Distributed Point Source Method for Modeling Scattered Ultrasonic Fields in the Presence of an Elliptical Cavity

Abstract

Scattering of ultrasonic waves by an elliptical cavity is modeled. The ratio of the semimajor to semiminor axes is varied from 1 to model a cylindrical cavity with a circular cross section to a large value to approximately model a Griffith crack. The distributed point source method (DPSM), which is a Green’s function-based semi-analytical technique, is adapted in the present modeling. DPSM generated results for slit opening and elliptical cavity are compared. In the elliptical cavity model, the entire cavity surface is considered traction free, whereas in the slit model, two parallel crack surfaces are assumed traction free and no special consideration is given to the crack tips. Because a Griffith crack under tensile loads opens like an ellipse, the elliptical cavity with a large semimajor to semiminor axes ratio can be considered as an open Griffith crack. Elliptical cavity model clearly shows large stress values near the crack tips. Earlier DPSM models did not consider these high stress concentrations. The assumption was that it would have negligible effect on the scattering pattern at the far field. The numerical results are presented for a cavity of length 4 mm when bounded ultrasonic beams of 1 and 2.25 MHz frequency strike the solid half-space.