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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]

A phase field model accounting for inhomogeneous and anisotropic elasticity has been used to investigate the consequences of inhomogeneous elasticity on the formation and coarsening of cuboidal microstructures in Ni-based superalloys. For that purpose, two- and three-dimensional calculations have been carried out considering high volume fractions of γ ′ precipitates, and accounting for their ordered crystal structure. The analysis of a substantial number of cases with different contrasts of elastic constants highlights the primary role played by the inhomogeneity Δ C ′ of the shear modulus C ′ on the shapes and spatial arrangements of the precipitates. This can be attributed to the sensitivity of the mechanisms involved in coarsening to Δ C ′ . Finally, scanning electron micrographs of the AM1 superalloy are statistically analyzed and discussed in light of the calculations. [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]

The formation of pores in CMSX-4 nickel based superalloys is detrimental to the service life of the material. A way to avoid the problem is to treat the superalloys under Hot Isostatic Pressing (HIP), which enables a large volume fraction of pores to be annihilated. This paper aims to understand the contribution of plastic activity related to the gliding of dislocations on the pore annihilation. Simulations based on a phase-field model of dislocation are performed and make it possible to consider the strong anisotropy of the CMSX-4 under HIP conditions in conjunction to the strong elastic heterogeneity introduced by the pore. For pores with a radius of few micrometers, it is shown that edge parts of dislocation lines that present an extra half atomic plane oriented towards the pore are stacked above and under it in the direction which is perpendicular to their slip-planes, causing an increase of the number of dislocation along the four octahedral directions of the FCC single crystal which intersect the pore center. Results are streamlined within the isotropic elastic theory of dislocations. Effects of elastic anisotropy and dislocation reactions are also investigated in order to specify what would be the dislocation configuration around a pore in CMSX-4 under HIP conditions. Notably, the elastic anisotropy is shown to significantly modify the arrangement of dislocations close to the pore equator. Simulations also allow for the characterization of pore/dislocation interactions when dislocations are involved in Low Angle Boundaries as experimentally observed. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: The phase-field approach is used to study the formation and ageing of bimodal microstructures in a model Ni-based superalloy. Particular attention is paid to the definition of interfacial energies in the presence of elastic strain fields and to the incorporation of these energies in the phase-field formalism. During a two-step annealing procedure, our model predicts the formation of large anisotropic precipitates (called secondary precipitates) and small, almost isotropic precipitates (called tertiary precipitates). Finally, the phase-field model is used to characterize the ageing of tertiary precipitates. In agreement with experiments, we show that the mean size of the tertiary precipitates first grows as and finally reaches a plateau. This peculiar behavior is explained using phase-field simulations with prescribed geometries and with the development of a simple analytic model. [Copyright &y& Elsevier]

Microstructure evolution during tensile creep of 〈 0 1 1 〉 -oriented samples of first-generation Ni-based single-crystal superalloys was investigated both experimentally and numerically. Based on scanning electron microscopy and 3-D volume reconstruction using a dual-beam system, it was shown that the initially cuboidal microstructure first elongates along the cubic axis perpendicular to the tensile axis, and then coalesces along the two other cubic directions. We found that the normal to the platelets, initially close to a cubic axis, slightly rotates towards the tensile axis direction and the destabilization of the platelet microstructure appears to control the onset of the tertiary creep stage. In a second part, microstructure evolutions are analyzed using 3-D phase-field simulations. The inhomogeneous and anisotropic elastic and plastic driving forces are discussed, as well as the importance of a small misorientation of the tensile axis from the [0 1 1] direction. Surprisingly, contrary to the case of 〈 1 0 0 〉 -oriented sample, complete rafting is not obtained in the simulations, suggesting that an additional mechanism at the level of individual dislocations could be missing. Finally, we have developed an energetic model for a perfectly rafted microstructure, which proves that plasticity in the γ phase is at the origin of the γ / γ ′ interface rotation during creep. [ABSTRACT FROM AUTHOR]

[Display omitted] Microstructure evolutions in Ni-base superalloys are investigated during [110] creep loading using 3D and 2D phase field simulations. A recently developed phase field model coupled to a crystal plasticity model based on dislocation densities is employed. The model uses a storage-recovery law for the dislocation density of each glide system and a hardening matrix to account for the short-range interactions between dislocations. We show that small misorientations of the tensile axis strongly modify the evolution: rafting is observed for small deviations, as opposed to a microstructure made of rod-like precipitates when loading is performed along a perfectly aligned [110] direction. Depending on the precise direction of the mechanical load, different evolutions are obtained accompanied by strong modification of the macroscopic creep behavior, explaining the variety of results observed experimentally. The relative role of inhomogeneous and anisotropic elastic and plastic driving forces is also investigated, plasticity being the main driving force for rafting in the considered case. In addition, our calculations show that the initial dislocation density slightly modifies the precipitates morphology but the creep curve is significantly impacted. [ABSTRACT FROM AUTHOR]