Most solders used in electronic systems have low-melting temperature and hence experience significant amount of creep deformation throughout their life-cycle because typical operational and test conditions represent high homologous temperature. Phenomenological and mechanistic models used in the literature for predicting creep response of both bulk and grain scale specimens are reviewed in this paper. The phenomenological models reviewed in this paper are based on purely empirical observations of the creep deformation behavior or derived from qualitative interpretation of the underlying microscale mechanisms. These models have some intrinsic disadvantages since they do not have explicit mechanistic dependence on microstructural features. Therefore, the constitutive relations derived using the above models are difficult to extrapolate beyond the test conditions. This paper also reviews how some of the above limitations can be mitigated by using mechanistic or microstructurally motivated models. Mechanistic models are capable of estimating the material creep response based on the detailed physics of the underlying mechanisms and microstructure. The microstructure and constitutive response of the most popular family of lead-free solders, namely, SnAgCu (SAC) solders, are significantly different from those of previously used eutectic Sn37Pb solder. The creep deformation in Sn37Pb solder occurs primarily through diffusion-assisted grain-boundary sliding. In SAC solder joints, dislocation-based creep deformation mechanisms such as glide, climb, detachment, and cross-slip appear to be the dominant mechanisms in coarse-grained joints. Mechanistic creep models are therefore based on the deformation mechanisms listed above.

References

1.
Shang
,
J. K.
,
Zeng
,
Q. L.
,
Zhang
,
L.
, and
Zhu
,
Q. S.
, “
Mechanical Fatigue of Sn-Rich Pb-Free Solder Alloys
,”
J. Mater. Sci. Mater. Electron.
,
18
(
1–3
), pp.
211
227
.
2.
Mattila
,
T. T.
, and
Kivilahti
,
J. K.
,
2012
, “
The Failure Mechanism of Recrystallization—Assisted Cracking of Solder Interconnections
,”
Recrystallization
,
K.
Sztwiertnia
, ed.,
InTech.
,
Chennai, India
.
3.
Reid
,
M.
,
Punch
,
J.
,
Collins
,
M.
, and
Ryan
,
C.
,
2008
, “
Effect of Ag Content on the Microstructure of Sn-Ag-Cu Based Solder Alloys
,”
Soldering Surf. Mount Technol.
,
20
(
4
), pp.
3
8
.
4.
Kim
,
H.
,
Zhang
,
M.
,
Kumar
,
C. M.
,
Suh
,
D.
,
Liu
,
P.
,
Kim
,
D.
,
Xie
,
M.
, and
Wang
,
Z.
,
2007
, “
Improved Drop Reliability Performance With Lead Free Solders of Low Ag Content and Their Failure Modes
,”
57th Electronic Components and Technology Conference
,
ECTC’07
, Reno, NV, May 29–June, 1, pp.
962
967
.
5.
Evans
,
R. W.
, and
Wilshire
,
B.
,
1985
, “
Creep of Metals and Alloys
,” Institute of Metals, London, UK.
6.
Viswanathan
,
R.
,
1989
,
Damage Mechanisms and Life Assessment of High-Temperature Components
,
ASM International
,
Novelty, OH
.
7.
Mott
,
N. F.
, and
Nabarro
,
F. R. N.
,
1948
, “
Dislocation Theory and Transient Creep
,”
Physical Society Bristol Conference Report
, pp.
1
19
.
8.
Garofalo
,
F.
,
1965
,
Fundamentals of Creep and Creep-Rupture in Metals
,
Macmillan
,
New York
.
9.
Roesler
,
J.
,
Harders
,
H.
, and
Baeker
,
M.
,
2010
,
Mechanical Behaviour of Engineering Materials: Metals, Ceramics, Polymers, and Composites
,
Springer
,
Berlin
.
10.
Laks
,
H.
,
Wiseman
,
C. D.
,
Sherby
,
O. D.
, and
Dorn
,
J. E.
,
1957
, “
Effect of Stress on Creep at High Temperatures
,”
ASME J. Appl. Mech.
,
24
(
2
), pp.
207
213
.
11.
Jones
,
D. R. H.
,
2004
, “
Creep Failures of Overheated Boiler, Superheater and Reformer Tubes
,”
Eng. Failure Anal.
,
11
(
6
), pp.
873
893
.
12.
Langdon
,
T. G.
, and
Mohamed
,
F. A.
,
1978
, “
A Simple Method of Constructing an Ashby-Type Deformation Mechanism Map
,”
J. Mater. Sci.
,
13
(
6
), pp.
1282
1290
.
13.
Wikipedia Contributors
,
2011
, “
Kelvin–Voigt Material
,” Wikipedia, The Free Encyclopedia, Last accessed Apr. 18, 2016, https://en.wikipedia.org/w/index.php?title=Kelvin%E2%80%93Voigt_material&oldid=692668704
14.
Stouffer
,
D. C.
, and
Dame
,
L. T.
,
1996
,
Inelastic Deformation of Metals: Models, Mechanical Properties, and Metallurgy
,
Wiley
,
New York
.
15.
Phillips
,
P.
,
1903
, “
The Slow Stretch in Indiarubber, Glass, and Metal Wires When Subjected to a Constant Pull
,”
Proc. Phys. Soc. London
,
19
(
1
), pp.
491
511
.
16.
Parker
,
E. R.
,
1958
, “
Modern Concepts of Flow and Fracture
,”
Trans. ASM
,
50
, pp.
52
104
.
17.
Bailey
,
R. W.
,
1935
, “
The Utilization of Creep Test Data in Engineering Design
,”
Proc. Inst. Mech. Eng.
,
131
(
1
), pp.
131
349
.
18.
Graham
,
A.
, and
Walles
,
K. F. A.
,
1955
, “
NGTE Reports Nos. R. 100 (1952), R. 137 (1953), R.189 and R. 190 (1956)
,”
J. Iron Steel Inst.
,
179
, p.
105
.
19.
Andrade
,
E. N. D. C.
,
1910
, “
On the Viscous Flow in Metals, and Allied Phenomena
,”
R. Soc. London Proc. Ser. A
,
84
(
567
), pp.
1
12
.
20.
Wyatt
,
O. H.
,
1953
, “
Transient Creep in Pure Metals
,”
Proc. Phys. Soc. Sect. B
,
66
(
6
), pp.
459
480
.
21.
Norton
,
F. H.
, and
Bailey
,
R. W.
,
1954
, “
Creep of Steel
,”
Trans. ASM
,
52
, p.
114
.
22.
Nadai
,
A.
,
1938
,
The Influence of Time Upon Creep
,
Macmillan Company
,
New York
.
23.
Harmathy
,
T. Z.
,
1967
, “
Deflection and Failure of Steel-Supported Floors and Beams in Fire
,”
ASTM STP 422
, pp.
40
62
.
24.
Orr
,
R. L.
,
Sherby
,
O. D.
, and
Dorn
,
J. E.
,
1953
, “
Correlations of Rupture Data for Metals at Elevated Temperatures
,”
Trans ASM
,
46
, pp.
113
128
.
25.
ECCC
,
1956
, “
Classical Work Hardening Model
,” ECCC, Rugby, UK.
26.
Ashby
,
M. F.
, and
Jones
,
D. R. H.
,
2011
,
Engineering Materials 1: An Introduction to Properties, Applications and Design
,
Elsevier
,
Waltham, MA
.
27.
Norton
,
F. H.
,
1929
,
Creep of Steel at High Temperature
, McGraw-Hill, New York.
28.
Wiese
,
S.
,
Schubert
,
A.
,
Walter
,
H.
,
Dukek
,
R.
,
Feustel
,
F.
,
Meusel
,
E.
, and
Michel
,
B.
,
2001
, “
Constitutive Behaviour of Lead-Free Solders vs. Lead-Containing Solders-Experiments on Bulk Specimens and Flip-Chip Joints
,”
51st Electronic Components and Technology Conference
, Orlando, FL, pp.
890
902
.
29.
Pang
,
J. H. L.
,
Low
,
T. H.
,
Xiong
,
B. S.
, and
Che
,
F.
,
2003
, “
Design for Reliability (DFR) Methodology for Electronic Packaging Assemblies
,”
5th Electronics Packaging Technology Conference
(
EPTC 2003
), Dec. 10–12, pp.
470
478
.
30.
Hart
,
E. W.
,
1976
, “
Constitutive Relations for the Nonelastic Deformation of Metals
,”
J. Eng. Mater. Technol.
,
98
(
3
), pp.
193
202
.
31.
Adams
,
P. J.
,
1986
, “
Thermal Fatigue of Solder Joints in Micro-Electronic Devices
,”
M.S. thesis
, Massachusetts Institute of Technology, Cambridge, MA.
32.
Wilde
,
J.
,
Becker
,
K.
,
Thoben
,
M.
, and
Cheng
,
Z. N.
,
2000
, “
Rate Dependent Constitutive Relations Based on Anand Model for 92.5Pb5Sn2.5Ag Solder
,”
IEEE Trans. Adv. Packag.
,
23
(
3
), pp.
408
414
.
33.
Wang
,
G. Z.
,
Cheng
,
Z. N.
,
Becker
,
K.
, and
Wilde
,
J.
,
1998
, “
Applying Anand Model to Represent the Viscoplastic Deformation Behavior of Solder Alloys
,”
ASME J. Electron. Packag.
,
123
(
3
), pp.
247
253
.
34.
Pei
,
M.
, and
Qu
,
J.
,
2005
, “
Constitutive Modeling of Lead-Free Solders
,”
ASME
Paper No. IPACK2005-73411.
35.
Chaboche
,
J. L.
, and
Rousselier
,
G.
,
1983
, “
On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept
,”
ASME J. Pressure Vessel Technol.
,
105
(
2
), pp.
153
158
.
36.
Choudhury
,
S. F.
, and
Ladani
,
L.
,
2015
, “
Effect of Intermetallic Compounds on the Thermomechanical Fatigue Life of Three-Dimensional Integrated Circuit Package Microsolder Bumps: Finite Element Analysis and Study
,”
ASME J. Electron. Packag.
,
137
(
4
), p.
041003
.
37.
Zhao
,
J.-H.
,
Gupta
,
V.
,
Lohia
,
A.
, and
Edwards
,
D.
,
2010
, “
Reliability Modeling of Lead-Free Solder Joints in Wafer-Level Chip Scale Packages
,”
ASME J. Electron. Packag.
,
132
(
1
), p.
011005
.
38.
Ladani
,
L. J.
, and
Dasgupta
,
A.
,
2008
, “
Damage Initiation and Propagation in Voided Joints: Modeling and Experiment
,”
ASME J. Electron. Packag.
,
130
(
1
), p.
011008
.
39.
Jong
,
W.-R.
,
Tsai
,
H.-C.
,
Chang
,
H.-T.
, and
Peng
,
S.-H.
,
2008
, “
The Effects of Temperature Cyclic Loading on Lead-Free Solder Joints of Wafer Level Chip Scale Package by Taguchi Method
,”
ASME J. Electron. Packag.
,
130
(
1
), p.
011001
.
40.
Pierce
,
D. M.
,
Sheppard
,
S. D.
,
Fossum
,
A. F.
,
Vianco
,
P. T.
, and
Neilsen
,
M. K.
,
2008
, “
Development of the Damage State Variable for a Unified Creep Plasticity Damage Constitutive Model of the 95.5Sn–3.9Ag–0.6Cu Lead-Free Solder
,”
ASME J. Electron. Packag.
,
130
(
1
), p.
011002
.
41.
Obaid
,
A. A.
,
Sloan
,
J. G.
,
Lamontia
,
M. A.
,
Paesano
,
A.
,
Khan
,
S.
,
Gillespie
,
J.
, and
John
,
J.
,
2004
, “
Experimental In Situ Characterization and Creep Modeling of Tin-Based Solder Joints on Commercial Area Array Packages at −40 °C, 23 °C, and 125 °C
,”
ASME J. Electron. Packag.
,
127
(
4
), pp.
430
439
.
42.
Basaran
,
C.
,
Zhao
,
Y.
,
Tang
,
H.
, and
Gomez
,
J.
,
2004
, “
A Damage-Mechanics-Based Constitutive Model for Solder Joints
,”
ASME J. Electron. Packag.
,
127
(
3
), pp.
208
214
.
43.
Wiese
,
S.
, and
Meusel
,
E.
,
2003
, “
Characterization of Lead-Free Solders in Flip Chip Joints
,”
ASME J. Electron. Packag.
,
125
(
4
), pp.
531
538
.
44.
Ham
,
S.-J.
, and
Lee
,
S.-B.
,
2003
, “
Measurement of Creep and Relaxation Behaviors of Wafer-Level CSP Assembly Using Moiré Interferometry
,”
ASME J. Electron. Packag.
,
125
(
2
), pp.
282
288
.
45.
Darbha
,
K.
, and
Dasgupta
,
A.
,
2000
, “
A Nested Finite Element Methodology (NFEM) for Stress Analysis of Electronic Products—Part II: Durability Analysis of Flip Chip and Chip Scale Interconnects
,”
ASME J. Electron. Packag.
,
123
(
2
), pp.
147
155
.
46.
Pang
,
J. H. L.
,
Seetoh
,
C. W.
, and
Wang
,
Z. P.
,
2000
, “
CBGA Solder Joint Reliability Evaluation Based on Elastic-Plastic-Creep Analysis
,”
ASME J. Electron. Packag.
,
122
(
3
), pp.
255
261
.
47.
Lau
,
J. H.
,
Lee
,
S.-W. R.
, and
Chang
,
C.
,
2000
, “
Solder Joint Reliability of Wafer Level Chip Scale Packages (WLCSP): A Time-Temperature-Dependent Creep Analysis
,”
ASME J. Electron. Packag.
,
122
(
4
), pp.
311
316
.
48.
Tribula
,
D.
, and
Morris
,
J. J. W.
,
1990
, “
Creep in Shear of Experimental Solder Joints
,”
ASME J. Electron. Packag.
,
112
(
2
), pp.
87
93
.
49.
Pao
,
Y.-H.
,
Badgley
,
S.
,
Jih
,
E.
,
Govila
,
R.
, and
Browning
,
J.
,
1993
, “
Constitutive Behavior and Low Cycle Thermal Fatigue of 97Sn-3Cu Solder Joints
,”
ASME J. Electron. Packag.
,
115
(
2
), pp.
147
152
.
50.
Pao
,
Y.-H.
,
Govila
,
R.
,
Badgley
,
S.
