Physical Origin of a Size Effect in Nanoindentation
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Physical Origin of a Size Effect in Nanoindentation A.J. Bushby1, J.R. Downes, N.B. Jayaweera, P. Kidd, A. Kelly2 and D.J. Dunstan Department of Physics, Queen Mary, University of London, London E1 4NS, UK. 1 Department of Materials, Queen Mary, University of London, London E1 4NS, UK. 2 Department of Materials Science and Metallurgy, University of Cambridge, Pembroke St., Cambridge CB2 3QZ, UK. ABSTRACT We have reported results of nanoindentation using spherical indenters to observe the full indentation stress-strain curve. We observe the onset of plasticity in semiconductor strainedlayer superlattices. These structures have alternating layers with strains of opposite sign. The yield pressure is reduced by the presence of the coherency strain. By varying the thicknesses and strains, we have been able to show that both sets of layers, compressive and tensile, reduce the yield pressure. This requires that a yield criterion must be satisfied over a volume, large enough to include layers of both sign. In these studies, we observe a large and reproducible size effect in the yield pressure. That is, with smaller radius indenters the mean pressure acting over the contact area at the deviation from purely elastic behaviour increases, by up to a factor of two for a 2µm radius indenter tip. Here we show how the requirement for meeting a yield criterion over a finite volume naturally leads to the size effect. Essentially, with smaller radius indenters, the peak stresses must be greater in order to satisfy the yield criterion over a finite volume. By integrating the strain energy over a suitable volume we show that there is a critical volume of ≈ 0.5µm radius over which yield is initiated for all indenter radii in the range 1-35µm. This is an important result for the understanding of nanoindentation and other systems in which stresses are highly inhomogeneous on a small scale. INTRODUCTION Size effects have been widely reported in nanoindentation since the work of Gane and Bowden in 1968 [1] who showed that for small scale contacts in gold the yield stress may approach the theoretical strength. Since then there have been many hardness size effects and discontinuous yield events reported in the literature and many attempts to explain the observed phenomena (e.g. see other papers in this volume). However, the origin of these size effects remains unclear. Nanoindentation experiments require sensitive measuring systems and good instrument calibration [2]. Notwithstanding these limitations, indentation size effects have been unambiguously demonstrated in metals [3]. Many studies have focused on the initiation of plasticity. The transition from elastic to plastic behaviour is often sudden (‘pop-in’) and has been associated with the nucleation of dislocations beneath the tip [4,5]. Other workers have suggested that fracture of the native oxide initiates yielding [6], or that dislocations nucleate at the interface between the oxide and underlying metal [7]. Michalske and Houston [8], considering the energy to extend a dislocation, hav
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