METALLURGICAL AND MATERIALS TRANSACTIONS A
	ABSTRACTS Volume 27A, No. 3, March 1996 This Month Featuring: The 1995 Institute of Metals Lecture and Robert Franklin Mehl Award; Symposium on Analysis and Modeling of Solidification; Transformation; Transport Phenomena; Mechanical Behavior; Welding & Joining; Solidification; Composite Materials. View March 1996 Table of Contents.

THE 1995 INSTITUTE OF METALS LECTURE AND ROBERT FRANKLIN MEHL AWARD

SYMPOSIUM ON ANALYSIS AND MODELING OF SOLIDIFICATION

Several fundamental ideas that have been developed and incorporated into contemporary analysis strategies include: rigorous formulations of morphological stability and phase selection, critical developments on heterogeneous nucleation, the influence of fluid flow, the development of nonequilibrium conditions at the interface, and sophisticated numerical techniques that show a time dependent evolution of the solidification microstructure from the atomic scale to the macroscopic level. These fundamental concepts have already been applied to processing techniques, particularly rapid solidification techniques such as laser welding, powder atomization and melt spinning, and composite synthesis where the solidification microstructure reflects the interaction of several concurrent phenomena.

One hallmark of the current efforts in the analysis and modeling of solidification is the identification of scaling relations where different domains of behavior can be characterized through appropriate length scales. These relations provide useful metrics to quantify behavior from the atomistic to the macroscopic scale. Another advance has been the increased recognition of the influence of fluid behavior on microstructure development. It is clear that the synergism between analysis and experimentation has yielded not only new levels of understanding but also new richness in microstructure classes which demand further exploration.

The analysis and modeling efforts have resulted in a significant leveraging of experiments and some level of predictive capability. However, experimental efforts are still crucial so that proper models are used in the analysis and the rate limiting kinetic behavior is properly defined. At the same time, modeling and analysis point the way to a clear definition of experimental efforts. In this regard, the current TMS symposium has been designed to integrate the analysis and modeling aspects of microstructure with critical experimental studies to present the current state of solidification microstructure development.

Nucleation-Controlled Solidification Kinetics
J.H. PEREPEZKO and M.J. UTTORMARK
Solidification microstructures are usually classified with the respect to the growth processes responsible for the observed morphology. However, experience has demonstrated that several regimes of processing conditions can be identified in which nucleation is the determining factor in the phase selection and the evolution of the solidification microstructure. Several of these regimes are analyzed to identify the influence of nucleation on the final microstructure. In most cases, nucleation occurs by heterogeneous catalysis with competitive kinetics between different sites and product structures. The proper analysis of heterogeneous nucleation requires a clear identification and description of active catalytic sites which has been a continuing challenge for both experiments and analysis since nucleation signatures can be masked by subsequent reactions. A strategy for the systematic exploration of heterogeneous nucleation in alloys is described that yields some information about possible atomistic and dynamic effects at the catalyst/melt interface that is of theoretical and practical interest. Additionally, computer simulation studies are described that elucidate some of the atomistic features of nucleation which become increasingly important when a multiplicity of nucleation sites is observed with a hierarchy of potency.

Crystallization of Amorphous Alloys
A.L. GREER
Crystallization of amorphous alloys is compared with conventional solidification of melts. Taking account of the temperature dependence of crystal nucleation and growth rates, the links between the two processes are explored. The fundamentals of nucleation and growth kinetics in amorphous alloys are reviewed. It is shown that the crystallization of amorphous alloys can be exploited (1) to obtain ultrafine grained microstructures with useful properties and (2) to elucidate nucleation mechanisms in conventional grain-refining practice.

Overview of Geometric Effects on Coarsening of Mushy Zones
S.P. MARSH and M.E. GLICKSMAN
An overview is presented of the thermodynamic, kinetic, statistical, and geometric factors that govern phase coarsening in dendritic mushy zones. The coarsening behavior of such systems is best quantified through the kinetics of the decay rate of the specific surface area, S_v. The geometry of the complex solid-melt interfaces comprising a mushy zone is described statistically as an areal distribution of local curvature parameters. These parameters capture both the intensive and extensive thermodynamic characteristics of the mushy zone. The effects of local interface shape, negative mean, and Gaussian curvatures and the appearance of inactive lengthscales on the coarsening kinetics of dendritic structures are discussed. The combined contribution of all these geometrical effects yields global coarsening rates for ramified mushy zones that are comparable to those predicted from theory for a collection of spherical particles having the identical volume fraction of solid.

