2, University of California, Santa Barbara, Santa Barbara, California, United States
We have developed a novel algorithm to generate 3D virtual representative twinned microstructures that are statistically equivalent to experimentally observed microstructures from electron back-scattered diffraction (EBSD) scans of a nickel-based superalloy sample. The distributions and correlations of various morphological and crystallographic information are extracted from EBSD data and then used to create virtual parent grain microstructures. To incorporate twins inside the parent grain microstructures, the distributions of twins with respect to parent grains, including the joint probability of number of twins and parent grain size, along with the conditional probability distributions of twin thickness and twin distance from parent centroids are employed. Then, subsequent to determination of morphological and geometrical information of twins through a Monte-Carlo scheme, the microstructure-based statistically equivalent representative volume elements (M-SERVEs) are generated. The statistics of M-SERVEs are compared and validated with respect to EBSD microstructural statistics, and the convergence of the results is studied with the aid of the Kolmogorov-Smirnov test. To study the mechanical behavior of the material, a crystal plasticity finite element model is presented, and the material parameters are calibrated and then validated using the experimental tests. Through the convergence study, the minimum size of M-SERVE required to capture the morphological and crystallographic statistics of EBSD scans as well as the minimum size of the property-based statistically equivalent representative volume elements (P-SERVE) necessary to reproduce the macroscopic material response in mechanical tests are reported. The framework is implemented to study the performance of polycrystalline microstructures under monotonic and fatigue loading. Finally, the weak regions of the polycrystal susceptible to crack nucleation are strengthened by locally varying the material parameters, representing the crystallography and morphology of subgrain structures, which in turn result in designing stronger superalloys across length scales.