Experiments on the solidification structure of alloy castings

Two related experimental programs on the solidification structure of alloy castings are reported. In the first, the grain structure of catalytically clean Ni?Cu alloys is examined as a function of the degree of supercooling below the equilibrium liquidus. For supercoolings greater than 85°C, the Ni?Cu alloys exhibit a structure which is in accord with previous observations in pure nickel,i. e., the structure is found to be coarse and dendritic in the range 85° to 150°C supercooling, but fine and equiaxed for supercoolings greater than 150°C. However, in the lower range of supercooling (<85°C) the structure is fine and equiaxed. It is concluded that solute elements can promote grain formation in certain castings at supercoolings insufficient to cause heterogeneous nucleation. To study the effect of solute elements on the structure of a solidifying material, castings of pure nickel and aluminum are compared with binary alloys of these base materials. Over the composition ranges studied in both alloy systems, the structure is observed to be related to a parameter which includes the slope of the liquidus, the bulk solute concentration, and the solute distribution coefficient. It is shown or is argued that heterogeneous nucleants are not involved and therefore another mechanism must be operating in determining the structure. In any event, these latter experiments suggest that an effective means of controlling the structure of castings is by appropriate selection of alloying additions on the basis of the alloy variables contained in such a parameter.     

Macrosegregation in castings rotated and oscillated during solidification

The macrosegregation present in stationary, rotated, and oscillated castings of Al-3 wt pct Ag was determined by measuring the distribution of radioactive silver added to the melt. Considerable scatter was observed in the measurements, the scatter being dependent on the sampling technique used. It was found that no significant macrosegregation was present in the stationary and rotated castings. Extensive macrosegregation was detected in the oscillated casting. For the oscillating case the macrosegregation can be accounted for on the basis of the long range movement of dendrite fragments which break and/or melt off in the solid-liquid interface region. This movement is a direct result of turbulent waves associated with the oscillation. The maximum silver concentration is shown to be related to the columnar-to-equiaxed transition.     

Modeling stress development during the solidification of gray iron castings

A method has been developed to predict stress development in gray iron foundry castings. A new yield function, based on theoretical developments by Frishmuth and McLaughlin,⁹ and on experiments by Coffin¹⁰ was implemented as a user-written element in a commercial finite element package. The yield function takes into account the strong dependence of the yield stress in cast irons on the loading path. Stresses resulting from thermal displacements in the cooling casting are computed using the new yield function in an elastic-viscoplastic stress analysis. In earlier work, techniques were developed to represent the mold in the thermal analysis by sets of boundary conditions on the surface of the part. For this work, a second user-written element was used to apply force-displacement boundary conditions on the surface of the casting to represent the mechanical constraint of the mold. The properties for this element were based on soil mechanics considerations. Example problems are given, showing a substantial difference in the computed stresses when using the present formulation, in comparison to results obtained with the more usual von Mises yield function. Formerly at the University of Illinois.     

Alpha case thickness modeling in investment castings

The alpha case thickness at the surface of a Ti-6Al-4V (wt pct) step wedge investment casting has been measured and successfully predicted. The prediction uses temperature-time results obtained from a heat flow simulation of the casting. The temperature-time results were coupled to a simple model for diffusion of oxygen into the beta phase during continuous cooling. Oxygen concentration and microhardness profiles were measured from the surface in contact with the ZrO₂ face coat of the shell mold into the interior of the casting. The oxygen content in the metal at the shell mold interface was between 5 and 9.5 wt pct in general agreement with a thermodynamic calculation for bcc Ti in contact with ZrO₂. At the limit of the alpha case region, as determined by standard metallographic technique, the oxygen concentration was found to be no more than 0.02 wt pct above the level of oxygen in the bulk alloy. Using this information and one particular literature value for the activation energy for diffusion of oxygen, a nearly linear relationship was obtained between the measured and predicted alpha case thicknesses at various positions on the casting surface. Reduction of the prefactor of this diffusion coefficient by a factor of 7.5 produces excellent agreement between predicted and measured alpha case thicknesses. Such a reduction is not inconsistent with the scatter of literature values for the diffusion coefficient.     

