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Update: Application of the Finite Element Method to Linear Elastic Fracture Mechanics

[+] Author and Article Information
Leslie Banks-Sills

Dreszer Fracture Mechanics Laboratory, School of Mechanical Engineering, Fleischman Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israel

Appl. Mech. Rev 63(2), 020803 (Feb 22, 2010) (17 pages) doi:10.1115/1.4000798 History: Received November 19, 2009; Revised November 27, 2009; Published February 22, 2010

Since the previous paper was written (Banks-Sills, 1991, “Application of the Finite Element Method to Linear Elastic Fracture Mechanics,” Appl. Mech. Rev., 44, pp. 447–461), much progress has been made in applying the finite element method to linear elastic fracture mechanics. In this paper, the problem of calculating stress intensity factors in two- and three-dimensional mixed mode problems will be considered for isotropic and anisotropic materials. The square-root singular stresses in the neighborhood of the crack tip will be modeled by quarter-point, square and collapsed, triangular elements for two-dimensional problems, respectively, and by brick and collapsed, prismatic elements in three dimensions. The stress intensity factors are obtained by means of the interaction energy or M-integral. Displacement extrapolation is employed as a check on the results. In addition, the problem of interface cracks between homogeneous, isotropic, and anisotropic materials is presented. The purpose of this paper is to present an accurate and efficient method for calculating stress intensity factors for mixed mode deformation. The equations presented here should aid workers in this field to carry out similar analyses, as well as to check their calculations with respect to the examples described.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Eight-noded (a) parent element in the ξη plane and (b) quarter-point element in the xy plane. (c) Quarter-point collapsed triangular element.

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Figure 2

Twenty-noded (a) parent element in the ξηζ space and (b) quarter-point element in the xyz space. (c) Quarter-point collapsed prismatic element.

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Figure 3

Crack tip coordinates

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Figure 4

Example of (a) line J-integral path Γ and (b) area A used to calculate area J-integral

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Figure 5

Mesh and integration paths about the crack tip for (a) square elements and (b) triangular elements about the crack tip

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Figure 6

Interface crack with crack tip coordinates shown

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Figure 7

Various regions for calculating the M-integral in thermal problems for (a) a homogeneous body or (b) an interface crack

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Figure 8

Components of the virtual crack extension

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Figure 9

Virtual crack extension along the crack front denoted on the finite element mesh

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Figure 10

Cross-sectional view of integration domains in the x1x2-plane for quarter-point (a) brick and (b) prismatic elements adjacent to the crack front. The numbers represent the integration volumes.

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Figure 11

Disk containing a crack subjected to various displacement fields on the outer boundary

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Figure 12

Meshes of the disk in Fig. 1 containing quarter-point (a) square and (b) collapsed, triangular elements about the crack tip

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Figure 13

Anisotropic disk containing a crack subjected to various displacement fields on the outer boundary. The material coordinates are denoted by x1 and x2, whereas the crack tip coordinates are x and y.

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Figure 14

Meshes of the disk in Fig. 1 containing quarter-point (a) square and (b) collapsed, triangular elements about the crack tip

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Figure 15

Central crack along the interface between two linear elastic, isotropic, and homogeneous materials

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Figure 16

Meshes containing quarter-point (a) square elements and (b) collapsed, triangular elements about the crack tip

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Figure 17

Meshes containing quarter-point (a) square elements and (b) collapsed, triangular elements about the crack tip.

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Figure 18

Double edge cracked infinite, bimaterial body subjected to thermal loading

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Figure 19

Meshes containing quarter-point (a) square elements and (b) collapsed, triangular elements about the crack tip for the thermal loading problem in Fig. 1

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Figure 20

Central crack of half-length a/W=0.07 in a body of height H/W=1 and thickness B/W=1 subjected to (a) tension and (b) pure shear

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Figure 21

Meshes containing quarter-point (a) brick and (b) collapsed, prismatic elements about the crack front for the three-dimensional body in Fig. 2

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Figure 22

The normalized stress intensity factor K̂III along the crack front for the problem in Fig. 2

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