The elastic interaction energy between several precipitates is of great interest since it may have a significant effect on the ordering of precipitates in many metallurgical systems. Most of the works on this subject assumed homogeneous systems, namely, the elastic constants of the matrix and the precipitates are identical. In this study the elastic fields, self and interaction energies of inhomogeneous anisotropic precipitates have been solved based on a new iterative approach and using the semi-analytic Fourier transforms method. We illustrate the calculation approach on γ`-Ni3Ti precipitates in A-286 steel and demonstrate that the influence of elastic inhomogeneity is in some incidences only quantitative while in others it has essential effect.
Assuming homogeneous system, disk shape precipitate is associated with minimum elastic energy. Only by taking into account the different elastic constants of the precipitate, the minimum self-energy is found to be associated with spherical shape, and indeed this is the observed shape of the precipitates in A-286 steel.
The elastic interaction energy between two precipitates was calculated for several configurations. Significant differences between the interactions in homogeneous and inhomogeneous were found for disk shape morphologies. Only quantitative differences (9% higher interaction between inhomogeneous precipitates) was found between two spherical precipitates, which are the actual shape of the γ`-Ni3Ti precipitates. The same tendencies with strain magnitude, interparticle distances and orientation were found in homogeneous and inhomogeneous systems.