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4 Introduction line tension effect explicitly. This kind of configuration has been used to simulate the spontaneous microstructure formation ([Lépinoux & Kubin 87]). Because of its simplicity, this 2D method can simulate dislocation motion up to relatively large strains. This method is still largely under development and applied to several studies, see for example [Cleveringa et al. 97]. 1.2.2 3D simulations of dislocation dynamics The motivation of a 3D DD can be summarized as the needs • to include the 3D nature of the dislocation behavior, cross-slip, junction formation, ... • to explain the formation of dislocation structures during the plastic deformation The first simulation in 3D is proposed in [Canova & Kubin 91]. Since then, the proposed method has been developed and applied to investigate the collective motion of dislocations under various conditions by two leading groups 1 in France. This method is based on the representation of dislocation lines by segments in an integer space. Other versions of DD in 3D have emerged since the end of 1990s, as will be detailed in Sec. 2.1.4. Due to the development of simulation methods and the increased computing power, these simulation methods have strengthened their positions in the field of crystal plasticity. The 3D discrete dislocation dynamics (DDD) method has proven to be a powerful tool to investigate the plasticity of metals and been expected to serve as a link between atomistic and continuum scale simulations (see Fig. 1.1). 1.3 Scope of Thesis This thesis aims at applying the 3D DDD method to both rigorous computations of dislocation- precipitate interactions and studying the effects of precipitates on the fatigue properties of metals. For the rigorous computations, we extended the code coupled with a finite element method ([Fivel 97]) in order to incorporate 3D precipitates with a differing elastic modulus. The interaction forces due to a second phase particle are computed and the effects of these forces on the flow stress and the subsequent hardening are investigated. 1 Génie Physique et Mécanique des Matériaux (GPM2) and Laboratoire d’Etude Métallurgique (LEM)
1.3 Scope of Thesis 5 Recently the 3D DDD method are applied successfully to the study of early fatigue crack initi- ation of 316L stainless steels ([Déprés 04]). The critical role of cross-slip was pointed out, which demonstrates the advantages of the 3D DD simulations over the 2D simulations. Inspired by this study, we applied the 3D DDD method to simulate the fatigue behavior of materials hardened by precipitates. It was found, however, that the feasible volume fraction of precipitates is quite small considering the performance of the currently available computing machines with a single processor and the computing efficiency of the serial 3D DDD code. This is due to the additional computational loads induced when many precipitates are introduced in the 3D DDD simulations, which are already computationally demanding because of the long-ranged stress field of a dislocation segment and the need to handle the dislocation interactions during the segment motions. Because of the inherent computational load of the 3D DDD simulations, a maximum strain which can be simulated in a reasonable time still remains in the order of 10 −3 in multislip condition. The easiest way to suffice the computational demands of the fatigue simulations of precipitation- hardened materials would be to waite until a faster single processor is available. Considering the relatively short period of a doctorate, however, it cannot be a good way to choose notwithstanding the speed of a single processor has improved tremendously 2 . The other way is to increase the computational capacity by collecting single processors and making them work together, that is, parallel computing. A parallel computer simply comprises a number of processors that solve a problem together to reduce the elapsed computation time. In fact, parallel computing has been widely adopted in many research fields to resolve the increase of the computational demands, which arises due to many reasons, e.g. encompassing sophisticated boundary conditions, involving nonlinear material behaviors and many unknowns. Evident successes of the parallel computing in the field of the computational plasticity can be found in both MD methods ([Abraham 97]) and continuum mechanics ([Demmel et al. 93], [Fahrat & Roux 94]). The parallel codes have enabled each model to perform large scale simulations in reasonable time. In MD simulations, for example, a volume of 0.01nm 3 can be treated over a period of time in the order of 10 −12 seconds using massively parallel machines ([Abraham 97]). As can be seen in many references including the few examples cited above, the subject of parallel 2 Semiconductor technology has been known to increase a processor clock rate by double in 18 months up to now. This is known as the Moore’s law first published in 1965 ([Moore 65]) and which still holds true today. Intel expects that it will continue at least through the end of this decade. In the end, the performance of a single processor computing device will reach an upper limit due to the physical limits of semiconductor technology
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
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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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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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