Journal of Materials Research


Correction factor for contact area in nanoindentation measurements

Michel Troyona1 c1 and Liye Huanga1

a1 Laboratoire de Microscopies et d'Etude de Nanostructures, EA 3799, Université de Reims, 51685 Reims Cedex 2, France


In the relationship between unloading contact stiffness, elastic modulus, and contact area, which is the fundamental basic equation for nanoindentation analysis, a multiplicative correction factor is generally needed. Sometimes this correction factor is called γ to take into account the elastic radial inward displacements, and sometimes it is called β to correct for the fact that the indenter shape is not a perfect cone. In reality, these two effects simultaneously coexist and thus it is proposed that this correction factor is α = βγ. From nanoindentation data measured on three materials of different elastic moduli with a sharp Berkovich indenter and a worn one, the tip of which was blunt, it is demonstrated that the correction factor α does not have a constant value for a given material and indenter type but depends on the indenter tip rounding and also on the deformation of the indenter during indentation. It seems that α increases with the tip radius and also with the elastic modulus of the measured materials.

(Received July 08 2004)

(Accepted October 28 2004)

(Online publication March 2005)

Key Words:

  • Hardness;
  • Nanoindentation


c1 Address all correspondence to this author. e-mail: