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 revolutio n, which has the cube-cube orientation relationship with the matrix, h as been calculated as a function of the orientation of the axis of rev olution 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} pla ne and disc on {111} plane, depending on the two shear moduli of preci pitate, i.e. mu(1) ((C-11* - C-12*)/2) and mu*(C-44*). This is true r egardless of the elastic property of the matrix phase when its anisotr opy factor is larger than 1. The conditions of the occurrence of each shape and orientation are greatly affected by the difference in the mi sfit accommodation behavior depending on the shape of precipitate. A r eview of the experimental observations indicates the presence of all f our different shapes and orientations in the case of GP zones in Al al loys. The conditions of their appearance are in good agreement with th e prediction of the present calculation.