Analytical,numerical, and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys

The present work focuses on the influence of alloy solute content, melt superheat, and metal/mold heat transfer on inverse segregation during upward solidification of Al-Cu alloys. The experimental segregation profiles of Al 4.5 wt pct Cu, 6.2 wt pct Cu, and 8.1 wt pct Cu alloys are compared with theoretical predictions furnished by analytical and numerical models, with transient h _i profiles being determined in each experiment. The analytical model is based on an analytical heat-transfer model coupled with the classical local solute redistribution equation proposed by Flemings and Nereo. The numerical model is that proposed by Voller, with some changes introduced to take into account different thermophysical properties for the liquid and solid phases, time variable metal/mold interface heat-transfer coefficient, and a variable space grid to assure the accuracy of results without raising the number of nodes. It was observed that the numerical predictions generally conform with the experimental segregation measurements and that the predicted analytical segregation, despite its simplicity, also compares favorably with the experimental scatter except for high melt superheat.     

Mechanism for Formation of Surface Scale during Directional Solidification of Ni-Base Superalloys

Surface scale occurs on the external surface of directionally solidified, single-crystal turbine components. It is one of the most important casting defects because it affects the grain orientation assessment and causes incipient surface melting during heat treatment. The formation of surface scale comprises a three-stage process: (1) formation of a 0.5- to 1.5-μm Al₂O₃ layer around the external surface of liquid metal as a result of the mold/metal reaction between the liquid and the mold prime coat; (2) separation of the solidified metal from the mold wall during cooling, where the Al₂O₃ layer is stripped away from the metal surface but remains adhered to the mold; and (3) subsequent oxidation of the “bare” metal to form an oxide scale at the surface. The scale comprises a mixture of oxides. It is found that TiO₂, Cr₂O₃, and Al₂O₃ form on components cast using the 1st generation alloy, SRR99; however, in the case of castings using the 3rd-generation alloy, CMSX10N it is a predominately nickel-rich oxide (likely to be NiO). On the unscaled surface, the mold and metal are in intimate contact during casting, and subsequent cooling and the Al₂O₃ layer around the external surface prevents subsequent oxidation of the casting surface.     

Determination of the heat-transfer coefficient between the AK7ch (A356) alloy casting and no-bake mold

The heat-transfer coefficient h between a cylindrical cast made of AK7ch (A356) aluminum alloy and a no-bake mold based on a furan binder is determined via minimizing the error function, which reflects the difference between the experimental and calculated temperatures in the mold during pouring, solidification, and cooling. The heat-transfer coefficient is h _L = 900 W/(m² K) above the liquidus temperature (617°C) and h _S = 600 W/(m² K) below the alloy solidus temperature (556°C). The variation in the heat-transfer coefficient in ranges h _L = 900–1200 W/(m² K) (above the alloy liquidus temperature) and h _S = 500–900 W/(m² K) (below the solidus temperature) barely affects the error function, which remains at ~22°C. It is shown that it is admissible to use a simplified approach when constant h = 500 W/(m² K) is specified, which leads to an error of 23.8°C. By the example of cylindrical casting, it is experimentally confirmed that the heat-transfer coefficient varies over the casting height according to the difference in the metallostatic pressure, which affects the casting solid skin during its solidification; this leads to a closer contact of metal and mold at the casting bottom.     

Determination of the interfacial heat transfer coefficient in a metal-metal system solving the inverse heat conduction problem

Simulation of several industrial processes involving solidification of metals requires characterization of heat transfer coefficient at the solidifying metal/metal-substrate interface. In the present investigation an attempt has been made to estimate this heat transfer coefficient, h_c, using simulated experiments in which the heat transfer from a heated stainless steel block (simulating solidifying metal) to a water cooled copper block (simulating metal-substrate) is monitored by continuously recording temperatures at a few internal locations both within the metal block and the substrate block. The problem of determining the interfacial heat transfer coefficient is recognized to be an inverse heat conduction problem (IHCP). A numerical method is employed to solve IHCP and to determine the h_c from the transient history of temperatures at a few locations. The effect of the physical nature of the interface, as well as the cooling conditions prevailing at the outer surface of the substrate on h_c is examined and discussed. While the physical nature of the interface, i.e. roughness on the metal as well as the substrate surfaces, has a significant effect on h_c, the cooling conditions have only a marginal effect. The h_c in the present investigation remains more or less time invariant.     

