Effect of the spherical indenter tip assumption on nanoindentation
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L.E. Levine Materials Science & Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8553 (Received 9 November 2006; accepted 6 March 2007)
One of the interests and challenges of nanoindentation is determining the shear stress at the onset of plastic yielding, which corresponds to dislocation nucleation. To extract this stress information from experimental load-displacement data, a spherical tip shape is usually assumed. However, it is well known that indenter tips have irregular shapes, especially at the small-length scales that are important for small loads. This will significantly affect the stress distribution under the indentation surfaces. In this work, an indenter tip shape is measured by atomic force microscopy. The measured indenter shape is input into a finite element analysis model for indentation simulations on 〈111〉-oriented single-crystal Al samples in the elastic regime. The resulting stresses, indentation force, and contact area are analyzed and compared to results from a fitted spherical indenter. The deviation of the assumed spherical indenter tip from the real measured indenter tip is studied.
I. INTRODUCTION
As a simple and effective experimental technique, nanoindentation is widely used to explore the mechanical properties of small volumes of materials on a local scale.1–3 For crystalline materials, there is a growing experimental and theoretical interest in pop-in events, which are characterized by sudden displacement bursts at specific indentation loads that produce discontinuous steps in otherwise smooth load–displacement curves during indentation,4–11 as illustrated schematically in Fig. 1. The first pop-in event is often identified as the initial dislocation nucleation; thus, the transition point from purely elastic to elastic/plastic deformation.10,11 The shear strength at this first pop-in event is generally found to be close to the theoretical strength of the material. The maximum resolved shear stress at the pop-in load is generally determined from elastic contact theory11–14 and finite element analysis (FEA) modeling.12,15 Nanoindentation is generally performed with a Berkovich indenter, which has the shape of a three-sided pyramid with triangular faces. However, it is well known that real pyramid indenter tips are not perfectly sharp but a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2007.0205 1656 J. Mater. Res., Vol. 22, No. 6, Jun 2007 http://journals.cambridge.org Downloaded: 14 Jul 2014
have irregular tip shapes, especially at the small-length scales that are important for small loads. The tip shape will significantly affect the stress distribution under the indentation surface. To extract pop-in shear-stress information from experimental data, a spherical tip shape is usually assumed.11–13 The radius of the assumed spherical tip is generally obtained from the tip manufacturer,5,11 from atomic force microscopy (AFM) or scanning electron microscopy (SEM) data,6,9 or by a Hertzian fit to th
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