Parametric study of an ultrasonic non-destructive testing problem based on the reciprocity principle and a hybrid numerical method

Abstract

Numerical simulations are needed for both the design and the improvement of Ultrasound Non-Destructive Testing techniques in industry. One typical configuration is the pulse echo immersion testing of a material with a possible crack. This is a large and multiscale elastodynamic problem, for which the computation may be intensive using standard discrete methods. Different approaches have been proposed to gain efficiency in terms of the computation time, as i) the hybridization of a discrete method with a semi-analytical formulation or ii) using the reciprocity principle to separate the calculation of the field radiated by the crack from the field in the same material. We present a numerical strategy based on those two approaches in order to perform 3D simulations with a possible parametrization of the crack geometry and location. First, the Spatial Impulse Response (SIR) of a focalized transducer in water is computed using a semi-analytical software. Then, we show that the calculation of the SIR can be pursued in the same elastic material using a FDTD method. To take into account the effects of the crack, this SIR is used in conjunction with the time domain reciprocity equation. This process allows performing an efficient computation of the echo signal from the crack. Results and comparisons with experimental measurements will be presented in a 2D case.