Application of anisotropic inclusion theory to the energy evaluation for the matrix channel deformation and rafting geometry of γ−γ′ Ni superalloys

Abstract

Uniaxial plastic strain along [0 0 1] is introduced in three types of matrix domains in γ−γ′ nickel superalloys: uniformly in the γ matrix, the horizontal matrix channels normal to [0 0 1] and the vertical channels normal to [1 0 0] and [0 1 0]. Using a mean field method, an elastic energy change due to the introduction of plastic strain (elongation or compression) in the three types of domains is calculated. It is also shown that the particle shape change from a cuboid to a disk, parallel to {0 0 1}, due to the elastic energy decrease, occurs only when the precipitate misfit is present. If there is no plastic strain in the matrix, these disks can be formed with random orientations, parallel to three types of {0 0 1} planes. It is only when there is a plastic strain in the matrix in addition to a precipitate misfit that the alignment of disks occurs on particular types of {0 0 1}. The choice of the alignment plane depends on the sign of the ratio of the plastic strain to the precipitate misfit strain.