Plasticity size effects in nanoindentation
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D.J. Dunstan Department of Physics, Centre for Materials Research, Queen Mary, University of London, London E1 4NS, United Kingdom (Received 16 June 2003; accepted 22 September 2003)
In conventional continuum mechanics, the yield behavior of a material is size independent. However, in nanoindentation, plasticity size effects have been observed for many years, where a higher hardness is measured for smaller indentation size. In this paper we show that there was a size effect in the initiation of plasticity, by using spherical indenters with different radii, and that the length scale at which the size effect became significant depended on the mechanism of plastic deformation. For yield by densification (fused silica), there was no size effect in the nanoindentation regime. For phase transition (silicon), the length scale was of the order tens of nanometers. For materials that deform by dislocations (InGaAs/InP), the length scale was of the order a micrometer, to provide the space required for a dislocation to operate. We show that these size effects are the result of yield initiating over a finite volume and predict the length scale over which each mechanism should become significant.
I. INTRODUCTION
Indentation has long been a useful technique for measuring the mechanical properties of materials. It can give a single value for the hardness of the material using conical or pyramidal indenters or it can provide the entire stress–strain curve, using spherical indenters. Experimental and analytic techniques have been developed, which provide data independent of the size of the indenter, and the validity of these methods has thoroughly been verified over a wide range of indenter sizes.1 However, at the nanoindentation scale it is now well established that plasticity size effects exist at length scales of the order micrometers.2,3 These have included, for instance, an apparent increase in the onset of plasticity,4 changes in yielding behavior,5–9 and hardness size effects.10–12 Many studies have concentrated on the initiation of plasticity in single-crystal metals, such as gold and tungsten.5–9 These studies have mostly considered discontinuous yielding (“pop-in”) from dislocation nucleation events or oxide film fracture. Lim et al.11,12 have unambiguously demonstrated the indentation size effect in experiments using copper samples and spherical indenters. For indenter radii greater than about 100 m, they showed that a single indentation response was obtained independent of the indenter size. However, for smaller indenters, the entire indentation stress–strain curve was translated upward to higher pressures and by as much as a factor of two for a 7 m radius indenter tip. J. Mater. Res., Vol. 19, No. 1, Jan 2004
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Continuum mechanics adequately describes the yield behavior of large structures subject to relatively uniform stresses via the traditional yield criteria, such as the von Mises criterion. Kiely and Houston8 refined this approach in experiments on gold si
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