Exploring the origins of the indentation size effect at submicron scales. Academic Article uri icon


  • The origin of the indentation size effect has been extensively researched over the last three decades, following the establishment of nanoindentation as a broadly used small-scale mechanical testing technique that enables hardness measurements at submicrometer scales. However, a mechanistic understanding of the indentation size effect based on direct experimental observations at the dislocation level remains limited due to difficulties in observing and quantifying the dislocation structures that form underneath indents using conventional microscopy techniques. Here, we employ precession electron beam diffraction microscopy to "look beneath the surface," revealing the dislocation characteristics (e.g., distribution and total length) as a function of indentation depth for a single crystal of nickel. At smaller depths, individual dislocation lines can be resolved, and the dislocation distribution is quite diffuse. The indentation size effect deviates from the Nix-Gao model and is controlled by dislocation source starvation, as the dislocations are very mobile and glide away from the indented zone, leaving behind a relatively low dislocation density in the plastically deformed volume. At larger depths, dislocations become highly entangled and self-arrange to form subgrain boundaries. In this depth range, the Nix-Gao model provides a rational description because the entanglements and subgrain boundaries effectively confine dislocation movement to a small hemispherical volume beneath the contact impression, leading to dislocation interaction hardening. The work highlights the critical role of dislocation structural development in the small-scale mechanistic transition in indentation size effect and its importance in understanding the plastic deformation of materials at the submicron scale.

published proceedings

  • Proc Natl Acad Sci U S A

author list (cited authors)

  • Ma, X., Higgins, W., Liang, Z., Zhao, D., Pharr, G. M., & Xie, K. Y.

citation count

  • 6

complete list of authors

  • Ma, Xiaolong||Higgins, Wesley||Liang, Zhiyuan||Zhao, Dexin||Pharr, George M||Xie, Kelvin Y

publication date

  • July 2021