1. Introduction

Continuous casting and rapid solidification of metallic fibres and wires with final diameters directly from the meltoffers many advantages compared with the conventionalwire drawing process.1,2) The newly developed shape flowcasting technique enables to produce wires with requiredcross section straight from the molten state. Fine grained,segregation free microstructures or amorphous fine wiresand surface quality improvements can be achieved, so af-fording a high level of strength by finish-drawing of the ascast wires. Microstructural inhomogeneities and materialdefects produced by rolling and/or drawing will be avoidedby using this technology.

The principal idea of ejecting molten material through around nozzle has been applied for several decades in thechemical industry for the fabrication of polymer or glass fibres. However, continuous casting of metallic fibres orwires has up to now no widespread industrial applications,because of the different physical properties of synthetics,glass and metallic melts. For example, at the process tem-perature, polymer and glass melts exhibit higher viscosities(103 vs. 103 Pa) and lower surface tensions (3102–101

vs. 1 N m1) than liquid metals. A metallic free flight jet ismainly controlled by inertia and surface forces, and less byviscous forces. This leads to much lower stability of metal-lic free flight jets with a short break-up length comparedwith high viscosity materials.

This paper describes and discusses the physical princi-ples and the controlling process parameters of the shapeflow casting technology, as well as microstructural featuresand mechanical properties of continuously cast wires of se-lected material systems.

2. Theoretical Background

2.1. Stability Criteria of a Metallic Free Flight Jet

Free flight jets of non-viscous fluid are in a state of un-stable equilibrium and will break after a certain time inter-val into droplets. This is a result of radial symmetric sur-face instabilities caused by differences in the internal jetpressure in the axial flow direction. Four different types ofjet disintegration are distinguished.3) These are dropping,varicose break-up, sinuous break-up and atomization insmall melt droplets. Operating in the varicose break-up region results in smooth wires, because of the laminar flow

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ISIJ International, Vol. 46 (2006), No. 12, pp. 1858–1864

Shape Flow Casting and In-rotating-liquid-spinning Processesfor the Continuous Production of Wires and of High-strength andSoft Magnetic Metallic Fibres

Georg FROMMEYER,1) Joachim GNAUK,1) Wolfgang FRECH2) and Susanne ZELLER1)

1) Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Str. 1, 40237 Düsseldorf, Germany. E-mail: frommeyer@mpie.de, gnauk@mpie.de, zeller@mpie.de 2) Verein Deutscher Ingenieure e.V., Graf-Recke-Str. 84, 40239 Düsseldorf,Germany. E-mail: kunststoffe@vdi.de

(Received on April 13, 2006; accepted on July 5, 2006 )

Computer-controlled facilities for continuous casting of metallic fibres and wires performing in-rotating-liquid-spinning (INROLISP) and shape flow casting (SFC) were designed and installed to determine and con-trol the near-net-shape casting processes over an extended production period. In particular, the flow behav-iour of the melt jet was experimentally investigated and theoretically described using fluid dynamic equa-tions. The controlling process parameters, such as the velocity of the melt jet, the stable free flight length,the nozzle geometry and cooling rate, were examined and optimised. Several pure metals as well as micro-crystalline and amorphous alloys were cast into continuous fibres and wires of high quality. Microstructuralfeatures and mechanical properties of rapidly quenched fibres and thin wires were also evaluated. Of greatpotential application is the production of amorphous softmagnetic Fe base and Co base thin wires with di-ameters of about 30 to 50 mm. These microwires are used as sensor cores in highly sensitive novel mag-netic field sensors based on a magneto-electric effect.Direct casting of wires with diameters up to 3 mm iscarried out using the shape flow casting technique. The SFC facility is an highly instrumented modifiedmeltspin facility, performing rapid substrate quenching. The process principles of the SFC technology, whichenable a flexible production of steel, nickel base alloy wires and other novel materials are presented. Themicrostructural features are correlated with the process parameters.

KEY WORDS: continuous casting; rapid solidification; shape flow casting; in-rotating-liquid spinning; fibres;wires.

dynamic of the jet. In this regime, the correlation:

...................(1)

describes the flow behaviour of the jet by the normalizedbreak-up length L/d and the dimensionless jet velocity, expressed by the Reynold (Rendr /m) and Ohnesorge(Ohm /√rsd) numbers. The materials parameters are asfollows: m is the dynamic viscosity, r is the density of themetallic jet, s defines the surface tension, n is the velocityand d is the nozzle diameter. The logarithmic factor takesthe ration of the nozzle diameter to the initial disturbance ofthe jet at the nozzle orifice into account.

