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Title: An analytical model for the flat punch indentation size effect
Authors: Campbell, C. J.
Gill, S .P. A.
First Published: 5-May-2019
Publisher: Elsevier
Citation: International Journal of Solids and Structures, 2019
Abstract: An analytical approximation for the indentation size effect (ISE) due to plane strain flat punch nanoindentation is derived. The flat punch ISE differs from that observed for self-similar (pointed) and spherical indenters in a number of ways: (1) the contact area does not change; (2) the contact pressure depends on two length scales not just one (the punch width and the indentation depth); (3) the profile of the punch is not differentially continuous, resulting in singular plastic strain gradients at the sharp edges, such that (4) the shape and connectivity of the plastic zones change with indentation depth and punch width, resulting in (5) changes in the proportion of the deformation accommodated by elasticity and plasticity are important, meaning that a fully elastoplastic model is required. Complete loading-unloading curves are modelled, with the calibration of geometrical parameters from finite element strain gradient plasticity simulations. As the punch width decreases, it is observed that there are increases in the indentation pressure, the relative size of the plastic zone(s) and the elastic component of the deformation. These predictions are found to compare favourably with experimental measurements in the literature. The model is extended to incorporate the consequence of imposing natural limitations on the maximum dislocation density at the edges. It is suggested that observable changes in the plastic zone morphology with the ISE make this an experimentally interesting area for the validation of size effects in plasticity.
DOI Link: 10.1016/j.ijsolstr.2019.05.004
ISSN: 0020-7683
Embargo on file until: 5-May-2020
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © Elsevier 2019. After an embargo period this version of the paper will be an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License (, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
Appears in Collections:Published Articles, Dept. of Engineering

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