Statistical Analyses of the Strengths of Particulate Reinforced Metal Matrix Composites (PRMMCs) Subjected to Multiple Tensile and Shear Stresses

Abstract

For design and application of particulate reinforced metal matrix composites (PRMMCs), it is essential to predict the material strengths and understand how do they relate to constituents and microstructural features. To this end, a computational approach consists of the direct methods, homogenization, and statistical analyses is introduced in our previous studies. Since failure of PRMMC materials are often caused by time-varied combinations of tensile and shear stresses, the established approach is extended in the present work to take into account of these situations. In this paper, ultimate strengths and endurance limits of an exemplary PRMMC material, WC-Co, are predicted under three independently varied tensile and shear stresses. In order to cover the entire load space with least amount of weight factors, a new method for generating optimally distributed weight factors in an n dimensional space is formulated. Employing weight factors determined by this algorithm, direct method calculations were performed on many statistically equivalent representative volume elements (SERVE) samples. Through analyzing statistical characteristics associated with results the study suggests a simplified approach to estimate the material strength under superposed stresses without solving the difficult high dimensional shakedown problem.