Role of boundary conditions in modeling the elastic fields around a misfitting precipitate

Calculation of the elastic fields about a misfitting precipitate (inclusion) in an infinite matrix requires that the boundary conditions (BC's) at the precipitate-matrix interphase interface first be established. These calculations are important not only as a problem in micromechanics but also in such as growth kinetics, morphological stability, and stress relaxation of precipitates formed during diffusional phase transformations. In mechanics, BC's are important in modeling debonding of interfaces, frictional stress of a shaft in a bearing, creep and anelasticity of polycrystals. This communication considers how the physical conditions observed at interphase interfaces can be related to the mathematical BC's that must be used in the calculations of elastic fields.