Local Solidification Research Articles

A diffusion boundary layer model of microsegregation

A microsegregation model, based on a boundary layer concept, is proposed for solidification of alloys. The model is derived by considering finite-rate solute diffusion both in the liquid and in the solid. A solutal Fourier number is used to characterize the extent of finite-rate solute diffusion in the liquid phase ahead of the moving solid/liquid interface. This new parameter is the liquid counterpart of the solutal Fourier number in the solid phase used before to characterize finite-rate back-diffusion in the solid. It can be obtained through the knowledge of either the local solidification time or the operating point of the cell/dendrite tip (among other parameters). The present microsegregation model covers the entire spectrum of solidification rates, up to the limit of a microsegregation free solid. The model predictions show good agreement with a previous rapid solidification experiment involving an Ag–Cu alloy. Also, a new relation is derived for the primary dendrite arm spacing.

The influence of cast structure on the austempering of ductile iron. Part 1: Modelling of the influence of nodule count on microsegregation

A numerical, non steady state microsegregation model is used to predict the extent of solute segregation in a ductile cast iron. The microsegregation of Mn and Mo to intercellular boundaries is shown to depend on the nodule count and the local solidification time. It is suggested that increased nodule count is the most effective way of reducing intercellular segregation in thicker components.

Morphological Transition of Rapidly Solidified Al-Cu Eutectic Ribbons with the Variation of Cooling Capacity of the Rotating Wheel.

The effects of the wheel surface condition were investigated on solidification behavior and microstructural evolution of Al-Cu eutectic ribbons. The local solidification velocity was controlled by the wheel surface condition which can be changed by either heating the wheel or coating the wheel surface with boron nitride. The origin of inhomogeneities in the Al-Cu eutectic ribbons both through the ribbon thickness and in the transverse plane was also studied. The average cooling rate of the ribbon during eutectic solidification was greatly changed by more than 1 order under the different wheel conditions. The change of the wheel surface condition brought a variety of changes in eutectic growth morphology. It is evident that the control of the wheel surface condition is significantly important in producing the ribbons with controlled microstructures which will guarantee the reliability of the ribbon materials in practical applications.

Cast structure and property variability in gamma titanium aluminides

Abstract Aspects of cast structure that influence mechanical property variability, and in particular tensile ductility, have been studied in a Ti-48Al-2Cr-2Nb titanium aluminide alloy. Macrostructure, porosity, microstructure and tensile properties have been characterized over a range of casting processing conditions. Local solidification times and subsequent solid-state cooling rates during casting have been characterized via local thermal measurements in combination with solidification modeling. Large variations in cooling rate during casting dramatically influence the initial cast structure as well as the distribution of defects such as porosity. Variations in as-cast structure persist through subsequent thermal and hot isostatic pressing cycles and contribute to the variability of tensile ductility. The current understanding of the relationship of tensile ductility to processing-induced changes in structure will be briefly discussed.

Eutectic reaction and nonconstant material parameters in micro-macrosegregation modeling

Recently, the authors presented a general framework for the calculation of the local solidification path in micro-macrosegregation computations (Reference 1). For a volume element whose overall solute content is not necessarily constant, the problems of solute diffusion in the primary solid phase and of remelting were addressed. In handling the eutectic reaction, the mass fraction and the solute profile in the primary phase at the beginning of the eutectic reaction were assumed to be “frozen.” In the present study, this restriction has been relaxed, as the solute diffusion in the primary phase occurring during the eutectic reaction is taken into account as well as that taking place for temperatures between the liquidus and the eutectic. It is shown that there is a potential for dissolving the secondary phase, which is controlled by diffusion in the primary phase. Other extensions of the former modeling concept made in the present study are to allow different densities of the liquid and solid phases, nonlinear phase diagram characteristics, and a temperature and/or solute concentration-dependent solute diffusivity in the primary phase. Assuming that the variations of enthalpy and of average solute concentration are known from the solution of the macroscopic continuity equations, modeling examples focusing on the extensions of the former model have been carried out.

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.

In-situ observation of cellular growth under rapid solidification conditions

Dynamic studies on the rapid solidification of binary CBr 4-C 2Cl 6 alloys at different hypoeutectic compositions were performed. The samples were solidified in fine glass tubes with a square cross-section by pulling the tube rapidly from a hot into a cold zone. Applying pulling velocities up to 30 mm s −1, local solidification velocities from 0.3 to 2 mm s −1 depending on the cooling temperature were achieved. Independent of concentration and solidification velocity, the observed interface morphologies revealed either a cylindrical or elongated cellular pattern, which are often separated by a boundary in pulling direction. The occurrence of these morphologies was found to change instantaneously. The spacings of the cylindrical and the elongated cells were measured as a function of concentration and solidification velocity. The results are discussed with respect to a recent theory for cellular growth.

