Locating a crack of arbitrary but known shape by the method of path-independent integrals

Abstract

The solution of a crack problem of an arbitrary, but known, shape inside an infinite plane isotropic elastic medium can be achieved in general by the method of complex singular integral equations and their numerical solution by using the Gauss- or the Lobatto-Chebyshev methods. In a few special cases, like straight or circular-arc-shaped cracks, this solution is available in closed form. In this paper we will not contribute to the above methods of solution of crack problems, but we will propose a method for the determination of the exact position of such a crack inside a closed contour in the elastic medium by gathering and using information along this contour only (by experimental techniques) and applying the method of complex path-independent integrals for the location of the crack. This paper constitutes a nontrivial generalization of relevant previous results by the author and it is of quite general applicability in fracture mechanics for nondestructive testing. Numerical results for the particular case of a straight crack are displayed for the illustration of the efficiency of the method. The generalization of the present results to the determination of additional geometric and loading parameters of the crack is also suggested very briefly and related numerical results, concerning the length of the crack and the pressure distribution on it, in the aforementioned numerical application are also presented.