Review of Models and the Disturbed State Concept for Thermomechanical Analysis in Electronic Packaging

[+] Author and Article Information
Chandra S. Desai, Russell Whitenack

Department of Civil Engineering and Engineering Mechanics, The University of Arizona, Tucson, AZ 85721

J. Electron. Packag 123(1), 19-33 (Jun 30, 2000) (15 pages) doi:10.1115/1.1324675 History: Received June 30, 2000
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.


Tummala, R. R., and Rymaszewski, E. J., eds., 1989, Microelectronic Packaging Handbook, Van Nostrand Reinhold, NY.
Knecht,  S., and Fox,  L. R., 1990, “Constitutive Relation and Creep-Fatigue Life Model for Eutectic Tin-Load Solder,” IEEE Trans., CHMT,13, No. 2, pp. 424–433.
Ikegami,  K., 1990, “Mechanical Problems in Production Process of Semiconductor Devices,” JSME International Journal,33, pp. 1–12.
Ishikawa, H., and Sasaki, K., 1992, “Constitutive Model for 60 Sn—40 Pb Solder Under Cyclic Loading,” Adv. in Elect. Packaging. Proc. Joint ASME/JSME Conf. in Elect. Packaging, W. T. Chen, and H. Abe, eds., Vol. 1, pp. 401–408.
Darveaux,  R., and Banerji,  K., 1992, “Constitutive Relations for Tin Based Solder Joints,” IEEE Trans. On CHMT,15, No. 6, pp. 1013–1024.
Frear, D. R., Morgan, H., Burchett, S., and Lau, J., 1994, The Mechanics of Solder Alloy Interconnects, Van Nostrand Reinhold, NY.
Desai, C. S., 1995, “Constitutive Modeling Using the Disturbed State as Micro-Structure Self-Adjustment Concept,” Chap. 8 in Continuum Models for Materials with Microstructure, H. B. Mühlhaus, ed., Wiley, U.K.
Desai, C. S., 2001, Mechanics of Materials and Interfaces: The Disturbed State Concept, CRC Press, Boca Raton, FL.
Lau, J. H., 1995, Ball Grid Array Technology, McGraw-Hill, NY.
Solomon, H. D., 1994, “Life Prediction and Accelerated Testing,” Chap. 6 in The Mechanics of Solder Alloy, D. Frear, et al., eds., Van Nostrand Reinhold, NY, pp. 198–313.
Suhir,  E., 1989, “Analytical Modeling in Electronic Packaging Structures: Its Merits, Shortcomings and Interaction with Experimental and Numerical Techniques,” ASME J. Electron. Packag., 111, pp. 157–161.
Desai, C. S., 1997, “Disturbed State Unified Constitutive Modelling for Thermomechanical Behavior and Computer Analysis of Chip-Substrate Systems,” Proc., Interpak 1997, Advances in Electronic Packaging, E. Suhir, M. Shiratori, G. C. Lee, and G. Subharayan, eds., ASME, New York, Vol. 2, pp. 1605–1611.
Chia, J., and Chia, H., 1997, “Implementation of Disturbance Function to Determine Thermal Fatigue Life of Solder Joints in QFP Packages,” Proc., Interpak 1997, Advances in Electronic Packaging, E. Suhir, M. Shiratori, G. C. Lee, and G. Subharayan, eds., ASME, New York, Vol. 2, pp. 1479–1485.
Desai,  C. S., Somasundaram,  S., and Frantziskonis,  G., 1986, “A Hierarchical Approach for Constitutive Modeling of Geologic Materials,” Int. J. Num. Analyt. Methods in Geomech.,10, pp. 225–257.
Desai,  C. S., and Toth,  J., 1996, “Disturbed State Constitutive Modeling Based on Stress-Strain and Nondestructive Behavior,” Int. J. Solids Struct., 33, No. 11, pp. 1619–1650.
Desai,  C. S., 1997, “Integrated Procedure for Microcrack Initiation and Growth and Fracture Using the Disturbed State Concept, Report, Dept. of Civil Eng. and Eng. Mechs., The Univ. of Arizona, Tucson, AZ.
