~~~ ~ ~ ~~ 

NASA Contractor Report 42 5 3 

Rapidly Solidified Titanium 

Alloys by Melt Overflow 

Thomas A. Gaspar, Thomas J. Bruce, Jr., 

and Lloyd E. Hackman 

Ribbon Technology Corporation 

Gahanna, Ohio 

Susan E. Brasmer and Jonathan A. Dantzig 

University of Illinois 

Urbana, Illinois 

William A. Baeslack I11 

The Ohio State University 

Columbus, Ohio 

Prepared for 

Langley Research Center 

under Contract NAS1-18288 

National Aeronautics and 

Space Administration 

Office of Management 

Scientific and Technical 

Information Division 

1989 
Executive Summary 

I A promising new technique for direct casting titanium 

ribbons for use in honeycomb structures emerged from this 

project. Our research demonstrated the feasibility of direct , casting Ti-6A1-4V alloy strip and Ti-14A1-21Nb alloy strip by 

combining plasma arc melting techniques with melt overflow rapid 

solidification technology. 

I 

, Ribtec designed and constructed a pilot plant-scale plasma 

melt overflow furnace to demonstrate the feasibility of casting 

titanium alloy ribbons. A rotatable hearth was invented for 

overflowing liquid titanium from the copper hearth onto the chill 

block to cast strip. The rotating hearth technique proved to be 

superior to a tilting hearth and a patent application was filed 

on the invention. 

I 

Over 64 experiments were performed to cast ribbons from CP 

titanium, Ti-6A1-4V alloy, and Ti-14A1-21Nb alloy. Evaluation of 

the direct cast strip shows a martensitic microstructure in Ti6A1-4V alloys and a fine acicular transformed structure in Ti14A1-21Nb alloys. The solid state cooling rate was estimated at 

40 C/s to 300 C/s based on microhardness measurements. 

The oxygen content of the Ti-14A1-21Nb increased only 340 

ppm after a single remelting. The loss of aluminum after 

remelting Ti-14A1-21Nb alloy was about 6% but it can be compensated for by sacrificial alloying. The aluminum and vanadium 

levels in Ti-6A1-4V alloy tended to fall after repeated 

remelting. 

The plasma melt overflow furnace is limited by melting 

capacity. It is anticipated that further improvements can be 

made to the direct cast strip by increasing melting capacity; by 

increasing the solid state cooling rate of the strip through 

belts, rolls, or forced convection cooling; by sacrificial 

alloying to maintain alloy chemistry levels; by working and 

conditioning the strip.after casting; and by refining the hearth 

design and operation. 
Introduction 

I This contract was awarded under Phase I1 of the NASA Small 

I Alloys by Melt Overflow" (NASA Contract NAS1-17978), successfully 

Business Innovation Research (SBIR) Program. The Phase I SBIR 

research program, entitled "Rapid Solidification of Low Density 

I demonstrated the feasibility of casting rapidly solidified 

aluminum alloys, magnesium alloys, and titanium alloys by the 

I melt overflow process in a series of laboratory-scale experiments. The Phase I1 project focused on the melting of titanium 

I alloys and casting them into strip. 

I 

Ribtec's melt overflow process involves the transfer of 

liquid metals and alloys from a molten reservoir onto the surface 

of a rotating chill block (Figure 1). Unlike conventional melt 

spinning techniques, the melt is not extruded through an orifice; 

rather, the molten material flows over a solid surface from a 

molten reservoir until it comes in contact with a moving chill 

surface. Rapidly solidified foils, fibers, flakes, filaments, 

strips, and particles are among the products that can be cast 

directly by melt overflow. In general, the final product form 

depends on the geometry of the casting surface. 

The Phase I1 project objective was to demonstrate the 

feasibility of casting 5 cm (2 in) wide titanium alloy strip 

suitable for use in honeycomb structures. Continuous strips 

2.4 m (8 ft) long and 0.125 mm (0.005 in) thick were requested. 

In order to demonstrate the feasibility of casting titanium alloy 

strip by melt overflow, a pilot-plant furnace was designed and 

constructed. Titanium alloys were melted by transferred plasma 

arc skull melting techniques under inert atmosphere. 

The Phase I1 research project was organized into seven 

different tasks. These seven tasks were: 

Task 1 - Design/Physical Modeling 

Task 2 - Mathematicgl Modeling 

Task 3 - Evaluate Plasma Arc Melting 

Task 4 - Construct Plasma Melt Overflow System 

Task 5 - Processing Experiments 

Task 6 - Microstructural Evaluation 

Task 7 - Process Evaluation 

Each task will be reviewed separately. 

Desiqn/Physical Modelinq 

Ribtec's original concept for direct casting titanium alloy 

strip combined transferred plasma arc melting with melt overflow 

casting. Titanium alloys were melted in a water-cooled copper 

3PRECEDlNG PAGE BLANK NOT FILMED 
hearth. The liquid titanium solidified against the inner wall of 

the hearth to form a skull in which the liquid reservoir was 

contained. All melting was performed at atmospheric pressure in 

an inert environment. 

The plasma was created by ionizing a gas in an electric arc 

that was established between the torch and the melt pool. The 

gases used for melting titanium were argon and helium. The 

plasma arc stream consisted of ions, electrons, and superheated 

gas molecules which could reach temperatures of 10,OOO"C or 

greater. The plasma torch needed to be manipulated to distribute 

the heat across a large surface for melting. 

In combining plasma melting techniques with the melt 

overflow casting process, a novel system was invented for 

rotating the copper hearth about the chill block to achieve melt 

overflow. A U.S. patent application has been filed on the 

invention. 

The plasma melt overflow system was physically modeled 

during experiments to cast lead in air on a copper chill block. 

We used an oxygen-acetylene torch for melting. Several different 

ribbon collection systems that employed continuous stainless 

steel belts or steel rolls for directing the strip were 

evaluated. 

A book of drawings of the.plasma melt overflow furnace was 

delivered to NASA with the Interim Report dated July 30, 1987. 

The detailed design of the plasma melt overflow system involved 

several different subsystems: electrical, hydraulic, water 

cooling, environmental, plasma skull melting, and melt overflow 

casting. 

Figure 2 shows a drawing of the plasma melt overflow furnace 

(from Ribtec assembly drawing No. 202-A-001) designed and 

constructed under this contract. The plasma melt overflow unit 

was designed for flexibility in conducting the processing 

experiments. The front door of the process chamber opened to 

expose a steel rack. The rack could be fully extended and 

carried a one-ton load. The water-cooled copper hearth and 

chill block assembly were mounted on the rack. Full extension of 

the rack allowed the easier removal of the hearth and chill 

block. Most maintenance was performed outside the process 

chamber. 

The plasma torch was mounted on a ball on the top of the 

furnace. The torch was manipulated in the X-Y and Z axes using 

hydraulic actuators. A crane operated over the furnace for 

removal of the plasma torch, chill block, hearth, or other 

massive components. The bottom door of the vessel opened to 

remove the cast strip. 

.7 . - ~ _. 4 ';. 
The three-piece hearth was composed of a water-cooled lip 

and two-piece melting cavity. The lips and inserts were machined 

from copper blocks and attached to the hearth. This allowed us 

to examine different lip geometries during the processing experiments. 

I 

The furnace design allowed for expansion of the furnace 

capabilities. These expanded capabilities may include, but are I not limited to, the following: 

a meltstock feed system 

additional viewports 

automated ribbon collection 

additional melting capability 

Mathematical Modelinq 

A mathematical model of the plasma melt overflow process was 

developed at the University of Illinois by Susan Brasmer and 

Professor Jonathan Dantzig. The model uses a commercial finite 

element code FIDAP run on a Sun 3/280 computer with some 

additional work done on a Silcon Graphics Iris 3020 work station. 

I The solution process consisted of four major sections. 

First, a velocity solution was obtained, assuming constant 

temperature and a fixed ribbon thickness. This solution was then 

used as an initial estimate for the next solution, where the 

temperatures were assumed constant, but the ribbon thickness was 

computed. Next, the first solution was used as an initial 

estimate for an advection-diffusion solution to a thermal problem 

to obtain an estimate for the temperature field. Finally, the 

advection-diffusion solution and the free surface solution were 

used as a starting point for the fully coupled velocity and 

temperature solutions. Laminar flow of the fluid was assumed 

throughout the solution. process. Each section of the solution 

procedure and results are described in detail in Susan Brasmer's 

thesis presented in Appendix A. 

The model solutions found that the viscosity of the liquid 

titanium and the velocity of the rotating chill wheel have the 

greatest influence on the velocity profile in the melt and the 

thickness of the resulting ribbon. Surface tension and the 

material depth on the pouring lip also influenced the velocity 

solutions. 

The chill wheel velocity affected the thickness of the 

ribbon in much the same manner as viscosity. For a constant 

viscosity, a high velocity value created a thin ribbon and 

decreasing the velocity increased the ribbon thickness. The 

similarity in the effects of viscosity and velocity makes sense 

5 
when one realizes that when the governing equations are nondimensionalized, the parameter which appears is the capillary 

number, Ca = pU/a, where: 

Ca [=] Capillary Number 

p [=] Viscosity 

U [=] Casting Speed 

a [=] Surface Tension 

The effect of capillary number on ribbon thickness is shown 

in Figure 3. Increasing velocity or viscosity increased the 

capillary number and resulted in a thinner ribbon. Similarly, 

decreasing surface tension increased the capillary number and 

also resulted in a thinner ribbon. 

The location and intensity of the torch also influenced the 

solidification of the ribbon. Raising the intensity or moving 

the torch closer to the ribbon raised the temperature of the melt 

in the ribbon and delayed solidification. The torch was modeled 

as a Gaussian distribution with a power of 75 kW. 

The results indicate that the thickness of the ribbon is 

dependent on the capillary number of the fluid and is determined 

by the shape of the meniscus before the ribbon solidifies. 

Results from the model indicate that the most practical way to 

change ribbon thickness is to change the velocity of the chill 

block since both viscosity and surface tension, the other 

factors that determine the capillary number, are difficult to 

change for a given material. 

Plasma Arc Meltinq 

The titanium alloys were melted in a water-cooled copper 

hearth using a transferred plasma arc. The goal of the plasma 

melting experiments was to produce a 2.25 kg (5 lb) melt pool 

suitable for casting strip by melt overflow. 

Successful operation of the plasma arc melting system 

presented the greatest challenge in successful completion of the 

research project. Numerous hardware problems were encountered in 

all components: the DC power supplies; the control console; the 

plasma torch; and the water-cooled copper hearth. Solutions were 

found for each of these problems, allowing titanium strip to be 

cast by melt overflow. 

The control circuits of the DC power supplies were not 

properly wired resulting in one power supply providing maximum 

output while the second power supply provided minimum output. 

Combining the outputs of both power supplies, in series or in 

parallel, resulted in large current fluctuations and unsteady 

6 
torch operation. After the control circuits were rewired, we 

were able to obtain power to melt sufficient quantities of 

titanium to cast into strip. 

The operation of the hollow anode plasma torches has been 

disappointing in that we have never achieved a 2.25 kg (5 lb) 

titanium melt pool for casting strip. Our first experiments used 

an argon plasma and produced a small volume of liquid titanium, 

roughly 10 cm (4 in) diameter and 1 cm (0.4 in) deep. We 

switched from an argon plasma to a helium plasma to achieve a 

larger melt pool. 

The thermal conductivity of helium is an order of magnitude 

greater than the thermal conductivity of argon at room temperature, and it increases faster with increasing temperature. The 

voltage of a helium plasma is 25% to 50% higher than for argon 

plasma at comparable stand-off distances. This increases the 

energy available for melting. Power levels of 70 kVA to 100 kVA 

were typical for helium plasma melting experiments. The use of 

a pure helium plasma increased the size of the melt pool to 

roughly 17.5 cm (7 in) diameter by 1 cm (0.4) deep which 

represents approximately 1.2 kg (2.5 lb) of liquid titanium. The 

1.2 kg (2.5 lb) melt capacity limits the width of the cast strip 

to approximately 5 cm (2 in) maximum if a significant length of 

strip is to be cast. 

