A micromechanical damage model of fiber composites with nonlinear interface: Bulk, tension and compression response

This paper describes a micromechanical model of the constitutive behavior of unidirectional fiber composites in which nonlinear behavior arises solely from the force-separation response of the interfaces. The direct method of composite materials theory is employed to obtain the effective property relations for a representative volume element while a local analysis of a solitary inclusion problem yields kinetic equations governing interface separation components. The resulting model, which involves no adjustable parameters, falls within the conceptual framework of continuum damage mechanics with "damage" variables that have a precise geometrical meaning. For equibiaxial loading the single damage variable is shown to be equivalent to the area density of voids surrounding the fibers. For complex planar loading more damage variables occur and these are shown to be the expansion coefficients arising in an eigenfunction representation of the average displacement jump at the inclusion-matrix interface. Local fields are determined by the dilute estimate and the Mori-Tanaka estimate assuming smooth interface response governed by a Needleman-type normal force-separation mechanism. Explicit results are presented for transverse uniaxial tension and transverse uniaxial compression loading of a composite reinforced by fibers in dilute concentration.