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Nickel-base superalloys display cuboidal precipitates aligned along the cubic directions, which are the elastic soft directions. At high precipitate volume fraction, the microstructure is often described as a regular array of precipitates organized on a simple cubic macro-lattice. In the present work, we use a stability analysis and 3D phase field simulations to show that such a regular array is in fact unstable whatever the volume fraction of precipitates. The two main instability modes are the longitudinal [100] mode and the transverse [110] mode along the [ 1 1 ¯ 0 ] eigenvector. We argue that these instabilities lead to formation of configurational defects closely related to experimentally observed branches and herringbone patterns. The rôles of elastic anisotropy and elastic homogeneity are also discussed. [ABSTRACT FROM AUTHOR]

An elasto-viscoplastic model is developed to study the microstructural evolution during creep loading in a model AM1 superalloy. Elastic anisotropy and inhomogeneity, as well as the description of long-range order in the γ ' phase, are included in the model. Plastic activity is introduced using a continuum crystal plasticity framework at the mesoscale. Special attention is paid to the corresponding parameter identification from experiments. Two-dimensional simulations of creep in the [100] direction are performed, and the results are compared to the predictions of an elastic phase field model, in order to characterize the influence of plastic activity on the microstructural evolution. In particular, our simulations show that plastic activity in the γ channels significantly increases the rafting kinetics and allows misalignments of rafts with respect to cubic directions. The simulation results are critically discussed and improvements to the model are proposed. [ABSTRACT FROM AUTHOR]

We present a general formalism for incorporating dislocations in Phase Field methods (PFM) based on the elastic equivalence between a dislocation loop and a platelet inclusion of specific stress-free strain. Dislocations may be elastically and dynamically coupled to any other field such as a concentration field. Special attention is paid to the treatment of dislocation cores after the discretization of real and reciprocal space required by the computer implementation of any PFM. In particular, we propose a method based on two length scales to account for dislocation cores much smaller than the grid spacing. The method is illustrated through the simulation of the motion of a dislocation loop in a microstructure representative of a late-stage γ/γ′ microstructure. [Copyright &y& Elsevier]

[Display omitted] We investigate the growth of Widmanstätten structures in metallic alloys with phase field calculations. We show that elastic energy anisotropy associated with shear dominated transformations is alone sufficient to give rise to plate or needle like precipitates with constant lengthening rates at constant supersaturations. We show that Ivantsov analytical solutions still provide good estimates of the diffusion flux around tips even when elasticity is accounted for. A careful analysis demonstrates that, for shear dominated transformations, (i) the lengthening direction lies in the habit plane determined by one of the minima of the elastic kernel; (ii) the tip shape and size are equilibrium features, driven by elastic forces, rather than dynamically determined as usually assumed; (iii) the tip size of acicular precipitates can be rationalized by the value of the elastic kernel in the lengthening direction. [ABSTRACT FROM AUTHOR]