Some Consequences of Thermosolutal Convection: The Grain Structure of Castings
G. HANSEN, A. HELLAWELL, S.Z. LU, and R.S. STEUBE
The essential principles of thermosolutal convection are outlined, and how convection provides a transport mechanism between the mushy region of a casting and the open bulk liquid is illustrated. The convective flow patterns which develop assist in heat exchange and macroscopic solute segregation during solidification; they also provide a mechanism for the transport of dendritic fragments from the mushy region into the bulk liquid. Surviving fragments become nuclei for equiaxed grains and so lead to blocking of the parental columnar, dendritic growth front from which they originated. The physical steps in such a sequence are considered and some experimental data are provided to support the argument.

Effects of Flow on Morphological Stability During Directional Solidification
S.H. DAVIS and T.P. SCHULZE
Research involving the interaction of flow with morphological instability during directional solidification of binary alloys is reviewed. In general, flow may arise during the solidification process from thermal and solutal buoyancy, changes in density upon solidification, thermocapillary forces at free boundaries, or external forcing of the system. We focus primarily on the last of these, giving details of the influence of various forced flows on the critical conditions for morphological instability. These flows include the asymptotic suction profile, stagnation-point flow, and periodically driven shear flows. Parallel shear flows are unable to stabilize morphological instabilities in three dimensions but may lead to new long-wave, traveling instabilities. Flow-induced, long-wave instabilities are also encountered in the presence of both steady and modulated stagnation-point flows. Unsteady, nonparallel shear flows may stabilize morphological instability if the flow parameters are adjusted properly.

Solidification of Binary Hypoeutectic Alloy Matrix Composite Castings
ANDREAS MORTENSEN and MERTON C. FLEMINGS
We consider a binary hypoeutectic alloy casting which solidifies in dendritic form in an unreinforced engineering casting and seek to predict its microstructure in a metal matrix composite. We focus on the case where the reinforcement is fixed in space and fairly homogeneously distributed. We assume that the reinforcement does not catalyze heterogeneous nucleation of the solid. We show that the reinforcement can cause several microstructural transitions in the matrix alloy, depending on the matrix cooling rate, the width, , of interstices left between reinforcing elements, and the initial velocity V of the solidification front. These transitions comprise the following: (1) coalescence of dendrite arms before solidification is complete, causing solidification to proceed in the later stages of solidification with a nondendritic primary phase mapping the geometry of interstices delineated by reinforcement elements; (2) sharp reduction or elimination of microsegregation in the matrix by diffusion in the primary solid matrix phase; and (3) a transition from dendrite to cell formation, these cells featuring significant undercoolings or a nearly plane front configuration when reinforcing elements are sufficiently fine. Quantitative criteria are derived for these transitions, based on previous work on composite solidification, observations from directional solidification experiments, and current solidification theory. Theory is compared with experimental data for aluminum-copper alloys reinforced with alumina fibers and for the dendrite to cell transition using data from directional succinonitrile-acetone solidification experiments. Theory and experiment show good agreement in both systems.

Numerical Modeling of Cellular/Dendritic Array Growth: Spacing and Structure Predictions
J.D. HUNT and S.-Z. LU
A numerical model of cellular and dendritic growth has been developed that can predict cellular and dendritic spacings, undercoolings, and the transition between structures. Fully self-consistent solutions are produced for axisymmetric interface shapes. An important feature of the model is that the spacing selection mechanism has been treated. A small, stable range of spacings is predicted for both cells and dendrites, and these agree well with experiment at both low and high velocities. By suitable nondimensionalization, relatively simple analytic expressions can be used to fit the numerical results. These expressions provide an insight into the cellular and dendritic growth processes and are useful for comparing theory with experiment.

Banded Solidification Microstructures
W. KURZ and R. TRIVEDI
Banded microstructures are composed of alternate structures or phases which develop mostly parallel to the transformation front. At low growth velocities, bands of the same microstructure but with different scales form through periodic fluctuations of the solidification system. On the other hand, banding can occur as a transformation microstructure when the growth front becomes unstable to oscillations. This instability is either due, at low velocities, to nucleation of another phase (peritectics) or, at high velocities, to nonequilibrium effects at the interface which lead to periodic changes of the microstructure. In this article, the inherent banded patterns of low velocity peritectic solidification and high velocity nonequilibrium solidification will be presented and their origin will be discussed.

