5.4 Applications of the model and discussions
5.4.3 The effects of C and V contents on sheet spacing of IP
The composition dependence of the sheet spacing can be addressed as well by the present model. Figure 5-6 shows the calculated dependence of sheet spacing on C and on V. It indicates that the sheet spacing increases with increasing either C or V content.
Figure 5-6 is also used to compare the results of Lagneborg and Zajac [13]. The dependence of sheet spacing on C content calculated by the present model is consistent with that predicted by Lagneborg and Zajac (Figure 12 in ref. [13]). On the contrary, it is interesting to note that in the work of Lagneborg and Zajac the superledge height increases with V content, which is consistent with our calculation showing in Figure 5-6, but the consequence on the resulting sheet spacing reveals an opposite feature (Figure
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13 in ref. [13]). This contradiction, however, is not well-addressed in their work.
Further experimental work is in progress to investigate these points.
Figure 5-6 The calculated sheet spacing changing with C and V contents
5.5 Conclusion
A new model describing the carbides periodically precipitating on a migrating α/
γ interface has been proposed. The present model follows the main two features of interphase precipitation: (a) the interphase precipitation is accomplished by ledge mechanism of γ→α transformation, and (b) the precipitation on interface is actually a multi-interaction of precipitation and transformation kinetics. The features of interests, the sheet spacing, the particle spacing, and the overall interface velocity, are now expressed in terms of α ledge and carbide nucleation rates and the driving force for γ→α transformation. As the transformation temperature and the composition of steel are given, the characteristics of interphase precipitation could be predicted.
The calculated sheet spacing of IP is compared successfully with measured data
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from literature. The particle spacing and interface velocity are calculated as well. The proposed superledge model consequently could be used to predict the precipitation kinetic (the sheet spacing and the particle spacing) in combination with the transformation kinetic (the interface velocity). In addition, the dependence of sheet spacing on C and V contents is calculated and discussed with the results of Lagneborg and Zajac. The variation of sheet spacing with C calculated by superledge model is consistent with their work, but a contradiction is observed as the V content is changed.
Future work is in progress to clarify this issue.
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List of symbols
ν ferrite ledge velocity
ν* ferrite ledge velocity at unpinning
ναγα overall interface velocity without the presence of carbides on the interface
ν
αγ overall interface velocity with carbide precipitation on the interface M ledge mobility of the unit ledge with a height of aM h ledge mobility of the ledge with a height of h Mα pre-exponential factor of ledge mobility Q activation energy for interface advancement
Qα activation energy for ferrite ledge nucleation
gp
D
driving force for carbide nucleationD
G austenite-to-ferrite transformation driving force Gα*D
maximum of Gibbs energy associated with the formation of a ferrite nuclei*
Gp
D maximum of Gibbs energy associated with the formation of a carbide nuclei
GZP
D carbide pinning force
GZP
D
α carbide nominal pinning force σα ferrite/austenite interface energyσ
p ferrite/carbide interface energyγ interfacial energy associated carbide precipitating on ferrite/austenite interface
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Nαα number of ferrite nucleation site on the ferrite/austenite interface
Nαp number of carbide nucleation site on the ferrite/austenite interface ω geometric factor for heterogeneous nucleation
ccγ carbon concentration in austenite
ccα equilibrium carbon concentration in ferrite cp solute concentration of carbide
cαp nominal solute concentration ccα nominal carbon concentration
D boundary solute diffusion coefficient fα volume fraction of ferrite
fγ volume fraction of austenite
fp volume fraction of carbide Vp molar volume of carbide V Fe molar volume of ferrite
J B ferrite ledge nucleation rate
J T ledge nucleation rate on the top of base ledge Jp carbide nucleation rate
Kp solubility product of carbide in austenite R carbide radius
unpin
R carbide radius at superledge unpinning
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a unit ledge height (ferrite lattice parameter) b ledge spacing
bp inter-particle spacing in one sheet of interphase precipitation dγ half of prior austenite grain size
l superledge spacing
λ
sheet spacing of interphase precipitation h ledge heighth* the critical height of superledge for unpinning
t* time for ledge to reach its critical height for unpinning from carbides τ characteristic time for steady-state ledge-wise growth
τ n time for a unit ledge to nucleate on the top of the base ledge
τα time for created unit ledge to spread over a distance of bp on the top of
base ledge
τ λ characteristic time for overall interface to advance in a distance of
λ
τw waiting time to build a superledge to unpin from carbides
τ
f time for unpinned superledge to merge neighboring superledgesτ
p carbide incubation time134
Chapter 6
The Feature evolutions of interphase precipitation with the progression of austenite-to-ferrite transformation
6.1 Introduction
The models reviewed and discussed previously have shown good agreements with experimental results and the temperature dependence of sheet spacing are correctly accounted for. It is worth noticing that the existing models did not consider the effect of carbon enrichment in austenite on the characteristics features of interphase precipitation.
This is because the analyzed materials in the proposed models were low carbon and low alloyed steels, the carbon enrichment in austenite would not affect greatly kinetics of austenite-to-ferrite transformation. It is expected that this would affect both the kinetics of austenite-to-ferrite transformation and the precipitation state. Furthermore, the transition from interphase precipitation to carbide fiber would be affected. To our knowledge, the existing models do not consider these two points.
Because the increased demands for medium carbon steels for automobile components and steel bars for construction uses [1, 4, 47, 52, 97], it is worthy to understand the mechanisms of their microstructure formation. The superledge model described in Chapter 5 was modified, and the evolutions of the characteristic features of interphase precipitation are clearly revealed. In order to account for γ composition evolution, the results were discussed in terms of transformation driving force, ferrite and carbide nucleation rates. Finally, the conditions were established for the transition of interphase precipitation to carbide fibers.
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