Approximate Description of Crack Kinking and Curving

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Abstract
An approximate description is given of the slightly out-of-plane growth of a straight crack under mixed-mode loading and in the presence of an in-plane stress. By using a perturbation technique, conditions are derived for the deviation of the crack from straightness. The allowance for the possible curvature of the quasi-statically growing crack, and the effect of the finite length of the main crack are included in the analysis, which retains second-order terms. In particular, it is shown that the curvature of the crack path depends on the in-plane stress and the derivatives of the stress-intensity factors with respect to the length of the main crack. The influence of the in-plane stress on the stability of the crack growth is also studied and the conclusions are the same as those reported by Cotterell and Rice.

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