Field reliability extrapolations from accelerated tests necessitate simulation of a variety of material behaviors under general loading conditions. The Hierarchical Incremental Single Surface (HiSS) yield function (Desai, C. S., 2001, Mechanics of Materials and Interfaces: The Disturbed State Concept, CRC Press, Boca Raton, FL.) has been applied extensively to a wide range of materials, from solders and silicon to ceramics and geotechnical materials, for simulating continuous-yield elastoplastic and elastoviscoplastic behavior. This work presents a continuous-yield function that avoids problems with HiSS for thermal and tensile loading. Validations are presented for eutectic data of Wang et al. (Wang, Z., Desai, C.S., and Kundu, T., 2001, “Disturbed State Constitutive Modeling and Testing of Joining Materials in Electronic Packaging,” report to NSF for Materials Processing and Manufacturing Division Grant 9812686, University of Arizona, Tucson, AZ). Limitations on the range of validity of the elastoplastic and the Perzyna elastoviscoplastic formulations are discussed.
Issue Section:
Research Papers
1.
Desai
, C. S.
, 2001, Mechanics of Materials and Interfaces: The Disturbed State Concept
, CRC Press
, Boca Raton, FL.2.
Wang
, Z.
, Desai
, C. S.
, and Kundu
, T.
, 2001, “Disturbed State Constitutive Modeling and Testing of Joining Materials in Electronic Packaging
,” report to NSF for Materials Processing and Manufacturing Division Grant 9812686, University of Arizona
, Tucson, AZ.3.
Rafanelli
, A. J.
, 1992, “Ramberg-Osgood Parameters for 63-37 Sn-Pb Solder
,” ASME J. Electron. Packag.
1043-7398, 114
, pp. 234
–238
.4.
Tribula
, D.
, and Morris
, J. W.
, 1990, “Creep in Shear of Experimental Solder Joints
,” ASME J. Electron. Packag.
1043-7398, 112
, pp. 88
–93
.5.
Mei
, Z.
, Morris
, J. W.
, and Shine
, M. C.
, 1991, “Superplastic Creep of Eutectic Tin-Lead Solders
,” ASME J. Electron. Packag.
1043-7398, 113
, pp. 109
–113
.6.
Guo
, Z.
, Sprecher
, A. F.
, and Conrad
, H.
, 1992, “Plastic Deformation Kinetics of Eutectic Pb–Sn Solder Joints in Monotonic Loading and Low Cycle Fatigue
,” ASME J. Electron. Packag.
1043-7398, 114
, pp. 112
–117
.7.
Hare
, E. W.
, and Stang
, R. G.
, 1995, “Stress Relaxation Behavior of Eutectic Tin-Lead Solder
,” J. Electron. Mater.
0361-5235, 24
(10
), pp 1473
–1484
.8.
Tien
, J. K.
, Hendrix
, B. C.
, and Attarwala
, A. J.
, 1991, “Understanding the Cyclic Mechanical Behavior of Lead/Tin Solder
,” ASME J. Electron. Packag.
1043-7398, 113
, pp. 115
–120
.9.
Hacke
, P. L.
, Sprecher
, A. F.
, and Conrad
, H.
, 1997, “Microstructure Coarsening During Thermomechanical Fatigue of Pb–Sn Solder Joints
,” J. Electron. Mater.
0361-5235, 26
(7
), pp 774
–782
.10.
Hacke
, P. L.
, Fahmy
, Y.
, and Conrad
, H.
, 1998, “Phase Coarsening and Crack Growth Rate During Thermo-Mechanical Cycling of 63Sn37Pb Solder Joints
,” J. Electron. Mater.
0361-5235, 27
(8
), pp 941
–947
.11.
Vianco
, P. T.
, Burchett
, S. N.
, Neilsen
, M. K.
, Rejent
, J. A.
, and Frear
, D. R.
