MATHEMATICAL-MODELING OF ULTRASONIC WAVE SCATTERING BY SUBSURFACE CRACKS

Scattering of ultrasonic signals by a sub-surface crack in a specimen which is immersed in a water bath has been analyzed on the basis of a mathematical model, which accounts for: (1) signal transmission across the water-solid interface; (2) partial illumination of the crack; (3) the relation between the crack-opening displacement and the received transducer signal; and (4) an accurate mathematical computation of the crack-opening displacement in the frequency domain. The modeling from the specified initial electrical pulse to the measured scattered signal is completed by converting the frequency-domain results to the time domain. Results are presented for both the pulse-echo and the pitch-catch configuration, and for a number of crack orientations and crack depths.