Refinement for stress intensity factor solution for a parabolic-shaped crack from the perturbation method

Abstract

This paper introduces an approximate stress intensity factor (SIF) solution for a parabolic-shaped crack from the perturbation method. It is found that the perturbation method can only provide accurate results for a small value of the involved parameter. The small value is defined such that: (1) the height of the curved configuration is much smaller than the crack length, (2) the derivative of the curved configuration function is much less than unity. A sufficient accurate numerical procedure for the curved crack is suggested. From the numerical solution and the closed form solution in the perturbation method for the stress intensity factor (SIF), a modified equation for SIFs is suggested. The undetermined coefficients in the equation is evaluated by using the least square procedure. Finally, for the parabolic-shaped crack, this paper provides numerical modification of SIF solution from the perturbation method.