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

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ABSTRACTThe 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.