The water-cooled copper hearth that was delivered from the 

manufacturer was unsuitable for use with melt overflow. We 

redesigned the hearth, making it 10 cm (4 in) shorter and 

completely changed the lip geometry. The design that worked best 

used a U-shaped copper block at the front of the hearth. Heat 

extracting copper inserts were bolted into the U-shaped slot to 

reduce the width of the slot. Liquid titanium overflowed the 

slot to cast strip. 

We monitored the water temperature in the plasma torch, 

copper hearth, and in a water-cooled copper chill block during 

experiments to cast Ti-6A1-4V alloy strip. The measurements were 

made with Type K thermocouples recorded on a Burr Brown PCI 

20,000 Data Acquisition System installed in a personal computer. 

The water temperature was plotted as a function of time for the 

plasma torch and hearth (Figure 4). The temperature of the 

cooling water in the plasma torch jumped 20°C after the arc was 

initiated, indicating that a significant amount of 12R heat was 

dissipated in the torch. The cooling water temperature increased 

more gradually above 4OoC, probably due to radiation heat 

transfer from the titanium melt pool. The cooling water 

temperature in the torch plummeted from 45°C to 22°C after the 

torch current was turned off. The hearth cooling water temperature increased linearly with a 6°C total increase recorded 

during the experiment. 

7 
Construct Plasma Melt Overflow System 

The components of the plasma melt overflow system were 

integrated and assembled at Ribtec in a laboratory dedicated to 

photograph of assembled plasma melt overflow furnace is shown in 

Figure 5. The construction of the plasma melt overflow furnace 

was completed in February 1988. 

the production of titanium and other advanced materials. A 

The integration of the different system components resulted 

in the following furnace operating procedure: 

1. Clean tundish (anode of plasma circuit) and 

ensure adequate electrical continuity between 

tundish and negative side leads. 

2. Check chill block rotation, tundish tilting 

mechanism, and other mechanicals. Check torch 

nozzle for obstructions. Check cooling water 

flow, hydraulics, and vacuum pumps. 

3. Add melting charge to tundish. 

4. Position torch tip 0.25 to 0.50 in (0.635 cm 

to 1.270 cm) from melt charge. 

5. Seal and evacuate chamber. 

6. When pressure in chamber has reached the 

desired vacuum, about 30 to 35 microns of Hg, 

turn off vacuum pumps. 

7. Turn on gas (Ar) supply and vent chamber with 

argon to atmospheric pressure. 

8. Turn on torch helium gas supply and regulate 

the plasma gas flow and pressure for arc start. 

The pressure and flow rates are 30 psi and 8 

scfm, respectively, for helium plasma. 

9. Turn on water, hydraulics, and main torch power 

supply. Make visual check of all interlocks 

for safety. 

10. Check open circuit voltage on main torch power 

supply 

11. Depress arc start button which automatically 

initiates pilot arc then transfers arc to the 

water-cooled hearth. 

8 
12. Reset torch gas flow and pressure to match 

manufacturer's current setting. 

13. Start chill block rotation and melt charge. 

14. When a sufficiently large melt pool is 

achieved, tip tundish and raise torch simultaneously without extinguishing arc to cast 

strip material. 

15. Extinguish plasma torch arc and turn off plasma 

gas supply. 

16. Evacuate the chamber. 

17. Open chamber and remove skull and cast 

material. 

Processins Experiments 

Sixty-four (64) experiments were performed to direct cast 

titanium strip in the plasma melt overflow furnace. Ti-6A1-4V 

alloy, Ti-14A1-21Nb alloy, and CP titanium were cast into strip. 

All of the casting experiments were performed on a knurled 

molybdenum solid substrate. Experiments performed at Ribtec have 

shown that molybdenum is an excellent substrate for casting both 

Ti-6A1-4V alloy and Ti-14A1-21Nb alloy. A pure helium plasma 

was used for melting the titanium alloys. 

Table I presents the physical dimensions of the strip cast, 

the alloy compositions, and the casting speed. The width and 

length of strip cast by plasma melt overflow appear to be 

suitable for use in honeycomb structures. However, the thickness 

of the cast strip varies from experiment to experiment and across 

the length and width of the strip for a single experiment. 

The process parameters that appear to have the greatest 

influence on the width of the cast strip are the crucible skull 

thickness, the hearth pour rate, the substrate speed and surface 

condition, and the physical properties of the liquid (viscosity 

and surface tension). Variations in the skull thickness at the 

pouring lip produces variations in melt depth against the chill 

block. In extreme cases, the liquid will solidify against the 

side walls of the pouring lip, thereby reducing the width of cast 

strip. The pour rate must be fast enough to supply liquid to 

completely fill the pour lip in order to cast full width strip. 

Defects on the substrate surface or excessive casting speed can 

result in narrowing of the cast strip. These effects are 

governed by the physical properties of the liquid being cast. 

9 
The process parameters that appear to have the greatest 

influence on the thickness of the cast strip are the casting 

speed, the depth of liquid in contact with the substrate, and the 

physical properties of the liquid (viscosity and surface 

tension). Two factors that influence the melt depth are the rate 

at which the hearth rotates about the chill block to overflow the 

liquid titanium on the moving substrate and the amount of 

superheat of the liquid. The tilt of the hearth is constant 

during each experiment but the volume of liquid being poured can 

vary depending on the geometry of the hearth and skull. The 

superheat varies from the liquidus temperature at the skull 

interface to the maximum temperature at the region the plasma arc 

stream contacts the surface. 

The mean thickness of the as-cast plasma melt overflow 

strip is plotted against capillary number in Figure 6. The 

capillary number is a dimensionless parameter which takes the 

viscosity (p), surface energy (a), and casting speed (U) into 

account. Figure 6 also presents the computed thicknesses from 

the mathematical model developed at the University of Illinois. 

The curves represent "best-fit" power series of the computed and 

experimental values. If the mathematical model is valid, the 

depth of liquid in contact with the chill block is less than 

4 mm. If the experimental data are fitted to the power series 

t = 270.557 + 2001.682 exp (-250 Ca), it suggests a melt depth of 

1 mm. 

The mathematical model agrees quite closely with the 

experimental data. There are few as-cast strip thickness values 

that fall below the zero depth curve in Figure 6. The model 

predicted slightly thicker titanium strip than was achieved 

experimentally, but the experimental values generally fall within 

the range calculated by the model. 

The depth of liquid in contact with the rotating chill block 

was not measured; therefore, we cannot compare the melt depth to 

those predicted by the mathematical model in Figure 6. We are 

not aware of any noncontacting technique for measuring the depth 

of the liquid titanium. Immersible probes may be used to measure 

melt depth with the risk of contamination of the titanium melt 

pool. If the immersed probe is heat extracting, the precision of 

the measurement would be low because of skull formation on the 

probe itself. If the level of the liquid changes with time, 

several probes would need to be immersed in sequence. The 

mathematical model was, therefore, useful in estimating values 

where measurements are difficult or impossible to make. 

Experiments were also performed to cast Ti-6A1-4V alloy 

strip on a water-cooled copper chill block. Figure 7 shows the 

temperature of the cooling water in the plasma torch and in the 

water-cooled chill block. The torch was turned off immediately 

after casting Ti-6A1-4V alloy strip. The temperature of the 

10 
chill block cooling water llspikesll about 10°C, 8 to 10 seconds 

after the casting takes place. The delay reflects the time 

required for conduction heat transfer from the solidified strip 

to the copper substrate and for convection heat transfer from the 

chill block to the cooling water. 

Microstructural Evaluation 

Specimens were cut from as-cast Ti-6A1-4V alloy strip and 

Ti-14A1-21Nb alloy strip cast by melt overflow. The specimens 

were mounted in thermosetting resin, ground, polished, and etched 

to reveal the microstructure. The etchant used with Ti-6A1-4V 

alloy strip was 95% H,O + 3.5% HNO, + 1.5% HC1. The etchant used 

with the Ti-14A1-21Nb alloy strip was 0.5% HF + 1.5% HC1 + 2.5% 

HNO, + 95.5% H,O (Keller's Reagent). The specimens were examined 

under a light microscope using differential interference-contrast 

(Nomarski) illumination. 

Figure 8 presents photomicrographs of the top and bottom 

surfaces of as-cast Ti-6A1-4V alloy strip. Figure 9 presents 

photomicrographs of the transverse and longitudinal cross 

sections of the as-cast Ti-6A1-4V alloy strip. Solidification 

begins at the substrate and grows radially outward into the melt 

from the chill block surface. The strip exhibits elongated, 

columnar beta grains in the longitudinal (Figure 9A) and 

transverse (Figure 9B) directions. The strip surface that 

contacted the substrate (Figure 8A) shows relatively equiaxed 

beta grains. Equiaxed beta grains are also found on the free 

surface of the cast strip (Figure 8C). 

After solidification, the Ti-6A1-4V alloy strip underwent a 

martensite transformation. Areas of grain boundary alpha (Figure 

8B) can be found along with the fine alpha-prime platelets 

inside the beta grains. The presence of grain boundary alpha 

indicates that solid state cooling is slow enough to allow alpha 

to form at the grain boundaries. 

The microstructure of the as-cast Ti-14A1-21Nb (alpha-two) 

strip is presented in Figure 10. The microstructure also 

consists of elongated, nearly columnar beta grains which appear 

equiaxed on the substrate surface (Figure 10A) and the top 

surface (Figure 1OC) of the strip with a cellular-dendritic solidification substructure within these grains. Higher 

magnification (Figures 10B, 10D) reveals an acicular transformed 

structure that is probably alpha-two or ordered alpha prime 

martensite. Further study by use of analytical microscopy 

techniques is needed to distinguish the phases present in the 

transformed structure. There may be variations in this transformed structure resulting from compositional variations due to 

segregation during solidification. 

11 
In comparing the substrate surface to the free surface of 

the as-cast Ti-14A1-21Nb alloy strip, it appears that the 

cellular dendritic substructure is coarser on the free-cast 

surface, reflecting a slightly lower cooling rate. 

Process Evaluation 

The titanium alloy strip direct cast by plasma melt overflow 

was further characterized by chemical analysis, microhardness 

measurements, and cold rolling. 

Chemical Analysis - The results of chemical analysis of the 

Ti-6A1-4V alloy strip are presented in Table 11. In general, 

blocks of Ti-6A1-4V alloy billets were initially melted to create 

a skull from which strip was cast. After casting, the skull was 

remelted again and again with Ti-6A1-4V alloy scrap used to 

replenish the liquid level. Therefore, the chemical composition 

of the strip combines the compositions of the original Ti-6A1-4V 

alloy billet and Ti-6A1-4V alloy scrap. The "starter materialtt 

shown in Table I1 is Ti-6A1-4V alloy scrap taken from a random 

sample. The intent was to compare the chemical compositions of 

the starting scrap with the final strip to estimate the level of 

contamination from remelting in the plasma furnace recognizing 

that there may be variations in the chemical composition of the 

starting materials. 

Table I1 compares the chemistry of strip cast from Ti-6A1-4V 

alloy billet (Experiment 36) with strip cast from a skull that 

had been remelted several times (Experiment 60). In general, the 

levels of interstitial elements increase as the skull is melted 

more often while the aluminum and vanadium levels decrease with 

more frequent remelting. 

The Ti-14A1-21Nb (alpha-two) alloy was melted from prealloyed plate purchased from Timet. The chemical analysis of the 

plate is compared to that of the strip in Table 111. Note that 

the analyses of the plate and strip were performed at different 

laboratories. The most striking result is a 6% depletion of 

aluminum from the melt which causes the niobium content to rise 

relative to the other elements. However, aluminum has the lowest 

boiling point of the three major alloying elements - 2450°C 

compared to 3260°C for titanium and 3300°C for niobium. We can 

compensate for the loss of aluminum by alloying. 

