Brittle Fracture Along Butt-Weld

Abstract

The perturbation analysis is extended from the first order to the second order with respect to the shape of the non-collinear crack path. Approximate descriptions of the stress intensity factors are obtained at the kinked-curved crack tip, where the cracked body is subjected to an arbitrary far field boundary condition. A kind of matched asymptotic expansion method is introduced in order to construct the solution, where the effects of the geometry of the domain are taken into account by alternately matching the far field asymptotic behavior and the near tip field asymptotic behavior in an ascending order of the square root of the crack extension length. The second order perturbation solution so obtained is applied to examine the relation between the energy criterion and the stress criterion for the crack propagation. As far as homogeneous materials are concerned, both criteria designate equivalent crack paths within the second order approximation theory. It should be contrasted for crack paths in materials with inhomogeneous fracture toughness, where the energy criterion predominates over the stress criterion. As a practical application of the method, morphological characteristics of brittle fracture along butt-weld are investigated, and the critical curves for the crack propagation along the degraded zone such as heat-affected zones are obtained under the combined effects of applied stresses, welding residual stresses, localized material deterioration, and defect sizes.