Doru M. Stefanescu

Behavior of ceramic particles at the solid- liquid metal interface in metal matrix composites

Directional solidification experiments have been conducted to document SiC particle behavior at the solid-liquid interface in Al-2 pct Mg (cellular interface) and Al-6.1 pct Ni (eutectic interface) alloys. Particle size ranged from 20 to 150 μm diameter. Although predictions based on the thermodynamic approach suggest that no engulfment is possible, it was demonstrated that particles can be entrapped in the solid if adequate solidification rates and temperature gradients are used. The main factors responsible for this behavior are considered to be the difference between the thermal conductivities of particles and metal, the buildup of volume fraction of particles at the interface, and the morphological instability of the interface induced by the particles. A model including the contribution of drag and thermal conductivity has been proposed. Calculation with this model produced numbers for the critical velocity slightly higher than those evaluated experimentally. Various factors which can account for this discrepancy are discussed.

Heat transfer-solidification kinetics modeling of solidification of castings

A close examination of the recent developments in the field of computer simulation of solidification process reveals that a combination of both macroscopic and microscopic models is necessary in order to accurately describe the solidification of castings. Currently available macroscopic models include models that describe heat transfer from metal to mold, fluid flow of liquid metal during mold filling, and stress field in the casting. At the microscopic level, the models should include more intricate issues such as solidification kinetics and fluid flow in the mushy zone. Although significant progress has been accomplished over the years in each field, the task of including all of these models into a comprehensive package is far from being complete. This paper describes the state of the art on coupling the macroscopic heat transfer (HT) and microscopic solidification kinetics (SK) models and introduces thelatent heat method as a more accurate method for solving the heat source term in the heat conduction equation. A new method for calculation of fraction of solid evolved during solidification based on computer-aided cooling curve analysis (CA-CCA), as well as a method based on nucleation and growth kinetics laws, is discussed. A new nucleation model based on the concept of instantaneous nucleation, which is used to describe equiaxed eutectic solidification of commercial alloys, has been introduced. It is demonstrated that the instantaneous nucleation model agrees well with the experimental results in terms of cooling curves and of evolution of the fraction of solid during solidification. Validation results are also shown for SK models that are based on CA-CCA coupled with HT models for eutectic Al-Si and gray cast iron alloys.

The influence of buoyant forces and volume fraction of particles on the particle pushing/entrapment transition during directional solidification of Al/SiC and Al/graphite composites

Directional solidification experiments in a Bridgman-type furnace were used to study particle behavior at the liquid/solid interface in aluminum metal matrix composites. Graphite or siliconcarbide particles were first dispersed in aluminum-base alloysvia a mechanically stirred vortex. Then, 100-mm-diameter and 120-mm-long samples were cast in steel dies and used for directional solidification. The processing variables controlled were the direction and velocity of solidification and the temperature gradient at the interface. The material variables monitored were the interface energy, the liquid/particle density difference, the particle/liquid thermal conductivity ratio, and the volume fraction of particles. These properties were changed by selecting combinations of particles (graphite or silicon carbide) and alloys (Al-Cu, Al-Mg, Al-Ni). A model which considers process thermodynamics, process kinetics (including the role of buoyant forces), and thermophysical properties was developed. Based on solidification direction and velocity, and on materials properties, four types of behavior were predicted. Sessile drop experiments were also used to determine some of the interface energies required in calculation with the proposed model. Experimental results compared favorably with model predictions.

An analytical model for solute redistribution during solidification of planar, columnar, or equiaxed morphology

Existing models for solute redistribution (microsegregation) during solidification were reviewed. There are no analytical models that take into account limited diffusion in both the liquid and the solid phases. A new analytical mathematical model for solute redistribution was developed. Diffusion in liquid and in solid was considered. This model does not require a prescribed movement of the interface. It can be used for one-dimensional (1-D) (plate), two-dimensional (cylinder), or three-dimensional (3-D) (sphere) calculations. Thus, it is possible to calculate microsegregation at the level of primary or secondary arm spacing for columnar dendrites or for equiaxed dendrites. The solution was compared with calculations based on existing models, as well as with some available experimental data for the segregation of base elements in as cast Al-4. 9 wt pct Cu, INCONEL 718, 625, and plain carbon (0. 13 wt pct C) steel.

Modeling of the liquid/solid and the eutectoid phase transformations in spheroidal graphite cast iron

A model of phase transformations in spheroidal graphite (SG) cast iron has been developed to quantitatively describe the microstructural evolution during solidification and the subsequent solid-state phase transformations (eutectoid reaction) during continuous cooling and to predict some of the microstructural characteristics of final phases formed in SG iron castings. Such characteristics include phase fractions, phase spacings, and grain dimensions. In the model, the nucleation and growth of primary dendrites and eutectics were described based on existing theories, whereas the mathematical formulation for the eutectoid reaction,i.e., the formation of pearlite and ferrite from the as-cast austenite, was developed based on theories as well as physical evidence obtained from the experimental work. The Johnson-Mehl equation and the Avrami equation were used to calculate the fraction of transformed phases under continuous cooling conditions. The role of the grain impingement factor used in these two equations and the significance of the additivity principle in treating nonisothermal transformations were briefly discussed. The latent heat method was used for the numerical treatment of the release of latent heat during phase transformations. A two-dimensional finite element code which can be used in either Cartesian or cylindrical coordinates (ALCAST-2D) was used to solve the time-dependent temperature distribution throughout the metal/mold system. Numerical predictions were validated against experimental results, and good agreement was obtained.