Based on the results presented in Table 111, the oxygen 

content of the Ti-14A1-21Nb alloy strip increased by 340 ppm 

after remelting and casting. The increases in other interstitial 

elements included carbon - 20 ppm; hydrogen - 12 ppm; and 

nitrogen - 40 ppm. These low values of interstitial elements 

indicate that the plasma melt overflow furnace and skull melting 

12 
procedures can effectively limit the interstitial contamination 

of titanium alloys during direct strip casting. 

Microhardness - The microhardness of as-cast Ti-14A1-21Nb 

(alpha-two) strip was measured using a diamond point indenter 

with a 500 gram load. Eight (8) measurements were taken across a 

cross section of strip. The mean microhardness was 490 on the 

Vickers scale with a standard deviation of 13. Researchers at 

The Ohio State University [l] plotted microhardness as a function 

of cooling rate showing a comparison of CCT samples with 

simulated gas tungsten arc (GTA) fusion and heat affected zone specimens for a Ti-14A1-21Nb alloy (Figure 11). A Vickers 

hardness of 490 intersects the curve presented in Figure 11 at a 

cooling rate of 40 C/s and again at 300 C/s. 

A continuous cooling transformation (CCT) diagram for the 

Ti-14A1-21Nb alloy is shown in Figure 12 [l]. The diagram 

indicates that the beta phase will be present in samples cooled 

at rates below 5" C/s and above 600 C/s. There is no evidence of 

the beta phase in the microstructure of the as-cast Ti-14A1-21Nb 

alloy strip (Figure 10). Further microstructural analysis using 

thin foil transmission electron microscopy (TEM) would allow us 

to estimate the cooling rate more precisely. So, we conclude 

that the solid state cooling rate is in the range of 40 C/s to 

300 C/s. 

Cold Rollinq - Surface roughness of the as-cast strip can be 

effectively reduced by cold rolling. Twenty-one percent (21%) 

cold rolling did not induce significant cracking and produced a 

relatively smooth surface. 

Variations in the thickness of the as-cast Ti-6A1-4V alloy 

be reduced by cold rolling. Thickness variations on the order of 

2 20% are Common for as-cast strip. After cold rolling, the 

thickness variation was reduced to roughly 5 6% longitudinally. 

These results are encouraging; however, further investigation is 

needed to optimize th-e thermomechanical processing of cast 

titanium alloy strip. 

The micrographs presented in Figure 13 show a representative 

transverse cross section and longitudinal cross section of cold 

rolled Ti-6A1-4V strip. It appears that the martensitic 

structure is beginning to be broken up after 21% cold reduction. 

In the transverse section (Figure 13A), the free-cast surface 

appears to be deformed more than the chill-cast surface because 

of the variation in thickness on the free-cast surface of the 

strip. 

Figure 13B shows a representative longitudinal cross 

section of Ti-6A1-4V alloy strip after 21% cold reduction. Shear 

bands are clearly evident across the longitudinal thickness of 

the strip. The strip is most heavily deformed along its length 

13 
during cold rolling while deformation across the width results 

from thickness variations. 

Conclusions 

. 

Direct casting of titanium alloy strip is feasible by 

combining transferred plasma arc melting techniques with 

melt overflow rapid solidification technology. 

The pilot plant-scale plasma melt overflow system constructed during this contract is limited by melting 

capacity. It is estimated that the 75 kW transferred 

plasma arc system melts about 1.2 kg (2.5 lb) of titanium 

per experiment. 

A rotatable water-cooled hearth was invented for overflowing 

the liquid titanium onto the chill block. This invention is 

a significant improvement over a tilting hearth. A U.S. 

patent application was filed on the invention. 

A mathematical model of the plasma melt overflow was 

developed to predict ribbon thickness as a function of 

casting speed (capillary number). The ribbon thicknesses 

calculated from the model are close to the thicknesses 

measured from as-cast strip, erring slightly on the high 

side. Both calculated and empirical data suggest it is 

possible to cast titanium strip 0.125 mm (0.005 in) thick. 

The rotatable hearth system is capable of casting titanium 

alloy strip of a suitable width and length for use in 

honeycomb structures. However, there are variations in 

thickness of the strip, both across the length and width of 

each strip sample and from sample to sample. 

The level of interstitial contaminants increases as the 

titanium alloys are remelted over and over while the 

aluminum and vanadium levels fall in the Ti-6A1-4V alloy. 

Aluminum depletion was particularly severe in the Ti-14A1- 

21Nb alloy. Sacrificial alloying can be used to compensate 

for unrecoverable losses during plasma melting. 

The microstructure of the Ti-6A1-4V alloy shows elongated 

beta grains normal to the chill surface with equiaxed beta 

at the substrate surface and free cast surface. The strip 

underwent a martensite transformation after solidification. 

The cooling rate of the Ti-14A1-21Nb alloy strip was 

estimated to range between 40 C/s and 300 C/s after solidif ication. The as-cast strip exhibited a fine acicular 

transformed microstructure. The solid state cooling rate 

14 
can be increased by decreasing the strip thickness or by 

increasing the heat transfer through use of belts, rollers, 

or forced gas convection. 

I b The surface roughness of Ti-6A1-4V alloy strip can be 

effectively removed by rolling. Other techniques, like 

grinding and slitting, might also be considered for 

I conditioning the as-cast strip for use in honeycomb 

structures. 

I 

I Recommendations 

b Evaluate different hearth geometries to improve the fluid 

1 flow and temperature distribution in the melt pools. 

b Reduce the variation in as-cast strip thickness. For the 

rotatable hearth, the thickness variations may be reduced 1 through a variable tilt rate. A secondary roll might also 

be effective in reducing thickness variations. 

I 0 Increase the melting capacity by installation of a larger 

i 

i 

plasma melting system in addition to the 75 kW system 

already installed. The existing hearth could be replaced 

l with a two-tier stationary hearth with melting performed in 

one section and strip casting in the second section. This 

concept appears to be feasible for strip less than 5 cm (2 

in) wide. 

I 

I 

0 I Investigate rolling, grinding, and/or slitting of the ascast strip to achieve final ribbon dimensions and surface 

finish. 

I 

I 0 Evaluate techniques for increasing the solid state cooling 

rate of the cast strip like secondary rollers, continuous 

belts, or forced convection cooling. 

0 Use sacrificial alloying to maintain aluminum and vanadium 

levels in alloys. Limit the number of times that the 

titanium skull is remelted to control the level of the 

interstitial contaminants. 

b Investigate casting of different titanium alloys that are 

candidates for use in honeycomb structures. 

References 

1. Mascorella, T. J., "Weldability of A Ti3Al-Nb Alloy", 

Master's Thesis, The Ohio State University (1987) 

15 
Table I 

Dimensions of Direct Cast Titaniun Strip 

Exp . # 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

61 

62 

63 

64 

- 

Casting 

0 

Speed 

3.2 

10.1 

N /A 

N/A 

7.6 

7.6 

7.6 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N /A 

N /A 

N/A 

N/A 

8.1 

8.1 

8.1 

3.4 

3.4 

3.4 

3.4 

3.4 

4.2 

5.0 

5 .O 

5.0 

5 -3 

2.3 

5.3 

5 -3 

5.3 

5.0 

3.4 

4.4 

3.4 

4.1 

4.1 

4.1 

3.8 

5.9 

3.4 

3.4 

4.2 

4.1 

4.2 

5.3 

5.3 

4.4 

4.2 

4.5 

5.7 

6.9 

7.4 

5.6 

7.4 

6.9 

5.3 

6.3 

5.3 

5.3 

Mean 

Thickness 

(mn) (in) 

0.343 

0.245 

0.377 

0.215 

0.337 

0.427 

0.415 

0.210 

0.302 

0.312 

0.618 

0.300 

0.410 

0.500 

0.560 

0.463 

0.340 

0.500 

0.533 

0.284 

0.310 

0.516 

0.381 

0.406 

0.381 

0.290 

0.345 

0.157 

0.345 

0.239 

0.356 

0.625 

0.385 

0.254 

0.305 

0.178 

0.698 

0.566 

0.930 

0.363 

0.643 

0.401 

0.413 

0.445 

0.676 

0.922 

0.500 

0.533 

0.338 

0.427 

0.203 

0.343 

0.427 

0.241 

0.211 

0.381 

0.218 

0.287 

0.170 

0.160 

0.279 

0.229 

0.406 

0.381 

0.014 

0.010 

0.015 

0.008 

0.013 

0.017 

0.015 

0.008 

0.012 

0.012 

0.024 

0.012 

0.016 

0.020 

0.022 

0.018 

0.013 

0.020 

0.021 

0.011 

0.012 

0.020 

0.015 

0.016 

0.015 

0.011 

0.014 

0.006 

0.014 

0.009 

0.014 

0.025 

0.015 

0.010 

0.012 

0.007 

0.027 

0.022 

0.037 

0.014 

0.025 

0.016 

3.019 

0.018 

0.027 

0.036 

0.020 

0.021 

0.013 

0.017 

0.008 

0.014 

0.017 

0.010 

0.008 

0.015 

0.009 

0.011 

0.007 

0.006 

0.011 

0.009 

0.016 

0.015 

Maximun 

Uidth 

(mn) (in) 

50.7 

30.0 

92.9 

38.8 

113.2 

71.4 

113.2 

54.9 

33.7 

48.5 

48.2 

12.9 

38.1 

47.8 

45.9 

27.4 

14.5 

46.7 

18.3 

17.8 

17.5 

42.7 

29.2 

17.0 

4.5 

23.5 

40.6 

50.8 

36.8 

58.4 

37.5 

111.8 

45.7 

19.1 

43.2 

57.7 

55.2 

54.9 

50.8 

55.9 

35.6 

27.9 

50.8 

50.8 

101.6 

19.1 

66.7 

18.4 

66.0 

50.8 

72.1 

95.8 

98.3 

43.2 

47.6 

54.0 

43.2 

45.7 

29.2 

42.5 

48.3 

48.9 

48.9 

48.9 

2.0 

1.2 

3.7 

1.5 

4.5 

2.8 

4.5 

2.2 

1.3 

1.9 

1.9 

0.5 

1.5 

1.9 

1 .8 

1.1 

0.6 

1.8 

0.7 

0.7 

0.7 

1.7 

1.2 

0.7 

0.2 

0.9 

1.6 

2.0 

1.5 

2.3 

1.5 

4.4 

1.8 

0.8 

1.7 

2.3 

2.2 

2.2 

2.0 

2.2 

1.4 

1.1 

2.0 

2.0 

4.0 

0.8 

2.6 

0.7 

2.6 

2.0 

2.8 

3 -8 

3.9 

1.7 

1.9 

2.1 

1.7 

1.8 

1.2 

1.7 

1.9 

1.9 

1.9 

1.9 

Length 

A!!L 

N/A* 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

N/A 

1 .8 

2.7 

2.7 

3.3 

2.7 

1.8 

1.8 

1.9 

3.0 

3.8 

5.1 

2.8 

3.1 

1.2 

2.0 

2.1 

2.3 

2.5 

0.5 

N/A 

1 .o 

2.1 

1.7 

1.7 

3.0 

1.7 

3.0 

3.1 

2.4 

4.9 

2.9 

N/A 

2.4 

1.8 

2.9 

1.4 

4.7 

7.6 

3.6 

8.2 

3.8 

2.6 

3.0 

3.0 

3.0 

3.0 

Alloy 

Ti -6Al-4V 

Ti -6Al -4V 

Ti-6Al-4V 

Ti-6AL-4V 

Ti-6Al-4V 

T i -6A 1 -4V 

Ti -6Al -4V 

T i -6A 1 -4V 

Ti-6Al-4V 

Ti-6Al-4V 

Ti -6A 1 -4V 

Ti -6A 1 -4V 

Ti -6Al-4V 

Ti -6Al -4V 

Ti-6AL-4V 

Ti-6Al-4V 

Ti -6Al -4V 

Ti-6Al-4V 

T i -6A 1 -4V 

Ti -6Al-4V 

Ti -6Al-4V 

Ti -6Al-4V 

T i -6A 1 -4V 

Ti-6Al-4V 

Ti-6Al-4V 

Ti -6AL -4V 

Ti-6AL-4V 

Ti-6Al-4V 

Ti-6AL-4V 

Ti -6Al-4V 

Ti-6Al-4V 

Ti -6Al -4V 

CP Ti 

CP Ti 

Ti-6Al-4V 

Ti -6Al-4V 

Ti -6AL -4V 

Ti-6AL-4V 

Ti -6AI-4V 

Ti-6Al-4V 

Ti-6Al-4V 

Ti -6AL -4V 

Ti-6Al-4V 

Ti-6Al-4V 

Ti -6Al-4V 

Ti -6Al-4V 

Ti -6AL -4V 

Ti-6Al-4V 

Ti-6Al-4V 

Ti -6Al-4V 

Ti-6Al-4V 

Ti-6Al-4V 

Ti-6Al-4V 

Ti-6Al-4V 

T i -6A 1 -4V 

Ti-6Al-4V 

Ti-6Al-4V 

Ti -6Al-4V 

Ti -6AL -4V 

Ti-6Al-4V 

Ti-14Al-21Nb 

Ti-14AL-21Nb 

Ti-14Al-21Nb 

Ti-14AL-21Nb 

* N/A = Not Available 

16 
Table I1 

* Results from Timet Certified Analysis, Heat T-8738, Test E-3755 

Chemical Analysis of Direct Cast 

Ti-6A1-4V Alloy Strip* (Wt %) 

Starter 

Material 

Exp. 

