A NEW CRYSTAL PLASTICITY CONSTITUTIVE EQUATION BASED ON CRYSTALLOGRAPHIC MISORIENTATION THEORY

Since plastic deformation of polycrystal sheet metal is greatly affected by its initial and plastic deformed textures, multi-scale finite element (FE) analysis based on homogenization with considering micro-polycrystal morphology is required [1]. We formulated a new crystal plasticity constitutive equation to introduce not only the effect of crystal orientation distribution, but also the size of crystal grain and/or the effect of crystal grain boundary for the micro-FE analysis. The hardening evolution equation based on strain gradient theory [2], [3] was modified to introduce curvature of crystal orientation based on crystallographic misorientation theory. We employed two-scale structure, such as a microscopic polycrystal structure and a macroscopic elastic/plastic continuum. Our analysis code predicts the plastic deformation of polycrystal metal in the macro-scale, and simultaneously the crystal texture and misorientation evolutions in the micro-scale. In this study, we try to reveal the relationship between the plastic deformation and the microscopic crystal misorientation evolution by using the homogenized FE procedure with the proposed crystal plasticity constitutive equation. The crystallographic misorientation evolution, which affects on the plastic deformation of FCC polycrystal metal, was investigated by using the multi-scale FE analysis. We confirmed the availability of our analysis code employing the new constitutive equation through the comparison of a uniaxial tensile problem with the numerical result and the experimental one.