The Ohnesorge diagram, shown in Fig. 1, illustrates thelimits of the coexisting regimes which are based on Eq. (1)of the described jet disintegration modes. With increasingRe number and jet velocity the transition from one stage toanother occurs. For continuous casting of fibres and wires,the different regimes of jet disintegration, characterized byRe numbers in the range 1 000Re10 000 and Ohnesorgenumbers of the order of Oh103, specifically for the coex-isting varicose and sinusoidal break-up stages are of greatimportance. Jet stability (Rayleigh waves) occurred at de-fined surface wavelengths.4,5) The disturbed jet surface canbe described by a differential change in the jet radius usingthe following equations:

.........(2)

Where r0 is the radius of the jet, d(z) is the amplitude ofthe wave-disturbed jet in the flow direction at a given coor-dinate z, and d0 defines the initial amplitude. l representsthe wavelength of the jet instability. The inner jet pressureis dependent on the surface tension and the curvatures ofthe varicose topology which is quantitatively described bythe following expression:

.........................(3)

where R1 and R2 are the radii of the sinusoidal jet surface inlongitudinal and radial direction. Maximal pressure differ-ences occur in the coexisting relative maxima and minima

regimes of the wave-shaped jet surface. Investigations onthe free flight jet stability showed that the amplitude of thedisturbance increases exponentially in time.6) This is quan-tified by:

...................(4)

where W is the amplification of the disturbance. Wmax is de-fined as:

.............................(5)

From this expression, the critical wavelength l crit2pr0√2 can be derived. The break up occurs when the dis-turbance is comparable to the jet radius and the time inter-val in which an unstable jet breaks up is given by Eq. (4):

...........................(6)

This was also confirmed by experiments using liquid gal-lium and water jets.7) The free flight length in which the jetbegins to be unstable is given by:

.............................(7)

In Fig. 2, the normalized exponent W√We r0/vs2 is plotted

as a function of the unstable wavelength l of the jet.

2.2. Velocity and Pressure Distribution in the Coolantin a Rotating Drum

A circular flow of liquid coolant in a rotating open drum,i.e. rigid body rotation, can be described by the Navier–Stokes equations,8) considering the acceleration forces in agravitation field. Therefore, the fluid dynamics are only de-termined by the primary flow, because a secondary flowcomponent does not exist. The integration of the Navier–Stokes equations by considering the boundary conditionsleads to the rotational velocity of the drum being given by:

...........................(8)

j is the angular velocity, R is the inner drum radius, and n

ν ϕ πt R Rn

˙ 260

lr

ss

v

Ωmax

ln 0

0δ

∆tr

s 1 0

0Ωmax

lnδ

Ωmax σρ8 0

3r

δ δπλ

( , ) exp( ) cosz t tz

0

2Ω

p zR R

( ) σ1 1

1 2

r z r z zz

( ) ( ) ( ) cos 0 0

2δ δ δ

πλ

with

L

d

d Re( ln3

2 0

Oh Oh)2

δ

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Fig. 1. Ohnesorge diagram showing the four regions of jet disin-tegration.

Fig. 2. Exponent of the amplitude of the disturbed jet as a func-tion of the break-up length.

defines the rotational frequency in revolutions per min.The pressure distribution in the laminar flowing coolant

is defined by:

....................(9)

and this expression allows the calculation of the surfaceshape of the coolant as a function of the angular velocity jand the axial coordinate z.

2.3. Jet Velocity in the Nozzle and at the Orifice

A quantitative description of a flow in a cylindrical tubeof constant cross-section is given by the Navier–Stokesequations. The requirements to be fulfilled are a stable lam-inar jet (Re2 300) and the friction at the tube wall causesa decrease in the boundary velocity (to vB0).

