Solution of three-dimensional crack problems by a finite perturbation method

Abstract

An incremental method is described for calculating stress intensity factors in arbitrarily shaped planar cracks subjected to a uniform remote stress. The method is based on recent work by Rice (J. appl. Mech. 52, 571, 1985; Fracture Mechanics : Perspectives and Directions (20th Symp.), ASTM-STP-1020. to appear. 1987), and gao and rice (Int. J. Fracture 33, 115, 1987a; J. appl. Mech. 54, 627, 1987b). who have developed a procedure for computing the variation in stress intensity factor caused by small changes in crack geometry. To date, this technique has only been used to calculate the effects of first-order perturbations in the shape of a crack. In this paper, the method is extended to arbitrarily large perturbations in geometry. Stress intensity factors are calculated by applying a succession of perturbations to a crack of some convenient initial geometry, such as a circular or a half-plane crack. Since this procedure reduces the analysis to evaluating repeatedly two integral equations defined only on the crack front, it has distinct advantages over other existing techniques. The accuracy of the method is demonstrated by calculating stress intensity factors for two test cases : an elliptical crack and a half-plane crack deforming into a prescribed sinusoidal shape of finite amplitude. As further examples of application of the method, solutions to the following problems are presented : a semi-infinite fatigue crack propagating through a particle; a semi-infinite crack trapped by a periodic array of tough particles ; and the unstable growth of a semiinfinite crack through material of decreasing toughness.

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