Seetharaman S. Fundamentals of metallurgy
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where
2
is secondary arm spacing (m) and T is local cooling rate (ëC/s). Using
equation 10.88 the secondary dendrite arm spacings were converted to cooling
rates and these results are shown in Fig. 10.41. Extrapolations of the local
cooling rates are in agreement with the cooling rates obtained by the surface
temperatures of the solidified steel.
In these results the effect of superheat is perhaps counter-intuitive as one
would expect increased superheat to increase gradients in the liquid and increase
the amount of heat transferred through the interface from the liquid, thus
reducing the growth rate via equation 10.40. However, as nucleation does not
occur until the temperature is significantly reduc ed, the effect of superheat in
droplet experiments is to extend the time before solidification initiates and to
10.40 Effect of superheat on secondary dendrite arm spacing.
10.41 Cooling rate in the casting as a function of superheat.
446 Fundamentals of metallurgy
allow better contact of the liquid to the mold before the shell is formed. As there
is considerable stirring in ejected droplets the superheat is dissipated very
quickly before the onset of solidification and significant undercooling is possible
due to the high heat transfer rates that are possible due to improved contact
between the mold and the shell. Thus any factor that reduces the equilibrium
temperature for solidification start (e.g. composition) will have a similar effect
as it will allow better contact of the liquid alloy to the mold surface before
initiation of solidification.
Another method of improving contact is to fill a mold more quickly. This can
be accomplished by increasing ejection pressure (Fig. 10.42) and if the liquid
covers the mold more quickly, the cooling rate increases due to better contact.
10.4.5 Interactions between the mold and the steel shell
During casting in an oscillating mold caster there is always a solid/liquid oxide
between the steel shell and the mold; however, in twin roll, horizontal and ingot
casting, the shell comes into direct contact with the mold. This leads to the
opportunity for material to be transported during solidification from the steel to
the mold surface and to affect the heat transfer rate. This was shown by first by
Strezov et al.
43,44
in dip experiments (Fig. 10.43) and by Evans
45,46
in droplet
experiments where in Mn-Si killed steels MnO-SiO
2
coats the mold surface and
leads to an increase in the heat transfer rate.
Misra et al.
38,39
later showed this to be a quite general phenomenon in steels
when liquid oxides are the stable natural oxide and showed that, due to contact
angle changes during cooling, the natural liquid inclusions can be physically
ejected onto the surface of the mold. Evaporation is also a mechanism by which
10.42 Effect of ejection pressure on surface cooling rate.
Solidification and steel casting 447
material can be transported onto mold surfaces and in aluminum killed steels
where the natural inclusions are solid, MnS films are found to build up on mold
surfaces.
38,39
In high manganese content steels, Mn evaporation rates are high
and MnO is deposited onto mold surfaces (Fig. 10.44).
47,48
When a liquid contacts a mold there is not perfect contact between the liquid
and the mold and, on the microscale, the liquid sits on top of the peaks of the
roughness of the mold. Thus there is intermittent contact between the mold and
10.43 Maximum heat flux as a function of repeated immersion.
43
10.44 MnO deposits on the mold surface during the casting of a high
manganese steel. Photograph by P. Nolli and M.E. Valdez.
448 Fundamentals of metallurgy
the liquid and there will be a significant contact interfacial heat transfer
coefficient. Initially, there will be gas in the voids between the mold and the
liquid and convection and radiation heat transfer will control the rate of heat loss
in these areas. A detailed description of this contact between the mold and the
liquid would be determined by the wettability between the liquid steel and the
mold, the ease of undercooling and the initial superheat (to allow contact before
solidification), the time for nucleation, the liquid coverage velocity and the
pressure under which the liquid is pressed against the mold. If casting in a
vacuum, one could force complete wetting by supplying enough force to
overcome the surface tension forces. The presence of surface films changes the
wettability betwee n the liquid and the surface and tends to fill in the valleys of
the roughnes s. In additi on, if the deposited film can melt during the
solidification process, one goes towards perfect wetting of the deposited film
to the shell and the elimination of areas of voids. Thus one can eliminate the
contact resistance and replace that resistance with a conduction resistance for
heat transfer through the deposited film. Thus, as long as the film is thin, and the
new conduction resistance is less than that for intermittent contact, the total heat
flux will increase.
Thus in twin roll casting, or in any casting where there can be interaction
between the steel and the mold, heat flux can vary locally and with time due to
the deposition of material on the mold surface. This can lead to significant
increases in heat flux, which if controlled can lead to increased productivity, but,
if uncontrolled, can lead to local variation in heat transfer rates and the onset of
cracking.
48
10.5 Conclusion
The contact between a liquid and a mold controls the details of initial heat
transfer rates in steel castings and is a key issue in the understanding of the
initial solidification structures that can be formed. In conventional casting the
solidification structure of a mold flux is a key component in the understanding
of heat transfer and recent studies have shown that mold sla gs are easy glass
formers and thus solidification structures are quite variable and determined by
local thermal gradients; however, TTT and CCT diagrams can be very useful in
understanding this behavior. Surface oscillation marks are caused by variation in
meniscus position during mold oscillation that affects local heat transfer rates.
This can lead to hook type marks in grades with small liquidus to actual solidus
gaps. In twin roll or ingot casting solidification structures are controlled by the
relative velocity between the mold and the steel, the chemical nature of the
surface of the mold, superheat and steel chemistry. Undercooling and extremely
high heat transfer rates can be measured at short times when liquid steel comes
into contact with a water-cooled mold and leads to very fine microstructures at
the casting surface .
Solidification and steel casting 449
10.6 Acknowledgements
All professors are only as good as their students and co-workers. Thus most
figures and photographs from a research group are taken from the work of a
graduate student or a visiting researcher. In this chapter I'd like to thank C.
Orrling, A. Badri, M.E. Valdez, R. Rastogi, N. Phinichka, P. Misra, H. To doroki,
I. Jimbo, T. Suzuki, Y. Kashiwaya and H. Shibata for their contributions both
intellectually and artistically.
10.7 References
1. M. Flemings: Solidification Processing, 1974, Butterworths, London.
2. W. Kurtz and D.J. Fisher: Fundamentals of Solidification, 1984, Trans Tech
Publication, Switzerland.
3. W.A. Tiller: The Science of Crystallization: Macroscopic Phenomena and Defect
Generation, 1991, Cambridge University Press, London.
4. W.A. Tiller: The Science of Crystallization: Microscopic Interfacial Phenomenon,
1991, Cambridge University Press, London.
5. V. Alexiades and A.D. Solomon, Mathematical Modeling of Melting and Freezing
Processes, 1993, Hemisphere Publishing Corporation.
6. Dimo Katsiev: Nucleation, 2000, Butterworth Heineman.
7. B. Mutaftschiev: The Atomic Nature of Crystal Growth, 2001, Springer Verlag,
Berlin.
8. S. Davis: The Theory of Solidification, 2001, Cambridge University Press, London.
9. D.M. Stefanescu: Science and Engineering of Casting Solidification, 2002, Kluwer
Academic/Plenum Publishers.
10. M. Rappaz, C. Beckermann and R. Trivedi (eds), Solidification Processes and
Microstructures, TMS, 2004.
11. J.W. Gibbs, The Scientific Papers, Vol. 1: The rmodyna mics, 1961, Dover
Publications, New York
12. M. Volmer and A. Weber: Z. Phys. Chem., 119, 1926, 277.
13. T. Tanaka, M. Nakamoto and J. Lee: Metal Separation Technologies III, R.E. Aune
and M. Kekkonen (eds), Helsinki University Publishing, 2004, 135±142.
14. J.R. Sambles: Proc. Roy. Soc. London A, vol. 423 A, 339±351.
15. B.L. Bramfit: Effect of Carbide and Nitride Addition on the Heterogeneous
Nucleation, Behaviour of Liquid Iron, Met. Trans, vol. 1, no. 7, July 1970.
16. O. Grong, Metallurgical Modeling of Welding, 2nd edn, The Institute of Materials,
1997.
17. M.E. Valdez, H. Shibata, S. Sridhar and A.W. Cramb: `The Solidification Rate of
Undercooled Pure Liquid Iron', TMS/AIST Conference, New Orleans, September
2004.
18. A.W. Cramb and M. Byrne (eds), Making Shaping and Treating of Steel ± Vol. 3,
Casting, AISE, 2003.
19. R. Rastogi, doctoral thesis, Carnegie Mellon University, 2000.
20. R. Rastogi and A.W. Cramb: Inclusion Formation and Agglomeration in Aluminum
Killed Steels, 84th Steelmaking Conference Proceedings, 2001, 789±829.
21. Y. Kashiwaya, C.E. Cicutti and A.W. Cramb: Crystallization Phenomena of Mold
450 Fundamentals of metallurgy
Slag for Continuous Casting, ISIJ International, vol. 38, no. 4, 1998, 357±365.
22. Y. Kashiwaya, C.E. Cicutti and A.W. Cramb: `Crystallization Behaviour of Slags',
Steelmaking Conference , 1998, vol. 81, 185±191.
23. C. Orrling, A . Tilliander, Y. Kas hiwaya and A.W. Cramb: `Melting and
Solidification of Slags', Steelmaking Proceedings, 1999, vol. 82, 417±425.
24. C. Orrling, S. Sridhar and A.W. Cramb: In situ Observation of the Role of Alumina
on the Solidification Behavior of Slags, ISIJ, 2000, 877±885.
25. C. Orrli ng an d AW. Cramb: `The Effect of Water Vapor on Mold Slag
Crystallization', Met Trans B, 2000, vol. 31B, 403±406.
26. C. Orrling, Y. Fang, N. Phinichka, S. Sridhar and A.W. Cramb: `Observation and
Measurement of Solidification Phenomena at High Temperatures', JOM-e, July
1999 (http://www.tms.org/pubs/journals/JOM/9907/Orrling/Orrling-9907.html).
27. C. Orrling, doctoral thesis, Carnegie Mellon University, 2000.
28. C.T. Mutale, T. Claudon and A.W. Cramb: `Observation of the Crystallization
Behavior of a Slag containing 46 wt.% CaO, 46 wt.% SiO
2
, 6 wt.% Al
2
O
3
, and 2
wt.% Na
2
O using the Double Hot Thermocouple Technique', unpublished research.
29. K. Prapakorn, C. Orrling and A.W. Cramb: `The Solidification Behavior of Calcium
Aluminate in Dry and Wet Atmospheres', European Casting Conference, vol. 2,
2002, 733±742.
30. A. Badri, doctoral research, Carnegie Mellon University, 2003.
31. A. Badri, T.T. Natarajan, C.C. Snyder, K.D. Powers, F.J. Mannion, and A.W.
Cramb: `A Mold Simulator for the Continuous Casting of Steel, Part 1, Steel Shell
Solidification Profiles', Met Trans B, 2004, vol. 36B, no. 3, 355±372.
32. A. Badri, T.T. Natarajan, C.C. Snyder, K.D. Powers, F.J. Mannion, M. Byrne and
A.W. Cramb: `A Mold Simulator for the Continuous Casting of Steel, Part 2, The
Formation of Oscillation Marks During the Continuous Casting of Low Carbon
Steels', Met Trans B, 2004, vol. 36B, no. 3, 373±416.
33. I.G. Saucedo: Continuous Casting, Volume 9: Initial Solidification and Strand
Surface Quality of Peritectic Steels, 1997, ISS±AIME, Warrendale, PA, 131±141.
34. H. Mizukami, T. Suzuki and T. Umeda: Tetsu-to-Hagane, 77, 10, 1991, 1672.
35. H. Mizukami, T. Suzuki and T. Umeda: Tetsu-to-Hagane, 78, 4, 1992, 580.
36. H. Mizukami, T. Suzuki and T. Umeda: Tetsu-to-Hagane, 78, 8, 1992, 1369.
37. H. Mizukami, T. Suzuki, T. Umeda and W. Kurtz: Material Science and Eng A, 173,
1993, 36.
