Hardening anisotropy of γγ′ superalloy single crystals—II. Numberical analysis of heterogeneity effects

In the first part of this study, the {gamma}/{gamma}{prime} superalloy single crystals yield stress and hardening anisotropy were experimentally estimated at 650 C, assuming homogeneous plasticity, G. Hoinard, R. Estevez and P. Franciosi, Acta Metall. 43, 1593 (1995). Here alloy morphology is regarded in two different ways: first as a two-phase anisotropic material with a uniform {gamma} matrix, describing the {gamma}{prime} precipitates arrangement with the help of an elementary pattern of inclusions; then treating the {gamma} matrix as a three (geometrical) phase medium, i.e., the three families of orthogonal {gamma} layers separating the precipitates, to estimate the matrix behavior heterogeneity in a 4-phase modelling of the alloy. Both {gamma} and {gamma}{prime} phases are treated as elastic-plastic crystalline media deforming by octahedral and cubic slip, and the models are based on the self consistent approximation. The alloy elasticity limit, internal stresses and hardening anisotropy are discussed with regard to the chosen behavior description for each phase, and behavior simulations are compared to experimental information.