A finite difference method for elastic wave scattering by a planar crack with contacting faces

This paper presents a finite difference time-domain technique for 2D problems of elastic wave scattering by cracks with interacting faces. The proposed technique introduces cracks into the finite difference model using a set of split computational nodes. The split-node pair is bound together when the crack is closed while the nodes move freely when open, thereby a unilateral contact condition is considered. The development of the open/close status is determined by solving the equation of motion so as to yield a non-negative crack opening displacement. To check validity of the proposed scheme, 1D and 2D scattering problems for which exact solutions are known are solved numerically. The 1D problem demonstrates accuracy and stability of the scheme in the presence of the crack-face interaction. The 2D problem, in which the crack-face interaction is not considered, shows that the proposed scheme can properly reproduce the stress singularity at the tip of the crack. Finally, scattered fields from cracks with interacting faces are investigated assuming a stick and a frictionless contact conditions. In particular, the directivity and higher-harmonics are investigated in conjunction with the pre-stress since those are the basic information required for a successful ultrasonic testing of closed cracks.