A model to predict the ultrasonic echo responses of small targets in solids

Abstract

A novel model is developed to predict the echo response of a small target at arbitrary position in the field of a circular transducer directly coupled to a solid. The waves incident on the target are calculated using an earlier model, which describes the field radiated into solids in terms of plane and edge waves and allows for the existence of both compression and shear waves. The new model treats the target as a point-like radiator with motion given by the normal component of the incident particle velocity. An expression for the overall echo impulse response is developed by invoking the principle of reciprocity, assuming a single transducer is used as both emitter and receiver. Simplifications inherent in the model keep computational times very short but allow predictions to be made with an accuracy adequate to show all of the major features of the responses. Comparisons of the predictions of the model with experimental measurements of echo responses from 2-mm-diam round-bottomed holes in steel show good agreement. The complicated multipulse structure of the echo response from even a point-like target is explained in terms of the scattering, mode conversion, and reception of plane and edgewaves. The implications of the results for quantitative nondestructive evaluation using ultrasound are discussed.