On the role of the transformation eigenstrain in the growth or shrinkage of spheroidal isotropic precipitations

The jumps of the strain and stress tensors on the surface of elastic homogeneous or inhomogeneous ellipsoidal inclusions embedded in an elastic matrix are obtained from results reported in the literature. They are used to derive closed-form expressions for the thermodynamic force in such matrix-inclusion systems that are subjected to a generally defined homogeneous transformation eigenstrain. A detailed study is presented for an isotropic spheroidal inclusion in an isotropic matrix in which the most important parameters are the inclusion's aspect ratio α and an eigenstrain triaxiality parameter d˜. The fluctuations of the thermodynamic force are investigated for a set of specific transformation eigenstrain tensors and are presented for inclusion shapes ranging from disk-like to fiber-like spheroids.