Simulation of the solidification of pure nickel via the phase-field method

Abstract

The Phase-Field method was applied to simulate the solidification of pure nickel dendrites and the results compared with those predicted by the solidification theory and with experimental data reported in the literature. The model's behavior was tested with respect to some initial and boundary conditions. For an initial condition without supercooling, the smooth interface of the solid phase nucleated at the edges of the domain grew uniformly into the liquid region, without branching. In an initially supercooled melt, the interface became unstable under 260 K supercooling, generating ramifications into the liquid region. The phase-field results for dendrite tip velocity were close to experimental results reported in the literature for supercooling above 50 K, but they failed to describe correctly the nonlinear behavior predicted by the collision-limited growth theory and confirmed by experimental data for low supercooling levels

Simulation of the Microstructural Evolution of Pure Material and Alloys in an Undercooled Melts via Phase-field Method and Adaptive Computational Domain

“…The value of j controls the number of preferential directions of the material's anisotropy, equaling 0 for the isotropic cases, 4 for anisotropy of 4 directions, and so on. The constant θ o is the interface orientation with respect to the maximum anisotropy, while ε and w are parameters associated with the interfacial energy (σ) and interface thickness (λ), as proposed by Boettinger et al For the interface mobility, we follow references Ferreira et al 1 and Boettinger et al 7 :…”

“…Furthermore, direct tracking of the interface position is not needed during numerical simulation of the solidification process. The phase-field models were developed mainly for studying solidification of pure materials 1 , being then extended to the solidification of binary 2 , ternary 3 , and quaternary in Salvino et al 4 alloys.…”

Predicting Secondary-Dendrite Arm Spacing of the Al-4.5wt%Cu Alloy During Unidirectional Solidification

“…The first models focused on pure materials. Such was the case, for example, of Kobayashi 3 , Kim et al 4 , and Ferreira et al 5 Binary alloys were then treated, e.g., in Oguchi and Suzuki 6 and Ode et al 7 Next, ternary alloys were attacked by Ferreira and de-Olivé Ferreira 8 and by Ode et al 9 A little more recently, quaternary alloys were dealt with in Salvino et al 10 Usually, phase-field works employ divided differences to obtain solutions to the equations. Moreover, in the case of alloys, dendrite growth is considered at constant temperature or constant cooling rate.…”

Numerical Simulation of Microstructural Evolution via Phase-Field Model Coupled to the Solutal Interaction Mechanism

“…Moreover, a commonly resorted way of including anisotropy in the model is to regard ε in Equation (13) as dependent on a so-called "growth angle", θ. The growth angle reflects the orientation of the normal to the interface with respect to the x axis, i.e., the longitudinal interface advance direction [16]:…”

“…Several different numerical approaches were proposed to that end. Some works have focused on pure materials [16]- [18], whereas others take heed of multicomponent alloys of metallurgical interest [1] [19]- [22]. In particular, the phase-field model has garnered wide acceptance, given its ability to simulate the solidification process in the presence of a complicated solid-liquid interface.…”