Nonlinearity of the Crystal Yield Function in the Rate-Independent Crystal Plasticity and Its Effect on the Evolution of Anisotropy

Abstract

In typical crystal plasticity framework, the constitutive functions for the slip rate is commonly described by the rate-dependent formulation to avoid the non-uniqueness of the active slip systems due to the interdependency of the slip systems. These rate-dependent models are computationally expensive as these models impose numerically stiff, highly nonlinear equations that need to be solved at every integration point. Alternatively, the rate-independent crystal plasticity model uses the crystal yield function to describe the slip deformation and plastic spin by the active slip systems without the non-uniqueness problem. In this study, the effect of nonlinearity between resolved shear stress and slip rate on the shape of the crystal yield function in the formulation of the rate-independent crystal plasticity was rigorously investigated. In addition to the effects of the crystal plasticity model, the influence of the nonlinearity of the single crystal yield function on the evolution of anisotropy for various polycrystalline materials was evaluated.