The effective yield strength of fiber-reinforced composites

This work is concerned with the determination of the effective properties of transversely isotropic fiber composites made up of two rigid-perfectly plastic phases in prescribed volume fractions. The phases are assumed to satisfy incompressible, isotropic yield criteria of the Mises type. To study the behavior of these composites we make use of variational principles, recently developed by Ponte Castafieda (1991, J. Mech. Phys. Solids39, 45-71), that provide a method for generating estimates for the effective properties of nonlinear composites from corresponding estimates for the effective properties of linear composites. We demonstrate that this method allows us to obtain simple expressions for the effective yield functions of rigid-perfectly plastic composites. Explicit results, corresponding to the Hashin-Shtrikman bounds, the self consistent and the generalized self consistent estimates, and the composite cylinder assemblage model are obtained for the class of rigid-perfectly plastic fiber composites. These estimates exhibit the existence of two distinct yielding modes, in agreement with corresponding experimental results.