Obtaining geometries of real cracks and using an efficient finite element method to simulate their ultrasonic array response

Stress corrosion cracks can be a serious issue in many industries, so it is imperative to be able to reliably inspect for them. However, the branched nature of these cracks causes difficulties when inspecting with a single ultrasonic transducer due to the scattering of ultrasound in various directions. An ultrasonic array is more suited to this application because it can inspect at many angles. In order to design an array, it is necessary to understand the ultrasonic scattering from these complex cracks. In this paper, images of real stress corrosion cracks are obtained by performing X-ray computed tomography of cracked parts. Image processing software is used to extract the crack geometries. Next, the Kirchhoff approximation is compared with an efficient frequency domain finite element (FE) method, in terms of their ability to correctly simulate the ultrasonic scattering from such cracks. The Kirchhoff approximation is dismissed because it does not simulate shadowing or multiple reflections between features, neither does it correctly simulate tip diffraction or scattering from small lengths, whilst the FE method correctly simulates all these interactions. A hybrid model is implemented, which combines the FE method with simple ray tracing to obtain a simulated ultrasonic array response. In particular, it is the full matrix capture data that is simulated. The hybrid model is validated using wire-cut branched shapes and is then used to simulate array data from the real crack geometries, which are approximately 4 mm deep. The paper concludes with a discussion on how the hybrid model and real crack geometries can be used to optimise an array design. This can be achieved by running the hybrid model for arrays of different parameters, such as the number of elements, and comparing the crack indications obtained with the different arrays.