Abstract

Aiming at the potential high-temperature packaging material of the wide band gap semiconductors, experimental and theoretical analysis on the compressive properties of sintered nano-silver was performed. The viscoplastic properties of sintered nano-silver were investigated by compressive experiments with five loading rates, and the effects of loading rate on the ultimate strength and elastic modulus of sintered nano-silver were analyzed. According to the microstructure characteristics of sintered nano-silver, the damage framework including void volume fraction was developed by extending the Gurson–Tvergaard–Needleman model, and the mathematical model between Bonora damage law and void volume fraction was proposed, in which the internal void was assumed to be sphere and cube. A modified constitutive model including the damage model was developed based on the unified creep and plasticity theory for describing the compressive properties of sintered nano-silver. The accuracy of the proposed model was verified by comparing it with the experimental data.

References

1.
Chen
,
T. F.
, and
Siow
,
K. S.
,
2021
, “
Comparing the Mechanical and Thermal-Electrical Properties of Sintered Copper (Cu) and Sintered Silver (Ag) Joints
,”
J. Alloys Compd.
,
866
, p.
158783
.
2.
Woods-Robinson
,
R.
,
Han
,
Y. B.
,
Zhang
,
H. Y.
,
Ablekim
,
T.
,
Khan
,
I.
,
Persson
,
K. A.
, and
Zakutayev
,
A.
,
2020
, “
Wide Band gap Chalcogenide Semiconductors
,”
Chem. Rev.
,
120
(
9
), pp.
4007
4055
.
3.
He
,
G.
,
Yao
,
Y.
, and
Yuting
,
Y.
,
2021
, “
Size Effect on the Fracture of Sintered Porous Nano-silver Joints: Experiments and Weibull Analysis
,”
J. Alloys Compd.
,
863
, p.
158611
.
4.
Chen
,
C. T.
,
Zhang
,
Z.
,
Kim
,
D. J.
,
Zhang
,
B.
,
Tanioku
,
M.
,
Ono
,
T.
,
Matsumoto
,
K.
, and
Suganuma
,
K.
,
2019
, “
Interfacial Oxidation Protection and Thermal-Stable Sinter Ag Joining on Bare Cu Substrate by Single-Layer Graphene Coating
,”
Appl. Surf. Sci.
,
497
, p.
143797
.
5.
Chen
,
C. T.
, and
Suganuma
,
K.
,
2019
, “
Microstructure and Mechanical Properties of Sintered Ag Particles With Flake and Spherical Shape From Nano to Micro Size
,”
Mater. Des.
,
162
, pp.
311
321
.
6.
Gong
,
H.
,
Wu
,
H. C.
, and
Yao
,
Y.
,
2021
, “
Creep of Sintered Porous Micron-Silver: Nanoindentation Experiment and Theoretical Analysis
,”
J. Mater. Sci.
,
56
(
10
), pp.
18281
18299
.
7.
Gong
,
H.
,
Yao
,
Y.
, and
Zhao
,
F. F.
,
2020
, “
Corrosion Effects on Sintered Nano-silver Joints and the Secondary Biological Hazards
,”
J. Mater. Sci.: Mater. Electron.
,
31
, pp.
7649
7662
.
8.
Yao
,
Y.
, and
Gong
,
H.
,
2019
, “
Damage and Viscoplastic Behavior of Sintered Nano-silver Joints Under Shear Loading
,”
Eng. Fract. Mech.
,
222
, p.
106741
.
9.
Liu
,
Y.
, and
Wang
,
L.
,
2015
, “
Enhanced Stiffness, Strength and Energy Absorption for Co-continuous Composites With Liquid Filler
,”
Compos. Struct.
,
128
, pp.
274
283
.
10.
Liu
,
Y.
,
Schaedler
,
T. A.
,
Jacobsen
,
A. J.
, and
Chen
,
X.
,
2014
, “
Quasi-static Energy Absorption of Hollow Microlattice Structures
,”
Composites, Part B
,
67
, pp.
39
49
.
11.
Yu
,
D. J.
,
Chen
,
X.
,
Chen
,
G.
,
Lu
,
G. Q.
, and
Wang
,
Z. Q.
,
2009
, “
Applying Anand Model to Low-Temperature Sintered Nanoscale Silver Paste Chip Attachment
,”
Mater. Des.
,
30
(
10
), pp.
4574
4579
.
12.
Chen
,
G.
,
Zhang
,
Z. S.
,
Mei
,
Y. H.
,
Li
,
X.
,
Yu
,
D. J.
,
Wang
,
L.
, and
Chen
,
X.
,
2014
, “
Applying Viscoplastic Constitutive Models to Predict Ratcheting Behavior of Sintered Nanosilver Lap-Shear Joint
,”
Mech. Mater.
,
72
, pp.
61
71
.
13.
Cai
,
W.
