Skip to main content

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

  • Chapter
  • 210 Accesses

Part of the book series: ICASE/LaRC Interdisciplinary Series in Science and Engineering ((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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.S. Stölken and A. G. Evans, Acta Mater., Vol. 46 (1998), pp. 5109–5115.

    Article  Google Scholar 

  2. N.A. Fleck and J.W. Hutchinson, Adv. In Applied Mechanics, Vol. 33 (1997), pp. 295–361.

    Article  Google Scholar 

  3. W.D. Nix and H. Gao, J. Mech. Phys. Solids, Vol. 46 (1998), pp. 411425

    Google Scholar 

  4. M.R. Begley and J.W. Hutchinson, J. Mech. Phys. Solids, Vol. 46 (1998), pp. 2049–2068.

    Article  MATH  Google Scholar 

  5. M. Madou, “Fundamental of Microfabrication”, 1999, CRC Press, Boca Raton, FL.

    Google Scholar 

  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. 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. 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. 197–202

    Google Scholar 

  9. H. Gao, Y. Huang, W.D. Nix and J.W. Hutchinson, J. Mech. Phys. Solids, Vol. 47 (1999), pp. 1239–63

    Article  MATH  MathSciNet  Google Scholar 

  10. Y. Huang, H. Gao, W.D. Nix and J.W. Hutchinson, J. Mech. Phys. Solids, Vol. 48 (2000), pp. 99–128

    Article  MATH  MathSciNet  Google Scholar 

  11. P. Shrotriya, S.M. Allameh, J. Lou, T. Buchheit and W.O. Soboyejo, Mechanics and Materials Journal, in press (2002)

    Google Scholar 

  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. 539

    Article  Google Scholar 

  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. 78–91

    Google Scholar 

  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.

    Article  Google Scholar 

  15. W.C. Oliver and G.M. Pharr, J. of Mater. Res., Vol. 7 (1992), pp. 156483

    Google Scholar 

  16. M. Zupan, M. Legros, B.R. Elliott and K.J. Hemker, Proceedings of the TMS Fall Meeting, 1999, pp. 525–536

    Google Scholar 

  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. 602–10

    Google Scholar 

  18. M.S. De Guzman, G. Neubauer, P. Flinn and W.D. Nix, Materials Research Symposium Proceedings, Vol. 308 (1993), pp. 613–18

    Article  Google Scholar 

  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. A. Needleman, Acta Mater., Vol 48 (2000), pp. 105–124

    Article  MathSciNet  Google Scholar 

  21. D. Weygand, L.H. Friedman, E. Van der Giessen and A. Needleman, Mater. Sci. and Eng. A, Vol. 309–310 (2001), pp. 420

    Article  Google Scholar 

  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. 41–53

    Google Scholar 

  23. J.Y. Shu, N.A. Fleck, E. Van der Giessen and A. Needleman, J. Mech. Phys. Solids, Vol. 49 (2001), pp. 1361–1395

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Kluwer Academic Publishers

About this chapter

Cite this chapter

Lou, J., Shrotriya, P., Allameh, S., Buchheit, T., Soboyejo, W.O. (2003). On the Role of Plasticity Length Scale Parameters in Multi-Scale Modeling. In: Harik, V.M., Salas, M.D. (eds) Trends in Nanoscale Mechanics. ICASE/LaRC Interdisciplinary Series in Science and Engineering, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0385-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-0385-7_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6479-0

  • Online ISBN: 978-94-017-0385-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics