Size Effects and Material Length Scales in Nanoindentation for Metals

  • George Z. VoyiadjisEmail author
  • Cheng Zhang
Reference work entry


In nanoindentation experiments at submicron indentation depths, the hardness decreases with the increasing indentation depth. This phenomenon is termed as the indentation size effect. In order to predict the indentation size effect, the classical continuum needs to be enhanced with the strain gradient plasticity theory. The strain gradient plasticity theory provides a nonlocal term in addition to the classical theory. A material length scale parameter is required to be incorporated into the constitutive expression in order to characterize the size effects in different materials. By comparing the model of hardness as a function of the indentation depth with the nanoindentation experimental results, the length scale can be determined. Recent nanoindentation experiments on polycrystalline metals have shown an additional hardening segment in the hardness curves instead of the solely decreasing hardness as a function of the indentation depth. It is believed that the accumulation of dislocations near the grain boundaries during nanoindentation causes the additional increase in hardness. In order to isolate the influence of the grain boundary, bicrystal metals are tested near the grain boundary at different distances. The results show that the hardness increases with the decreasing distance between the indenter and the grain boundary, providing a new type of size effect. The length scales at different distances are determined using the modified model of hardness and the nanoindentation experimental results on bicrystal metals.


Nanoindentation Indentation size effect Nonlocal theory Strain gradient plasticity Grain boundary Bicrystal Length scale 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringLouisiana State UniversityBaton RougeUSA
  2. 2.Medtronic, Inc.TempeUSA

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