The shape and orientation of the minimum strain energy of coherent ellipsoidal precipitate in an anisotropic cubic material

The elastic strain energy of perfectly coherent ellipsoid of revolution, which has the cube-cube orientation relationship with the matrix, has been calculated as a function of the orientation of the axis of revolution and of shape factor in anisotropic cubic crystalline materials. The minimum strain energy condition occurs at four different shapes and orientations, i.e. sphere, rod along 〈001〉 axis, disc on 001 plane and disc on 111 plane, depending on the two shear moduli of precipitate, i.e. μ*₁((C*₁₁—C*₁₂)/2) and μ* (C*₄₄). This is true regardless of the elastic property of the matrix phase when its anisotropy factor is larger than 1. The conditions of the occurrence of each shape and orientation are greatly affected by the difference in the misfit accommodation behavior depending on the shape of precipitate. A review of the experimental observations indicates the presence of all four different shapes and orientations in the case of GP zones in Al alloys. The conditions of their appearance are in good agreement with the prediction of the present calculation.