Dislocation density based crystal plasticity finite element simulation of Al bicrystal with grain boundary effects
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Dislocation density based crystal plasticity finite element simulation of Al bicrystal with grain boundary effects Zhe Leng*, David P. Field*, Alankar Alankar** *
School of Mechanical and Materials Engineering, Washington State University * [email protected], **[email protected] ** Los Alamos National Laboratory, Los Alamos 87544, NM [email protected]
ABSTRACT Crystal plasticity finite element method is a useful tool to investigate the anisotropic mechanical behaviors as well as the microstructure evolution of metallic materials and it is widely used on single crystals and polycrystalline materials. However, grain boundary involved mechanisms are barely included in the polycrystalline models, and modeling the interaction between the dislocation and the grain boundaries in polycrystalline materials in a physically consistent way is still a long-standing, unsolved problem. In our analysis, a dislocation density based crystal plasticity finite element model is proposed, and the interaction between the dislocation density and the grain boundaries is included in the model kinematically. The model is then applied to Al bicrystals under 10% compression to investigate the effects of grain boundary character, e.g. grain boundary misorientation and grain boundary normal, on the stress state and the microstructure evolution. The modeling results suggest a reasonable correspondence with the experimental result and the grain boundary character plays a crucial role in the stress concentration and dislocation patterning. INTRODUCTION Grain boundaries play an important role in determining the mechanical properties of metallic materials; they act as dislocation sources or provide a strengthening mechanism by impeding dislocation motion. Dislocations can pile-up, be transmitted or be absorbed by grain boundaries based on the local stress state and the grain boundary character. At present, only a few crystal plasticity finite element models account for the presence of grain boundaries, and treatments of grain boundaries vary from different models, such as the interface of different sections [1] or elements with specified properties [2]. In this study, a dislocation density based crystal plasticity finite element model is applied to incorporate the interaction between the dislocations and the grain boundaries. The dislocation density is tracked as state variables and the evolution of the total dislocations includes generation and annihilation. The non-zero flux divergence gives rise to the geometrically necessary dislocation (GND) density. The grain boundary effects are applied for the near grain boundary region, and an additional energy barrier and a critical geometrical factor are considered for the dislocation transmission event. The energy barrier comes from the elastic energy of dislocation debris remaining in the interface during the transmission event. The simulation is conducted on bi-crystal aluminum specimens under 10% compression to check the stress state and microstructure evolution, such as GND patterning. CRYST
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