The Paraxial Approximation for Radiation of a Planar Ultrasonic Transducer at Oblique Incidence Through an Interface

Refining Automated Ultrasonic Inspections with Simulation Models

“…The on-axis valley was surprising because the transducer was planar and the water path was chosen to place the last "normal" on-axis valley just above the interface. A comparison with the "Edge Element" method of Lerch and Schmerr [5] showed the same result. …”

Modeling the Ultrasonic Radiation of Shear Wave Angle Beam Transducers

“…From this integral and through the use of the angular spectrum of plane waves [5] and the method of stationary phase for double integrals [6], the displacement field for S-waves transmitted into the second medium can be found to be [7] : (2) where PI' P2 are the densities of media 1 and 2, respectively, c lp is the compressional wave speed in medium 1, c 2s is the shear wave speed in medium 2, r;;'P is the fluid (pwave )/solid (s-wave) transmission coefficient (based on a stress/pressure ratio), 8 1 1" 8 2s are the incident and refracted angles, respectively, d is a polarization unit vector, and DIp' D 2s are the direct ray distances in the first and second media (see Figure la). To use this fluid-solid model for an angle beam probe inspection problem, we need only to replace r;;'P by the corresponding transmission coefficient for a smooth solid-solid interface, as mentioned previously.…”

“…As mentioned in [2], the configuration can be broken down into two sub-problems: the calculation of the incident wave field in the wedge, and the propagation of this incident wave field through the solid/solid interface into the second medium (which would be the medium containing the weld). Previous work of Schmerr and Sedov [3] indicates that as one moves sufficiently deep into the wedge, the incident P-waves in this material become identical to those of an equivalent fluid medium, and the incident S-waves in the wedge are negligible.…”

“…To date, three different beam models have been derived and studied. They are the Surface Integral model [2], the Boundary Diffraction Wave (BDW) Paraxial model [2], and the Edge Element model. Each has certain advantages and disadvantages associated with it, as will be seen in later sections of this paper.…”

The Wavefield of an Ultrasonic Angle Beam Shear Wave Transducer: An Elastodynamic Approach

“…Over the past few years, we have turned our attention specifically to the incident wavefields produced by these transducers and investigated a number of beam models that can be applied to these types of inspection problems. Comparisons of models based on Gauss-Hermite expansions, boundary diffraction waves, paraxial and non paraxial approxirnations have been made [2,3] for unfocused transducers residing in a fluid and oriented obliquely incident to planar fluidsolid interfaces (see Figure 1a). In these models, the firstmedium was taken tobe a fluid, while in reality, angle beam transducers actually employ a contact compressional wave transducer acting on the surface of an elastic solid wedge.…”