Isothermal solidification kinetics of diffusion brazing

Diffusion brazing (DB) is a process that produces interface-free joints that approach the bulk properties of the material that is to be joined. Solid-state diffusion of the melting point depressant (MPD) element into the joint metal causes the solid/liquid (S/L) interface to advance until the joint is solidified. The time required to complete this isothermal solidification stage was modeled using a moving boundary analysis. Precision measurements of the interlayer width as a function of time were made on the copper-silver system. The bonding apparatus consisted of a suspended load feedback system that prevented leakage of joint metal due to extrusion or surface wetting, thus preserving mass balance. The interlayer width vs bonding time measurements obtained were found to be within a factor of 4 of the theoretical model. The difference was ascribed to the difficulty in accurately measuring the actual liquid width and loss of silver due to vaporization. Large spherical protrusions grow during bonding, which further roughens the interface. However, experimental and predicted concentration profiles of silver were found to be in complete agreement. As the liquid remaining in the grain boundary grooves is diffused away, porosity can develop due to volume changes. By holding the joint at temperature for extended periods, complete solidification followed by homogenization will occur. Selecting the appropriate bonding temperature to achieve a specified maximum concentration of braze metal at the joint is dependent on both the isothermal solidification and homogenization kinetics.     

Numerical modeling of solidification combustion synthesis

A numerical study of self-propagating combustion synthesis is carried out to determine the effect of the heat of reaction(Q), the activation energy (E), the frequency factor (K₀), thermal conductivity(K*), and initial temperature(T ₀ on the combustion velocity and combustion temperature in the presence of cooling at one end. The numerical procedure allows for the formation and solidification of nonstoichiometric combustion products. This includes the phase change of the product through its solidification and eutectic range. Calculations are carried out for the Ti-C system with an objective of predicting solutions which are comparable to previously reported, experimentally determined values. Calculations are also compared with the thin zone analytical solution to the combustion problem. The use of lowK ₀ values to bring the solutions close to the experimentally determined numbers is discussed. Solutions are presented to elucidate the effect of relevant parameters on the thickness of the combustion and preheat zones. Conditions where extinction is expected to occur are identified. The effect of the thermal conductivity on the velocity may be to increase or decrease the velocity, depending on the value ofK ₀. At lowK ₀ values, an increase in the thermal conductivity may lead to a decrease in the combustion velocity. The effect of the initial temperature on the combustion velocity and temperature is to increase both; however, the increase in the combustion temperature may not be proportional to the increase in the initial temperature. The activation energyE has a pronounced effect on reducing the combustion velocity while not influencing the combustion temperature. The time rate of the solidification process which determines the final microstructure is discussed. Formerly Fellow, Department of Materials Science and Engineering, University of Cincinnati, is Scientist, Los Alamos National Laboratory, Los Alamos, NM 87545. This paper is based on a presentation made in the symposium “Reaction Synthesis of Materials” presented during the TMS Annual Meeting, New Orleans, LA, February 17–21, 1991, under the auspices of the TMS Powder Metallurgy Committee.     

Interface attachment kinetics in alloy solidification

The current status of our understanding of nonequilibrium interface kinetics during solidification is reviewed. Measurements of solute trapping and kinetic interfacial undercooling during rapid alloy solidification are accounted for by the continuous growth model (CGM) without solute drag. Disorder trapping has been predicted and observed in the rapid solidification of ordered intermetallic compounds. In systems that undergo either solute or disorder trapping, a transition from short-range diffusion-limited to collision-limited growth occurs, which originates in the reduced driving free energy for the formation of such metastable materials, resulting in three orders of magnitude change in the interface mobility. Applications to cellular and dendritic growth are discussed. A correlation is presented for estimating the diffusive speed—the growth rate necessary for substantial solute trapping—for alloy systems in which it has not, or cannot, be measured. The raw data for Si(Bi) solute trapping measurements to which many models have been compared are presented in the Appendix.     