, and
Jih
,
E.
,
1993
, “
An Experimental and Finite Element Study of Thermal Fatigue Fracture of PbSn Solder Joints
,”
ASME J. Electron. Packag.
,
115
(
1
), pp.
1
8
.
51.
Darveaux
,
R.
, and
Banerji
,
K.
,
1992
, “
Constitutive Relations for Tin-Based Solder Joints
,”
IEEE Trans. Compon. Hybrids Manuf. Technol.
,
15
(
6
), pp.
1013
1024
.
52.
Igoshev
,
V. I.
, and
Kleiman
,
J. I.
,
2000
, “
Creep Phenomena in Lead-Free Solders
,”
J. Electron. Mater.
,
29
(
2
), pp.
244
250
.
53.
US Department of Commerce
, “
Lead-Free Solder Data
,” Last accessed Mar. 01, 2015, http://www.nist.gov/mml/msed/solder.cfm
54.
Shi
,
X. Q.
,
Wang
,
Z. P.
,
Zhou
,
W.
,
Pang
,
H. L. J.
, and
Yang
,
Q. J.
,
2002
, “
A New Creep Constitutive Model for Eutectic Solder Alloy
,”
ASME J. Electron. Packag.
,
124
(
2
), pp.
85
90
.
55.
Motalab
,
M.
,
Basit
,
M.
,
Suhling
,
J. C.
, and
Lall
,
P.
,
2013
, “
A Revised Anand Constitutive Model for Lead Free Solder That Includes Aging Effects
,”
ASME
Paper No. IPACK2013-73232.
56.
Vianco
,
P.
,
Rejent
,
J.
, and
Kilgo
,
A.
,
2004
, “
Creep Behavior of the Ternary 95.5Sn-3.9Ag-0.6Cu Solder—Part I: As-Cast Condition
,”
J. Electron. Mater.
,
33
(
11
), pp.
1389
1400
.
57.
Wong
,
B.
,
Helling
,
D. E.
, and
Clark
,
R. W.
,
1988
, “
A Creep-Rupture Model for Two-Phase Eutectic Solders
,”
IEEE Trans. Compon. Hybrids Manuf. Technol.
,
11
(
3
), pp.
284
290
.
58.
Mei
,
Z.
,
Morris
,
J. J. W.
, and
Shine
,
M. C.
,
1991
, “
Superplastic Creep of Eutectic Tin-Lead Solder Joints
,”
ASME J. Electron. Packag.
,
113
(
2
), pp.
109
114
.
59.
Syed
,
A. R.
,
1995
, “
Creep Crack Growth Prediction of Solder Joints During Temperature Cycling—An Engineering Approach
,”
ASME J. Electron. Packag.
,
117
(
2
), pp.
116
122
.
60.
Syed
,
A.
,
2004
, “
Accumulated Creep Strain and Energy Density Based Thermal Fatigue Life Prediction Models for SnAgCu Solder Joints
,”
54th Electronic Components and Technology Conference
, June 1–4, Vol.
1
, pp.
737
746
.
61.
Ma
,
H.
,
2009
, “
Constitutive Models of Creep for Lead-Free Solders
,”
J. Mater. Sci.
,
44
(
14
), pp.
3841
3851
.
62.
Clech
,
J.-P.
,
2007
, “
Review and Analysis of Lead-Free Solder Material Properties
,”
Lead-Free Electronics
,
E.
Bradley
,
C. A.
Handwerker
,
J.
Bath
,
R. D.
Parker
, and
R. W.
Gedney
, eds.,
Wiley
,
New York
, pp.
47
123
.
63.
Zhang
,
Q.
, and
Dasgupta
,
A.
,
2006
, “
Constitutive Properties and Durability of Selected Lead-Free Solders
,”
Lead-Free Electronics
,
S.
Ganesan
, and
M.
Pecht
, eds.,
Wiley
,
New York
, pp.
237
381
.
64.
Chen
,
T.
, and
Dutta
,
I.
,
2008
, “
Effect of Ag and Cu Concentrations on the Creep Behavior of Sn-Based Solders
,”
J. Electron. Mater.
,
37
(
3
), pp.
347
354
.
65.
Ma
,
H.
,
Suhling
,
J. C.
,
Lall
,
P.
, and
Bozack
,
M. J.
,
2006
, “
Effects of Aging on the Stress-Strain and Creep Behaviors of Lead Free Solders
,”
The Tenth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronics Systems
,
ITHERM’06
, San Diego, CA, May 30–June 2, pp.
961
976
.
66.
Ma
,
H.
,
Suhling
,
J. C.
,
Zhang
,
Y.
,
Lall
,
P.
, and
Bozack
,
M. J.
,
2007
, “
The Influence of Elevated Temperature Aging on Reliability of Lead Free Solder Joints
,”
57th Electronic Components and Technology Conference
,
ECTC’07
, Reno, NV, May 29–June 1, pp.
653
668
.
67.
