On the Role of Plasticity Length Scale Parameters in Multi-Scale Modeling

  • J. Lou
  • P. Shrotriya
  • S. Allameh
  • T. Buchheit
  • W. O. Soboyejo
Part of the ICASE/LaRC Interdisciplinary Series in Science and Engineering book series (ICAS, volume 9)

Abstract

This chapter presents a recent study of the effects of plasticity strain gradient length scale parameters on the plastic deformation of LIGA Ni MEMS structures plated from sulfamate baths. Micro-tensile experiments were explored in current study to evaluate the basic tensile properties for LIGA Ni MEMS structures at micron scale. The composite length scale parameter [1] was obtained from the micro-bend techniques, and the stretch gradient length scale parameter [1–4] was extracted from the nano-indentation experiments. A constitutive expression, which is an extension of the traditional J2 theory, was obtained for the LIGA Ni MEMS structures. This constitutive equation can be used for the further modeling of plasticity of LIGA Ni MEMS structures plated under similar conditions. The implications of plasticity length scale parameters are discussed for multi scale modeling between the micron- and nano-scales.

Key words

multi-scale models MEMS Plasticity nano-indentation length scales 

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References

  1. 1.
    J.S. Stölken and A. G. Evans, Acta Mater., Vol. 46 (1998), pp. 5109–5115.CrossRefGoogle Scholar
  2. 2.
    N.A. Fleck and J.W. Hutchinson, Adv. In Applied Mechanics, Vol. 33 (1997), pp. 295–361.CrossRefGoogle Scholar
  3. 3.
    W.D. Nix and H. Gao, J. Mech. Phys. Solids, Vol. 46 (1998), pp. 411425Google Scholar
  4. 4.
    M.R. Begley and J.W. Hutchinson, J. Mech. Phys. Solids, Vol. 46 (1998), pp. 2049–2068.CrossRefMATHGoogle Scholar
  5. 5.
    M. Madou, “Fundamental of Microfabrication”, 1999, CRC Press, Boca Raton, FL.Google Scholar
  6. 6.
    T. Christensen, T. Buchheit, D.T. Schmale and R.J. Bourcier, Microelectromechanical Structures for Materials Research, S. Brown et al., Editors, Materials Research Society, 1999, pp. 185–191.Google Scholar
  7. 7.
    Last, H., Hemker, K.J. and Witt, R. MEMS, Materials Science of Microelectromechanical Systems (MEMS) Devices II, de Boer et al., Editors, Materials Research Society, 2000, pp. 191–196.Google Scholar
  8. 8.
    Z.L. Xie, D. Pan, H. Last, and K.J. Hemker, Materials Science of Microelectromechanical Systems (MEMS) Devices II, de Boer et al., Editors, Materials Research Society, 2000, pp. 197–202Google Scholar
  9. 9.
    H. Gao, Y. Huang, W.D. Nix and J.W. Hutchinson, J. Mech. Phys. Solids, Vol. 47 (1999), pp. 1239–63CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Y. Huang, H. Gao, W.D. Nix and J.W. Hutchinson, J. Mech. Phys. Solids, Vol. 48 (2000), pp. 99–128CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    P. Shrotriya, S.M. Allameh, J. Lou, T. Buchheit and W.O. Soboyejo, Mechanics and Materials Journal, in press (2002)Google Scholar
  12. 12.
    T.E. Buchheit, D. A. LaVan, J. R. Michael, T.R. Chrinstenson and S. D. Leith, Metallurgical and Materials Transactions, Vol. 33A (2002), pp. 539CrossRefGoogle Scholar
  13. 13.
    W.N. Sharpe, B. Yuan, R. Vaidyanathan, R.L. Edwards, Proc. Of the SPIE — The Int. Society for Optical Engineering, Symposium on Microlithography and Metrology in Machining II, “New test structures and techniques for measurement of mechanical properties of MEMS materials”, Vol. 2880 (1996), pp. 78–91Google Scholar
  14. 14.
    W.W. Gerberich, W. Yu, D. Kramer, A. Strojny, D. Bahr, E. Lilleodden and J. Nelson, J. Mater. Res., Vol. 13 (1998), pp. 1–19.CrossRefGoogle Scholar
  15. 15.
    W.C. Oliver and G.M. Pharr, J. of Mater. Res., Vol. 7 (1992), pp. 156483Google Scholar
  16. 16.
    M. Zupan, M. Legros, B.R. Elliott and K.J. Hemker, Proceedings of the TMS Fall Meeting, 1999, pp. 525–536Google Scholar
  17. 17.
    N.A. Stelmashenko, M.G. Walls, L.M. Brown and Y.V. Milman, Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures, eds. M. Nastasi, D.M. Parkin and H. Gleiter, NATO ASI Series E 233 (1993), pp. 602–10Google Scholar
  18. 18.
    M.S. De Guzman, G. Neubauer, P. Flinn and W.D. Nix, Materials Research Symposium Proceedings, Vol. 308 (1993), pp. 613–18CrossRefGoogle Scholar
  19. 19.
    J. Lou, S. Allameh, T. Buchheit and W.O. Soboyejo,, Mechanical Properties of MEMS Structures, Kluwer Academic Publishers, Assinipi lake, MA, in press (2002)Google Scholar
  20. 20.
    A. Needleman, Acta Mater., Vol 48 (2000), pp. 105–124CrossRefMathSciNetGoogle Scholar
  21. 21.
    D. Weygand, L.H. Friedman, E. Van der Giessen and A. Needleman, Mater. Sci. and Eng. A, Vol. 309–310 (2001), pp. 420CrossRefGoogle Scholar
  22. 22.
    S. Suresh and K.J. Van Vliet, Proceedings of the Eighth International Fatigue Congress, Volume 1/5, A.F. Blom, Editor, Fatigue 2002, 2002, pp. 41–53Google Scholar
  23. 23.
    J.Y. Shu, N.A. Fleck, E. Van der Giessen and A. Needleman, J. Mech. Phys. Solids, Vol. 49 (2001), pp. 1361–1395CrossRefMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • J. Lou
    • 1
  • P. Shrotriya
    • 1
  • S. Allameh
    • 1
  • T. Buchheit
    • 2
  • W. O. Soboyejo
    • 1
  1. 1.Princeton Materials Institute and Department of Mechanical and Aerospace EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Mechanical Reliability and Modeling DepartmentSandia National LaboratoriesAlbuquerqueUSA

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