###### Abstract  
Ultrasonic Non-Destructive Testing (NDT) methods are broadly used for detection and characterization/imaging of cracks. Simulation is of great interest for designing such NDT methods. To model the ultrasonic 3D response of a crack, ultrasonic high frequency asymptotic (semi-analytical) models (such as the Physical Theory of Diffraction--PTD) are known to provide accurate predictions for most classical NDT configurations, and 3D numerical models have also emerged more recently. The aim of this paper is to carry out for the first time an experimental and theoretical comparison of 3D models for ultrasonic NDT of embedded cracks in 3D configurations. Semi-analytical models and a hybrid 3D FEM strategy--combining high-order spectral Finite Elements Method (FEM) for flaw scattering and an asymptotic ray model for beam propagation--have been compared. Both numerical validations and comparisons between simulation and experiments prove the effectiveness of PTD in numerous configurations but validate and demonstrate the improvement provided by the 3D hybrid code, notably for small flaws compared to the wavelength and for shear waves. Non-Destructive Testing (NDT); ultrasounds; crack; scattering; numerical models comparison; experimental validation +
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diffraction. Recently, an approach based on the Huygens-Fresnel diffraction theory has been proposed [17] to evaluate the signals diffracted by the edges, but it is equivalent [18] to KA and limited to 2D time-of-flight diffraction (TOFD) configurations; it also cannot describe head waves [19; 20]. Uniform corrections of GTD which are able to predict a spatially uniform scattered field has led to recent developments for elastic waves. An elastodynamic version of the Uniform Asymptotic Theory (UAT) [21] was first proposed [4]; however, the UAT requires an artificial extension of the scattering surface and additional costly tracing of fictitious rays reflected on this extended surface. The elastodynamic Uniform Theory of Diffraction (UTD) [22] has also been established for the scattering from a stress-free half-plane and represents a good alternative even if leading to small differences with UAT. Finally, an ultrasonic system model accounting for both reflection and diffraction has been proposed for 3D crack-like flaws in 3D configurations [23]. It is based on the Physical Theory of Diffraction (PTD), initially developed in electromagnetism [24] and extended to elastodynamics [25]. For a half-plane, PTD has been shown to be identical to UAT at the used leading order. Moreover, the region of the model's validity has been extended [26] to cover some transition zones surrounding critical rays, where the shear diffracted waves and head waves interfere. Important efforts have been made to propose an analytical modelling of some head waves contributions, notably lateral waves in the TOFD configuration [27; 28]: for planar surfaces, lateral waves are head waves propagating along such surfaces, and recent advances have been obtained in their modelling [29; 30; 31; 32; 33]; for complex or cylindrical surfaces, lateral waves can include bulk wave contributions [34]. The PTD-based system model [26] can be considered as the most sophisticated and valid semi-analytical approach existing at the present date. Nevertheless, the ultrasonic high frequency asymptotic models, despite providing accurate predictions in a wide range of situations, have a limited domain of validity identified through various experimental validation campaigns [35; 36; 37]: they can fail at predicting responses from defects in some complex configurations when creeping and bulk head waves or caustics occur. In the same way, their precision drops for defects with characteristic dimension of the order of the wavelength. To overcome these limitations, the use of hybrid models such as the 2D CIVA ATHENA model [5] combining numerical and asymptotic methods has been demonstrated as an effective strategy.