0
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

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

## Abstract

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.

<>

## Figures

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

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.

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.

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.

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

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.

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections