Matthew John M. Krane

Transport Phenomena and Microstructural Development

During Materials Processing

The main thrust of my research is the study of materials processing at the micro- and macroscale.  This research focuses on the prediction of macroscopic transport phenomena as well as microstructure development during processing of materials.  The main tool we use for understanding materials behavior during processing is numerical simulation.  A careful integration of predictive models that describe the multiscale phenomena dominating the development of microstructure is necessary to advance the fundamental science and practice of materials processing. The results of these predictions are compared to results from bench top experiments and tests performed in industrial settings.  

Much of the work done in this group has concerned phase changes during processing.  From a microscopic point of view, a solidification problem is one of understanding the growth of several solid phases from a liquid, which most often occurs by the growth of microscopic dendritic structures. The morphology, the crystal structure, and the freezing/melting behavior of those dendrites and the mass diffusion fields around them have significant influence on the properties of the final cast part. The predictions of these structures and the solid-solid phase changes during laser heating or more traditional heat treatments on new alloys are all topics of current research. 

The macroscopic transport phenomena (heat/mass transfer, fluid mechanics) during processing is also of great interest.  Gradients of temperature and composition (and electromagnetic effects) can drive fluid flow in liquid metal processing, which gives rise to columnar-to-equiaxed transitions in the grain structure and defects such as macrosegregation.  Predictions of such effects, as well as the transient shape of the solid-liquid interface, time to complete freezing, and interactions with the developing microstructure, aid in understanding the complicated physics of solidification and in diagnosing problems in processing and suggesting solutions.
Some specific areas of interest are:

Solidification Defects in Electroslag Remelting of Ni-Based Superalloys

The challenge in this project is to understand and predict formation of segregation defects in electroslag remelting (ESR) of Ni superalloys in order to define defect-free processing windows. We are studying the formation of segregation defects in ESR with physical and computational models of the transport phenomena and solidification behavior of Ni-based superalloys.

The model of the basic transport phenomena in ESR is complete, including Joulean heating in the slag, AC current through the ingot and slag, multicomponent solidification, and fluid flow. The model predicts correctly trends in centerline and surface segregation as function of radius and melt rate.


Funding: Office of Naval Research, GAANN.

Electroslag remelting: (a) Schematic of process. (b) Final distribution of molybdenum mass fractions for three Ni-25 Mo-8 Cr (approximately Haynes 242 alloy) ingots of different radii with filling velocities near 0.50 m/hr: R = 10 cm, 20 cm, and 30 cm (left to right).
(c) Molybdenum composition and liquid pool shape development in R = 20 cm ingot at 500 kg/hr.
Electroslag remelting: (a) Schematic of process. (b) Final distribution of molybdenum mass fractions for three Ni-25 Mo-8 Cr (approximately Haynes 242 alloy) ingots of different radii with filling velocities near 0.50 m/hr: R = 10 cm, 20 cm, and 30 cm (left to right). (c) Molybdenum composition and liquid pool shape development in R = 20 cm ingot at 500 kg/hr.

Modeling of Dendrite Development Using a Modified Cellular Automaton (CA) (with Prof. David Johnson and Kevin P. Trumble)

The model used here is a coupled cellular automata (CA)-finite volume procedure. The CA governs the growth of the solid phases, and is followed by the simulation of the mass diffusion. As growth of the solid phase occurs, nonuniform compositional fields are formed in the liquid and solid due to the solute partitioning and rejection into the liquid. Subsequent solute diffusion in the liquid and the solid is predicted by the solution of the species conservation equation in two dimensions using an implicit finite volume method.
Careful study of the behavior of the CA and its interaction with the diffusion model has led us to the prediction of ranges of grid spacing and time step that can be used in these simulations. These ranges are functions of alloy properties and process parameters and are used to find numerical parameters that will give a stable and physically realistic morphology. Some results from this model are seen below.


Funding: NASA, Indiana 21st Century Fund

Pb-5wt%Sn dendrite
Pb-5wt%Sn dendrite, cooled by a constant heat transfer coefficient boundary at the bottom. Blue indicates solid region, while the shading shows liquid composition.  (from R. Shao, PhD dissertation, School of Materials Engineering, Purdue University, August 2007)

Animation of solid morphology and liquid composition during growth of a dendrite (11MB .AVI)

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Macrosegregation in Vacuum Arc Remelting of Titanium Alloys

Vacuum arc remelting (VAR) is a semi-continuous process widely used to improve the cleanliness and refine the structure of ingots of specialty steels, superalloys and Ti based alloys. The process is performed in vacuum via melting the consumable electrode and collecting the solidifying metal in a water cooled copper crucible. The heat required for remelting is released by an electric arc between the consumable electrode and liquid metal. The solidifying liquid metal in the crucible is affected by electromagnetic and buoyancy forces resulting in the formation of flow patterns which penetrate the mushy zone and result in ingot scale macrosegregation. Macrosegregation compromises the quality of produced ingots and leads to formation of many types of defects, including beta fleck in Ti-10V-2Fe-3Al.

