Paraxial ray-tracing approach for the simulation of ultrasonic inspection of welds

On-site inspection of bimetallic or austenitic welds can be very difficult to interpret owing to their internal structures. Skewing and splitting of the ultrasonic beam may occur due to the anisotropic and inhomogeneous properties of the welding material. In this paper, we present a ray-based method to simulate the propagation of ultrasonic waves in such structures. The formalism is based on dynamic ray tracing system in Cartesian coordinates along a reference ray. Standard ray tracing consists in the solution of a system of linear ordinary differential equations of the first order and is used to determine the trajectory of the ray. Likewise, dynamic ray tracing (DRT) also called paraxial ray tracing consists in the solution of an additional system of linear ordinary differential equations along the ray allowing paraxial quantities to be computed. It is used to evaluate the geometrical spreading and amplitude along the ray and in its vicinity. DRT is applied on a smooth representation of the elastic properties of the weld obtained thanks to an image processing technique applied on a macrograph of the weld. Simulation results are presented and compared to finite elements and experimental results.