Zhang
,
Y.
,
Cai
,
Z.
,
Suhling
,
J. C.
,
Lall
,
P.
, and
Bozack
,
M. J.
,
2008
, “
The Effects of Aging Temperature on SAC Solder Joint Material Behavior and Reliability
,”
58th Electronic Components and Technology Conference
,
ECTC 2008
, Lake Buena Vista, FL, May 27–30, pp.
99
112
.
68.
Mustafa
,
M.
,
Cai
,
Z.
,
Suhling
,
J. C.
, and
Lall
,
P.
,
2011
, “
The Effects of Aging on the Cyclic Stress-Strain Behavior and Hysteresis Loop Evolution of Lead Free Solders
,”
61st Electronic Components and Technology Conference
(
ECTC
), IEEE, pp.
927
939
.
69.
Xiao
,
Q.
,
Nguyen
,
L.
, and
Armstrong
,
W. D.
,
2004
, “
Aging and Creep Behavior of Sn3.9Ag0.6Cu Solder Alloy
,”
54th Electronic Components and Technology Conference
, June 1–4, Vol.
2
, pp.
1325
1332
.
70.
Chauhan
,
P.
,
2012
, “
Microstructural Characterization and Thermal Cycling Reliability of Solders Under Isothermal Aging and Electrical Current
,”
Ph.D. thesis
, University of Maryland, College Park, MD.
71.
Arrowood
,
R.
,
Mukherjee
,
A.
, and
Jones
,
W.
,
1990
, “
Chapter 3 in Solder Mechanics: A State of the Art Assessment
,”
TMS
,
Warrendale, PA
.
72.
Senkov
,
O. N.
, and
Myshlyaev
,
M. M.
,
1986
, “
Grain Growth in a Superplastic Zn-22% Al Alloy
,”
Acta Metall.
,
34
(
1
), pp.
97
106
.
73.
Hacke
,
P. L.
,
Sprecher
,
A. F.
, and
Conrad
,
H.
,
1997
, “
Microstructure Coarsening During Thermo-Mechanical Fatigue of Pb-Sn Solder Joints
,”
J. Electron. Mater.
,
26
(
7
), pp.
774
782
.
74.
Conrad
,
H.
,
Guo
,
Z.
,
Fahmy
,
Y.
, and
Yang
,
D.
,
1999
, “
Influence of Microstructure Size on the Plastic Deformation Kinetics, Fatigue Crack Growth Rate, and Low-Cycle Fatigue of Solder Joints
,”
J. Electron. Mater.
,
28
(
9
), pp.
1062
1070
.
75.
Jung
,
K.
, and
Conrad
,
H.
,
2001
, “
Microstructure Coarsening During Static Annealing of 60Sn40Pb Solder Joints: I Stereology
,”
J. Electron. Mater.
,
30
(
10
), pp.
1294
1302
.
76.
Cuddalorepatta
,
G.
,
Williams
,
M.
, and
Dasgupta
,
A.
,
2010
, “
Viscoplastic Creep Response and Microstructure of As-Fabricated Microscale Sn-3.0Ag-0.5Cu Solder Interconnects
,”
J. Electron. Mater.
,
39
(
10
), pp.
2292
2309
.
77.
Deshpande
,
V. T.
, and
Sirdeshmukh
,
D. B.
,
1962
, “
Thermal Expansion of Tin in the β–γ Transition Region
,”
Acta Crystallogr.
,
15
(
3
), pp.
294
295
.
78.
Subramanian
,
K. N.
, and
Lee
,
J. G.
,
2004
, “
Effect of Anisotropy of Tin on Thermomechanical Behavior of Solder Joints
,”
J. Mater. Sci. Mater. Electron.
,
15
(
4
), pp.
235
240
.
79.
Lee
,
J. G.
,
Telang
,
A.
,
Subramanian
,
K. N.
, and
Bieler
,
T. R.
,
2002
, “
Modeling Thermomechanical Fatigue Behavior of Sn-Ag Solder Joints
,”
J. Electron. Mater.
,
31
(
11
), pp.
1152
1159
.
80.
Matin
,
M. A.
,
Coenen
,
E. W. C.
,
Vellinga
,
W. P.
, and
Geers
,
M. G. D.
,
2005
, “
Correlation Between Thermal Fatigue and Thermal Anisotropy in a Pb-Free Solder Alloy
,”
Scr. Mater.
,
53
(
8
), pp.
927
932
.
81.
Park
,
S.
,
Dhakal
,
R.
,
Lehman
,
L.
, and
Cotts
,
E. J.
,
2007
, “
Grain Deformation and Strain in Board Level SnAgCu Solder Interconnects Under Deep Thermal Cycling
,”
IEEE Trans. Compon. Packag. Technol.
,
30
(
1
), pp.
178
185
.
82.
Wiese
,
S.
, and
Wolter
,
K.-J.
,
2004
, “
Microstructure and Creep Behaviour of Eutectic SnAg and SnAgCu Solders
,”
Microelectron. Reliab.
