Models for the computation of ultrasonic fields and their interaction with defects in realistic NDT configurations

A Hybrid T Matrix/Boundary Element Method for Elastic Wave Scattering from a Defect Near a Non-planar Surface

“…For these computations Auld's reciprocity relation [10] is convenient to use, since it only presupposes knowledge of the action of the probe acting as transmitter. Auld's result relates two elastodynamic states: state (1) with displacement u (1) and corresponding traction t (1) = σ (1) · n obtained when the transmitting probe (T) acts as a transmitter in the presence of the scatterer, and state (2) with displacement u (2) and corresponding traction t (2) = σ (2) · n obtained when the receiving probe (R) acts as a transmitter in the absence of the scatterer. The result is then that the change δΓ in transmission coefficient (or reflection coefficient in the common case of pulseecho testing where the same probe acts as both transmitter and receiver) due to the presence of the scatterer is given by:…”

“…Auld's relation then yields: (4) i (x)σ (2) ij (x)n j (x) ds. (5.11) This signal response is useful for comparisons, as it gives the response of an unflawed medium.…”

“…Most complete models seem to depend on high frequency approximations (ray theory, geometrical theory of diffraction, and Kirchhoff theory), see e.g. Chapman [1], Calmon et al [2] and Rose [3]. Boström and Wirdelius [4] give a model based on the T matrix concept, in principle without any approximations, see e.g.…”

Application of Ultrasonic Beam Modeling to Phased Array Testing of Complex Geometry Components

“…The Champ-Sons model has been developed for several years [6], and validated using comparisons with other models -angular spectrum and finite elements method [7] -, and experiments [8]. This model, based on the Rayleigh integral extended to take account of refraction through a Fluid/Solid interface, gives accurate and quantitative results assuming that both field computation and source points are not close to the interface (about…”

“…The Rayleigh integral extended to take into account the refraction postulates that the elastic field is the sum of contributions of running source points of the transducer (see Calmon et al [6] for a review), which can be expressed as : (1) where u(r, t) is the acoustic quantity considered (e.g. vector displacement, scalar potential), DF(r lr ) is the divergence factor, C:' u (9 f , t) is the transmission coefficient, and v n (r lr , t -t shape (r lr ) -Tpalh (r lr ,r» is the delayed particle velocity of an elementary source point of the radiating surface Tr.…”