Effect of surface elasticity on transient elastic field around a mode-III crack-tip under impact loads

Abstract We analyze the transient response of a linearly elastic solid weakened by a nanoscale crack (nanocrack) when the solid is subjected to anti-plane impact loading. We account for the nanoscale by incorporating surface elasticity into the model of deformation. The problem is formulated as a nonclassical mixed initial–boundary value problem. Most significant is the fact that both surface stress and surface mass inertia are included in the boundary condition on the crack surface. By applying Laplace and Fourier transform methods, we reduce the associated boundary value problem in the Laplace transform domain to a singular integro-differential equation. The latter is solved numerically leading to the determination of the corresponding stress intensity factors in the (Laplace) transformed domain. The Gaver-Stehfest algorithm is then applied to perform a numerical inversion of the Laplace transform from which we obtain dynamic stress intensity factors in the time domain. Numerical results characterizing the transient response of the crack-tip field are presented with particular emphasis on the influence of surface elasticity on the dynamic fracture parameters.