Review Article

Creep Constitutive Models Suitable for Solder Alloys in Electronic Assemblies

[+] Author and Article Information
Subhasis Mukherjee

Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: smukher1@umd.edu

Mohammed Nuhi

Department of Reliability Engineering,
University of Maryland,
College Park, MD 20742
e-mail: nuhimohamad@gmail.com

Abhijit Dasgupta

Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: dasgupta@umd.edu

Mohammad Modarres

Department of Reliability Engineering,
University of Maryland,
College Park, MD 20742
e-mail: modarres@umd.edu

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received December 29, 2015; final manuscript received April 4, 2016; published online June 8, 2016. Assoc. Editor: Eric Wong.

J. Electron. Packag 138(3), 030801 (Jun 08, 2016) (13 pages) Paper No: EP-15-1143; doi: 10.1115/1.4033375 History: Received December 29, 2015; Revised April 04, 2016

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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


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.
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.
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. [CrossRef]
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.
Evans, R. W. , and Wilshire, B. , 1985, “Creep of Metals and Alloys,” Institute of Metals, London, UK.
Viswanathan, R. , 1989, Damage Mechanisms and Life Assessment of High-Temperature Components, ASM International, Novelty, OH.
Mott, N. F. , and Nabarro, F. R. N. , 1948, “ Dislocation Theory and Transient Creep,” Physical Society Bristol Conference Report, pp. 1–19.
Garofalo, F. , 1965, Fundamentals of Creep and Creep-Rupture in Metals, Macmillan, New York.
Roesler, J. , Harders, H. , and Baeker, M. , 2010, Mechanical Behaviour of Engineering Materials: Metals, Ceramics, Polymers, and Composites, Springer, Berlin.
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.
Jones, D. R. H. , 2004, “ Creep Failures of Overheated Boiler, Superheater and Reformer Tubes,” Eng. Failure Anal., 11(6), pp. 873–893. [CrossRef]
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. [CrossRef]
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
Stouffer, D. C. , and Dame, L. T. , 1996, Inelastic Deformation of Metals: Models, Mechanical Properties, and Metallurgy, Wiley, New York.
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. [CrossRef]
Parker, E. R. , 1958, “ Modern Concepts of Flow and Fracture,” Trans. ASM, 50, pp. 52–104.
Bailey, R. W. , 1935, “ The Utilization of Creep Test Data in Engineering Design,” Proc. Inst. Mech. Eng., 131(1), pp. 131–349. [CrossRef]
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.
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. [CrossRef]
Wyatt, O. H. , 1953, “ Transient Creep in Pure Metals,” Proc. Phys. Soc. Sect. B, 66(6), pp. 459–480. [CrossRef]
Norton, F. H. , and Bailey, R. W. , 1954, “ Creep of Steel,” Trans. ASM, 52, p. 114.
Nadai, A. , 1938, The Influence of Time Upon Creep, Macmillan Company, New York.
Harmathy, T. Z. , 1967, “ Deflection and Failure of Steel-Supported Floors and Beams in Fire,” ASTM STP 422, pp. 40–62.
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.
ECCC, 1956, “ Classical Work Hardening Model,” ECCC, Rugby, UK.
Ashby, M. F. , and Jones, D. R. H. , 2011, Engineering Materials 1: An Introduction to Properties, Applications and Design, Elsevier, Waltham, MA.
Norton, F. H. , 1929, Creep of Steel at High Temperature, McGraw-Hill, New York.
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.
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.
Hart, E. W. , 1976, “ Constitutive Relations for the Nonelastic Deformation of Metals,” J. Eng. Mater. Technol., 98(3), pp. 193–202. [CrossRef]
Adams, P. J. , 1986, “ Thermal Fatigue of Solder Joints in Micro-Electronic Devices,” M.S. thesis, Massachusetts Institute of Technology, Cambridge, MA.
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. [CrossRef]
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. [CrossRef]
Pei, M. , and Qu, J. , 2005, “ Constitutive Modeling of Lead-Free Solders,” ASME Paper No. IPACK2005-73411.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Wiese, S. , and Meusel, E. , 2003, “ Characterization of Lead-Free Solders in Flip Chip Joints,” ASME J. Electron. Packag., 125(4), pp. 531–538. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Tribula, D. , and Morris, J. J. W. , 1990, “ Creep in Shear of Experimental Solder Joints,” ASME J. Electron. Packag., 112(2), pp. 87–93. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Darveaux, R. , and Banerji, K. , 1992, “ Constitutive Relations for Tin-Based Solder Joints,” IEEE Trans. Compon. Hybrids Manuf. Technol., 15(6), pp. 1013–1024. [CrossRef]
Igoshev, V. I. , and Kleiman, J. I. , 2000, “ Creep Phenomena in Lead-Free Solders,” J. Electron. Mater., 29(2), pp. 244–250. [CrossRef]
US Department of Commerce, “ Lead-Free Solder Data,” Last accessed Mar. 01, 2015, http://www.nist.gov/mml/msed/solder.cfm
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
Ma, H. , 2009, “ Constitutive Models of Creep for Lead-Free Solders,” J. Mater. Sci., 44(14), pp. 3841–3851. [CrossRef]
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.
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.
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. [CrossRef]
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.
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.
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.
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.
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.
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.
Arrowood, R. , Mukherjee, A. , and Jones, W. , 1990, “ Chapter 3 in Solder Mechanics: A State of the Art Assessment,” TMS, Warrendale, PA.
Senkov, O. N. , and Myshlyaev, M. M. , 1986, “ Grain Growth in a Superplastic Zn-22% Al Alloy,” Acta Metall., 34(1), pp. 97–106. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Wiese, S. , and Wolter, K.-J. , 2004, “ Microstructure and Creep Behaviour of Eutectic SnAg and SnAgCu Solders,” Microelectron. Reliab., 44(12), pp. 1923–1931. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Arzt, E. , and Göhring, E. , 1998, “ A Model for Dispersion Strengthening of Ordered Intermetallics at High Temperatures,” Acta Mater., 46(18), pp. 6575–6584. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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.
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. [CrossRef]
Rösler, J. , and Arzt, E. , 1990, “ A New Model-Based Creep Equation for Dispersion Strengthened Materials,” Acta Metall. Mater., 38(4), pp. 671–683. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Stroh, A. N. , 1958, “ Dislocations and Cracks in Anisotropic Elasticity,” Philos. Magazine, 3(30), p. 625–646. [CrossRef]
Nemat-Nasser, S. , and Hori, M. , 1999, Micromechanics: Overall Properties of Heterogeneous Materials, 2nd ed., Elsevier, North Holland.
Mura, T. , 1987, Micromechanics of Defects in Solids, Springer, Dordrecht, The Netherlands.
Eshelby, J. D. , 1959, “ The Elastic Field Outside an Ellipsoidal Inclusion,” Proc. R. Soc. Lond. Ser. Math. Phys. Sci., 252(1271), pp. 561–569. [CrossRef]
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. [CrossRef]
Eshelby, J. D. , Read, W. T. , and Shockley, W. , 1953, “ Anisotropic Elasticity With Applications to Dislocation Theory,” Acta Metall., 1(3), pp. 251–259. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]


Grahic Jump Location
Fig. 1

Typical creep curve for a viscoplastic material

Grahic Jump Location
Fig. 2

Discrepancies in creep data for models used by several authors [61]

Grahic Jump Location
Fig. 3

Multiple length scales in SAC solder

Grahic Jump Location
Fig. 4

Recovery of dislocations from nanoscale Ag3Sn dispersoids by (a) Orowan climb mechanism and (b) dislocation detachment mechanism



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In