A theory of caustics for mixed-mode fast running cracks

The method of caustics (shadow spot method) has proven to be a powerful optical method to measure stress intensity factors in static and dynamic fracture mechanics problems. In this paper, a theory of caustics was developed for elastodynamically propagating cracks under inplane mixed-mode conditions. Complex potentials for the general solutions of a near-tip field which have been previously derived by the authors were used in this theoretical development. Completely analytical expressions were derived for the caustic curves as well as for the initial curves for fast running cracks under inplane mixed-mode conditions. The effects of crack velocity and mixed-mode condition on the caustic pattern and the initial curve were investigated. New procedures were also proposed for the evaluation of the dynamic stress intensity factors K_I and K_II using the overall dimensions of the caustic pattern. The method of caustics developed here enables one to study quantitatively various mixed-mode dynamic fracture phenomena such as crack branching, crack curving, and crack kinking.