A model-based approach to crack sizing with ultrasonic arrays

Ultrasonic phased array systems have become increasingly popular in the last 10 years as tools for flaw detection and characterization within the nondestructive testing industry. The existence and location of flaws can often be deduced via images generated from the data captured by these arrays. A factor common to these imaging techniques is the subjective thresholding required to estimate the size of the flaw. This paper puts forward an objective approach which employs a mathematical model. By exploiting the relationship between the width of the central lobe of the scattering matrix and the crack size, an analytical expression for the crack length is reached via the Born approximation. Conclusions are then drawn on the minimum resolvable crack length of the method and it is thus shown that the formula holds for subwavelength defects. An analytical expression for the error that arises from the discrete nature of the array is then derived and it is observed that the method becomes less sensitive to the discretization of the array as the distance between the flaw and array increases. The methodology is then extended and tested on experimental data collected from welded austenitic plates containing a lack-of-fusion crack of 6 mm length. An objective sizing matrix (OSM) is produced by assessing the similarity between the scattering matrices arising from experimentally collected data with those arising from the Born approximation over a range of crack lengths and frequencies. Initially, the global minimum of the OSM is taken as the objective estimation of the crack size, giving a measurement of 7 mm. This is improved upon by the adoption of a multifrequency averaging approach, with which an improved crack size estimation of 6.4 mm is obtained.