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Simulation of ultrasonic Non Destructive Testing (NDT) is helpful for evaluating performances of inspection techniques and requires the modelling of waves scattered by defects. Two classical flaw scattering models have been previously usually employed and evaluated to deal with inspection of planar defects, the Kirchhoff approximation (KA) for simulating reflection and the Geometrical Theory of Diffraction (GTD) for simulating diffraction. Combining them so as to retain advantages of both, the Physical Theory of Diffraction (PTD) initially developed in electromagnetism has been recently extended to elastodynamics. In this paper a PTD-based system model is proposed for simulating the ultrasonic response of crack-like defects. It is also extended to provide good description of regions surrounding critical rays where the shear diffracted waves and head waves interfere. Both numerical and experimental validation of the PTD model is carried out in various practical NDT configurations, such as pulse echo and Time of Flight Diffraction (TOFD), involving both crack tip and corner echoes. Numerical validation involves comparison of this model with KA and GTD as well as the Finite-Element Method (FEM).

This paper aims at describing the theoretical fundamentals of a reciprocity-based ultrasonic measurement model. This complete inspection simulation can be decomposed in two modeling steps, one dedicated to transducer radiation and one to flaw scattering and echo synthesis. The physical meaning of the input/output signals used in these two modeling tools is defined and the theoretical principles of both field calculation and echo computation models are then detailed. The influence on the modeling results of some changes in the simulated configuration (as the incident angle) or some input signal parameters (like the frequency) are studied: it is thus theoretically established that the simulated results can be compared between each other in terms of amplitude for numerous applications when changing some inspection parameters in the simulation but that a calibration for echo calculation is generally required.

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