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

Abstract

Predicting the material strengths of particulate reinforced metal matrix composites (PRMMCs) and understanding how these properties are related to the constituents and microstructural features are essential for material designers and application engineers. To this end, a computational approach consists of the direct methods, homogenization, and statistical analyses is introduced in our previous studies [1,2]. Since in various engineering applications failure of PRMMC materials are caused by time-varied combinations of tensile and shear stresses, to take into account of such situations the established approach is extended in the present work. 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, and 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.