Cohesive force across the tip of a longitudinal-shear crack and Griffith's specific surface energy

TLDR

The cohesive force across the fault plane is examined to understand rupture mechanics at the tip of a longitudinal‑shear crack, a more physically meaningful assumption than earlier models by Barenblatt. The study aims to elucidate the physical mechanism of rupture at the crack tip by analyzing the cohesive force across the fault plane. The authors derive the elastic field and rupture‑growth condition from a displacement‑discontinuity‑dependent cohesive force model. They find the tip stress field is nonsingular for various cohesive‑force models, and the rupture‑growth condition aligns with Griffith and Kostrov criteria while providing a clearer definition of specific surface energy.

Abstract

The cohesive force across the fault plane is considered in order to understand the physical mechanism of rupture at the tip of a longitudinal-shear crack. The elastic field around the tip of a crack and the condition of rupture growth are systematically derived from the assumption that the cohesive force is given as a function of the displacement discontinuity. This assumption is more physically meaningful than those originally used by G. I. Barenblatt in 1959 and 1962. The stress field around the tip is calculated for several models of cohesive force, and is shown to be nonsingular even at the tip. The condition of rupture growth that is used to determine the rupture velocity turns out to be equivalent to the Griffith criterion and the relation employed by B. V. Kostrov in 1966, but the specific surface energy is defined more clearly in this paper.