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Yi Kong School of Civil Engineering, The University of Sydney, NSW 2006, Australia; and State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China

Luming Shen School of Civil Engineering, The University of Sydney, NSW 2006, Australia

Pranesh Dayal and Mark Hoffman School of Materials Science and Engineering, UNSW Australia, Sydney, NSW 2052, Australia (Received 23 July 2014; accepted 5 January 2015)

The finite element method is used to simulate indentation with a 100 nm spherical indenter on Al/Pd multilayer thin films and Al and Pd monolayer thin films. The elastic/plastic properties of bulk Al and Pd and the material formulation are obtained by molecular dynamics simulations of tensile and indentation loadings. Hill’s plasticity with isotropic hardening is found to best represent the stress–strain response of both bulk Al and Pd. The Pd monolayers appear the hardest and the Al monolayers the softest. The indentation hardness of both monolayered and multilayered films is found to increase with the indentation depth and appears independent of the layer order and thickness in the multilayer films. The hardness values determined by the finite element method simulations are close to those obtained using the well-known formula of Field and Swain. No hardness enhancement in very thin multilayered films (3–5 nm per layer) is evident, in contrast to experimental reports.

I. INTRODUCTION

A common technique for measuring elastic and plastic properties of bulk materials and thin films at a submicron level is instrumented nanoindentation in which the force– displacement (P–h) curves are continuously recorded throughout the experiment and analytical models are applied to extract the required properties. This technique is particularly relevant for thin films where standard mechanical property testing is not possible. One property measured using instrumented nanoindentation is the hardness (H), which is defined as the indentation force divided by the contact area, measured as the projected area of the imprint after unloading. In the conventional indentation tests, the contact area can be directly measured from the residual impression left after unloading. In nanoindentation tests, however, the size of the impression is too small to be measured directly and indirect methods are used instead. Field and Swain1 developed a method for spherical indentation on bulk materials, which is based on the experimental load–displacement curve and indenter shape alone, without the need of measuring the impression area. Contributing Editor: Susan B. Sinnott a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2015.10 J. Mater. Res., 2015

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In recent times, multilayered films consisting of alternating nanometer thickness layers of two different metals (nanofilms) have demonstrated enhanced indentation hardness.2–8 In general, this enhancement goes beyond the rule of mixtures and increases as the layer thickness decreases to a few n