Papers by Author: Shaun McFadden

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: The main objective of the research project of the European Space Agency (ESA) - Microgravity Application Promotion (MAP) programme entitled Columnar-to-Equiaxed Transition in SOLidification Processing (CETSOL) is the investigation of the formation of the transition from columnar to equiaxed macrostructure that takes place in casting. Indeed, grain structures observed in most casting processes of metallic alloys are the result of a competition between the growth of several arrays of dendrites that develop under constrained and unconstrained conditions, leading to the CET. A dramatic effect of buoyancy-driven flow on the transport of equiaxed crystals on earth is acknowledged. This leads to difficulties in conducting precise investigations of the origin of the formation of the equiaxed crystals and their interaction with the development of the columnar grain structure. Consequently, critical benchmark data to test fundamental theories of grain structure formation are required, that would benefit from microgravity investigations. Accordingly, the ESA-MAP CETSOL project has gathered together European groups with complementary skills to carry out experiments and to model the processes, in particular with a view to utilization of the reduced-gravity environment that will be afforded by the International Space Station (ISS) to get benchmark data. The ultimate objective of the research program is to significantly contribute to the improvement of integrated modelling of grain structure in industrially important castings. To reach this goal, the approach is devised to deepen the quantitative understanding of the basic physical principles that, from the microscopic to the macroscopic scales, govern microstructure formation in solidification processing under diffusive conditions and with fluid flow in the melt. Pertinent questions are attacked by well-defined model experiments on technical alloys and/or on model transparent systems, physical modelling at microstructure and mesoscopic scales (e.g. large columnar front or equiaxed crystals) and numerical simulation at all scales, up to the macroscopic scales of casting with integrated numerical models.

Abstract: 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.