during CDRX an...
Figure 6.13. Illustration of the interaction between a particle (red surface) ...
Figure 6.14. 3D GG LS simulations for Inconel 718 with an idealized spherical ...
Figure 6.15. Microstructure evolution at different times for a heterogeneous S...
Figure 6.16. Snapshots of austenite decomposition into ferrite in a 2D microst...
Figure 6.17. Snapshots of coarsening and dissolution of second-phase particles...
Chapter 7
Figure 7.1. CA spaces with different cell geometries (a) square, (b) hexagonal...
Figure 7.2. Different neighborhood definitions in CA space (a) von Neumann; (b...
Figure 7.3. Different neighborhood definitions in the 3D CA space (a) von Neum...
Figure 7.4. The basic concept of the neighborhood selection algorithm in the r...
Figure 7.5. Illustration of the periodic boundary condition concept in the 2D ...
Figure 7.6. Concept of a space iteration direction in the (a) classical CA and...
Figure 7.7. Different computational domains hexagonal cell shape in (a) 2D, (b...
Figure 7.8. Initial 200 × 200 × 200 μm microstructure obtained by the Monte Ca...
Figure 7.9. Initial 200 × 200 × 200 μm microstructure obtained by the cellular...
Figure 7.10. Example of (a) an optical microscopy image of the microstructure ...
Figure 7.11. Artificial energy distributed (a) homogeneously, (b) heterogeneou...
Figure 7.12. Shape of growing recrystallized grains (white grains – deformed m...
Figure 7.13. Generation of the CA SRX model input data based on the DMR FE cal...
Figure 7.14. Concept of data transfer between two computational domains, FE an...
Figure 7.15. Information on initial data for the CA SRX model after deformatio...
Figure 7.16. Influence of recovery module on the SRX kinetics during heating t...
Figure 7.17. Area with nucleation potential sites for different critical equiv...
Figure 7.18. Grain boundary mobility as a function of misorientation: (a) expo...
Figure 7.19. Results of grain growth with different values of misorientations ...
Figure 7.20. Recrystallization kinetic for heating simulation (heating rate of
Figure 7.21. Evaluation of a grain boundary curvature during recrystallization
Figure 7.22. Illustration of the curvature-driven grain growth (cellular autom...
Figure 7.23. Example of results obtained from CA SRX simulation: (a) initial m...
Figure 7.24. CPU parallelization concept applied to the SRX model
Figure 7.25. Speedup from (a) 2D and (b) 3D investigations for a different num...
Guide
Cover Page
Table of Contents
Title Page
Copyright Page
Preface
Begin Reading
List of Authors
Index
WILEY END USER LICENSE AGREEMENT
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SCIENCES
Mechanics, Field Director – Gilles Pijaudier-Cabot
Numerical Methods in Mechanics, Subject Head – Sylvain Drapier
Digital Materials
Continuum Numerical Methods at the Mesoscopic Scale
Coordinated by
Marc Bernacki
Samuel Forest
First published 2024 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK
www.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
www.wiley.com
© ISTE Ltd 2024The rights of Marc Bernacki and Samuel Forest to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.
Library of Congress Control Number: 2024943341
British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78945-197-9
ERC code:PE1 Mathematics PE1_13 Probability PE1_14 StatisticsPE8 Products and Processes Engineering PE8_3 Civil engineering, architecture, maritime/hydraulic engineering, geotechnics, waste treatment PE8_7 Mechanical and manufacturing engineering (shaping, mounting, joining, separation)
Preface
Marc BERNACKI1and Samuel FOREST2
1CNRS UMR 7635, Centre for Material Forming (CEMEF), MINES Paris, PSL Research University, Sophia Antipolis, France
2CNRS UMR 7633, Centre des Matériaux, MINES Paris, PSL Research University, Evry, France
Digital materials have now become an integral part of design methods for industrial components and structures. Their mechanical properties can be predicted from a description of the microstructure and behavior laws of the constituents. This topic is now well established through the concept of integrated computational materials engineering (ICME).
This book covers a wide range of material properties from transport phenomena to the mechanics of materials and microstructure changes in physical metallurgy. It is not, however, an exhaustive review of numerical simulation methods for these phenomena, but rather a current look at the continuum simulation of elasticity, viscoplasticity, phase changes and grain boundary migration in metals, alloys and composites.