A model for macrosegregation and its application to Al-Cu castings

A macrosegregation model has been developed to evaluate solute redistribution during solidification of casting alloys. The continuum formulations were used to describe the macroscopic transports of mass, energy, and momentum, associated with the microscopic transport phenomena, for two-phase systems. It was assumed that liquid flow is driven by thermal and solutal buoyancy, as well as by solidification contraction. The movement of free surface was also considered to ensure volume con-servation. In numerical calculations, the solidification event was divided into two stages. In the first stage, the liquid containing freely moving equiaxed grains was described through the relative vis-cosity concept. In the second stage, when a fixed dendritic network formed after dendrite coherency, the mushy zone was treated as a porous medium. After validation of the proposed model for the case of segregation in a bottom-chilled unidirectionally solidified casting of Al-Cu alloys, the nu-merical model was applied to the study of three different castings with simple geometry. It was found that solutal convection tends to decrease the macrosegregation generated by thermal convec-tion. When shrinkage-driven convection was also considered, segregation was again increased, with highly segregated areas forming away from the riser and next to the mold wall. It was demonstrated that solidification contraction has a stronger effect on the liquid flow in the mushy region than buoyancy. The model also was applied to assess the probability of pore formation based on the pressure drop concept. While in the absence of experimental data for the critical pressure drop it was not possible to uniquely predict the formation of porosity, it was possible to indicate the regions where porosity may form preferentially.

Directional solidification of Cu-Pb and Bi-Ga monotectic alloys under normal gravity and during parabolic flight

Cu-Pb and Bi-Ga monotectic alloys of nominal hypermonotectic compositions were directionally solidified under various furnace translation rates, temperature gradients, and gravity levels. Gravity was varied by solidifying the alloys under ground conditions and in the furnace aboard NASA KC-135 aircraft, flying on parabolic trajectories. High translation rates, high gradients, high gravity levels, and higher density and lower thermal conductivity of the L2 phase favored the formation of fiber composite structure, while the opposite conditions resulted in structures consisting of L2 droplets in α matrix. A modified particle engulfment theory as originally enunciated by Ulhmannet al. is proposed to explain these observations.

Melt convection effects on the critical velocity of particle engulfment

Liquid convection ahead of the solidifying interface alters particle behavior in the vicinity of the interface. This effect has not been quantified to date. Relevant directional solidification experiments were conducted using samples of varying thicknesses, as well as normal and low-gravity experiments. A mixture of transparent biphenyl matrix and spherical glass particles, as well as one of succinonitrile matrix with polystyrene particles were used. Two experimental setups were used: a horizontal gradient heating facility (HGF) for horizontal solidification, and a Bridgman-type furnace (BF) for vertical solidification. The convection level during solidification in the HGF was varied by changing the distance between the glass slides containing the composite sample. The BF was used on ground and during parabolic flights, and thus the convection level was changed by alternating low-gravity and high-gravity solidified regions. It was found that the convection level and/or particle buoyancy significantly influences the critical velocity for particle engulfment. At higher natural convection during solidification the critical velocity increases by up to 40%. At very high convection levels engulfment may become impossible because particles fail to interact with the interface. A systematic analysis of some theoretical models was performed in an attempt to evaluate the present level of theoretical understanding of the problem. Methods of evaluating the surface energies required for model validation are also presented.

Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part I. Model development and discussion

An analytical model that describes solidification of equiaxed dendrites has been developed for use in solidification kinetics-macrotransport modeling. It relaxes some of the assumptions made in previous models, such as the Dustin-Kurz, Rappaz-Thevoz, and Kanetkar-Stefanescu models. It is assumed that nuclei grow as unperturbed spheres until the radius of the sphere becomes larger than the minimum radius of instability. Then, growth of the dendrites is related to morphological instability and is calculated as a function of melt undercooling around the dendrite tips, which is controlled by the bulk temperature and the intrinsic volume average concentration of the liquid phase. When the general morphology of equiaxed dendrites is considered, the evolution of the fraction of solid is related to the interdendritic branching and dynamic coarsening (through the evolution of the specific interfacial areas) and to the topology and movement of the dendrite envelope (through the tip growth velocity and dendrite shape factor). The particular case of this model is the model for globulitic dendrite. The intrinsic volume average liquid concentration and bulk temperature are obtained from an overall solute and thermal balance around a growing equiaxed dendritic grain within a spherical closed system. Overall solute balance in the integral form is obtained by a complete analytical solution of the diffusion field in both liquid and solid phases. The bulk temperature is obtained from the solution of the macrotrasport-solidification kinetics problem.

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.