Finite Element Studies of Homogeneous and Heterogeneous Dislocation Nucleation based on the Rice-Peierls Framework

Abstract

The study of dislocation nucleation has gained increasing attentions recently primarily due to the advancement of small scale mechanical testing methods. Based on the classic Rice model of dislocation nucleation from a crack tip in which the dislocation core is modeled by a continuous slip field, a nonlinear finite element method can be formulated with the interplanar potential as the input, and the development of interplanar slip field can be solved from the resulting boundary value problems. The effects of geometric boundary conditions, loading patterns, etc. can be conveniently determined, as opposed to the time consuming molecular simulations. To validate the method, we compare the simulations results of homogeneous dislocation nucleation and heterogeneous dislocation nucleation from a two-dimensional crack tip to the literature results. As proposed by Rice and Beltz (J. Mech. Phys. Solids, 1994), the activation energy for dislocation nucleation from a three-dimensional crack tip depends on the finite thickness in the direction parallel to the crack tip, which has been successfully reproduced in the finite element simulation results reported here.

Strength statistics of single crystals and metallic glasses under small stressed volumes

“…The transition between these two states experiences a saddle point configuration which has a higher energy than the stable solution, and the energy difference between the saddle point and stable configurations is the activation energy. Such a general view has be adopted for various types of dislocation models, including the Volterra dislocation analysis [91,[132][133][134], the Peierls dislocation model [135][136][137][138][139][140], or molecular dynamics [131,142]. The saddle point configuration can be guessed in simple cases, e.g., a circular dislocation loop in homogeneous dislocation nucleation, or a half loop from a crack tip or surface steps.…”