Dendrite Arm Coarsening Research Articles

Microsegregation during Solidification of an Al-Cu Binary Alloy at Largely Different Cooling Rates (0.01 to 20,000 K/s): Modeling and Experimental Study

Microsegregation in the Al 4 wt pct Cu alloy was investigated experimentally in a large range of cooling rates from 0.01 to 20,000 K/s using different solidification techniques. The microstructure was modeled using two-dimensional (2-D) pseudo-front tracking (PFT) developed by Jacot and co-workers. The experimentally determined amount of nonequilibrium eutectics increases with the cooling rate in the range 0.01 to 3 K/s and then decreases in the range 20 to 20,000 K/s. The fraction of eutectic calculated from the 2-D PFT model shows not only the same tendency, but also agrees quantitatively very well with the experiments over the range of cooling rates. It can also be explained qualitatively how the observed in terms of coarsening of the secondary dendrite arms and the back diffusion in the way both depend on the local solidification time.

Instability of primary dendrite arms in columnar Chernov crystals

Some features of dendrite coarsening are studied on individual columnar dendrites in a large steel ingot. The coarsening of dendrite arms in Chernov columnar crystals is observed only in the zone of conventional solidification. In the tips of crystals that penetrate into the shrinkage cavity of the ingot, the initial sizes of the dendrite arms do not change. The coarsening of the primary arms is shown to cause crystal fragmentation into individual dendrites.

Dendrite growth modelling of cast magnesium alloy

Cast magnesium alloy are commonly used in 3C electronic and auto industry. Therefore, microstructure simulation of Mg alloy during solidification process not only has important academic values, but also has strong background in industrial application. Based on the crystallographic feature of magnesium alloy with hexagonal close packed structure, two-dimensional growth model of dendrite was established, which employed dendrite shape functions to describe the growing contours of dendrite arms and considered the kinetics of dendrite growth and the coarsening of the secondary dendrite arms. Then a new stochastic simulation method named virtual growth centre calculation model was proposed. Finally, a step shaped sample casting of magnesium alloy was cast to validate the proposed models.

Approximate Analytical Models for Microsegregation Considering the Effect of Dendrite Arm Coarsening

In this study, simple analytical microsegregation models for constant cooling and parabolic growth are proposed considering dendrite arm coarsening effect with and without back diffusion. These simple models are compared with the Mortensen exact model and Voller’s models. It is shown that these analytical models can be used to predict approximately microsegregation in a binary alloy.

Simple Analytical Models for Dendrite Arm Coarsening under High and Medium Temperature Gradients

The coarsening of secondary dendrite arms is discussed in terms of two different driving forces, which are the curvature effect and the temperature gradient zone melting (TGZM) effect. It is shown that the driving force due the TGZM effect can be higher than that due to the curvature effect at high temperature gradients and equal to each other at medium temperature gradients. For such high and medium temperature gradients, simple analytical models are proposed to predict the coarsening kinetics of secondary arms during solidification in a binary alloy. The prediction of the present analytical model agrees with experimental data obtained from the solidification of Fe – 1.6 wt. % Mn – 0.75 wt. % C steel.

Back Diffusion of Manganese during Solidification of Carbon Steels

In this study, back diffusion of manganese in solid between secondary arms in the ternary Fe – 1.6 wt % Mn – 0.1, 0.21, 0.4 and 0.75 wt % C alloys was investigated in unidirectionally solidified quenched specimens which solidified in the range of 0.25 K/s to 4.15 K/s cooling rates. Manganese back diffusion in the solid phase during the growth has a large influence on microsegregation when the first solid formed is delta-ferrite. A decrease in Cmin after 0.1 wt % C has been observed because the fraction of delta phase decreases with increasing carbon content. Only a small rise during the growth was found in both 0.4 and 0.8 wt % C steels but there was no difference between them indicating that both solidify as austenite. Secondary dendrite arms grown at the lowest cooling rate (around 0.3 K/s) always disappeared at the end of solidification for all steels. These high increases in Cmin were attributed to the high coarsening, back diffusion and TGZM processes. The Cmin calculations obtained from the secondary dendrite arm coarsening model are in a good agreement with the experimental measurements.

