Prediction of micro and nanoindentation size effect from conical or pyramidal indentation

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It is well-known by now that the hardness of the material at the micron and submicron length scales is dependent on the indent size. The objective of this work is to formulate a micromechanical-based model that can be used to predict simultaneously the indentation size effect (ISE) from both micro and nanoindentations by conical or pyramidal (Berkovich and Vickers) indenters. This model is based on the evolution of geometrically necessary dislocations (GNDs) beneath the indenter which is nonlinearly coupled to the evolution of statistically stored dislocations (SSDs) through the Taylor's hardening law. It is shown through comparisons with micro and nanoindentation experimental data that the proposed model gives much better predictions of hardness at small indentation depths as compared to the Nix-Gao model. It is concluded that when using the Taylor's hardening law a simple sum of flow stresses from SSDs and GNDs is more adequate than the simple sum of SSD and GND densities. Moreover, it is shown that the length scale responsible for the ISE is proportional to the spacing between dislocations. Thus, it is concluded that materials with smaller length scales are harder but exhibit lower ISE.

Original languageBritish English
Pages (from-to)787-802
Number of pages16
JournalMechanics of Materials
Issue number8
StatePublished - Aug 2007


  • Geometrically necessary dislocations
  • Gradient plasticity
  • Indentation size effect
  • Length scale
  • Microindentation
  • Nanoindentation


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