Shaun McFadden

Analysis of an Equiaxed Dendrite Growth Model with Comparisons to In-Situ Results of Equiaxed Dendritic Growth in an Al-Ge Alloy

The Lipton Glicksman Kurz (LGK) growth model is commonly used to predict growth rates for equiaxed dendrites in solidifying mushy zones. However, the original LGK method treats an isolated dendrite growing in an infinite volume of liquid. In an equiaxed mushy zone, with multiple nucleation events, thermal and solutal interactions take place between the equiaxed dendrites. A modified version of the LGK model was developed that allows for measurement of the solute build-up ahead of the dendrites. To investigate the validity of the model, comparisons are made with results obtained from in-situ synchrotron X-ray videomicroscopy of solidification in a Bridgman furnace of an Al-12wt.%Ge alloy inoculated with Al-Ti-B grain refiner. Comparisons between the original LGK and modified LGK models are presented for discussion. The modified LGK model shows realistic tip temperature trends.

Modeling of heat and solute interactions upon grain structure solidification

Simulations of several laboratory experiments developed for the study of structure and segregation in casting are presented. Interaction between the development of dendritic grain structure and segregation due to the transport of heat and mass by diffusion and convection is modeled using a Cellular Automaton - Finite Element model. The model includes a detailed treatment of diffusion of species in both the solid and liquid phases as presented elsewhere in this volume [1]. Applications deal with prediction of columnar and equiaxed grain structures, as well as inter-dendritic and inter-granular segregations induced by diffusion and macrosegregation induced by thermosolutal buoyancy forces.

Macroscopic model for predicting columnar to equiaxed transitions using columnar front tracking and average equiaxed growth

A macroscopic model of Columnar-to-Equiaxed Transition (CET) formation is presented. The growth of a columnar zone and an equiaxed zone are treated separately and modeled on a fixed grid. The model uses a columnar Front Tracking (FT) formulation to compute the motion of the columnar front and the solidification of the dendritic columnar mushy zone. The model for the equiaxed zone calculates the average growth of equiaxed grains within the control volumes of undercooled liquid. The proposed model, which calculates the average equiaxed growth, is different from previous FT models which consider each equiaxed grain envelope separately. A lognormal size distribution model of seed particles is used for the equiaxed nucleation in the undercooled liquid zone. After nucleation, average equiaxed growth is computed by considering the equiaxed envelopes as spherical. The extended volume concept is used to deal with grain impingement. The Scheil equation is used to calculate the solid fraction and latent heat release. When the equiaxed fraction is great enough, advancement of the columnar front is halted and the CET position is determined. CET formation was simulated for directional solidification of an aluminium-silicon alloy. The results were compared with a previous FT-CET prediction model as well as with experimental data. Agreement was found in both cases.

Analysis of a Microgravity Solidification Experiment for Columnar to Equiaxed Transitions with Modeling Results

This paper studies the Columnar to Equiaxed Transition (CET) in an Al-7wt%Si binary alloy with and without Al-Ti-B grain refiner. A microgravity experiment was designed to produce a CET in this alloy system. The experiment was flown onboard the MAXUS-7 sounding rocket platform, which achieved twelve minutes of microgravity. Examples of CET were successfully produced during the unmanned flight. Temperature data were recorded from thermocouples in the crucible walls of the furnace. Post-mortem material characterization of the grain structure was also performed. Subsequently a model of the furnace, which used a front-tracking model of solidification and an inverse heat calculation method, was developed. In this paper, results from the model are compared to the experimental findings; agreement is found with the CET predictions. The results from the model are then used to compare findings with the CET criterion of Hunt from the literature. Agreement is found between the model predictions and the Hunt criterion.

Prediction of the Formation of an Equiaxed Zone Ahead of a Columnar Front in Binary Alloy Castings: Indirect and Direct Methods

The as-cast properties of components with a columnar grain structure are very different from those with an equiaxed one. Under certain solidification conditions, zones of both structures can occur in an alloy casting; the boundary between the zones is the columnar-to-equiaxed transition (CET). A front-tracking model of dendritic solidification has been developed, which can predict the nucleation and growth of solid in undercooled liquid during a casting process. The growth process is described by dendrite tip kinetics, and is fully coupled to a fixed-grid control volume model of heat transfer during solidification. Using the front-tracking model, two methods for predicting the likelihood of an equiaxed zone forming ahead of a columnar front have been formulated, namely, an indirect method and a direct method. The indirect method is based on modelling the growth of the columnar front in the absence of equiaxed nucleation. The bulk liquid undercooling is monitored and an equiaxed indicator is calculated at each time step based on the extent of such undercooling at that time. The equiaxed indicator is a measure of the relative likelihood of an equiaxed zone forming. In the direct method nucleation and growth of individual equiaxed grains is treated ahead of the advancing columnar front. In this case, if impingement of neighbouring fronts is treated, the simulation to complete solidification will yield the macrostructure and the CET. In this paper, details of both methods of equiaxed prediction are presented. Results from the indirect method are compared to experimental results found in literature and agreement is found.

