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REVIEW ARTICLES

Stress singularities in classical elasticity–I: Removal, interpretation, and analysis

[+] Author and Article Information
GB Sinclair

Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803-6413

Appl. Mech. Rev 57(4), 251-298 (Oct 12, 2004) (48 pages) doi:10.1115/1.1762503 History: Online October 12, 2004
Copyright © 2004 by ASME
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References

Figures

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Some singular configurations: a) three-point-bend test piece of fracture mechanics, b) section through a tire on a relatively rigid pavement, c) section through a piston with a ring pressed into a cylinder wall, d) section of a shaft with a stress-free keyway under torsion and lateral loading, e) adhesive butt joint under tension, f ) rough heavy block sticking to an elastic base, g) steel chisel just starting to indent a wooden slab, h) displacement shape functions as submodel boundary conditions
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Tensile crack in a hardening material
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Genesic Griffith crack configuration
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Pressurized crack configuration
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Barenblatt’s crack tip
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Schematic of cohesive stress-separation law
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Sketches of atomic or molecular “springs” at a sharp crack-tip for various boundary conditions: a) classical stress-free conditions, b) Barenblatt’s cohesive stress conditions, c) consistent cohesive stress conditions, d) alternate cohesive stress conditions
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Crack flank configurations when introducing cohesive stresses: a) mathematically sharp crack, b) stress-free crack, c) intervening crack
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Contact configurations: a) unloaded roller bearing, b) loaded roller bearing, c) journal bearing under load, d) piston ring pressing against a cylinder wall (deformation not indicated)
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Local contact configuration at C in Fig. 10b: coordinates and consequences of singularities
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Tensile stress ahead of a crack and displacements accompanying a small extension under symmetric (Mode I) loading
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Modes of deformation at a crack tip: a) Mode I, b) Mode II, c) Mode III
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An interface crack configuration
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Crack-tip models for the interface crack: a) contact zone model, b) crack opening angle model, c) intervening layer model with constant moduli, d) intervening layer model with continuously varying moduli
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Tensile stress ahead of a reentrant corner and displacements accompanying a small extension under symmetric loading
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K-controlled annulus at a crack tip
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Size dependence of fracture toughness
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Finite element grids for reentrant corner under tension: a) initial grid with 48 elements, b) first refinement with 192 elements
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Local arrangement of quarter-point elements at a crack tip (following ANSYS recommendations)
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Some limiting configurations for doublet states: a) concentrated moment, b) force doublet without a moment, c) center of compression

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