A spectral method for sizing cracks using ultrasonic arrays

Ultrasonic phased array systems are becoming increasingly popular as tools for the inspection of safety-critical structures within the non-destructive evaluation industry. The data-sets captured by these arrays can be used to image the internal structure of individual components, allowing the location and nature of any defects to be deduced. Although there exist strict procedures for measuring defects via these imaging algorithms, sizing flaws which are smaller than two wavelengths in diameter can prove problematic and the choice of threshold at which the defect measurements are made can introduce an aspect of subjectivity. This paper puts forward a completely objective approach specific to cracks based on the Kirchhoff scattering model and the approximation of the resulting scattering matrices by Toeplitz matrices. A mathematical expression relating the crack size to the maximum eigenvalue of the associated scattering matrix is derived. Analysis of this approximation shows that the method will provide a ...