Estimating the response of polycrystalline materials using sets of weighted statistical volume elements

The traditional representative volume element (RVE) is usually obtained through an iterative procedure based on the convergence of a selected material property. Although RVEs produced in this manner are generally presumed to automatically capture the salient features of the underlying microstructure, they typically do not achieve this requirement. Alternatively, one can identify a weighted set of statistical volume elements (WSVEs) that captures selected dominant components of n-point spatial correlations of the microstructure to prescribed accuracy. The main advantage of using WSVEs is that the key microstructural features are captured within sets of computationally manageable models ensuring reliable calculation of the material behavior and its variance in an efficient manner. In this paper, this concept of WSVEs is applied and validated for a nearly randomly oriented body-centered cubic β-Ti alloy. Specifically, two WSVE sets composed of members with an average of 100 grains and 200 grains, respectively, are derived from a 4300-grain reconstruction of real microstructure based on the dominant two-point spatial correlation statistics identified by principal component analyses. Crystal plasticity formulation is used to model the behavior of the material under selected globally applied loading conditions. The WSVEs obtained in this work were validated by comparing their overall stress–strain responses with those of a traditional 500-grain RVE. Furthermore, the frequency plots of the microscale cumulative shear strains obtained using the WSVEs compared favorably with those obtained using the traditional RVE. It is concluded that WSVE sets based on microstructure provide a viable practical alternative to the traditionally defined RVE in estimating the response of large polycrystalline microstructure datasets, with reasonable accuracy and significantly smaller computational resource needs.