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RESEARCH PAPERS

Asymptotic Crack-Tip Fields in Perfectly Plastic Solids Under Mixed Mode II/III Loading Conditions

[+] Author and Article Information
J. Pan, P.-C. Lin

Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109

J. Pressure Vessel Technol 129(4), 664-669 (Aug 15, 2006) (6 pages) doi:10.1115/1.2767355 History: Received December 21, 2005; Revised August 15, 2006

In this paper, governing equations and solutions for asymptotic singular and nonsingular crack-tip sectors in perfectly plastic materials are first summarized under combined in-plane and out-of-plane shear loading conditions. The crack-tip fields under mixed mode II/III loading conditions are then investigated. An assembly of crack-tip sectors is adopted with stress discontinuities along the border of the two constant stress sectors. The solutions of the crack-tip fields under pure mode II, mixed mode II/III, and nearly pure mode III loading conditions are presented. The trends of the angular variations of the mixed mode II/III crack-tip stresses agree with those of the available computational analysis and the asymptotic analysis for low strain hardening materials. The pure mode II crack-tip stresses are similar to those of Hutchinson, and the nearly pure mode III stresses are similar to those of the pure mode III crack-tip field of Rice.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

A crack and the associated coordinate systems

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Figure 2

A possible assembly of plastic sectors for the mixed mode II/III crack-tip field

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Figure 3

The angular variations of the crack-tip stresses under pure mode II loading conditions (M23p=1) based on the crack-tip field shown in Fig. 2

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Figure 4

The angular variations of the crack-tip stresses for M23p=0.5 based on the crack-tip field shown in Fig. 2

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Figure 5

The angular variations of the crack-tip stresses under nearly pure mode III loading conditions (M23p=0.000001) based on the crack-tip field shown in Figure 2

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Figure 6

Pure mode II crack-tip field of Hutchinson (14). (a) The assembly of plastic sectors; (b) the angular variations of the crack-tip stresses.

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Figure 7

Pure mode III crack-tip field of Rice (17). (a) The assembly of plastic sectors; (b) the angular variations of the crack-tip stresses.

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