X-ray-based measurement of composition during electron beam melting of AISI 316 stainless steel: Part I. Experimental setup and processing of spectra

An energy dispersive X-ray (EDX) detector mounted on a laboratory scale electron beam furnace (30 kW) was employed to assess the potential use of X-rays as a means of on-line liquid alloy composition monitoring during electron beam (EB) melting of alloys. The design and construction of the collimation and protection systems used for the EDX are described in Part I. X-ray spectra are obtained from a sample of AISI 316 stainless steel at both beam idle (in the absence of liquid metal) and high power (in the presence of liquid metal). Two different types of molds are employed: (1) a water-cooled copper mold and (2) a ceramic lined water-cooled copper mold. Various strategies for signal processing and filtration are presented and compared. Correction factors for beam voltage were developed and applied in order to develop correlations between the mole fraction and normalized X-ray intensity for Cr-K _α, and Fe-K _α based on an analysis of the vapor condensate. Correlations were also developed relating the change in the X-ray intensities to time for (a) Mo-L, (b) Cr-K _α, (c) Fe-K _α, and (d) Ni-K _α. The stability of the electron beam was found to be the principal source of error, and suggestions for further improvements are also discussed. The study confirms the feasibility of the method and is the first reported study of on-line analysis of a high-temperature liquid alloy. In Part II, the technique is applied to the study of the complex evaporation processes occurring during EB melting.     

Determination of interface heat transfer coefficient between aluminum casting and graphite mold

To produce castings of titanium, nickel, copper, aluminum, and zinc alloys, graphite molds can be used, which makes it possible to provide a high cooling rate. No die coating and lubricant are required in this case. Computer simulation of casting into graphite molds requires knowledge of the thermal properties of the poured alloy and graphite. In addition, in order to attain adequate simulation results, a series of boundary conditions such as heat transfer coefficients should be determined. The most important ones are the interface heat transfer coefficient between the casting and the mold, the heat transfer coefficient between the mold parts, and the interface heat transfer coefficient into the environment. In this study, the interface heat transfer coefficient h between the cylindrical aluminum (99.99%) casting and the mold made of block graphite of the GMZ (low ash graphite) grade was determined. The mold was produced by milling using a CNC milling machine. The interface heat transfer coefficient was found by minimizing the error function reflecting the difference between the experimental and simulated temperatures in a mold and in a casting during pouring, solidification, and cooling of the casting. The dependences of the interface heat transfer coefficient between aluminum and graphite on the casting surface temperature and time passed from the beginning of pouring are obtained. It is established that, at temperatures of the metal surface contacting with a mold of 1000, 660, 619, and 190°C, the h is 1100, 4700, 700, and 100 W/(m² K), respectively; i.e., when cooling the melt from 1000°C (pouring temperature) to 660°C (aluminum melting point), the h rises from 1100 to 4700 W/(m² K), and after forming the metal solid skin on the mold surface and decreasing its temperature, the h decreases. In our opinion, a decrease in the interface heat transfer coefficient at casting surface temperatures lower than 660°C is associated with the air gap formation between the surfaces of the mold and the casting because of the linear shrinkage of the latter. The heat transfer coefficient between mold parts (graphite–graphite) is constant, being 1000 W/(m² K). The heat transfer coefficient of graphite into air is 12 W/(m² K) at a mold surface temperature up to 600°C.     

Determination of interface heat-transfer coefficients for permanent-mold casting of Ti-6Al-4V

Interface heat-transfer coefficients (h ₀) for permanent-mold casting (PMC) of Ti-6Al-4V were established as a function of casting surface temperature using a calibration-curve technique. Because mold geometry has a strong effect on h ₀, values were determined for both of the two limiting interface types, “shrink-off” and “shrink-on.” For this purpose, casting experiments with instrumented molds were performed for cylinder- and pipe-shaped castings. The measured temperature transients were used in conjunction with two-dimensional (2-D) axisymmetric finite-element method (FEM) simulations to determine h ₀(T). For the shrink-off interface type, h ₀ was found to decrease linearly from 2000 to 1500 W/m² K between the liquidus and the solidus, from 1500 to 325 W/m² K between the solidus and the gap-formation temperature, and at a rate of 0.3 W/m² K/K thereafter. For the shrink-on interface type, h ₀ was found to increase linearly from 2000 to 2500 W/m² K between the liquidus and the solidus temperatures, from 2500 to 5000 W/m² K between the solidus and the gap-formation temperature, and to remain constant thereafter. The shrink-on values were up to 100 times the shrink-off values, indicating the importance of accounting for the interface geometry in FEM simulations of this process. The FEM-predicted casting and mold temperatures were found to be insensitive to certain changes in the h ₀ values and sensitive to others. A comparison to published h ₀ values for PMC of aluminum alloys showed some similarities and some differences.     

