Analysis on mechanical states and stable shapes of coherent precipitates in elastically anisotropic materials with a superellipsoidal approximation

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When a misfit precipitate generates in a material, it causes two changes of the free energy of the material. One is the change in the precipitate/matrix interface energy and the other is that in the elastic strain energy. Both of the changes depend on the precipitate shape and the equilibrium shape of the precipitate is determined by the sum of the interface energy and the elastic strain energy. The interface energy and the elastic strain energy are proportional to the surface area and the volume of the precipitate, respectively, Hence the interface energy and the elastic strain energy are dominant for smaller and larger precipitates, respectively.In some alloys with coherent precipitates, shape transitions of the precipitates from spherical to cuboidal are observed with increasing the precipitate size. The energy analysis on the change of the equilibrium shape becomes straightforward if its possible shapes can be described geometrically. The shape transitions can be geometrically approximated with variations of shapes of superspheres. In the present study, the elasticォenergy caused by super ellipsoidal precipitates embedded in cubic materials is discussed. The equilibrium shape of the precipitates is obtained as the shape that causes the minimum of sum total of the elastic strain energy and interface energy. It is shown that the present analysis reasonably explains experimental results on the shape change of the precipitates in Ni-Ni3AI and Cu-Cr-Co alloys.