Generalized stress intensity factors in the interaction between two fibers in matrix

Abstract

To evaluate the mechanical strength of fiber reinforced composites it is necessary to consider singular stresses at the end of fibers because they cause crack initiation, propagation, and final failure. The singular stress is expressed by generalized stress intensity factors defined at the corner of fibers. As a 2D model an interaction between rectangular inclusions under longitudinal tension is treated in this paper. The body force method is used to formulate the problem as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknown functions are the densities of body forces distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. In order to analyze the problem accurately, the unknown functions are expressed as piecewize smooth functions using two types of fundamental densities and power series, where the fundamental densities are chosen to represent the symmetric stress singularity of 1/r ^1−λ ₁ and the skew-symmetric stress singularity of 1/r ^1−λ ₂. Then, generalized stress intensity factors at the end of inclusions are systematically calculated for various locations, spacings and elastic modulus of two rectangular inclusions in a plate subjected to longitudinal tension.