Research Papers

On Crack-Tip Stresses as Crack-Tip Radii Decrease

[+] Author and Article Information
G. B. Sinclair1

Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803

G. Meda

Science and Technology Division, Corning Incorporated, Corning, NY 14831

B. S. Smallwood

 Newell Rubbermaid Incorporated, Huntersville, NC 28078

The expressions in Eq. 5 are not given in Inglis (2) or in other forms of this solution available in literature. Accordingly, we draw on their derivation in an internal report (11).

See Sinclair and Beisheim (20) available online.


Corresponding author.

J. Appl. Mech 78(1), 011004 (Oct 12, 2010) (8 pages) doi:10.1115/1.4002236 History: Received January 31, 2009; Revised April 12, 2010; Posted July 27, 2010; Published October 12, 2010; Online October 12, 2010

In classical elasticity, when cracks are modeled with stress-free elliptical holes, stress singularities occur as crack-tip root radii go to zero. This raises the question of when crack-tip stresses first start to depart from physical reality as radii go to zero. To address this question, here, cohesive stress action is taken into account as radii go to zero. To obtain sufficient resolution of the key crack-tip fields, two highly focused numerical approaches are employed: finite elements with successive submodeling concentrated on the crack-tip and numerical analysis of a companion integral equation with considerable discretization refinement at the crack-tip. Both numerical approaches are verified with convergence checks and test problems. Results show that for visible cracks, classical elasticity analysis leads to physically sensible stresses, provided that crack-tip radii are accounted for properly. For microcracks with smaller crack-tip radii, however, cohesive stress action also needs to be included if accurate crack-tip stresses are to be obtained. For cracks with yet smaller crack-tip radii, cracks close and stresses throughout the crack plane become uniform.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 4

Finite element meshes: (a) global coarse mesh, (b) global medium mesh, (c) submodel region, and (d) submodel coarse mesh

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Figure 5

Maximum stresses for cracks with cohesive stress action

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Figure 6

Normal stress distributions on the crack plane in the immediate vicinity of the crack-tip for a microcrack (2b≈1 μm)

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Figure 1

Genesic Griffith crack configuration

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Figure 2

Cohesive stress-separation law

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Figure 3

Tensile specimens: (a) specimen in a state of plane strain and (b) specimen with a cohesive law on its midplane




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