Generalized Stress Intensity Factors at the Fiber End in a Hexagonal Array of Fibers

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. To obtained the magnitude of the singular stress, in this paper, an interaction among a hexagonal array of cylindrical inclusions under longitudinal tension is considered. The body force method is applied to a unit cell region; then, the problem is formulated as a system of singular integral equations, where unknowns are densities of body forces distributed in infinite bodies having the same elastic constants as those of the matrix and inclusions. The unknown functions are expressed as piecewise smooth functions using fundamental densities and power series. Here, the fundamental densities are chosen to represent the symmetric strees singularity, and the skew-symmetric stress singularity. Then, generalized stress intensity factors at the fiber end are systematically calculated with varying the elastic ratio, length, and spacing of fibers. The region when the interaction effect is less than 1% is shown in a figure as a function of fiber length.