Understanding material variability and the accuracy of homogenization theory in polycrystalline materials through direct numerical simulations

Using a massively parallel finite-element code, we perform an ensemble of 3D Direct Numerical Simulations (DNS) in which polycrystalline microstructures are embedded throughout a macroscale structure. A crystal-plasticity model is used to model the material response at the grain scale. The largest simulations model 400,000 grains within a macroscale structure using 35 million finite elements and 1000 processors. The DNS results are compared with corresponding simulations based on the governing equations and material properties obtained from first-order homogenization theory. Evidence is sought for any higher-order effects due to a finite microstructure, including surface effects. The example material is stainless steel 304L which possesses an austenitic (FCC) microstructure. For this material, each grain possesses a relatively large elastic anisotropy ratio, making it a seemingly ideal material to display higher-order effects. Simulations are performed in both linear and plastic regimes