,
44
(
12
), pp.
1923
1931
.
83.
Dutta
,
I.
,
Park
,
C.
, and
Choi
,
S.
,
2004
, “
Impression Creep Characterization of Rapidly Cooled Sn–3.5Ag Solders
,”
Mater. Sci. Eng. A
,
379
(
1–2
), pp.
401
410
.
84.
Kerr
,
M.
, and
Chawla
,
N.
,
2004
, “
Creep Deformation Behavior of Sn–3.5Ag Solder/Cu Couple at Small Length Scales
,”
Acta Mater.
,
52
(
15
), pp.
4527
4535
.
85.
Mathew
,
M.
,
Yang
,
H.
,
Movva
,
S.
, and
Murty
,
K.
,
2005
, “
Creep Deformation Characteristics of Tin and Tin-Based Electronic Solder Alloys
,”
Metall. Mater. Trans. A
,
36
(
1
), pp.
99
105
.
86.
Ochoa
,
F.
,
Deng
,
X.
, and
Chawla
,
N.
,
2004
, “
Effects of Cooling Rate on Creep Behavior of a Sn-3.5Ag Alloy
,”
J. Electron. Mater.
,
33
(
12
), pp.
1596
1607
.
87.
Arzt
,
E.
, and
Göhring
,
E.
,
1998
, “
A Model for Dispersion Strengthening of Ordered Intermetallics at High Temperatures
,”
Acta Mater.
,
46
(
18
), pp.
6575
6584
.
88.
Cuddalorepatta
,
G.
, and
Dasgupta
,
A.
,
2010
, “
Multi-Scale Modeling of the Viscoplastic Response of As-Fabricated Microscale Pb-Free Sn3.0Ag0.5Cu Solder Interconnects
,”
Acta Mater.
,
58
(
18
), pp.
5989
6001
.
89.
Gong
,
J.
,
Liu
,
C.
,
Conway
,
P. P.
, and
Silberschmidt
,
V. V.
,
2006
, “
Modelling of Ag3Sn Coarsening and Its Effect on Creep of Sn–Ag Eutectics
,”
Mater. Sci. Eng. A
,
427
(
1–2
), pp.
60
68
.
90.
Chawla
,
N.
, and
Sidhu
,
R. S.
,
2006
, “
Microstructure-Based Modeling of Deformation in Sn-Rich (Pb-free) Solder Alloys
,”
J. Mater. Sci. Mater. Electron.
,
18
(
1–3
), pp.
175
189
.
91.
Pei
,
M.
, and
Qu
,
J.
,
2007
, “
Hierarchical Modeling of Creep Behavior of SnAg Solder Alloys
,”
57th Electronic Components and Technology Conference
, Reno, NV, May 29–June 1, pp.
273
277
.
92.
Mukherjee
,
S.
,
Dasgupta
,
A.
,
Zhou
,
B.
, and
Bieler
,
T. R.
,
2014
, “
Multiscale Modeling of the Effect of Micro-Alloying Mn and Sb on the Viscoplastic Response of SAC105 Solder
,”
J. Electron. Mater.
,
43
(
4
), pp.
1119
1130
.
93.
Chauhan
,
P.
,
Mukherjee
,
S.
,
Osterman
,
M.
,
Dasgupta
,
A.
, and
Pecht
,
M.
,
2013
, “
Effect of Isothermal Aging on Microstructure and Creep Properties of SAC305 Solder: A Micromechanics Approach
,”
ASME
Paper No. IPACK2013-73164.
94.
Mukherjee
,
S.
,
Zhou
,
B.
,
Dasgupta
,
A.
, and
Bieler
,
T. R.
,
2016
, “
Multiscale Modeling of the Anisotropic Transient Creep Response of Heterogeneous Single Crystal SnAgCu Solder
,”
Int. J. Plast.
,
78
, pp.
1
25
.
95.
Rösler
,
J.
, and
Arzt
,
E.
,
1990
, “
A New Model-Based Creep Equation for Dispersion Strengthened Materials
,”
Acta Metall. Mater.
,
38
(
4
), pp.
671
683
.
96.
Arzt
,
E.
, and
Rösler
,
J.
,
1988
, “
The Kinetics of Dislocation Climb Over Hard Particles—II: Effects of an Attractive Particle-Dislocation Interaction
,”
Acta Metall.
,
36
(
4
), pp.
1053
1060
.
97.
Arzt
,
E.
, and
Wilkinson
,
D. S.
,
1986
, “
Threshold Stresses for Dislocation Climb Over Hard Particles: The Effect of an Attractive Interaction
,”
Acta Metall.
,
34
(
10
), pp.
1893
1898
.
98.
Rosler
,
J.
,
2003
, “
Particle Strengthened Alloys for High Temperature Applications: Strengthening Mechanisms and Fundamentals of Design
,”
Int. J. Mater. Prod. Technol.