Cellular simulation of the dendrite growth in Al-Si alloys

A cellular model for a computer simulation of dendrite growth in alloys is described. In this model temperature and concentration at the interphase boundary are not prescribed as boundary conditions but their evolution is calculated with the use of transport equations and a kinetic equation which relates the local solidification rate in each cell containing the interface with thermo-chemical conditions and an interface curvature averaged through the cell. The simulation was carried out for Al-Si alloys. The dependence of the growth velocity and tip radius on the supercooling are computed and compared with analytical model data.

The effect of solidification on the formation and growth of inclusions in low carbon steel welds

Weld metal transformations in low carbon steels are strongly dependent on the size and size distribution of non-metallic inclusions. Since inclusions are nucleants to proeutectoid phases, the presence of these second phase particles shift the continuous cooling transformation (CCT) curves to shorter times. Thus, the modelling of the formation and growth of inclusions is desirable to predict weld metal microstructure and properties. In this study, a new model is proposed considering solute redistribution during solidification. The model predicts the weld metal inclusion size distribution, considering diffusion-controlled deoxidation as the primary growth mechanism. An interesting feature of this model is that it predicts the change in the shape of the size distribution curve with the solute composition and the local solidification time.

Modeling of microsegregation in macrosegregation computations

A general framework for the calculation of micro-macrosegregation during solidification of metallic alloys is presented. In particular, the problems of back diffusion in the primary solid phase, of eutectic precipitation at the end of solidification, and of remelting are being addressed for an open system,i.e., for a small-volume element whose overall solute content is not necessarily constant. Assuming that the variations of enthalpy and of solute content are known from the solution of the macroscopic continuity equations, a model is derived which allows for the calculation of the local solidification path (i.e., cooling curve, volume fraction of solid, and concentrations in the liquid and solid phases). This general framework encompasses four microsegregation models for the diffusion in the solid phase: (1) an approximate solution based upon an internal variable approach; (2) a modification of this based upon a power-law approximation of the solute profile; (3) an approach which approximates the solute profile in the primary phase by a cubic function; and (4) a numerical solution of the diffusion equation based upon a coordinate transformation. These methods are described and compared for several situations, including solidification/remelting of a closed/open volume element whose enthalpy and solute content histories are known functions of time. It is shown that the solidification path calculated with method 2 is more accurate than using method 1, and that 2 is a very good approximation in macrosegregation calculations. Furthermore, it is shown that method 3 is almost identical to that obtained with a numerical solution of the diffusion equation (method 4). Although the presented results pertain to a simple binary alloy, the framework is general and can be extended to multicomponent systems.

Prediction of dendrite arm spacing for low alloy steel casting processes

Simple mathematical expressions to predict the primary dendrite arm spacing (PDAS) and secondary dendrite arm spacing (SDAS) suitable for steel casting processes are presented. The equations of the PDAS and SDAS were based on previously published experimental data for low alloy steels. Good agreement was obtained between previous measurements of dendrite arm spacing (DAS) and the model predications in the range of cooling rate occurring in steel casting processes. The results indicated that the cooling rate and carbon content basically govern the calculation of PDAS, especially for low carbon steel. However, the carbon content governs the selection of mathematical expression to predict SDAS for low alloy steels. Dendritic growth is the most common crystallization mechanism in industrial steels. Many empirical expressions have been employed to correlate the PDAS and SDAS with growth rate, temperature gradient, cooling rate, and local solidification time. However, the comparative advantages of the various expressions with respect to the accuracy with different types of steels remain unclear. Thus, the aim of the present study is to develop simple expressions to predict DAS as a function of carbon content and thermal conditions of low alloy steels.

Porosity formation in AI-9 Wt Pct Si-3 Wt Pct Cu alloy systems: Metallographic observations