, 1999, “Coarsening of the Sn–Pb Solder Microstructure in Constitutive Model-Based Predictions of Solder Joint Thermal Mechanical Fatigue
,” J. Electron. Mater.
0361-5235, 28
(11
), pp. 1290
–1298
.12.
Stone
, D. S.
, 1990, “The Creep-Fatigue Interaction in Solders and Solder Joints
,” ASME J. Electron. Packag.
1043-7398, 112
, pp. 100
–103
.13.
Attarwala
, A. I.
, Tien
, J. K.
, Masada
, G. Y.
, and Dody
G.
, 1992, “Confirmation of Creep and Fatigue Damage in Pb∕Sn Solder Joints
,” ASME J. Electron. Packag.
1043-7398, 114
, pp. 109
–111
.14.
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.
0361-5235, 28
(9
), pp. 1062
–1070
.15.
Choi
, S.
, Bieler
, T. R.
, Lucas
, J. P.
, and Subramaniam
, K. N.
, 1999, “Characterization of the Growth of Intermetallic Interfacial Layers of Sn-Ag and Sn-Pb Eutectic Solders and Their Composite Solders on Cu Substrate During Isothermal Long-Term Aging
,” J. Electron. Mater.
0361-5235, 28
(11
), pp. 1209
–1215
.16.
Ross
, R. G.
, 1991, “A Systems Approach to Solder Joint Fatigue in Spacecraft Electronic Packaging
,” ASME J. Electron. Packag.
1043-7398, 113
, pp. 121
–128
.17.
Konetzki
, R. A.
, Zhang
, M. X.
, Sluzewski
, D. A.
, and Chang
, Y. A.
, 1990, “Oxidation of (Pb,Sn) and (Pb, In) Alloys
,” J. Electron. Packag.
1043-7398, 112
, pp. 175
–178
.18.
Frear
, D. R.
, Sorensen
, N. R.
, and Martens
, J. S.
, 1995, “Test Methodologies to Perform Valid Accelerated Thermomechanical Fatigue Tests of Solder Joints
,” Fatigue of Electronic Materials
, ASTM STP 1153, S. A.
Schroeder
and M. R.
Mitchell
, Eds., ASTM
, Philadelphia, PA, pp. 95
–109
.19.
Dube
, M.
, 2004, “Constitutive Modeling of Joining Materials in Electronic Packaging
,” Ph.D. dissertation, University of Arizona, Tucson.20.
Drexler
, K. E.
, 1992, Nanosystems: Molecular Machinery, Manufacturing and Computation
, Wiley Interscience
, New York.21.
Pelesko
, J. A.
, and Bernstein
, D. H.
, 2003, Modeling MEMS and NEMS
, Chapman and Hall/ CRC
, Boca Raton, FL.22.
Lyshevski
, S. E.
, 2002, MEMS and NEMS: Systems, Devices and Structures
, CRC Press
, Boca Raton, FL.23.
Lee
, W. W.
, Nguyen
, L. T.
, and Selvaduray
, G. S.
, 2000, “Solder joint fatigue models: Review and applicability to chip scale packages
,” Microelectron. Reliab.
0026-2714, 40
, pp. 231
–244
.24.
Desai
, C. S.
, and Whitenack
, R.
, 2001, “Review of Models and the Disturbed State Concept for Thermomechanical Analysis in Electronic Packaging
,” ASME J. Electron. Packag.
1043-7398, 123
, pp. 19
–33
.25.
Andersen
, I.
, Guven
, I.
, Madenci
, E.
, and Gustaffson
, G.
, 2000, “The Necessity of Reexamining Previous Life Prediction Analyses of Solder Joints in Electronic Packages
,” IEEE Trans. Compon., Packag. Manuf. Technol., Part A
1070-988623
(3
), pp. 516
–520
.26.
Dube
, M.
, and Sahay
, C.
