Effect of t-stresses on the path of a three-dimensional crack propagating quasistatically under type I loading

We consider a three-dimensional semi-infinite almost planar crack, propagating quasistatically under type 1 singular loading. Treating the distortion from planar geometry as a perturbation we evaluate the type II stress intensity factor arising from this distortion including the effect of non-singular T-stresses. Using these results we perform a linear stability analysis by assuming that the crack propagates locally in the direction of pure type I. We obtain a stability diagram as function of Tx and Tz reflecting the interaction between the effects due to the T-stresses and the stabilizing effect which arises from the perturbed geometry of the crack. From this we infer four types of stability of the crack : monotonous stability, oscillatory stability, monotonous instability and oscillatory instability. Additionally we find that for certain values of the ratio Tz/T~ a small interval of wavelengths of the perturbation will be selected as the crack propagates, so that the components corresponding to these wave lengths will grow expontially while all other components are suppressed. Copyright © 1996 Elsevier Science Ltd.