Materials Science Forum Vols. 790-791

Abstract: Experimental evidence [Ohno 1987] revealed the influence of some pouring techniques on the as-cast structure. In the current work the process of pouring of the molten Al-4.0 wt.%Cu via one or multiple streams into a graphite mold is studied using a 3-phase model by considering the nucleation, the initial growth and transport of globular equiaxed crystals. The three phases are the melt, air and globular equiaxed crystals. Results showed that pouring via multiple streams increases the volume fraction and number density of crystals in the as-filled state. The subsequent solidification is calculated using a 5-phase mixed columnar-equiaxed solidification model. The five phases are the extradendritic melt, the solid dendrite and interdendritic melt inside the equiaxed grains, the solid dendrite and interdendritic melt inside the columnar grains. As final result the as-cast structure including the distinct columnar and equiaxed zones, columnar-to-equiaxed transition (CET), grain size, macrosegregation, and rest eutectic is predicted. Effect of melt convection and crystal sedimentation during the pouring and solidification is taken into account. The predicted as-cast structure, under the influence of single/multiple jet pouring, is evaluated bycomparison with the available experiments of Ohno.

Abstract: In static castings of multi-component alloys, visually observable bands of channels, with high solute concentration, can form in the final solidified product. The phenomenological explanation for these formations is that perturbations during the solidification process lead to preferred flow paths in the solid-liquid mushy region. Once these flow paths are initiated, the higher solute liquid that flows in them suppresses the solidification rate and thus provides a mechanism through which the preferred paths can evolve into high concentration channels. Models of solidification that couple heat transfer, fluid and flow and mass transport appear able to predict the formation of these channels. In many cases, however, the formation of these numerical channels is highly dependent on the nature of the numerical calculation. In particular, geometric attributes of the channels is a strong function of the size of the computational grid and in some cases the particular method (code) used. In this work, after discussing what might drive the observed discrepancies in predictions, a grid convergence study is undertaken. This study shows that for the case of a side cooled solidification of a binary (Al-4.5wt%Cu) in a square (40mm x 40mm) domain, it is possible to approach grid converged results of the solution of the standard mixture model for macrosegregation. Achieving this level of convergence requires the use of an explicit time stepping scheme to couple the thermal and solute fields along with a Carman-Kozeny permeability and lever rule microsegregation models. The results indicate that to reach grid convergence the size of a grid cell has to be on the order ~0.25-0.5 mm.

Abstract: Meso-scale modeling through the use of a granular-type model is a key new tool for predicting solidification-related defects. In the present study, the application of a granular-type model to welding microstructure is presented, along with application challenges and solutions. This new model can simulate the solidification of a weld pool at the mesoscale, i.e. both solid grains and liquid are included. Consequently, the behaviour of the semisolid structure within the weld pool can be studied. By means of this 3D meso-scale model, the continuous network of liquid channels that forms at the last stages of solidification have been investigated, allowing for prediction of the variation in the distribution of liquid channel width as a function of welding parameters.

Abstract: This article is to assess the modeling treatment of the growth kinetics (finite or infinite diffusion in liquid and solid phases) during solidification and its influence on the calculation of macrosegregation. A model of diffusion-governed growth kinetic for ternary alloy is developed and used for this assessment. Solidification of a 2D casting (50 x 50 mm²) of a ternary alloy (Fe-0.45 wt.% C-1.06 wt.%Mn) is considered. The result shows that finite diffusion in liquid, important for the initial stage of solidification, plays very important role in the formation of macrosegregation. Moreover, the role of the finite diffusion kinetics in the formation of macrosegregation shows differently in the two extreme cases of solidification structures (columnar or equiaxed).

Abstract: For the characterization of the equiaxed polycrystalline structure the Dirichlet tessellation is often used. The results of this space decomposition Voronoi polyhedrons are convex but not necessarily bounded. Size, volume and other characteristics of these bodies are the random variables. Parameters of the Averaged Voronoi Polyhedron are used in the presented paper for the modeling of the diffusion controlled peritectic transformation. Proposed model takes into account decreasing of the transformation interface surface in the remote regions of the diffusion field due to the probabilistic grains impingements. The results of the modeling are compared with the microstructure of the Pb-32 wt.% Bi alloy and thermal analysis results.