38. N. Phinichka, P. Misra, Y. Fang and Alan W. Cramb: `Initial Solidification
Phenomena in the Casting of Steels', Innovation and Excellence in Continuous
Casting, 2nd edn, Stahl Eisen, 2003, 65±78.
39. P. Misra, N. Phininchka and A.W. Cramb: `The Effect of the Presence of Liquid
Films on a Copper Mold Surface on the Rate of Heat Transfer during the
Solidification of Steel Droplets', ISS Transactions 2003, Iron and Steelmaker, vol.
30, no. 10, 2003, 46±55.
40. H. Todoroki, R. Lertarom, I. Jimbo, T. Suzuki and A.W. Cramb: `Solidification of
Steel Droplets against a Water Cooled Copper Mold', Proceedings of the McLean
Symposium, ISS, 1998, 155±175.
41. H. Todoroki, R. Lertarom, I. Jimbo, T. Suzuki and A.W. Cramb: `Initi al
Solidification of Iron, Nickel and Steel Droplets', TMS Meeting, San Diego, 1998.
42. H. Todoroki, Y. Suzuki and A.W. Cramb: `Initial Solidification of Iron, Nickel and
Steel Droplets', ISS Transactions, 1999, I&SM, vol. 26, no. 4, 57±71.
Solidification and steel casting 451
43. L. Strezov and J. Herbertson, `Experimental studies of interfacial heat transfer and
initial solidification pertinent to strip casting', ISIJ International, 38(9), 1998, 959±
966.
44. L. Strezov, J. Herbertson and G.R. Belton: `Mechanism of initial melt/substrate heat
transfer pertinent to strip casting', Metallurgical and Materials Transaction B, 31B,
October 2000, 1023±1030.
45. T. Evans, PhD Thesis, University of Newcastle, 2000.
46. T. Evans and L. Strezov: Metallurgical and Materials Transaction B, 31B, October
2000, 956±966.
47. D. Choo, P. Nolli, P. Misra, M.J. Ha and A.W. Cramb: `The Effect of Surface Oxide
Films on Heat Transfer Behavior in the Strip Casting Process', AISE Conference,
Pittsburgh, 2003.
48. P Nolli, D.K. Choo and A.W. Cramb: `The Effect of Suface Oxide Films on Heat
Transfer Behavior in the Strip Casting Process', TMS/AIST Conference, September
2004.
452 Fundamentals of metallurgy
11.1 Introduction
Metal working processes encompass a wide range of strain, strain rates and
temperatures. Strains range from less than 0.01 (for example in skin-pass rolling
of interstitial free steel) up to around 1 (cold rolling of strip, extrusion, etc.).
Typical strain rates and temperatures are given in Table 11.1 (which is partly an
extract from Frost and Ashby (1982)).
For plastic forming processes the most important characteristics of the
material are:
· the ability to distribute strains;
· the deformation resistance; and
· the resulting properties of the formed part.
11
Analysing metal working processes
G E N G B E R G , SSAB Tunnpla
Ê
t AB and MIK Research AB (MIKRAB) and
L K A R L S S O N , Dalarna University, Sweden
Table 11.1 Characteristics of metal working processes and typical values for some
common testing methods
Process Strain rate (s
ÿ1
) Temperature
Cold working (rolling, forging, 1± 2000 RT, slight adiabatic heating
levelling, . . .)
Wire drawing (sheet, tube drawing) 1±20 000 RT± 0.3 T
m
, adiabatic heating
Explosive forming 10±1000 RT
Machining 100±100 000 RT±0.4 T
m
, adiabatic heating
Warmworking (rolling, forging, . . .) 1± 1000 0.35± 0.5 T
m
Hotworking (rolling, forging, . . .) 1±1000 0.55± 0.85 T
m
Extrusion 0.1±100 0.7± 0.95 T
m
Testing method
Tensile up to 1000 RT
Tensile and compression up to 100 up to T
m
Hopkinson bar up to 4000 RT
RT: room temperature,T
m
: melting temperature in degrees Kelvin.
