S. Ghosh, S. Keshavarz and G. Weber. Inelastic Behavior of Materials and Structures Under Monotonic and Cyclic Loading, Advanced Structured Materials, Vol. 57, pages 67- 90, (2015).
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A hierarchical crystal plasticity constitutive model, comprising three different scales for polycrystalline microstructures of Ni-based superalloys, is developed. Three scales, dominant in models of polycrystalline Ni-based superalloys, are: (i) the sub-grain scale of γ –γ microstructure, characterized by 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 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 subgrain 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. Microtwinning initiation and evolution models are incorporated in the single crystal AECP 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.