Abstract: The critical nucleus size—above which nuclei grow, below dissolve—during diffusion controlled nucleation in binary solid-solid phase transformation process is calculated using kinetic Monte Carlo (KMC). If atomic jumps are slower in an A-rich nucleus than in the embedding B-rich matrix, the nucleus traps the A atoms approaching its surface. It doesn’t have enough time to eject A atoms before new ones arrive, even if it would be favourable thermodynamically. In this case the critical nucleus size can be even by an order of magnitude smaller than expected from equilibrium thermodynamics or without trapping. These results were published in [Z. Erdélyi et al., Acta Mater. 58 (2010) 5639]. In a recent paper M. Leitner [M. Leitner, Acta Mater. 60 (2012) 6709] has questioned our results based on the arguments that his simulations led to different results, but he could not point out the reason for the difference. In this paper we summarize our original results and on the basis of recent KMC and kinetic mean field (KMF) simulations we show that Leitner’s conclusions are not valid and we confirm again our original results.

Abstract: This paper shows how to move from a specification of free energy for the solidification of a binary alloy to the dynamical equations using the elegance of a dissipative bracket analogous to the Poisson bracket of Hamiltonian mechanics. A key new result is the derivation of the temperature equation for single-phase thermal-solutal models, which contains generalisations and extra terms which challenge standard models. We also present, for the first time, the temperature equation for thermal multi-phase field models. There are two main ingredients: one, the specification of the free energy in terms of the time and space dependent field variables: $n$-phases $\phi_i$, a concentration variable $c$, and temperature $T$; two, the specification of the dissipative bracket in terms of these variables, their gradients and a set of diffusion parameters, which may themselves depend on the field variables. The paper explains the method within this context and demonstrates its thermodynamic admissibility.

Abstract: A model for simulating mushy zone resolidification in a temperature gradient is presented. For describing macroscopic mass transport in the liquid phase in the mushy zone, an extended diffusion equation is solved numerically using the Finite Difference Method. Temperature dependent local equilibria at each position in the mushy zone are calculated using the thermodynamic software package ChemApp. The resolidification model treats multicomponent alloying systems and accounts for multiphase equilibria. Simulation results for peritectic Cu-40wt%Al and eutectic Al-5wt%Si-1wt%Mg alloys are compared with microstructures from temperature gradient annealing experiments. It is shown that the model is well suited to predict mushy zone resolidification in multicomponent and multiphase alloys. The predicted evolution of the liquid fraction is qualitatively in full agreement with the observed microstructures, including local remelting at the peritectic temperature prior to resolidification, an effect that was first predicted by the model and confirmed by the experiments.

Abstract: A numerical model is developed to describe the dendritic growth of multicomponent aluminium alloys, based on a coupled deterministic continuum mechanics heat and species transfer model and a stochastic localized growth model that takes into account the undercooling temperature, curvature, kinetic, and thermodynamic anisotropy. The stochastic model receives temperature and concentration information from the deterministic model and the deterministic heat and species diffusion equations receive the solid fraction information from the stochastic model. The heat and species transfer models are solved on a regular grid by the standard explicit Finite Difference Method (FDM). The dendritic growth model of multicomponent alloy [1,2] is solved by a novel Point Automata (PA) approach [3,4] where the regular cells of the Cellular Automata (CA) method are replaced by the randomly distributed points and neighborhood configuration, similar as appears in meshless methods. The PA method was developed in order to circumvent the mesh anisotropy problem, associated with the classical CA method. The present paper extends our previous developments of Pa method to multicomponent alloys. A comparison of the results, obtained by the PA and CA method is shown for Al-5.3% Zn-2.35% Mg-1.35% Cu-0.5% alloy.

Abstract: The simulation of macrosegregation in a 2.45-ton steel ingot with the three-phase mixed columnar-equiaxed model was presented previously. The results showed an overestimation of the intensity of bottom negative segregation. The reason is due to the assumed globular morphology for the equiaxed crystal. Therefore, in this paper a simple approach is suggested to treat the dendritic morphology of equiaxed crystals. Three aspects are improved: the drag force between the moving equiaxed crystals and the surrounding melt, the mechanism of the columnar-to-equiaxed transition, the packing limit of the equiaxed crystals. The modified model is used to calculate the macrosegregation of the same ingot. It is found that the modified model predicts less severe negative segregation in the bottom equiaxed zone than the previous globular equiaxed model does, i.e. it agrees better to the experiment. The model considering simplified-dendritic morphology improves the calculation accuracy.