Marcelo Aquino Martorano

Heat transfer coefficient at the metal-mould interface in the unidirectional solidification of Cu-8%Sn alloys

Abstract The heat transfer coefficient at the metal–mould interface of a unidirectional solidification system was calculated by an algorithm that uses the whole domain method for the inverse solution to the heat conduction differential equation with phase change. Experimental curves of temperature as a function of time, collected during solidification of Cu–8%Sn alloys subject to four different conditions, were used as input to the algorithm. Accordingly, the heat transfer coefficient at the metal–mould interface was obtained for those conditions. The estimated heat transfer coefficient values are in good agreement with the ones published in the literature.

Columnar front tracking algorithm for prediction of the columnar-to-equiaxed transition in two-dimensional solidification

A novel algorithm to track the columnar front in one- (1D) and two-dimensional (2D) solidification problems has been developed and coupled with the governing equations of a deterministic model to predict the columnar-to-equiaxed transition (CET). The new algorithm, inspired by the cellular automaton (CA) technique, requires a CA mesh as coarse as that for the numerical solution of the governing equations. Front positions predicted with the new algorithm during transient and steady-state growth under given 1D and 2D temperature fields matched the results from analytical solutions. The time evolution of the columnar front agreed well with the published results for the 1D and 2D solidification of an Al–3(wt%) Cu alloy. Some discrepancy observed in the CET position was attributed to the different implementation of the columnar front blocking criterion and to the nonisothermal character of the front line.

Dendrite structure control in directionally solidified bronze castings

Tin bronze (Cu-8%Sn) was cast into cylindrical samples using a unidirectional solidification device monitored by thermocouples. Four cylindrical samples were obtained under four different experimental conditions where pouring temperature, heat extraction and addition of inoculant changed. Thermocouple temperature curves did not show any strong effect of inoculant additions, though, at the beginning of solidification, recalescence seemed to decrease with an increase in inoculant efficiency. Macrostructures of samples were examined on longitudinal sections and an increase in the columnar zone length was observed when the pouring temperature and the heat extraction flux were raised simultaneously. Secondary and primary dendrite plates were seen to form from the coalescence of secondary dendrite arms. Dendrite arm spacing was measured and related to the local solidification time and to the cooling rate, showing some agreement with relationships published in the literature.

Microsegregation and dendrite arm coarsening in tin bronze

Abstract 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.

Micro-macroscopic coupling in the cellular automaton model of solidification

A cellular automaton (CA) model to predict the formation of grain macrostructure during solidification has been implemented and the coupling between the microscopic and the macroscopic submodels has been investigated. The microscopic submodel simulates the nucleation and growth of grains, whereas the macroscopic solves the heat conduction equation. The directional solidification of an Al-7 wt. (%) Si alloy was simulated, enabling the calculation of the temperature and solid fraction profiles. The calculated temperature was used to obtain the solid fraction profile by an application of Scheil equation. This solid fraction disagrees with that calculated in the micro-macro coupling of the model, although this coupling is completely based on Scheil equation. Careful examination of the discrepancies shows that it is a result of the undercoolings for nucleation and growth of grains and also of the interpolations of enthalpy change and temperature from the finite volume mesh to the CA cell mesh.

Modelling grain boundary migration during geometric dynamic recrystallization

High-angle grain boundary migration is predicted during geometric dynamic recrystallization (GDRX) by two types of mathematical models. Both models consider the driving pressure due to curvature and a sinusoidal driving pressure owing to subgrain walls connected to the grain boundary. One model is based on the finite difference solution of a kinetic equation, and the other, on a numerical technique in which the boundary is subdivided into linear segments. The models show that an initially flat boundary becomes serrated, with the peak and valley migrating into both adjacent grains, as observed during GDRX. When the sinusoidal driving pressure amplitude is smaller than 2π, the boundary stops migrating, reaching an equilibrium shape. Otherwise, when the amplitude is larger than 2π, equilibrium is never reached and the boundary migrates indefinitely, which would cause the protrusions of two serrated parallel boundaries to impinge on each other, creating smaller equiaxed grains.

