Yield surface simulation for partially recrystallized aluminum polycrystals on the basis of spatially discrete data

The paper presents simulations of the yield surface evolution of plastically deformed aluminum polycrystals during recrystallization. The yield surfaces are calculated using a viscoplastic Taylor–Bishop–Hill strain rate polycrystal homogenization method. The input data for the yield surface calculations are the crystal orientations, their volume fractions, and their shear stresses. While the crystal orientations determine the kinematic portion of the yield surface the threshold shear stress of each individual orientation determines the kinetic portion of the yield surface. The input data for the homogenization calculations are generated through a spatially discrete simulation, where crystal deformation and primary static partial recrystallization are simulated by coupling a viscoplastic crystal plasticity finite element model with a cellular automaton. The crystal plasticity finite element model accounts for crystallographic slip and for crystal rotation during plastic deformation using space and time as independent variables and the crystal orientation and the accumulated slip as dependent variables. The cellular automaton uses a switching rule which is formulated as a probabilistic analogue of Turnbullʹs rate equation for the motion of grain boundaries. The actual decision about a switching event is made using a simple-sampling Monte Carlo step. The automaton uses space and time as independent variables and the crystal orientation and a stored energy measure as dependent variables. The kinetics produced by the switching algorithm are scaled through grain boundary mobility and driving force data. The crystallographic texture and the orientation-dependent resistance to shear are for each interpolation point extracted after each time step during recrystallization. The data serve as input for the calculation of discrete yield surfaces.