Analysis of Intensity of Singular Stress Fields at the End of a Cylindrical Inclusion under Asymmetric Uniaxial Tension.

Abstract

This paper deals with generalized stress intensity factors at the end of an elastic cylindrical inclusion in an infinite body under asymmetric uniaxial tension. These stress intensity factors control singular stress fields at the end of inclusion. The problem is solved on the superposition of two auxiliary loads;(i)biaxial tension and (ii)plane state of pure shear. The problem is formulated as a system of integral equations with Caushy-type or logarithmic-type singularities, where un-knowns are densities of body force distributed in infinite bodies having the same elastic constants as those of the matrix and inclusion. In the numerical analysis, the unknown functions of the body force densities are expressed as fundamental density functions and weight functions. Fundamental density functions are chosen to express the symmetric stress singularity of the from 1/γ1-λ11/γ1-λ3 and the skew-symmetric stress singularity of the form 1/γ1-λ21/γ1-λ4. 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 cylindrical inclusion under longitudinal tension and the ones of a rectangular inclusion under transverse tension.