Microsegregation In Multicomponent Alloys Research Articles

Correction: Simulation of Microsegregation in Multicomponent Alloys During Solidifi cation

Correction: Simulation of Microsegregation in Multicomponent Alloys During Solidifi cation

A modified cellular automaton method for polydimensional modelling of dendritic growth and microsegregation in multicomponent alloys

Numerous numerical models for simulating solidification of metals on a microscopic scale have been proposed in the past, among them are most importantly the phase-field method and models based on cellular automata. Especially the models based on cellular automata (adopting the virtual front tracking (VFT) concept) published so far are often only suitable for the consideration of one alloying element. Since industrial alloys are usually constituted of multicomponent alloys, the possibility of applying cellular automata is rather limited. With the aim of enhancing this modelling technique, a new, modified VFT model, which allows for the treatment of several alloying elements, in the low Péclet number regime is presented. The model uses the physical fundamentals of solute and heat diffusion in two dimensions as a basis for determining the solidification progress. By a new and effective approach, based on a functional extrapolation of the concentration gradient, dendritic growth in multicomponent Fe-C-Si-Mn-P-S alloys could be studied. The model shows the typical behaviour of dendritic solidification, such as parabolic tip and secondary dendrite arm formation as well as selection of preferably aligned columnar dendrites. A validation of the model is performed by the evaluation of morphological parameters and comparing them to experimentally determined values. The results for free and constrained dendritic growth effectively demonstrate the capabilities of this new model. The model is especially attractive for bridging the gap between one-dimensional microsegregation models and multidimensional morphology models with regard to modelling the complex interrelations between segregation on a multidimensional level and morphology formation.

Simulation of Microsegregation in Multicomponent Alloys During Solidification

AbstractA phase‐field model is applied to the simulation of microsegregation and microstructure formation during the solidification of multicomponent alloys. The results of the one‐dimensional numerical simulations show good agreement with those from the Clyne–Kurz equation. Phase‐field simulations of non‐isothermal dendrite growth are examined. Two‐dimensional computation results exhibit different dendrites in multicomponent alloys for different solute concentrations. Changes in carbon concentration appear to affect dendrite morphology. This is due to a larger concentration and a lower equilibrium partition coefficient for carbon. On the other hand, changes in phosphorus concentration affect the dendrites and interface velocity in multicomponent alloys during solidification when phosphorus content is increased from 10−3 mol% P. With additional manganese, the solidification kinetics slow down; dendrite morphology, however, is not affected. The potential of the phase‐field model for applications pertaining to solidification has been demonstrated through the simulations herein.

Polydimensional modelling of dendritic growth and microsegregation in multicomponent alloys

Various models for simulating dendritic solidification have been proposed in the past. However, those models based on cellular automata (adopting the virtual front-tracking (VFT) concept) are often only suitable for the consideration of one alloying element. As typical industrial alloys are constituted of numerous alloying elements, the application of these models to practical alloys is therefore rather limited. In order to overcome this drawback, a new, modified VFT model, which allows for the treatment of several alloying elements in the low Péclet number regime, is presented. By a new and effective approach, based on a functional extrapolation of the concentration gradient, we are able to study dendritic growth in multicomponent Fe–C–Si–Mn–P–S alloys. Comparisons with well-established analytical models confirm the correctness of the model; results for free and constrained dendritic growth effectively demonstrate the capabilities of this new model.

Phase field modeling for dendritic morphology transition and micro-segregation in multi-component alloys

By using the phase field model for the solidification of multi-component alloys and coupling with real thermodynamic data, the dendritic morphology transition and the dendritic micro-segregation of Ni-Al-Nb ternary alloys are simulated in two cases, i.e., varying the alloy composition at a fixed under-cooling and varying the undercooling at a fixed alloy composition. The simulated results indicate that with the increase of the dimensionless undercooling U ( U =? T /? T 0, where ? T is the undercooling and ? T 0 the temperature interval between the solidus and liquidus), the dendritic morphology transfers from dendritic to globular growth in both cases. As to the dendritic micro-segregation, both cases present a regularity of increasing at first and then decreasing.

