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A stochastic model for the size dependence of spherical indentation pop-in

Published online by Cambridge University Press:  23 September 2013

P. Sudharshan Phani ,
Kurt E. Johanns ,
Easo P. George  and
George M. Pharr
P. Sudharshan Phani
Affiliation:
Department of Materials Science and Engineering, The University of Tennessee, Knoxville, Tennessee 37996
Kurt E. Johanns
Affiliation:
Department of Materials Science and Engineering, The University of Tennessee, Knoxville, Tennessee 37996
Easo P. George
Affiliation:
Department of Materials Science and Engineering, The University of Tennessee, Knoxville, Tennessee 37996; and Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
George M. Pharr*
Affiliation:
Department of Materials Science and Engineering, The University of Tennessee, Knoxville, Tennessee 37996; and Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
*
a)Address all correspondence to this author. e-mail: pharr@utk.edu
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Abstract

A simple stochastic model is developed to determine the pop-in load and maximum shear stress at pop-in in nanoindentation experiments conducted with spherical indenters that accounts for recent experimental observations of a dependence of these parameters on the indenter radius. The model incorporates two separate mechanisms: pop-in due to nucleation of dislocations in dislocation-free regions and pop-in by activation of preexisting dislocations. Two different types of randomness are used to model the stochastic behavior, which include randomness in the spatial location of the dislocations beneath the indenter and randomness in the orientation of the dislocations, i.e., randomness in the stress needed to activate them. In addition to correctly predicting the experimentally observed average maximum shear stress at pop-in, the model also correctly describes the scatter in pop-in loads and how it varies with indenter radius. Monte Carlo simulations are used to validate the model and visualize the scatter expected for a limited number of tests.

Keywords

nanoindentationdislocationsstrength

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Type
Articles
Information
Journal of Materials Research , Volume 28 , Issue 19 , 14 October 2013 , pp. 2728 - 2739
Copyright
Copyright © Materials Research Society 2013 

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References

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