LOCATING THE CRACK-TIP OF A SURFACE-BREAKING CRACK - PART I - LINE CRACK

Four distinct algorithms to locate the crack tip of a surface-breaking crack using only the arrival time information of the first diffracted waves are described and compared. To illustrate these algorithms, a l ine crack in a half-plane is considered. The first two algorithms are based mainly on elementary geometric arguments, where the crack tip is formulated as the intersecting point of two ellipses (algorithm 1) an d/or three circles (algorithm 2). The other two algorithms are formula ted as optimization problems, where cost functions based upon the arri val time data of diffracted waves are constructed. The unknown crack t ip coordinates are then determined by minimizing the cost functions th rough the Lagrange multiplier method (algorithm 3) or the simplex meth od (algorithm 4). In the numerical experiments, the exact arrival time s are superimposed by Gaussian error with different levels to simulate the real extracted arrival times from experimental signals. The numer ical optimization method (algorithm 4) is found to have the best perfo rmance with respect to noise, as well as for accuracy. Moreover, the r ecovery of the crack length is much more robust than the orientation a nd depth. (C) 1998 Elsevier Science B.V. All rights reserved.