Schematic of VAR process
Schematic of VAR process

Macrosegregation is the result of two physical phenomena: solute partitioning and fluid flow. Partitioning by itself results in a microscale redistribution of solute between solid and liquid phase at the solid-liquid interface during alloy solidification. However, it is the fluid flow that transports the interdendritic liquid out of the mushy zone and replaces it with fluid of a different composition. This solute advection is the prime cause of macrosegregation.

The flow in the pool during VAR is mostly determined by buoyancy and electromagnetic forces. Density differences caused by nonuniform liquid composition and temperature give rise to the buoyancy force. The electromagnetic (Lorentz) force is a result of the strong electrical current passing through the liquid pool. At low values of arc current the Lorentz force is weak, and the flow is dominated by buoyancy forces, but, as the arc current increases, the strength of electromagnetic force increases as well, resulting its domination of pool flow.

In case of Ti-10-2-3 alloy, the solutal buoyancy is relatively weak, and, at lower powers, the thermal buoyancy forms a clockwise flow cell. Hot liquid at the top of the pool is cooled by the water-cooled crucible, and moves downward along the liquidus interface (seen below as the fraction solid = 0.01 line). At higher powers, the Lorentz force acts across the liquid pool pushing the liquid from the surface downward along the centerline of the ingot, displacing the cold liquid from the bottom of the pool upward along the liquidus interface. So a higher current leads to a change in the flow regime and flow cell direction.

Funding: Specialty Metals Processing Consortium, Purdue Research Foundation

Streamlines in liquid pool during VAR


Streamlines in liquid pool during VAR at (a) low power, with a clockwise, thermally driven flow cell, and (b) high power, with a counterclockwise, Lorentz driven flow cell. The centerline of the cylindrical ingots is on the left and the metal is cooled from the bottom and the right. (from D. Zagrebelnyy, PhD dissertation, School of Materials Engineering, Purdue University, May 2007).

Final Fe macrosegregation patterns in VAR of Ti-10-2-3


Final Fe macrosegregation patterns in VAR of Ti-10-2-3. Steady state current is: (a) 15 kA, (b) 20 kA, (c) 26 kA, and (d) 39 kA. Cases (a) and (b) are from buoyancy dominated flows, while cases (c) and (d) are driven primarily by electromagnetic forces. (from D. Zagrebelnyy, PhD dissertation, School of Materials Engineering, Purdue University, May 2007).

 

Beta transus temperatures for Ti-10-2-3 ingots above


Beta transus temperatures for Ti-10-2-3 ingots above. Steady state current is: (a) 15 kA, (b) 20 kA, (c) 26 kA, and (d) 39 kA. (from D. Zagrebelnyy, PhD dissertation, School of Materials Engineering, Purdue University, May 2007).

Animation of transient sump profile, streamlines, and Fe composition (I=26kA) (4.5MB .AVI)

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Solidification Microstructure in Metal Matrix Composites (with Prof. Kevin P. Trumble)

A potential method for producing selectively reinforced, single crystal superalloy castings was investigated. Porous particulate alumina preforms were infiltrated with liquid Ni-based superalloy CMSX-4 under a gas pressure of 1 atm, and then the alloy was solidified directionally through the preform at different rates. Optical microscopy and Laue X-ray diffraction showed that the orientation of the metallic grains was unaffected by the preform and no stray grains were nucleated there. In the particular experimental configuration, single grain orientations (i.e. single crystals) were achieved at cooling rates ~ 15oC/min. Furthermore, the microsegregation pattern in the composite region showed that the alloy solidified from the center of the interstices toward the alumina particles, further indicating that nucleation did not occur on the preform. Microsegregation in the composite region is lower than in the unreinforced regions due to geometric confinement of solidification in the narrow spaces between the ceramic particles. Predictions of dendritic development in metal matrix composites is a topic of ongoing research.  For this work, we are using the CA-FV model shown above.


Funding: Indiana 21st Century Fund, NSF

The alloy-composite interface of the sample cooled at 30 o C/min
 

The alloy-composite interface of the sample cooled at 30o C/min showing that when interparticle space is greater than the dendritic arm spacing structure forms. (from Shao et al., Metall. Mater. Trans. A, 36A, pp. 2461-2469, 2005)

Dendrite morphology of growth in 500 ?m channels


Dendrite morphology of growth in 500 ?m channels: (a) 16.9 s (b) 17.6 s (c) 20.0 s (d) 23.5 s (e) 26.0 s (f) 28.0 s (g) 36.5 s (h) 208.4 s. Figure (a)-(e) show the concentration field, and (f) shows the final microstructure at the eutectic temperature. (from R. Shao, PhD dissertation, School of Materials Engineering, Purdue University, August 2007).

Animation of dendrite growth (200K .AVI)

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Selected Referred Journal and Proceedings Articles

D. Zagrebelnyy and M. J. M. Krane, “Segregation development in multiple melt vacuum arc remelting,” accepted for Liquid Metal Processing and Casting, P. D. Lee and A. Mitchell (eds.) (2007).

I. Vušanovic and M. J. M. Krane, “Macrosegregation in horizontal direct chill casting (HDC) of aluminum binary alloys billets- influence of casting parameters,” accepted for Solidification Processing 07, H. Jones et al. (eds.) (2007).

S. A. Cefalu and M. J. M. Krane, “Comparison of predictions of microsegregation in the Ni-Cr-Mo system to experimental measurements,”, Mat. Sci. & Engr. (A), 454-455, pp. 371-378 (2007).

H. J. Kim, M. J. M. Krane, K. P. Trumble, and K. J. Bowman, “Analytical fluid flow models for tape casting,”  J. Amer. Cer. Soc., 89, pp. 2769–2775 (2006).

M. J. M. Krane, S. A. Cefalu, D. Zagrebelnyy and K. J. VanEvery, “Segregation development in electroslag remelting processes,” Modeling of Casting, Welding and Advanced Solidification Processes - XI, Ch.-A. Gandin, M. Bellet and J. Allison (eds.), TMS (2006).

R. Shao, K. P. Trumble, and M. J. M. Krane, “Infiltration and directional solidification of CMSX-4 through a particulate ceramic preform,” Metall. Mater. Trans. A, 36A, pp. 2461-2469 (2005).

I. Vušanovi?, B. Šarler and M. J. M. Krane, “Microsegregation during the solidification of an Al–Mg–Si alloy in the presence of  back diffusion and macrosegregation,” Mat. Sci. & Engr. (A), 413-414, pp. 217-222 (2005).

M. J. M. Krane, “Macrosegregation development during solidification of a multicomponent alloy with free-floating solid particles,” Appl. Math. Modelling, 28, pp. 95-107 (2004).

S. A. Cefalu, K. J. VanEvery, and M. J. M. Krane, “Modeling of electroslag remelting of Ni-Cr-Mo alloys,” in Multiphase Phenomena and CFD Modeling and Simulation in Materials Processing, L. Nastac and B. Q. Li (eds.), TMS, pp. 279-288 (2004).

S. Raghavan, D. R. Johnson, and M. J. M. Krane, “A cellular automaton for growth of solutal dendrites: Factors influencing grid dependent orientation,” in Solidification Processes and Microstructures: A Symposium in Honor of Prof. Wilfried Kurz, M. Rappaz, C. Beckermann, and R. Trivedi (eds.), TMS, pp. 413-418 (2004).

S. A. Cefalu and M. J. M. Krane, “Microsegregation in ternary alloys solidifying in an open system,” Mat. Sci. & Engr. (A), A359, pp. 91-99 (2003).

S. Raghavan, D. R. Johnson, and M. J. M. Krane, “Different rule sets for cellular automata modeling of peritectic dendritic growth,” in Modeling of Casting, Welding and Advanced Solidification Processes - X, D. Stefanescu, J. Warren, M. Jolly and M. Krane (eds.), TMS, pp. 107-114 (2003).

C. W. Seager, K. Kokini, K. P. Trumble, and M. J. M. Krane, “The influence of CuAlO2 on the strength of eutectically bonded copper/alumina interfaces,” Scripta Materialia, 46, pp. 395-400 (2002).

C. J. Vreeman, J. D. Schloz, and M. J. M. Krane, “Direct chill casting of aluminum alloys: Modeling and experiments on industrial scale ingots,” ASME J. Heat Transfer,124, pp. 947-953  (2002).