#36 

Exp. 

#60 Method 

Carbon 0.02 0.03 0.04 Leco WR-12 

Hydrogen 0.0055 0.0041 0.0047 Leco Hot Extraction, 

Oxygen 0.185 0.209 0.259 Leco TC 136 

Nitrogen 0.009 0.038 0.066 Leco TC 136 

Aluminum 6.20 6.05 5.90 Beckman Spectraspan, 

Vanadium 4.09 3.95 3.52 Beckman Spectraspan, 

534-600 

VI D.C. Plasma 

VI D.C. Plasma 

*Results from Sherry Laboratories, Muncie, Indiana, Report #L-5166 

Table I11 

Chemical Analysis of Direct Cast 

Ti-14A1-21Nb Alloy Strip (Wt %) 

Exp. 

Plate* #61* * Method** 

Carbon 0.018 0.020 Leco WR-12 

Hydrogen 0.005 0.0062 Leco Hot Extraction, 

Oxygen 0.050 0.084 Leco TC 136 

Nitrogen 0.012 0.016 Leco TC 136 

Aluminum 14.20 13.35 Beckman Spectraspan, 

Niobium 21.30 21.70 Beckman Spectraspan, 

534-600 

VI D.C. Plasma 

VI D.C. Plasma 

17 
Solidified Ribbon 

Cruc i b I e F 

Figure 1. Schematic of the Melt Overflow Process 

18 
Figure 2. Schematic of Plasma Melt Overflow Furnace 

19 
1500 

1000 

500 

A 

- 

- 

- 

- 

- 

0 

0 

0 

a 

0 

A 

A 0 

0 

A 

A 

A Depth = 0 mm 

0 Depth = 1 mm 

0 Depth = 4 mm 

a 

a - 

of--- t = 748.3 + 8056e-250Ca 

t = 298.0 + 1446e-2'0Ca 

'A 

plasma torch 

hearth I 

0 2 4 

TIME (min) 

Figure 4. Water Temperature During Plasma Arc Melting 

20 
ORIGINAL PAGE 

BLACK AND WHlTE PHOTOGRAPH 

Figure 5. Photograph of Plasma Melt Overflow Furnace 

21 
0 Depth = 1 mm 

0 Depth = 4 mm 

1500 

1000 

500 

0 

I A Experiment I 

- 

- 

- 

- 

- 

t4-= 1 9.74Ca-0.924

- A 

te,p= 16.1 6Ca-0.7597 

t,m=22.84Ca-o.64*

b,,,,,,=4.167Ca-0.906

- 

- 

I I I I I I I I I I I I I J 

Figure 6. Computed Versus Cast Strip Thickness 

22 
do 

7 6 

eo 

58 

44 

30 

20 

10 

0 

/? li 

'i 

0 2 4 6 

strip cast TIME (min) 

Figure 7. Water Temperature During Ti-6A1-4V Alloy Strip Casting 

23 
- 

50 Frn 

10 pm 

50 pm 

A 

B 

C 

Figure 8. Microstructure of As-Cast Ti-6A1-4V Alloy Strip 

(a) Chill Cast Surface 

(b) Chill Cast Surface 

(c) Free Cast Surface 
50 pm 

50 pm 

FREE 

SURFACE 

A 

CHILL 

SURFACE 

FREE 

SURFACE 

B 

CHILL 

SURFACE 

Figure 9. Microstructure of As-Cast Ti-6A1-4V Alloy Strip 

(a) Longitudinal Cross Section 

(b) Transverse Cross Section 

25 
- 

50 

- 

50 

A B 

30 pm 

30 pm 

C D 

Figure 10. Microstructure of As-Cast Ti-14A1-21Nb Alloy Strip 

(a) Chill Cast Surface 

(b) Chill Cast Surface 

(c) Free Cast Surface 

(d) Free Cast Surface 

26 
600 

550 

500 

450 

400 

350 

300 

* Fusion zone samples 

+ Heat-affected zone samples 

F I . . I I I.. . 1 1 * 1 ..I * m I I ..l' 

1 10 100 1000 

Cooling Rate from 1200 C to transformation (c/s) 

Figure 11. Graph of Microhardness as a Function of Cooling Rate 

for Ti-14A1-21Nb Alloy Showing Comparison of CCT 

Samples with Simulated GTA Fusion & Heat-Affected 

Zone Specimens 

27 
1200 

1100 

1000 

900 

800 

700 

600 

1 OO°C/sec 2O0C/sec 5OC/sec 

I 10 100 1000 

TIME (sec) 

Figure 12. CCT Diagram for Ti-14A1-21Nb Alloy 

28 
50 pm 

ORIGINAL PAGE 

BLACK AND WHITE PhOTOGRAPH 

FREE 

SURFACE 

A 

CHILL 

SURFACE 

FREE 

SURFACE 

B 

CHILL 

SURFACE 

Figure 13. Micrographs of Cold Rolled Ti-6A1-4V Alloy Strip 

(a) Transverse Cross Section 

(b) Longitudinal Cross Section 

29 
APPENDIX A 

A-l 
A MATJDlATICAL MODEL OF THE 

MELT OVERFLOW WID SOLIDIFICATION PROCESS 

BY 

SUSAN E. BRASMER 

B.S., University of Illinois, 1979 

THESIS 

Submitted in partial fulfillment of the requirements 

for the degree of Master of Science in Mechanical Engineering 

in the Graduate College of the 

University of Illinois at Urbana-Champaign, 1988 

Urbana, Illinois 

PRECEDING PAGE BLANK 'NOT FILMED 

A-3 
The melt overflow solidification process is a method for producing a thin, 

continuous ribbon of rapidly solidified metal with unique strength, magnetic, 

and corrosion properties. The process being studied was developed in 1983 by 

the Ribbon Technology Corporation (Ribtec) of Gahanna, Ohio [ 11. The material 

produced with this process may be used in place of rolled strip for honeycomb 

and similar aerospace structural applications. A finite element model of this 

process has been created to study the factors that influence the formation of 

the ribbon and to suggest improvements to the manufacturing process. While 

the process is applicable to a number of alloys, including aluminum, 

magnesium, titanium, nickel, and copper, this work has focused on titanium. 

A- 4 
Acknowledgements 

I would first like to thank Professor Jon Dantzig for all his advice and 

support during the course of this project. With his guidance, I learned not 

only to "guess the answer", but also how to prove or disprove the accuracy of 

that guess. My thanks also go to Mr. Tom Gaspar and Ribbon Technology 

Corporation for their support of the project. Finally, and most importantly, I 

would like to thank my parents and family for all their love and support 

through the years. 

A-5 
TABLE OF CONTENTS 

Section 

I . 

I1 . 

I11 . 

IV . 

V . 

VI . 

VI1 . 

VI11 . 

IX . 

X . 

Page 

Introduction .................. A-7 

Method ..................... A-9 

Results .................... A-19 

Discussion ................... A-22 

Conclusion ................... A-24 

Figures .................... A-25 

Appendix1 ................... A-56 

Appendix I1 .................. A-58 

Appendix I11 .................. A-62 

References ................... A-64 

A-6 
The promise of improvements in the magnetic, mechanical, and 

corrosion properties of a number of alloys has led to great interest in rapid 

solidification processes such as the melt overflow method. Previous studies 

[2,3] have shown that rapid cooling rates, on the order of lo5 to lo6 K/s, are 

necessary for the formation of the amorphous or microcrystalline phases 

which produce the property improvements. In general, the rapid 

solidification processes used to produce these high cooling rates can be 

characterized as ones in which a large, cold substrate extracts heat from a thin 

section of melt. The melt overflow process developed by the Ribbon 

Technology Corporation is one such method. 

In the melt overflow process, a ribbon of metal is formed by the contact 

of molten metal in a specially shaped hearth with a rotating cylindrical chill 

block (Figure 1). Heat is extracted from the molten metal by the chill block, 

and the metal solidifies into a thin ribbon, which is carried off by the 

momentum imparted to it by the rotating chill block. Due to the high cooling 

rates involved in the process, amorphous or microcrystalline phases may 

appear in the microstructure of the ribbon. This microstructure in turn 

affects the characteristic properties of the solidified metal. 

The experimental configuration studied uses a water cooled chill block 

25.4 cm in diameter, made of copper, bronze, or steel. The metal is first melted 

in a copper hearth, which consists of a cylindrical bowl 10 cm in diameter and 

4 cm deep, machined into a solid block of copper. An angled pouring lip is also 

machined into the block. The test setup being investigated utilizes a 75 kW 

plasma arc torch to melt a titanium alloy. The torch is centered over the 

hearth, but may also be made to traverse across the top surface of the melt 

(Figure 2). Once the metal is melted, the hearth is tipped toward the wheel, 

allowing the metal to come into contact with the rotating chill block, where it 

then solidifies into a thin, continuous ribbon. The top surface of the melt is 

exposed to the local environment throughout the process. 

A number of factors influence the formation of the ribbon. These can be 

divided into two main groups. The first group is the material properties, such 

A- 7 
as density, viscosity, and surface tension, which are inherent properties of the 

material being cast. The second group is the processing parameters, such as 

the speed of rotation of the chill block, and the intensity and location of the 

torch used to heat the metal, the hearth material, wheel material, coolant 

application, etc. These factors are dependent on the experimental prototype 

which is being studied. It is the purpose of this study to investigate how these 

factors, individually and in combinations, affect the solidification process. In 

particular, one primary goal is to predict the thickness of the solidified 

ribbon. The thickness of the ribbon affects how the ribbon will solidify, 

which determines the microstructure. 

