On the size of the representative volume element used for the strength prediction: A statistical survey applied to the particulate reinforce metal matrix composites (PRMMCs)

Abstract

Particulate reinforced metal matrix composites (PRMMCs) are typical random heterogeneous materials whose global behavior depends on the microstructural characterisics. Recently a numerical approach was developed (Hachemi et al., Int J Plast 63:124-137, 2014 [1], Chen et al. Direct methods for limit and shakedown analysis of structures, 2015 [2]), by applying it to a typical PRMMC material WC/Co, we presented how the ultimate strength and endurance limit can be predicted from the material microstructures. Due to the randomness in the microstructures of PRMMCs, size of the representative volume element (RVE) has a nontrivial influence over the predicted effective behaviors. In order to understand how size of RVEs contribute to the result and based on that to eliminate its influence, a numerical investigation is performed in the present study. In this study, a large number of representative volume element (RVE) samples representing a representative PRMMC material, WC-20 Wt% Co, were built from artificial microstructures. The samples are obviously different in size, and by deploying the established numerical approach to these samples, ultimate strength and endurance limit were calculated. Afterwards, the derived material strengths were analyzed by multiple inferential statistical models. The statistical study reveals how strength and other effective material properties react to the change of the RVE size. On that basis, the study proposed a feasible and computationally inexpensive solution to minimize the size effect.