Morphological Instabilities of Lamellar Eutectics
ALAIN KARMA and ARMAND SARKISSIAN
We present the results of a numerical study based on the boundary integral technique of interfacial pattern formation in directional solidification of thin-film lamellar eutectics at low velocity. Microstructure selection maps that identify the stability domains of various steady-state and nonsteady-state growth morphologies in the spacing-composition ( - C₀) plane are constructed for the transparent organic alloy CBr₄-C₂Cl₆ and for a model eutectic alloy with two solid phases of identical physical properties. In CBr₄-C₂Cl₆, the basic set of instabilities that limit steady-state growth is richer than expected. It consists of three primary instabilities, two of which are oscillatory, which bound the domain of the commonly observed axisymmetric lamellar morphology, and two secondary oscillatory instabilities, which bound the domain of the nonaxisymmetric (tilted) lamellar morphology. The latter is predicted to occur over a hypereutectic range of composition which coincides well with experiment. Moreover, the steady tilt bifurcation lies between but does not directly bound either of these two domains, which are consequently disjoint. Four stable oscillatory microstructures, at least three of which have been seen experimentally, are predicted to occur in unstable regimes. In the model alloy, the structure is qualitatively similar, except that a stable domain of tilted steady-state growth is not found, in agreement with previous random-walk simulations. Furthermore, the composition range of stability of the axisymmetric morphology decreases sharply with increasing spacing away from minimum undercooling but extends further off-eutectic than predicted by the competitive growth criterion. In addition, oscillations with a wavelength equal to two lead to lamella termination at a small distance above the onset of instability. The implications of these two features for the eutectic to dendrite transition are examined with the conclusion that in the absence of heterogeneous nucleation, this transition should be histeritic at small velocity and temperature gradient.

The Phase-Field Method: Simulation of Alloy Dendritic Solidification during Recalescence
WILLIAM J. BOETTINGER and JAMES A. WARREN
An overview of the phase-field method for modeling solidification is given and results for nonisothermal alloy dendritic growth are presented. By defining a "phase-field" variable and a corresponding governing equation to describe the state (solid or liquid) in a material as a function of position and time, the diffusion equations for heat and solute can be solved without tracking the liquid-solid interface. The interfacial regions between liquid and solid involve smooth, but highly localized variations of the phase-field variable and the composition. Simple finite-difference techniques on a uniform mesh can be used to treat the evolution of complex growth patterns. However, large-scale computations are required. The method has been applied to a variety of problems, including thermally driven dendritic growth in pure materials, solute-driven isothermal dendritic growth in alloys, eutectic growth (all at high supercoolings or supersaturations), solute trapping at high velocity, and coarsening of liquid-solid mixtures. To include thermal effects in solute-driven dendritic growth in alloys, a simplified approach is presented here that neglects the spatial variation of temperature in the computational domain but provides for changes with time and thus includes recalescence. Growth morphologies and solute patterns in the liquid and solid obtained for several values of an imposed heat flux are compared to results for isothermal growth.

Interface Attachment Kinetics in Alloy Solidification
MICHAEL J. AZIZ
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.

Effects of Shear Flow and Anisotropic Kinetics on the Morphological Stability of a Binary Alloy
S.R. CORIELL, B.T. MURRAY, A.A. CHERNOV, and G.B. McFADDEN
The effect of a parallel shear flow and anisotropic interface kinetics on the onset of instability during the directional solidification of a binary alloy at constant velocity is calculated. The model for anisotropy is based on the motion of steps. A shear flow (linear Couette flow or asymptotic suction profile), parallel to the crystal-melt interface in the same direction as the step motion, decreases interface stability in that the critical solute concentration decreases. A shear flow counter to the step motion enhances stability for small shear rates; for larger shear rates, the neutral curve develops a bimodal structure, and the critical solute concentration slowly decreases with shear rate.

Prediction of Grain Structures in Various Solidification Processes
M. RAPPAZ, Ch.-A. GANDIN, J.-L. DESBIOLLES, and Ph. THÉVOZ
Grain structure formation during solidification can be simulated via the use of stochastic models providing the physical mechanisms of nucleation and dendrite growth are accounted for. With this goal in mind, a physically based cellular automaton (CA) model has been coupled with finite element (FE) heat flow computations and implemented into the code 3-MOS. The CA enmeshment of the solidifying domain with small square cells is first generated automatically from the FE mesh. Within each time-step, the variation of enthalpy at each node of the FE mesh is calculated using an implicit scheme and a Newton-type linearization method. After interpolation of the explicit temperature and of the enthalpy variation at the cell location, the nucleation and growth of grains are simulated using the CA algorithm. This algorithm accounts for the heterogeneous nucleation in the bulk and at the surface of the ingot, for the growth and preferential growth directions of the dendrites, and for microsegregation. The variations of volume fraction of solid at the cell location are then summed up at the FE nodes in order to find the new temperatures. This CAFE model, which allows the prediction and the visualization of grain structures during and after solidification, is applied to various solidification processes: the investment casting of turbine blades, the continuous casting of rods, and the laser remelting or welding of plates. Because the CAFE model is yet two-dimensional (2-D), the simulation results are compared in a qualitative way with experimental findings.