, 1996, “Uniform Entry Flow at Low Reynolds Numbers
,” ASME Int. Mech. Eng. Conf. and Exp., Atlanta, GA
.27.
Dieter
, G. E.
, 1961, Mechanical Metallurgy
, McGraw-Hill
, New York.28.
Hirsch
, P. B.
, ed., 1975, The Physics of Metals 2. Defects
, Cambridge University Press
, Cambridge, UK.29.
Gittus
, J.
, 1975, Creep, Viscoelasticity and Creep Fracture in Solids
, Applied Science Publishers
, London.30.
Cadek
, J. A.
, 1988, Creep in Metallic Materials
, Elsevier
, Amsterdam.31.
Mura
, T.
, 1994, “A Theory of Fatigue-Crack Initiation
,” Mater. Sci. Eng., A
0921-5093, 176
, pp. 61
–70
.32.
Bonda
N. R.
, and Noyan
, I. C.
, 1996, “Effect of Specimen Size in Predicting the Mechanical Properties of PbSn Solder Alloys
,” IEEE Trans. Compon., Packag. Manuf. Technol., Part A
1070-9886, 19
(2
), pp. 208
–212
.33.
Sharma
, P.
, Ganti
, S.
, Dasgupta
, A.
, and Loman
, J.
, 2003, “Prediction of Rate-Independent Constitutive Behavior of Pb-Free Solders Based on First Principles
,” IEEE Trans. Compon. Packag. Manuf. Tech.
26
(3
), pp. 659
–666
.34.
Wen
, S.
, and Keer
, L. M.
, 2002, “A Theory of Fatigue: A Physical Approach with Application to Lead-Rich Solder
,” ASME J. Appl. Mech.
0021-8936, 69
, pp. 1
–10
.35.
Wong
B.
, and Helling
, D. E.
, 1990, “A Mechanistic Model for Solder Joint Failure Prediction under Thermal Cycling
,” ASME J. Electron. Packag.
1043-7398, 112
, pp. 104
–109
.36.
Zubelewicz
, A.
, Berriche
, R.
, Keer
, L. M.
, and Fine
, M. E.
, 1989, “Lifetime Prediction of Solder Materials
,” ASME J. Electron. Packag.
1043-7398, 111
, pp. 179
–182
.37.
Sharma
, P.
, and Dasgupta
, A.
, 2002, “Micro-Mechanics of Creep-Fatigue Damage in Pb–Sn Solder Due to Thermomechanical Cycling-Part II: Mechanistic Insights and Cyclic Durability Predictions from Monotonic Data
,” ASME J. Electron. Packag.
1043-7398, 124
, pp. 298
–304
.38.
Tribula
, D.
, Grivas
, D.
, Frear
, D. R.
, and Morris
, J. W.
, 1989, “Observations on the Mechanisms of Fatigue in Eutectic Pb-Sn Solder Joints
,” ASME J. Electron. Packag.
1043-7398, 111
, pp. 83
–89
.39.
Igoshev
, V. I.
, and Kleiman
, J. I.
, 2000, “Creep Phenomena in Lead-Free Solders
,” J. Electron. Mater.
0361-5235, 29
(2
), pp 244
–250
.40.
Qian
, Z.
, Ren
, W.
, and Liu
, S.
, 1999, “A Damage Coupling Framework of Unified Viscoplasticity for the Fatigue of Solder Alloys
,” ASME J. Electron. Packag.
1043-7398, 121
, pp. 162
–168
.41.
Ju
, S. H.
, Sandor
, B. I.
, and Plesha
, M. E.
, 1996, “Life Prediction of Solder Joints by Damage and Fracture Mechanics
,” ASME J. Electron. Packag.
1043-7398, 118
, pp. 193
–200
.42.
Zhang
, X.
, Lee
, S.-W. R.
, and Pao
, Y.-H.
, 2000, “A Damage Evolution Model for Thermal Fatigue Analysis of Solder Joints
,” ASME J. Electron. Packag.
