Quarter-point elements for curved crack fronts

doi:10.1016/0045-7949(83)90010-X

Computers & Structures

Volume 17, Issue 2, 1983, Pages 227-231

https://doi.org/10.1016/0045-7949(83)90010-X Get rights and content

Abstract

Ingraffea et al.[1] have presented a consistent method to compute stress-intensity factors from wedge quarter-point element nodal displacements for the straight crack front. The method was generalized to permit functional evaluation of stress-intensity factors along the crack front. Here the method is generalized for curved crack fronts.

References (7)

A.R. Ingraffea et al.
Stress-intensity factor computation in three dimensions with quarter-point elements
Int. J. Num. Meth. Engng
(1980)
M.A. Hussain et al.
Three-dimensional singular element
Comput. Structures
(1981)
O.C. Zienkiewicz et al.
Isoparametric and associated element families for two- and three-dimensional analysis

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Citation Excerpt :
An accurate angular distribution is reproduced when a group of these elements are arranged around the crack front. In the case of curved crack fronts, the mid-side nodes of the element face opposing the crack front must be moved in a way that a parabolic-cylindrical surface is defined [31,32]. Quarter-point fifteen-noded pentahedral element (Fig. 1f): This element is generated by placing the mid-side nodes near the crack front of an isoparametric fifteen-noded pentahedral at the quarter-point position.
This paper discusses the reproduction of the square root singularity in quarter-point tetrahedral (QPT) finite elements. Numerical results confirm that the stress singularity is modeled accurately in a fully unstructured mesh by using QPTs. A displacement correlation (DC) scheme is proposed in combination with QPTs to compute stress intensity factors (SIF) from arbitrary meshes, yielding an average error of 2–3%. This straightforward method is computationally cheap and easy to implement. The results of an extensive parametric study also suggest the existence of an optimum mesh-dependent distance from the crack front at which the DC method computes the most accurate SIFs.
A numerical analysis of flat internal cracks under mixed mode loading
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A numerical/analytical approach is proposed to determine the stress intensity factors K_I, K_II, and K_III of a 3D internal crack. The main point of this approach is the meshing technique that can model very sharp crack fronts. The meshing technique is based on an elliptical coordinate transformation that starts from a circular crack. It allows the obtainment of a curved crack front with elements normal to the crack front. Remarkable accuracy can be obtained for elliptical crack fronts with axes ratio smaller that 0.01. Accuracy demonstration is provided for cylindrical element with an inclined internal crack subjected to uni-axial tension. This case corresponds to crack propagation for all three modes of loading, the solution of which can checked with references’ results.
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Mode-I crack projection procedure using the strain energy density criterion
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A practice used in linear elastic fracture mechanics is the projection of a crack onto a plane normal to the principal tensile stress axes for computing the stress intensity factor K_I. The minimum strain-energy criterion is applied for different crack configurations with the introduction of a safety factor S_i which is the ratio of the strain energy density factor of the projected crack and that of the original crack. Numerous crack configurations are investigated to illustrate the degree of conservativeness of the crack projection procedure.

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Quarter-point elements for curved crack fronts

Abstract

Stress-intensity factor computation in three dimensions with quarter-point elements

Int. J. Num. Meth. Engng

Three-dimensional singular element

Comput. Structures

Isoparametric and associated element families for two- and three-dimensional analysis