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.

References

References
1.
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
.10.1115/1.3443401
2.
Tvergaard
,
V.
,
1981
, “
Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions
,”
Int. J. Fract.
,
17
, pp.
389
407
.10.1007/BF00036191
3.
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
.10.1016/j.euromechsol.2011.05.008
4.
Duva
,
J. M.
, and
Hutchinson
,
J. W.
,
1984
, “
Constitutive Potentials for Dilutely Voided Nonlinear Materials
,”
Mech. Mater.
,
3
, pp.
41
54
.10.1016/0167-6636(84)90013-9
5.
Thoré
,
P.
,
Pastor
,
F.
, and
Pastor
,
J.
,
2011
, “
Hollow Sphere Models, Conic Programming and Third Stress Invariant
,”
Eur. J. Mech. A
,
30
, pp.
63
71
.10.1016/j.euromechsol.2010.09.004
6.
Leblond
,
J.-B.
,
Perrin
,
G.
, and
Suquet
,
P.
,
1994
, “
Exact Results and Approximate Models for Porous Viscoplastic Solids
,”
Int. J. Plasticity
,
10
, pp.
213
225
.10.1016/0749-6419(94)90001-9
7.
Richelsen
,
A. B.
, and
Tvergaard
,
V.
,
1994
, “
Dilatant Plasticity or Upper Bound Estimates for Porous Ductile Solids
,”
Acta Metall. Mater.
,
42
, pp.
2561
2577
.10.1016/0956-7151(94)90198-8
8.
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
.10.1016/j.ijsolstr.2011.01.031
9.
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
.10.1016/j.ijsolstr.2012.08.019
10.
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
.10.1080/14786435.2011.561811
11.
Rice
,
J. R.
, and
Tracey
,
D. M.
,
1969
, “
On the Ductile Enlargement of Voids in Triaxial Stress Fields
,”
J. Mech. Phys. Solids
,
17
, pp.
201
217
.10.1016/0022-5096(69)90033-7
12.
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
.
13.
Lebensohn
,
R. A.
,
2001
, “
N-Site Modeling of a 3-D Viscoplastic Polycrystal Using Fast Fourier Transform
,”
Acta Mater.
,
49
, pp.
2723
2737
.10.1016/S1359-6454(01)00172-0
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