Crystal Plasticity FE Simulation for Size Effect of Mg-Based LPSO Phase Using Dislocation-Based Higher-Order Stress Model

Abstract

The dislocation-based crystal plasticity model has been extended to a model considering higher-order stress by explicitly considering the mechanical work induced by the strain gradient. Furthermore, a finite element (FE) analysis is performed for a single crystal with a long-period stacking ordered (LPSO) phase on the basis of the obtained model. The mesh dependence of the kink band formation is discussed from the viewpoints of the strain gradient, size effect and higher-order boundary condition. Then, it is shown that the mesh dependence of kink deformation in the FE analysis can be removed even when the size effect parameter is relatively small. The width of the kink band is determined by the intrinsic length scale. When the kink band occurs in the entire specimen, work hardening can be reproduced by appropriately defining the boundary conditions for slip. The effect of length scale ratio on the kink deformation is small. Moreover, it is shown that the disclination quadrupole structure in the kink band can be expressed qualitatively by using incompatibility of crystal slip.