3D DISCRETE DISLOCATION DYNAMICS APPLIED TO ... - NUMODIS

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2 Introduction Time (sec) 10 3 1 10 -3 10 -6 10 -9 10 -12 Molecular Dynamics 10 -11 10 -10 10 -9 10 -8 10 -7 10 -6 Single crystal models Dislocation Dynamics 10 -5 Space (m) Homogenization technique Polycrystal models Continuum mechanics Figure 1.1: Figure illustrating length and time scales of each model. Solid lines represent the limit ranges imposed by the intrinsic physics of the model. Dashed lines represent the limit imposed by the available computing power. of the DD simulations. Continuum mechanics treat the behavior of a continuum medium by a set of equations and boundary conditions. There are a wide range of numerical techniques which can solve the equations. Finite difference and finite element methods are two broad subsets of such techniques. In these methods, a continuum domain of interest is subdivided into discrete cells or elements, in which the values of certain physical quantities are determined by solving a system of equations. The output of a typical application to the metallic plasticity is the deformation behavior of the simulated volume, for which a governing constitutive equation is assumed. As introduced briefly above, MD, DD and continuum methods have their own characteristic length and time scale. Fig. 1.1 shows such ranges of length and time scales of each method. As the performance of each numerical method is improved, the volume and the physical time which can be simulated are increasing (top and right domain limit of each method in Fig. 1.1). Recently the length and time scales of the various methods begin to be overlapped. This gives a great impetus to exchange information in order to build up a unified model of the metallic plasticity, which would be able to predict the behavior of a material from the fundamental properties of the material. 10 -4 10 -3 10 -2 10 -1 1
1.2 Dislocation dynamics 3 (a) Weak obstacles (b) Hard obstacles Figure 1.2: 2D simulations of dislocations moving through a random array of point obstacles: Effects of obstacles’ strength ([Foreman & Makin 66]) 1.2 Dislocation dynamics 1.2.1 2D simulations of dislocation dynamics Based on the well understood elementary properties of a single dislocation, numerical DD methods have been developed first in 2D. Dislocation dynamics in 2D can be further divided in terms of the crystallographic orientation of the plane used for the simulations: (i) parallel and (ii) perpendicular to dislocation lines. In the case (i), the plane of the simulations is parallel to the glide plane of dislocation lines, thus nei- ther cross-slip nor climb of dislocations are allowed. This configurations have been applied initially to study line tension and the shape of a dislocation under stress ([Brown 64]). The dynamical movements of dislocations have also been simulated in the case of a glide plane containing random distribution of point obstacles ([Foreman & Makin 66]). The effects of obstacles’ strength on the initial flow-stress have been studied, and some of the simulation results are shown in Fig. 1.2. This type of 2D simulations is still in use to study the effect of particles’ parameters on the flow stresses, see for example [Mohles & Nembach 01]. In the case (ii), dislocations are perpendicular to the simulation plane, that is, dislocations are infinite, parallel to each and have the same character. This configuration can simulate the multi- plication, annihilation, cross-slip and climb of dislocations. It is, however, difficult to include the
Page 1 and 2: INSTITUT NATIONAL POLYTECHNIQUE DE
Page 3: Acknowledgements First of all, I ex
Page 6 and 7: Résumé La dynamique des dislocati
Page 8 and 9: viii CONTENTS 2.3.5 Plastic strain
Page 11: Chapter 1 Introduction 1.1 Computat
Page 15 and 16: 1.3 Scope of Thesis 5 Recently the
Page 17: 1.3 Scope of Thesis 7 coupling meth
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Page 61 and 62: Chapter 3 Parallelization of the Di
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3.1 An introduction to Supercomputi
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3.2 Towards a parallel DDD code 61
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3.3 Parallelization of the serial D
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3.4 Performance improvment 81 Speed
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3.4 Performance improvment 87 Y Z I
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3.5 Application to Stage I-II trans
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Chapter 4 Dislocation-precipitate i
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4.1 Image stresses due to a 3D part
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4.2 A simple case of dislocation-pa
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4.3 Fatigue simulations of material
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Chapter 5 Conclusions and perspecti
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namics codes into a parallel versio
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Bibliography [Abraham 97] Abraham F
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BIBLIOGRAPHY 155 [Devincre & Robert
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BIBLIOGRAPHY 157 [Khraishi et al. 0
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BIBLIOGRAPHY 159 [Risbet et al. 03]
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3D DISCRETE DISLOCATION DYNAMICS APPLIED TO ... - NUMODIS

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