On the nature of the so-called subsurface longitudinal wave and/or the surface longitudinal “creeping” wave

Abstract

The elastic wave field of certain angle beam probes used for nondestructive testing of solid materials, like steel, has been shown to exhibit a so-called subsurface longitudinal wave, i.e., a wavefront traveling with the pressure wave speed having a beam angle of approximate 74° in steel. In addition, this wavefront is supposed to be connected to the stress-free surface via a headwave, which radiates a nearly plane wave with shear velocity into the bulk material under an angle of 33°, approximately, and giving rise to a strongly attenuated longitudinal “creeping” wave on the surface. In the present paper we utilize a new numerical scheme for the computation of elastodynamic wave fields in nearly arbitrary environments, called elastodynamic finite integration technique (EFIT), to predict the above-mentioned wave features quantitatively. Furthermore, we employ several analytical and analytical-numerical integration procedures to evaluate the angle beam probe plane wave spectrum in terms of an inverse spatial Fourier transform. This gives rise to a theoretical interpretation of the physical origin of the numerically computed EFIT wavefronts. Essential results are as follows: the particular wavefronts of angle beam probes, as referred to in this paper, are exclusively associated with afinite aperture radiating into an elastic half-space; they cannot be explained in terms ofsingle homogeneous and inhomogeneousplane waves. The subsurface longitudinal wave emerges from the superposition of the edge pressure waves of the transducer, resulting in a propagation with pressure wave speed, but, in the near-field, where it is often employed, it is not longitudinally polarized. On the surface, and very close to it, the superposition of the subsurface longitudinal wave and the head waves associated with the probe edges gives rise to a strongly attenuated wavefront exhibiting longitudinal as well as transverse particle displacement components, but neither a surface wave nor a creeping wave is really involved. The bulk shear wavefront is not an appendix of the head wave but the “geometric optical” shear wave radiation pattern of the finite probe.