The formation of porosity in Al-9 wt Pct Si-3 wt Pct Cu-X alloys was studied as a function of (1) the hydrogen content of the melt; (2) the melt treatment additives, namely, modifier (Sr), grain refiner (TiB2), and primary silicon refiner (P); (3) alloying elements for precipitation hardening such as Mg and Zn; (4) intermetallics (α-iron, β-iron, sludge, and Al2Cu); and (5) solidification conditions (so-lidification time and solidus velocity). The results were statistically analyzed, based on the quanti-tative image analysis data of the porosity observed in samples obtained from a set of 72 solidification experiments. Metallographic aspects of pore size and pore morphology related to the preceding parameters and the possible mechanisms of porosity formation are highlighted in this article. The results show that a melt hydrogen content of 0.1 mL/100 g Al has the same effect on percentage porosity as that obtained with an addition of 185 ppm strontium to the melt. Grain refiner particles, phosphorus, and magnesium reduce percentage porosity, although in different magnitudes. A Mg-Sr or Mg-GR combination further reduces the percentage porosity observed in the casting. Theβ needles of the Al5FeSi intermetallic phase are very active as pore nucleation sites. All intermetallics,viz. β needles, α-Chinese script phase, Al2Cu phase, and sludge restrict pore growth and expansion. In-creasing the local solidification time or the solidus velocity increases the pore parameters. Pore growth in the two cases is attributed, respectively, to a diffusion-controlled growth process and to the formation of hot spots.

NATURAL CONVECTION DURING MELTING AND SOLIDIFICATION OF PURE METALS IN A CAVITY

An enthalpy-porosity fixed-grid method has been applied to the melting and solidification of pure metals in a rectangular cavity. Flow structures and isotherms are compared with literature information based on multidomain analysis. During solidification, recirculation cells are observed to vanish with time, whereas the multidomain method predicted their enlargement. The cell near the interface significantly affects the local solidification rate at the cavity top. Results of the present study agree well with the experimental data in the literature. The effect of neglecting the viscous diffusion term for a phase change problem involving low Prandtl number liquid metals is also studied. The maximum value of the stream function is higher by 10% and the melt volume by 5%, in the absence of viscous effects.

Simplified method of porosity prediction in directionally solidified Al–4·5 wt-%Cualloy

AbstractAn experiment was carried out to verify a simplified theory of porosity formation during the unidirectional solidification of Al–4·5 wt-%Cu alloy in cylindrical moulds 1·5 and 2·4 cm in diameter. For specimens 1·5 cm in diameter, a higher thermal gradient G and a lower solidus velocity Vs at low drawing speeds are measured compared with the specimens 2·4 cm in diameter, while this difference tends to be reversed at high drawing speeds. The experimental results also conjirm the roles of interdendritic fluid flow and surface tension effects in the formation of porosity. The porosity content tends to increase with increasing local solidification time or a decrease in G0·4/Vs1·6when this parameter is less than about 1·0 K0·4min1·6cm−2.MST/3122

A metallographic study of porosity and fracture behavior in relation to the tensile properties in 319.2 end chill castings

A metallographic study of the porosity and fracture behavior in unidirectionally solidified end chill castings of 319.2 aluminum alloy (Al-6.2 pct Si-3.8 pct Cu-0.5 pct Fe-0.14 pct Mn-0.06 pct Mg-0.073 pct Ti) was carried out using optical microscopy and scanning electron microscopy (SEM) to determine their relationship with the tensile properties. The parameters varied in the production of these castings were the hydrogen (∼0.1 and ∼0.37 mL/100 g Al), modifier (0 and 300 ppm Sr), and grain refiner (0 and 0.02 wt pct Ti) concentrations, as well as the solidification time, which increased with increasing distance from the end chill bottom of the casting, giving dendrite arm spacings (DASs) ranging from ∼15 to ∼95 /im. Image analysis and energy dispersive X-ray (EDX) analysis were employed for quantification of porosity/microstructural constituents and fracture surface analysis (phase identification), respectively. The results showed that the local solidification time(viz. DAS) significantly influences the ductility at low hydrogen levels; at higher levels, however, hydro-gen has a more pronounced effect (porosity related) on the drop in ductility. Porosity is mainly observed in the form of elongated pores along the grain boundaries, with Sr increasing the porosity volume percent and grain refining increasing the probability for pore branching. The beneficial effect of Sr modification, however, improves the alloy ductility. Fracture of the Si, β-Al5FeSi, α- Al15(Fe,Mn)3Si2, and Al2Cu phases takes place within the phase particles rather than at the particle/Al matrix interface. Sensitivity of tensile properties to DAS allows for the use of the latter as an indicator of the expected properties of the alloy.

