Solving ultrasonic ray tracing in parts with multiple material layers through Root-Finding methods

Ultrasonic testing has been used for material analysis and inspection since 1930's. Nevertheless, the applicability of ultrasonic waves to new complex cases is still growing, thanks to the availability of powerful electronics and software. However, the complication that slows down the deployment of ultrasonic inspection to geometric complex parts and structures arises from the wave refraction phenomenon. A clear understanding of the ultrasound wave propagation, impacted by refractions, is crucial to interpret the data obtained from the inspection of multi-layered/multi-medium test subjects as it is not always possible to assume that mechanical waves travel in straight lines. This work presents suitable approaches for solving the ray-tracing problem in multi-layered structures. Accurate benchmarking shows that the use of the Newton-Raphson root-finding method allows a threefold reduction of the computation time, when compared to the bisection-based root-finding methods. An effective combination of the Newton-Raphson methods with bisection-type iterations is also proposed and discussed. Although the work repeatedly refers to the field of ultrasonic inspection, the presented findings are relevant and applicable to areas beyond material inspection.