An Adaptive Mesh Refinement Scheme for Solidification Problems
NAGENDRA PALLE and JONATHAN A. DANTZIG
Methods for adaptive mesh refinement, based on a quadtree data structure, have been developed with the specific objective of tracking solid/liquid front movement in two-dimensional solidification problems. These methods include mesh refinement and unrefinement algorithms for the finite element method applied to transient problems. An a posteriori error estimator is described to locate regions in the finite element mesh needing refinement. One- and two-dimensional example applications are given, showing how the methods can be used to resolve a moving solidification front and its associated boundary layer in binary alloy solidification.

TRANSFORMATION

₁ Plates from the ₃ Phase in a Cu-Zn-Au Alloy

TRANSPORT PHENOMENA

MECHANICAL BEHAVIOR

Mechanical Behavior and Properties of Mechanically Alloyed Aluminum Alloys
H.R. LAST and R.K. GARRETT, Jr.
The fracture and deformation behaviors of several product forms produced from mechanically alloyed (MA) aluminum alloys 9052 and 905XL were studied. The main operative strengthening mechanism is strengthening due to the submicron grain size. Ductility and toughness were found to be controlled by the morphology of the prior particle boundaries. We propose that the work-hardening behavior of these MA alloys is similar to the behavior exhibited by a deformed fcc alloy that (a) contains rigid barriers to dislocation motion, (b) deforms by wavy slip, and (c) forms a cell substructure upon deformation.

Effect of Carbide Precipitation on the Creep Behavior of Alloy 800HT in the Temperature Range 700°C to 900°C
E. EL-MAGD, G. NICOLINI, and M. FARAG
The creep behavior of alloy 800HT was studied at 700°C, 800°C, and 900°C under stresses ranging from 30 to 170 MPa. Samples that were tested in the as-quenched condition after solution treatment exhibited longer creep life than those that were overaged before testing. This difference in creep life was found to increase at lower creep stresses at a given temperature. This phenomenon is attributed to the precipitation of M₂₃C₆ carbides during the early stages of creep, which strengthen the material by exerting threshold stresses on moving dislocations and thereby reducing the creep rate. A model is developed to describe the influence of carbide precipitation during creep on the behavior of the material under different creep temperatures and stresses. Comparison with the experimental results shows that the model gives accurate predictions of the creep behavior of the material in the range of stresses and temperatures used in the present study. In addition to its predictive value, the model is useful in understanding the factors that affect the creep behavior of materials when precipitation of hard phases is taking place during creep. The strengthening effect of particle precipitation during creep, as represented by the value of the threshold stress, is shown to be a complex function of the supersaturation of the matrix, the applied creep stress, and the test temperature.

Effect of Thermal Cycling on the Mechanical Properties of 350-Grade Maraging Steel
U.K. VISWANATHAN, R. KISHORE, and M.K. ASUNDI
The effects of retained austenite produced by thermal cycling on the mechanical properties of a precipitation-hardened 350-grade commercial maraging steel were examined. The presence of retained austenite caused decreases in the yield strength (YS) and ultimate tensile strength (UTS) and effected a significant increase in the tensile ductility. Increased impact toughness was also produced by this treatment. The mechanical stability of retained austenite was evaluated by tension and impact tests at subambient temperatures. A deformation-induced transformation of the austenite was manifested as load drops on the load-elongation plots at subzero temperatures. This transformation imparts excellent low-temperature ductility to the material. A wide range of strength, ductility, and toughness can be obtained by subjecting the steel to thermal cycling before the precipitation-hardening treatment.

