3-D Stress Intensity Factors due to Full Autofrettage for Inner Radial or Coplanar Crack Arrays and Ring Cracks in a Spherical Pressure Vessel

M. Perl, M. Steiner

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Three dimensional, Mode I, Stress Intensity Factor (SIF) distributions for radial or coplanar crack arrays as well as ring cracks emanating from the inner surface of an autofrettaged spherical pressure vessel are evaluated. The 3-D analysis is performed via the finite element (FE) method employing singular elements along the crack front. A novel realistic autofrettage residual stress field incorporating the Bauschinger effect is applied to the vessel. The residual stress field is simulated in the FE analysis using an equivalent temperature field. Numerous radial and coplanar crack array configurations are analyzed as well as ring cracks of various depths. SIFs distributions are evaluated for arrays of radial or coplanar cracks consisting of cracks of depth to wall thickness ratios of a/t=0.1-0.6, and ellipticities of a/c=0.2-1.0 prevailing in a fully autofrettaged spherical vessels, ϵ=100%, of different geometries R 0 /R i =1.1, 1.2, and 1.7. SIFs are evaluated for radial arrays containing n=1-20 cracks, and for arrays of coplanar cracks of δ=0-0.95 densities. Furthermore, SIFs for inner ring cracks of various crack depth to wall thickness ratios of a/t=0.025-0.6 are also evaluated. In total, about three hundred different crack configurations are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly demonstrate the favorable effect of autofrettage which may considerably reduce the prevailing effective stress intensity factor, thus delaying crack initiation and slowing down crack growth rate, and hence, substantially prolonging the total fatigue life of the vessel. Furthermore, the results emphasize the importance of properly accounting for the Bauschinger effect including re-yielding, as well as the significance of the three dimensional analysis herein performed. 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)3625-3646
Number of pages22
JournalProcedia Structural Integrity
StatePublished - 1 Jan 2016
Event21st European Conference on Fracture, ECF21 - Catania, Italy
Duration: 20 Jun 201624 Jun 2016
Conference number: 21


  • Autofrettage
  • Coplanar crack arrays
  • Crescentic crack
  • Lunular crack
  • Radial crack arrays
  • Ring cracks
  • Spherical pressure vessel
  • Stress intensity factors

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • General Materials Science
  • Civil and Structural Engineering


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