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TECHNICAL PAPERS

A Plane Stress Perfectly Plastic Mode I Crack Solution With Continuous Stress Field

[+] Author and Article Information
David J. Unger

Department of Mechanical and Civil Engineering, University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722 e-mail: du2@evansville.edu

J. Appl. Mech 72(1), 62-67 (Feb 01, 2005) (6 pages) doi:10.1115/1.1828061 History: Received July 21, 2003; Revised August 13, 2004; Online February 01, 2005
Copyright © 2005 by ASME
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References

Hutchinson,  J. W., 1968, “Plane Stress and Strain Fields at the Crack Tip,” J. Mech. Phys. Solids, 16, pp. 337–347.
Unger, D. J., 2001, Analytical Fracture Mechanics, Dover Publications, Mineola, NY.
von Mises, R., 1949, “Three Remarks on the Theory of the Ideal Plastic Body,” Reissner Anniversary Volume, Contributions to Applied Mechanics, J. W. Edwards, Publisher, Inc., Ann Arbor, MI, pp. 415–429.
Unger,  D. J., 1990, “Analytic Continuation of Stresses across a Mode I Elastoplastic Interface,” Eng. Fract. Mech., 36, pp. 763–776.
Unger,  D. J., 1998, “Stress across an Elastoplastic Boundary of a Mode I Crack Parabolic to Hyperbolic Plasticity Transition,” Theor. Appl. Fract. Mech., 30, pp. 195–208.
Zwillinger, D., 1989, Handbook of Differential Equations, Academic Press, San Diego.
Freudenthal, A. M., and Geiringer, H., 1958, “The Mathematical Theories of the Inelastic Continuum,” Elasticity and Plasticity, Handbuch der Physik, VI , Flügge, S., ed., Springer-Verlag, Berlin, pp. 229–433.
Geiringer, H., 1973, “Ideal Plasticity,” Mechanics of Solids III, Handuch der Physik, VIa/3 , Truesdell, C., ed., Springer-Verlag, Berlin, pp. 403–533.
Dong,  P., and Pan,  J., 1990, “Plane-Stress Mixed-Mode Near-Tip Fields in Elastic Perfectly Plastic Solids,” Eng. Fract. Mech., 37, pp. 43–57.
Shih, C. F., 1973, Elastic-Plastic Analysis of the Combined Mode Crack Problem, PhD thesis, Harvard University, Cambridge.
Narasimhan,  R., and Rosakis,  A. J., 1988, “A Finite Element Analysis of Small-Scale Yielding near a Stationary Crack under Plane Stress,” J. Mech. Phys. Solids, 36, pp. 77–117.
Sham,  T.-L., and Hancock,  J. W., 1999, “Mode I Crack Tips with Incomplete Crack Tip Plasticity in Plane Stress,” J. Mech. Phys. Solids, 47, pp. 2011–2027.
Rice, J. R., 1982, “Elastic-Plastic Crack Growth,” Mechanics of Solids, H. G., Hopkins, and M. J., Sewell, eds., Pergamon Press, Oxford, pp. 539–562.
Broberg, K. B., 1999, Cracks and Fracture, Academic Press, San Diego.
Narasimhan,  R., Rosakis,  A. J., and Hall,  J. F., 1987, “A Finite Element Study of Stable Crack Growth under Plane Stress Conditions: Part I-Elastic Perfectly-Plastic Solids,” ASME J. Appl. Mech., 54, pp. 838–845.

Figures

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The von Mises yield condition (elliptically shaped) with inscribed Tresca yield condition. After 3.
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The alternative von Mises yield condition (parabolically shaped) compared to the Tresca yield condition. After 3.
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Predicted elastic-plastic boundaries around a crack tip for different yield criteria using the elastic stress field
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Slip lines across an elastic-plastic boundary under the Tresca yield condition. After 245.
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Characteristics for plane stress mode I crack under the von Mises yield condition (elliptically shaped). After 1.
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Stress field for plane stress mode I crack under the von Mises yield condition (elliptically shaped). After 1.
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Characteristics for plane stress mode I crack under the alternative von Mises yield condition (parabolically shaped)
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Stress field for plane stress mode I crack under alternative von Mises yield condition (parabolically shaped)

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