1043-7398, 122
, pp. 200
–206
.43.
Gurson
, A. L.
, 1977, “Continuum Theory of Ductile Rupture by Void Nucleation and Growth
,” J. Eng. Mat. Tech.
, Paper No. 76-Mat-CC.44.
Needleman
, A.
, and Tvergaard
, V.
, 1984, “An Analysis of Ductile Rupture in Notched Bars
,” J. Mech. Phys. Solids
0022-5096, 32
(6
), pp. 461
–490
.45.
Li
, H.
, 2003, “FEM Analysis with DSC Modeling for Materials in Chip-Substrate Systems
,” Ph.D. dissertation, University of Arizona, Tucson, AZ.46.
Dishongh
, T. J.
, and Desai
, C. S.
, 1999, “Calibration of the disturbed state model for thermo-mechanical behavior of various solders
,” InterPACK ’99: Pacific RIM/ASME International Intersociety Electronics Photonic Packaging Conference ’Advances in Electronic Packaging 1999
, ASME EEP
26-1
, Maui, HI, pp 433
-439
.47.
Desai
, C. S.
, Basaran
, C.
, Dishongh
, T. J.
, and Prince
, J. L.
, 1998, “Thermomechanical analysis in electronic packaging with unified constitutive model for materials and joints
,” IEEE Trans. Compon., Packag. Manuf. Technol., Part B
1070-9894, 21
(1
), pp. 87
–97
.48.
Desai
, C. S.
, Chia
, J.
, Kundu
, T.
, and Prince
, J. L.
, 1997, “Thermomechanical response of materials and interfaces in electronic packaging: Part I-unified constitutive model and calibration
,” ASME J. Electron. Packag.
1043-7398, 119
(4
), pp. 294
–300
.49.
Shi
, X. Q.
, Zhou
. W.
, Pang
, H. L.J.
, and Wang
, Z. P.
, 1999, “Effect of Temperature and Strain Rate on the Mechanical Properties of 63Sn∕37Pb Solder Alloy
,” ASME J. Electron. Packag.
1043-7398, 21
, pp 179
–185
.50.
Chia
, J. H.
, 1994, “Constitutive Modeling of Thermomechanical Response of Materials in Semiconductor Devices with Emphasis on Interface Behavior
,” Ph.D. Dissertation, University of Arizona, Tucson, AZ.51.
Cook
, R. D.
, Malkus
, D. S.
, and Plesha
, M. E.
, 1989, Concepts and Applications of Finite Element Analysis
, Wiley
.52.
Knecht
, S.
, and Fox
, L.
, 1991, Solder Joint Reliability: Theory in Application
, J. H.
Lau
, ed., Van Nostrand-Reinhold
, New York, Chap. 16.53.
Perzyna
, P.
, “Fundamental Problems in Viscoplasticity
,” 1996, Adv. Appl. Mech.
0065-2156, 9
, pp. 243
–377
.54.
Stephens
, J. J.
, and Frear
D. R.
, 1999, “Time-dependent deformation behavior of near-eutectic 60Sn-40Pb solder
,” Metall. Mater. Trans. A
1073-5623, 30
(5
), pp. 1301
–1313
,55.
Whitenack
, R.
, (2002) private communication.56.
Li
, H.
, (2002), private communication57.
Desai
, C. S.
, Wang
Z.
, and Dube
, M.
, 2001, “New Thermomechanical Device and Testing Towards Modeling Behavior of Joining Materials
,” Proc. IPAC’01 The Pacific Rim/ASME International Electronic Packaging Technical Conference and Exhibition, Kauai, HI
.58.
Pan
, T.-Y.
, 1991, “Thermal Cycling Induced Plastic Deformation in Solder Joints-Part I: Accumulated Deformation in Surface Mount Joints
,” ASME J. Electron. Packag.
1043-7398, 113
, pp. 8
–15
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