Approximate description of crack kinking and curving

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 Cotter-ell and Rice.