Guo,  Q., Cutiongco,  E. C., Keer,  L. M., and Fine,  M. E., 1992, “Thermomechanical Fatigue Life Prediction of 63 Sn/37 PB Solder,” ASME J. Electron. Packag., 114, pp. 145–151.
Coffin, L. F., Jr., 1969, “Predictive Parameters and Their Application to High Temperature, Low-Cycle Fatigue,” Proc., Second Int. Conf. on Fracture, Chapman and Hall, London, pp. 643–654.
Manson, S. S., 1966, Thermal Stress and Low Cycle Fatigue, McGraw-Hill, NY.
Norris, K. C., and Landzberg, A. H., 1969, “Reliability of Controlled Collapse Interconnections,” IBM J. Res. Dev., May, pp. 266–271.
Engelmaier, W., 1984, “Functional Cycles and Surface Mounting Attachment Reliability,” Surf. Mount. Technol., Int. Soc. of Hybrid Microelectronics, Monogram Series 6984-002, Silver Springs, MD, p. 87.
Ostergren,  W. J., 1976, “A Damage Function and Associated Failure Equations for Predicting Hold Time and Frequency Effects in Elevated Temperature, Low Cycle Fatigue,” J. Test. Eval., 4, No. 5, pp. 327–339.
Charles,  H. K., and Clatterbaugh,  G. V., 1990, “Solder Joint Reliability—Design Implications from Finite Element Modeling and Experimental Testing,” ASME J. Electron. Packag., 112, pp. 135–146.
Rice,  J. R., 1968, “A Path Independent Integral and Approximate Analysis of Strain Concentration by Notches and Cracks,” ASME J. Appl. Mech., 35, pp. 379–386.
Dowling, N. E., and Begley, J. A., 1976, “Fatigue Crack Growth During Gross Plasticity and the J-Integral Mechanics of Crack Growth, Cracks and Fracture,” ASTM STP 590, pp. 82–103.
Guo, Z., Sprecher, A. F., and Conrad, H., 1992, “Effect on Sn Content on Crack Growth Rate in Low-Cycle Fatigue of Pb-Sn Solder Joints,” Proc., 7th Electronic Materials and Processing Congress, Cambridge, MA, pp. 209–216.
Lau, J. H., 1993, “Thermal Fatigue Life Prediction of Flip Chip Solder Joints by Fracture Mechanics Method,” Int. J. Eng. Fracture Mechanics, pp. 643–654.
Frear,  D. R., and Vianco,  P. T., 1994, “Intermetallic Growth and Mechanical Behavior of Low and High Melting Temperature Solder Alloys,” Metall. Mater. Trans. A, 25A, pp. 1509–1523.
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., 118, pp. 193–200.
Kachanov, L. M., 1986, Introduction to Continuum Damage Mechanics, Martinus Nijhuft Publ., Dordrecht, The Netherlands.
Murakami,  S., 1983, “Notes on Continuum Damage Mechanics and Its Application to Anisotropic Creep Damage Theory,” ASME J. Eng. Mater. Technol., 105, pp. 95–105.
Perzyna,  P., 1966, “Fundamental Problems in Viscoplasticity,” Adv. Appl. Mech., 9, pp. 243–377.
Subramanyan,  R., Wilcox,  J. R., and Li,  C., 1989, “A Damage Integral Approach to Thermal Fatigue of Solder Joints,” Trans. IEEE Comp., Hyb. And Plant Tech.,12, No. 4, pp. 480–491.
Ellyin,  F., and Golos,  K., 1988, “Multiaxial Fatigue Damage Criterion,” ASME J. Eng. Mater. Technol., 110, pp. 63–68.
Heiduschke,  K., 1998, “Solder Joint Lifetime Assessment of Electronic Devices,” Int. J. Numer. Methods Eng., 41, pp. 211–231.
Maciucescu, L., Sham, T. L., and Krempl, E., 1998, “VBO: A State Variable Constitutive Equation for a Solder Alloy,” ASME J. Electron. Packag., in press.
Fong, J. T., 1975, “Energy Approach for Creep-Fatigue Interactions in Metals at High Temperatures,” ASME J. Pressure Vessel Technol., pp. 214–222.
