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Research Papers

On the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material

[+] Author and Article Information
Dorinamaria Carka

Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, 210 East 24th Street, C0600 Austin, TX 78712-0235

Chad M. Landis

Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, 210 East 24th Street, C0600 Austin, TX 78712-0235landis@mail.utexas.edu

J. Appl. Mech 78(1), 011006 (Oct 12, 2010) (6 pages) doi:10.1115/1.4001748 History: Received February 01, 2010; Revised April 16, 2010; Posted May 11, 2010; Published October 12, 2010

The path-dependence of the J-integral is investigated numerically via the finite-element method, for a range of loadings, Poisson’s ratios, and hardening exponents within the context of J2-flow plasticity. Small-scale yielding assumptions are employed using Dirichlet-to-Neumann map boundary conditions on a circular boundary that encloses the plastic zone. This construct allows for a dense finite-element mesh within the plastic zone and accurate far-field boundary conditions. Details of the crack tip field that have been computed previously by others, including the existence of an elastic sector in mode I loading, are confirmed. The somewhat unexpected result is that J for a contour approaching zero radius around the crack tip is approximately 18% lower than the far-field value for mode I loading for Poisson’s ratios characteristic of metals. In contrast, practically no path-dependence is found for mode II. The applications of T- or S-stress, whether applied proportionally with the K-field or prior to K, have only a modest effect on the path-dependence.

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Figures

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Figure 1

Plastic zone shapes for mode I, mode II, and mixed-mode loading with KI=KII for an elastic-perfectly plastic material with ν=0.3 and S=T=0

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Figure 3

Values for the J-integral for a circular contour of radius r computed by the domain integral method near a crack tip under mode I loading in an elastic-perfectly plastic material with ν=0.3. The markers correspond to different points along the load history and different sizes of the plastic zone relative to the minimum radial dimension of the elements surrounding the crack tip.

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Figure 4

The effects of the strain hardening exponent in mode I and the mode-mix for perfect plasticity on the relative decrease in J at the crack tip. As for the previous results, ν=0.3 and S=T=0.

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Figure 5

The effects of Poisson’s ratio on the relative decrease in J at the crack tip for pure mode I loading in an elastic-perfectly plastic material

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Figure 6

The effects of the nonsingular S- and T-stresses on the relative decrease in J at the crack tip for pure mode I loading in an elastic-perfectly plastic material with ν=0.3. The dashed lines represent solutions when the nonsingular stresses are applied proportionally with KI and the solid curves are for when S or T is applied prior to KI.

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Figure 2

Angular variations in the Cartesian components of the stress around a crack tip in an elastic-perfectly plastic material with ν=0.3 and S=T=0 for (a) mode I, (b) mode II, and (c) KI=KII. Solid lines are the solutions for flow theory and dashed lines are for deformation theory.

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