A statically admissible solution for a perfectly plastic material in plane stress is presented for the mode I crack problem. The yield condition employed is an alternative type first proposed by von Mises in order to approximate his original yield condition for plane stress while eliminating most of the elliptic region as pertaining to partial differential equations. This yield condition is composed of two intersecting parabolas rather than a single ellipse in the principal stress space. The attributes of this particular solution of the mode I problem over that previously obtained are that it contains neither stress discontinuities nor compressive stresses anywhere in the field.
A Plane Stress Perfectly Plastic Mode I Crack Solution With Continuous Stress Field
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, July 21, 2003; final revision, August 13, 2004. Associate Editor: K. Ravi-Chandar. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Unger, D. J. (February 1, 2005). "A Plane Stress Perfectly Plastic Mode I Crack Solution With Continuous Stress Field ." ASME. J. Appl. Mech. January 2005; 72(1): 62–67. https://doi.org/10.1115/1.1828061
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