Effective properties of short-fiber composites with Gurtin-Murdoch model of interphase

A mathematical model employing the concept of the energy-equivalent inhomogeneity combined with the method of conditional moments has been applied to analyze short-fiber composites. The fibers are parallel, randomly distributed, and their interphase is assumed to be adequately described by the Gurtin-Murdoch material surface model. The properties of the energy-equivalent fiber, incorporating properties of the original fiber and its interphase, are determined on the basis of Hill's energy equivalence principle assuming its cylindrical shape. To describe random distribution of fibers a statistical method, the method of conditional moments, has been employed. Closed-form formulas for the components of the effective stiffness tensor of short-fiber reinforced composites have been developed which, in the limit, compare well with the results available in the literature for infinite parallel fibers with Gurtin-Murdoch interphase model. Influence of fiber length on contribution of the surface effects to the effective properties of the material containing cylindrical cavities has been analyzed for all five independent components of its stiffness tensor, and for two sets of surface properties in the Gurtin-Murdoch model.