Dynamic mode-III interface crack in a bi-material strip

An interfacial crack is placed within a two-phase elastic strip subjected to an out-of-plane loading. In the unperturbed state, the crack propagates with a constant speed V along the interface. The Dirichlet boundary conditions are applied to the upper and lower sides of the strip. The exterior boundary is subjected to a regular small perturbation; in addition, it is assumed that the crack speed changes by a small amount epsilon phi'(t), where phi is a smooth function of time t. The asymptotic model presented in this paper delivers an approximation for the stress-intensity factor and an integro-differential equation for the perturbation function phi. A particular feature of the model is in the use of skew-symmetric dynamic weight functions, attributed to the interfacial crack problem in a strip.