Constitutive modeling and related numerical issues in conjunction with the macroscopic analysis and simulation of cold compaction and subsequent solid phase sintering of hard-metal are discussed. A key ingredient is the concept of sintering stress, which is derived as a thermodynamically consistent dissipative stress, based on a simplified microstructural arrangement with spherical pores. In order to account for the temperature effect on the rate-dependent response during the sintering phase, the concept of viscoplastic admissibility is employed as part of the model framework. A generic class of pressure-sensitive models is considered, and the particular model chosen for calibration is based on quasistatic and dynamic yield surfaces that are elliptic in the meridian planes of the stress space. Implicit integration is used for the pertinent evolution equations. The paper is concluded by a numerical investigation of the compaction and sintering of a specimen, whereby the model is calibrated using experimental data from free and uniaxially loaded sintering experiments (within a joint research project).

Issue Section:
Technical Papers
Keywords:
cermets, powder metallurgy, sintering, stress analysis, internal stresses, density, digital simulation, modelling, viscoplasticity, cold working, yield stress, porous materials, porosity
Topics:
Compacting, Sintering, Stress, Modeling, Temperature
1.
Shima
,
S.
, and
Oyane
,
M.
,
1976
, “
Plasticity Theory for Porous Metals
,”
Int. J. Mech. Sci.
,
18
, pp.
285
–
291
.
2.
Weber, G. G., and Brown, S. B., 1976, “Simulation of the Compaction of Powder Components,” Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge.
3.
Fleck
,
N. A.
,
Kuhn
,
L.
, and
McMeeking
,
R. M.
,
1992
, “
Yielding of Metal Powder Bonded by Isolated Contacts
,”
J. Mech. Phys. Solids
,
40
(
5
), pp.
1139
–
1162
.
4.
Fleck
,
J. M.
,
1995
, “
On the Cold Compaction of Powders
,”
J. Mech. Phys. Solids
,
43
(
9
), pp.
1409
–
1431
.
5.
Oliver
,
J.
,
Oller
,
S.
, and
Cante
,
J. C.
,
1996
, “
A Plasticity Model for Simulation of Industrial Powder Compaction Processes
,”
Int. J. Solids Struct.
,
33
, pp.
3161
–
3178
.
6.
Reid
,
C. R.
,
1994
, “
Numerical Simulation of Free Shrinkage Using a Continuum Theory for Sintering
,”
Powder Technol.
,
81
, pp.
287
–
291
.
7.
Svoboda
,
A.
,
Ha¨ggblad
,
H.-A˚.
, and
Na¨sstro¨m
,
M.
,
1996
, “
Simulation of Hot Isostatic Pressing of Metal Powder Components to Near Net Shape
,”
Eng. Comput.
,
13
(
5
), pp.
13
–
37
.
8.
Brandt
,
J.
, and
Nilsson
,
L.
,
1998
, “
Fe-Simulation of Compaction and Solid State Sintering of Cemented Carbides
,”
Mech. Cohesive-Frict. Mater.
,
3
(
2
), pp.
181
–
205
.
9.
Redanz
,
P.
, 1998, “Numerical Modelling of Cold Compaction of Metal Powder,” Journal of Mechanical Sciences, 40(11), pp. 1175–1189.
10.
Reid
,
C. R.
, and
Oakberg
,
R. G.
,
1990
, “
A Continuum Theory for the Mechanical Response of Materials to the Thermodynamic Stress of Sintering
,”
Mech. Mater.
,
10
, pp.
203
–
213
.
11.
Riedel, H., 1990, “A Constitutive Model for the Finite-Element Simulation of Sintering-Distortion and Stresses,” Messing et al. ed., Ceramic Powder Ceramics III, American Ceramic Society, Westerville, pp. 619–630.
12.
Shinagawa
,
K.
,
1996
, “
Finite Element Simulation of Sintering Process (Microscopic Modeling of Powder Compacts and Constitutive Equation for Sintering)
,”
JSME Int. J., Ser. A
,
39
, pp.
565
–
572
.
13.
Svoboda
,
J.
,
Riedel
,
H.
, and
Gaebel
,
R.
,
1996
, “
Model for Liquid Phase Sintering
,”
Acta Mater.
,
44
, pp.
3215
–
3226
.
14.
Xu
,
K.
, and
Mehrabadi
,
M. M.
,
1997
, “
Micromechanical Model for the Initial Rearrangement Stage of Liquid Phase Sintering
,”
Mech. Mater.
,
25
, pp.
137
–
157
.
15.
McMeeking
,
R. M.
, and
Kuhn
,
L. T.
,
1992
, “
A Diffusional Creep Law for Powder Compacts
,”
Acta Metall.
,
40
, pp.
961
–
969
.
16.
Cocks
,
A. C. F.
, and
Du
,
Z.-Z.
,
1993
, “
Pressureless Sintering and Hiping of Inhomogeneous Ceramic Compacts
,”
Acta Metall. Mater.
,
41
, pp.
2113
–
2126
.
17.
Riedel
,
H.
,
Kozak
,
V.
, and
Svoboda
,
J.
,
1994
, “
Densification and Creep in the Final Stage of Sintering
,”
Acta Metall. Mater.
,
42
, pp.
3093
–
3103
.
18.
Perzyna
,
P.
,
1966
, “
Fundamental Problems in Viscoplasticity
,”
Adv. Appl. Mech.
,
9
, pp.
243
–
377
.
19.
Johansson
,
M.
, and
Runesson
,
K.
,
1997
, “
Viscoplasticity with Dynamic Yield Surface Coupled to Damage
,”
Computational Mechanics
,
20
, pp.
53
–
59
.
20.
Simo
,
J. C.
, and
Miehe
,
C.
,
1992
, “
Associative Coupled Thermoplasticity at Finite Strains: Formulation, Numerical Analysis and Implementation
,”
Comput. Methods Appl. Mech. Eng.
,
98
(
1
), pp.
41
–
104
.
21.
Simo
,
J. C.
, and
Ortiz
,
M.
,
1985
, “
Unified Approach to Finite Deformation Elastoplastic Analysis Based on the Use of Hyperelastic Constitutive Equations
,”
Comput. Methods Appl. Mech. Eng.
,
49
(
2
), pp.
221
–
245
.
22.
Haglund, S. A., A˚gren, J., Lindskog, P., and Uhrenius, B., 1996, “Modelling of Solid State Sintering of Cemented Carbides,” R. G. Cornwall, R. M. German, and G. L. Messing, eds, Sintering 1995-1996, Marcel Dekker, Westerville.
23.
Lindskog, P., 1995, “Mechanical Properties of Hard Metal During Sintering,” Technical Memo, Sandvik Coromant AB.
24.
Redanz, P., and Tvergaard, V., 1998, “Analysis of Shear Band Instabilities in Sintered Metals,” Int. J. Solids Struct., submitted.
25.
Riedel
,
H.
, and
Sun
,
D.-Z.
, 1992, “Simulation of Die Pressing and Sintering of Powder Metals, Hard Metals and Ceramics,” Numerical Methods in Industrial Forming Processing, pp. 883–886.
26.
Ma¨hler, L., Ekh, M., and Runesson, K., 1999, “A Class of Thermo-Hyperelastic-Viscoplastic Models for Porous Materials: Theory and Numerics,” Report F218, Department of Solid Mechanics, Chalmers University of Technology, SE-412 96 Go¨teborg, Sweden.
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