Fracture stress obtained from the elastic crack tip enclave model

Abstract

The fracture stress of an elastic-plastic solid is calculated by making an approximate analysis of the crack model in which a small enclave that is surrounded by a plastic region is considered to exist at the crack tip. An attempt is made to improve Thomson's earlier analysis of this crack model by ensuring that displacements as well as traction stresses are continuous across elastic-plastic boundaries and by ensuring that the correct fracture equation is obtained for the limiting case of a perfectly elastic and a perfectly plastic solid. The fracture stress is found to increase if either or both the yield stress of the material is lowered or the rate of plastic work-hardening is reduced. It is found that the fracture stress, in contrast to Thomson's result, it is always proportional to the square root of the true surface energy of the solid.