,
Wang
,
P.
, and
Fan
,
J.
,
2020
, “
A Variable-Order Fractional Model of Tensile and Shear Behaviors for Sintered Nano-silver Paste Used in High Power Electronics
,”
Mech. Mater.
,
145
, p.
103391
.
14.
Su
,
Y. T.
,
Fu
,
G. C.
,
Liu
,
C. Q.
,
Zhang
,
K.
,
Zhao
,
L. G.
,
Liu
,
C. Y.
,
Liu
,
A.
, and
Song
,
J. N.
,
2021
, “
Thermo-elasto-plastic Phase-Field Modelling of Mechanical Behaviours of Sintered Nano-silver With Randomly Distributed Micro-pores
,”
Comput. Methods Appl. Mech. Eng.
,
378
, p.
113729
.
15.
Long
,
X.
,
Jia
,
Q.
,
Shen
,
Z.
,
Liu
,
M.
, and
Guan
,
C.
,
2021
, “
Strain Rate Shift for Constitutive Behaviour of Sintered Silver Nanoparticles Under Nanoindentation
,”
Mech. Mater.
,
158
, p.
103881
.
16.
Qian
,
C.
,
Sun
,
Z. C.
,
Fan
,
J. J.
,
Ren
,
Y.
,
Sun
,
B.
,
Feng
,
Q.
,
Yang
,
D. Z.
, and
Wang
,
Z. L.
,
2020
, “
Characterization and Reconstruction for Stochastically Distributed Void Morphology in Nanosilver Sintered Joints
,”
Mater. Des.
,
196
, p.
109079
.
17.
Xiao
,
G. H.
,
Yuan
,
G. Z.
,
Jia
,
C. N.
,
Yang
,
X. X.
,
Li
,
Z. G.
, and
Shu
,
X. F.
,
2014
, “
Strain Rate Sensitivity of Sn-3.0Ag-0.5Cu Solder Investigated by Nanoindentation
,”
Mater. Sci. Eng. A
,
613
, pp.
336
339
.
18.
Mcdowell
,
D. L.
,
Miller
,
M. P.
, and
Brooks
,
D. C.
,
1994
, “
A Unified Creep-Plasticity Theory for Solder Alloys
,”
ASTM International
,
1153
, pp.
42
59
.
19.
Mcclintock
,
F. A.
,
1971
, “Chapter 2. Plasticity Aspects of Fracture,”
Engineering Fundamentals and Environmental Effects
,
Academic Press
, pp.
41
225
.
20.
Rice
,
J. R.
, and
Tracey
,
D. M.
,
1969
, “
On the Ductile Enlargement of Voids in Triaxial Stress Fields
,”
J. Mech. Phys. Solids
,
17
(
3
), pp.
201
217
.
21.
Gurson
,
A. L.
,
1977
, “
Continuum Theory of Ductile Rupture by Void Nucleation and Growth. 1. Yield Criteria and Flow Rules for Porous Ductile Media
,”
ASME J. Eng. Mater. Technol.
,
99
(
1
), pp.
2
15
.
22.
Tvergaard
,
V.
,
1981
, “
Influence of Voids on Shear Band Instabilities Under Plane-Strain Conditions
,”
Int. J. Fract.
,
17
(
4
), pp.
389
407
.
23.
Tvergaard
,
V.
,
1982
, “
On Localization in Ductile Materials Containing Spherical Voids
,”
Int. J. Fract.
,
18
(
4
), pp.
237
252
.
24.
Tvergaard
,
V.
, and
Needleman
,
A.
,
1984
, “
Analysis of the Cup-Cone Fracture in a Round Tensile Bar
,”
Acta Metall.
,
32
(
1
), pp.
157
169
.
25.
Bonora
,
N.
,
1997
, “
A Nonlinear CDM Model for Ductile Failure
,”
Eng. Fract. Mech.
,
58
(
1–2
), pp.
11
28
.
26.
Siow
,
K. S.
,
2012
, “
Mechanical Properties of Nano-silver Joints as Die Attach Materials
,”
J. Alloys Compd.
,
514
, pp.
6
19
.
27.
Gong
,
H.
,
Wu
,
H.
,
Guo
,
H.
, and
Yao
,
Y.
,
2021
, “
Compressive Properties and Microstructure Evolution of Sintered Nano-silver
,”
J. Phys. Conf. Ser.
,
2011
(
1
), p.
012061
.
28.
Yao
,
Y.
,
He
,
X.
,
Keer
,
L. M.
, and
Fine
,
M. E.
,
2015
, “
A Continuum Damage Mechanics-Based Unified Creep and Plasticity Model for Solder Materials
,”
Acta Mater.
,
83
, pp.
160
168
.
29.
Yao
,
Y.