The elementary mechanisms of deformation and damage in materials involve complex atomic processes, which are now well explored by appropriate numerical simulations such as molecular dynamics. In contrast, this book shows how these mechanisms can be integrated into a continuum approach to the physics and mechanics of materials at the mesoscopic scale. It therefore focuses on the mechanics of continuous media and the continuum thermodynamics of irreversible processes. These models take into account the heterogeneities of materials, namely, their polycrystalline and/or composite nature, and constitute an intermediate step toward the establishment of effective laws for engineers in the calculation of structures and manufacturing processes.
The scientific topics selected in the book focus on the homogenization theory developed for periodic or random composite materials. The mean field approach is based on an idealization of the microstructure and provides estimates of the mean stresses and strains in the various phases present. These models can be fed by the full-field approach, where the representative elementary volume is the key concept. Plasticity is also given a significant place in this book, particularly at the grain scale, thanks to crystal plasticity in its discrete form, namely, the dynamics of dislocations, or its continuous form, which evaluates the quantities of slip and strain hardening associated with each slip system. Another strong point is the treatment of moving surfaces within the microstructure of materials, whether for phase changes, grain boundary migration and recrystallization. Statistical methods are used extensively to take account of the random nature of the distribution of constituents, dislocations and cracks, and also to exploit the large volumes of data produced by these simulations.
The book is structured into two parts. The first three chapters are devoted to mean-field and full-field approaches to establish the constitutive laws of elastoviscoplastic heterogeneous materials. The next four chapters focus on the numerical simulation of microstructure evolution, with particular attention paid to the modeling of the motion of interfaces (grain boundaries, moving interfaces for phase changes, etc.) and a whole range of numerical front-tracking or front-capturing methods that are now well established or in full development.
The first chapter is a summary presentation by Sylvain Queyreau of the methods and results of discrete dislocation dynamics (DDD) simulations. It begins with a description of the simulation technique, which is based on the elastic theory of dislocations in crystals, as well as on information relating to the core of dislocations and dislocation interaction rules derived from molecular dynamics analyses and microscopic observations. The method is capable of making predictions about the behavior of the single crystal, in particular the strain hardening laws. Recent developments address the response of polycrystals to complex loading, particularly cyclic loading conditions.
In the second chapter, Dominique Jeulin immediately places the question of the representative volume element (RVE) at the heart of the debate on the construction of the effective behavior of heterogeneous materials. He promotes statistical analysis of the morphology of phase distribution within the microstructure and the construction of random morphological models on which to base simulations of physical and mechanical properties. He proposes a precise statistical definition of the size of the RVE according to the precision required for the targeted property estimates. It emphasizes the biases associated with the choice of boundary conditions applied to the boundaries of the domain and stresses the importance of the concept of integral range for the definition of the RVE. The approach is highly effective for predicting linear material properties such as thermal and electrical conductivity, permeability and elasticity, but also acoustics and wave propagation. The statistical definition of the RVE, initially developed for linear properties, is extended here to the nonlinear case by using the space average of the local energy. Finally, the approach is heuristically extended to the elastoplastic behavior of heterogeneous materials, in particular metallic polycrystals and porous media.
The micromechanics of materials is addressed in Chapter 3 within the framework of the mean field approach. In a discipline whose history, outlined in the introduction, has been particularly rich over the last 60 years, the chapter focuses on the thorny issue of homogenization in the case of elastoviscoplastic behavior of the phases involved. The translated field method is highlighted and compared with other models available in the literature. It is first applied to the case of two-phase composites and then to metallic polycrystals. The second part of the chapter concerns the pragmatic approach developed by Cailletaud and Pilvin, which has proven its worth in the prediction of complex loading paths, particularly cyclic loading. It is extended here to the case of large deformations of metallic polycrystals in order to predict the evolution of the crystallographic texture and internal stresses for different deformation paths encountered particularly during metal forming.
