<p>The desire to apply ultrasonic testing to geometrically complex structures, and to anisotropic, inhomogeneous materials, together with the advent of more powerful electronics and software, is constantly pushing the applicability of ultrasonic waves to their limits. Any mechanical wave that passes from one medium to another or through a medium with gradually changing properties experiences a variation in its propagation direction. This phenomenon is known as refraction. It makes not always intuitive to predict the path a wave takes, especially in parts with complex geometries or with multiple internal material discontinuities. Ultrasonic inspection of planar components is relatively straightforward. However, the inspection of components with nonplanar surface geometries, such as weld-caps, curved pipes, and curved composite structures is more challenging and requires specific technologic solutions. Various works have addressed the inspection of curved components and developed ways to couple the ultrasonic transducers with the material under test, using flexible ultrasonic arrays conforming to the surface, deploying a rigid array on a nearby planar surface to image the region of interest from the side either directly or by using signals reflected from the back wall of the component. Another option is to use an intermediary layer (e.g., a solid shoe with a surface conformal with that of the component or water), to couple the transducer to the component. However, the imaging speed depends on the complexity of the surface and the total number of image pixels, and this is a key concern for industrial end-users. To increase imaging speed, and improve focusing and/or steering of phased array ultrasonic beams on the desired position, several works have investigated ways to compute the ultrasonic ray paths. A general ray tracing model based on Snell’s law, suitable for calculating the proper incident angle of single element probes and the proper time delay of phased array probes in two and three dimensional multi-layer parts, and in anisotropic and inhomogeneous materials, is still missing. This contribution presents a generalized iterative method for the computation of ultrasonic ray paths, when ultrasonic source and target are separated by multiple complex material interfaces in the two dimensional and three-dimensional domains. Starting from a review of the well-known bisection method, this work extends the applicability of the method to cases with increasing complexity. An application example, in the field of in-process weld inspection, shows that the introduced generalised bisection method can enable the computation of optimum incidence angles and focal delays for accurate ultrasonic focusing. There is no restriction on the analytical interfaces to be surjective. Interface folding is permitted. It is not necessary to know, a priori, with what sequence the interfaces are crossed by the rays. The presented implementation of the method completes each iteration of the bisection method in 4ms, for a case with a single interface, and in 960ms for the case with 52 interfaces.</p>

Three-Dimensional Ultrasonic Ray Tracing in Multi-Layered Structures

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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