The correlation of indentation experiments

TLDR: In this article, a simplified theoretical model of this behaviour is obtained by extending R. Hill's theory of expanding a cylindrical or spherical cavity in an elastic-plastic material to ensure compatibility between the volume of material displaced by the indenter and that accommodated by elastic expansion.

Abstract: The theory of rigid perfectly-plastic solids predicts indentation pressures, using wedge-shaped or conical indenters, which depend only on the geometry of the indenter and the yield stress of the material. With blunt wedges or with materials having a low ratio of Young's modulus, E, to yield stress, Y, the material displaced by the indenter is accommodated by an approximately radial expansion of the surrounding material. The indentation pressure then falls below the rigid perfectly-plastic value. In these circumstances, measurements of indentation pressure for a variety of indenter geometries are shown to correlate with the single parameter (E/Y) tan β, where β is the angle of inclination of the indenter to the surface at the edge of the indentation. This parameter may be interpreted as the ratio of the strain imposed by the indenter to the yield strain of the material. A simplified theoretical model of this behaviour is obtained by extending R. Hill's theory of expanding a cylindrical or spherical cavity in an elastic-plastic material to ensure compatibility between the volume of material displaced by the indenter and that accommodated by elastic expansion.