The constant stress term

Abstract

The importance of retaining the second, constant stress term of the series expansion for local stress is demonstrated both analytically and numerically. It is shown how the standard singular expressions for the stress and displacement field in the vicinity of the crack tip need to be corrected. A load applied parallel to the crack shows up solely and entirely in this constant term. Omitting this term not only denies the physical presence of such a load and hence violates the principle of the uniqueness of the solution of boundary value problems of linear elasticity, but also misleads one into thinking that load biaxiality does not influence fracture behavior. It is shown analytically and numerically that the standard expressions are correct only for equal tension-tension loading. The numerical results show that K I is independent of a horizontal load only when the constant stress term is included.