A THEORY OF CAUSTICS FOR MIXED-MODE FAST-RUNNING CRACKS (HIGHER-ORDER THEORY)

A higher-order theory of caustics for mixed-mode running cracks is developed by using the general asymptotic solutions for a dynamically propagating crack tip. The analytical expressions are obtained for the Jacobian equation that determines the initial curve, and for the image equations on a screen. With the use of the higher-order coefficients determined by the finite-element simulations of actual dynamic fracture experiments, the effects of the higher-order terms on the caustic curve are investigated on the basis of the present theory. It was found that the r1/2 stress field plays an important role in the formation of caustic patterns. A higher-order theory of caustics for stationary cracks is also derived in this paper.