Locating the Crack Tip Using Displacement Field Data: A Comparative Study

The evaluation of stress intensity factors from experimentally determined crack-tip stress or displacement fields almost always requires that the location of the crack tip is identified beforehand. In this work, a study has been performed to compare how different methods to locate the crack-tip position from the displacement field around a crack tip obtained by digital image correlation influence the estimation of stress intensity factors. The methods used were two constrained Newton type methods: the trust-region reflective Newton method and quasi-Newton method; an unconstrained direct search method: the NelderMead Simplex method; a constrained genetic algorithm; and a constrained Pattern Search (PS) method. It is shown that the Newton type methods are less accurate compared with the direct search methods studied. The PS method was found to be the most accurate. Furthermore, the PS method was found to be about twice as fast as the Simplex method and 10 times faster than a Genetic Algorithm for the same computing hardware and the same input data.