A Theory of Fatigue: A Physical Approach With Application to Lead-Rich Solder

[+] Author and Article Information
S. Wen, L. M. Keer

Department of Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60201

J. Appl. Mech 69(1), 1-10 (Jun 08, 2001) (10 pages) doi:10.1115/1.1412453 History: Received March 07, 2001; Revised June 08, 2001
Copyright © 2002 by ASME
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SEMATECH, 1999, The International Technology Roadmap for Semiconductors: 1999 Edition, International SEMATECH, Austin, TX.
Lee,  W. W., Nguyen,  L. T., and Selvaduray,  G. S., 2000, “Solder Joint Fatigue Models: Review and Applicability to Chip Scale Packages,” Microelectron. Reliab., 40, pp. 231–244.
Vaynman,  S., and Zubelewicz,  A., 1990, “Fatigue Life Prediction For Low-Tin Lead-Based Solder At Low Strains,” Weld. J. (Miami), 69, pp. S395–S398.
Frear,  D. R., Grivas,  D., and Morris,  J. W., 1988, “Thermal Fatigue in Solder Joints,” Journal of Metals 40, pp. 18–22.
Rathore,  H. S., Yih,  R. C., and Edenfeld,  A. R., 1973, “Fatigue Behavior of Solders Used in Flip-Chip Technology,” J. Test. Eval., 1, pp. 170–178.
Stolkarts,  V., Keer,  L. M., and Fine,  M. E., 1999, “Damage Evolution Governed by Microcrack Nucleation With Application to the Fatigue of 63Sn-37Pb Solder,” J. Mech. Phys. Solids, 47, pp. 2451–2468.
Vaynman, S., 1987, “Isothermal Fatigue of 96.5Pb-3.5Sn Solder,” Ph.D. dissertation, Northwestern University, Evanston, IL.
Lawson, L. R., 1989, “Thermomechanical Fatigue of 97Pb-3Sn,” Ph.D. dissertation, Northwestern University, Evanston, IL.
Forsyth,  P. J. E., 1953, “Exudation of Material From Slip Bands at the Surface of Fatigued Crystals of an Aluminum-Copper Alloy,” Nature (London), 171, pp. 172–173.
Mavoori, H., 1996, “Mechanical Properties and Fatigue Lifetime Prediction of Solders for Electronic Applications: Tin-Silver and Tin-Zinc Eutectics,” Ph.D. dissertation, Northwestern Universty, Evanston, IL.
Lin,  T. H., and Ito,  Y. M., 1969, “Micromechanics of a Fatigue Crack Nucleation Mechanism,” J. Mech. Phys. Solids, 17, pp. 511–523.
Mura,  T., and Nakasone,  Y., 1990, “A Theory of Fatigue Crack Initiation in Solids,” ASME J. Appl. Mech., 57, pp. 1–6.
Mura,  T., 1994, “A Theory of Fatigue-Crack Initiation,” Mater. Sci. Eng., A, 176, pp. 61–70.
Shodja,  H. M., Hirose,  Y., and Mura,  T., 1996, “Intergranular Crack Nucleation in Bicrystalline Materials Under Fatigue,” ASME J. Appl. Mech., 63, pp. 788–795.
Fine,  M. E., 2000, “Phase Transformation Theory Applied to Elevated Temperature Fatigue,” Scr. Mater., 42, pp. 1007–1012.
Lin,  T. H., Wong,  K. K. F., Teng,  N. J., and Lin,  S. R., 1998, “Micromechanic Analysis of Fatigue Band Crossing Grain Boundary,” Mater. Sci. Eng., A, 246, pp. 169–179.
Hirth, J. P., and Lothe, J., 1982, Theory of Dislocations, 2nd Ed., John Wiley and Sons, New York.
Lin, T. H., 1992, “Micromechanics of Crack Initiation in High-Cycle Fatigue,” Advances in Applied Mechanics, Vol. 29, Academic Press, New York, pp. 1–62.
Suresh, S., 1998, Fatigue of Materials, 2nd Ed., Cambridge University Press, Cambridge, U.K.
Dingli,  J. P., Abdul-Latif,  A., and Saanouni,  K., 2000, “Predictions of the Complex Cyclic Behavior of Polycrystals Using a Self-Consistent Modeling,” Int. J. Plast. 16, pp. 411–437.
Chin, G. Y., 1973, “The Role of Preferred Orientation in Plastic Deformation,” Inhomogeneity of Plastic Deformation, ASM, Metals Park, OH, pp. 83–111.
Yue,  Z. F., Tao,  X. D., Ying,  Z. Y., and Li,  H. Y., 2000, “A Crystallographic Model for the Orientation Dependence of Low Cyclic Fatigue Property of a Nickel-Base Single Crystal Superalloy,” Appl. Math. Mech., 21, pp. 415–424 (English Edition).
Zhang,  Z. F., and Wang,  Z. G., 1998, “Effect of Component Crystal Orientations on the Cyclic Stress-Strain Behavior of Copper Bicrystals,” Mater. Sci. Eng., A, 255, pp. 148–153.
Henderson,  M. B., and Martin,  J. W., 1996, “The Influence of Crystal Orientation on the High Temperature Fatigue Crack Growth of a Ni-Based Single Crystal Superalloy,” Acta Mater., 44, pp. 111–126.
Li,  X. W., Wang,  Z. G., and Li,  S. X., 1999, “Influence of Crystallographic Orientation on Cyclic Strain-Hardening Behaviour of Copper Single Crystals,” Philos. Mag. Lett., 79, pp. 869–875.
Tan,  X., Gu,  H., Laird,  C., and Munroe,  N. D. H., 1998, “Cyclic Deformation Behavior of High-Purity Titanium Single Crystals: Part I. Orientation Dependence of Stress-Strain Response,” Metall. Mater. Trans. A, 29, pp. 507–512.
Bonda,  N. R., and Noyan,  I. C., 1996, “Effect of the Specimen Size in Predicting the Mechanical Properties of PbSn Solder Alloys,” IEEE Trans. Compon. Pack. Manufact. Tech., Part A, 19, pp. 208–212.
Bonda,  N. R., and Noyan,  I. C., 1992, “Deformation Inhomogeneity and Representative Volume in Pb/Sn Solder Alloys,” Metall. Trans. A, 23, pp. 479–484.
Guo,  Q., Cutiongco,  E. C., Keer,  L. M., and Fine,  M. E., 1992, “Thermomechanical Fatigue Life Prediction of 63Sn/37Pb Solder,” ASME J. Electron. Packag., 114, pp. 145–151.
Stauffer, D., and Aharony, A., 1992, Introduction to Percolation Theory, 2nd Ed., Taylor & Francis, Washington, DC.
Adams,  B. L., Boehler,  J. P., Guidi,  M., and Onat,  E. T., 1992, “Group Theory and Representation of Microstructure and Mechanical Behavior of Polycrystals,” J. Mech. Phys. Solids, 40, pp. 723–737.
Bunge,  H. J., 1987, “Three-Dimensional Texture Analysis,” Int. Mater. Rev., 32, pp. 265–291.
Park,  N. J., and Bunge,  H. J., 1990, “Determination of the Orientation Distribution Function of a Cuznal Shape Memory Alloy,” Z. Metallkd., 81, pp. 636–645.
Kumar,  S., Kurtz,  S. K., and Agarwala,  V. K., 1996, “Micro-Stress Distribution Within Polycrystalline Aggregate,” Acta Mech., 114, pp. 203–216.
Barrett, C. S., and Massalski, T. B., 1980, Structure of Metals: Crystallographic Methods, Principles and Data, 3rd Rev. Ed., Pergamon, New York.
Lawson,  L. R., 1987, “Thermal Cycling Apparatus For Thermomechanical Fatigue Testing,” Rev. Sci. Instrum., 58, pp. 1942–1944.
Marinescu, G. M., Chen, Y. Y. T., Li, H. H., Beaumont, M., Chen, J. C. F., and Ho, C. Y., 1999, “Thermal, Mechanical, Electrical, and Physical Properties of Selected Packaging Materials,” Report No. CINDAS Report 126, Center for Information and Numerical Data Analysis and Synthesis (CINDAS) of Purdue University, West Lafayette, IN.
Liang,  J., Gollhardt,  N., Lee,  P. S., Schroeder,  S. A., and Morris,  W. L., 1996, “A Study of Fatigue and Creep Behavior of Four High Temperature Solders,” Fatigue Fract. Eng. Mater. Struct., 19, pp. 1401–1409.