Three-dimensional probabilistic simulation of solidification grain structures: Application to superalloy precision castings

A two-dimensional (2-D) probabilistic model, previously developed for the prediction of microstructure formation in solidification processes, is applied to thin section superalloy precision castings. Based upon an assumption of uniform temperature across the section of the plate, the model takes into account the heterogeneous nucleation which might occur at the mold wall and in the bulk of the liquid. The location and crystallographic orientation of newly nucleated grains are chosen randomly among a large number of sites and equiprobable orientation classes, respectively. The growth of the dendritic grains is modeled by using a cellular automaton technique and by considering the growth kinetics of the dendrite tips. The computed 2-D grain structures are compared with micrographie cross sections of specimens of various thicknesses. It is shown that the 2-D approach is able to predict the transition from columnar to equiaxed grains. However, in a transverse section, the grain morphology within the columnar zone differs from that of the experimental micrographs. For this reason, a three-dimensional (3-D) extension of this model is proposed, in which the modeling of the grain growth is simplified. It assumes that each dendritic grain is an octaedron whose half-diagonals, corresponding to the <100> crystallographic orientations of the grain, are simply given by the integral, from the time of nucleation to that of observation, of the velocity of the dendrite tips. All the liquid cells falling within a given octaedron solidify with the same crystallographic orientation of the parent nucleus. It is shown that the grain structures computed with this 3-D model are much closer to the experimental micrographie cross sections.     

Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part II. Computation problems and validation on INCONEL 718 superalloy castings

In Part I of the article, a new analytical model that describes solidification of equiaxed dendrites was presented. In this part of the article, the model is used to simulate the solidification of INCONEL 718 superalloy castings. The model was incorporated into a commercial finite-element code, PROCAST. A special procedure called microlatent heat method (MLHM) was used for coupling between macroscopic heat flow and microscopic growth kinetics. A criterion for time-stepping selection in microscopic modeling has been derived in conjunction with MLHM. Reductions in computational (CPU) time up to 90 pct over the classic latent heat method were found by adopting this coupling. Validation of the model was performed against experimental data for an INCONEL 718 superalloy casting. In the present calculations, the model for globulitic dendrite was used. The evolution of fraction of solid calculated with the present model was compared with Scheil’s model and experiments. An important feature in solidification of INCONEL 718 is the detrimental Laves phase. Laves phase content is directly related to the intensity of microsegregation of niobium, which is very sensitive to the evolution of the fraction of solid. It was found that there is a critical cooling rate at which the amount of Laves phase is maximum. The critical cooling rate is not a function of material parameters (diffusivity, partition coefficient,etc.). It depends only on the grain size and solidification time. The predictions generated with the present model are shown to agree very well with experiments.     

Mathematical modeling of porosity formation in solidification

Shrinkage porosity and gas porosity occur simultaneously and at the same location when conditions are such that both may exist in a solidifying casting. Porosity formation in a solidifying alloy is described numerically, including the possible evolution of dissolved gases. The calculated amount and size of the porosity formed in Al-4.5 pct Cu plate castings compares favorably with measured values. The calculated distribution of porosity in sand cast Al-4.5 pct Cu plates of 1.5 cm thickness matches experimental measurements. The decrease of the hydrogen content by strong degassing and the increase of mold chilling power are recommended to produce sound aluminum alloy castings. The calculated results for steel plate castings are in agreement with the experimental work of Pellini. The present modeling has clarified the basis of empirical rules for soundness and suggests that the simultaneous occurrence of shrinkage and gas evolution is an essential mechanism in the formation of porosity defects.     

Coarsening kinetics during solidification of Ni-Al-Ta dendritic monocrystals

Several dendritic monocrystals of nickel-rich Ni-Al-Ta alloys were directionally solidified at about 0.25 m/h⁻¹ under a gradient of 8 × 10⁻³ K/m⁻¹. The solid-liquid interface was fossilized at a given moment by rapidly quenching the remaining liquid. In some specimens crystal pulling was interrupted for various lengths of time prior to quenching. The quenched solid-liquid interfaces were used for a convenient and rapid evaluation of: 1) isothermal coarsening kinetics of the dendritic solid at a temperature between the liquidus and the eutectic temperatures and; 2) dendrite coarsening kinetics during solidification. It was found that extension to the ternary Ni-Al-Ta system of a model previously developed for binary systems predicted isothermal dendrite coarsening kinetics in close agreement with experimental results. Agreement for coarsening kinetics during solidification was less good. An increase in tantalum or aluminum contents slowed down coarsening, yielding finer microstructures. At equal atomic percental increase in concentration, the effect of tantalum was more significant than that of aluminum.     

