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**Published:** Jan 1990

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**Source: **STP1074-EB

Rules for the meshing of finite element problems with elastic cracks have never been established. Therefore finite element results for crack problems presented in the literature are of uncertain accuracy. This paper establishes the finite element meshing criteria, based upon a “least dimension” concept, necessary to calculate mixed-mode stress-intensity factors in linear elastic crack problems to a pre-specified accuracy.

Finite element convergence studies, using meshes which consist of eight-noded quadrilateral elements and corresponding six-noded quarter-point singularity elements, are presented for several benchmark problems with known stress-intensity factor solutions. It is assumed that the stress-intensity factors are extracted from the analysis using the displacement correlation method, a common practice in the analysis of mixed-mode problems.

The convergence studies give the analyst valuable information about meshing requirements for arbitrary crack problems. In performing a convergence study for such analyses, three key meshing parameters associated with a given crack tip must be considered: size of the crack tip elements, number of crack tip elements surrounding the crack tip, and size of regular elements near the crack tip. Recommendations for each of these three parameters to achieve an efficient mesh and a prespecified accuracy are presented.

**Keywords:**

finite element, crack, singularity, convergence study, stress-intensity factor, linear elastic fracture mechanics

**Author Information:**

Gerstle, WH *Assistant Professor and Graduate Student, University of New Mexico, Albuquerque, NM*

Abdalla, JE *Assistant Professor and Graduate Student, University of New Mexico, Albuquerque, NM*

**Committee/Subcommittee:** E08.06

**DOI:** 10.1520/STP19011S