Directional coarsening in Ni–base superalloys: analytical results for an elasticity–based model

Directional coarsening in Ni–base superalloys is investigated by means of an analytical approach, focusing on the prediction of the rafting direction. Closed–form results for the prediction of the rafting direction are derived using the assumption of elastic material behaviour in matrix and precipitate; no restrictions are placed on particle shape, particle interactions and the elastic constants of the two phases other than the requirement of cubic symmetry. An appropriate representation of Eshelby's force on an interface is derived and the concept of a load–equivalent eigenstrain is developed. With these requisites, the symmetry of the system allows for the identification of simple criteria for the prediction of the rafting direction. Morphology maps are presented as dimensionless load and elastic mismatch parameter diagrams for the two– and three–dimensional case. In these diagrams, two curves separate regions of different expected rafting directions. The results confirm and extend those previously found under various restrictions. Specifically, the role of the volume fraction of the γ–phase is assessed; one of the two direction reversal curves is found to be independent of the volume fraction.