The approach used was to construct a finite element model which 

simulates the fluid and heat flow in the solidification process. Process 

dynamics, which determine ribbon thickness and freezing rate, were 

incorporated into this model through the material properties, geometry and 

boundary conditions. The thickness of the ribbon was solved for in the 

simulation, and by examining the velocity and temperature profiles calculated 

in the model, the cooling rate in the ribbon could be determined and the 

resulting microstructure estimated. The model is two-dimensional and can be 

thought of as a thin slice passing through the centerline of the hearth and 

chill block. With the model, the effects of a number of variables can be studied 

more quickly and easily than is possible with an experimental prototype of the 

process. It is possible to change a parameter, such as the speed of rotation of 

the chill wheel, merely by changing one or two numbers in the input file and 

rerunning the model. Additionally, parameters that would be difficult or 

impossible to change in an experiment, such as material viscosity or surface 

tension, can be investigated with the model. In this way, the influence of 

single parameters or combinations of parameters can be studied. 

Once the temperature profile in the solidifying ribbon was known, it was 

possible to estimate the microstructure of the ribbon. For a typical alloy, 

variation in the values of G, the imposed temperature gradient, and V, the 

growth rate of the cells or dendrites, affects the resulting microstructure in 

the material. The ratio of G to V determines the morphology of the material. 

Low G/V values indicate plane front or cellular growth, while higher values 

indicate dendritic growth. The product of G and V, which is equal to the 

A- 8 
cooling rate T for one dimensional heat flow, determines the spacing of the 

cells or dendrites. For low values of GV, coarse cells or dendrites would be 

expected, while high values indicate fine spacings (Figure 3) [4]. Studies have 

indicated that cooling rates in the range of lo5 to lo6 K/s are necessary to 

produce the desired properties in the rapidly solidified metal. If these rates 

cannot be achieved, undesirable growth morphologies or spacings may appear 

in the material and limit its applications. 

The commercial finite element code FIDAP, developed and marketed by 

Fluid Dynamics International of Evanston, Illinois, was used for the model. 

FIDAP is designed to analyze viscous incompressible fluid flows, both 

isothermal and temperature dependent [5]. Some of the specific features of 

this code will be discussed later. The analysis was run primarily on a Sun 

3/280 computer with some additional work done on a Silicon graphics Ins 3020 

workstation. 

The solution process consisted of four major sections (Figure 4). First, a 

velocity solution was obtained, assuming constant temperature and a fixed 

ribbon thickness. This solution was then used as an initial estimate for the 

next solution, where the temperatures were assumed constant, but the ribbon 

thickness was computed. Next, the first solution was used as an initial estimate 

for an advection-diffusion solution to a thermal problem to obtain an estimate 

for the temperature field. Finally, the advection-diffusion solution and the 

free surface solution were used as a starting point for the fully coupled 

velocity and temperature solutions. Laminar flow of the fluid was assumed 

throughout the solution process. Each section of the solution procedure is 

described in detail below. 

This step-by-step approach to the solution was used to ensure that the 

model was properly constructed and to diminish the effect of any 

nonlinearities in the problem on the solution process. It is important to note 

that none of the four sub-problems in the solution process is particularly easy 

to solve. The mesh geometry and density, the material properties, the velocity 

and temperature boundary conditions, and the solution procedure used all 

A-9 
have major impacts on these problems and an error in any of these areas can 

result in either nonconvergence of the solution or an inaccurate solution. By 

taking a step-by-step approach to the solution, these errors can be dealt with 

as they arise and confidence can be taken that the final answer obtained is 

indeed correct. 

It is also important to note that the final solution to the coupled velocity 

and temperature problem includes in it all the important features of the melt 

overflow process. Since the free and fixed velocity solutions and the 

advection-diffusion solution are used as input to the coupled problem, all the 

process features included in these solutions are carried over to the coupled 

solution. Thus, a true representation of the physics of the melt overflow 

process appears in the solution to the coupled velocity and temperature 

problem. 

The first step in the construction of the model was the formation of the 

finite element mesh. Because we were primarily interested in the 

solidification process, only the melt itself was included in the model. The 

effects of the torch, hearth, and chill wheel were taken into account through 

the boundary conditions for the model. To allow a greater element density in 

the ribbon area and to reduce computational time, only half of the melt in the 

hearth was included in the model. Symmetry was assumed along the hearth 

centerline. This is not strictly correct, but the approximation should have 

negligible effect on the modeling of the ribbon formation, because the 

asymmetry appears far from the symmetry plane. 

The geometry of the finite element mesh was set up to resemble that of 

the experimental melt overflow process being used by Ribtec. The model was 

constructed for a hearth tip angle of 5 degrees from horizontal. The thickness 

of the ribbon was initially estimated as 0.25 cm. The rest of the dimensions of 

the model are shown in Figure 5. The mesh was generated by first specifying 

16 major keypoints in integer and geometric space. The keypoints were 

connected with lines or curves and surfaces were created by specifying their 

corners. 

A-10 
The elements used for the melt were four noded linear isoparametric 

quadrilateral elements (Figure 6). The pressure degrees of freedom were 

constant within each element, and not continuous across element boundaries. 

A discretized pressure variable was used, adding an additional degree of 

freedom to the problem. While it is sometimes possible to use a penalty method 

to eliminate the pressure variables, it was not advisable to do so for the free 

surface velocity solution due to nonlinearities which can appear in the model 

[6]. For consistency, the mixed formulation, retaining pressure degrees of 

freedom, was used throughout the solution process. 

In addition to the quadrilateral elements, two noded boundary elements 

were created on the top of the melt surface, on the melt-chill wheel interface 

surface, and on the melt-hearth interface surface (Figure 7). Boundary 

elements have a local normal and tangential coordinate system which 

facilitate their use in imposing convective and radiative heat flux boundary 

conditions and in defining free surface boundaries. In order to use the 

velocity solution as input later to the temperature problem, two sets of 

boundary elements. were defined along the same surface to allow for the 

application of boundary conditions in the temperature solution, as well as the 

velocity solution. An example of this is along the top surface of the melt 

where there were velocity slip elements and, in the temperature solution, 

radiation boundary elements. Doubly defined boundary elements also existed 

on the melt-chill wheel interface surface and the melt-hearth interface 

surface. For the velocity solution only, the two sets of boundary elements 

were identically defined. The full mesh consisted of 1808 nodes and 2167 

elements (Figure 8). 

FIDAP allows for the use of both constant and temperature dependent 

material property values in the analysis. The temperature dependence of 

viscosity, specific heat, thermal conductivity, surface tension, and the thermal 

heat transfer coefficient may all be described by a series of points defining a 

temperature-material property curve. Since the fluid being modelled was 

assumed to be incompressible, the fluid density must be constant. The material 

property values used in the model were those of pure titanium and are listed in 

Appendix I. All values used were in the cgs system. 

A-ll 
The suface tension value played a major role in the solution of the free 

surface problem. In addition to the value of the surface tension, the solution 

procedure required that values of two angles be provided, corresponding to 

the contact angles that the tangent to the surface made with the global x-axis 

at the ends of the surface (Figure 9). These angles were necessary to provide 

continuity with the rest of the mesh at the fixed end points of the free surface. 

A temperature dependent curve for viscosity was included in the model 

for the temperature solutions. This curve used the value of 0.04 g/cm-s [7] for 

the viscosity of the metal above the solidification temperature and 1~10~~ 

g/cm-s for the solidified metal. The latent heat of fusion for the metal was 

included either as a temperature dependent specific heat curve (Figure lo), or 

through a temperature dependent enthalpy curve, using a technique 

developed by Lemmon [XI and implemented by Dantzig [9] (Figure 11). In the 

former case the area under the spike in the curve was equivalent to the latent 

heat of fusion, and in the latter case the latent heat is given by the enthalpy 

difference at the freezing point. 

The solution process began with a steady-state, isothermal solution to the 

velocity problem, using a mesh for an assumed fixed ribbon thickness. At this 

point the energy equation was not included and only the momentum 

equations, without the bouyancy terms, were solved. The governing equations 

for this problem are; 

p u-vu = -vp + p v2u 

-- - 

v-u = 0 

where p is density, U is velocity, p is pressure, and p is viscosity. A steady-state 

analysis was performed using Stokes flow as the initial iterate for the solution. 

In Stokes flow, the convective term on the left-hand side of Eq. (1) is ignored. 

This provided a reasonable initial estimate, allowing convergence in the 

solution procedure used for the full nonlinear problem [lo]. 

Several solution techniques, such as sucessive substitution, NewtonRaphson, and quasi-Newton, were possible for these problems. In general, 

A-12 
sucessive substitution had the best convergence radius, but took the largest 

number of iterations to converge. Conversely, the Newton-type methods 

required fewer iterations, but had smaller radii of convergence. It was 

possible to speed up convergence by starting the sol,ution with several 

iterations of successive substitution, then switching to one of the Newton-type 

methods. Typically, three steps of sucessive substitution were used followed by 

ten steps of quasi-Newton to obtain solutions. For all the problems, 

convergence was declared when the relative changes in the solution iterates 

changed by less than 0.1%. and the residuals were also less than 0.1% of their 

initial values. 

The boundary conditions imposed on the model for the fixed ribbon 

velocity solution are shown in Figure 12. Along the bottom edge of the mesh, 

where the melt is in contact with the copper hearth, both the normal and 

tangential components of velocity were set to zero. Along the top surface of 

the melt, the normal component of velocity was set to zero. The surface 

representing the interface between the ribbon and the chill block has a 

normal velocity of zero, and tangential velocity equal to the tangential speed 

of the rotating chill. The boundary conditions on the remaining surfaces 

were left free, corresponding to no shear stress. A typical input file for the 

fixed ribbon velocity problem appears in Appendix 11. 

Solutions were obtained corresponding to a number of experimental 

conditions. The tangential velocity of the chill wheel was varied between 1.0 

and 10.0 m/s to simulate different casting rates. The viscosity was also varied 

to study its affect on the solution. Several mesh densities were also tried to 

study the effect on convergence. 

Once these solutions were obtained, they were used as initial guesses to 

obtain the velocity solution which estimated the thickness of the solidified 

ribbon. FIDAP is able to solve fluid flow problems which include free or 

moving fluid boundaries which satisfy the following criteria: the models must 

be two dimensional and the moving surface cannot undergo major changes in 

shape or position compared to the initial mesh [ll]. For this model, neither of 

these limitations posed a major problem. The model was already being 

approached as a two dimensional problem, and by using some care in the 

A-13 
choice of the initial mesh for the free surface problem convergence problems 

associated with major shape and position changes were avoided. 

The top surface of the melt in the vicinity of the ribbon was designated as 

a free surface in this problem. The nodes on this surface were allowed to move 

with respect to a series of specified reference points, and their final positions 

were calculated by the program. This was done by introducing an additional 

degree of freedom for the position of the nodes on the free surface. If these 

nodes were allowed to move indiscriminately, the element mesh could become 

severely distorted. To prevent this, the motion of the free nodes was 

constrained to remain along a set of pre-designated line, referred to as spines, 

in such a way that the initial distance ratio between the moving nodes on each 

spine is always maintained (Figure 13). The reader is referred to reference 

[12] for further details. 

Because the nodes were free to move along the spine in the solution 

procedure, it was important to start with a set of spines which were as nearly 

perpendicular to the final streamlines as possible, within the general 

restrictions of the problem geometry. If this were not done, movement of the 

nodes along the spines could cause elements to become severely distorted and 

result in a solution which failed to converge. Keeping the spines reasonably 

parallel reduced or eliminated this problem in most instances. Increasing, or 

in some cases reducing, mesh density in the region of the spines could also 

reduce convergence problems associated with element distortion. 