Code-to-code verification of an axisymmetric model of the Bridgman solidification process for alloys

Purpose Numerical models of manufacturing processes are useful and provide insight for the practitioner; however, model verification and validation are a prerequisite for expedient application. This paper aims to detail the code-to-code verification of a thermal numerical model for the Bridgman solidification process of alloys in a two-dimensional axisymmetric domain, against an established commercial code (ANSYS Fluent); the work is considered a confidence building step in model development. Design/methodology/approach A grid sensitivity analysis is carried out to establish grid independence, and this is followed by simulations of two transient solidification scenarios: pulling rate step change and ramp input; the results of which are compared and discussed. Findings Good conformity of results is achieved; hence, the non-commercial model is code-to-code verified; in addition, the ability of the non-commercial model to deal with radial heat flow is demonstrated. Originality/value The ability of the home made model for Bridgman furnace solidification to deal with cases where significant radial heat transfer occurs in the sample was demonstrated. The introduction of front tracking to model the macroscopic growth of dendritic mush and the region of undercooled liquid is identified as the next step in model development.

REVIEW OF THE MAXUS 8 SOUNDING ROCKET EXPERIMENT TO INVESTIGATE SOLIDIFICATION IN A TI-AL-NB ALLOY

Proceedings of the 20th European Space Agency Symposium on European Rocket and Balloon Programmes and Related Research (Hyeres, Provence, France, 22-26 May 2011)

Tensile Superplasticity in Nanomaterials - Some Observations and Reflections

The synthesis of nanocrystalline materials has provided new opportunities to explore grain size dependent phenomenon to a much finer scale. Superplasticity is a well-established grain size dependent phenomenon. In this paper, we analyze some of the tensile superplasticity data obtained in the last few years on Ti-6Al-4V, Ni 3 Al, and 1420-Al alloy processed by severe plastic deformation (SePD). The experimental results show higher flow stresses for superplasticity in nanocrystalline materials than in microcrystalline materials. It is suggested that the conventional slip accommodated grain boundary sliding is likely to be difficult in nanomaterials.

A front tracking model of the MAXUS-8 microgravity solidification experiment on a Ti-45.5at.% Al-8at.%Nb alloy

On 26th March 2010 the MAXUS-8 sounding rocket was launched from the Esrange Space Center in Sweden. As part of the Intermetallic Materials Processing in Relation to Earth and Space Solidification (IMPRESS) project, a solidification experiment was conducted on a Ti-45.5at.%Al-8at.%Nb intermetallic alloy in a module on this rocket. The experiment was designed to investigate columnar and equiaxed microstructures in the alloy. A furnace model of the MAXUS 8 experiment with a Front Tracking Model of solidification has been developed to determine the macrostructure and thermal history of the samples in the experiment. This paper gives details of results of the front tracking model applied to the MAXUS 8 microgravity experiment. A model for columnar growth is presented and compared to experimental results for furnace A of the experiment module.

Sensitivity analysis of dendritic growth kinetics in a Bridgman furnace front tracking model

A directional solidification experiment of a Ti-Al-Nb-B-C alloy by power down method is simulated using a Bridgman furnace front tracking model. The effect of varying the dendritic growth parameters; C, the columnar dendrite growth coefficient, and n, the undercooling exponent, is investigated. A matrix of growth coefficients and undercooling exponents - at three levels each, based around a growth law for Ti-46wt.%Al - is applied in simulations, and the effect on columnar dendrite tip temperature, tip velocity, and tip temperature gradient is observed. The simulation results show that the dendrite tip velocity and temperature gradient at the tip are practically unaffected by the use of different growth parameters. However, the predicted columnar dendrite tip undercooling did vary to give the required dendrite tip velocity. This finding has implications for the analysis of microstructural transitions, such as the Columnar to Equiaxed Transition (CET). In conclusion, it is suggested that, for transient solidification conditions, a CET prediction criterion based on tip undercooling is preferable to one that uses growth velocity.