Modelling of Nanoindentation of Compliant Layers on Stiffer Substrates using Finite Element Analysis
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1025-B08-07
Modelling of Nanoindentation of Compliant Layers on Stiffer Substrates using Finite Element Analysis Charles A Clifford, and Martin P Seah National Physical Laboratory, Teddington, TW11 0LW, United Kingdom ABSTRACT Nanoindentation using an Atomic Force Microscope (AFM) or a nanoindenter was modelled using Finite Element Analysis (FEA). Force versus indentation depth data were measured for a system consisting of a compliant layer on a stiffer substrate. It was found that the FEA results may be expressed analytically by a simple function that describes the reduced modulus value obtained with Oliver and Pharr’s method for any moduli values, thickness of layer or radius of the indenter tip. Initial results obtained by varying the Poisson's ratio of the layer and substrate are also presented. INTRODUCTION Nanoindentation using AFM or a dedicated nanoindenter can be used to measure material properties such as modulus for homogenous materials [1] and can aid in identifying the material. The direct method to measure modulus involves calibrating all parameters. For example, one such parameter for AFM nanoindentation that needs calibrating is the spring constant, kz, of the AFM cantilever [2,3]. A draft international standard on methods to calibrate kz is currently being written under the auspices of ISO/TC 201/SC 9. The nanoindentation of layered materials and the measurement of the layer modulus involves further measurement challenges. To measure the modulus of the top layer accurately, one of two approaches may be taken. The first method involves indenting to shallow enough depth so as not to sense the underlying substrate. In the past, this has been typically represented by Bückle’s rule [4] that states that the substrate will not significantly affect the mechanical properties of an overlayer provided that the indentation is to no more than one tenth the layer thickness. Bückle’s rule was originally developed for the measurement of hardness but has since been more widely applied to modulus. The second method, on the other hand, takes the substrate properties into account through the use of models. Here the properties of the substrate must be known to enable the unknown properties of the coating to be determined. In this paper, we describe the finite element modelling of the nanoindentation process of a spherical tip indenting an elastic system consisting of a compliant layer on a stiffer substrate. EXPERIMENT Nanoindentation was modelled using the commercial ABAQUS finite element software (Abaqus Inc, Pawtucket, USA). The mesh consisted of a horizontal layer of variable thickness on a substrate. A higher mesh density was used near the contact area to model the stress field more accurately. The indenter tip was modelled as a rigid spherical shape and placed at the centre of the axisymmetric mesh. Both the coating and the substrate were assumed to be totally elastic.
In all cases, a displacement-controlled indentation was modelled to a depth of less than 100 nm and force versus indentation depth curves extrac
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