In order to better understand this free surface problem, a smaller model 

of the ribbon region was constructed (Figure 14). This model had the same 

basic dimensions as the larger version, but contained only the ribbon itself 

and a portion of the fluid leading up to it. Since the free surface problem was 

difficult to solve because of the added degrees of freedom at the free nodes, and 

the small radius of convergence of the Newton-type methods used to solve it, 

an initial mesh which was close to the ultimate solution was necessary. By 

constructing the smaller model of the ribbon region, it was possible to make 

the necessary adjustments to the mesh and rerun the model in less time than 

would have been required to solve the larger model from the outset. It was 

often necessary to make several mesh adjustments before a converged solution 

A-14 
was obtained. Changes in material properties and processing parameters also 

necessitated a change in the initial mesh. Once experience with the solution 

of free surface problems was gained, the results from the smaller model were 

incorporated in the complete model of the process. 

The geometry of the complete free surface model was the same as that 

used for the fixed ribbon velocity solution. Four noded quadrilateral elements 

were again used for the melt itself with two noded boundary elements on the 

outside surfaces. The material properties were the same as those for the fixed 

ribbon velocity problem, with the addition of surface tension, which plays an 

important role in the free surface solution. The boundary conditions were 

similar to those in the fixed ribbon problem, with one important exception. 

For the free surface solution, the zero normal velocity boundary condition on 

the top surface of the melt was removed to allow this surface to move (Figure 

15). The final solution will automatically satisfy this condition. A typical 

input file for the free surface velocity solution appears in Appendix 11. 

The isothermal fixed ribbon and free surface velocity solutions were next 

used to obtain temperature solutions for the problem. First, the fixed ribbon 

solution was used to solve the associated advection-diffusion problem. In this 

case, only the energy equation was solved, the velocity solution being in from 

a restart file, and assumed to 

problem is; 

p CpU-V T = kV2T 

- 

be unchanged. The governing equation for this 

where p is density, Cp is specific heat, U is velocity, T is temperature, and k is 

therm a1 conductivity . 

The mesh used for the temperature solution was the same one used for 

the velocity solution, and there were again a number of boundary conditions 

to be considered (Figure 16). At the surfaces where the melt was in contact 

with the hearth, convective heat transfer takes place. Convective boundary 

elements were specified on these surfaces. This type of element requires that 

a value for the heat transfer coefficient and T, be provided. The heat transfer 

A-15 
coefficient used for the melt-hearth interface was the ratio of thermal 

conductivity for the copper hearth, kcu , to the average thickness of the 

hearth, Ax. The value for this model was 0.1 cal/cm-s-C . T, was 25 C, 

corresponding to cooling water. 

At the surface where the ribbon was in contact with the chill block, 

convective heat transfer was again considered the most important heat 

transfer mechanism present. Convective boundary elements were again 

specified. The heat transfer mechanism in this area is not well understood and 

previous studies of heat transfer in rapidly solidified metal ribbons have 

assumed that the metal was in contact with the chill wheel for some period of 

time, with the convection between these two surfaces dominating the heat 

flow [13]. However, studies in continuous castings have shown that as the 

metal solidifies it shrinks away from the surrounding mold and an air gap 

forms between the metal and the mold. The heat transfer coefficient in these 

problems was modelled as a combination of conduction and radiation across the 

air gap [14]. This study initially assumed that a process similar to that in 

continuous casting occurs in the melt overflow process, and the heat transfer 

coefficient used for the ribbon-chill block contact surface was similar to 

values used in continuous casting simulations (0.05 cal/cm2-s-C) 

Along the top surface of the melt, radiative heat transfer dominates. 

Here, radiative boundary elements were specified. This type of element 

requires that the emissivity, the Stefan-Boltzmann constant, and T, be 

provided. A value of 0.2 was used for the emissivity of molten titanium [15], the 

Stefan-Boltzmann constant, in the appropriate units, was 5.67 x cal/cm2 - 

s-K4 and T, was 25 C. 

Finally, a distributed heat flux was applied to top of the melt to simulate 

the plasma arc torch used to heat the titanium. In the absence of accurate data 

describing the torch being used in the experimental setup, two approaches 

were taken. In one approach, a ramped heat flux was used to simulate the 

torch (Figure 17). The heat flux extended across the top of the melt to the same 

diameter as the bowl of the hearth. The area under the ramped curve was 

equated to half of the 75 kW power of the torch, since the model was assumed to 

be symmetric about the hearth centerline, and the heat flux to be applied at 

A-16 
each node in the affected area was calculated. In the second approach, a 

Gaussian distribution was assumed for the torch and the same affected area was 

used (Figure 18). The area was again equated to half of the torch power and 

the heat flux at each node was calculated. Since it was possible to move the 

torch across the top of the melt, different torch locations were investigated. 

The thermal boundary condition on the two remaining surfaces, the top 

surface of the ribbon and the edge of the melt at the righthand side of the 

model, were left free. The condition that was then applied by FIDAP was that 

q=O on these surfaces. Note that the ribbon actually continues past the ends of 

the mesh and the righthand side of the model was actually the centerline of 

the bowl of the hearth. 

In addition to the thermal boundary conditions, velocity boundary 

conditions were required on most of the same surfaces. These were the 

boundary conditions which were doubly defined in the velocity solution. On 

the top of the melt, the ribbon-chill wheel interface, and the melt-hearth 

interface, boundary slip elements were defined to keep the velocity vectors in 

the local normal-tangent coordinate system. 

Solutions of the thermal problem were obtained for a number of different 

combinations of variables. The main variables were the speed of rotation of 

the chill block, the heat transfer coefficient at the ribbon-chill wheel 

interface, the method of incorporating latent heat of fusion into the problem, 

and the intesity and location of the heat flux for the torch. 

The advection-diffusion solution was close enough to the final solution 

that the velocity and temperature solutions could be solved in a coupled 

analysis using the quasi-Newton procedure [ 161. The isothermal, free surface, 

velocity solution was then the initial guess for the velocity solution, and the 

advection-diffusion solution provided the initial guess for the temperature 

solution. The complete momentum and energy equations were then solved 

together. The bouyancy term remained discarded from the momentum 

equations. The governing equations for the coupled velocity and temperature 

problem are; 

A-17 
A typical input file for both the advection-diffusion and the coupled problems 

appears in Appendix 111. 

For free surface problems, Newton-type solution methods are generally 

used since they eliminate the need to interpolate the velocity degrees of 

freedom at the free nodes to their new locations at every iteration [17]. This 

necessitated that a "good" initial guess for the velocity solution and the initial 

mesh be available because of the smaller radius of convergence of these 

solution techniques. The velocity solution for the fixed ribbon problem was 

thus used as this initial guess. 

It was often possible to obtain a converged solution for a particular set of 

conditions by starting with a converged solution for a different set of 

conditions. For example, it was possible to obtain a velocity solution for low 

viscosity values, 0.04 g/cm-s , by first obtaining a velocity solution at a higher 

viscosity value, such as 1.00 dcm-s, and using that solution as the initial guess 

for the low viscosity solution. This approach was usually successful over a 

wide range of values and was often the fastest way to obtain a set of converged 

solutions. It was of particular use in the solution of the free surface problem, 

which had an inherently small radius of convergence. It was generally 

easier to solve the free surface problem by starting with an initial mesh in the 

ribbon region which was smaller than the final free surface mesh in this 

region. Whether this is true of free surface problems in general is unknown. 

For the advection-diffusion solution and the coupled solution it was 

possible to use either successive substitution or the Newton based solution 

techniques. The same time versus convergence tradeoffs discussed earlier 

were applicable, and typically the quasi-Newton method was used. 

A-18 
The values of the speed of rotation of the chill wheel, and the viscosity of 

the melt were varied to determine how they affected the velocity solution. The 

solution consists of the magnitude and direction of the velocity at each node, 

and the pressure in each element in the mesh. From this information the 

velocity streamlines can be calculated. 

The solutions to the fixed ribbon velocity problems studied exhibit some 

common characteristics (Figures 19-23). The magnitude of the vectors in the 

hearth portion of the melt is low and the vectors are directed toward the 

ribbon, as would be expected since the driving force in the velocity problem is 

the momentum imparted to the melt by the rotating chill wheel, which directs 

the flow away from the hearth. The velocity of the melt increases along the 

pouring lip, approaching the chill wheel. In the ribbon region, a momentum 

boundary layer forms, originating at the wheel side of the ribbon and 

growing outward. 

For a constant wheel velocity value, changes in viscosity resulted in 

changes in the velocity profile of the region in the immediate vicinity of the 

melt-chill block interface. For low values of viscosity ( < 0.2 g/cm-s) a small 

recirculation zone was found in the area of the initial point of contact of the 

melt with the chill wheel (Figure 19). Similar recirculation zones have been 

seen in analyses of planar flow casting in aluminum [18]. The viscosity also 

had an effect on the thickness of the momentum boundary layer, with the 

thickness of this layer being smaller at low viscosities compared to high 

viscosities (Figure 20). 

Changes in the velocity of the rotating chill block also has an effect on 

the velocity profile of the fixed ribbon. Changes in velocity effect the vector 

profile in much the same way changes in viscosity effect it. For low viscosity 

values, high velocities make the recirculation zone more pronounced than 

lower velocities (Figure 21). The thickness of the momentum boundary layer 

is also thicker at higher velocities than at lower velocities (Figure 22). 

A-19 
The depth of the melt on the pouring lip also affected the velocity profile 

in the melt. The mesh was constructed by assuming that the top surface of the 

melt was horizontal, and at the same height as the end point of the pouring lip 

(Figure 5). Decreasing the depth of the melt on the pouring lip had little 

effect on the size of the recirculation zone (Figure 23). 

Once a satisfactory model for the fixed ribbon velocity solution was 

obtained, the free surface velocity solution was attempted. Once again, the 

velocity of the chill wheel and the viscosity of the melt were vaned. These two 

values, along with the surface tension value, played the major roles in 

determining the thickness of the ribbon. Now, the viscosity of the melt had a 

direct influence on the thickness of the resulting ribbon. For a constant 

velocity, a high value for viscosity (100 g/cm-s) resulted in a ribbon thickness 

on the order of 200 microns. As viscosity was reduced, the thickness of the 

ribbon increased to about 5000 microns (Figure 24). 

The chill wheel velocity also affected the thickness of the ribbon in much 

the same manner as viscosity. For a constant viscosity, a high velocity value 

created a thin ribbon and de,creasing the velocity increased the ribbon 

thickness. The similarity in the effects of viscosity and velocity makes sense 

when one realizes that when the governing equations are nondimensionalized, the parameter which appears is capillary number, Ca = pU/o. 

Increasing the velocity or viscosity increased the capillary number and 

resulted in a thinner ribbon. Similarly, decreasing the surface tension 

increased the capillary number and also resulted in a thinner ribbon. The 

effect of capillary number on ribbon thickness is shown in Figure 25. 

Increasing velocity or viscosity increased the capillary number and resulted 

in a thinner ribbon. Similarly, decreasing surface tension increased the 

capillary number and also resulted in a thinner ribbon. 

The depth of the melt leading into the ribbon also had an effect on the 

thickness of the ribbon. It was again assumed that the top of the melt would be 

a horizontal line at the same height as the end point of the pouring lip. If the 

depth was increased, the thickness of the ribbon increasing correspondingly. 

An increase of 0.1 cm in depth lead to an increase of about 200 microns in the 

ribbon thickness (Figure 26). 

A- 20 
The advection-diffusion temperature solution was first solved using the 

fixed ribbon velocity solution. Typical temperature profiles for this type of 

problem are shown in Figures 27-31. The temperature was very high directly 

beneath the torch and falls off quickly away from the torch. The effect of 

cooling on both sides of the pouring lip, radiation on the top surface and 

convection on the bottom, can be seen in the temperature profiles in this 

region. The influence of the chill wheel can be seen in the ribbon region, 

with the isotherms moving outward from the chill wheel side of the ribbon. 

The intensity of the torch influenced the magnitude of the temperature 

profiles in the melt, but did not change the shape of the profiles significantly. 

Figure 27 shows the profiles for torch values of 75 kW and 50 kW for a gaussian 

heat flux. Using a ramped heat flux in place of the gaussian flux changes the 

temperature profile directly beneath the torch, but had little effect on the 

temperature profiles in the pouring lip and ribbon (Figure 28). 