Heat transfer and microstructure during the early stages of metal solidification

Transient heat transfer in the early stages of solidification of an alloy on a water-cooled chill and the consequent evolution of microstructure, quantified in terms of secondary dendrite arm spacing (SDAS), have been studied. Based on dip tests of the chill, instrumented with thermocouples, into Al-Si alloys, the influence of process variables such as mold surface roughness, mold material, metal superheat, alloy composition, and lubricant on heat transfer and cast structure has been determined. The heat flux between the solidifying metal and substrate, computed from measurements of transient temperature in the chill by the inverse heat-transfer technique, ranged from low values of 0.3 to 0.4 MW/m2 to peak values of 0.95 to 2.0 MW/m2. A onedimensional, implicit, finite-difference model was applied to compute heat-transfer coefficients, which ranged from 0.45 to 4.0 kW/m2 °C, and local cooling rates of 10 °C/s to 100 °C/s near the chill surface, as well as growth of the solidifying shell. Near the chill surface, the SDAS varied from 12 to 22 (µm while at 20 mm from the chill, values of up to 80/smm were measured. Although the SDAS depended on the cooling rate and local solidification time, it was also found to be a direct function of the heat-transfer coefficient at distances very near to the casting/chill interface. A three-stage empirical heat-flux model based on the thermophysical properties of the mold and casting has been proposed for the simulation of the mold/casting boundary condition during solidification. The applicability of the various models proposed in the literature relating the SDAS to heat-transfer parameters has been evaluated and the extension of these models to continuous casting processes pursued.

Spray forming of Al/SiC metal matrix composites

SummaryThis paper describes the as‐sprayed microstructure of a model Al‐4wt%Cu/SiC particulate (Al4Cu/SiCp) metal matrix composite (MMC) manufactured by spray forming, and the relationship between microstructure and solidification conditions during manufacture.Injection of SiCp into the melt atomization region during the spray forming of Al4Cu results in significant SiCp incorporation into molten droplets during atomization, and relatively little incorporation during flight to the substrate and at deposition. SiCp clustering is evident in the Al4Cu droplets and results in clustering in the as‐sprayed MMC deposit.Matrix dislocation and precipitation microstructures are dependent upon local solidification conditions during spray forming. Increased dislocation density and increased quantity of fine‐scale θ′‐Al2Cu precipitation is found in the α‐Al(Cu) matrix where local deposit cooling rates are high, i.e. in the vicinity of the substrate/deposit interface and when increased spray distances are used in manufacture. Lower dislocation density and increased quantity of grain‐boundary θ‐Al2Cu is found where deposit cooling rates are relatively low, i.e. distant from the substrate/deposit interface and at decreased spray distances. In all cases, dislocation densities are higher in α‐Al(Cu)/SiCp interfacial regions than in the α‐Al(Cu) matrix.There is no evidence of α‐Al(Cu)/SiCp interfacial reaction in the as‐sprayed condition indicating that cooling rates during spray forming are sufficiently rapid to prevent reaction.

Dendrite arm spacing — Local solidification time relationship: An experimental model for a 70-30 brass and its comparison with some theoretical models

Dendrite arm spacing — Local solidification time relationship: An experimental model for a 70-30 brass and its comparison with some theoretical models

The role of the pressure index in porosity formation in A356 alloy castings

Porosity formation in A356 aluminium plate castings was studied experimentally and theoretically. Analysis of a model introduced in this paper led to the formulation of a pressure index, P*, which was expressed in terms of the thermal parameters G, Vs and tf (where G is the thermal gradient, Vs is the solidus velocity and tris the local solidification time), and the alloy's physical constants. The index, determined from the effects of local pressure drops based on Darcy's law and surface tension within the interdendritic liquid, was employed to estimate the formation of porosity in A356 alloy castings. The experimental and theoretical results indicated that porosity content is inversely proportional to P*, and that porosity content tends to decrease with increasing G0.38/V1.62 when this parameter is less than 0.05°C0.38 min1.62 cm−2. As the value of G0.38/V1.62 is increased over approximately 0.05 °C0.38 min1.62 cm−2, the porosity content was found to be independent of this parameter.

Further discussions on the solute redistribution during dendritic solidification of binary alloys

After a review over former works about the solute redistribution during dendritic solidification, a new“local solute redistribution equation ”is deduced based on Flemings's model, where lim-ited diffusion in solid during solidification is carefully treated. Because a form parameter is also included, the equation can be used for the solidification processes with different shapes of den-drites. By solving the equation at the condition of directional solidification, more completefs-C, functions for both needlelike and platelike dendritic solidifications with both linear and parabolic solidification rates are obtained. As examples, the volume fractions of nonequilibrium phase in Al-4.5 pct Cu alloy is evaluated with differentfs-Cl functions. On the thinking that the dendrites in actual solidification process is usually between needlelike and platelike ones, the volume fraction of the nonequilibrium phase is suggested to be in the region between the one calculated by the model for platelike dendrites and that for needlelike dendrites. The relationship between the region and local solidification time is also presented by figures, which are compared with the data of former researchers.