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Triangular quarter‐point elements as elastic and perfectly‐plastic crack tip elements
Author(s) -
Barsoum Roshdy S.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620110109
Subject(s) - singularity , fracture (geology) , crack tip opening displacement , plasticity , point (geometry) , fracture mechanics , finite element method , quadratic equation , structural engineering , materials science , crack growth resistance curve , mechanics , geometry , crack closure , mathematics , engineering , composite material , physics
Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid‐side node near the crack tip at the quarter point, are shown to embody the (1/√ r ) singularity of elastic fracture mechanics and the (1/ r ) singularity of perfect plasticity. The procedure of performing the fracture analysis for the case of small scale yielding is discussed, and the finite element results are compared with theoretical results. The proposed elements have wide application in the fracture analysis of structures where ductile fracture is investigated. They permit a determination of the relationship between crack tip field parameters, loading, and geometry. And for a given fracture criterion can be applied to the prediction of fracture in structures such as pressure vessels under in service conditions.