The Effect of the Transition Metal Oxide Content of a Mold Flux on the Radiation Heat Transfer Rates

Heat transfer in the mold of a steel continuous casting machine strongly influences cast surface quality. Transition metal oxides have been widely used in mold slags in continuous casting to aid in liquid pool formation and enhance melting rates. Although a few research studies have been carried out to investigate the thermal properties of mold slags containing transition metal oxides, very few studies have directly correlated their effect on radiation heat transfer rate in continuous casting. This study investigates the radiation heat transfer rates across a mold flux film and determines the influence of the transition metal oxides, MnO and Fe₂O₃, on these rates. It is found that additions of 10% MnO or 5% Fe₂O₃ reduce the radiation heat transfer rate by approximately 25% and increase the adsorption coefficient from 400 to 1800 m^?1.     

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.     

Steady-State rates of dissolution of stationary iron,cobalt, and nickel cylinders in liquid copper

The steady-state rate of dissolution of each metal, υ, is determined as a function of its initial concentration in the melt at temperatures in the range 1468 to 1653 K. In the dissolution of an iron or a cobalt cylinder in pure liquid copper, υ increases with increasing temperature and logv varies linearly with 1/T. In every system investigated, υ deviates negatively from the dissolution rate, υ₁, expressed by an equation in which it is proportional to the difference between the saturation concentration, X _i ^s (molar fraction), and the bulk concentration, X _i ^b , of a dissolving substance,ι, and follows another equation in which the dissolution rate is proportional to the difference between the activities of ι at X _i ^s and X _i ^b The dissolution rates of iron and cobalt are considered to be controlled by diffusion in the melt. The latter equation is derived from the assumption that the rate of diffusion is proportional to the activity gradient of ι. According to this equation, the deviation of υ from υ, is explained in terms of the ratio of the activity coefficient of ι at X _i ^b , γ_i, to that at X _i ^s , γ _i ^s , and the ratio of (∂ν/∂X _i ^b )T,X _i ^b =0 to ∂υ₁/∂X _b ⁱ )_T equals that of γ_i, at infinite dilution to γ _i ^s . When the standard state of the activity is chosen so that it approaches X_i as X_i approaches zero, the logarithm of the rate constant defined by the latter equation is represented by a straight line as a function of 1/T for all the systems investigated.     

X-ray-based measurement of composition during electron beam melting of AISI 316 stainless steel: Part I. Experimental setup and processing of spectra

An energy dispersive X-ray (EDX) detector mounted on a laboratory scale electron beam furnace (30 kW) was employed to assess the potential use of X-rays as a means of on-line liquid alloy composition monitoring during electron beam (EB) melting of alloys. The design and construction of the collimation and protection systems used for the EDX are described in Part I. X-ray spectra are obtained from a sample of AISI 316 stainless steel at both beam idle (in the absence of liquid metal) and high power (in the presence of liquid metal). Two different types of molds are employed: (1) a water-cooled copper mold and (2) a ceramic lined water-cooled copper mold. Various strategies for signal processing and filtration are presented and compared. Correction factors for beam voltage were developed and applied in order to develop correlations between the mole fraction and normalized X-ray intensity for Ni−K _α, Cr−K _α, and Fe−K _α based on an analysis of the vapor condensate. Correlations were also developed relating the change in the X-ray intensities to time for (a) Mo−L, (b) Cr−K _α, (c) Fe−K _α, and (d) Ni−K _α. The stability of the electron beam was found to be the principal source of error, and suggestions for further improvements are also discussed. The study confirms the feasibility of the method and is the first reported study of on-line analysis of a high-temperature liquid alloy. In Part II, the technique is applied to the study of the complex evaporation processes occurring during EB melting.     

