Indentation-induced deformation at ultramicroscopic and macroscopic contacts
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Depth-sensing indentation at ultramicroscopic and macroscopic contacts (“nanoindentation” and “macroindentation,” respectively) was performed on four brittle materials (soda-lime glass, alumina titanium carbide, sapphire, and silicon) and the resulting load–displacement traces examined to provide insight to the elastic and plastic deformation scaling with contact size. The load–displacement traces are examined in terms of the unloading stiffness, the energies deposited during loading and recovered on unloading, and the effect of the indenter tip radius on the loading curve. The results of the analyses show that the elastic and plastic deformation during loading and unloading is invariant with the scale of the contact, and the unloading curve is best described by neither a conical tip nor a paraboloid of revolution, but of some compromise.
I. INTRODUCTION
Depth-sensing indentation is a popular technique for examining the elastic, plastic, and fracture properties of metals, ceramics, polymers, and films at both ultramicroscopic and macroscopic contact dimensions.1–15 In both cases, the load, P, and indenter displacement, h, are continuously measured during the load–unload contact cycle—usually with a Vickers or Berkovich tip. To date, it has been (implicitly) assumed that the relationships derived from elastic contact theory can be used to deconvolute the resulting P–h traces and determine the contact area, modulus, and hardness to read independent of the scale of contact. Here the P–h traces from nanoindentation and macroindentation of four brittle materials are analyzed to gain insight into the applicability of the theoretical indentation relationships to a large range of contact dimensions. II. THEORETICAL BACKGROUND
The indentation loading half-cycle is associated with both plastic and elastic deformation inside the contact region and elastic deformation outside the contact region (discounting “pile-up” or “sink-in” effects), as shown in
a)
Present address: Advanced Mechanical Technology, Mechanical Research and Development, Seagate Technology, Bloomington, MN 55435. b) Address all correspondence to this author. e-mail: [email protected] 124
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J. Mater. Res., Vol. 19, No. 1, Jan 2004 Downloaded: 02 Apr 2015
Fig. 1(a).6,8,16 The indenter tip has total axial displacement, h, relative to the surface and contact displacement, hc, associated with the radial contact dimension, 2a. The unloading half-cycle is associated with elastic recovery inside and outside the contact region, resulting in a residual impression of depth hr < hc, Fig. 1(b).6,8,16 The resulting load–displacement (P–h) trace can be used to extract the projected contact area at peak load, Ap, hardness, H, and plane-strain modulus, E* ⳱ E / (1 – 2), where E is the Young’s modulus and is the Poisson’s ratio. Figure 2 is the P–h trace from an 11 N Vickers indentation on soda-lime glass. During loading, the load is quadratic in the displacement, P∼h2, as suggested by Tabor,17 until the peak load, Pmax, and displacement,
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