Appraising Kirchhoff approximation theory for the scattering of elastic shear waves by randomly rough defects

Elastic shear wave scattering by randomly rough surfaces

“…There is an important difference between the incident shear and incident longitudinal cases for the modeconverted waves [16]. In the former case, the reflected angle α sp , becomes complex once a critical angle is passed:…”

“…Certain inspection configurations achieve better sensitivity for smaller cracks with shear waves rather than with longitudinal waves [14,15]. As explained by [16], KA theory has a smaller range of validity for shear wave incidence. Two of the key factors are multiple scattering and surface wave mode conversion, which are exacerbated by reduction in correlation length.…”

“…The extension of the same statistical approach [8] to shear wave incidence is far from straightforward, but critical for practical NDE applications [14,15]. Firstly, the range of validity of KA is much smaller for shear, rather than longitudinal, wave incidence as explained by [16]. KA validity breaks down at half the roughness (in terms of units of incident wavelength) due to multiple scattering and surface wave mode conversions that do not arise for analogous longitudinal cases.…”

“…This result is similar to the longitudinal result derived in [4] but for shear incidence, there are differences related to the critical angle and a reduced range of validity. The reason is that KA theory breaks down for shear incidence for short correlation lengths [16]. For finite crack dimensions of practical interest, i.e.…”

“…For finite crack dimensions of practical interest, i.e. L ≤ 8mm [15,16], the relatively larger correlation lengths required for KA validity invalidate the important assumption L λ 0 used in the derivation above to obtain the analytical formulae for total and diffuse intensities. In the next section, we explain how a correction to the formulae enables the stationary phase approach to also be used for cases of long correlation length.…”