University of Leicester
An analytical model for the flat punch indentation size effect - unmarked.pdf (1008.21 kB)
Download file

An analytical model for the flat punch indentation size effect

Download (1008.21 kB)
journal contribution
posted on 2019-05-21, 09:05 authored by C. J. Campbell, S .P. A. Gill
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.


This work was performed as part of a EURAMET joint research project (StrengthABLE) with funding from the European Community's Seventh Framework Programme, ERA-NET Plus, under Grant agreement no. 217257.



International Journal of Solids and Structures, 2019

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Engineering


  • AM (Accepted Manuscript)

Published in

International Journal of Solids and Structures





Copyright date


Publisher version


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.



Usage metrics

    University of Leicester Publications