Transient analysis of multiple parallel cracks under anti-plane dynamic loading

• The problem of multiple parallel cracks under anti-plane dynamic loading is studied using dislocation method.
• A fundamental solution for a screw dislocation that suddenly appear has been derived.
• The fundamental solution consists of a term associated with the plane wave emitted from the slip plane and another term with the bulk wave radiated from the dislocation core. The solution given previously by Ayatollahi and Monfared (2102) contains only the bulk wave term.
• A space–time integral equation relating tractions on the crack planes and the dislocation densities is derived.
• The numerical examples show that higher dynamic overshoots than that for a single crack might be induced and that it takes longer time to approach to the steady state if multiple reflections between the cracks occur.

The problem of a homogeneous linear elastic body containing multiple non-collinear cracks under anti-plane dynamic loading is considered in this work. The cracks are simulated by distributions of dislocations and an integral equation relating tractions on the crack planes and the dislocation densities is derived. The integral equation in the Laplace transform domain is solved by the Gaussian–Chebyshev integration quadrature. The dynamic stress intensity factor associated with each crack tip is calculated by a numerical inverse Laplace scheme. Numerical results are given for one crack and two or three parallel cracks under normal incidence of a plane horizontally shear stress wave.