From the Navier–Stokes equations it follows that thepressure distribution in the cross-section of the tube in z-direction is constant. This is the well-known Hagen–Poiseuille flow. The following equation describes the veloc-ity as a function of the radial (r) and axial (z) coordinates:

.........................................(10)

The laminar flow in a nozzle of constant cylindricalcross-section can be described by le0.03dRe. For Re num-bers of the order of 2 000 the run in length is le60d (withd the nozzle diameter). The friction acting in the boundarylayer of the tube wall causes a dissipation of the kinetiu en-ergy. Consequently, a pressure loss of the jet in the nozzleoccurs. This is expressed by the formula:

.............................(11)

where x is the pressure loss coefficient that varies between0.01 and 0.04. For the carried out casting process of iron ornickel base alloy wires using |v |1.5 m s1 the pressureloss of the jet is about 103 MPa. The calculation of theoutflow velocity at the nozzle orifice is given by theBernoulli equation:

.....................(12)

where Dp is the pressure and gh(t) is the specific time dependent potential energy of an incremental flow jet.

2.4. Heat Transport

The heat transport mechanisms which govern the coolingof the metallic jet are as follows:• enforced convection in the melt jet inside the run in

length of the nozzle;• convection in the free flight jet caused by the relative ve-

locity between the jet and the surrounding atmosphere;• thermal radiation of the free flight jet;• heat transfer between the solidified jet and the substrate

(groove profile) of the casting wheel;

• heat conductivity in the melt and the substrate and heattransport due to thermal radiation.For the performed process parameter variation the heat

losses of the free flight jet was estimated to about 0.1 W s1.The heat transport by thermal radiation of the free jet sur-face in a time interval was calculated using the followingequation:

............(13)

A is the radiation surface of the wire, kB is Boltzmann’sconstant, e defines the radiation number, e is the emissioncoefficient, TS is the absolute surface temperature and TE isthe environment temperature. The heat loss was determinedto be about 0.065 W s1. The important steps of the heattransport are the heat transfer at the liquid–solid interfaceand the thermal conductivity of the substrate. From meltspinning experiments it is well known that the heat transfercoefficient a at the interfaces between the molten metalstream and the substrate surfaces is of the order of5105 W m1 K1 or somewhat higher. The Fourier’s differ-ential equation in cylindrical coordinates is as follows:

...........(14)

The source term WQ/rCP describes the time dependentheat contributing during liquid solid phase transformation,was numerically solved by computation using the ‘cast’program.

3. Experimental Procedures

3.1. Continuous Casting of Fine Wires and Fibres

An instrumented and computerized in-rotating-liquidspinning facility was built-up for the continuous casting offibres and thin wires on a semi-production scale (see Fig.3). The drum is 886 mm in diameter and made of acrylicglass for observing and monitoring the flow dynamics ofthe metallic jet. The drum was fixed on a high precisiondriving shaft to maintain the flow stability of the coolant inthe velocity range 5–25 m s1.

For each run, about 250 g of the alloy was melted inquartz or ceramic (Al2O3 ZrO3) crucibles in argon atmos-phere, using a high frequency induction coil. The metallicjet was formed by a precise boron nitride nozzle, applyingan argon inert gas pressure of about 5105 Pa. The distancebetween the nozzle tip and the coolant surface was pre-cisely adjustable by a step motor and the injection angle bya tilting device. High resolution cameras monitored the out-flow of the jet, the jet impinging on the coolant surface andentering the coolant. Deionized water with small amountsof tensides for reducing the surface tension was used as acoolant. the instrumented facility allows the quantitative de-termination of the important process parameters, as pre-sented in Table 1.

The stability of the jet is strongly affected by the preci-sion of the nozzle geometry. For the fabrication of high

∂∂

⋅∂∂

⋅∂∂

⋅

ϑ ϑ ϑt

ar r r

W

C

2

2

1 ˙Q

Pρ

Q e A kT T

⋅ ⋅ ⋅

B

S E

100 100ε

4 4

v 2

1 2∆p

h tρ

g ( )

/

δ ξρ

p2

2| |rv

v v( , ) | |r zR p

z

r

R

r

R

2 2 2

41 2 1

µδδ

r

p r z r z C( , ) ( ˙ ) ρ

ϕ ρ2

g

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quality fibres with round cross-sections and smooth sur-faces, an optimized nozzle geometry with sharp edges atthe orifice was designed.9)

3.2. Jet Behaviour

The wave-length of the sinusoidal jet disturbance was de-termined for several metallic melts to be D1.5pd. Thisvalue is in agreement with the theoretical prediction of√2 pd. The term ln(d/2d0) for the initial disturbance wascalculated to be about 8. This confirms the results ofLiebermann.10)

The jet velocity was calculated using the Bernoulli equa-tion and additional terms, such as the nozzle friction andcapillary forces.11) The jet pressure decreases in the run-inlength and at the exit of the nozzle. This was taken into ac-count by the additional loss factor rv2x /2. The experimen-tal data agree well with the calculated values for x0.3.The optimum ratio of the jet velocity to the tangential ve-locity of the coolant is vT

jet/vTcoolant0.9. Figure 4 shows the

linear relationship between the coolant velocity and the jetvelocity for a ratio c varying in the range 0.8c1.0.

