THE DIPPING ANTIPLANE CRACK

We derive the elastostatic field arising from the introduction of a 2-D dipping antiplane crack at the surface of an elastic half-space having a pre-existing uniform field. The problem is equivalent to that of two identical, joined, antiplane cracks in an infinite, uniformly strained medium; each crack is inclined by the same amount from the axis of symmetry, giving rise to a bent crack. For cracks with the same depth of crack tip beneath the surface, the amount of elastic energy released increased with the angle from the vertical. However, the rate of energy release with increasing angle is less than the rate of increase of surface energy. Plane, vertical cracks are favoured energetically in infinite, homogeneous media, while bent cracks are favoured in heterogeneous media where a crack must deviate from straight line growth in order to bypass a high-strength barrier. We compare the trade-offs in total energy of bent cracks with barrier energies.