Exact solutions of stress intensity factor histories for a half plane crack in a transversely isotropic solid under transient point shear loading on the crack faces (Q1434741)

The author performs a three-dimensional analysis for a transversely isotropic solid containing a half plane crack, with the crack faces subjected to point shear forces varying with time as a heaviside function at a finite distance \(\ell\) from the crack edge. Note that, in contrast to the static case, which was studied before by many authors (using potential theory), when dynamic loading is present, the governing equations become hyperbolic ones, and the potential theory no longer applies. To this end, a vector Wiener-Hopf problem, generated from the coupling of modes II and III due to the action of shear loading is considered. The solution is treated as the superposition of two subproblems. Exact expressions for the modes II and III, as well as some features of the solutions through numerical results are discussed.