Order of the singular stress fields of through-thickness cracks

Abstract

Using the principle of superposition, the singular stress fields of the mode I through-thickness cracks are obtained by combining the following two singular stress solutions. The first singular stress solution is in the form of r ^-1/2 g(θ, z) in cylindrical coordinates system (r, θ, z). It can be evaluated by Hartranft's three-dimensional crack solution. Based on the loading similarity, the second singular stress solution is in the form of R ^-1/2 f (θ, ϑ) in spherical coordinates system (R, θ, ϑ) and ν is the Poisson's ratio. A full three-dimensional finite element analysis without imposing any assumption on the order of singularity is executed to check the assumptions. We show that the solution can not be simply separated either in cylindrical or spherical coordinates, but rather, a combination of them. The variation of stress intensity factors in the vicinity of the free surface perpendicular to the crack plane from free surface state to plane strain state is also discussed.