Modélisation des effets de diffraction pour le calcul des échos de géométrie pour le calcul des échos de géométrie en CND par ultrasons

This thesis is part of the development of models integrated in the Non-Destructive Testing (NDT) software platform CIVA. So far, the specimen echoes (entry or backwall surfaces, …) or echoes produced by specimen interfaces have been modeled in CIVA using a “ray” model. This model, called “specular model”, is based on geometrical elastodynamics and therefore is mainly concerned with specular reflections on scatterers. The aim of this thesis is to extend this ray model to account for specimen wedges diffraction. The Geometrical Theory of Diffraction (GTD), a diffraction ray model, was a starting point to do such an extension. However, GTD diverges at observation directions close to incident and reflected shadow boundaries.In this thesis, we then formulate a GTD uniform theory within the context of elastodynamics, the Uniform Theory of Diffraction (UTD), which leads to a uniform total field (geometrical + diffracted fields) and is amenable to simple implementation. First, UTD was developed for a simple canonical geometry, a half-plane, to show its feasibility and then for a complex canonical geometry, a wedge whose faces are stress-free. The developed UTD solutions were validated numerically and UTD for a wedge was implemented in CIVA in a 2D configuration (incidence and observation directions are in the plane perpendicular to the wedge edge). The mixed model “specular model + UTD” was compared to other CIVA models for specimen echoes simulation and a good agreement was obtained between these models, then allowing us to validate our approach. In addition to its non-uniformity, another drawback of the GTD methodology is its restricted application to canonical geometries (half-plane, wedge, …) , as it mainly allows for the treatment of infinite edge diffraction. To overcome this limitation, two incremental methods involving a sum of spherical waves emitted by discretization points on the diffracting edge have been developed. The first model, called the Incremental Theory of Diffraction (ITD), is extended from electromagnetism, and the second, called “Huygens model”, is based on the Huygens principle. These models have been applied to the GTD solution for a half-plane in CIVA to model 3D defects echoes diffraction and have then been successfully validated against experimental data in 3D NDT configurations. These incremental models are not applied to the developed UTD wedge, this last model being 2D (infinite wedge and the diffraction problem is invariant along the edge wedge), but they will be useful when a GTD solution for the diffraction by a solid wedge will be developed in 3D configurations.The UTD solution for a wedge developed during this thesis has been established using a GTD solution limited to wedge angles less than 180° (Laplace transform method). Therefore, this UTD approach does not cover all ultrasonic NDT configurations. A preliminary study has then been carried out for a wedge at interfaces fluid/void in order to extend the results to a wider range of wedge angles. In this study, diffraction is modeled using to the so-called “spectral functions method”. Results obtained with this method are compared with those of the Sommerfeld method for this diffraction problem. This comparison allows us to assess the accuracy of the “spectral functions method”, which could also be used in elastodynamics to treat diffraction problems with all wedge angles.Cette thèse propose donc, en élastodynamique, une théorie uniforme de la GTD, appelée Théorie Uniforme de la Diffraction (UTD), qui permet d’obtenir un champ total (champ géométrique et champ diffracté) uniforme, et qui s’avère simple à implémenter. Elle a été développée dans un premier temps pour le cas simple d’un demi-plan afin de démontrer sa faisabilité, puis pour le cas d’un dièdre à interface solide/vide par la suite. Les solutions UTD développées ont été validées numériquement et l'UTD pour le dièdre a été implémentée avec succès dans CIVA dans une configuration 2D (incidence et observation perpendiculaires à l’arête infinie du dièdre). Le modèle combiné « modèle spéculaire + UTD » a ensuite été comparé aux autres modèles de simulation d'échos de géométrie existant dans CIVA, et un bon accord est obtenu entre ces différents modèles, permettant ainsi de valider notre approche. Outre la non-uniformité, une autre limitation de la GTD est qu’elle n’est définie que pour des géométries canoniques (demi-plan, dièdre,…) et ne modélise donc la diffraction que par des arêtes de longueur infinie. Pour prendre en considération la taille finie de l’arête, deux modèles « incrémentaux » 3D consistant à sommer des ondes sphériques émises par des points de discrétisation de l’arête ont été développés. Le premier modèle, appelé Incremental Theory of Diffraction (ITD), est inspiré de l'électromagnétisme et le second, appelé « modèle Huygens », repose sur le principe de Huygens. Ces modèles ont été couplés dans CIVA à la solution GTD du demi-plan pour fournir une modélisation 3D d’échos de diffraction de défauts et ont ensuite été validés avec succès par comparaison à des résultats expérimentaux dans des configurations CND 3D. Ces méthodes incrémentales ne sont pas appliquées au modèle UTD dièdre développé, ce dernier étant 2D (arête infinie et invariance du problème de diffraction le long de l’arête), mais seront utiles lorsqu’une solution GTD de diffraction par un dièdre inclus dans un solide isotrope sera mise au point en 3D.La solution UTD pour le dièdre, développée au cours de cette thèse, a été élaborée en se servant d'une solution GTD limitée à des dièdres d'angle inférieur à 180° (méthode de la Transformée de Laplace). Elle ne permet donc pas de traiter toutes les configurations d'intérêt en CND par ultrasons. Une étude préliminaire a tout d'abord été réalisée pour un dièdre à interface liquide/vide afin de traiter la diffraction pour tout angle de dièdre. Celle-ci est modélisée en employant la méthode dite des "fonctions spectrales". Les résultats obtenus par cette méthode ont été comparés à ceux de la méthode de Sommerfeld pour ce problème de diffraction. Cette comparaison nous permet de connaitre la précision de calcul de la méthode des "fonctions spectrales" dont l’extension au cas élastodynamique pourra être envisagée afin de traiter la diffraction pour des dièdres d’angle quelconque et inclus dans un solide

