A multiscale model for nickel-based directionally solidified materials

In this paper, the so-called “ β rule” is used to simulate the anisotropic behaviour of directionally solidified superalloys. First, the “mean-field” model is extended to the general case of heterogeneous local elasticity. Two other models also designed using the “self-consistent” framework are applied to make comparisons, either with the assumption of a purely elastic accommodation of grains (Kröner-Weng model) or the translated field theory. As a reference, full-field simulations using a representative volume element (RVE) and a crystal plasticity finite element model (CPFEM) are carried out. Results show that the β rule is able to predict the overall response of the material for various cases such as one-dimensional or two-dimensional cyclic loading with or without a mean stress. Otherwise, local estimations are studied for both mean-field and full-field models. The local responses of the β rule are consistent when they are compared to those of CPFE simulations.