A unified viscoplastic constitutive model for the fatigue life prediction of solder alloy 63Sn-37Pb is presented. The model incorporates the strain rate effect, the creep-plastic interaction and the dwell time effect under cyclic strain and stress loading. The applicability of this constitutive model is examined with cyclic strain tests with different strain rates, and cyclic stress tests under different stress waveforms in order to verify the progressive viscoplastic deformation of 63Sn-37Pb solder alloy. The investigation reveals that the material constants in the constitutive model can be determined by performing simple tests such as creep and cyclic tension-compression loading. The predictions using the constitutive model are found to agree well with the experimental results of the solder alloy under different loading. The agreement demonstrates that the model can satisfactorily describe the viscoplastic deformation behaviour under cyclic strain loading or stress loading.
PaydarN.TongY.AkayH. U.A finite element study of factors affecting fatigue life of solder joints. Trans. ASME, J. Electron. Packaging, 1994, 116, 265–273.
2.
BhattiP. K.GschwendK.KwangA. Y.SyedR. A.Three dimensional creep analysis of solder joints in surface mount device. Trans. ASME, J. Electron. Packaging, 1995, 117, 20–25.
3.
LingS.DasguptaA.1997, A nonlinear multi-domain thermomechanical stress analysis method for surfacemount solder joints. Part 2: Viscoplastic analysis. Trans. ASME, J. Electron. Packaging, 1997, 119, 177–182.
4.
FuC.McDowellD. L.UmeI. C.A finite element procedure of a cyclic thermoviscoplasticity model for solder and copper interconnects. Trans. ASME, J. Electron. Packaging, 1998, 120, 24–34.
5.
IshikawaH.SasakiK.OhguchiK.Prediction of fatigue failure of 60Sn-40Pb solder using constitutive model for viscoplasticity. Trans. ASME, J. Electron. Packaging, 1996, 118, 164–169.
6.
VaynmanS.FineM. E.JeannotteD. A.Isothermal fatigue failure mechanisms in low tin lead based solder. In TMS-AIME Symposium on Effect of Load and Thermal Histories on Mechanical Behavior of Materials (Eds LiawP. R.NicholasT.), Denver, Colorado, 1987, pp. 127–137 (Metallurgical Society of AIME, Warrendale, Pennsylvania).
7.
VaynmanS.MorrisE. F.JeannotteD. A.Low cycle isothermal fatigue of solder materials. In Solder Mechanics: A State of the Art Assessment (Eds FrearD. R.JonesW. B.KinsmanK. R.), 1991, Ch. 4, pp. 155–189.
8.
YangX. J.ChowC. L.LauK. J.A time-dependent cyclic failure model of 63Sn/37Pb solder alloy. Int. J. Fatigue, 2003, 25, 533–546.
9.
ShiX. Q.ZhouW.PangH. L. J.WangZ. P.Effect of temperature and strain rate on mechanical properties of 63Sn/37Pb solder alloy. Trans. ASME, J. Electron. Packaging, 1999, 121, 179–185.
10.
ShiX. Q.PangH. L. J.ZhouW.WangZ. P.Low cycle fatigue analysis of temperature and frequency effects in eutectic solder alloy. Int. J. Fatigue, 2000, 22, 217–228.
11.
BussoE. P.KitanoM.KumazawaT.Modeling complex inelastic deformation processes in IC package's solder joints. Trans. ASME, J. Electron. Packaging, 1994, 116, 6–15.
12.
BussoE. P.KitanoM.KumazawaT.A visco-plastic constitutive model for 60/40 tin-lead solder used in IC package joints. Trans. ASME, J. Engng Mater. Technol., 1992, 114, 331–337.
13.
SolomonH. D. Creep, Strain rate sensitivity and low cycle fatigue of 60/40 solder. Brazing Soldering, 1986, 11, 68–75.
14.
SolomonH. D.TolksdorfE. D.Energy approach to the fatigue of 60/40 solder. Part 1: Influence of temperature and cycle frequency. Trans. ASME, J. Electron. Packaging, 1995, 117(6), 130–135.
15.
SolomonH. D.TolksdorfE. D.Energy approach to the fatigue of 60/40 solder. Part 2: Influence of hold time and asymmetric loading. Trans. ASME, J. Electron. Packaging, 1996, 118(6), 67–71.
16.
