The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The matrix material is first assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion suggested in Liao et al. 1997, “Approximate Yield Criteria for Anisotropic Porous Ductile Sheet Metals,” Mech. Mater., pp. 213–226. Three fitting parameters are suggested for the closed-form yield criterion to fit the results based on the modified yield criterion to those of finite element computations. When the strain hardening of the matrix is considered, the computational results of the macroscopic stress-strain behavior are in agreement with those based on the modified anisotropic Gurson’s yield criterion under uniaxial and equal biaxial tensile loading conditions.

1.
Gurson
,
A. L.
,
1977
, “
Continuum theory of ductile rupture by void growth: part I—yield criteria and flow rules for porous ductile media
,”
ASME J. Eng. Mater. Technol.
,
99
, p.
2
2
.
2.
Yamamoto
,
H.
,
1978
, “
Conditions for shear localization in the ductile fracture of void-containing materials
,”
Int. J. Fract.
,
14
, p.
347
347
.
3.
Needleman
,
A.
, and
Triantafyllidis
,
N.
,
1978
, “
Void growth and local necking in biaxial stretched sheets
,”
ASME J. Eng. Mater. Technol.
,
100
, p.
164
164
.
4.
Saje
,
M.
,
Pan
,
J.
, and
Needleman
,
A.
,
1982
, “
Void nucleation effects on shear localization in porous plastic solids
,”
Int. J. Fract.
,
19
, p.
163
163
.
5.
Tvergaard
,
V.
,
1981
, “
Influence of voids on shear band instabilities under plane strain conditions
,”
Int. J. Fract.
,
17
, p.
389
389
.
6.
Tvergaard
,
V.
,
1982
, “
On localization in ductile materials containing spherical voids
,”
Int. J. Fract.
,
18
, p.
237
237
.
7.
Pan
,
J.
,
Saje
,
M.
, and
Needleman
,
A.
,
1983
, “
Localization of deformation in rate sensitive porous plastic solids
,”
Int. J. Fract.
,
21
, p.
261
261
.
8.
Tvergaard
,
V.
, and
Needleman
,
A.
,
1984
, “
Analysis of the cup-cone fracture in a round tensile bar
,”
Acta Metall.
,
32
, p.
157
157
.
9.
Hill
,
R.
,
1948
, “
A theory of the yielding and plastic flow of anisotropic metals
,”
Proc. R. Soc. London, Ser. A
,
A193
, p.
281
281
.
10.
Hill
,
R.
,
1979
, “
Theoretical plasticity of textured aggregates
,”
Math. Proc. Cambridge Philos. Soc.
,
85
, p.
179
179
.
11.
Gotoh
,
M.
,
1977
, “
A theory of plastic anisotropy based on a yield function of fourth order (plane stress state)
,”
Int. J. Mech. Sci.
,
19
, p.
505
505
.
12.
Budianski, B., 1984, “Anisotropic plasticity of plane-isotropic sheets,” Dvorak, G. J. and Shield, R. T. eds., Mechanics of Material Behavior, Elsevier, Amsterdam, p. 15.
13.
Logan
,
R. W.
, and
Hosford
,
W. F.
,
1980
, “
Upper-bound anisotropic yield locus calculations assuming 〈111〉 pencil glide
,”
Int. J. Mech. Sci.
,
22
, p.
419
419
.
14.
Bassani
,
J. L.
,
1977
, “
Yield characterization of metals with transversely isotropic plastic properties
,”
Int. J. Mech. Sci.
,
19
, p.
651
651
.
15.
Barlat
,
F.
,
Lege
,
D. J.
, and
Brem
,
J. C.
,
1991
, “
A six-component yield function for anisotropic materials
,”
Int. J. Plast.
,
7
, p.
693
693
.
16.
Barlat
,
F.
,
Maeda
,
Y.
,
Chung
,
K.
,
Yanagawa
,
M.
,
Brem
,
J. C.
,
Hayashida
,
Y.
,
Lege
,
D. J.
,
Matsui
,
K.
,
Murtha
,
S. J.
,
Hattori
,
S.
,
Becker
,
R. C.
, and
Makosey
,
S.
,
1997
, “
Yield function development for aluminum alloy sheets
,”
J. Mech. Phys. Solids
,
45
, p.
1727
1727
.
17.
Liao
,
K.-C.
,
Pan
,
J.
, and
Tang
,
S. C.
,
1997
, “
Approximate yield criteria for anisotropic porous ductile sheet metals
,”
Mech. Mater.
26
, p.
213
213
.
18.
Chen, B., Wu, P. D., MacEwen, S. R., Xia, Z. C., Tang, S. C., and Huang, Y., 2000, “Dilational plasticity for porous anisotropic aluminum sheet based on Barlat et al.’s model,” Presented at SAE 2000 World Congress, Detroit, MI, Mar. 6–9.
19.
Hom
,
C. L.
, and
McMeeking
,
R. M.
,
1989
, “
Void growth in elastic-plastic materials
,”
ASME J. Appl. Mech.
,
56
, p.
309
309
.
20.
Jeong
,
H.-Y.
, and
Pan
,
J.
,
1995
, “
A macroscopic constitutive law for porous solids with pressure-sensitive matrices and its implications to plastic flow localization
,”
Int. J. Solids Struct.
,
32
, p.
3669
3669
.
21.
Liao
,
K.-C
,
Friedman
,
P. A.
,
Pan
,
J.
, and
Tang
,
S. C.
,
1998
, “
Texture development and plastic anisotropy of B. C. C. strain hardening sheet metals
,”
Int. J. Solids Struct.
,
35
, p.
5205
5205
.
22.
Hibbitt, H. D., Karlsson, B. I., and Sorensen, E. P., 1998, ABAQUS User Manual, Version 5–8.
23.
Pardoen
,
T.
, and
Hutchinson
,
J. W.
,
2000
, “
An extended model for void growth and coalescence
,”
J. Mech. Phys. Solids
,
48
, p.
2467
2467
.
24.
Huang
,
H.-M.
,
Pan
,
J.
, and
Tang
,
S. C.
,
2000
, “
Failure prediction in anisotropic sheet metals under forming operation with consideration of rotating principal stretch directions
,”
Int. J. Plast.
,
16
, p.
611
611
.
25.
Huang, H.-M., Pan, J., and Tang, S. C., 2001, “Failure prediction in anisotropic sheet metals containing voids under biaxial straining conditions with pre-bending/unbending,” Int. J. Plast.
26.
Chien, W. Y., Huang, H.-M., Pan, J., and Tang, S. C., 2000, “Approximate yield criterion for anisotropic porous sheet metals and its applications to failure prediction of sheet metals under forming processes,” to appear in Multiscale Deformation and Fracture in Materials and Structures, The James Rice 60th Anniversary Volume, T.-J. Chuang and J. W. Rudnicki, eds., Kluwer Academic Publisher, The Netherlands.
27.
Tandon
,
G. P.
, and
Weng
,
G. J.
,
1988
, “
A theory of particle-reinforced plasticity
,”
ASME J. Appl. Mech.
,
55
, p.
126
126
.
You do not currently have access to this content.