Modeling of diffraction effects for specimen echoes simulations in ultrasonic Non-Destructive Testing (NDT)

Abstract : 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.
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Audrey Kamta Djakou. Modeling of diffraction effects for specimen echoes simulations in ultrasonic Non-Destructive Testing (NDT). Acoustics [physics.class-ph]. Université du Maine, 2016. English. ⟨tel-01374154⟩

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