Nonradial edge crack in a circular disk
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NONRADIAL EDGE CRACK IN A CIRCULAR DISK O. P. Datsyshyn1,2 and I. A. Rudavs’ka1
UDC 539.375
We deduce a singular integral equation of the problem of stress-strain state of a circular disk weakened by a rectilinear nonradial edge crack whose lips are subjected to the action of an arbitrary self-balanced load. For the case of a pressure uniformly distributed over the crack lips, we compute the stress intensity factors as functions of the orientation and crack length. Keywords: round disk, nonradial edge crack, singular integral equation, stress intensity factors.
The solutions of the problems of stress-strain state for round disks weakened by cuts (cracks) are of high importance both for the fundamental problems of the mathematical theory of cracks and for the applied problems [in particular, for the prediction of strength and durability of the elements of tribojoints (first of all, of the rolling bodies)]. In this case, it is necessary to know the stress intensity factors at the crack tips. For the radial edge cracks, there are numerous results obtained by using various approaches with various accuracies and available in the literature (see, e.g., the handbooks [1–3]). The solutions of the problems and the detailed analysis of the stress intensity factors for disks weakened by cracks can be found in [4, 5]. The results accumulated for disks containing edge radial cracks are obtained mainly for two cases of symmetric loading, i.e., for the disk subjected to the action of uniform tension (uniformly distributed pressure acts upon the opposite crack lips) or the disk subjected to eccentric tension by concentrated forces symmetric about the crack line. Numerous problems posed for edge and internal cracks located along the diameter of the disk were solved by the method of singular integral equations by Libatskii [6, 7]. Their numerical solutions were obtained by the method of collocations with regard for the types of the singularities of stresses at the crack tips. The solution (determination of the stress intensity factors) of the problems of eccentric tension of circular disks containing radial edge cracks is connected to the design of specimens for the experimental determination of the characteristics of crack resistance of materials [8]. These studies were described in detail in [3]. The numerical results accumulated for the case of pressure uniformly distributed over the lips of a radial edge crack formed in a disk can be found in [4]. They were obtained as a result of the numerical solution of singular integral equations by the method of mechanical quadratures. In [9], Gregory presented the exact analytic solution of a problem of this sort. At the same time, the data on the stress intensity factors for nonradial edge cracks formed in disks are absent in the literature up to now, although they are of the fundamental importance for fracture mechanics, just as the data on the stress intensity factors for the half plane weakened by edge cracks. In what follows, we solve this problem by the method of singular integral e
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