E. Yogeswaren
John G. Harris
Theor. Appl. Mech. UIUC, 216 Talbot Lab., 104 S. Wright St., Urbana, IL 61801
A mathematical model describing how a confocal arrangement of two focused ultrasonic transducers is used to interrogate a complex interface between two materials by scanning the focal point across the interface is outlined. A complex interface is one that has roughness and partial contact at several length scales, many of which are equal to or smaller than the wavelength in the material. When the focused ultrasound strikes such an interface, though the focal region be small, multiple scattering takes place among the scatterers within and adjacent to the focal region, making it unclear how the interface is being sampled. To clarify this issue a specific interface model, consisting of a planar array of multiple small cracks having arbitrary lengths and spacings, is used. This interface is interrogated by a focused, antiplane shear wave. The model shows that what is measured are the multiply scattered signals averaged over the aperture of the transducer, and that the dominant contribution comes from the scattered signals that phase match to the interrogating signal. Expressions relating the modeled reflected and transmitted signals to the convolution of the incident wave field with the crack-opening displacements at the focal region are given. Numerical examples are worked out for similar and contrasting materials on each side of the interface. [Work supported by the NSF.]