Length-scale-based hardening model for ultra-small volumes

J. M. Jungk, W. M. Mook, M. J. Cordill, M. D. Chambers, W. W. Gerberich, D. F. Bahr, N. R. Moody, J. W. Hoehn

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Understanding the hardening response of small volumes is necessary to completely explain the mechanical properties of thin films and nanostructures. This experimental study deals with the deformation and hardening response in gold and copper films ranging in thickness from 10 to 400 nm and silicon nanoparticles with particle diameters less than 100 nm. For very thin films of both gold and copper, it was found that hardness initially decreases from about 2.5 to 1.5 GPa with increasing penetration depth. Thereafter, an increase occurs with depths beyond about 5-10% of the film thickness. It is proposed that the observed minima are produced by two competing mechanisms. It is shown that for relatively deep penetrations, a dislocation back stress argument reasonably explains the material hardening behavior unrelated to any substrate composite effect. Then, for shallow contacts, a volume-to-surface length scale argument relating to an indentation size effect is hypothesized. A simple model based on the superposition of these two mechanisms provides a reasonable fit to the experimental nanoindentation data.

Original languageEnglish (US)
Pages (from-to)2812-2821
Number of pages10
JournalJournal of Materials Research
Issue number10
StatePublished - Oct 2004

Bibliographical note

Funding Information:
The authors J.M.J., J.W.H., and W.W.G. would like to acknowledge support through Seagate Technology and The Center for Micromagnetics and Information Technology. D.F.B. and M.J.C. would like to acknowledge the financial support of the PECASE program administered through Sandia National Laboratories. W.M.M. and W.W.G. were also supported by the National Science Foundation under Grant No. DMI-0103169 and an NSF-IGERT program through Grant No. DGE-0114372 and the United States Department of Energy Office (U.S. DOE) of Science. N.R.M. would like to recognize the support of the U.S. DOE through Contract No. DE-AC04-94AL85000 and thank D.P. Adams, Sandia National Laboratories, Albuquerque, NM and N.Y.C. Yang, Sandia National Laboratories, Livermore, CA for their technical assistance and many helpful discussions.


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