Interfacial transport kinetics during the solidification of silicon

Studies of the temperature dependence of interfacial reaction kinetics have recently been made in experiments on crystal nucleation and growth in undercooled liquid Si, allowing estimation of the apparent activation energy over a fairly wide range in temperature. The activation energy inferred from growth experiments, at temperatures near the equilibrium melting temperature (T_m), is ∮.2eV while nucleation experiments at temperatures near 2T_m/3 indicate a value of 1.09 eV. This discrepancy can be resolved if the interfacial kinetics are described by a Fulcher-Vogel expression rather than an Arrhenius one, consistent with interfacial atomic mobility being free-volume limited. The ideal glass transition temperature indicated by a free-volume analysis is 1040 ± 100 K for liquid Si; however, experimental measurements of the solidification rate for amorphous Si indicate a slightly lower value.     

Current development in quantitative phase-field modeling of solidification

The quantitative phase-field simulations were reviewed on the processes of solidification of pure metals and alloys.The quantitative phase-field equations were treated in a diffuse thin-interface limit, which enabled the quantitative links between interface dynamics and model parameters in the quasi-equilibrium simula-tions.As a result, the quantitative modeling is more effective in dealing with microstructural pattern for-mation in the large scale simulations without any spurious kinetic effects.The development of the quanti-tative phase-field models in modeling the formation of microstructures such as dendritic structures, eutec-tic lamellas, seaweed morphologies, and grain boundaries in different solidified conditions was also re-viewed with the purpose of guiding to find the new prospect of applications in the quantitative phase-field simulations.     

Directional solidification of large superalloy castings with radiation and liquid-metal cooling: A comparative assessment

A columnar-grain variant of single-crystal RENé N4 has been directionally solidified (DS) over a range of conditions in order to assess the possible benefits of the use of liquid metal-enhanced cooling for large cross-sectional castings. Castings were solidified at a rate of 2.5 mm/min using conventional radiation cooling and at rates between 2.5 and 8.5 mm/min using liquid-metal cooling (LMC) with tin as a cooling medium. Thermocouples inserted in the casting directly measured thermal gradients during solidification. The LMC process exhibited higher gradients at all withdrawal rates. The higher thermal gradients resulted in a refined structure measurable by the finer dendrite-arm spacing. Additionally, the conventionally cast material exhibited several freckle-type defects, while none were observed in the liquid-metal-cooled castings.     

Microscopic modeling of fundamental phase transformations in continuous castings of steel

A model has been developed to describe the microscopic behavior of phase transformation of carbon steels in the range of cooling rate occurring in continuous casting. In the liquid-to solidphase transformation, this model simulates the phenomena of dendrite nucleation and growth during solidification. Both δ- and γ-dendrites are involved. The nucleation and growth model has been established on the basis of published experimental data and previous work. Also, a model of the peritectic transformation of carbon steels has been included. In the solid-to solidphase transformation, the model considers the δ→ γ, γ→ α, and γ→ α + Fe₃C phase transformations. The δ→ γ and γ→ α phase transformations have been modeled by using the Johnson-Mehl equation, also known as the Avrami equation. For the pearlite transformation, a nucleation law, as well as the growth kinetics, has been established. Good agreement has been found between the prediction of the model and the experimental data.     

A general enthalpy method for modeling solidification processes

In the present work, a general implicit source-based enthalpy method is presented for the analysis of solidification systems. The proposed approach is both robust and efficient. The performance of the method is illustrated by application to a number of problems taken from recent metallurgical literature.     

Thermal analysis of isothermal solidification kinetics duirng transient liquid-phase sintering

A technique for experimentally measuring the kinetics of isothermal solidification during transient liquid-phase sintering (TLPS) has been successfully developed using differential scanning calorimetry (DSC). Comparison of these data with a model based on diffusion of Sn solute into an array of spherical Pb particles reveals very good agreement between predicted and measured solidification rates. The DSC technique and the solid-state diffusion model represent valuable tools in investigating the parameters that control TLPS, such as powder size, solder composition, process temperature, and heating rate.