Computer simulation of a random distribution of nonequiaxial inclusions in a two-phase matrix structure

A program for the computer simulation of a random distribution of constant-size nonequiaxial rectangular inclusions (l _x , l _y , l _z ) arranged in a specified volume with sides X, Y, and Z in length is described in order to subsequently determine the dependence of the projection (P) of inclusions onto the orthogonal planes on the thickness (L) of the analyzed layer of the form P = V + AL ^B , where V is the volume number of inclusions and A and B are the empiric coefficients and to evaluate other parameters of the structure. The use of this program yielded the acquisition of the P−L curves for the representative volume and various combinations of inclusion numbers and sizes for the first time. The results will be further applied in order to investigate the relationship between new (P, A, B) and conventional (V, l _i , L _i , S) characteristics of the structure, as well as to consider their relations with properties.     

Henrian activity coefficient of As in Cu-Fe mattes and white metal

A transpiration method was used to evaluate the Henrian activity coefficient of As (γ _As ^o ) in Cu-Fe mattes and white metal. Values for the activity coefficient of As (γ _As) have been evaluated as a function of the Cu/Fe molar ratio from 1 to ∞, as a function of the sulfur deficiency (defined as SD=X _s−1/2X _Cu−X _Fe, where X _i is the mole fraction of the ith species) from −0.02 to +0.02 and at temperatures between 1493 and 1573 K. The activity coefficient for arsenic in the matte was found to have a weak dependence on both temperature and the Cu/Fe molar ratio, but a strong dependence on SD. Analysis of γ _As as a function of the trace-element concentration reveals that the activity coefficient is highly dependent on the As content, even at trace concentrations where Henrian behavior is expected. That dependency is attributed to uncertainty in the reported value of the saturation pressure of monatomic arsenic (P _As ^o ) and highlights problems in comparing results and specifying Henrian values for the activity coefficient. A method is presented whereby the impact of P _As ^o on computed values of γ _As is significantly reduced to obtain an approximate Henrian value of the activity coefficient.     

Analysis of the motion of a flat jet in a direct strip casting feeding system

The motion and shape of a vertically falling flat rectangular jet of liquid metal issuing from an inclined plane is analysed numerically and analytically. The jet is affected by surface tension and gravity. The main interest in this problem originates from the technological application of the direct strip casting process, which is a novel process to cast steel strips in a thickness range from 2 to 15 mm with a minimum or no hot-rolling. In this process the liquid metal is fed onto a single endless horizontal belt that runs between two rollers. The bottom of the belt is cooled by water. One of the techniques to feed the liquid metal is down an inclined plane. Due to disturbances in the flow, for instance slag in the liquid metal, the jet issuing from the inclined plane may split into two or several jets. The large convergence of the individual jets causes an unfavourable non uniform distribution of the liquid metal over the belt. In the analysis of the present paper it is shown, using an expansion in the inverse Froude number, that the convergence of a single jet depends to zero order on the inverse square root of the Weber number We^?1/2 = (γl(ρw₀² h₀))^1/2. Small convergence of the jet is found for large Weber numbers, which can be accomplished with a large initial velocity w₀.     

Transient fluid flow and superheat transport in continuous casting of steel slabs

The turbulent flow of molten steel and the superheat transport in the mold region of a continuous caster of thin steel slabs are investigated with transient large-eddy simulations and plant experiments. The predicted fluid velocities matched measurements taken from dye-injection experiments on full-scale water models of the process. The corresponding predicted temperatures matched measurements by thermocouples lowered into the molten steel during continuous casting. The classic double-roll flow pattern is confirmed for this 132×984 mm slab caster at a 1.52 m/min casting speed, with about 85 pct of the single-phase flow leaving the two side ports of the three-port nozzle. The temperature in the top portion of the molten pool dropped to about 30 pct of the superheat-temperature difference entering the mold of 58 °C. About 12 pct of the superheat is extracted at the narrow face, where the peak heat flux averages almost 750 kW/m² and the instantaneous peaks exceed 1500 kW/m². Two-thirds of the superheat is removed in the mold. The jets exiting the nozzle ports exhibit chaotic variations, producing temperature fluctuations in the upper liquid pool of ±4 °C and peak heat-flux variations of±350 kW/m². Employing a static-k subgrid-scale (SGS) model into the three-dimensional (3-D) finite-volume code had little effect on the solution.     

