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Investigation of Stress-Strain Constitutive Behavior of Intermetallic Alloys

Published online by Cambridge University Press:  02 October 2017

H. C. Cheng ,
H. C. Hu ,
R. Y. Hong  and
W. H. Chen
H. C. Cheng*
Affiliation:
Department of Aerospace and Systems EngineeringFeng Chia UniversityTaichung, Taiwan
H. C. Hu
Affiliation:
Department of Power Mechanical EngineeringNational Tsing Hua UniversityHsinchu, Taiwan
R. Y. Hong
Affiliation:
Department of Power Mechanical EngineeringNational Tsing Hua UniversityHsinchu, Taiwan
W. H. Chen*
Affiliation:
Department of Power Mechanical EngineeringNational Tsing Hua UniversityHsinchu, Taiwan
*
*Corresponding author (hccheng@fcu.edu.tw; whchen@pme.nthu.edu.tw)
*Corresponding author (hccheng@fcu.edu.tw; whchen@pme.nthu.edu.tw)
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Abstract

The study aims to estimate the stress-strain constitutive behavior of intermetallic compounds (IMCs) observed in a solder interconnect from experimental nanoindentation responses through a modified analysis procedure for improved solution robustness based on Cheng and Cheng's and Dao et al.'s models. On the basis of parametric finite element nanoindentation simulation and dimensional analysis together with the concept of representative strain, a set of universal dimensionless functions are established, by which a forward and reverse analysis algorithm are created to predict nanoindentation responses from given elastoplastic properties and vice versa, respectively. The proposed analysis procedure is validated through comparison with the experimental nanoindentation responses and limited literature data. The results show that the proposed analysis procedure is an effective means for plastic property characterization of micro/nanoscale IMCs. The representative strain is found to be 0.056, which differs from the Dao et al.'s and Giannakopoulos and Suresh's estimate. Besides, though generally brittle and hard in nature, the IMCs in a micro/nanoscale thickness show high plasticity, and comprise a yield strength surpassing most typical engineering metals.

Keywords

Intermetallic compoundStress-strain constitutive behaviorSharp nanoindentationFinite element simulationDimensional analysis
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 3 , June 2018 , pp. 349 - 361
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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References