,
18
(
1/2/3
), pp.
70
90
.
99.
Mukherjee
,
S.
,
Dasgupta
,
A.
,
Zhou
,
B.
, and
Bieler
,
T.
,
2013
, “
Multiscale Modeling of Anisotropic Creep Response of Heterogeneous Single Crystal SnAgCu Solder
,” JIEP-IEEE-IMAPS, ICEP-2013 Conference, Osaka, Japan, Apr. 10–12.
100.
Lehman
,
L.
,
Athavale
,
S.
,
Fullem
,
T.
,
Giamis
,
A.
,
Kinyanjui
,
R.
,
Lowenstein
,
M.
,
Mather
,
K.
,
Patel
,
R.
,
Rae
,
D.
,
Wang
,
J.
,
Xing
,
Y.
,
Zavalij
,
L.
,
Borgesen
,
P.
, and
Cotts
,
E.
,
2004
, “
Growth of Sn and Intermetallic Compounds in Sn-Ag-Cu Solder
,”
J. Electron. Mater.
,
33
(
12
), pp.
1429
1439
.
101.
Salam
,
B.
,
Virseda
,
C.
,
Da
,
H.
,
Ekere
,
N. N.
, and
Durairaj
,
R.
,
2004
, “
Reflow Profile Study of the Sn-Ag-Cu Solder
,”
Solder. Surf. Mount Technol.
,
16
(
1
), pp.
27
34
.
102.
Allen
,
S. L.
,
Notis
,
M. R.
,
Chromik
,
R. R.
, and
Vinci
,
R. P.
,
2004
, “
Microstructural Evolution in Lead-Free Solder Alloys: Part I—Cast Sn–Ag–Cu Eutectic
,”
J. Mater. Res.
,
19
(
5
), pp.
1417
1424
.
103.
Sarah
,
L.
, and
Allen
,
M. R. N.
,
2004
, “
Microstructural Evolution in Lead-Free Solder Alloys—Part II: Directionally Solidified Sn-Ag-Cu, Sn-Cu and Sn-Ag
,”
J. Mater. Res.
,
19
(05), pp.
1425
1431
.
104.
Amagai
,
M.
,
Watanabe
,
M.
,
Omiya
,
M.
,
Kishimoto
,
K.
, and
Shibuya
,
T.
,
2002
, “
Mechanical Characterization of Sn–Ag-Based Lead-Free Solders
,”
Microelectron. Reliab.
,
42
(
6
), pp.
951
966
.
105.
Guo
,
F.
,
Lucas
,
J. P.
, and
Subramanian
,
K. N.
,
2001
, “
Creep Behavior in Cu and Ag Particle-Reinforced Composite and Eutectic Sn-3.5Ag and Sn-4.0Ag-0.5Cu Non-Composite Solder Joints
,”
J. Mater. Sci. Mater. Electron.
,
12
(
1
), pp.
27
35
.
106.
Qiang Xiao
,
H. J. B.
,
2004
, “
Aging Effects on Microstructure and Tensile Property of Sn3.9Ag0.6Cu Solder Alloy
,”
ASME J. Electron. Packag
,
126
(
2
), pp.
208
212
.
107.
Pang
,
J. H. L.
,
Low
,
T. H.
,
Xiong
,
B. S.
,
Luhua
,
X.
, and
Neo
,
C. C.
,
2004
, “
Thermal Cycling Aging Effects on Sn–Ag–Cu Solder Joint Microstructure, IMC and Strength
,”
Thin Solid Films
,
462–463
, pp.
370
375
.
108.
Plumbridge
,
W.
,
Gagg
,
C.
, and
Peters
,
S.
,
2001
, “
The Creep of Lead-Free Solders at Elevated Temperatures
,”
J. Electron. Mater.
,
30
(
9
), pp.
1178
1183
.
109.
Yu
,
D. Q.
,
Zhao
,
J.
, and
Wang
,
L.
,
2004
, “
Improvement on the Microstructure Stability, Mechanical and Wetting Properties of Sn–Ag–Cu Lead-Free Solder With the Addition of Rare Earth Elements
,”
J. Alloys Compd.
,
376
(
1–2
), pp.
170
175
.
110.
Korhonen
,
T.-M. K.
,
Turpeinen
,
P.
,
Lehman
,
L. P.
,
Bowman
,
B.
,
Thiel
,
G. H.
,
Parkes
,
R. C.
,
Korhonen
,
M. A.
,
Henderson
,
D. W.
, and
Puttlitz
,
K. J.
,
2004
, “
Mechanical Properties of Near-Eutectic Sn-Ag-Cu Alloy Over a Wide Range of Temperatures and Strain Rates
,”
J. Electron. Mater.
,
33
(
12
), pp.
1581
1588
.
111.
Erinç
,
M. E.
,
Schreurs
,
P. J.
,
Zhang
,
G. Q.
, and
Geers
,
M. G. D.
,
2004
, “
Characterization and Fatigue Damage Simulation in SAC Solder Joints
,”
Microelectron. Reliab.