The value of the convective heat transfer coefficient used on the chill 

wheel side of the ribbon played a major role in the solidification 

characteristics of the ribbon, but had little influence on the thickness. This 

was also a surprising result. The initial value, 0.05 cal/cm2-s-C, used was 

consistent with values used for continuous casting models, discussed earlier. 

However this value proved to be too low for this model, since temperature 

isotherms in the ribbon show that the ribbon would not have solidified before 

leaving the wheel (Figure 29). This is inconsistent with experimental 

observations. Increasing the value to 7.0 to 8.0 cal/cm2-s-C, consistent with 

values found in other studies of rapid solidification processes [19], resulted in 

an isotherm for the solidus which originated close to the initial point of 

contact between the melt and the chill wheel, and ended on the top surface of 

the melt (Figure 30). This meant that the ribbon has solidified completely 

when using the higher value for hwheel. 

Based on the isotherms and the velocity of the chill wheel being used, the 

cooling rate for the ribbon could be estimated. First, two points on the ribbon 

surface were chosen and the temperatures at the points and the distance 

between them was obtained from the thermal solution. The change in time 

A-21 
between the points was calculated from the velocity and the distance. Finally 

the cooling rate was calculated from the temperature difference and the 

change in time. For a velocity of 5.0 m/s and hwheel value of 7.0 cal/cm2-s-C 

the estimated cooling rate is 1.6~10~ K/s. The temperature gradient, G, was 

estimated from the isotherms and the distance between them. For the same 

velocity and hwheel values as before, a temperature gradient of lx103 K/cm 

was estimated and a growth velocity, V, of 1.6~10~ cm/s was calculated. 

Using earlier solutions for the velocity problems and the advectiondiffusion problem as input, the fully coupled velocity and temperature 

solution and free surface problem was solved. The temperature profiles from 

these solutions were essentially the same as those obtained in the advectiondiffusion problems (Figure 3 1). The velocity solutions are also similar, with 

some changes in the pouring lip and ribbon region observed. Changes in the 

torch once again had the same effects in the coupled solutions as they had in 

the advection-diffusion solutions. 

Iv. Discuss ion 

The fixed ribbon and free surface velocity solutions have shown that the 

viscosity of the melt and the velocity of the rotating chill wheel have the 

greatest influence on the velocity profile in the melt and the thickness of the 

resulting ribbon. Surface tension and the material depth on the pouring lip 

also influenced the velocity solutions. 

In both the fixed ribbon and free surface solutions it was seen that 

viscosity and velocity influenced the formation of a recirculation zone in the 

melt just before the melt-chill wheel interface. The recirculation zone is not 

desirable because it allows cooling of the melt during recirculation and 

possible freeze-off of the metal before it reaches the chill wheel. This can best 

be avoided by keeping casting speeds low and maintaining a sufficient 

thickness of material on the pouring lip. While it is difficult to control the 

viscosity of the melt for any given metal, it important understand the 

influence of viscosity if other metals or alloys are to be cast. For similar 

casting speeds, metals with lower viscosities will experience more problems 

with recirculation and freeze-off. 

A-22 
I 

Viscosity and velocity also played major roles in determining ribbon 

thickness. The results indicate that the thickness of the ribbon is dependent 

on the capillary number of the fluid and is determined by the shape of the 

meniscus before the ribbon solidifies. Results from the model agree well with 

early experimental results from the melt overflow process. This also indicates 

that the only practical way to change ribbon thickness is to change the 

velocity of the chill wheel, since both viscosity and surface tension, the other 

factors that determine capillary number, are difficult to change for a given 

material. 

In the thermal results, the heat transfer between the melt and the chill 

wheel proved to be the main factor in the formation of the solidified ribbon. 

The conclusion reached, that hwheel had to be between 7.0 and 8.0 cal/cm*-s-C 

for the ribbon to solidify, is in agreement with experimental rapid 

solidification studies, but disagrees with the initial assumption that the heat 

transfer mechanism occurring was similar to that of continuous casting. It is 

still unclear what sort of heat transfer mechanism takes place between the 

ribbon and the chill wheel and further study is needed to better understand 

this process. 

The location and intensity of the torch also influenced the solidification 

of the ribbon. Raising the intensity or moving the torch closer to the ribbon 

raised the temperature of the melt in the ribbon and delayed solidification. 

The torch was modelled as a gaussian distribution with a power of 75 kW which 

was centered over the hearth. This type of distribution and power level may 

or may not be correct and as further experimental data on the torch becomes 

available, the torch heat flux should be modified accordingly. 

The cooling rate in the ribbon was calculated to be 1.6~10~ K/s, which is 

also in agreement with other studies of rapid solidification processes. This 

cooling rate is within the region of lo5 to lo6 K/s necessary for the formation 

of amorphous or microcrystalline phases in the ribbon. 

, 

A-23 
This study of the melt overflow rapid solidification process has shown 

that the process can be used to produce a thin, continuous ribbon with 

amorphous or microcrystalline phases in the microstructure. The capillary 

number, which relates the velocity of the chill wheel, and the viscosity and 

surface tension of the melt, appears to be the main factor in determining the 

thickness of the ribbon while the heat transfer coefficient between the 

ribbon and the chill wheel is the main factor in determining the location of 

the solidification front in the ribbon. Further work needs to be done to better 

understand the influence of the capillary number on ribbon thickness and to 

better understand the heat transfer mechanism between the ribbon and chill 

wheel. 

A-24 
Solidified Ribbon 

Melt Overflow Process 

(Figure 1) 

A-25 
K 

w 

A-26 
102 

1 

10-4 

10-1 103 

Influence of Tempcrature Gradient, G, 

and Growth Rate, V, on Microstructure 

(Figure 3) 

A-27 
AdvectionDiffusion Coupled 

Solution Process 

(Figure 4) 

A-28 
E 

V 

VI 

1 

In 

\9 

.- 

A-29 
S 

4 

I 

I 

2 

- 

1 

I 

I 

Four Noded Linear Isoparametric 

Quadrilateral Elements 

(Figure 6) 

A-30 
n t 

Two Noded Boundary Elements 

(Figure 7) 

A-31 
Finite Element Mesh 

(Figure 8) 

A-32 
Surface Tension Angles 

(Figure 9) 

A-33 
Heat 

t - 

1660 1671 

Temperature 

Latent Heat of Fusion - Specific Heat Method 

(Figure 10) 

of Fusion 

A-34 
t 

1660 1671 

Temperature 

Latent Heat of Fusion - Enthalpy Method 

(Figure 11) 

A-35 
un=o I 

Ut = tangential speed 

of chill wheel \A 

ut = 0 J 

Velocity Boundary Conditions 

(Figure 12) 

A-36 
Base 

Free Surface Spines 

(Figure 13) 

A-37 
Small Model for Free Surface Problem 

(Figure 14) 

A-38 
of chill wheel 

Free Surface Boundary Conditions 

(Figure 15) 

A-39 
Temperature Boundary Conditions 

(Figure 16) 

A-40 
Ramped Heat Flux for Torch 

(Figure 17) 

A- 41 
Gaussian Heat Flux for Torch 

(Figure 18) 

A-42 
0RIGINA.L PAGE 

BLACK A:\3 i:J'HiTE PHOTOGRAPH 

Effect of Viscosity on the Formation 

of the Recirculation Zone 

(Figure 19) 

A-43 
0 

ri 

hi 

vi 

W 

sc :0 

gh 

SCC IS 

S t 

it Y 

Effect of Viscosity on the 

Momemtum Boundary Layer 

(Figure 20) 

A-44 
ORlGlNAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

low 

velocity 

high 

velocity 

Effect of Velocity on the Size 

of the Recirculation Zone 

(Figure 21) 

A-45 
low 

velocity 

high 

velocity 

Effect of Velocity on the 

Momentum Boundary Layer 

(Figure 22) 

ORlGlNAL PAGE 

BLACK AND WHITE PHOTOGRAPH A-46 
0RIGINP.L PAGE 

BLACK AND WHITE PHOTOGRAPH 

incre 

melt 

depth 

Effect of Melt Depth on the Size 

of the Recirculation Zone 

(Figure 23) 

a S ;e :d 

A-4 7 
low 

viscosity 

high 

viscosity 

Effect of Viscosity on 

Ribbon Thickness 

(Figure 24) 

ORlGlNAL PAGE 

E’dCi(; AND WHITE PH(aPOGRAP9 

A-48 
Computed vs. Measured Thickness 

A 

A 

0 

A 0 

0 

0 

0 

0 

0 

A Depth = 0 mm 

0 Depth = 1 mm 

0 Depth = 4 mm 

0 

CI- t = 748.3 + 8056e-250Ca 

t = 298.0 + 1446e-250Ca 

0 

0' I I I I I 1 I I I I I I I I I 

0.00 0.01 0.02 0.03 

Capillary Number (pU/@ 

Effect of Capillary Number on 

Ribbon Thickness 

(Figure 25) 

A-49 
increa 

melt 

depth 

sed 

Effect of Melt Depth on 

Ribbon Thickness 

(Figure 26) 

A-5 0 
50 kW 

75 

Effect of Torch Intensity on 

Temperature Profiles 

(Figure 27) 

kW 

A-5 1 
Ramped 

Gaussian 

Effect of Ramped vs. Gaussian Torch Profile 

on Temperature Profiles 

(Figure 28) 

OR 1 G 1 N AL Fi7G E 

BLACK AND WHITE PHOTC!G4A?H 

A-5 2 
Temperature Profiles for 

hwheel of 2.0 

(Figure 29) 

A-5 3 
Temperature Profiles for 

hwheel of 7.0 

(Figure 30) 
Temperature Profile for 

Fully Coupled Problem 

(Figure 31) 

A-55 
Material Properties of Titanium 

density .......... 4.51 g/cm3 

surface tension ...... 1600. dyne/cm 

surface tension angles ... 80.86 degrees 

185.0 I, 

thermal conductivity .... 0.41 cal/cm-s-C 

emissivity ......... 0.2 

Temperature Dependent Properties 

viscosity. ........ 0.01 g/cm-s 

IX 1022 g/cm-s 

specific heat. ...... 0.1 cal/g-C 

10.1 

0.1 

11 

11 

enthalpy ........ 0.0 

270.0 

365.0 

615.0 

1429.0 

heat transfer 

coefficient (wheel) ... 7.0 cal/cm2-s-C 

(< 1660 C) 

(> 1670 C) 

(-1.0e12 to 1660 C) 

(1661 to 1670 C) 

(1671 to 1.0e12 C) 

( OC) 

( 1660 C) 

( 1671 C) 

( 3500 C) 

(10000 C) 

heat trans fer 

coefficient (crucible) . . 0.1 cal/crn2-s-C 

A-5 6 
reference 

temperature ...... 25.0 

S tefan-Boltzman 

constant ...... 5.67e- 12 

C 

A-5 7 
Velocity Solution Input File 

*TITLE 

MELT OVERFLOW PROCESS - VELOCITY SOLUTION 

*FIMESH(IMAX=6, JMAX=3) 

EXPI 

/123456 

1 31 51 67 73 103 

EXPJ 

/1234 

1 7 15 

POINT 

1111 0. 0. 

2 2 1 1 10.244 0. 

