The effect of a three- dimensional quarter-circle corner crack on the stress intensity factors of a nonaligned semi-elliptical surface crack in an semi-infinite solid under uniaxial tension

Cesar Levy, Mordechai Perl, Qin Ma

Research output: Contribution to journalArticlepeer-review


The Fitness-for-Service (FFS) approach requires the evaluation of the mutual impact of nonaligned, multiple cracks on each other. As such, initially one must resolve whether existing, nonaligned, parallel cracks in the structure should be treated as merged or as separate, multiple cracks for FFS evaluation. Criteria and standards found in existing literature on how to deal with multiple, nonaligned cracks are very source dependent, and those guidelines are often developed from on-site, service inspections without exact and methodical substantiation. Based on this determination, the authors previously reported on the impact of an embedded crack on an edge crack using a two-dimensional model, and, more recently using a three-dimensional (3D) model, on the impact of a semicircular surface crack on a quarter-circle corner crack. However, actual crack shapes identified using nondestructive techniques are 3D in nature, normally not semicircular, and their impact are of mutual importance. Thus, the stress intensity factor (SIF) distribution along the semi-elliptical surface crack is as significant as the SIF distribution of the corner crack in the application of FFS standards. Therefore, nonaligned cracks with varied arrangements and shapes and the SIFs along their crack fronts are considered crucial in order to obtain more practical information on the application of rules provided in FFS codes. In this study, over 330 different cases are solved and the behavior of the SIF distribution along a 3D semi-elliptic nonaligned surface crack is assessed when affected by a quarter-circle corner crack of various geometries in an infinitely large solid. For a given geometry of a quarter-circle corner crack, a detailed examination of the corner crack's impact on the 3D SIFs of the surface crack is carried out as a function of the surface crack's ellipticity, and the horizontal (H) and vertical (S) separation distances between the two cracks. The analysis was replicated for various arrangements of separation distances S and H. The results from this study are considered noteworthy to the understanding of the relation between the criteria and standards in FFS community and the consequence of their application in engineering practice. The results demonstrate that the 3D SIFs along the crack front of the semi-elliptical surface crack can be affected profoundly by the presence of the quarter-circle corner crack. The corner crack's existence may amplify or diminish the SIF of the surface crack for those points of the semi-elliptic surface crack front that approach the closest quarter-circle corner crack tip. Furthermore, when the two cracks are overlapped, the behavior of the SIF distribution as a function of separation distance is different in the vertical direction than in the horizontal direction due to a process called shielding. As the separation distances between the cracks increase in either direction, there is a separation distance after which the cracks can be treated as separate cracks, and, this distance is dependent on the relative crack lengths.

Original languageEnglish
Article number031505
JournalJournal of Pressure Vessel Technology, Transactions of the ASME
Issue number3
StatePublished - 1 Jun 2021


  • Fitness-for-service
  • Nonaligned
  • Quarter-circle corner crack
  • Semi-elliptical crack
  • Stress intensity factors

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Mechanics of Materials
  • Mechanical Engineering


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