Transient diffraction of an elastic wave by an extending crack is considered, with the distinction that the crack may propagate under an arbitrary angle with its own plane. The incident wave is a plane horizontally-polarized wave. It is assumed that crack propagation at a constant velocity is generated at the instant that the tip of a semi-infinite crack is struck. An expression is derived for the stress intensity factor in terms of the speed of crack propagation and the angle of crack propagation. For a step-stress incident wave a solution for the particle velocity is sought which shows dynamic similarity inside the circular region of the diffracted wave. A crucial step in the analysis is the use of Chaplygin's transformation, which reduces the problem to the solution of Laplace's equation in a semi-infinite strip containing a slit.
ASJC Scopus subject areas
- Applied Mathematics