Simulations of three-dimensional dendritic growth using a coupled thermo-solutal phase-field model

Using a phase field model, which fully couples the thermal and solute concentration field, we present simulation results in three dimensions of the rapid dendritic solidification of a class of dilute alloys at the meso scale. The key results are the prediction of steady state tip velocity and radius at varying undercooling and thermal diffusivities. Less computationally demanding 2-dimensional results are directly compared with the corresponding 3-dimensional results, where significant quantitative differences emerge. The simulations provide quantitative predictions for the range of thermal and solutal diffusivities considered and show the effectiveness and potential of the computational techniques employed. These results thus provide benchmark 3-dimensional computations, allow direct comparison with underlying analytical theory, and pave the way for further quantitative results

Simulation of Intermetallic Solidification using Phase-Field Techniques

We present current ideas towards developing a phase-field model appropriate to the solidification of intermetallic phases. Such simulation presents two main challenges (i) dealing with faceted interfaces and (ii) the complex sub-lattice models used to describe the thermodynamics of such phases. Although models are already existent for the simulation of faceted crystals, some of these can be shown to produce highly unrealistic Wulff shapes. The model present here uses a parameterization of the Wulff shape as a direct input to the model, allowing the simulation of arbitrary crystal shapes. In addition, an anti-trapping current that can be used with arbitrary (including sub-lattice) thermodynamics is presented. Such antitrapping currents are vital in the simulation of intermetallic phases where the steep liquidus slope means small deviations in solute partitioning behaviour can translate to a significant change in tip undercooling

solidification

new approach to multi-phase field for th

Phase field modelling of hopper crystal growth in alloys

Abstract Here we use phase field to model and simulate “hopper” crystals, so named because of their underlying cubic structure but with a hopper-like depression on each of the six faces. Over the past three decades simulations of single phase solidification have successfully explored dendritic structures, in two and three dimensions, formed under high undercooling from a slight perturbation in anisotropy. More recently we see the modelling of faceted structures at near equilibrium, and also, under high undercooling, the formation of dendritic-like structures in two dimensions which retain some faceting in the dendrite arms. A cubic hopper crystal appears to be a hybrid structure, somewhere between a perfect cube and a dendrite, and, to date, has not appeared in the modelling literature. In this paper we describe a model for faceted cubic growth and explore results, necessarily in three dimensions, that include perfect cube, hopper and dendritic. We also touch briefly on one other morphology—octahedral

An adaptive mesh method for phase-field simulation of alloy solidification in three dimensions

We present our computational method for binary alloy solidification which takes advantage of high performance computing where up to 1024 cores are employed. Much of the simulation at a sufficiently fine resolution is possible on a modern 12 core PC and the 1024 core simulation is only necessary for very mature dendrite and convergence testing where high resolution puts extreme demands on memory. In outline, the method uses implicit time stepping in conjunction with an iterative solver, adaptive meshing and a scheme for dividing the work load across processors. We include three dimensional results for a Lewis number of 100 and a snapshot for a mature dendrite for a Lewis number of 40