Three-dimensional stress intensity factors for ring cracks and arrays of coplanar cracks emanating from the inner surface of a spherical pressure vessel

M. Perl, V. Bernshtein

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Certain spherical pressure vessels are composed of two hemispheres joined together by a girth weld. These vessels are susceptible to multiple cracking along the weld resulting in one or more cracks developing from the inner surface of the vessel and creating either a ring (circumferential) crack, or an array of coplanar cracks on the equatorial-weld plane. In order to assess the fracture endurance and the fatigue life of such vessels it is necessary to evaluate the Stress Intensity Factors (SIFs) distribution along the fronts of these cracks. However, to date, only two solutions for the SIF for an internal ring crack as well as two 3-D solutions for a single internal semi-elliptical crack prevailing in various spherical pressure vessels are available. In the present analysis, mode I SIF distributions for a wide range of ring, lunular, and crescentic cracks are evaluated. The 3-D analysis is performed, via the FE method employing singular elements along the crack front. SIFs for numerous ring cracks of different depths prevailing in thin, moderately thick, and thick spherical vessels are evaluated first. Subsequently, three-dimensional mode I SIF distributions along the crack fronts of a variety of lunular and crescentic crack array configurations are calculated for three spherical vessel geometries, with outer to inner radii ratios of R 0/R i=1.01, 1.1, and 1.7. SIFs are evaluated for arrays of density δ=0-0.99; for a wide range of crack-depth to wall-thickness ratios, a/t, from 0.025 to 0.95; and for various lunular and crescentic cracks with ellipticities, i.e., the ratio of crack-depth to semi-length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are considerably affected by the three-dimensionality of the problem and by the following parameters: the crack density of the array-δ, the relative crack depth-a/t, crack ellipticity-a/c, and the geometry of the spherical vessel-η. Furthermore, it is shown that in some cases the commonly accepted approach that the SIF for a ring crack of any given depth is the upper bound to the maximum SIF occurring in an array of coplanar cracks, of the same depth, is not universal.

Original languageEnglish
Pages (from-to)71-84
Number of pages14
JournalEngineering Fracture Mechanics
StatePublished - 1 Nov 2012


  • 3-D cracks
  • Circumferential cracks
  • Coplanar cracks
  • Crescentic cracks
  • Lunular cracks
  • Ring cracks
  • Spherical pressure vessels

ASJC Scopus subject areas

  • Materials Science (all)
  • Mechanics of Materials
  • Mechanical Engineering


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