Numerical Computation of Complex Stress Intensity Factors of Interface Cracks in Bi-Materials Based on Photoelastic Theory

Abstract

This paper presents a new numerical method for obtaining the complex stress intensity factor with an interface crack in bi-materials using photoelastic isochromatic fringe numbers N. The theoretical solution of stress field at the crack tip was deduced from Muskhelishvilis stress function and an undetermined term σ0 which is a function of material properties was added to this theoretical solution. A partial differential iterative equation with fast convergence was formed by applying the photoelastic theory. The complex stress intensity factor K=K1+iK2 and σ0 were obtained by Newton-Raphson iteration method and K domain was discussed. The simulant photoelastic isochromatic fringe pattern could be generated through image processing and numerical calculation according to K and σ0. The simulant isochromatic fringe pattern accords with experimental photoelastic isochromatic fringe pattern, so it is practicable for this numerical method of obtaining the complex stress intensity factor.