1. Tsai, H.-Y. and Kuo, C.-W., “Thermal Stress and Failure Location Analysis for Through Silicon Via in 3D Integration,” Journal of Mechanics, 32, pp. 47–53 (2016).Google Scholar
2. Suganuma, K., “Advances in Lead-Free Electronics Soldering,” Current Opinion in Solid State & Materials Science, 5, pp. 55–64 (2001).CrossRefGoogle Scholar
3. Benabou, L., Sun, Z., Pougnet, P. and Dahoo, P. R., “Continuum Damage Approach for Fatigue Life Prediction of Viscoplastic Solder Joints,” Journal of Mechanics, 31, pp. 525–531 (2015).Google Scholar
4. Cheng, H.-C., Cheng, T.-H., Chen, W.-H., Chang, T.-C. and Huang, H.-Y., “Board-Level Interconnect Reliability Assessment of Silicon Interposer-Based 2.5D IC Integration under Drop Impact,“ IEEE Transactions on Components, Packaging and Manufacturing Technology, 6, pp. 1493–1504 (2016).CrossRefGoogle Scholar
5. Cheng, H.-C., Li, R.-S., Lin, S.-C., Chen, W.-H. and Chiang, K.-N., “Macroscopic Mechanical Constitutive Characterization of Through-Silicon-Via (TSV)-Based 3D Integration,” IEEE Transactions on Components, Packaging and Manufacturing Technology, 6, pp. 432–446 (2016).Google Scholar
6. Chen, W.-H., Yu, C.-F., Cheng, H.-C. and Lu, S.-T., “Crystal Size and Direction Dependence of the Elastic Properties of Cu3Sn Through Molecular Dynamics Simulation and Nanoindentation Testing,” Microelectronics Reliability, 52, pp. 1699–1710 (2012).Google Scholar
7. Song, J.-M., Shen, Y.-L., Su, C.-W., Lai, Y.-S. and Chiu, Y.-T., “Strain Rate Dependence on Nanoindentation Responses of Interfacial Intermetallic Compounds in Electronic Solder Joints with Cu and Ag Substrates,” Materials Transactions, 50, pp. 1231–1234 (2009).Google Scholar
8. Deng, X., Chawla, N., Chawla, K. K. and Koopman, M., “Deformation Behavior of (Cu, Ag)-Sn Intermetallics by Nanoindentation,” Acta Materialia, 52, pp. 4291–4303 (2004).Google Scholar
9. Liao, L.-L. and Chiang, K.-N., “Nonlinear and Temperature-Dependent Material Properties of Au/Sn Intermetallic Compound,” Journal of Mechanics, DOI: 10.1017/jmech.2017.21 (2017).Google Scholar
10. Su, Y.-F., Chiang, K.-N. and Liang, Steven Y., “Design and Reliability Assessment of Novel 3D-IC Packaging,” Journal of Mechanics, 33, pp. 193–203 (2017).Google Scholar
11. Chan, Y. C., Tu, P. L., Tang, C. W., Hung, K. C. and Lai, J. K. L., “Reliability Studies of μBGA Solder Joints-Effect of Ni-Sn Intermetallic Compound,” IEEE Transactions on Advanced Packaging, 24, pp. 25–32 (2001).CrossRefGoogle Scholar
12. Yao, D. and Shang, J. K., “Effect of Aging on Fatigue Crack Growth at Sn-Pb/Cu Interfaces,” Metallurgical and Materials Transactions A, 26, pp. 2677–2685 (1995).Google Scholar
13. Kim, J. Y., Sohn, Y. C. and Yu, J., “Effect of Cu Content on the Mechanical Reliability of Ni/Sn-3.5Ag System,” Journal of Materials Research, 22, pp. 770–776 (2007).CrossRefGoogle Scholar
14. Frear, D. R., Burchett, S. N., Morgan, H. S. and Lau, J. H., eds., The Mechanics of Solder Alloy Interconnects, Van Nostrand Reinhold, New York, p. 60 (1994).Google Scholar
15. Oliver, W. C. and Pharr, G. M., “An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments,” Journal of Materials Research, 7, pp. 1564–1583 (1992).CrossRefGoogle Scholar
16. Cheng, Y. T. and Cheng, C. M., “Analysis of Indentation Loading Curves Obtained Using Conical Indenters,” Philosophical Magazine Letter, 77, pp. 39–47 (1998).Google Scholar
17. Dao, M., Chollacoop, N., Van Vliet, K. J., Venkatesh, T. A. and Suresh, S., “Computational Modeling of the Forward and Reverse Problems in Instrumented Sharp Indentation,” Acta Materialia, 49, pp. 3899–3918 (2001).Google Scholar
18. Tunvisut, K., Busso, E. P., O’Dowd, N. P. and Brantner, H. P., “Determination of the Mechanical Properties of Metallic Thin Films and Substrates From Indentation Tests,” Philosophical Magazine A, 82, pp. 2013–2029 (2002).CrossRefGoogle Scholar
19. Cheng, Y. T. and Cheng, C. M., “Scaling, Dimensional, and Indentation Measurements,” Materials Science and Engineering R, 44, pp. 91–149 (2004).CrossRefGoogle Scholar
20. Antunes, J. M., Fernandes, J. V., Menezes, L. F. and Chaparro, B. M., “A New Approach for Reverse Analyses in Depth-Sensing Indentation Using Numerical Simulation,” Acta Materialia, 55, pp. 69–81 (2007).Google Scholar
21. Nakamura, T. and Gu, Y., “Identification of Elastic– plastic Anisotropic Parameters Using Instrumented Indentation and Inverse Analysis,” Mechanics of Materials, 39, pp. 340–356 (2007).Google Scholar
22. Takagi, H., Dao, M., Fujiwara, M. and Otsuka, M., “Experimental and Computational Creep Characterization of Al-Mg Solid-Solution Alloy Through Instrumented Indentation,” Philosophical Magazine, 83, pp. 3959–3976 (2003).CrossRefGoogle Scholar
23. Sharma, G., Ramanujan, R. V., Kutty, T. R. G. and Prabhu, N., “Indentation Creep Studies of Iron Aluminide Intermetallic Alloy,” Intermetallics, 13, pp. 47–53 (2005).Google Scholar
24. Maier, V., Merle, B., Göken, M. and Durst, K., “An Improved Long-Term Nanoindentation Creep Testing Approach for Studying the Local Deformation Processes in Nanocrystalline Metals at Room and Elevated Temperatures,” Journal of Materials Research, 28, pp. 1177–1188 (2013).Google Scholar
25. Wu, W., Qin, F., An, T. and Chen, P., “A Study of Creep Behavior of TSV-Cu Based on Nanoindentaion Creep Test,” Journal of Mechanics, 32, pp. 717–724 (2016).Google Scholar
26. Giannakopoulos, A. E. and Suresh, S. “Determination of Elastoplastic Properties by Instrumented Sharp Indentation,” Scripta Materialia, 40, pp. 1191–1198 (1999).Google Scholar
27. Ogasawara, N., “Representative Strain of Indentation Analysis,” Journal of Materials Research, 20, pp. 2225–2234 (2005).Google Scholar
28. Chollacoop, N., Dao, M. and Suresh, S., “Depth-Sensing Instrumented Indentation with Dual Sharp Indenters,” Acta Materialia, 51, pp. 3713–3729 (2003).Google Scholar
29. Bucaille, J. L., Stauss, S., Felder, E. and Michler, J., “Determination of Plastic Properties of Metals by Instrumented Indentation Using Different Sharp Indenters,” Acta Materialia, 51, pp. 1663–1678 (2003).Google Scholar
30. Pharr, G. M., “Measurement of Mechanical Properties by Ultra Low Load Indentation,” Materials Science and Engineering A, 253, pp. 151–159 (1998).CrossRefGoogle Scholar
31. King, R. B., “Elastic Analysis of Some Punch Problems for a Layered Medium,” International Journal of Solids and Structures, 23, pp. 1657–1664 (1987).Google Scholar
32. Lee, J., Lee, C. and Kim, B., “Reverse Analysis of Nano-Indentation Using Different Representative Strains and Residual Indentation Profiles,” Materials and Design, 30, pp. 3395–3404 (2009).CrossRefGoogle Scholar
33. Chicot, D. et al., “Mechanical Properties of Porosity-Free Beta Tricalcium Phosphate (β-TCP) Ceramic by Sharp and Spherical Indentations,” New Journal of Glass and Ceramics, 3, pp. 16–28 (2013).Google Scholar