Stress and displacement fields due to a penny-shaped shear crack with non-uniform traction

Abstract

Summary The stress field around, and the displacement distribution, on a penny-shaped shear crack with non-uniform stress distribution on it in an infinite solid has been researched. A Hankel transform development of our mixed-boundary value problem yields two simultaneous pairs of dual integral equations. To solve two simultaneous pairs of dual integral equations, we have extended Titchmarsh-Busbridge's techniques (Titchmarsh, Busbridge). The method of solution, proposed here, is also available to solve general simultaneous pairs of dual integral equations. Assuming that the stress distribution on the crack is only the function of its radius, the exact, closed-form solution for this problem has been found. Detailed formulae for the displacements and stresses are given, and the slip on the crack and the stress-intensity factors are determined. The calculations show that the slip on the fault may be very irregular due to heterogeneous stress drop, and the presence of fault heterogeneities may considerably affect the stability of shear faulting. In addition, the asperity model has been discussed. It has been found that, for the fault with an asperity, the local stress drop at the asperity is (S/Sa)1/2 times the stress drop inferred from Keilis-Borok's formula (Keilis-Borok) on the basis of the observed moment and the observed or estimated fault area, where 5 is the fault area and Sa is the asperity area.