Strain Energy Density Failure Criterion: Mixed-Mode Crack Growth

So far, we have studied growth of a crack only for the case when the load is applied normal to the crack and such that the crack propagates in a self-similar manner. However, often the loads are not aligned to the orientation of the crack. In such cases, the crack-tip stress field is no longer governed by a single opening-mode stress intensity factor K_I but by a combination of the three stress intensity factors K_I, K_II, and K_III. Moreover, the direction of crack initiation is not known a priori but depends on a failure criterion involving some combination of K_I, K_II, and K_III. As a rule the crack follows a curved path.