Hierarchical crystal plasticity FE model for nickel-based superalloys: Sub-grain microstructures to polycrystalline aggregates

A hierarchical crystal plasticity constitutive model, comprising three different scales for polycrystalline microstructures of Ni-based superalloys, is developed in this paper. Three scales, dominant in models of polycrystalline Ni-based superalloys, are: (i) the sub-grain scale of γ-γ′γ-γ′ microstructure, characterized by γ′γ′ precipitate size and their spacing; (ii) grain-scale characterized by the size of single crystals; and (iii) the scale of polycrystalline representative volume elements. A homogenized activation energy-based crystal plasticity (AE-CP) FEM model is developed for the grain-scale, accounting for characteristic parameters of the sub-grain scale γ-γ′γ-γ′ morphology. A significant advantage of this AE-CP model is that its high efficiency enables it to be effectively incorporated in polycrystalline crystal plasticity FE simulations, while retaining the accuracy of detailed sub-grain level representative volume element (SG-RVE) models. The SG-RVE models are created for variable morphology, e.g., volume fraction, precipitate shape and channel-widths. The sub-grain crystal plasticity model incorporates a dislocation density-based crystal plasticity model augmented with mechanisms of anti-phase boundary (APB) shearing of precipitates. The sub-grain model is homogenized for developing parametric functions of morphological variables in evolution laws of the AE-CP model. Micro-twinning initiation and evolution models are incorporated in the single crystal AE-CP finite element models for manifesting tension–compression asymmetry. In the next ascending scale, a polycrystalline microstructure of Ni-based superalloys is simulated using an augmented AE-CP FE model with micro-twinning. Statistically equivalent virtual polycrystals of the alloy CMSX-4 are created for simulations with the homogenized model. The results of simulations at each scale are compared with experimental data with good agreement.