Crystal plasticity FE simulation for kink band formation in Mg-based LPSO phase using dislocation-based higher-order stress model

Abstract

The dislocation-based crystal plasticity model considering higher-order stress has been constructed and a finite element (FE) analysis is conducted for both a single crystal and polycrystal 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 scale ratio 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 the micro-scale ratio on the kink deformation is small. The disclination quadrupole structure in the kink band can be expressed qualitatively by using the incompatibility of crystal slip. Moreover, it is shown the back stress behaves as the resistance to the slip deformation in a polycrystal consisting of LPSO phases in shape of rectangular strip.

Keywords

• plasticity
• magnesium alloy
• dislocation
• finite element method
• crystal plasticity
• size effect