MEAN STRESSES IN MICROSTRUCTURES DUE TO INTERFACE STRESSES - A GENERALIZATION OF A CAPILLARY EQUATION FOR SOLIDS

We derive a general expression for the mean stress in a solid induced by the stresses of areal and linear defects such as grain boundaries a nd triple junction lines. The mean stress is a function of measurable stereological quantities, weighted areas of interfaces and lengths of the linear defects, not their curvatures. Generally the stress is non- hydrostatic. For anisotropic and textured microstructures, the mean st ress depends on stereological moments of the interface orientation dis tribution function, but otherwise it is independent of the geometry of the microstructure. In two limiting cases, isolated spherical particl es (in a matrix or not) and layer structures, the solution for the str ess reduces to results which have been derived previously. These solut ions can be used to determine average interface stresses from experime ntal lattice constant data. Although the specific interface area is al ways the important quantity in this relation, for the spheres this are a/volume reduces to the particle curvatures commonly used in the liter ature for many microstructures. (C) 1997 Acta Metallurgica Inc.