[SY-C2] Symposium C-2

[SY-C2] Meshfree Analysis for Kink Band Formation in Mg-based LPSO Phase Based on Crystal Plasticity Cosserat Model Considering Disclination Density

^○Yuichi Kimura¹, Yuichi Tadano², Kazuyuki Shizawa³ (1.Grad. School of Science and Technology, Keio Univ., Japan, 2.Dept. of Mechanical Engineering, Saga Univ., Japan, 3.Dept. of Mechanical Engineering, Keio Univ., Japan)

Mg alloys with a long period stacking ordered structure (LPSO) phase has attracted attention as a next-generation structural material due to its high strength and low specific weight. The strength of this alloy is mainly attributed to the kink deformation in LPSO phase. Since the boundary between the kink and matrix has a large misorientation similar to that of a grain boundary, dislocation glides are prevented at the kink boundary. The clarification of detailed behavior of kink formation through numerical simulation is highly expected. Whereas the mechanism of kink band formation has conventionally been explained by the motion and accumulation of dislocations, it is recently attempted to express its process from the point of view of a rotational crystal defect called the disclination. The authors have developed a crystal plasticity Cosserat model classified into couple stress theory with a microscopic rotational degree of freedom to describe the disclination, and carried out FE analyses on a single crystal of LPSO phase. However, the FEM using C⁰ continuous shape function is not applicable for the Cosserat model because such function cannot ensure the continuity of higher-order gradient of displacement field peculiar to the Cosserat model and the analysis is limited to the infinitesimal deformation.
In this study, a meshfree method is introduced into our numerical scheme instead of the FEM and it is shown that this method can express the continuous higher-order gradient of displacement field and can be adapted to boundary conditions for microscopic rotation originating in the disclination. Also, a new boundary value analysis suitable for the crystal plasticity couple stress model is presented in the category of finite deformation theory. Then, a meshfree analysis based on the present model considering disclination density is conducted to reproduce the kink formation based on disclination behaviors, and it is shown that this model can predict the kink deformation through a quadrupole structure of disclination and array structures of GN dislocation formed around the kink band. Furthermore, the size effect on the deformation response and the mesh independence of kink band width of the present model are investigated and the influence of the boundary condition for microscopic rotation on the kink deformation is discussed.