Hostname: page-component-84b7d79bbc-rnpqb Total loading time: 0 Render date: 2024-07-26T05:48:42.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermodynamic Formulation of Endochronic Cyclic Viscoplasticity With Damage- Application to Eutectic Sn/Pb Solder Alloy

Published online by Cambridge University Press:  05 May 2011

C. F. Lee  and
Y. C. Chen
C. F. Lee*
Affiliation:
Dept. Eng. Science College of Eng, Nat. Cheng-Kung Univ, Tainan, Taiwan 70101, R.O.C.
Y. C. Chen*
Affiliation:
Engineering Div. TSMC, Sinshih, Tainan County, Taiwan 74147, R.O.C.
*
*Professor
**Engineer
Get access

Abstract

In this paper, an endochronic theory of cyclic viscoplasticy with damage is established based on the irreversible thermodynamics of continuous media with internal state variables containing an isotropic damage parameter. The constitutive equations derived have the same mathematical form as those of convectional endochronic theory without damage, except the effective stress with damage is used. This result coincides with the Lemaitre's statements of stain equivalence principle.

Using the experimental cyclic stress-strain curves of 63Sn/37Pb solder bars, corrected from the uniaxially constant displacement amplitude cyclic tests under MTS Tytron microtester, the computational results of cyclic stess-strain curves with several degrees of damage can reproduce the experimental data quite well. Based on compressive buckling appeared in the vicinity of the compressive end parts of the hysteresis loop, the critical values of damage are determined between 0.3 and 0.4.

The evolution equation of damage proposed in terms of the intrinsic damage time scale and its results in the modified Coffin-Manson LCF law can be extended in the future research for a statistical theory of life distribution under low cycle fatigue tests.

Keywords

Endochronic cyclic viscoplasticity with damageEutectic Sn/Pb solderEvolution equation of cyclic damageIntrinsic damage time scaleCritical damage valueModified Coffin-Manson LCF law with Damage.
Type
Articles
Information
Journal of Mechanics , Volume 23 , Issue 4 , December 2007 , pp. 433 - 444
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Frear, D. R., Jones, W. B. and Kinsman, K. R., Solder Mechanics: A state of the Art Assessment, TMS. Pub. Co., U.S.A. (1991).Google Scholar
2.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
3.Mc Dowell, D. L., Miller, M. P. and Brooks, D. C., “A Unified Creep-Pasticity Theory for Solder Alloys,” in Fatigue of Electronic Materials, eds. Schroder, S. A. and Mitchell, M. R., ASTM STP1153, pp. 42–59 (1994).CrossRefGoogle Scholar
4.Sasaki, K., Ohguchi, K-I. and Ishikawa, H., “Viscoplastic Deformation of 40Pb/60Sn Solder Alloys-Experiments and Constitutive Moleling,” J. Electronic Packaging, ASME, pp. 379–387 (2001).CrossRefGoogle Scholar
5.Lemaitre, J., A Course on Damage Mechanics, Springer-Verlag, Germany (1992).Google Scholar
6.Stolkarts, V., Keer, L. M. and Fine, M. E., “Damage Evolution Governed by Microcrack Nucleation with Application to the Fatigue of 63Sn/37Pb Solder,” J. Mech. Phys. Solid, 47, pp. 2451–2468 (1999).CrossRefGoogle Scholar
7.Stolkarts, V., Keer, L. M. and Fine, M. E., “Constitutive and Cyclic Damage Model of 63Sn/37Pb Solder,” J. Electronic Packaging, ASME, 123, pp. 351–355 (2001).Google Scholar
8.Wen, S., Keer., L. M., Vaynman, S. and Lawson, L. R., “A Constitutive Model for a High Lead Solder,” IEEE Trans. Components and Packaging Tech., 25, pp. 23–31 (2002).Google Scholar
9.Zhang., X. and Lee, Ricky, S-W., “Thermal Fatigue Life Prediction for Solder Joints with the Consideration of Damage Evolution,” 1998IEEE/CPMT Electronic Packaging Technology Conference, pp. 279–285 (1998).Google Scholar
10.Reda Taha, M. M. and Shrive, N. G., “A Model of Damage and Creep Interaction in a Quasi-Brittle Composite Material under Axial Loading,” Journal of Mechanics, 22, pp. 339–347 (2006).Google Scholar
11.Valanis, K. C., “An Energy-Probability Theory of Fracture (An endochronic theory),” J. de Me'canique, 14, pp. 843–862, France (1975).Google Scholar
12.Valanis, K. C. and Wu., H. C., “Fracture of Plastic Materials under Proportional Straining, Part I: Theoretical Foundations, Part II: Applications to Gray Cast Iron,” J. de Me'canique, 15, pp. 543–577, France (1976).Google Scholar
13.Valanis, K. C., “A Probabilistic Endochronic Theory of Fracture,” Defects and Fracture, Eds. Sih, G.. C. and Zorski, H., pp. 179–198 (1982).Google Scholar
14.Valanis, K. C., “A Theory of Damage in Brittle Materials,” Eng. Fracture Mech., 36, pp. 403–416 (1990).Google Scholar
15.Valanis, K. C., “A Global Damage Theory and Hyperbolicity of the Wave Problem,” J. Appl. Mech., ASME, 58, pp. 311–316 (1991).Google Scholar
16.Chow, C. L. and Chen, X. F., “Three-Dimensional Fracture Analysis of CT Specimens with a Ductile Damage Model Based on Endochronic Plasticity Theory,” Int. J. Fracture, 69, pp. 229–249 (1994/1995).Google Scholar
17.Valanis, K. C., “Endochronic Theory with Proper Hysteresis Loop Closure Properties,” System, Science and Softwave, La Jolla, CA, U.S.A., Report No.SSS-R-80-4182, August 1979.Google Scholar
18.Valanis, K. C. and Lee, C. F., “Endochronic Theory of Cyclic Plasticity with Applications,” ASME J. Appl. Mechanics, 51, pp. 367–374 (1984).Google Scholar
19.Budiansky, B, and O'Connell, R. J., “Elastic Moduli of a Cracked Solder,” Int. J. Solids Struct., 12, pp. 81–97 (1976).Google Scholar
20.Hsieh, W. Y., “Fatigue Test and Analysis for Eutectic Solder in Electronic Packaging,” National Chung Cheng University, Master Thesis (2002).Google Scholar
21.Chao, Y. C., “Measurements and Analysis of Reliability and Electrical Characteristics for Electronic Package Components,” National Chung Cheng University, Ph.D. Dissertation (2003).Google Scholar
22.Lee, C. F., “Recent Finite Element Applications of the Incremental Endochronic Plasticity,” Int. J. Plasticity, 11, pp. 843–865 (1995).Google Scholar