Numerical Approaches for microscopic modelling of solute redistribution during solidification of binary alloys

In the present study, two numerical approaches for single-domain modelling of microsegregation during solidification of binary alloys are presented. In the first approach, the concentration jump at the moving solid/liquid interface is formulated using a volumetric term and a Boolean function. The governing solute redistribution equation, valid for the whole domain comprising the solid and liquid regions, is derived in terms of the liquid phase composition. The effects of microstructure coarsening on microsegregation has been described and included in the model. In the second approach, the continuum mixture theory is utilized to derive a single domain solute redistribution equation in terms of the mixture composition. The solidification front motion and dendrite arm coarsening effects are accommodated by considering the representative elementary volume to consist of solid, interdendritic, and extradendritic liquid phases. Numerical solutions have been obtained using a control-volume based finite-difference method with a fixed grid. Good agreement has been observed between the predictions of the present fixed-domain models and the exact analytical and experimental results.

Experimental study of structure formation in binary Al–Cu alloys at different cooling rates

A series of casting experiments was performed with binary Al–Cu alloys with varying cooling rates, cooling conditions and copper concentration. The quantitative relationships between the cooling rate ( V c) and composition, on one hand and the dendrite arm spacing (DAS) and grain size ( D gr) on the other hand, are clarified in the form of coefficients in equation DAS ( D gr ) = A V c − n , where coefficient A is shown to strongly depend on the copper concentration. Increasing the amount of copper in the alloy causes refinement of both dendrite arm spacing and grain size. The amount of non-equilibrium eutectic depends on the cooling rate in a more complex manner with initial increase in the range of slow cooling (<1 K/s) and then gradual decrease in the range of 1–10 K/s. Some models of microsegregation are tested but fail to reproduce the experimentally observed dependences. The reasons for such a behaviour are discussed in terms of dendrite arm coarsening, eutectic reaction undercooling, structure refinement and homogenization upon cooling in the solid state.

On secondary dendrite arm coarsening in peritectic solidification

Abstract A model for isothermal coarsening of secondary dendrite arms in peritectic reaction and transformation (liquid + primary-phase → peritectic-phase) is proposed to evaluate the secondary dendrite arm spacing ( λ 2 ) of the primary phase in directional solidification of peritectic alloys. The model defines three stages for thin-arm dissolution (or thick-arm coarsening), i.e. the initial, intermediate and final stages: the initial thin-arm dissolution through the primary phase is sustained solely by the Gibbs–Thomson effect; the intermediate thin-arm dissolution through the peritectic phase is driven by Gibbs–Thomson effect but retarded by the peritectic reaction and transformation; the final dissolution through the primary and peritectic phases is enhanced by the Gibbs–Thomson effect and the phase transformation. The kinetics of peritectic reaction and transformation were found to be crucial to determine the thin-arm dissolution, which were characterized by the reaction constant ( f ) and the diffusion coefficient of solute in solid peritectic-phase ( D S ), respectively. The present model shows that λ 2 V m is constant for a given Pb–Bi peritectic alloy, where V is growth velocity, and the factor, m , ranges from 1/3 to 1/2, rather than that normally observed (e.g. 1/3) for single-phase solidification. It is also notable that the calculated λ 2 for a Zn–7.37 wt.% Cu peritectic alloy was reasonably consistent with our earlier experiments for various growth velocities.

A simple model for dendrite arm coarsening during solidification in multicomponent alloys

A simple model for dendrite arm coarsening during solidification in multicomponent alloys

Numerical Simulation of Dendrite Arm Coarsening in the Case of Ternary Al Alloys

Numerical Simulation of Dendrite Arm Coarsening in the Case of Ternary Al Alloys

Microsegregation and dendrite arm coarsening in tin bronze

Specimens of the peritectic alloy Cu–10 wt-%Sn were subjected to various cooling rates typically observed in industrial casting processes. Some of the specimens were quenched immediately after the end of solidification to avoid further solute homogenisation of the dendrite structure during cooling to room temperature. Characterisation of specimens was carried out by measuring the distribution of secondary arm spacings and two microsegregation indices, namely the volume fraction of non-equilibrium phase and the segregation deviation parameter, calculated from a large number of microanalyses at random points. A tendency of increasing microsegregation with an increase in cooling rate was observed. The microsegregation results were compared with those of a comprehensive microsegregation model using different equations for coarsening of secondary dendrite arms. The comparison indicated that predictions are more accurate when an empirical equation for coarsening, based on the relationship between secondary arm spacing and cooling rate, is used.

Characteristics of TiC dendrites in as solidified Ti–Al–C alloys

Results are reported on the dendrite secondary arm spacing of a series of as cast Ti–C and Ti–Al–C alloys in the composition range up to 10 at.-%C and 15 at.-%Al. The presence of Al leads to a significant decrease in the dendrite spacing, an effect of potential interest for improving mechanical properties. The structural refinement is attributed mainly to the slower diffusion of Al as compared with carbon, in the solute partitioning required for coarsening of dendrite arms.

