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By Grant Steven, Qing Li, Zhongpu Zhang

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To achieve these goals, an Armstrong-Frederick nonlinear kinematic hardening rule is implemented in the CP framework to consider the backstress evolution, and a texture-based representative volume element (TBRVE) is developed to include the crystalline texture information. The TBRVE consists of a certain number of grains and orientations of the polycrystal, which conveniently represents the global texture and can capture the mechanical response of the material including the BE under cyclic loading.

A brief description of the model is given in this section and more details can be found in [17-19]. (1): F = Fe F p , (1) where F e represents the elastic deformation gradient which is composed of the elastic stretching and rigid body rotation of the configuration, and F p describes crystallographic slip along slip planes. The plastic velocity gradient L p is defined as the sum of the shear rates on all slip systems: N Lp = F p Fp−1 = ∑ γα ( sα ⊗ nα ) , (2) α =1 where γ α is the plastic shearing rate on the α-slip system, N is the number of slip system, s α is the slip direction, nα is the normal to the slip plane, and ⊗ is the dyadic product.

04. Given the dislocation interactions observed, the stress-strain curve is somewhat less non-linear than expected. The stress reversal corresponds with the annihilation of dislocations, and indicates that (at least when the GB is not penetrated), dislocation motion may be Applied Mechanics and Materials Vol. 553 33 elastic and reversible [8]. The stress relax images a change in the slip system after dislocations “penetrated” the GB. Dislocations also tended to form stacking faults after penetrating the GB, which suggests that Σ5 GBs will act as a pinning site for trailing partials.

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