Evaluating the utility of a phase distribution parameter in calculating the bulk viscous strength of two-phase composites

The position of the bulk strength of a composite material between the isostress and isostrain-rate bounds is in part a function of the spatial distribution of the contrasting phases. Here I explore whether a constant value can adequately parameterize a given spatial distribution and, if so, if that parameter value is predictable. I use a two-dimensional finite element calculation scheme for linearly viscous materials to calculate bulk strength. Constant values of two tested parameters satisfactorily describe the bulk strength at viscosity contrasts less than ∼50 for a given phase distribution and modal abundance. Neither tested parameter is constant with changes in mode. The values of the examined phase distribution parameters do not appear to be predictable based on a qualitative analysis of the spatial distribution. Thus although a constant parameter value can adequately describe a given phase distribution, because that parameter is not determinable a priori, accurate measurement of the bulk strength of a composite requires a numerical calculation method.