The spectral functions method for acoustic wave diffraction by a stress-free wedge: Theory and validation

International audienceNon Destructive Examination (NDE) of industrial structures requires the modeling of specimen geometry echoes generated by the surfaces (entry, backwall ...) of inspected blocks. For that purpose, the study of plane wave diffraction by a wedge is of great interest. The work presented here is preliminary research to model the case of an elastic wave diffracted by a wedge in the future, for which there exist various modeling approaches but the numerical aspects have only been developed for wedge angles lower thanπ. The spectral functions method has previously been introduced to solve the 2D diffraction problem of an immersed elastic wedge for angles lower thanπ. As a first step, the spectral functions method has been developed here for the diffraction on an acoustic wave by a stress-free wedge, in 2D and for any wedge angle, before studying the elastic wave diffraction from a wedge. In this method, the solution to the diffraction problem is expressed in terms of two unknown functions called the spectral functions. These functions are computed semi-analytically, meaning that they are the sum of two terms. One of them is determined exactly and the other is approached numerically, using a collocation method. Asuccessful numerical validation of the method for all wedge angles is proposed, by comparison with the GTD (Geometrical Theory of Diffraction) solution derived from the exact Sommerfeld integral

Two Elastodynamic Incremental Models: The Incremental Theory of Diffraction and a Huygens Method

International audienceThe elastodynamic Geometrical Theory of Diffraction (GTD) has proved to be useful in ultrasonic Non-Destructive Testing (NDT) and utilizes the so-called diffraction coefficients obtained by solving canonical problems, such as diffraction from a half-plane or an infinite wedge. Consequently applying GTD as a ray method leads to several limitations notably when the scatterer contour cannot be locally approximated by a straight infinite line: when the contour has a singularity (for instance at a corner of a rectangular scatterer), the GTD field is therefore spatially non-uniform. In particular, defects encountered in ultrasonic NDT have contours of complex shape and finite length. Incremental models represent an alternative to standard GTD in the view of overcoming its limitations. Two elastodynamic incremental models have been developed to better take into consideration the finite length and shape of the defect contour and provide a more physical representation of the edge diffracted field: the first one is an extension to elastodynamics of the Incremental Theory of Diffraction (ITD) previously developed in electromagnetism while the second one relies on the Huygens principle. These two methods have been tested numerically, showing that they predict a spatially continuous scattered field and their experimental validation is presented in a 3D configuration