Effects of mechanical properties on the contact profile in Berkovich nanoindentation of elastoplastic materials
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Chunhui Yanga) School of Engineering, Deakin University, Geelong, Victoria 3220, Australia (Received 3 May 2011; accepted 16 September 2011)
Pile-up or sink-in is always a concern in a nanoindentation test because it gives rise to errors in the estimation of the projected contact area when it is theoretically analyzed with the classic Oliver–Pharr method. In this study, a three-dimensional finite element model is developed to simulate nanoindentation with a perfect Berkovich tip. The variation of the contact profile with respect to the work-hardening rate n and the ratio of yield stress to elastic modulus ry/E has been studied for a wide range of elastoplastic materials. The numerical results show that a low ry/E not only facilitates the pile-up for materials with little or no work-hardening but also enhances the sink-in for materials with a high work-hardening rate. It is attributed to the lateral-flow dominated plastic deformation in low work-hardening materials and the normal-flow dominated plastic deformation in high work-hardening materials, respectively. Because of the large sink-in, for the materials with high n and low ry/E, significant errors in the calculation of the projected contact area can be generated by using the classic Oliver–Pharr method.
I. INTRODUCTION
The nanoindentation test has been widely used to measure the mechanical properties of materials at small length scales, which is especially useful for thin films and nanostructured materials.1–7 The basis for the nanoindentation test is that the projected contact area can be estimated from the load–displacement curve, rather than by imaging the indentation impression like a microhardness test.1,2 The Oliver–Pharr method2 has been commonly adopted to determine the projected contact area and extract the hardness and elastic modulus from the load– displacement curves. In the classic Oliver–Phar method, knowing the loading force P at indentation depth h, the contact depth hc is estimated by hc 5 h 2 P / S, in which the stiffness S 5 dP / dh is the initial slope of the unloading curve and e is a constant related to the geometry of the indenter (e 5 0.75 is the commonly used empirical value5). For a Berkovich indenter, the projected contact area Ac is calculated as Ac ¼ 24:5h2c . Then, the hardness H can be determined with H 5 P / Ac. Materials with a low work-hardening rate normally pile up, whereas those with a high work-hardening rate sink in.8–11 The variation in contact area due to pile-up or sink-in produces errors in the Oliver–Pharr method. Once pile-up or sink-in occurs, the projected contact area may be a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.333 J. Mater. Res., Vol. 27, No. 1, Jan 14, 2012
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underestimated or overestimated, respectively. Then, the errors generated in the calculation of the projected contact area leads to a higher or lower hardness than its true value. Therefore, it is important to understand how greatly the c
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