Garud,  Y. S., 1981, “A New Approach to the Evaluation of Fatigue Under Multiaxial Loadings,” Trans. ASME, 103, pp. 118–125.
Dasgupta,  A., Oyan,  C., Barker,  D., and Pecht,  M., 1992, “Solder Creep-Fatigue Analysis by an Energy-Partitioning Approach,” ASME J. Electron. Packag., 114, p. 152.
Sarihan, V., 1993, “Energy-based Methodology for Damage and Life Prediction of Solder Joints Under Thermal Cycling,” Proc., IEEE, 43rd ECTC Conference.
Zubelewicz,  A., and Keer,  L. M., 1989, “Micromechanically Based Constitutive Modeling of Crystalline Materials,” Int. J. Solids Struct., 25, No. 7, pp. 797–801.
Zubelewicz,  A., Guo,  Q., Cutiongco,  E. C., Fine,  M. E., and Keer,  L. M., 1990, “Micromechanical Method to Predict Fatigue Life of Solder,” ASME J. Electron. Packag., 112, p. 179.
Desai,  C. S., Dishongh,  T., and Deneke,  P., 1998, “Disturbed State Constitutive Model for Thermomechanical Behavior of Dislocated Silicon with Impurities,” J. Appl. Phys., 84, pp. 5977–5984.
Chia,  J., and Desai,  C. S., 1994, “Constitutive Modeling of Thermomechanical Response of Materials in Semiconductor Devices Using the Disturbed State Concept,” Report to NSF, Dept. of Civil Eng. and Eng. Mechs., The Univ. of Arizona, Tucson, AZ.
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, Part II—Unified Constitutive Models, Validation and Design,” ASME J. Electron. Packag., 119, pp. 294–330 and 301–309.
Roscoe,  K. H., Schofield,  A., and Wroth,  C. P., 1958, “On the Yielding of Soils,” Geotechnique, 8, pp. 22–53.
Desai,  C. S., Basaran,  C., Dishongh,  T., 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, 21, pp. 87–97.
Desai,  C. S., and Ma,  Y., 1992, “Modeling of Joints and Interfaces Using the Disturbed State Concept,” Int. J. Num. Analyt. Methods in Geomech.,16, pp. 623–653.
Raissain, M., Desai, C. S., and Lee, J. T., 1999, “A Unified Model Based on Disturbed State Concept and Multi Domain Method for Design and Reliability in Electronic Packaging,” Proc., Interpak 99, Hawaii.
Desai,  C. S., Park,  I. J., and Shao,  C., 1998, “Fundamental Yet Simplified Model for Liquefaction Instability,” Int. J. Num. Analyt. Methods in Geomechanics,22, pp. 721–748.
Desai,  C. S., 2000, “Liquefaction Using Disturbance and Energy Approaches,” J. of Geotech. And Geoenv. Eng., ASCE, 126, No. 7, pp. 618–631.
de Borst,  R., Sluys,  L. J., Mühlhaus,  H. B., and Pamin,  J., 1993, “Fundamental Issues in Finite Element Analyses of Localization of Deformation,” J. Eng. Comput.,10, pp. 99–121.
Bazant,  Z. P., 1994, “Nonlocal Damage Theory Based on Micromechanics and Crack Interactions,” J. Eng. Mech. Div., Am. Soc. Civ. Eng., 120, pp. 593–617.
Desai,  C. S., Basaran,  C., and Zhang,  W., 1997, “Numerical Algorithms and Mesh Dependence in the Disturbed State Concept,” Int. J. Numer. Methods Eng., 40, pp. 3059–3083.
Desai,  C. S., and Zhang,  W., 1998, “Computational Aspects of Disturbed State Constitutive Models,” Int. J. Computer Methods in Appl. Mech. and Eng.,151, pp. 361–376.
Basaran,  C., Desai,  C. S., and Kundu,  T., 1998, “Thermo-mechanical Finite Element Analysis of Problems in Electronic Packaging Using the Disturbed State Concept: Part I—Theory and Formulation, Part II—Verification and Application,” ASME J. Electron. Packag., 120, pp. 41–47, 48–53.
