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Load-Displacement Behavior During Sharp Indentation of Viscous-Elastic-Plastic Materials

Published online by Cambridge University Press:  17 March 2011

Michelle Oyen-Tiesma ,
Yvete A. Toivola  and
Robert F. Cook
Michelle Oyen-Tiesma
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota Minneapolis, MN 55455
Yvete A. Toivola
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota Minneapolis, MN 55455
Robert F. Cook
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota Minneapolis, MN 55455
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Abstract

A constitutive equation is developed for geometrically-similar sharp indentation of a material capable of elastic, viscous, and plastic deformation. The equation is based on a series of elements consisting of a quadratic (reversible) spring, a quadratic (time-dependent, reversible) dashpot, and a quadratic (time-independent, irreversible) slider—essentially modifying a model for an elastic-perfectly plastic material by incorporating a creeping component. Load-displacement solutions to the constitutive equation are obtained for load-controlled indentation during constant loading-rate testing. A characteristic of the responses is the appearance of a forward-displacing “nose” during unloading of load-controlled systems (e.g., magnetic-coil-driven “nanoindentation” systems). Even in the absence of this nose, and the associated initial negative unloading tangent, load-displacement traces (and hence inferred modulus and hardness values) are significantly perturbed on the addition of the viscous component. The viscous-elastic-plastic (VEP) model shows promise for obtaining material properties (elastic modulus, hardness, time-dependence) of time-dependent materials during indentation experiments.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 649: Symposium Q – Fundamentals of Nanoindentation & Nanotribology II , 2000 , Q1.5
Copyright
Copyright © Materials Research Society 2001

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References

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