Mean field estimates of the response of fiber composites with nonlinear interface

This paper presents a theory of the effective response of composites contai ning general, nonlinearly separating inclusion-matrix interfaces. The direc t method of composite materials theory is utilized to pass from local nonli near behavior of a solitary inclusion problem to nonlinear aggregate respon se. Interaction effects at finite volume concentration are captured in the representative solitary problem by employing the Mori-Tanaka mean field est imate. The resulting model falls within the conceptual framework of continu um damage mechanics in that nonlinear effective response depends on interna l variables that are governed by local evolution equations. The damage vari ables turn out to be the expansion coefficients arising in an eigenfunction representation of the displacement jump at a representative inclusion-matr ix interface. Interfaces are generally modeled according to a nonlinear for ce-separation law that allows for both normal and shear decohesion (X-.P. X u, A. Needleman, Modell. Simul. Mater. Sci. Eng. 1 (1993) ill). Detailed ca lculations of effective stress-strain response are carried out for the case of transverse shear and plane dilatation of unidirectional fiber composite s at various values of concentration and interface constitutive constants. The effects of the various parameters on bifurcation of equilibrium separat ion in the solitary inclusion problem and on overall composite stability ar e demonstrated as well. (C) 2000 Elsevier Science Ltd. All rights reserved.