Intensity of Singular Stress Fields at the End of a Cylindrical Inclusion

In short fiber reinforced composite it is known that the singular stress at the end of fibers causes crack initiation, propagation, and final failure. The singular stress field is controlled by the generalized stress intensity factors defined at the end of the inclusion. In this study the stress intensity factors are discussed for an elastic cylindrical inclusion in an infinite body under (A) asymmetric uniaxial tension in the x direction, and (B) symmetric uniaxial tension in the z direction. These problems are formulated as a system of integral equations with Cauchy-type or logarithmic-type singularities, where densities of body force distributed in infinite bodies having the same elastic constants as those of the matrix and inclusion are unknown. In the numerical analysis, the unknown body force densities are expressed as fundamental density functions and weight functions. Here, fundamental density functions are chosen to express the symmetric and skew-symmetric stress singularities. Then, the singular stress fields at the end of a cylindrical inclusion are discussed with varying the fiber length and elastic ratio. The results are compared with the ones of a rectangular inclusion under longitudinal and transverse tension.