Elastic-Plastic Instability Caused by the Size Effect and Its Influence on Rubbing Wear

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Abstract
The yield strength of many materials is much higher for minute specimens than for bulk samples. The region around the point of highest shear stress in a solid undergoing deformation by a small spherical indenter can be regarded as such a minute specimen which may be ``protected'' by the size effect against plastic yielding if it is small enough. Formulating the effective yield strength and the elastic stress under the indenter in terms of a common parameter provides a basis for assessing the influence of size scale on the plastic yield threshold. Four size categories are identified, including a critical case for which a small change of loading may cause a discontinuous transition from the elastic to the plastic regime throughout the region of contact, and another, more frequently encountered, in which the supportable pre-yield elastic stress is materially enhanced. The latter effect may exert an important influence on the rate of rubbing wear since it can make available a wider range of loading for which a low wear rate prevails. Reported wear tests on steel riders and on sapphire phonograph styli confirm these predictions qualitatively.

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