Bending of crystalline plates under the influence of surface stress - a finite element analysis

Changes in the surface stress Delta tau((s)) at the solid-vacuum and the: s olid-liquid interface are typically measured via the Sending of a (thin) cr ystalline plate. The bending is converted into Delta tau((s)) with the help of elasticity theory. Although the conversion is trivial for the unconstra ined bending of an elastic isotropic substrate, it becomes less straightfor ward for single crystals. In this paper we firstly consider the analytical solution for the free two-dimensional bending of a cubic substrate under th e influence of a homogeneous, but anisotropic surface stress. Secondly, the bending is calculated numerically for the experimentally mostly realized c ase of a sample with (100) or (111) surfaces clamped along one edge. In pri nciple, separate numerical calculations are required for each individual ma terial and surface orientation. It is shown that a parameterized form of th e analytical solution for the unconstrained bending can still be used in mo st cases. The appropriate parameters are calculated for various Poisson rat ios and crystal anisotropies. (C) 2000 Elsevier Science B.V. All rights res erved.