Analysis of nanoindentation load-displacement loading curves
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Analysis of nanoindentation load-displacement loading curves S. V. Hainsworth, H. W. Chandler,a) and T. F. Page Materials Division, Department of Mechanical, Materials and Manufacturing Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, United Kingdom (Received 13 November 1995; accepted 8 April 1996)
Nanoindentation load-displacement curves provide a “mechanical fingerprint” of a materials response to contact deformation. Over the last few years, much attention has been focused on understanding the factors controlling the detailed shape of unloading curves so that parameters such as true contact area, Young’s modulus, and an indentation hardness number can be derived. When the unloading curve is well behaved (by which we mean approximating to linear behavior, or alternatively, fitting a power-law relationship), then this approach can be very successful. However, when the test volume displays considerable elastic recovery as the load is removed [e.g., for many stiff hard materials and many inhomogeneous systems (e.g., those employing thin hard coatings)], then the unloading curve fits no existing model particularly well. This results in considerable difficulty in obtaining valid mechanical property data for these types of materials. An alternative approach, described here, is to attempt to understand the shapes of nanoindentation loading curve and thus quantitatively model the relationship between Young’s modulus, indentation hardness, indenter geometry, and the resultant maximum displacement for a given load. This paper describes the development and refinement of a previous approach by Loubet et al.1 originally suggested for a Vickers indenter, but applied here to understand the factors that control the shape of the loading curve during nanoindentation experiments with a pointed, trigonal (Berkovich) indenter. For a range of materials, the relationship P Km d2 was found to describe the indenter displacement, d, in terms of the applied load P. For each material, Km can be predicted from the Young’s modulus (E) and the hardness (H). The result is that if either E or H is known, then the other may be calculated from the experimental loading curve. This approach provides an attractive alternative to finite element modeling and is a tractable approach for those cases where analysis of unloading curves is infeasible.
I. INTRODUCTION
Continuously recording indentation techniques (e.g., nanoindentation) have become rapidly established as a means of determining the near-surface mechanical properties of materials because of their ability to measure mechanical properties at high resolutions in load, position, and displacement. A typical nanoindentation is shown in Fig 1(a) along with a nanoindentation load-displacement curve in Fig. 1(b). The continuously sensed load and displacement provide a mechanical fingerprint2 of a material’s response to deformation from which, in principle, traditional mechanical property parameters such as Young’s modulus (
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