On the statistical determination of strength of random heterogeneous materials

This paper introduces a numerically-based methodology for determining the load-bearing capacity of particulate reinforced metal matrix composites (PRMMC) under both monotonic and cyclic loading. A multi-scale approach combining shakedown analysis with homogenization was used to evaluate the influence exerted by the composite structure on the global behavior of PRMMCs. The results were interpreted using statistical methods in order to take account of the randomness associated with the composite structure of the material. The general work flow of the approach can be summarized as follows: first, a large number of representative volume elements (PRMMC) were constructed from real material images using an in-house code. Next, lower bound limit and shakedown problems were solved via the interior-point method. Finally, results were converted to their corresponding macro quantities and evaluated statistically. With this approach we investigated a representative PRMMC structure, WC/Co, with two different binder contents and scrutinized the contribution of the composite structure over composite strength.