An algorithm for identifying a crack within a measured displacement field

Abstract

This paper discusses an algorithm for the detection of crack damage in plate structures based on the governing differential equation (GDE) of in-plane displacement of a plate. A state-of-the-art 3D scanning laser Doppler vibrometer, which is able to provide very accurate measurements of a three-dimensional displacement field, was utilized to implement the algorithm. To evaluate the GDE from the measured displacements, a 2D Savitzky–Golay differentiating filter was used. The potential of this algorithm for detecting a crack was compared against another two algorithms which are based on displacement measurements. The first is an algorithm based on the error in smoothed to measured displacements and the other uses surface strains normalized by their mean. To investigate the efficiency of the algorithms in detecting crack damage, a number of PMMA plate specimens were fabricated with a range of crack lengths extending from a V-notch and tested under a cyclic, quasi-static, uni-axial load. For each algorithm, the crack location could be positively identified. However, the two algorithms based on the error in smoothed to measured displacements and surface strains normalized by their mean were found to be dependent on the direction of the applied load, whereas, theoretically the algorithm based on the GDE of in-plane displacement would work regardless of the direction of the applied load.