A multiscale model for nickel-based directionally solidified materials. (April 2019) - Coudon, F.; Cailletaud, G.; Cormier, J.; Marcin, L.
Abstract: 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. Highlights: A micromechanical model is developed for directionally solidified alloys. The new extension of the so-called β rule takes into account both elastic and plastic accommodations of grains. Parameters of the transition rule are adjusted by means of crystal plasticity finite element simulations. Results are compared to other analytical solutions based on the self-consistent scheme and the full-field model. The model provides decent results for uniaxial, biaxial and with a mean stress cyclic loadings.