Crack transient torsional wave interaction in an elastic bi-material

An infinitely long cylindrical elastic solid of finite radius (fibre or inner medium) is imbedded in another infinite elastic cylindrical solid (matrix or outer medium) to form an elastic bi-material composite perfectly bonded at their bi-material interface. The early-time response of the composite to a sudden twist applied axisymmetrically over a stationary penny-shaped crack which appears over a cross-section of the fibre and terminates orthogonally at the bi-material interface, is investigated. The magnitude of the applied twist is assumed to be less than that for which debonding or crack propagation can take place. For a bi-material composite the square of whose matrix shear-wave speed is less than twice the square of whose fibre shear-wave speed, uniform asymptotic analytic results, whose accuracy can be improved by taking higher order terms in the solution, are obtained for the time-dependent surface displacement gradient normal to the plane of the crack and outside the crack region, the dynamic stress intensity factor, and also the stress singularity strength eigenvalue-all as functions of the fibre-matrix material disparities.