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Temperature and Frequency Modified Fatigue Initiation Life of Solder Alloys Predicted by Endochronic Cyclic Damage-Coupled Viscoplasticity

Published online by Cambridge University Press:  16 June 2011

C. F. Lee ,
S. I. Jeng  and
M. T. Liu
C. F. Lee*
Affiliation:
Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
S. I. Jeng
Affiliation:
Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
M. T. Liu
Affiliation:
Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
*Professor, corresponding author
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Abstract

In this paper, an evolution equation of cyclically internal damage in the intrinsic damage time scale after the threshold cycles N0 was extended by employing its damage parameters proposed to be dependent of frequency (v) and temperature (T) under cyclic fatigue loading. The resulting damage-coupled endochronic viscoplasticity can drive v and T modified power form equations of cyclic damage and its fatigue initiation life = N1 + N0. Under fatigue tests with T effect and N0 = 0, the power form equation of N1(T)/(Th), named as T-LCM (T modified Lee Coffin-Manson) equation for fatigue initiation life can bederived. The T modified factor (Th) depends on the T dependent material elastic modulus, the cyclicstress-strain response and the damage parameters. Theoretical predictions in the life data ofSn/3.8Ag/0.7Cu solder alloy under cyclic strain test with Tϵ [298,393] K were very well.

Also under fatigue tests with v effect only, the power form equation of /v-LCM (v modified Lee-Coffin-Manson) equation for fatigue initiation life can be derived. The v modified parameter depends on the v dependent cyclic stress-strain response and the damage parameters. Theoreticalpredictions in the life data of 96.5Sn/3.5Ag solder alloy with surface cracking effect i.e. N0 ≠ 0 during cyclicstrain tests with v ϵ [0.001,1] Hz were quite well.

Obviously, the values of power exponents C in the T-LCM and the v-LCM equations can not be determinedsimply by the least square method as in the Coffin-Manson empirical formulae. Also, they must bejustified by constrains imposed in the material parameters defining in the cyclic stress-strain response andthe accumulation behavior of cyclic damage.

The resultant equations derived here and the Δ-LCM equation derived under Δ angle proportional cyclicstrain tests can be combined together to form a T-v-ΔLCM equation for fatigue life studies in the solderalloys using bulk specimens or BGA solider joint specimens.

Keywords

Damage-coupled endochronic viscoplasticityv or T LCM equation for fatigue initiation lifeSn/3.8Ag/0.7Cu T modified life96.5Sn/3.5Ag v modified life
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 2 , June 2011 , pp. 267 - 277
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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References

1. Lau, J. H., Reliability of RoHS-Compliant 2D and 3D IC Interconnects, McGraw Hill Comp. Inc. (2011).Google Scholar
2. Lee, C. F. and Chen, Y. C., “Thermodynamic Formulation of Endochronic Cyclic Viscoplasticity with Damage-Application to Eutectic Sn/Pb Solder Alloy,” Journal of Mechanics, 23, pp. 433–444 (2007).CrossRefGoogle Scholar
3. Park, T. S. and Lee, S. B., “Low Cycle Fatigue Testing of Ball Grid Array Solder Joints under Mixed-Mode Loading Conditions,” Journal of Electronic Packaging, ASME, 127, pp. 237–244 (2005).CrossRefGoogle Scholar
4. Soloman, H. D., “Predicting Thermal and Mechanical Fatigue Life from Isothermal Low Cycle Data,” Solder Joint Reliability, Chap. 14, Lau, J. H., Reinhold, van Nostrand, Ed., pp. 406–454, New York (1991).CrossRefGoogle Scholar
5. Lee, C. F., Lee, T. K., Lin, T. T. and Lin, H. Y., “Cyclic Stress-Strain Behavior of BGA (Sn/3.5Ag/0.75Cu) Solder Joint under Cyclically Oblique Displacement Tests and Endochronic Viscoplastic Predictions,” Journal of Mechanics, 26, pp. 453–463 (2010).CrossRefGoogle Scholar
6. Lee, C. F., Lin, T. T. and Tsai, P. S., “Endochronic Fatigue Life Prediction of Sn/3.5Ag/0.75Cu BGA Solder Joints under Oblique Displacement Cyclic Tests,” Journal of Mechanics, 27, pp. 195–204 (2011).CrossRefGoogle Scholar
7. Kanchanomai, C., Miyashita, Y., Mutoh, Y. and Mannan, S. L., “Influence of Frequency on Low Cycle Fatigue Behavior of Pb-Free Solder 96.5Sn—3.5Ag,” Material Science and Engineering A 345, pp. 90–98 (2003).CrossRefGoogle Scholar
8. Zeng, Q. L., Wang, Z. G., Xian, A. P. and Shang, J. K., “Cyclic Softening of the Sn-3.8Ag-0.7Cu LeadFree Solder Alloy with Equiaxed Grain Structure,” Journal of Electronic Materials, 34, pp. 62–67 (2005).CrossRefGoogle Scholar
9. Stolkarts, V., Keer, L. M. and Fine, M. E., “Damage Evolution Governed by Microcrack Nucleation with Application to the Fatigue of 63Sn-37Pb Solder,” Journal of Mechanical Physics in Solids Packaging, 47, pp. 2451–2468 (1999).CrossRefGoogle Scholar
10. Shang, J. K., Zeng, Q. L., Zhang, L. and Zhu, Q. S., “Mechanical Fatigue of Sn-rich Pb-free Solder Alloys,” Journal of Material Science: Material In Electronics, 18, pp. 211–227 (2007).Google Scholar
11. Lee, C. F. and Shieh, T. J., “Theory of Endochronic Cyclic Viscoplasticity of Eutectic Tin/Lead Solder Alloy,” Journal of Mechanics, 22, pp. 181–191 (2006).CrossRefGoogle Scholar
12. Lee, C. F., Lee, Z. H. and Ou, S. H., “The Endochronic Viscoplasticity for Sn/3.9Ag/0.6Cu Solder Under Low Strain Rate Fatigue Laoding Coupled Thermal Cycling,” Journal of Mechanics, 25, pp. 261–270 (2009).CrossRefGoogle Scholar
13. Zhu, Q. S., Wang, Z. G., Wu, S. D. and Shang, J. K., “Enhanced Rate-Dependent Tensile Deformation in Equal Channel Angularly Pressed Sn-Ag-Cu Alloy,” Material Science and Engineering A 502, pp. 153–158 (2009).CrossRefGoogle Scholar
14. Valanis, K. C. and Lee, C. F., “Some Recent Developments of the Endochronic Theory with Applications,” Nuclear Engineering and Design, 69, pp. 327–344 (1982).CrossRefGoogle Scholar
15. Kanchanomai, C. and Mutoh, Y., “Fatigue Crack Initiation and Growth in Solders Alloys,” Fatigue & Fracture of Engineering Materials & Structures, 30, pp. 443–457 (2006).CrossRefGoogle Scholar
16. Vaynman, S, Fine, M. E. and Jeannotte, D. A., “Low Cycles Isothermal Fatigue life of Solder Materials,” Chap. 4, Solder Mechanics—A State of the Art Assessment, Ferry, D. R., Jones, W. B. and Kinsman, K. R., Eds., The Minerals, Metals & Materials Society, pp. 155–189 (1991).Google Scholar