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On the Combined Effect of Pressure and Third Invariant on Yielding of Porous Solids With von Mises Matrix

[+] Author and Article Information
Oana Cazacu

e-mail: cazacu@reef.ufl.edu

Benoit Revil-Baudard

Department of Mechanical and Aerospace Engineering,
University of Florida,
REEF, 1350 N. Poquito Rd.,
Shalimar, FL 32579

Ricardo A. Lebensohn

Los Alamos National Laboratory,
MS G755,
Los Alamos, NM 87545

Mihail Gărăjeu

Université Aix-Marseille,
CNRS, M2P2 UMR7340,
Marseille 13397, France

1Corresponding author.

Manuscript received November 5, 2012; final manuscript received March 14, 2013; accepted manuscript posted March 21, 2013; published online August 22, 2013. Assoc. Editor: Younane Abousleiman.

J. Appl. Mech 80(6), 064501 (Aug 22, 2013) (5 pages) Paper No: JAM-12-1504; doi: 10.1115/1.4024074 History: Received November 05, 2012; Revised March 14, 2013; Accepted March 21, 2013

In this work it is shown that the exact plastic potential for porous solids with von Mises perfectly plastic matrix containing spherical cavities should involve a very specific coupling between the mean stress and the third invariant of the stress deviator. Furthermore, a new approximate plastic potential that preserves this key feature of the exact one is developed. Unlike all existing analytical criteria for porous solids with von Mises matrix, this new criterion displays a lack of symmetry with respect to both the hydrostatic and deviatoric axes. A full-field approach is also used to generate numerical gauge surfaces. These calculations confirm the aforementioned new features of the dilatational response.

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References

Gurson, A. L., 1977, “Continuum Theory of Ductile Rupture by Void Nucleation and Growth—Part I: Yield Criteria and Flow Rules for Porous Ductile Media,” ASME J. Eng. Mater., 99, pp. 2–15. [CrossRef]
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Monchiet, V., Charkaluk, E., and Kondo, D., 2011, “A Micromechanics-Based Modification of the Gurson Criterion by Using Eshelby-Like Velocity Fields,” Eur. J. Mech. A, 30, pp. 940–949. [CrossRef]
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Julien, J., Garajeu, M., and Michel, J.-C., 2011, “A Semi-Analytical Model for the Behavior of Saturated Viscoplastic Materials Containing Two Populations of Voids of Different Sizes,” Int. J. Solids. Struct., 48, pp. 1485–1498. [CrossRef]
Lebensohn, R. A., and Cazacu, O., 2012, “Effect of Single-Crystal Plastic Deformation Mechanisms on the Dilatational Plastic Response of Porous Polycrystals,” Int. J. Solids Struct., 49, pp. 3838–3852. [CrossRef]
Lebensohn, R. A., Idiart, M. I., Ponte Castaneda, P., and Vincent, P.-G., 2011, “Dilatational Viscoplasticity of Polycrystalline Solids With Intergranular Cavities,” Phil. Mag., 91, pp. 3038–3067. [CrossRef]
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Michel, J. C., Moulinec, H., and Suquet, P., 2000, “A Computational Method Based on Augmented Lagrangians and Fast Fourier Transforms for Composites With High Contrast,” Comp. Mod. Eng. Sci., 1(2), pp. 79–88.
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Figures

Grahic Jump Location
Fig. 1

Yield surface of the porous solid according to proposed criterion corresponding to axisymmetric stress states for which J3Σ≤0 (point line) and J3Σ≥0 (solid line), respectively, in comparison with Gurson [1] criterion (interrupted line) for the same porosity (f = 0.05)

Grahic Jump Location
Fig. 2

Zoom on the tensile quadrant of the yield surface according to the new yield criterion corresponding to axisymmetric stress states for which J3Σ≤0 (point line) and J3Σ≥0 (solid line), and Gurson [1] criterion (interrupted line), for porosity f = 0.05, within the following ranges: (a) (Σm≥0, 0.8 < Σe < (1−f)); (b) (Σm≥0, 0.3 < Σe < 0.8); (c) (Σm≥0, 0 < Σe < 0.5)

Grahic Jump Location
Fig. 3

Yield surfaces according to the new yield criterion (solid lines) and points belonging to gauge surfaces calculated with the FFT-based model for a periodic until cell (symbols). In all cases, porosity f = 0.05; axisymmetric stress states corresponding to J3Σ≤0 (interrupted line and squares, respectively) and J3Σ≥0 (solid line and circles, respectively).

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