Mechanics and Energetics of Kink Deformation Studied by Nonlinear Continuum Mechanics Based on Differential Geometry

Abstract

This study conducts dislocation-based modeling and numerical analysis for kink deformation using the theory of nonlinear continuum mechanics based on differential geometry. The kinematics of the continuum is represented by the reference, intermediate, and current states, which are related to the multiplicative decomposition of the deformation gradient into plasticity and elasticity. The intermediate state is determined by the Cartan first structure equation, whereas the current state is obtained from the stress equilibrium equation. Kink deformation is modeled by a planar array of edge dislocations, and the governing equations are solved numerically using the finite element method. Quantitative verification of the model is conducted by comparing the bending angle at a kink interface and the theoretical prediction given for the tilt grain boundary. We construct two types of ortho-type kink models for several interface lengths to understand the energetics and mechanics of the kink growth process. The present numerical analysis demonstrates the significant stress concentration at the growth front due to the formation of wedge disclination. We also discuss the material strengthening mechanism from elastic strain energy, nonsingular stress fields, and nonlinear elastic interaction between the disclinations.