The ability to distribute strains is mainly governed by the work hardening and
strain-rate sensitivity. It is also affected by the strain path.
The purpose of this paper is to outline the, in our view, most essential
material properties for metal working processes and the microstructural reasons
for them. We recognise that the presence and development of crystallographic
texture is quite an important part but our purpose is not to give an extensive
description of this, only to point out some consequences. For further reading we
recommend a book by Kocks, Tome and Wenk (1998). Another aspect that is
only briefly covered is the influence of stress states and changes in strain paths
during processing or between consecutive process steps.
11.2 Work hardening
As commonly accepted the flow stress, , is usually proportional to the square
r oot of the dislocation density, . For a polycry stalline material the
proportionality constant can be seen as the product of the Taylor factor, m,
the strength of the barriers (such as attractive junctions between dislocations), ,
the shear modulus, G, and Burgers' vector, b. The rates of dislocation generation
and recovery/annihilation thus determines the work hardening rate.
0
m G b
p
11:1
d
dt
d
dt
generation
d
dt
recovery
11:2
0
are all other contributions to the flow stress except deformation hardening.
Dislocation generation is affected mainly by other dislocations, their ability to
cross-slip and grain and phase boundaries. Recovery is usually considered to be
due to cross-slip and climb and of course recrystallisation contributes to
annihilation of dislocations.
11.2.1 Single phase materials
The shear strain obtained by slip of one dislocation is given by the relative
displacement of the dislocation in the slip plane times Burgers' vector over the
height. For dislocations per unit area slipping an average distance of L
during the time increment t the relation to the normal strain increment, , can
be written as
d
dt
generation
m
b L
d
dt
11:3
The mean free distance of slip is for Frank networks limited by the distance
between individual dislocations, 1=
p
, while for heterogeneous dislocation
structures by the cell or subgrain sizes. This implies that strai n hardening varies
454 Fundamentals of metallurgy
between linear and parabolic. The tendency to form substructures is closely
related to the ability of dislocations to leave their original slip plan, either by
cross-slip or a combination of cross-slip and climb. Both are thermally activated
processes, cross-slip by bringing two partials together allowing them to slip on a
secondary slip system and climb by diffusion. Body centred cubic (bcc) metals
normally have very large stacking fault energies and a large number of possible
slip systems while a large variety of stacking fault energies is found for face
centred cubic (fcc) metals.
During deformation grains change their shapes and rotate. In order to account
for the different changes in individual grains it has been proposed that
additional, `geometrically necessary', dislocations are created at the boundaries
to accommodate the differences (Ashby 1971). The corresponding geometrical
dislocation slip distance is proportional to the grain size, d . For small grain sizes
this is manifested as an increased hardening rate (Chandrasekaran 2003).
BergstroÈm has proposed a model where the recovery term is due to
remobilisation of dislocations (BergstroÈm 1983). In his formulation
d
dt
recovery
ÿ
d
dt
11:4
where is measure of remobilisation. Another approach is to assume that
dislocations are increasing their link length by diffusion controlled climb
(Friedel 1964). We can write this as
d
dt
recovery
ÿM
2
; M
D
s
Gb
3
kT ln l=b
11:5
where M is the mobility for the process, D
s
is the self-diffusion coefficient, k is
Bolzmann's constant and l is the average dislocation link length.
Elements in solid solution will affect the generation process mainly by
changing the stacking fault energy and the recovery process by reducing the
mobility.
11.2.2 Multi-phase materials
When we are considering secondary phases in a continuous matrix their effect
will depend on their size relative to the average dislocation link length. When
the second phase is smaller then it will constitute a barrier to a single dislocation
and can be treated as conventional precipitation hardening. In this case the effect
on work hardening is insignificant (extra dislocation length is created, for
example, as Orowan loops around the particles). If, on the other hand, the second
phase is larger than the dislocation mean link length then we have to consider
the phases as regions of different plastic properties. The less deforming phases
(or constituents) will cause the generation of geometric ally necessary
dislocations in the softer parts in the same way as was discussed above for
Analysing metal working processes 455