,
Keer
,
L. M.
, and
Fine
,
M. E.
,
2010
, “
Modeling the Failure of Intermetallic/Solder Interfaces
,”
Intermetallics
,
18
(
8
), pp.
1603
1611
.
30.
Kossakowski
,
P. G.
,
2012
, “
Prediction of Ductile Fracture for S235JR Steel Using the Stress Modified Critical Strain and Gurson-Tvergaard-Needleman Models
,”
J. Mater. Civ. Eng.
,
24
(
12
), pp.
1492
1500
.
31.
Xue
,
L.
,
2008
, “
Constitutive Modeling of Void Shearing Effect in Ductile Fracture of Porous Materials
,”
Eng. Fract. Mech.
,
75
(
11
), pp.
3343
3366
.
32.
Nahshon
,
K.
, and
Hutchinson
,
J. W.
,
2008
, “
Modification of the Gurson Model for Shear Failure
,”
Eur. J. Mech. A. Solids
,
27
(
1
), pp.
1
17
.
33.
Wu
,
H. F.
,
Zhuang
,
X. C.
, and
Zhao
,
Z.
,
2022
, “
Extended GTN Model for Predicting Ductile Fracture Under a Broad Range of Stress States
,”
Int. J. Solids Struct.
,
239–240
, p.
111452
.
34.
Yang
,
X.
,
Li
,
Y. Z.
,
Jiang
,
W.
,
Duan
,
M. G.
,
Chen
,
D.
, and
Li
,
B.
,
2021
, “
Ductile Fracture Prediction of Additive Manufactured Ti6Al4V Alloy Based on an Extended GTN Damage Model
,”
Eng. Fract. Mech.
,
256
, p.
107989
.
35.
Chu
,
C. C.
, and
Needleman
,
A.
,
1980
, “
Void Nucleation Effects in Biaxially Stretched Sheets
,”
ASME J. Eng. Mater. Technol.
,
102
(
3
), pp.
249
256
.
36.
Oral
,
A.
,
Anlas
,
G.
, and
Lambros
,
J.
,
2012
, “
Determination of Gurson-Tvergaard-Needleman Model Parameters for Failure of a Polymeric Material
,”
Int. J. Damage Mech.
,
21
(
1
), pp.
3
25
.
37.
Malcher
,
L.
,
Andrade Pires
,
F.
, and
César de Sá
,
J. M. A.
,
2014
, “
An Extended GTN Model for Ductile Fracture Under High and Low Stress Triaxiality
,”
Int. J. Plast.
,
54
, pp.
193
228
.
38.
Bonora
,
N.
, and
Newaz
,
G. M.
,
1998
, “
Low Cycle Fatigue Life Estimation for Ductile Metals Using a Nonlinear Continuum Damage Mechanics Model
,”
Int. J. Solids Struct.
,
35
(
16
), pp.
1881
1894
.
39.
Kachanov
,
M.
,
1958
, “
On the Time to Failure Under Creep Conditions
,”
Izv. Akad. Nauk. USSR. Otd. Tekhn. Nauk.
,
8
, pp.
26
31
.
40.
Bataille
,
J.
, and
Kestin
,
J.
,
1979
, “
Irreversible Processes and Physical Interpretation of Rational Thermodynamics
,”
J. Non-Equilib. Thermodyn.
,
4
(
4
), pp.
229
258
.
41.
Lemaitre
,
J.
,
1996
,
A Course on Damage Mechanics
,
Springer
,
Berlin
.
42.
Yao
,
Y.
,
An
,
R.
, and
Long
,
X.
,
2017
, “
Effect of Electric Current on Fracture and Constitutive Behavior of SN-Ag-Cu Solder Joints
,”
Eng. Fract. Mech.
,
171
, pp.
85
97
.
43.
Carr
,
J.
,
Milhet
,
X.
,
Gadaud
,
P.
,
Boyer
,
S. A. E.
,
Thompson
,
G. E.
, and
Lee
,
P.
,
2015
, “
Quantitative Characterization of Porosity and Determination of Elastic Modulus for Sintered Micro-Silver Joints
,”
J. Mater. Process. Technol.
,
225
, pp.
19
23
.
44.
Ribeiro
,
J.
,
Santiago
,
A.
, and
Rigueiro
,
C.
,
2016
, “
Damage Model Calibration and Application for S355 Steel
,”
Procedia Struct. Integrity
,
2
, pp.
656
663
.
45.
Chaboche
,
J. L.
,
2008
, “
A Review of Some Plasticity and Viscoplasticity Constitutive Theories
,”
Int. J. Plast.
,
24
(
10
), pp.
1642
1693
.
46.
Long
,
X.
,
He
,
X.
, and
Yao
,
Y.
,
2017
, “
An Improved Unified Creep-Plasticity Model for SnAgCu Solder Under a Wide Range of Strain Rates
,”
J. Mater. Sci.
,
52
(
10
), pp.
6120
6137
.
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