Generalized Stress Intensity Factors of a V-Notched Bar under Bending.

Abstract

In this study, generalized stress intensity factors KI, λ1, KII, λ2, and KIII, λ4 are calculated for a V-shaped notched round bar under bending using the singular integral equation of the body force method. 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 an infinite body. In order to analyze the problem accurately, the unknown functions are expressed as piecewise 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/γ1-λ1 and the skew-symmetric stress singularity of 1/γ1-λ2, and 1/γ1-λ4. Then, generalized stress intensity factors at the notch tip are systematically calculated for various shapes of V-shaped notches. The accuracy of Benthem-Koiter's formula proposed for a circumferential crack is also examined through the comparison with the present analysis.