3 121 0. 3.75031 

4 2 2 1 10.99083 4.71186 

5 3 2 1 19.38125 6.86281 

6 4 2 1 21.844 7.620 

11 5 2 1 21.89888 8.79939 

12 6 2 1 23.02756 15.95693 

13 1 3 1 0. 5.64864 

14 2 3 1 10.99083 6.52353 

15 3 3 1 19.0 7.3 1093 

/13 1 3 1 0. 5.83771 

/14 2 3 1 10.99083 6.79929 

/15 3 3 1 19.0 7.5 

/16 4 3 1 21.1 8.2 

16 4 3 1 21.1 8.3 

/17 5 3 1 21.41962 8.87658 

17 5 3 1 21.41962 , 9.1 

18 6 3 1 22.78024 15.99342 

19. 0 0 0 34.544 7.620 

LINE 

*$ 

12 

A-5 8 
13 

24 

34 

45 

56 

13 14 

14 15 

15 16 

16 17 

17 18 4. 3 

12 18 

3 13 

4 14 

5 15 

6 16 

11 17 

ARC 

6 11 19 

CURVE 

11 12 5 4. 3 

21.91199 8.93231 

21.94259 9.19933 

2 1.979 17 9.46795 

22.02190 9.73822 

22.06840 9.99687 

SURFACE 

14 

3 18 

ELEMENT(QUAD,NODESA,ALL) 

ELEMENT(B0UNDARY ,NODES=2) 

12 18 

1 2 

1 2 

24 

24 

4 6 

A-5 9 
~ 

46 

ELEMENT(BC 

6 12 

6 12 

J-NDARJ ODES=2,CR IS,CR 

ELEMENT(B0UNDARY ,NODES=2,CRNS,CFNF) 

18 13 

18 13 

BCNODEO 

12 18 

6 12 20. 

46 

1 2 

24 

BCNODEWFREE) 

18 18 

BCNODE(UY) 

46 

6 12 

1 2 

2 4 

15 13 

/tangential comp. of vel. set to zero for initial slip problem 

/18 15 

BCNODE(UX) 

6 6 20. 

BCNODE(UY) 

13 13 

B CNODE(UY,FREE) 

15 15 

BCNODE(SURFACE) 

15 13 1. 

NUMBER 

2 1 

SPINES 

13 3 18 

END 

A-60 
*PROBLEM(STEADY,NONLINEAR,FREE) 

/*PROBLEM(STEADY ,NONLINEAR) 

/ 

*PRESSURE(MIXED DISCONTINUOUS) 

*EXECUTION(NEWJOB) 

*SOLUTION(N.R.=15,VELCONV=.OOl ,RFSCONV=.OO 1) 

*OPTIONS(STRESSDIVERGENCE) 

*ICNODE(VELOCITY,READ) 

*DATAPRINT( NONE) 

*DENSITY(CONSTANT=4.5 1) 

*VISCOSITY (CONSTANT=0.04) 

*SURFACETENSION(CONSTANT= 1600,ANG 1=80.85,ANG2= 185.0) 

*NODES(FIMESH) 

*EEMENTS(QUAD,NODES=4,FIMESH) 

*ELEMENTS(SLIP,NODES=2,FIMES H) 

*ELEMENTS(SLIP,NODES=2,FIMESH) 

*ELEMENTS(SLIF',NODES=2,FIMESH) 

*ELEMENTS(SLIP,NODES=2,FIMESH) 

*ELEMENTS( SLIP,NODES=2,FIMESH) 

*ELEMENTS (SLIP,NODES=2,FIMESH) 

*ELEMENTS (SLIP,NODES=:!,FIMESH) 

*ELEMENTS (SLIP,NODES=2,FIMES H) 

*ELEMENTS (SLIP,NODES=2,FIMES H) 

/*ELEhENTS(SLIP,NODES=2,FIMESH) 

/*ELEMENTS( SLIP,NODES=2,FIMESH) 

*ELEMENTS(SURFACE,NODES=2,FIMESH) 

*ELEMENTS(SURFACE,NODES=2,FIMESH) 

*PRINT0 UT (N ONE) 

*END 

I 

I 

A-6 1 

, 
Temperature Solution Input File 

*TITLE 

MELT OVERFLOW RIBBON SIMULATION - TEMPERATURE 

/*PROBLEM(STEADY ,NONLINEAR,2-D,ADV-DIF) 

/*PROBLEM(STEADY ,NONLINEAR,2-D, ADV-DIF,FREE) 

*PROBLEM( STEADY ,NONLINEAR,2-D ,STRONGLY - CPLD) 

/*PROBLEM(STEADY ,NONLINEAR,2-D,STRONGLY-CPLD,FREE) 

*PRESSURE(MIXED DISCONTINUOUS) 

*EXECUTION(NEWJOB) 

/*EXECUTION(RESTART) 

*SOLUTION(Q.N.=l O,VELC=.OO 1 ,RESCONV=.OO 1 ,ACCF=.5) 

*ICNODE(VELOCITY,READ) 

/*ICNODE(TEMPERATURE,READ) 

* DATAPRINT(N0NE) 

/ TITANIUM PROPERTY DATA 

*DENSITY(SET= l.CONSTANT4.5 1) 

*VISCOSITY(SET= 1 ,CURVE=4) 

-1.OE12,1660,1671,1.OE12,1.OE22,1.OE22,.01,.01 

/*SPECIFICHEAT(SET= 1 ,CURVE=6) 

/-3.OE12.1660,166 1,1670,167 1,3.OE12 

/0.1,0.1,10.1,10.1,0.1,0.1 

*SPECIFICHEAT(SET=l ,SUBROUTINE= 12) 

5,1 

0.0,1660,1671,3500,10000 

0.0,270,365,6 15,1429 

*CONDUCTIVITY(SET= 1 ,CONSTANT=OAl) 

*SURFACETENSION(SET= 1 ,CONSTANT= 160O,ANG1=80.85 ,ANG2=5) 

*VOLUMEXPANSION(SET= 1 ,CONSTANT=O. JZEFTEMp=25) 

*NODES(CARTESIAN,FIMESH) 

*HTRANSFER(SET= 1 ,CONSTANT=7.0,REFTEMP=25) 

*HTRANSFER(SET=2,CONSTANT=O. 1 ,REFTEMP=25) 

*EMISSIVITY (SET= 1 ,CONSTANT=~.~,REFTEMPP=~~,STEFB=~. 67E- 12) 

A-6 2 
*ELEMENTS(QUAD,NODESd,FIMESH,ALL,MDENS= 1 ,MVISC=l ,MSPHT=l ,MCOND= 1,M 

EXP=l) 

*ELEMENTS(SLIP,NODES=2,FIMESH) 

*ELEMENTS(CONVECTION,NODES=2,FIMESH,MCNV=2) 

*ELEMENTS(SLIP,NODES=2,FIMESH) 

*ELEMENTS(CONVECTION,NODES=2,FMESH,MCNV=2) 

*ELEMENTS (SLIP,NODES=2,FIMES H) 

*ELEMENTS (CONVECTION,NODES =2 ,FIMES H,MCNV= 1 ) 

*ELEMENTS (SLIP,NODES=2,FIMESH) 

*ELEMENTS(CONVECTION,NODES=2,FIMESH,MCNV= 1) 

/*ELEMENTS(SLIP,NODES=2,FIMESH) 

*ELEMENTS(SURFACE,NODES=2,FIMESH) 

*BCNODE(HEAT,NODES=2) 

1773,1774,1,0,9.65625 

1804,1805,0,299.34375,309 

1805,1806,0,309,1927 

1806,1807,0,1927,12332 

1807,1808,0,12332,77076 

*END 

A-6 3 
xb References 

1. L. E. Hackman and T. Gasper: Industrial Heating, Jan 1986, p. 23. 

2. S. Kavesh: in Metallic Glasses , J. Gilman and H. Leamy, eds., American 

Society for Metals, Metals Park, OH, pp36-40. 

3. T. Anthony and H. Cline: Journal of Applied Physics 1978, vol 49, 

pp 829-832. 

4. W. Kurz and D.J. Fisher: Fundamentals of Solidification, Trans Tech 

Publications, Aedermannsdorf, Switzerland, 1986, p. 91. 

5. M.S. Engelman: FIDAP Theoretical Manual, Fluid Dynamics International, 

Evanston,IL, 1987, p. 1-1. 

6. M.S. Engelman: FIDAP Theoretical Manual, Fluid Dynamics International, 

Evanston,IL, 1987, p. 10-1. 

7. A.D. Agayev, V.I. Kostikov, and V.N. Bobkovskiy: Russian Metallurgy, 1980, 

VOl. 3, pp.33-35. 

8. E. Lemmon: Numerical Methods in Heat Transfer, John Wiley and Sons, 

New York, 1981. 

9. J.A. Dantzig: Personal Conversation 

10. M.S. Engelman: FIDAP Theoretical Manual, Fluid Dynamics International, 

EvanstonJL, 1987, p. 10-9. 

11. M.S. Engelman: FIDAP Theoretical Manual, Fluid Dynamics International, 

Evanston,IL, 1987, p. 8-1 

12. M.S. Engelman: FIPREP Users Manual, Fluid Dynamics International, 

EvanstonJL, 1987, pp. 10-7 - 10-17. 

A-6 4 
13. E.M. Gutierrez and J. Szekely: Metalluryical Transactions, Dec. 1986, Vol. 

17B, pp. 695-703. 

14. J.A. Dantzig and J.W. Kelly: unpublished research, University of Illinois at 

Urbana-Champaign, 19 88. 

15. H.W. Deem and C.F. Lucks: Survev of Phvsical Property Data for Titanium 

and Titanium Allovs, Battelle Memorial Institute, Columbus, OH, 1956, 

p. 19. 

16. M.S. Engelman: FIDAP Theoretical Manual, Fluid Dynamics International, 

Evanston,IL, 1987, p. 2-6. 

17. M.S. Engelman: FIDAP Theoretical Manual, Fluid Dynamics International, 

EvanstonJL, 1987, p. 10-7. 

A-6 5 
Report Documentation Page 

1. Report No. 2. Government Accession No. 

NASA CR-4253 

4. Title and Subtitle 

17. Key Words (Suggested by AuthorkJJ 

Rapid Solidification 

Titanium Alloys 

Rapidly Solidified Titanium Alloys by Melt Overflow b 

18. Distribution Statement 

Unclassified-Unlimited 

Subject Category 26 

Thomas A. Gaspar, Thomas J. Bruce, Jr., Lloyd E. 

Hackman, Susan E. Brasmer, Jonathan A. Dantzig, and 

William A. Baeslack 111 

9. Performing Organization Name and Address 

9. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 

Unc la s s i f ied Unclassified 100 

Ribbon Technology Corporation 

Box 30758 

Gahanna, OH 43230 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Langley Research Center 

Hampton, VA 23665-5225 

15. Supplementary Notes Langley Technical Monitor: R. Keith Bird 

22. Price 

A0 5 

3. Recipient's Catalog No. 

5. Report Date 

September 1989 

6. Performing Organization Code 

8. Performing Organization Report No. 

10. Work Unit No. 

324-02-00 

11. Contract or Grant No. 

NASl-18288 

13. Type of Report and Period Covered 

Contractor Report 

14. Sponsoring Agency Code 

(SRIR Phase 11. Final Report 

T.A. Gaspar , T.J. Bruce and L.E. Hackman: Ribbon Technology Corp., Gahanna, OH. 

S.E. Brasmer and J.A. Dantzig: University of Illinois, Urbana, Illinois. W.A. 

Baeslack 111: The Ohio State University, Columbus, OH. Appendix A of this report was 

offered as a thesis in partial fulfillment of the requirements of a Master of Science 

in Mechanical Engineering, University of Illinois, Urbana, IL. 

A pilot plant scale furnace was designed and constructed for casting titanium alloy 

strip. The furnace combines plasma arc skull melting techniques with melt overflow 

rapid solidification technology. A mathematical model of the melting and casti-ng 

process was developed. The furnace cast strip of a suitable length and width for us 

with honeycomb structures. 

successfully cast into strip. 

microhardness, chemical analysis and cold rolling. 

16. Abstract 

Titanium alloys Ti-6A1-4V and Ti-14A1-21Nb were 

The strip was evaluated by optical metalloygraphy,