Elastic effects associated with the formation of precipitates in a free thin layer: Part i. the elastic fields

The present study is concerned with the relationship between the elastic strains and stresses that are associated with the presence of dilating precipitates in a thin isotropic, homogenous free layer, and the resulting microstructure. The elastic fields near the free surfaces of the thin layer are calculated using a superposition of two known solutions in the theory of linear elasticity. The redistribution of the elastic fields in the layer, with respect to that in an infinite matrix, is interpreted as resulting from the reduced constraints on the displacements parallel to the free surfaces. The reduced constraints enable the setting up of large lateral tensile strains and stresses between the precipitate and the free surfaces. The most significant result is that the hydrostatic stress component in the vicinity of the precipitate has the same sign as the transformation strain of the precipitate. In part II, the elastic interaction energies between precipitates and free surfaces will be deduced and their influence on the development of the microstructure will be discussed.