Determination of the RVE size for polycrystal metals to predict monotonic and cyclic elastoplastic behavior: Statistical and numerical approach with new criteria

The determination of the size of the Representative Volume Element "RVE" is extremely important to predict mechanical and physical effective properties of heterogeneous materials. In the present work, the optimal size of RVE for polycrystal materials, which is made-up of grains having a polyhedron Voronoi shape, is investigated for the prediction of an elastoplastic behavior using the crystal plasticity model. Ten realizations with a different number of grains ranging from 10 to 250 have been used in the numerical simulation. The homogenization technique combined with the Finite Element Method (FEM) is used to obtain the macroscopic strain and stress. Several new criteria are introduced as indicators for estimating the optimal RVE's size. Their formulation is based on the standard deviation with respect to the average value of different mechanical quantities. These criteria ensure that, for an optimal RVE size, the response of the crystalline aggregate is not sensitive to the orientations evolution and grains' dimensions. It turns out that, for the cyclic behavior, the influence of the loading mode is very important, in particular the asymmetrical stress mode. The influence of the value of strain or stress used to perform different simulation tests on the RVE size has been analyzed. The simulation results are in good agreement with the experimental results from the literature.