C. J. Vreeman, M. J. M. Krane and F. P. Incropera, “The effect of free-floating dendrites and convection on macrosegregation in direct chill cast aluminum alloys.  Part I:  Model development,” Int. J. Heat Mass Transfer,  43, pp. 677-686 (2000).

M. J. M. Krane, F. P. Incropera and D. R. Gaskell, “Solidification of ternary metal alloys:  A comparison of experimental measurements and model predictions in a Pb-Sb-Sn system,” Metallurgical and Materials Transactions A, 29A, 843-853 (1998).

M. J. M. Krane and F. P. Incropera, “Solidification of ternary metal alloys.  Part II:  Predictions of convective phenomena and solidification behavior in Pb-Sb-Sn alloys,” Int. J. Heat Mass Transfer, 40, 3837-3847 (1997).

M. J. M Krane, F. P. Incropera and D. R. Gaskell, “Solidification of ternary metal alloys.  Part I:  Model development,” Int. J. Heat Mass Transfer, 40, 3828-3835 (1997).

M. J. M. Krane and F. P. Incropera, “A scaling analysis of the unidirectional solidification of a binary alloy,” Int. J. Heat Mass Transfer, 39, 3567-3579 (1996).

R. J. Krane and M. J. M. Krane, “The optimum design of stratified thermal energy storage systems.  Part I:  Development of the basic analytical model,” ASME J. Energy Res. Tech., 114, 197-203 (1992).

R. J. Krane and M. J. M. Krane, “The optimum design of stratified thermal energy storage systems. Part II:  Completion of the analytical model, presentation and interpretation of the results,” ASME J. Energy Res. Tech., 114, 204-208 (1992).

Selected Conference Presentations

D. Zagrebelnyy and M. J. M. Krane, "Transient Conditions in VAR of Ti-10-2-3 and Their Impact on Macrosegregation," in symposium on "Materials Processing under the Influence of External Fields," 2007 TMS Annual Meeting, Orlando, FL (2/07).

M. J. M. Krane, N. Green, and M. Jolly, "Processing effects on the solidification microstructures in the constrained geometry of a metal matrix composite," in symposium on "Advanced Metallic Composites and Alloys for High Performance Applications," 2007 TMS Annual Meeting, Orlando, FL (2/07).

K. J. VanEvery, M. J. M. Krane, and R. Trice, "Parametric study of suspension plasma spraying," in symposium on "TBCs: Advanced Manufacturing Processes and New Compositions,", Cocoa Beach 2007, Daytona Beach, FL (1/07).

K. J. VanEvery, M. Krane, and R. Trice, "An investigation of the processing parameters for suspension spraying," in symposium on "Surface Protection for Enhanced Materials Performances," Materials Science & Technology 2006, Cincinnati, OH (9/06).

Invited Talk: M. J. M. Krane, "Modeling transport phenomena in remelting processes," in symposium on "Process Modelling & Simulation Using Computational Techniques," Materials Congress 2006, London, UK (4/06).

Invited Talk: M. J. M. Krane, S. A. Cefalu, K. J. VanEvery, and D. Zagrebelnyy, "Transport phenomena and macrosegregation in VAR and ESR," in symposium on "Materials Design Approaches and Experiences II," 2006 TMS Annual Meeting, San Antonio, TX (3/06).

T. Morillon, M. Dayananda, and M. J. M. Krane, "Predictions of secondary phase dissolution during heat treatment of a Ni-Cr-Mo alloy," in symposium on "Modeling Heat Treating Processes," ASM Heat Treating Society Conference and Exposition, Pittsburgh, PA (9/05).

K. J. VanEvery and M. J. M. Krane, "Predictions of segregation related defects in vacuum arc remelting of titanium alloys," in symposium on "Materials Processing Fundamentals," 2005 TMS Annual Meeting, San Francisco, CA (2/05).

S. A. Cefalu, K. VanEvery and M. J. M. Krane, "Modeling the electroslag remelting of Ni-8 Cr-25 Mo alloy," in symposium on "CFD Modeling and Simulation of Materials Processes," 2004 TMS Annual Meeting, Charlotte, NC (3/04).

K. VanEvery, D. Zagrebelnyy, S. Cefalu, and M. J. M. Krane, "Predictions of segregation related defects in vacuum arc remelting of titanium alloys," in symposium on "Control of Melt-Related Defects in High-Temperature Alloys," 2003 TMS Fall Meeting, Chicago, IL (11/03).