Intensity of singular stress at the fiber end in a hexagonal array of fibers

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 field is controlled by generalized stress intensity factor (GSIF) defined at the fiber end. In this study, periodic and zigzag arrays of cylindrical inclusions under longitudinal tension are considered in comparison with the results for a single fiber. The unit cell region is approximated as an axi-symmetric cell; then, the body force method is applied, which requires the stress and displacement fields due to ring forces in infinite bodies having the same elastic constants as those of the matrix and inclusions. The given problem is solved on the superposition of two auxiliary problems under different boundary conditions. To obtain the GSIF accurately, the unknown body force densities are expressed as piecewise smooth functions using fundamental densities and power series. Here, the fundamental densities are chosen to represent the symmetric stress singularity, and the skew-symmetric stress singularity. The GSIFs are systematically calculated with varying the elastic modulus ratio and spacing of fibers. The effects of volume fraction and spacing of fibers are discussed in fiber-reinforced plastics.