Dishongh, T. J., and Desai, C. S., 1999, “Calibration of the Disturbed State Model for Thermomechanical Behavior of Various Solders,” Proc., Interpak 99, Hawaii.
Zwick, J. W., Desai, C. S., and Ferdie, R. D., 1999, “Thermo-structural Analysis of a 313-Pin Plastic Ball Grid Array (PBGA),” Proc., NAFEMS Int. Conf., Newport, RI.
Zwick, J. W., and Desai, C. S., 1999, “Structural Reliability of PBGA Solder Joints with the Disturbed State Concept,” Proc., Interpak 99, Hawaii.
Solomon, H. D., 1985, “Low Cycle Fatigue of 60/40 Solder Plastic Strain Limited vs Displacement Limited Testing,” Proc., ASM Elect. Packaging Materials and Processes, pp. 29–47.
Gerke, R. D., 1994, “Ceramic Solder-Grid-Array Interconnection Reliability Over a Wide Temperature Range,” Proc., Nat. Elect. Packaging and Production Conf., Anaheim, CA, pp. 1087–1094.
Pecht, M. G., and Nash, F. R., 1994, “Predicting the Reliability of Electronic Equipment,” Proc., IEEE, Vol. 82, No. 7, pp. 992–1004; Perzyna, P., 1966, “Fundamental Problems in Viscoplasticity,” Advances in Applied Mechanics, Academic Press, NY, pp. 244–368.
Darveaux, R., 1995, “Optimizing the Reliability of Their Small Outline Package (TSOP) Solder Joints,” Advances in Electronic Packaging, ASME, EEP Vol. 10-2, pp. 675–681.
Gaffarian, R., 1997, “Ball Grid Array Packaging RTOP; Interim Environmental Test Results,” Jet Propulsion Laboratory, California Inst. Tech., Pasadena, CA.


Grahic Jump Location
Yield function F in J2D−J1 stress space
Grahic Jump Location
Disturbance and cyclic behavior
Grahic Jump Location
Relation between ξD,N, and parameter b. (a) Relation between deviatoric strain trajectory, ξD, and cycle number, N; (b) determination of parameter b from finite element analysis.
Grahic Jump Location
Solder element and loading wave forms (Chia and Desai 44)
Grahic Jump Location
Finite element mesh for solder bump in 313-Pin PBGA and cyclic loading (Zwick et al. 58)
Grahic Jump Location
Contours of disturbance and fractional volumes for different criteria (Zwick et al. 58) (percentage package failures is based on a total of 4 packages tested). (a) Contours of disturbance; (b) fractional volume versus cycles
Grahic Jump Location
Fractional volume versus cycles with different number of elements and Nr=10 (percentage package failures is based on a total of 4 packages tested)
Grahic Jump Location
Fractional volume versus cycles for different Nr values for two different disturbance criteria (percentage package failures is based on a total of 4 packages tested)
Grahic Jump Location
Distribution of disturbance from full cycle and accelerated analysis
Grahic Jump Location
Comparison of predicted disturbance distributions at N=4000 for different b values, Nr=10
Grahic Jump Location
Finite element mesh with 256 elements
Grahic Jump Location
Computed stress and disturbance at point A (Fig. 19) for 16, 64, and 256 element meshes. (a) Axial stress versus strain; (b) disturbance versus deviatoric plastic strain trajectory.
Grahic Jump Location
Cyclic softening behavior: 60/40 (Sn/Pb) solder γ̇=5 percent and temperature=350 K (Chia and Desai 44)
Grahic Jump Location
Plots of various quantities versus number of cycles: 60/40 (Sn/Pb) solder, shear strain range=±2 percent at typical temperature=350 K (Chia and Desai 44)
Grahic Jump Location
Comparison of the predicted and Solomon’s results for fatigue life of 60/40 (Pb/Sn) solder joints: (a) 300 K, (b) 400 K (Chia and Desai 44)
Grahic Jump Location
Comparison of J-integral and creep-fatigue damage analysis (Ju et al. 29)
Grahic Jump Location
313-PBGA and NASTRAN Model (Zwick and Desai 59)
Grahic Jump Location
Symbolic representations of DSC




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