Modeling of imperfect bonding in fiber reinforced brittle matrix composites

Abstract

The present work is aimed at evaluating the effective thermoelastic moduli of continuous fiber reinforced brittle matrix composite systems in which debonding and slipping between the constituents occurs. Among the issues addressed is the fact that several definitions of composite strain may be used in the computation of effective moduli. The effective modulus theory relates the averages of the stress and strain tensors over a representative volume element through the effective elastic constants. Physical measurement of composite strain, however, is done by the use of strain gages which report the values on the lateral surfaces. Under perfect bonding, both the mathematical and physical definitions of composite strains are equivalent if the body is subjected to prescribed displacements that would lead to constant strain in a homogeneous medium. However, under imperfect bonding conditions at the interface, it is shown that the two definitions do not necessarily lead to the same value of composite strain and hence the effective moduli. This difference has been critically examined under conditions leading to fiber slipping and complete interfacial separation. It is further shown that the composite effective stiffness tensor becomes unsymmetric under certain interfacial conditions. These facts call into question the applicability of effective modulus theory as it is now being practiced. The fiber-matrix (debonding) separation problem is also modeled as a matrix weakened by cylindrical voids in place of the fibers, where the strain field within the void region does not vanish, in an attempt to provide a more realistic solution for this problem. In order to conduct this study, some preliminary groundwork is also done to develop new theorems for composite stress and strain in the presence of two-dimensional stress fields under arbitrary interface boundary conditions.