The theory of critical distances

This paper summarises the keynote talk opening the session on ‘Critical Distance Theories of Fracture’; my aim is to describe the methodology used, to demonstrate its applicability in predicting experimental data on fracture and fatigue, to discuss the fundamental basis of the theory and, to suggest areas for future work in this field. The Theory of Critical Distances (TCD) is the name which I have given to a group of theories used for predicting the effects of notches and other stress-concentration features. These theories have a long history, but currently they are being investigated by only a small number of researchers worldwide. This is a pity, because the TCD is capable of accurate predictions in a wide variety of situations. The essential elements are an elastic stress analysis and a material-dependent critical distance, a parameter which we call L. The value of L can be written in terms of other material parameters as: $$ L = \frac{1} {\pi }\left( {\frac{{K_c }} {{\sigma _o }}} \right)^2 $$ (1)