Thermodynamic modeling of binary and ternary metallic solutions

A model is proposed for describing heat of mixing behavior in binary and ternary metallic solutions. The binary model, which has the form, ΔH ^M =α₁ X _A ² X _B +α₂ X _A X _B ² −α₃ X _A ² X _B ² , whereX _A andX _B are mole fractions of componentsA andB and α₁, α₂, and α₃ are constants, is applied to the heat of mixing values for 84 solid and liquid systems and the results are compared with the subregular model. The ternary model, which is composed of the sum of the binary equations and a ternary interaction term of the form α _ABC X _A X _B X _C , was applied to the Bi−Cd−Pb, Cd−Pb−Sn, and Cd−Pb−Sb systems. There was excellent agreement both as to the shapes of the isoenthalpy of mixing curves and as to the heat of mixing values in the ternary systems when the model was used to predict the experimental values.     

Internal stresses and structures developed during creep

Specimens of 304 stainless steel subjected to different thermomechanical histories develop different internal stresses, σ _i , and different substructures. Creep rate is uniquely related not to the applied stress, σ _A , but to the effective stress, σ^*=(σ _A −σ _i ). Values of σ^* are determined from experimental results and σ _i calculated from σ _i =(σ _A −σ^*). Results show σ _i increases with the applied stress according to σ _i ∝σ _A ^1.7 . Transmission electron microscopic observations show that the density of dislocations within subgrains, ϱ _D , and the subgrain diameter,D, vary with applied stress according to: ϱ _D ∝σ _A ^K ,D ∝ σ _A ^−0.8 , whereK=1.4 to 2.0. Subgrain misorientation is independent of creep stress, strain, or temperature. The contributions of these structural variables to the internal stress are discussed.     

Stable nonlinear relaxations in multiphase Al-Zn alloy

Experiment reveals the characteristics of stable damping in a multiphase Al-Zn eutectoid alloy as follows: (1) the whole damping (Q ⁻¹) has the same dependence on measuring frequency (f);i.e., Q ^-1 ∝f ⁻ⁿ , wheren is a parameter independent of temperature; (2) in a low-temperature (low-T) and low-strain-amplitude (low-A _ε) region,Q ⁻¹ = (B/f ⁿ) exp (-nH/kT) (whereB is a constant,H is the phase interface or interphase boundary atom diffusion activation energy,k is Boltzmann’s constant, andT is the absolute temperature);n andH are independent ofA _ε. The damping originates from an anelastic motion of phase interface; (3) in an intermediate region, including low-T and high-A _ε, middle-T and middle-A _ε, and high-T and low-A ^ε regions, we still have the equationQ ⁻¹ = (C/f ⁿ ) exp (-nH/kT), but the damping has a normal amplitude effect:C, n, andH all vary withA _ε. The damping results from a nonlinear relaxation of phase interface; and (4) in a high-T and high-A _ε region, there is no longer a linear relationship between InQ ⁻¹ and 1/T, whereas relationQ ⁻¹ ∝f ⁻ⁿ is still satisfied;n increases asA _ε increases; and the damping has a normal amplitude effect, but it is weaker than that in case (3). The damping may be attributed to another kind of nonlinear relaxation between phase interfaces.     

Molding of temperature field for the induction skull melting process of Ti-47Ni-9Nb

Based on the direct finite-difference method, a numerical model for simulating the temperature field in the charge during the induction skull melting (ISM) process has been developed in this article. The related factors, including water-cooling boundaries, the induction-heating electromagnetic stirring hump, and the power distribution in the charge, had been analyzed. The interfaces between the charge and crucible were treated as radiation boundaries before the charge was melted and as a combined boundary of radiation and conduction after the charge was melted. The free surface was treated as a radiation boundary. The relationship between the height of the electromagnetic stirring hump, charge weight, and melting power was derived based on the law of mass conservation. Based on the law of energy conservation, the distribution density of the induction current was attained. With the complied program, the temperature fields in the charge of Ti-47Ni-9Nb under different melting powers and/or charge weights were calculated. The results show that increasing the rate of the melting power has no influence on melt temperature. The ratio of melt weight to charge weight is determined by the melting power and charge weight. The melt temperature can be expressed as T=A ₀+A ₁×P+A ₂×P ², in which the coefficients A ₀, A ₁, and A ₂ are cubic functions of the charge weight, and P is the melting power.