A Complete Perfectly Plastic Solution for the Mode I Crack Problem Under Plane Stress Loading Conditions

[+] Author and Article Information
David J. Unger

Department of Mechanical and Civil Engineering, University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722du2@Evansville.edu

J. Appl. Mech 74(3), 586-589 (May 26, 2006) (4 pages) doi:10.1115/1.2338055 History: Received July 11, 2005; Revised May 26, 2006

A continuous stress field for the mode I crack problem for a perfectly plastic material under plane stress loading conditions has been obtained recently. Here, a kinematically admissible velocity field is introduced, which is compatible with the continuous stress field obtained earlier. By associating these two fields together, it is shown that they constitute a complete solution for the uncontained plastic flow problem around a finite length internal crack, having a positive rate of plastic work. The yield condition employed is an alternative criterion first proposed by Richard von Mises in order to approximate the plane stress Huber-Mises yield condition, which is elliptical in shape, to one that is composed of two intersecting parabolas in the principal stress plane.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

A comparison of the Huber-Mises yield locus (ellipse) with the parabolic Mises yield locus (parabolas). After (3).

Grahic Jump Location
Figure 2

Stresses of the perfectly plastic plane stress mode I crack problem under the parabolic Mises yield condition (2)

Grahic Jump Location
Figure 3

Perfectly plastic velocity field for the plane stress mode I crack problem under the parabolic Mises yield condition



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