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INTERNAL LENGTH GRADIENT APPROACH TO PYRAMIDAL/SPHERICAL NANOINDENTATION EXPERIMENTS

Volume 13, Issue 3, 2022, pp. 47-66
DOI: 10.1615/NanoSciTechnolIntJ.2022041078
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A. K. Kampouris
Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
Avraam A. Konstantinidis
Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
R. Yang
Chinese Academy of Sciences, Beijing 100190, China
Y. Bai
Chinese Academy of Sciences, Beijing 100190, China
Elias C. Aifantis
Aristotle University of Thessaloniki, Thessaloniki 54124, Greece; Michigan Technological University, Houghton, MI 49931, USA; Mercator Fellow, Friedrich-Alexander University, Erlangen-Nuremberg, 90762 Fürth, Germany

ABSTRACT

The well-established indentation size effect is modeled herein within the framework of the internal length gradient approach. The internal length (IL) parameter multiplying the Laplacian of stress term introduced in classical type flow stress expressions to account for local heterogeneity (nonlocality) is assumed to obey a power-law dependence on strain, in order to describe the effect of deformation-induced micro/nanostructure evolving during the indentation process. The model is calibrated to fit experimental pyramidal and spherical indentation measurements for different metals and the corresponding IL parameters are estimated in each case. A sphero-pyramidal analysis is also presented, accounting for the bluntness of the Berkovich tips, for the case of thin films and small volumes, where indentation depths are usually up to a few nm.

KEY WORDS: indentation size effect, pyramidal nanoindentation, spherical nanoindentation, internal length gradient plasticity theory
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