Microsegregation in Al–4.5Cu wt.% alloy: experimental investigation and numerical modeling

Microsegregation in Al–4.5 wt.%Cu alloy was investigated experimentally using directional solidification and electron probe microanalysis (EPMA). The degrees of dendrite tip undercooling were measured for growth rates from 0.0038 to 0.2 mm s −1 with a temperature gradient of 50°C cm −1 at the liquid–solid interfaces. A modified Scheil model incorporating back diffusion, undercooling and dendrite arm coarsening was used to calculate the degrees of microsegregation. The partition coefficients obtained from the thermodynamic models of the solid and liquid phases and the measured cooling curves were used as the inputs to carry out the microsegregation calculation. While the calculated results using the Scheil model deviate significantly from the experimental data, those from the modified Scheil model are much better. Out of the three geometrical models, i.e. plate, sphere and cylinder, to approximate the shapes of the dendrites, the sphere is the best. However, the calculated results using the spherical model is near accord with the data for small fractions of solids and those using the cylinder is better at large fractions of solids. Two different thermodynamic descriptions of the Al–Cu system were used to demonstrate the importance of reliable phase diagram data in studying the degree of microsegregation.

Investigation of Secondary Dendrite Arm Coarsening of Al-Cu-Si Alloy

Changing of dendritic structure was investigated during isothermal coarsening. A simple equation λ m 2 - λ m 2.0 = K.(t-t 0 ), describes the isothermal coarsening. In this equation λ 2.0 was determined by interrupted solidification than m and K were calculated by Csebisev approximation method The average coarsening parameter was calculated by the method of Tensi and Fuchs and was compared with our results.

Microstructure and microsegregation in Al-rich Al–Cu–Mg alloys

Microstructure and microsegregation in two directionally solidified Al alloys, Al–3.9Cu–0.9Mg and Al–15Cu–1Mg (in wt%), were investigated for cooling rates between 0.78 and 0.039 K/s. Transverse and longitudinal sections were examined to exhibit dendritic microstructures. Fractions of solids formed were determined using quantitative image analysis and solute redistribution in the primary phase was determined using area scans. The model employed to calculate microsegregation is based on the Scheil model but including solid-state diffusion, dendrite arm coarsening and undercooling of the dendrite tip and the formation of eutectic. The model-calculated results were found to be in good agreement with the experimentally determined concentration distributions in the primary α phase and the amounts of phases formed. It was found that the dendrite morphology was best described by a cylindrical arm geometry and that the accuracy of the phase diagram could have a significant influence on the microsegregation predictions. For the alloy with low copper content, two types of embedded droplets were observed.

Discussion of “Effect of dendrite arm coarsening on microsegregation”

Discussion of “Effect of dendrite arm coarsening on microsegregation”

A model for columnar-dendritic solidification of binary alloys accounting for dendrite tip undercooling

A simplified model for predicting microsegregation during columnar-dendritic solidification of binary alloys is developed, in which back diffusion, dendrite arm coarsening and dendrite tip undercooling are simultaneously incorporated. The inclusion of tip undercooling is accomplished by modifying the initial conditions of the existing solute diffusion model, in such forms that tip undercooling depresses the beginning of solidification below the liquidus temperature, and that the secondary arm spacing evolves in accordance with the minimum undercooling theory. Sample calculations for the well-known benchmark system show that the present predictions not only consist with the extablished limiting cases, but also agree favorably with the available experimental data within a reasonable tolerance. In particular, a typical decreasing trend in the eutectic fraction at high cooling rates is successfully resolved. Comparison of the individual and combined effects of characteristic parameters in reference with the limiting cases reveals the interactions among parameters. Every parameter plays the role of reducing the eutectic fraction, and the degree of influence depends primarily on the cooling rate. Coarsening enhances the effect of tip undercooling, while suppressing that of back diffusion. A vigorous back diffusion seems to restrain the apperance of the undercooling effect. Overall, each contribution of the three parameters to microsegregation is estimated to be of the same order, which suffices to justify the present study.

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.

Models for the isothermal coarsening of secondary dendrite arms in multicomponent alloys

Models for the isothermal coarsening of secondary dendrite arms for binary alloys are simply expanded to correlate the secondary dendrite arm spacing to local solidification time, melting temperature of the liquid, and the properties of the solute elements in multicomponent alloys. An equation is derived. Calculations using the equation show reasonable qualitative agreement with experiment.