Quasi‐static crack models and the frictional stress threshold criterion for slip arrest

Summary. Two‐dimensional crack problems in elastic homogeneous isotropic media are considered which describe rupture over a fault surface characterized by non‐uniform stress drop. Solutions can be found in which the stress field is finite at the crack tips and the rupture surface is not assigned a priori, but is part of the solution. These crack models are found to be consistent with the frictional stress threshold criterion for slip arrest over pre‐existing fault surfaces. A crack is found to stop when its contribution to the stress field is opposite to the stress drop at the crack tips. The quasi‐static propagation of a crack up to the arrest configuration is studied in terms of the minimum energy principle. The crack spontaneously propagates in such a way as to make the value of the stress intensity factor at one tip equal to the value at the other tip. Furthermore a tip propagating in a region with higher friction is found to move more slowly than the other tip propagating in a region with lower friction. Simple criteria for fracture arrest are derived, in terms of a properly averaged stress drop. Piecewise constant stress drop profiles are explicitly considered yielding a variety of solutions which can be applied to modelling asperities or barriers over a fault plane. The evaluation of the amount of the energy released during the quasi‐static crack propagation shows that stopping phases cannot be efficiently radiated if the crack comes to rest in a low friction region.