The Theory of Critical Distances: A link to micromechanisms

The Theory of Critical Distances (TCD) is a methodology for prediction of the effect of stress concentration features on material failure, especially cracking-related mechanisms such as fatigue and brittle fracture. It has a long history but has become much more relevant to industrial problems in recent years thanks to the widespread availability of finite element analysis and other numerical simulation tools. An ongoing fundamental challenge is to understand the physical significance of the TCD parameters, in particular the value of the critical length L, in relation to the underlying micromechanisms of crack extension and toughening. A novel approach is presented here, in which the TCD is used to make predictions of the notch fracture behaviour of three different model materials having different crack extension mechanisms. Three different notch types (circular holes, long slots and short cracks) were investigated. In all cases the value of L was shown to be simply related to a microstructural length parameter but this relationship depended on the mechanism involved. These results provide some insights into the distinctive behaviour of different materials, especially polymers such as PMMA which display crazing behaviour, and fibre composites such as carbon/epoxy laminates.