Combination of finite element analysis and analytical crack tip solution for mixed mode fracture

Abstract

A finite element program was developed which combines the analytical crack tip solution with a conventional finite element analysis and evaluates various crack tip parameters as part of the solution. This program was used to analyze cracked specimens subjected to mixed mode loading. The importance of retaining the second term of the series expansion for local stress, a contribution which is independent of the distance from the crack tip, was demonstrated. It was first shown analytically that the presence of a load applied parallel to the crack reveals itself only through this constant second term, which vanishes only for specific loading conditions. The results of the numerical analysis demonstrate that the stress intensity factor K I is independent of the load applied parallel to the crack only when this term is included in the analytical crack tip solutions. Failure to include the constant term has the effect that K I varies with the horizontal load. The parameter K 11 is independent of this load in both cases. This indicatesonce again that it is this constant term which accounts solely and entirely for the presence of a load applied parallel to the crack.