**Published:** Jan 1979

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**Source: **STP677-EB

The plane problem of a uniform array of equal depth radial cracks originating at the internal boundary of a pressurized circular ring is considered. The finite element method using 12-node quadrilateral, isoparametric elements is adopted. The collapsed singular elements recently developed by the authors are used around the crack tip. The stress intensity factors at a crack tip can be obtained for any finite number of radial cracks and for a large variety of diameter ratios and crack-depth to wall-thickness ratios.

For the special case of a single radial crack and two diametrically opposed radial cracks, stress intensity factors have been obtained by Bowie and Freese using modified mapping-collocation method and by Shannon using a very large number of constant-strain triangular elements. Results of these two different approaches agree quite well except for shallow cracks relative to the cylinder wall thickness. The present finite element results using a maximum of seventeen elements are in better agreement with those of Bowie and Freese, including the results for shallow cracks.

For the case of 40 radial cracks in a cylinder of diameter ratio 2.0, Goldthorpe obtained an empirical formula for the stress intensity factor based on an approximate procedure applied to data of Tweed and Rooke for 40 radial cracks from a hole in an infinite plate. The present results agree with Goldthorpe's results for shallow cracks. For large crack-depth to wall-thickness ratios, Goldthorpe's formula tends to be too low for the stress intensity factors.

The current study has shown that the ring with two diametrically opposed cracks is in general the weakest configuration (highest value in *K*^{I}). In the range of diameter ratio 1.5 to 2.5, the ring with three radial cracks is also weaker than that with only one radial crack. For more than three cracks, the denser the radial cracks are the more stable the ring will be.

**Keywords:**

fracture properties, stress intensity factors, multiple cracks, cylinders, isoparametric elements, crack-tip elements, fatigue (materials), crack propagation

**Author Information:**

Pu, SL *Mathematician and mechanical engineer, Armament Research and Development Command, Benet Weapons Laboratory, Watervliet, N. Y.*

Hussain, MA *Mathematician and mechanical engineer, Armament Research and Development Command, Benet Weapons Laboratory, Watervliet, N. Y.*

**Committee/Subcommittee:** E08.06

**DOI:** 10.1520/STP34943S