Ph.D. Proposal Presentation by Laurent Capolungo
Friday, March 25, 2005
(Dr. Jianmin Qu, Co-Chair)
"Modeling of the Size Effect in the Plastic Behavior of Polycrystalline Materials"
The behavior of polycrystalline materials is affected by many factors, such as strain rate, temperature, or grain size. While the effects of strain rate and temperature are now well understood, the effect of the grain size is far from being elucidated. The appearance of nanocrystalline materials has revealed the existence of a very interesting phenomenon, often referred to as the breakdown of the Hall Petch law. This phenomenon suggests that the behavior of polycrystalline materials is considerably affected by its characteristic length. In order to provide a better understanding of the size effect and of the contribution of various deformation mechanisms operating at different grain sizes, a composite model will be developed. The material will be assimilated as a composite with two phases: (1) an inclusion phase accounting for the grain cores and (2) a matrix phase accounting for both grain boundaries and triple junctions. In a first step, local constitutive laws will be developed to take into account various phenomena. The constitutive law of the inclusion phase will account for the dislocation glide mechanism which is ruled by two phenomena: (1) the statistical storage of dislocation resulting from the dependence of the mean free path of dislocations on the presence of subgrains and on the interaction of dislocations with grain boundaries, and (2) the dynamic recovery. The possible size effect of the dynamic recovery will be investigated. Moreover, the emission of dislocations by grain boundary sources, which typically occurs when the grain size is in the nanorange, will be taken into account. The constitutive law of the matrix phase will be based on the climb of dislocations resulting from the penetration of emitted dislocations. In order to extract the macroscopic behavior of the material, several micromechanical schemes will be tested. In order to obtain more information about the local effect of dislocations, the constitutive laws will be modified in order to be incorporated in a strain gradient plasticity model. Hence, the effect of texture will be investigated. Finally, the crystal plasticity model will be implemented in a finite element software which will enable the observations of the localized phenomena in each phase.