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|Title:||A GRIFFITH CRACK LOCATED ASYMMETRICALLY IN AN INFINITELY LONG ELASTIC STRIP|
|Publisher:||PERGAMON-ELSEVIER SCIENCE LTD|
|Citation:||ENGINEERING FRACTURE MECHANICS, 49(2), 195-211|
|Abstract:||Of concern in this paper is the distribution of stress in the vicinity of a Griffith crack located in a strip of finite width parallel to the edges. The edges of the strip are free from tractions and the crack is opened out by the application of a uniform internal pressure on its faces. The crack is not necessarily situated on the centreline of the strip, and so the mode II stress intensity factor is not necessarily zero even though the loading is purely of mode I type. By means of Fourier transforms the problem is reduced to that of solving a pair of simultaneous singular integral equations of Cauchy type. The mode I and mode II stress intensity factors are computed and presented in tables and figures for various combinations of h/delta and delta/a, where 2delta is the strip width, 2a is the crack length and h is the distance of the crack from the centreline of the strip. For large delta/a one can derive approximate expressions for stress intensity factors by retaining terms up to a certain order of a/delta, say, (a/delta)6. A comparison between the numerical results obtained from the approximate expressions and those obtained from the direct numerical solution of singular integral equations shows that the approximate expressions are good only for h = 0 and perhaps for small values of h/delta. It is observed that the convergence of the numerical results increases with the increase in the value of (delta - h)/a. This suggests that one should obtain approximate formulae for the stress intensity factors by retaining terms of a certain order of a/(delta - h). It is obviously done for the case when h = 0. However, for nonzero values of h/delta, the problem does not seem to be an easy one. A limiting case of the strip problem described above is a half plane problem. The latter problem of determining the distribution of stress in the neighbourhood of a crack, subjected to a uniform internal pressure and situated in the half plane parallel to its boundary, has been studied in the literature independently. We deduce the formulae for the half plane problem from the formulae for the strip problem and compare our results with those in the literature.|
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