Theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation for work-hardening materials

In our previous paper, the expanding cavity model (ECM) and Lame solution were used to obtain an analytical expression for the scale ratio between hardness (H) to reduced modulus (E-r) and unloading work (W-u) to total work (W-t) of indentation for elastic-perfectly plastic materials. In this paper, the more general work-hardening (linear and power-law) materials are studied. Our previous conclusions that this ratio depends mainly on the conical angle of indenter, holds not only for elastic perfectly-plastic materials, but also for work-hardening materials. These results were also verified by numerical simulations.

Theoretical foundation of Zisman's empirical equation for wetting of liquids on solid surfaces

Theories of wetting of liquids on solid surfaces under the condition that van der Waals force is dominant are briefly reviewed. We show theoretically that Zisman's empirical equation for wetting of liquids on solid surfaces is a linear approximation of the Young-van der Waals equation in the wetting region, and we express the two parameters in Zisman's empirical equation in terms of the dielectric polarizabilities of the solid and liquids. The materials contained in this paper are suitable for physics teaching of wetting phenomena for undergraduate, graduate, general physicist, etc.