Size dependent hardness of silver single crystals
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The hardness of thick, high-purity, epitaxially grown silver on sodium chloride is found to be dependent on the size of the indentation for sizes below ~10 yttm. The measurement of the size effect has been made in two ways. In one, the hardness has been calculated from the load-displacement curve obtained from an instrumented microhardness testing machine and assuming a geometric self-similarity in the indenter shape. In the other measurement, the hardness was obtained from the load exerted by the microhardness tester divided by the indentation impression area as measured by atomic force microscopy. The observed variation in microhardness with indentation size is consistent with a simplified strain gradient plasticity model in which the densities of the geometrically necessary and statistically stored dislocations are fitting parameters. An equally good fit can also be made with a simple geometric scaling relationship. Transmission electron microscopy observations of a thin (—50 nm) epitaxial gold film embedded in the silver layers revealed that the deformation was primarily restricted to the sharp edges of the indentation. In addition, deformation twinning within the indentation impression was observed on the {111} planes.
I. INTRODUCTION The indentation hardness of a ductile metal is usually considered to be a measure of its yield stress in compression.1 According to conventional plasticity theory, in which all material properties are length scale independent, the measured hardness values should be independent of the indentation size.2 Likewise, simple dislocation models of hardness based on punching of prismatic loops are independent of indentation size. However, there is ample experimental data in the literature2"6 showing a size dependence of the measured hardness when the size of the indentation is in the range of 0.1 to 10 /im. In the majority of experiments the hardness increases with decreasing load, but there are instances in which the hardness falls with decreasing load.7 The origin of the observed size dependence has been the subject of considerable dispute. There have been suggestions that the size dependence is a consequence of inadequate measurement capabilities, a topic discussed below, or of poorly characterized surfaces. For instance, surface artifacts, such as the presence of an abraded surface layer,8 and chemical contamination9 can cause an apparent increase in hardness at small loads. More recently, it has been proposed that many size effects in plastically deforming materials have a physical basis that can be described in terms of strain gradient plasticity.WA1 In this formulation of plasticity theory the constitutive law contains strain gradient as a variable, and hence there is an intrinsic length scale. This theory is based on the observation that gradients of plastic J. Mater. Res., Vol. TO, No. 4, Apr 1995
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shear result in the storage of the so-called geometrically necessary dislocations,n-n which affect the yield stress in a simil
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