Stress intensity factors for a crack in planar disking

Abstract

Disking is a relatively new manufacturing process for cutting/slicing brittle plates and rods. In the planar disking configuration, a pre-cracked plate is placed against an elastic plate and the two are squeezed together by fluid pressure. At a critical pressure the crack runs across the thickness of the brittle plate producing a clean cut. In this paper a fracture criterion is developed for the process using linear elastic fracture mechanics. The geometry of the process is modeled here as two perfectly bonded, infinite elastic layers with a crack perpendicular to the interface. The problem is formulated in terms of a singular integral equation with the derivative of the crack surface displacement (dislocation density) as the unknown function. Numerical quadrature is used to determine the stress intensity factors as a function of the parameters of the problem.