Numerical models of the effect of heterogeneity on the behavior of graded materials

Gradients in the elastic modulus of a surface can affect the hardness of that surface, as demonstrated in recent papers [1, 2]. It has been experimentally verified that enhanced hardness can be obtained by dispersing a variable concentration of second phase particles in a matrix and cosintering. However, the nature of the processing conditions results in a microstructure that has variations in its lateral (in-surface-plane) properties and variations about the optimal gradient due to the discrete nature of the second phase particulate microstructure: these materials have stochastically graded microstructures, In this paper, we generate a series of microstructures that have the same average surface gradient, but with variable placement of the second phase, in order to analyze numerically the effect of stochasticity on the predicted optimal material properties. We characterize the effect of stochastic placement of second phase particles on the hardness and toughness of these materials which have a specified gradient in their surface elastic coefficients.