A note on locating straight-crack tips in finite plane elastic media
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Date
1986-09
Authors
Ioakimidis, Nikolaos
Journal Title
Journal ISSN
Volume Title
Publisher
Martinus Nijhoff Publishers
Abstract
The method of complex path-independent integrals is an interesting method and practically useful in some problems of plane isotropic elasticity. Here this method is applied to the problem of locating the tips a and b of an unloaded straight crack [a, b] lying inside a finite plane isotropic elastic medium. This is achieved through the generalization of previous related results concerning two simpler cases of this problem. For this task the two complex potentials Phi(z) and Omega(z) of Kolosov–Muskhelishvili are assumed to be known in advance on a closed contour C surrounding the unloaded straight crack [a, b] with C perhaps coinciding with the boundary of the isotropic elastic medium under consideration. Then by using the Cauchy theorem in complex analysis and four appropriate complex path-independent integrals I0, I1, I2 and I3, which are based on the square of the sum of these two complex potentials, we can easily determine the two crack tips a and b of the present straight crack [a, b] in closed form. This is achieved through the derivation and use of two simple equations including the aforementioned four complex path-independent integrals. The present approach appropriately modified is also directly applicable when the closed contour C surrounds only one crack tip (either b or a) and it leads to the location of this particular crack tip. Naturally, in this computationally much simpler case, a second closed contour C* should be similarly used for the location of the other crack tip (now either a or b). Modifications and generalizations of the present approach based on complex path-independent integrals are also possible.