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Energy-Based Micromechanics Analysis on Fatigue Crack Propagation Behavior in Sn-Ag Eutectic Solder

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Sn-Ag-eutectic-based solders are replacing Sn-Pb eutectic solders in the electronics industry. The current paper extends the recently developed approach based on phase transformation theory, micromechanics, and fracture mechanics to treat fatigue crack nucleation and propagation for steels and alloys to predict fatigue crack propagation in solder alloys. To verify the proposed method, fatigue experiments were conducted on Sn-3.5Ag solder alloys. Finite element analysis is performed to predict the stress intensity factor range ΔK and the required energy U to increase the crack by a unit area. Unified creep-plasticity theory and a cohesive zone model are incorporated to predict the creep and hysteresis effects on fatigue crack propagation in solder and the interfacial behavior between the solder alloy and the intermetallic layer, respectively. With U determined numerically, the predicted fatigue crack propagation rate using phase transformation theory is compared with experimental data for Sn-3.5Ag and Sn-37Pb eutectic solders. Reasonable agreement between theoretical predictions and experimental results is obtained.

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Abbreviations

ΔA :

area of crack

A :

material constant

da/dN :

area of crack growth per cycle

b :

specimen thickness

B :

a dimensionless constant

C :

matrix of the elastic constants

d :

drag strength

D :

material constant

E :

Young’s modulus

G :

Shear modulus

J :

J-integral value

k :

universal gas constant

ΔK :

stress intensity factor range

ΔK c :

critical stress intensity factor

l, m, n :

material constant

N :

direction of the deformation loading

Q :

apparent activation energy

R :

radius of the yield space

S :

deviatoric stress tensor

S v :

viscous overstress

T :

temperature

U :

the energy to propagate a unit fatigue crack surface

ΔW :

the energy required to increase the crack area by ΔA

ΔW 1a :

the gain in energy per unit area due to loss of defects as the crack advances ΔA under constant ΔK (the stress intensity range)

ΔW 1b :

the energy per unit area consumed by the extension of the plastic zone

ΔW 2 :

the stored elastic energy

ΔW 3 :

the plastic work per unit area transferred to heat for each cyclic loading step

α :

deviatoric back stress

β :

material constant

γ T :

total surface energy per unit area of crack

μ :

material constants

σ :

maximum stress in the cycle

σ y :

yield stress

ν :

Poisson’s ratio

\( {\dot {{\varvec \upvarepsilon}}} \) :

total strain rate

\({\dot {{\varvec \upvarepsilon}}}^{{\rm{in}}} \) :

inelastic strain rate

Θ :

diffusivity term

χ :

coefficient of thermal expansion

η :