3.3. Principle of the SFC Process

In the SFC process—melt spinning on a rotating profiledsubstrate surface—pure metals or alloys are melted and superheated in inert gas atmosphere using high-temperatureresistant ceramic or quartz crucibles. The surface of themelt is pressurized by argon gas, resulting in a pressure dif-ference between the crucible and its surroundings thatcauses the melt to accelerate in a round nozzle.

This melt-flux exits the nozzle in the form of a free jetwhich, after travelling just a few millimetres, strikes the ro-tating surface of the substrate at a defined angle of immer-sion (a). The bottom side of the cylindrical jet is stabilizedby the semicircular groove of the substrate and the top sideby surface tension. Groove diameters ranging from 1.5 to3 mm have been used to cast wires close to final dimension,as shown in the schematic drawing of Fig. 5.

SFC technology is a combination of the INROLISP (in-rotating-liquid-spinning) and the PFC (planar flow casting)process.12–14) Due to the achieved high cooling rates of103 K s1 the SFC process belongs to the realm of rapidsolidification technology.

3.4. Influence Variables and Process Parameters

Direct wire casting requires precise coordination ofprocess parameters. Figure 6 shows the basic function ofthe continuous casting process and a summary of the mostimportant process variables.

The filling of the wire cross section, which is fixed by thegeometry of the semicircular groove profile, requires a con-tinuous mass flow (m), which is defined by the circumferen-tial velocity (w) of the melt. The adequate pressure of ejec-tion can be calculated from mrwA allowing for the conti-nuity and Bernoulli’s equation, Eq. (10), for incompressiblefluids. The calculations were supplemented by experiments,in which the ideal mass of a defined piece of wire was cal-culated from its density and known ideal cross section andcompared with the actual mass. By taking measurements onan alloy it is possible to plot an alloy-specific characteristiccurve from which the ejection pressure can be read off withallowance for the alloy-dependent viscosity (h) and surface

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Fig. 3. Instrumented and computerized in-rotating-liquid spin-ning facility for the continuous casting of rapidlyquenched fibres.

Fig. 4. Coolant velocity vs. the tangential component of the jetvelocity.

Fig. 5. Photograph of the SFC facility. The control unit, meas-urement logger and video unit are in the front, the posi-tioning unit and casting ring (substrate) are placed in theback.

Table 1. Summary of process parameters.

tension (s). Table 2 presents the investigated process pa-rameters and their experimentally determined optimumranges.

4. Results and Discussion

4.1. Properties of As-cast Amorphous and Microcrys-talline Thin Wires and Fibres

A large variety of metallic alloys, such as Pd77Cu6Si17,Cu98Al2, Fe77Si10B13, Fe40Ni40B20, Fe90Si10 and Ni3Al, werespun into fibres of 60–300 mm in diameter. Figure 7 showsa representative scanning electron microscopy (SEM)image of a continuously cast thin Ni3Al wire. The surface isquite smooth and the weak flow pattern in the axial direc-tion on the mantel zone is caused by a thin stabilizing oxidesurface layer. The jet diameter was determined to be about160 mm and the variation in the diameter was less than 3%.The diameter of the fibres can be reduced of about 5–10%

as a result of the relaxation of the jet velocity in the laminarstreaming coolant. The flow dynamics of the jet and espe-cially the jet stability correspondent well with the theory ofWeber.4)

Table 3 presents some mechanical properties of selectedcrystalline and amorphous materials. The high strengthwires and fibres exhibit tensile strengths of the order of3 000 MPa and are potential materials for fibre-reinforcedcomposites and high strength ropes. Thin wires of about250–350 mm in diameter with ultimate tensile strengths ofabout 1 200 MPa are also potential candidates for tyre cordin high performance tyres. Functional materials, such asnoble metals of high electrical conductivity, soft magnetichigh-silicon steel wires containing about 6 wt% Si are feasi-ble for electro-magnetic sensors. Other applications areminiature motors and switching devices. Fine wires ofshape memory alloys are used for surgery purposes.

