Continuum model of mode-III crack propagation with surface friction

A two-dimensional model of mode-III crack propagation with a velocity strengthening surface friction is investigated theoretically. Using the Wiener-Hopf technique developed by Langer and Nakanishi [Phys. Rev. E 48, 439 (1993)] with the condition that the stress should not diverge at the crack tip, we determine the crack propagation speed for given external load. It is shown that the maximum crack speed is slower than the sound speed contrary to the case studied by Langer and Nakanishi. It is also demonstrated that the crack speed does not grow quickly as the externally applied stress is increased beyond a threshold stress if the friction stress is comparable with the distortion stress. In the case of no cohesive stress, a divergence around the crack tip exists, but the velocity strengthening friction makes it weaker than the ordinary inverse square root divergence.