A Three-Dimensional Weight Function Method

Leslie Banks-Sills*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this investigation, an exact three-dimensional weight function is developed for the elliptical crack family. Closed form expressions for the weight function of the penny-shaped and elliptical crack in an infinite body subjected to symmetric applied stresses are obtained. Several loadings are considered that lead to exact solutions which agree with those in the literature. Since crack-opening displacements for more complicated crack geometries do not appear in the literature, an approximate weight function is proposed. When applied to the geometries with known solutions, excellent agreement is obtained. When employed to determine the stress-intensity factor for a semielliptical and quarter-elliptical crack in a plate subjected to bending stresses, it produces results which are good for short cracks.

Original languageEnglish
Title of host publication19th National Symposium on Fracture Mechanics
EditorsThomas A. Cruse
PublisherASTM International
Number of pages17
ISBN (Electronic)9780803109728
StatePublished - 1988
Event19th National Symposium on Fracture Mechanics - San Antonio, United States
Duration: 30 Jun 19862 Jul 1986

Publication series

NameASTM Special Technical Publication
VolumeSTP 969
ISSN (Print)0066-0558


Conference19th National Symposium on Fracture Mechanics
Country/TerritoryUnited States
CitySan Antonio


  • elliptical cracks
  • fracture
  • fracture mechanics
  • stress-intensity factor
  • three-dimensional weight function
  • weight function


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