ULTRASONIC PROBE MODELING AND NONDESTRUCTIVE CRACK DETECTION

The mathematical modeling of a typical situation in ultrasonic nondestructive testing for defects is considered. The first objective is the modeling of a reasonably general type of ultrasonic probe. This is performed by prescribing the traction vector on the surface of an elastic half-space. The effective probe area may be rectangular or elliptic and the traction may or may not include the tangential part (glued or fluid-coupled probe, respectively). The probe can be of P, SV, or SH type and of any angle. The traction is either constant across the probe (piston-type source) or it may taper off toward the edges. Numerical results for some representative cases are given showing snapshots of the field beneath the probe. The second objective of the paper is to include the presented probe model into a complete model of the ultrasonic testing situation. To this end the probe field is, via a series of transformations, expressed in spherical vector waves centered at the defect. The influence of the defect is given by its transition matrix. To model the electric signal obtained from the receiving probe, a reciprocity argument is used, giving this signal essentially as a product of the spherical expansion coefficients of the transmitting probe, the transition matrix of the defect, and the spherical expansion coefficients of the receiving probe. For a defect that is a penny-shaped crack or a spherical cavity some numerical examples are given showing the received signal as a function of position on the scanning surface. © 1995, Acoustical Society of America. All rights reserved.