Spontaneous growth of an in-plane shear crack

Abstract

We consider the nonsteady growth of a two-dimensional in-plane shear crack under the influence of a critical stress intensity factor criterion at the crack tips and dynamical frictional stresses on the fracture surface. For a spontaneous rupture initiating at a point and extending bilaterally, the dynamic stress distribution must be known in advance to determine the stress intensities at the crack tips. When these stresses are scaled with respect to the singular stresses at the respective crack tips, an approximation that was found to be suitable for problems of the growth of anti-plane shear cracks that tear with high velocities, is also found to be suitable in the present case. The region of validity of this approximation is tested for the in-plane mode of crack growth by comparison with cases of crack histories that are solvable exactly. For the latter purpose, we use the exact solution to the self-similar problem of uniform bilateral growth of in-plane cracks, which is found by functionally invariant methods. For low rupture speeds, iterative methods based on this approximation can be developed to improve the solution. For the self-similar cases, rupture velocities cannot be greater than the Rayleigh wave velocity in the medium; we have only considered those cases of non-uniform crack propagation for which this limit also applies.