Proposition of a Crystal Plasticity Constitutive Equation Based on Crystallographic Misorientation Theory

Abstract

In this study, we try to reveal the relationship between the plastic deformation and the microscopic crystal misorientation evolution by using the homogenized finite element (FE) procedure with the proposed crystal plasticity constitutive equation. Since plastic deformation of polycrystal sheet metal is greatly affected by its initial and plastic deformed textures, multi-scale FE analysis based on homogenization theory with considering micro polycrystal morphology is required. 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 was modified to consider curvature of crystal orientation by using 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 macro-scale, and simultaneously crystal texture and misorientation evolutions in the micro-scale. The crystallographic misorientation evolution induced by the plastic deformation of polycrystal aluminum alloy was investigated by using the multi-scale FE analysis with new proposed hardening evolution equation. We confirmed the availability of our analysis code employing the new constitutive equation through the comparison with numerical and experimental results of uniaxial tensile problem.