Diffuse-interface polycrystal plasticity: Expressing grain boundaries as geometrically necessary dislocations

摘要

The standard way of modeling plasticity in polycrystals is by using thecrystal plasticity model for single crystals in each grain, and imposingsuitable traction and slip boundary conditions across grain boundaries. In thisfashion, the system is modeled as a collection of boundary-value problems withmatching boundary conditions. In this paper, we develop a diffuse-interfacecrystal plasticity model for polycrystalline materials that results in a singleboundary-value problem with a single crystal as the reference configuration.Using a multiplicative decomposition of the deformation gradient into latticeand plastic parts, i.e. F(X,t) = F^L(X,t) F^P(X,t), an initial stress-freepolycrystal is constructed by imposing F^L to be a piecewise constant rotationfield R^0(X), and F^P = R^0(X)^T, thereby having F(X,0) = I, and zero elasticstrain. This model serves as a precursor to higher order crystal plasticitymodels with grain boundary energy and evolution.