Calculation of the velocity of creeping waves and their application to non-destructive testing

A method of ultrasonic inspection called ‘time-of-flight’ is intended to provide accurate sizing of crack-like defects in structures such as pressure vessels and piping and the principles can also be applied to the sizing of volumetric defects. Accurate measurement can only be made if the velocity of the ultrasonic wave is known along the entire path. For structures that have curved surfaces (as do pressure vessels and piping) and for the sizing of volumetric defects, this aspect is important for the so-called creeping waves that propagate around the curved surfaces, comparable to the ‘lateral’ or ‘near-surface’ waves on a flat plate. It is shown that the velocity of creeping waves is a sensitive function of the curvature of the surface. The velocity can be predicted accurately from the bulk wave velocity and the radius of curvature of the defect. Detailed calculations are made for steel and are discussed in terms of 4 MHz ultrasonic waves. The results have consequences relating to the accurate sizing by time-of-flight methods of volumetric defects or for accurate depth determination of crack-like defects in pressure vessels and piping.