material constants

References

  1. P.C. Paris, Fatigue Frac. Eng. Mater. Struct. 21, 535 (1998)

    Article  Google Scholar 

  2. L. Leicht, A. Skipor, Int. J. Microcircuits Electron. Pkg. 22, 57 (1999)

    Google Scholar 

  3. X. Liu, V.K. Sooklal, M.A. Verges, M.C. Larson, Microelectron. Reliability 46, 1128 (2006)

    Article  CAS  Google Scholar 

  4. P. Towashiraporn, G. Subbarayan, C.S. Desai, Int. J. Solids Struct. 42, 4468 (2005)

    Article  Google Scholar 

  5. D. Shangguan, Solder. Surf. Mount Tech. 11, 27 (1999)

    Article  CAS  Google Scholar 

  6. D.R. Frear, J.W. Jang, J.K. Lin, C. Zhang, JOM 53, 28 (2001)

    Article  CAS  Google Scholar 

  7. D.H. Kim, P. Elenius, S. Barrett, IEEE Trans. EPM 25, 84 (2002)

    CAS  Google Scholar 

  8. A.F. Bower, D. Craft, Fatigue Frac. Eng. Mater. Struct. 21, 611 (1998)

    Article  Google Scholar 

  9. H.N. Hashemi, P. Yang, Int. J. Fatigue 23, 325 (2001)

    Article  Google Scholar 

  10. M. Erinc, P.J.G. Schreurs, G.Q. Zhang, M.G.D. Geers, J. Mater. Sci. 16, 700 (2005)

    Google Scholar 

  11. M.E. Fine, Scrip. Mater. 42, 1007 (2000)

    Article  CAS  Google Scholar 

  12. P.B. Shrikant, M.E. Fine, Mater. Sci. Eng. A 314, 90 (2001)

    Article  Google Scholar 

  13. P.K. Liaw, S.I. Kwun, M.E. Fine, Metal. Trans. A 12, 49 (1981)

    Article  CAS  Google Scholar 

  14. J.K. Shang, Q.L. Zeng, L. Zhang, Q.S. Zhu, J. Mater. Sci. 18, 211 (2007)

    Article  CAS  Google Scholar 

  15. C. Kanchanomai, Y. Mutoh, Fatigue Frac. Eng. Mater. Struct. 30, 443 (2007)

    Article  CAS  Google Scholar 

  16. Y. Yao, M.E. Fine, L.M. Keer, Int. J. Frac. FRAC799 2007 (in press and to be available online)

  17. C. Kanchanomai, W. Limtrakarn, Y. Mutoh, Mech. Mater. 37, 1166 (2005)

    Article  Google Scholar 

  18. ASTM: E647, ASTM Standards 03.01, 562 (1998)

  19. T. Mura, Micromechanics of Defects in Solids, 2nd ed. (Netherlands: Martinus Nijhoff, 1991)

    Google Scholar 

  20. N.W. Klingbeil, Int. J. Fatigue 25, 117 (2003)

    Article  CAS  Google Scholar 

  21. M.L. Benzeggagh, M. Kenane, Composites Sci. Tech. 56, 439 (1996)

    Article  CAS  Google Scholar 

  22. D.L. McDowell, M.P. Miller, D.C. Brooks, Fatigue Electro. Mater. ASTM STP 1153, 42 (1994)

    Google Scholar 

  23. S. Wen, L.M. Keer, H. Mavoori, J. Electron. Mater. 30, 1190 (2001)

    Article  CAS  Google Scholar 

  24. J. Lubliner, Int. J. Non-linear Mech. 7, 237 (1972)

    Article  Google Scholar 

  25. W. Prager, J. Appl. Mech., Trans. Am. Soc. Mech. Eng. 23, 493 (1956)

    Google Scholar 

  26. S. Wen (Ph.D. dissertation, Northwestern University, 2001)

  27. F. Wang, L.M. Keer, S. Vaynman, S. Wen, IEEE Trans. CPT 27, 718 (2004)

    CAS  Google Scholar 

  28. S. Vaynman, S.A. McKeown, IEEE Trans. CHMT 16, 317 (1993)

    CAS  Google Scholar 

  29. S. Vaynman, A. Zubelewicz, Welding J. 69, 395 (1990)

    Google Scholar 

  30. H. Mavoori (Ph.D. dissertation, Northwestern University, 1996)

  31. R. Darveaux, K. Banerji, IEEE Trans. CHMT 15, 1013 (1992)

    CAS  Google Scholar 

  32. NIST Database for Solder Properties, Release 4.0 (2002)

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Acknowledgement

The authors acknowledge support by Semiconductor Research Corporation (SRC) Contract No. 1393.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Rd., Room A236, Evanston, IL, 60208, USA

    Yao Yao & Leon M. Keer

  2. Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, IL, 60208, USA

    Semyon Vaynman & Morris E. Fine

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  1. Yao Yao
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  2. Semyon Vaynman
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  3. Leon M. Keer
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  4. Morris E. Fine
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Correspondence to Yao Yao.

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Yao, Y., Vaynman, S., Keer, L. et al. Energy-Based Micromechanics Analysis on Fatigue Crack Propagation Behavior in Sn-Ag Eutectic Solder. J. Electron. Mater. 37, 339–346 (2008). https://doi.org/10.1007/s11664-007-0356-5

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