Instabilities in the periodic arrangement of elastically interacting precipitates in nickel-base superalloys

Abstract

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 [110] 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.

Phase-field modeling of microstructure evolution: Recent applications, perspectives and challenges

“…The phase-field method has been used extensively to simulate precipitation in a wide range of metallic alloys, such as Ni [42,, Ti [68][69][70][71][72][73][74][75], Al [76][77][78][79][80][81][82][83][84][85], and Mg [86][87][88][89][90][91][92][93][94][95][96] alloys. Research studies have covered a series of aspects related to the growth and coarsening of precipitates, such as the shape and distribution of precipitates [47,80,88], the interactions between precipitations and external stress fields, such as the stress fields caused by other precipitates [89,94] or lattice defects [88,92], and the directional coarsening (rafting) and stability of cuboidal matrix/precipitate microstructures in superalloys [55][56][57][58][59][60][61][62]…”

Phase-field modeling of γ/γ″ microstructure formation in Ni-based superalloys with high γ″ volume fraction

“…close and the analytic model shows the same plateau for large misfit ratios. Figure 5b) shows the orientation dependent elastic relaxation function B ( n) that quantifies soft and hard crystallographic directions independent of the precipitate shape [15,46,81]. It is defined as…”

“…It is limited by being only a realistic description of a uniform single-variant microstructure that does not take into account the kinetics of precipitate growth that might have strong influence on the shapes of experimentally observed precipitates [91]. It was also found that a periodic arrangement of precipitates must not always be a stable configuration [46]. CONCLUSION We evaluate influencing factors on equilibrium shapes of γ precipitates in Ni-based superalloys considering one S l a m a e t a l .…”

“…The phase-field method is frequently used to study the temporal evolution of γ/γ microstructures [32][33][34][35][36][37] as well as γ/γ systems [38,39]. The variational formulation of the phase-field method makes it a useful tool to determine equilibrium precipitate morphologies [40][41][42][43][44][45] and precipitate interactions [46]. In the scope of this work, we develop a phase-field model to extensively evaluate factors influencing two-dimensional γ precipitate shapes.…”

Phase-field study of elastic effects on precipitate evolution in (Al)0.05CrFeNi

“…The elastic effect observed in the experiments is well studied through PF models for binary and ternary systems [36][37][38][39][40][41]. Degeiter, et al [42] studied the microstructure formation in Nickel-based alloys based on PF simulations, and revealed that the periodic arrangement of cuboidal precipitates is unstable, which may lead to the formation of defects related to experimental observations. Hong et al [43,44], investigated the precipitation process of β phase in Mg based binary and ternary alloys, results show that the growth behavior of the precipitates determined by the elastic strain energy minimization.…”