The second part of the book, devoted to the simulation of evolving microstructures during thermomechanical treatments, begins with a presentation of the Vertex method in Chapter 4. The migration of grain boundaries and the growth of new grains are modeled by tracking grain boundaries, triple lines and vertices whose movements are dictated by surface energy, grain boundary curvature and, possibly, the energy stored in the grains in the form of dislocation densities assumed homogeneous per grain. Topological changes in the microstructure represent a major challenge in the tracking of these geometric objects within representative elementary volumes. Robust methods are now available and have proved their worth in simulating numerous metallurgical phenomena such as dynamic recrystallization or grain growth with second-phase particles and anisotropic properties of grain boundaries.
Predicting microstructural evolution during complex transformation processes, including mechanical, thermal and metallurgical aspects, is now possible thanks to the thermodynamics of continuous media and irreversible processes. This energy-based approach combines mechanical contributions (elasticity, viscoplasticity and strain hardening), chemical contributions (multi-constituent diffusion) and phase changes (oxidation, diffusive and displacive transformations). Electromagnetic coupling is also possible. The implementation of this holistic modeling is enhanced by the phase field method, which enables the kinetics and dynamics of interface motion to be calculated by formulating coupled free energy potentials and substituting diffuse interfaces for ideal surfaces. This is the subject of Chapter 5 by Ingo Steinbach and Oleg Schchyglo. The theoretical part of the chapter presents the multi-phase and multi-component formulation, which enables realistic alloy compositions to be addressed and the evolution of phase diagrams to be taken into account in detail. The phase field method excels in predicting changes in phase morphology, both coalescence and separation, but is often unsuitable for nucleation processes. Illustrations concern multi-component solidification, martensitic transformation and recrystallization phenomena.
The level-set method is described in Chapter 6 for applications to diffusive phase transformations (Oswald ripening and precipitate coalescence), grain growth and static or dynamic recrystallization in polycrystals. The driving pressures for interface migration are described in detail, as is the finite element numerical implementation. The crucial ingredient of the underlying model is the interface mobility law linking its velocity to the driving pressures of curvature and the stored energy jump in the case of recrystallization, or the Gibbs free energy jump in the case of diffusive phase changes. The technical subtleties of implementing these methods in finite element codes are explained, and the applications concern both 2D and 3D simulations, with original methods for meshing grain boundaries and interfaces. Once again, particular attention is paid to the treatment of multiple junctions. Large-scale computations of polycrystalline aggregates are used to study the influence of grain boundary types on their growth in relation to the anisotropy of surface energies.
The last chapter describes the latest advances in cellular automata methods applied to the computational mechanics of materials, and more specifically to recrystallization in metals and alloys during thermo-mechanical treatments. These are discrete approaches as opposed to the continuous approaches described in Chapters 4–6. Cellular automata, based on the consideration of a finite number of cells to which a certain number of variables are attached, are particularly suitable for introducing the stochastic aspects of the phenomena involved. They use the notion of cell neighborhood and transition rules to update the state of each cell. In particular, the method makes it possible to track the moving fronts within evolving microstructures during static recrystallization. It incorporates the influence of curvature, stored energy, thermal activation of the various phenomena and nucleation probabilities. Examples based on complex morphologies of polycrystalline microstructures from 3D electron backscattered diffraction (EBSD) analysis are presented.
The book is far from being an exhaustive snapshot of the numerical mechanics of materials in 2024, since only a very limited number of topics have been covered. The choice of topics is not only related to their importance in current research, but also to the tastes of the editors of this book, whom the reader should forgive. Other themes could have been explored, for example, a more in-depth study of the mechanics of composite materials in relation to their complex 3D microstructures, mechanical and electromagnetic couplings, the dynamics of microstructures (dispersion of elastic waves in metamaterials or high-speed deformation and damage), elastodynamics in polycrystalline materials, etc. Finally, the numerical mechanics of materials is now opening up to the methods of artificial intelligence, which is revolutionizing its algorithms. There is no doubt that this combination will produce astonishing successes, provided that the physics of the phenomena remains a requirement in the development of these methods.
We would like to thank Sylvain Drapier for his initiative in proposing this subject in the book series on computational mechanics, as well as all the authors of the chapters for their ambitious contributions and for their unfailing patience during the long preparation of the book. The quality of the result is all the more appreciated!
September 2024
