A method of caustics for the direct experimental measurement of the [formula omitted] in nonlinear and dynamic fracture mechanics problems

Abstract

This paper presents a methodology for the direct experimental measurement of the T ∗- integral . The method of caustics (the shadow pattern method) has proven to be a powerful optical method with which to measure stress intensity factors in static and dynamic fracture mechanics problems. An attempt has been made to extend the method of caustics to problems in nonlinear and dynamic fracture mechanics. The formation process of the caustic pattern for an elastoplastic crack tip in a compact-tension specimen was simulated by a finite-element analysis. The stimulated and actual caustic patterns agreed with each other very well. The relations between the T ∗- integral and the size of the caustic pattern were obtained for various optical set-ups. The experimental measurement of the caustic pattern in the dynamic tear test specimen of a nuclear pressure vessel steel was also carried out. High-speed photographs of the caustic patterns were taken using a laser caustic method, which can be quickly synchronized to the initiation of impact loading by a hammer that was dropped on the specimen. The time variation of the T ∗- integral during impact loading was evaluated by using the relation between the T ∗- integral and the size of the caustic pattern that was obtained by the numerical simulation. The hybrid numerical-experimental method developed here, in conjunction with laser caustic high-speed photography, has made it possible to measure the T ∗- integral for an elastoplastic material under impact loading conditions.