Elastic Deformation Of Substrate Research Articles

Formulation and a new solving approach to the problem of the wetting-induced deformation

ABSTRACT Although elastic deformation of substrate caused by wetting has been studied extensively, the influence of capillary effect and surface elasticity on the wetting-induced deformation is still an open question. This issue is investigated from the perspective of continuum mechanics. Based on the analysis of the composition of total energy, the self-energy of the triple contact line is introduced as a new energy form, and the governing equations of the wetting-induced deformation are derived from minimization of the total energy. Among them, two sets of new equations describe the equilibrium of the triple contact line in the non-pinned and pinned states, respectively. The results show that the equilibrium of the triple contact line depends not only on its capillary line tension and elastic line tension but also on its curvature. In particular, we discover that the surface/interface elastic stress and surface/interface tension are mutually independent in the equilibrium of the non-pinned triple contact line, while they are correlated with each other in the pinned state of the triple contact line. When the surface/interface elasticity is overlooked, the elastic deformation of a semi-infinite substrate caused by a cap-shaped droplet is calculated analytically through a new approach in which the deformed wetting interface is approximately taken as a rotational ellipsoid surface. The calculation reproduces the deformation pattern of the substrate observed in the soft-substrate wetting experiments.

Determination of film-only hardness by eliminating the effects of elastic deformation of substrate

A method is developed for the determination of the film-only hardness of thin films deposited on substrates by nanoindentation. The method is suitable for tests in low load range where the substrate only deforms elastically. The basic assumption is that the difference between the displacement recorded during unloading at a certain load and that recorded during loading at the same load only contains the displacement due to the elastoplastic deformation in the film, whereas the displacements due to the elastic deformation of the substrate during unloading and loading are equal and eliminated. With this assumption, one can derive the unloading curve of a hypothetical bulk model made of the film material, from which the hardness of the film material can be evaluated through conventional Oliver and Pharr's method. The validity of the approach was examined by applying the method to hafnium boride thin films deposited on silicon and fused quartz substrates.