Computation of solidification paths in multiphase alloys with back-diffusion

Mathematical modeling of microsegregation in multicomponent alloys is a considerable challenge since solidification implies generally the formation of many different solid phases, each one changing the dynamics of phase transformation as the morphology becomes very complex and the kinetics phenomena more diverse. Before sophisticated models based on the resolution of partial differential mass conservation equations can give reliable predictions in multiphase alloys, there is a need to calculate solidification paths based on the incremental mass conservation equation and the back-diffusion parameters. The incremental mass balance proposed in this contribution was written without considering a specific migration mechanism. This decoupling allowed an easy integration of a microsegregation model enabling the evaluation of back-diffusion parameters. In this paper, Ohnaka’s microsegregation model was chosen because it allows a simple and elegant inclusion of the cross interdiffusion coefficients in the calculation of back-diffusion parameters. The model assumes that complete mixing prevails in the liquid phase and that equilibrium conditions can be applied for a sub-system having a composition defined according to the mobility of species and a set of empirical parameters. A large range of solidification paths lying between Scheil and global equilibrium conditions can be calculated and used to explain experimental observations. The model was applied on a ternary Al–Mg–Mn alloy for comparison purposes, with the software DICTRA. An excellent agreement between the two models was obtained using similar assumptions. The scheme was also applied on AA6111 and allowed us to understand large deviations observed between the amounts of secondary phases obtained with DSC experiments and those predicted by Scheil or equilibrium conditions.

A technique for characterizing microsegregation in multicomponent alloys and its application to single-crystal superalloy castings

Instrumental errors in microsegregation measurements in multicomponent alloys complicate the treatment of randomly sampled data. In this article, two new alloy-independent data treatment algorithms are presented that are capable of separating the effects of scatter in the data from the underlying segregation trends, assigning each measurement location a unique fraction solid. These new methods are physically reasonable and result in improved estimates of segregation parameters, particularly the solute partitioning at the dendrite tip. This is demonstrated by determining the microsegregation in four successive generations of single-crystal (SX) nickel-based superalloys. Artificial, noise-induced, tails commonly seen in the microsegregation profiles are also minimized. A methodology for evaluating sorting schemes is introduced that does not depend upon a priori knowledge of the partitioning direction. Comparison is made to both other sorting methods and CALPHAD predicted partition coefficients. Implications for alloy design are reported, illustrating the interaction between solute species such as Ru, Re, Co, and W.

Computational and experimental investigation of microsegregation in an Al-rich Al–Cu–Mg–Si quaternary alloy

A new micromodel was developed to predict the microstructure and microsegregation in multicomponent alloys during dendritic solidification. The micromodel was directly coupled with multicomponent phase diagram calculations using a user friendly and robust phase diagram calculation engine—PanEngine. Solid back diffusion, undercooling and coarsening effects were included in this model, and the experimentally measured cooling curves were used as the inputs to carry out the microsegregation calculations. Microsegregation in Al–4.5 wt%Cu–1 wt%Si–0.5 wt%Mg alloy was experimentally investigated from directional solidification and electron probe microanalysis. Calculated results using this model are in accord with the experimental data, while results from the Scheil model deviate significantly from the experimental data.

Predicting microstructure and microsegregation in multicomponent alloys

Accurate predictions of microstructure and microsegregation in metallic alloys are highly important for applications such as process optimization and alloy development. This article gives an overview of the methods developed during the past 30 years for solidification simulation on a microscopic scale, with a special emphasis on multicomponent alloys. Analytical approaches as well as advanced numerical models coupled with greatly simplified phase diagrams and thermodynamically calculated phase diagrams have been critically reviewed. Factors that influence the predictions, such as solid-state diffusion, coarsening of dendrite arms, undercooling effects, and, most importantly, the accuracy of the phase diagram are discussed, and suggestions for further research are given.

An extended numerical procedure for predicting microstructure and microsegregation of multicomponent alloys

A numerical model for the prediction of microstructure and microsegregation in multicomponent alloys during dendritic solidification using a finite difference scheme is presented. The main kinetic and thermodynamic effects that can influence microsegregation (solid state back diffusion, secondary dendrite arm coarsening, primary tip and eutectic undercooling and the thermodynamic correction of the interface concentrations) are accounted for. The liquid/solid phase equilibria in the thermodynamically stable and metastable range are calculated with thermodynamically formulated phase diagrams. For the calculation at high cooling rates non-equilibrium phase diagrams for multi-component alloys are assessed. The consideration of undercooling effects extends the applicability of the model to very low and very high cooling rates. The model thus covers the whole range of cooling conditions where dendritic solidification occurs. As compared with other models in the literature, the number of adjustable parameters is reduced to a minimum.