,
44
(
9
), pp.
1287
1292
.
112.
Telang
,
A. U.
,
Bieler
,
T. R.
,
Lucas
,
J. P.
,
Subramanian
,
K. N.
,
Lehman
,
L. P.
,
Xing
,
Y.
, and
Cotts
,
E. J.
,
2004
, “
Grain-Boundary Character and Grain Growth in Bulk Tin and Bulk Lead-Free Solder Alloys
,”
J. Electron. Mater.
,
33
(
12
), pp.
1412
1423
.
113.
Telang
,
A. A.
,
Bieler
,
T. R.
,
Choi
,
S.
, and
Subramanian
,
K. K.
,
2002
, “
Orientation Imaging Studies of Sn-Based Electronic Solder Joints
,”
J. Mater. Res.
,
17
(09), pp.
2294
2306
.
114.
Chen
,
C. R.
, and
Li
,
S. X.
,
1998
, “
Distribution of Stresses and Elastic Strain Energy in an Ideal Multicrystal Model
,”
Mater. Sci. Eng. A
,
257
(
2
), pp.
312
321
.
115.
Stroh
,
A. N.
,
1958
, “
Dislocations and Cracks in Anisotropic Elasticity
,”
Philos. Magazine
,
3
(
30
), p.
625
646
.
116.
Nemat-Nasser
,
S.
, and
Hori
,
M.
,
1999
,
Micromechanics: Overall Properties of Heterogeneous Materials
, 2nd ed.,
Elsevier
,
North Holland
.
117.
Mura
,
T.
,
1987
,
Micromechanics of Defects in Solids
,
Springer
,
Dordrecht, The Netherlands
.
118.
Eshelby
,
J. D.
,
1959
, “
The Elastic Field Outside an Ellipsoidal Inclusion
,”
Proc. R. Soc. Lond. Ser. Math. Phys. Sci.
,
252
(
1271
), pp.
561
569
.
119.
Rangaraj
,
S.
, and
Kokini
,
K.
,
2002
, “
Time-Dependent Behavior of Ceramic (Zirconia)-Metal (NiCoCrAlY) Particulate Composites
,”
Mech. Time Depend. Mater.
,
6
(
2
), pp.
171
191
.
120.
Eshelby
,
J. D.
,
Read
,
W. T.
, and
Shockley
,
W.
,
1953
, “
Anisotropic Elasticity With Applications to Dislocation Theory
,”
Acta Metall.
,
1
(
3
), pp.
251
259
.
121.
Zhao
,
J.-H.
,
Su
,
P.
,
Ding
,
M.
,
Chopin
,
S.
, and
Ho
,
P. S.
,
2006
, “
Microstructure-Based Stress Modeling of Tin Whisker Growth
,”
IEEE Trans. Electron. Packag. Manuf.
29
(
4
), pp.
265
273
.
122.
Zhao
,
J.-H.
,
Su
,
P.
,
Ding
,
M.
,
Chopin
,
S.
, and
Ho
,
P. S.
,
2005
, “
Microstructure-Based Stress Modeling of Tin Whisker Growth
,” Electronic Components and Technology, 2005.
ECTC '05
, pp.
137
144
.
123.
Subramanian
,
K. N.
,
2007
, “
Role of Anisotropic Behaviour of Sn on Thermomechanical Fatigue and Fracture of Sn-Based Solder Joints Under Thermal Excursions
,”
Fatigue Fract. Eng. Mater. Struct.
,
30
(
5
), pp.
420
431
.
124.
Telang
,
A. U.
, and
Bieler
,
T. R.
,
2005
, “
Characterization of Microstructure and Crystal Orientation of the Tin Phase in Single Shear Lap Sn–3.5Ag Solder Joint Specimens
,”
Scr. Mater.
,
52
(
10
), pp.
1027
1031
.
125.
Ubachs
,
R. L. J. M.
,
Schreurs
,
P. J. G.
, and
Geers
,
M. G. D.
,
2007
, “
Elasto-Viscoplastic Nonlocal Damage Modelling of Thermal Fatigue in Anisotropic Lead-Free Solder
,”
Mech. Mater.
,
39
(
7
), pp.
685
701
.
126.
Park
,
S.
,
Dhakal
,
R.
, and
Gao
,
J.
,
2008
, “
Three-Dimensional Finite Element Analysis of Multiple-Grained Lead-Free Solder Interconnects
,”
J. Electron. Mater.
,
37
(
8
), pp.
1139
1147
.
127.
Zamiri
,
A.
,
Bieler
,
T. R.
, and
Pourboghrat
,
F.
,
2009
, “
Anisotropic Crystal Plasticity Finite Element Modeling of the Effect of Crystal Orientation and Solder Joint Geometry on Deformation After Temperature Change
,”
J. Electron. Mater.
,
38
(
2
), pp.
231
240
.
You do not currently have access to this content.