Communication: Discussion of "A Fully Plastic Microcracking Model for Transgranular Stress Corrosion Cracking in Planar Slip Materials"
M.J. KAUFMAN

WELDING & JOINING

Analysis of Heat-Affected Zone Phase Transformations Using In Situ Spatially Resolved X-Ray Diffraction with Synchrotron Radiation
J.W. ELMER, JOE WONG, M. FRÖBA, P.A. WAIDE, and E.M. LARSON
Spatially resolved X-ray diffraction (SRXRD) consists of producing a submillimeter size X-ray beam from an intense synchrotron radiation source to perform real-time diffraction measurements on solid materials. This technique was used in this study to investigate the crystal phases surrounding a liquid weld pool in commercial purity titanium and to determine the location of the phase boundary separating the high-temperature body-centered-cubic (bcc) phase from the low-temperature hexagonal-close-packed (hcp) phase. The experiments were carried out at the Stanford Synchrotron Radiation Laboratory (SSRL) using a 0.25 x 0.50 mm X-ray probe that could be positioned with 10-µm precision on the surface of a quasistationary gas tungsten arc weld (GTAW). The SRXRD patterns were collected using a position-sensitive photodiode array in a -2 geometry. For this probe size, integration times of 10 s/scan at each location on the specimen were found adequate to produce high signal-to-noise (S/N) ratios and quality diffraction patterns for phase identification, thus allowing real-time diffraction measurements to be made during welding. The SRXRD results showed characteristic hcp, bcc, and liquid diffraction patterns at various points along the sample, starting from the base metal through the heat-affected zone (HAZ) and into the weld pool, respectively. Analyses of the SRXRD data show the coexistence of bcc and hcp phases in the partially transformed (outer) region of the HAZ and single-phase bcc in the fully transformed (inner) region of the HAZ. Postweld metallographic examinations of the HAZ, combined with a conduction-based thermal model of the weld, were correlated with the SRXRD results. Finally, analysis of the diffraction intensities of the hcp and bcc phases was performed on the SRXRD data to provide additional information about the microstructural conditions that may exist in the HAZ at temperature during welding. This work represents the first direct in situ mapping of phase boundaries in fusion welds.

Effect of Homogenization Heat Treatment on the Microstructure and Heat-Affected Zone Microfissuring in Welded Cast Alloy 718
XIAO HUANG, M.C. CHATURVEDI, and N.L. RICHARDS
The effect of homogenization temperature on microfissuring in theheat-affected zones of electron-beam welded cast INCONEL 718 has been studied. The material was homogenized at various temperatures in the range of 1037°C to 1163°C and air-cooled. The homogenized material was then electron-beam welded by the bead-on-plate welding technique. The microstructures and microfissuring in the heat-affected zone (HAZ) were evaluated by analytical scanning electron microscopy (SEM). The grain boundary segregation of various elements was evaluated by secondary ion mass spectroscopy (SIMS). It was observed that the total crack length (TCL) of microfissures first decreases with homogenization temperature and then increases, with a minimum occurring in the specimen heat treated at 1163°C. This trend coincides with the variation in segregation of B at grain boundaries with homogenization temperature and has been explained by equilibrium and nonequilibrium segregation of B to grain boundaries during the homogenization heat treatment. No other element was observed to segregate at the grain boundaries. The variation in volume fraction of phases like -Ni₃Nb, MC carbide, and Laves phases does not follow the same trend as that observed for TCL and B segregation at the grain boundaries. Therefore, microfissuring in HAZ of welded cast INCONEL 718 is attributed to the segregation of B at the grain boundaries.

Influence of Chromium and Impurities on the Grain-Refining Behavior of Aluminum
A. ARJUNA RAO, B.S. MURTY, and M. CHAKRABORTY
The grain-refining behavior of high purity aluminum (HPAl) and commercial purity aluminum (CPAl) containing Fe and Si as impurities (<0.2 wt pct each) has been studied with and without the presence of Cr in small and large quantities (0.2 and 2 wt pct). The Al-5Ti-1B master alloy ingot (0.2 wt pct) was used as a grain refiner. The emphasis was on the influence of individual elements and their interactions with the other elements on the grain-refining behavior of Al. Good grain refinement with insignificant fading in CPAl was observed in comparison to HPAl. Similar results were obtained with a small concentration of Cr in HPAl in HPAl-0.2 wt pct Cr alloy. The CPAl and HPAl-0.2 wt pct Cr alloy have given the best grain-refining results among all the cases studied. A combination of small quantities of Fe, Si, and Cr (CPAl-0.2 wt pct Cr) has shown early and significant fading. A large concentration of Cr (2 wt pct) has shown a poisoning effect irrespective of the presence or absence of impurities such as Fe and Si in Al. Thus, Cr was found to be beneficial for grain refinement at smaller concentrations in the absence of impurities. But at higher concentrations of Cr, it had an adverse effect, i.e., led to coarser grain sizes both in the presence and absence of impurities.

SOLIDIFICATION

COMPOSITE MATERIALS