Asymptotics of Ultrasonic Sounding Field in Anisotropic Materials

Abstract

To model the wave field of an ultrasonic transducer in materials with strong anisotropy (monocrystalline alloys of turbine blades, composite materials, welded joints, etc.), a physically descriptive asymptotic representation is obtained for quasi-spherical body waves excited by a surface source in an arbitrarily anisotropic elastic half-space. The asymptotics is derived by the stationary phase method from the integral representation of the solution in terms of contour integrals of the inverse Fourier transform. The peculiarities of their derivation and numerical implementation are discussed on the examples of a transversely isotropic composite material and a monocrystalline nickel alloy with cubic anisotropy. The dependence of  the stationary points on the direction is more complicated here than in the isotropic case, up to the appearance of multiple stationary points and folds, giving rise to additional wave fronts and caustics. A comparison is made with the plane waves described by eigensolutions of the classical Christoffel equation. It is shown that, despite the phenomenon of multiple wave fronts, varying the plane-wave orientation allows us to obtain the same group velocity vectors as for any of the waves described by the asymptotics.