Generic Gtd-kirchhoff Scattering Model for the Ultrasonic Response of Planar Defects

Simulation is helpful for evaluating the performances of inspection techniques and requires the modeling of waves scattering from defects. Two classical flaw scattering models have been previously evaluated and implemented in the CIVA platform developed by CEA/LIST to deal with planar defects: the geometrical theory of diffraction (GTD) and the Kirchhoff approximation (KA). These two approaches appear to be complementary. Combining them so as to retain only their advantages, we have developed a combined model (the so-called Kirchhoff & GTD) using a procedure similar to the physical theory of diffraction (PTD). Both theoretical and experimental validations of the Kirchhoff & GTD model have been carried out in various practical NDE (pulse echo and TOFD) configurations studying both direct and corner echo modes. Theoretical validations have consisted in comparisons between this new model and other scattering models (GTD, KA and a finite-element method). Whereas the previously existing models were notably useful to respectively simulate specular reflection echoes for Kirchhoff and edges diffractions for GTD, the performed validations have shown that the Kirchhoff & GTD model provides a generic modeling of both the two main scattering phenomena arising from a planar flaw: specular reflection and edges diffraction. INTRODUCTION: AVAILABLE SCATTERING MODELS IN CIVA The CIVA software platform is developed at CEA-LIST and partners in the aim of simulating non-destructive evaluation [1]. Most of the developed models are based on semi-analytical methods. The ultrasonic simulation tools in CIVA allow one to fully predict the results of an ultrasonic inspection in a range of applications which requires the computation of the beam propagated, as well as its interaction with flaws [2]. The transducer field is calculated using a pencil method derived from the Rayleigh integral for acoustic radiation [3]. Indeed, inside the coupling material, the Rayleigh integral is computed directly by summing the contributions to the field of each source point of the discretized transducer surface [2]. In the specimen the pencil method which is an extension of ray theory [4] is applied. The beam to flaw interaction is dealt with different modelling approaches depending on the defect and the inspection characteristics. Three kinds of models for the scattering of ultrasound by flaws have been integrated: approximate analytical solutions, exact analytical solutions and numerical modelling methods. In the last release CIVA 11, numerous improvements of these methods have been added as described hereafter. The developed approximate analytical solutions are respectively: the Kirchhoff approximation [5] to deal with specular reflections from volumetric voids (spherical or hemispherical holes, SDHs) and cracks (rectangular, CAD or elliptical planar, FBHs, multifaceted, branched). This approximation is mostly valid if the observation direction is close to reflection and is particularly suitable to simulate specular reflection, corner effects, etc. The corresponding integrated model requires the meshing of the defect surface. The Kirchhoff model has been extended in Civa11 to deal with anisotropy and impedant (non-rigid) interfaces [6]. 675 M or e In fo a t O pe n A cc es s D at ab as e w w w .n dt .n et /? id = 18 54 4 the geometrical theory of diffraction (GTD) to treat scattering from crack edges [7,8]. This approximation is valid away from specular angles and forward paths. The corresponding integrated model requires the meshing of the flaw contour. In Civa 11, the GTD model has been extended to deal with indirect echoes (diffraction echoes after reflection on the specimen surfaces) and has become a 3D GTD model which uses 3D GTD diffractions coefficients. the modified Born approximation to deal with solid inclusions. It provides an analytical solution for some flaw geometries (spherical, cylindrical and ellipsoidal) without any meshing of the flaw [9]. The modified Born model has been extended in Civa11 to deal with any incidence on inclusions. An exact analytical solution for the scattering from a cylindrical cavity, based on the Separation Of Variables (SOV) method, has been used since Civa 10 to simulate the response of a side drilled hole [5]. This model is in addition available in CIVA 11 for solid spherical inclusions. The main general assumptions applied to deal with the application of the semi-analytical models are described in [2,5]. These previous methods have been experimentally validated in the most commonly used configurations [10]. Since CIVA10.1 release, it is also possible to use a 2D numerical method to model the beam/flaw interaction especially in some complex configurations. Indeed, the hybrid model CIVA/ATHENA [11] is available for simulating the 2D response of SDHs and cracks (rectangular, CAD, multifaceted, branched) and uses the following principle. The pencil method used for CIVA beam calculations is applied to deal with most of the propagation, while intricate interaction phenomena located in a small region surrounding the defects are computed numerically by the finite elements (FEM) code ATHENA developed by EDF. In Civa 11, another approximate analytical solution has led to the development of a new model called Kirchhoff & GTD (as shown in Figure 1) which is the subject of this paper. Figure 1: choice of the Kirchhoff & GTD in CIVA 11. PRINCIPLE OF THE KIRCHHOFF & GTD MODEL The Kirchhoff & GTD model [12] is devoted to the simulation of both reflection and diffraction echoes from crack-like flaws. The two previous approaches (Kirchhoff and GTD) appear to be complementary. Combining them so as to retain only their advantages, we have developed a hybrid model (the so-called Kirchhoff & GTD) using a procedure [12] similar to the physical theory of diffraction (PTD)[13]. Indeed, the Kirchhoff model is useful for the modelling of echoes due to specular reflections but is less accurate for observation directions far from the specular one since it doesn’t model correctly and quantitatively edges diffraction. On the other hand, contrary to Kirchhoff, the GTD model is not valid for specular observation direction since the GTD coefficient diverges but GTD is very effective to predict edge diffractions echoes in most configurations.