4.2. Continuous Casting and Properties of ThickerWires Using the SFC Technology

For optimizing the casting process parameters video im-ages were recorded and analyzed. A representative one is il-lustrated in Fig. 8. The jet of the molten metal strikes theguide groove of the rotating casting ring with constant takeoff angles and jet velocities, but with different wetting be-haviour of the substrate by varying its contact temperature.

The jet velocity was calculated using the Bernoulli equa-tion with additional terms, such as nozzle friction and cap-illary forces, see Eq. (10). The jet pressure decreases in therun-in length and at the nozzle orifice. This was taken intoaccount by an additional loss factor xrv2/2. The experimen-tal data agree well with the calculated values for x0.3 to

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Fig. 6. Schematic drawing of the SFC process and the keyprocess parameters, listed up below. h : dynamic viscos-ity; D: diameter of the groove profile; r : density of themelt; s : surface tension; DT: superheating of the melt; T:melting point; a : angle of the melt jet.

Fig. 7. SEM image of the surface of an as-cast Ni3Al fibre of160 mm in diameter.

Table 2. Process parameters for the continuous casting ofwires by the SFC technology.

Table 3. Mechanical properties of thin wires of different ma-terials.

0.4. The optimum ratio of the horizontal component of thejet velocity and the tangential velocity of the rotating castring was determined to be 0.95 in order to keep the momen-tum component perpendicular to the groove surface mini-mal.

The heat transfer coefficient and the cooling rates wereestimated from on-line temperature measurements of themelt puddle and of the solidified wire section after solidifi-cation is finished. The heat transfer coefficient at the meltpuddle-groove interface was estimated to about 5105

W m2 K1 whereas in the solidified region the heat transferis decreasing to 5104 W m2 K1 or even lower.15) How-ever, the heat transfer is mainly depending upon the thermalcontact between the liquid melt puddle or the as-solidifiedribbon and the groove surface at the actual temperature.Figures 9(a), 9(b) show a selected area of the measured andcomputed temperature distributions in the melt puddle inthe longitudinal (a) and transverse (b) sections. The temper-ature distribution is marked by the isotherms for an as solidifying stainless steel wire. The estimated maximumcooling rate in the contact zone is about 5104 K s1. Thecooling rate on the free surface of the solidified wire islower than 104 K s1.16)

After completing the initial parameter studies on a largevariety of metallic alloys of different compositions, meltingtemperatures, cooling rates, and heat transfer coefficientsattention was focused on the continuous casting of diversaustenitic stainless steel wires, ferritic heat resistant iron-chromium-aluminium alloy and nickel-chromium base ma-terial. These alloys are of great importance for industrialapplications. Figure 10 shows an as cast and as rolled or asdrawn stainless steel wire of about d3 mm in diameterafter final dressing and straightening by cold drawing ap-plying a degree of deformation of h15%.

The main task of the performed study was to achievefiner grain sizes by rapid quenching and improved mechani-cal properties, such as higher strength combined with highproduction efficiency. Table 4 presents several continuouslycast and rapidly solidified materials and some physical andmechanical properties.

5. Summary

Continuous casting and rapid solidification enable a lowcost production of fibres and wires in the diameter range

from 50 mm to 3 mm by performing a high process flexibil-ity. Other advantages are the amorphous solidification andthe fabrication of fine-grained microstructures possessingimproved mechanical and specific physical properties. Thesuccessful implementation of in-rotating-liquid-spinningand the shape flow casting technologies may cut out severalforming and heat treatment stages necessary for the produc-tion of high quality stainless steel or heat resistant wires of

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Table 4. Investigated alloys and selected properties.

Fig. 8. Laminar flow behaviour of a flowing out melt jet with op-timal melt-substrat contact (heat transfer coefficientK105 W m2 K1).

Fig. 9. Longitudinal (a) and cross sectional (b) views of the cal-culated temperature profiles of the melt puddle of a solid-ifiying wire.

Fig. 10. As cast stainless steel wire samples after dressing bycold rolling or drawing.

up to 3 mm in diameter and thin wires or fibres (30 to180 mm) of extremely high strength possessing specific softmagnetic properties. The study of the process parametersserve to optimize the continuous casting processes. The ac-tual cooling and solidification rates are high enough toachieve the amorphous state and/or finer grain sizes, andless segregations of alloying and tramp elements in the finalfibre and wire products.

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