Smaller is tougher

A. R. Beaber, J. D. Nowak, O. Ugurlu, W. M. Mook, S. L. Girshick, R. Ballarini, W. W. Gerberich

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Smaller is stronger is now a tenet generally consistent with the predominance of evidence. An equally accepted tenet is that fracture toughness almost always decreases with increasing yield strength. Can smaller is tougher then be consistent with these two tenets? It is taught in undergraduate engineering courses that one design parameter that allows for both increased strength and fracture toughness is reduced grain size. The present study on the very brittle semiconductor silicon proves this exception to the rule and demonstrates that smaller can be both stronger and tougher. Three nanostructures are considered theoretically and experimentally: thin films, nanospheres, and nanopillars. Using a simple work per unit fracture area approach, it is shown at small scale that toughness is inversely proportional to the square root of size. This is supported by experimental evidence from in situ electron microscopy nanoindentation at length scales of less than a micron. It is further suggested that dislocation shielding can explain both strength and toughness increases at the small scales.

Original languageEnglish (US)
Pages (from-to)1179-1189
Number of pages11
JournalPhilosophical Magazine
Issue number7-9
StatePublished - Mar 2011

Bibliographical note

Funding Information:
This work was supported by the National Science Foundation (CTS-0506748), the Air Force Office of Scientific Research (AOARD-08-4134), and the Abu Dhabi–Minnesota Institute for Research Excellence (ADMIRE), a partnership between the Petroleum Institute (PI) of Abu Dhabi and the Department of Chemical Engineering and Materials Science of the University of Minnesota. Parts of this work were carried out in the Institute of Technology Characterization Facility, University of Minnesota, a member of the NSF-funded Materials Research Facilities Network (


  • brittle-ductile transition
  • fracture mechanics
  • fracture toughness
  • in situ nanoindentation
  • nanoparticle
  • silicon

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