Mathematical modelling of microsegregation in eutectic and peritectic binary alloys

Abstract A mathematical model of microsegregation for eutectic and peritectic binary alloys was implemented using a finite volume method to solve the differential equations for mass transport. In this model simple ideas are used to handle phase boundaries and coarsening without the need to employ node jumping schemes or any transformation of variables to fix the domain size. Some model results were compared with available analytical solutions, revealing excellent agreement, which proved the approach useful to solve dissolution and diffusion coupled problems as well as microsegregation ones. Furthermore, good agreement was observed between the model results and measurements of eutectic volume fractions published previously for an Al–Cu alloy. The model was also capable of showing some important features of a typical peritectic transformation. Some instability was observed during model calculations, but it was easily handled by a time step refining technique.

Silicon refining by a metallurgical processing route

Directional solidification experiments were carried out in a Bridgman furnace to remove carbon and metallic impurities from silicon. For carbon removal, solidification was achieved by extracting the mold from the hot into the cold zone of the furnace, while for the removal of metallic impurities, solidification occurred by cooling the furnace with a motionless mold. In the experiments of carbon removal, a mold extraction rate of 5 µm/s results in an ingot with columnar grain structure aligned in the ingot axial direction and a macrosegregation of carbon and SiC particles to the ingot top regions. However, at a mold extraction rate of 80 µm/s, the grain structure consisted of columnar grains aligned in the radial direction and SiC particles were observed throughout the ingot, showing lower macrosegregation with a carbon concentration still larger at the ingot top. In the metallic impurities removal experiment, an ingot with a columnar grain structure aligned in the ingot axial direction was obtained and the concentration profiles showed significant metallic impurities macrosegregation to the ingot top.

MEASUREMENT OF COOLING CURVES IN CENTRIFUGAL CASTING OF A FERROUS ALLOY

A sensor was developed to measure the cooling curves inside a ferrous alloy during its solidification as centrifugally cast tubes. The temperature evolution at some points within the alloy is necessary to evaluate the heat transfer through the outer surface of the tube during the centrifugal casting process. Serious difficulties exist in this type of measurement, because of the rotation of the mold and the relatively high temperature at which the ferrous alloy is poured. The sensor consists of sheathed thermocouples positioned by a convenient support internally to the rotating mold, within the metal layer. Although the sensor is subjected to thermal and mechanical stresses during the melt pouring and solidification, it must maintain its mechanical and thermal characteristics to temperatures of the order of the melting point of the ferrous alloy. Therefore, the thermocouple sheaths and support have been made of refractory metals, namely, tantalum and niobium, to resist the high temperature. Moreover, the sensor was designed to have low thermal inertia, allowing its temperature to increase above the liquidus temperature of the alloy before solidification of the surrounding liquid metal. Because the sensor is embedded in the solidified tube after solidification, a special design was necessary to allow stripping the tube out of the mold without disturbing the system.© 2008 ASME

Implementation and Validation of a Multiphase Multigrain Model of Equiaxed Solidification

A multiphase and multigrain mathematical model for the solidification of binary alloys is proposed, implemented, and validated. The model equations are derived using the volume averaging method and considering the conservation principles of mass, energy, and chemical species applied to a representative elementary volume. In the present model, grains that nucleate at different temperatures are grouped in different classes and are followed individually, enabling calculations of different growth velocities for globulitic and dendritic grains growing simultaneously. The proposed model is capable of predicting final average grain size, cooling curves during the complete primary and eutectic solidification, and the volume fraction of eutectic. These predictions are compared with experimental results for the solidification of cylindrical bars of Al-Si alloys with different Si concentrations and different amounts of inoculant additions, showing good agreement.