Large-scale three-dimensional phase field simulation of γ ′-rafting and creep deformation

Abstract

Three-dimensional phase field simulations of coupled / 0 microstructural evolution and plastic deformation in single crystal Ni-Al are carried out at micrometer scales. Coherent / 0 microstructures and plastic deformation in -channels are described using a single, consistent methodology based on Khachaturyan's phase field microelasticity approach to coherent precipitates and dislocations. In particular, a new set of phase fields is introduced to characterize local density of dislocations from individual active slip systems. To increase the length scale of the phase field simulations, the Kim-Kim-Suzuki (KKS) treatment of / 0 interfaces was adopted. The rafting kinetics, precipitate-matrix inversion process and the corresponding creep deformation are characterized with respect to parameters such as applied stress and lattice misfit. The simulation results on 0 -rafting kinetics and morphological evolution of the / 0 microstructures are compared with available experiment. The model can be used to carry out parametric studies of the effects of material and processing parameters such as alloy composition, external stress and working temperature on 0 -rafting kinetics, morphological evolution and the corresponding creep deformation.

An integrated full-field model of concurrent plastic deformation and microstructure evolution: Application to 3D simulation of dynamic recrystallization in polycrystalline copper

“…These models, while providing certain connection between microstructure and crystal plasticity, still lack a dynamic coupling between the two. On the other hand, phase-field models incorporating either continuum plasticity (Gaubert et al, 2010) or dislocation density fields (Zhou et al, 2010) have also been developed to study rafting in Ni-based superalloys. These models are mainly rooted in the PF framework and significant advances are required in order to generalize the approach and incorporate a wider range of existing constitutive theories.…”

“…At the mesoscale, this understanding has been implemented into physics-based constitutive theories (Arsenlis and Parks, 2002;Arsenlis et al, 2004;Cheong and Busso, 2004;Ma et al, 2006;Gao and Huang, 2003;Beyerlein and Tomé, 2008) and implemented into homogenized deformation models such as self-consistent schemes (Lebensohn and Tomé, 1993;Niezgoda et al, 2014) or full-field simulations such as finite element based crystal plasticity (FE-CP) (Kalidindi et al, 1992;Beaudoin et al, 1995;Roters et al, 2010) or fast Fourier transform (FFT) based crystal plasticity (FFT-CP) models (Lebensohn, 2001;Lebensohn et al, 2012;Eisenlohr et al, 2013). On the other hand, the microstructural evolution in crystals, such as grain growth (Chen and Yang, 1994;Kazaryan et al, 2002;Moelans et al, 2008b), static recrystallization (Moelans et al, 2013), rafting in superalloy (Zhou et al, 2010;Gaubert et al, 2010) and many other phenomena (Chen, 2002;Wang and Li, 2010) have been well studied using phase-field (PF) simulations. The nonboundary tracking field description of microstructures and the incorporation of thermodynamics-based free energy formulation have made PF a very powerful and robust tool in simulating and predicting the microstructural evolution often in a quantitative manner (Chen, 2002;Boettinger et al, 2002;Shen et al, 2004;Moelans et al, 2008b;Steinbach, 2009;Wang and Li, 2010).…”

Phase-Field Modeling of Equilibrium Precipitate Shapes Under the Influence of Coherency Stresses

“…This is shown in Figure 2, where the thick dark line represents the analytical solution obtained from Eq. [41]. Maxima or unstable solutions occur for q ¼ 0 for all the characteristic lengths beyond critical value.…”

“…[41], we plot the shape factors corresponding to the equilibrium solution as a function of the characteristic length. This is shown in Figure 2, where the thick dark line represents the analytical solution obtained from Eq.…”

“…Apart from the determination of equilibrium shapes, the diffuse-interface methods have also been used for the study of growth and coarsening of multi-particle systems, [27,[29][30][31][32][33][34] instabilities, [35] and rafting. [36][37][38][39][40][41] In all the above studies, the central focus of investigation has been the study of equilibrium shapes of precipitates where the anisotropy exists only in the elastic energy. The coupled influence of both the interfacial energy and elastic anisotropies on the equilibrium morphologies is performed using the boundary integral method by Leo et al [42] In a study by Greenwood et al, [43] the authors have developed a phase-field model of microstructural evolution, where they study the morphological evolution of solid-state dendrites as function of anisotropies in both surface as well as elastic energy.…”