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Understanding nanoindentation unloading curves

Published online by Cambridge University Press:  31 January 2011

G. M. Pharr  and
A. Bolshakov
G. M. Pharr
Affiliation:
Department of Materials Science and Engineering, The University of Tennessee, and Metals and Ceramics Division, Oak Ridge National Laboratory, Knoxville, Tennessee
A. Bolshakov
Affiliation:
Houston Technology Center, Baker Atlas/INTEQ, Houston, Texas
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Abstract

Experiments have shown that nanoindentation unloading curves obtained with Berkovich triangular pyramidal indenters are usually welldescribed by the power-law relation P = α(h − hf)m, where hf is the final depth after complete unloading and α and m are material constants. However, the power-law exponent is not fixed at an integral value, as would be the case for elastic contact by a conical indenter (m = 2) or a flat circular punch (m = 1), but varies from material to material in the range m = 1.2–1.6. A simple model is developed based on observations from finite element simulations of indentation of elastic–plastic materials by a rigid cone that provides a physical explanation for the behavior. The model, which is based on the concept of an indenter with an “effective shape” whose geometry is determined by the shape of the plastic hardness impression formed during indentation, provides a means by which the material constants in the power law relation can be related to more fundamental material properties such as the elastic modulus and hardness. Simple arguments are presented from which the effective indenter shape can be derived from the pressure distribution under the indenter.

Type
Articles
Information
Journal of Materials Research , Volume 17 , Issue 10 , October 2002 , pp. 2660 - 2671
Copyright
Copyright © Materials Research Society 2002

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