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

Directional coarsening in Ni-base superalloys is investigated by means of a n analytical approach, focusing on the prediction of the rafting direction. Closed-form results for the prediction of the rafting direction are derive d using the assumption of elastic material behaviour in matrix and precipit ate; no restrictions are placed on particle shape, particle interactions an d the elastic constants of the two phases other than the requirement of cub ic symmetry. An appropriate representation of Eshelby's force on an interfa ce is derived and the concept of a load-equivalent eigenstrain is developed . With these requisites, the symmetry of the system allows for the identifi cation of simple criteria for the prediction of the rafting direction. Morp hology maps are presented as dimensionless load and elastic mismatch parame ter diagrams for the two- and three-dimensional case. In these diagrams, tw o curves separate regions of different expected rafting directions. The res ults confirm and extend those previously found under various restrictions. Specifically, the role of the volume fraction of the gamma'-phase is assess ed; one of the two direction reversal curves is found to be independent of the volume fraction.