GuoQ.CutiogcoE. C.KeerL. M.FineM. E.Thermomechanical fatigue life prediction of 63Sn/37Pb solder. Trans. ASME, J. Electron. Packaging, 1992, 114, 145–151.
17.
HongB. Z.Analysis of thermomechanical interactions in a miniature solder system under cyclic fatigue loading. J. Electron. Mater., 1999, 28(9), 1071–1077.
18.
HongB. Z.BurrellL. G.Modeling thermally induced viscoplastic deformation and low cycle fatigue of CBGA solder joints in a surface mount package. IEEE Trans Components, Packaging, Mfg Technol. A, 1997, 20(3), 280–285.
19.
McDowellD. L.MillerM. P.BrooksD. C.A unified creep-plasticity theory for solder alloys. Fatigue of Electronic Materials, ASTM STP 1153, 1994, pp. 42–59 (American Society for Testing and Materials, Philadelphia, Pennsylvania).
20.
ShineM. C.FoxL. R.Fatigue of solder joints in surface mount devices. Low Cycle Fatigue, ASTM STP 942, 1994, pp. 588–610 (American Society for Testing and Materials, Philadelphia, Pennsylvania).
21.
WenL. C.RossR. G.Comparison of LCC solder joint life predictions with experimental data. Trans. ASME, J. Electron. Packaging, 1995, 117, 109–115.
22.
FrearD. R.BurchettS. N.NeilsenM. K.StephensJ. J.Microstructurally based finite element simulation of solder joint behavior. Soldering Surface Mount Technol., 1997, 2, 39–42.
23.
LauJ. H.PaoY. H.Solder Joint Reliability of BGA, CSP, Flip Chip and Fine Pitch SMT Assemblies, 1997 (McGraw-Hill, New York).
24.
SkiporA. F.HarrenS. V.BotsisJ.On the constitutive response of 63/37 Sn/Pb eutectic solder. Trans. ASME, J. Engng Mater. Technol., 1996, 118, 1–11.
25.
MaciucescuL.ShamT.-L.KremplE.Modeling the deformation behavior of a Sn-Pb solder alloy using the simplified viscoplasticity theory based on overstress (VBO). Trans. ASME, J. Electron. Packaging, 1999, 121, 92–98.
26.
LiS. R.A methodology for fatigue prediction of electronic components under random vibration load. Trans. ASME, J. Electron. Packaging, 2001, 123, 394–400.
27.
ZhangX.LeeS.-W. R.PaoY. H.A damage evolution model for thermal fatigue analysis of solder joints. Trans. ASME, J. Electron. Packaging, 2000, 122, 200–206.
28.
YangX. J.Constitutive description of temperature-dependent nonproportional cyclic viscoplasticity. Trans. ASME, J. Engng Mater. Technol., 1997, 119, 12–19.
29.
ChabocheJ. L.RousselierG.On the plastic and viscoplastic constitutive equations. Part 1: Rules developed with internal variable concept. Trans. ASME, J. Pressure Vessel Technol., 1983, 105, 153–158.
30.
SasakiK.OhguchiK.IshikawaH.Viscoplastic deformation of 40Pb/60Sn solder alloysâε”experiments and constitutive modeling. Trans. ASME, J. Electron. Packaging, 2001, 123, 379–387.
31.
ChowC. L.WeiY.Constitutive modeling of material damage for fatigue failure prediction. Int. J. Damage Mechanics, 1999, 8, 355–375.
32.
WeiY.ChowC. L.NeilsenM. K.FangH. E.Damage mechanics based fatigue life prediction for 63Sn-37Pb solder material. In Proceedings of the ASME International Mechanical Engineering Congress and Exposition, 2000, EEP-Vol. 28, pp. 161–165 (American Society of Mechanical Engineers, New York).
33.
BariS.HassanT.Kinematic hardening rules in uncoupled modeling for multiaxial ratcheting simulation. Int. J. Plasticity, 2001, 17, 885–905.
34.
OhnoN.WangJ.-D.Kinematic hardening rules with critical state of dynamic recovery. Part 1: Formulations and basic features for ratcheting behavior. Int. J. Plasticity, 1993, 9, 375–390.
35.
JiangY.SehitogluH.Modeling of cyclic ratcheting plasticity. Part 1: Development of constitutive relations. Trans. ASME, J. Appl. Mechanics, 1996, 63, 720–725.
