On the practical application of the method of complex path-independent integrals to problems of fracture mechanics
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Date
1988-03
Authors
Ioakimidis, Nikolaos
Journal Title
Journal ISSN
Volume Title
Publisher
Kluwer Academic Publishers
Abstract
Real and complex path-independent integrals have been already repeatedly used for the determination of quantities of interest in fracture mechanics (mainly stress intensity factors at crack tips), but they have also been used for the location of crack tips in plane isotropic elastic media. Here by appropriately using both experimental optical methods of pseudocaustics and of caustics for a plane isotropic elastic medium it is observed that it is possible to experimentally measure the second derivative Phi’(z) = phi’’(z) (with z = x+iy) of the first complex potential phi(z) of Kolosov–Muskhelishvili. Next, by additionally experimentally measuring an auxiliary complex function S(z, z bar) (either by appropriately using the method of caustics or, alternatively, the method of photoelasticity) we can compute the first derivative Psi(z) = psi’(z) of the second complex potential psi(z) of the same authors. In this way, a variety of complex path-independent integrals based on Phi’(z), Psi(z) and, possibly, additional analytic functions can be computed on a closed contour C of the isotropic elastic medium under consideration and these computations permit, for example, the computation of stress intensity factors at crack tips.