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Cyclic peak stresses plot for 96.5Pb-3.5Sn solder
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Microcracks appeared on the surface of a 96.5Pb-3.5Sn solder specimen after about 6800 cycles under strain-controlled fatigue test (25°C, Δε=0.006)
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(a) Striations on the surface of a 96.5Pb-3.5Sn solder specimen after strain-controlled isothermal fatigue test (adopted from S. Vaynman’s Ph.D. dissertation 7, Fig. 45); (b) microcracked grain after strain controlled thermomechanical fatigue test (adopted from L. Lawson’s Ph.D. dissertation 8, Fig. 17)
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The originally smooth surface of 96.5Pb-3.5Sn solder specimen now shows an agglomeration of extrusions, intrusions, striations of PSB and microcracks, with the pattern orienting at roughly 45 deg to the loading axis (vertical)
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Schmid factor m for a slip system within a crystal that undergoes uniaxial loading
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The Schmid factor and the critical number of cycles to initiate a microcrack: m-N curve
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Contours of a constant Schmid factor for uniaxial tension based on {111}〈110〉 slip (reproduced with modification from Fig. 2 (21))
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Peak shear stresses change with number of cycles for silver modified PbSn solder with a strain rate of 0.003/sec (data taken from J. Liang et al., Fig. 7(a)(38))
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Peak stresses evolution during fatigue testing and definition of fatigue point
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Fatigue process illustration when stresses are assumed uniform throughout the structure
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(a) Fatigue and inelastic strain under strain-controlled isothermal fatigue test (εmin=0,ramp=2.5 s, partial data from S. Vaynman); (b) fatigue and stresses under strain-controlled isothermal fatigue test (εmin=0,ramp=2.5 s, partial data from S. Vaynman); (c) fatigue and inelastic strain under strain-controlled thermomechanical fatigue testing—conducted by L. Lawson during 1987–1989; (d) fatigue and stresses range under strain-controlled thermomechanical fatigue testing—conducted by L. Lawson during 1987–1989; (e) fatigue and inelastic strain under isothermal and thermomechanical fatigue testing—conducted by L. Lawson during 1987–1989 (temperatures are 15–60°C, 25–80°C, 60°C, 80°C, and 100°C; strain ranges from 0.3–3 percent; strain rate from 1.15×10−5∼3.0×10−3 s−1); (f ) fatigue and true stresses under isothermal and thermomechanical fatigue testing—conducted by L. Lawson during 1987–1989 (temperatures are 15–60°C, 25–80°C, 60°C, 80°C, and 100°C; strain ranges from 0.3–3 percent; strain rate from 1.15×10−5∼3.0×10−3 s−1)




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