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Mathematical modeling of the hot strip rolling of microalloyed Nb, multiply-alloyed Cr-Mo, and plain C-Mn steels

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Abstract

Industrial mill logs from seven different hot strip mills (HSMs) were analyzed in order to calculate the mean flow stresses (MFSs) developed in each stand. The schedules were typical of the processing of microalloyed Nb, multiply-alloyed Cr-Mo, and plain C-Mn steels. The calculations, based on the Sims analysis, take into account work roll flattening, redundant strain, and the forward slip ratio. The measured stresses are then compared to the predictions of a model based on an improved Misaka MFS equation, in which solute effects, strain accumulation, and the kinetics of static recrystallization (SRX) and metadynamic recrystallization (MDRX) are fully accounted for. Good agreement between the measured and predicted MFSs is obtained over the whole range of rolling temperatures. The evolution of grain size and the fractional softening are also predicted by the model during all stages of strip rolling. Special attention was paid to the Nb steels, in which the occurrence of Nb(C, N) precipitation strongly influences the rolling behavior, preventing softening between passes. The present study leads to the conclusion that Mn addition retards the strain-induced precipitation of Nb; by contrast, Si addition has an accelerating effect. The critical strain for the onset of dynamic recrystallization (DRX) in Nb steels is derived, and it is shown that the critical strain/peak strain ratio decreases with increasing Nb content; furthermore, Mn and Si have marginal but opposite effects. It is demonstrated that DRX followed by MDRX occurs under most conditions of hot strip rolling; during the initial passes, it is due to high strains, low strain rates, and high temperatures, and, in the final passes, it is a consequence of strain accumulation.

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Abbreviations

ε :

true strain

ε :

true strain rate (1/s)

ε a :

accumulated true strain

ε c :

critical strain for the initiation of dynamic recrystallization

ε f :

retained strain present in the material after leaving the finishing train

Z:

Zener-Hollomon parameter = ε · exp(Q def / RT)(1/s)

ε p :

peak strain

T :

absolute temperature (K)

Q def :

activation energy for deformation (J/mol)

X :

fractional softening

t 0.5 :

time for 50 pct softening (s)

R:

gas constant = 8.31 (J/mol·K)

d 0 :

initial grain size (µm)

T nr :

interpass recrystallization stop temperature (K)

t ps :

precipitation start time

T RH :

absolute reheat temperature (K)

T pass :

absolute pass temperature (K)

T :

cooling rate (°C/s)

H :

strip thickness before passes

h :

strip thickness after all passes

σ M :

mean flow stress

X dyn :

fractional softening attributable to dynamic recrystallization

σ ss :

steady-state stress

K :

parameter that converts flow stress to mean flow stress

K s :

supersaturation ratio

t ip :

interpass time

Nbeff :

effective Nb concentration

d :

grain size

d° α :

ferrite grain size when the austenite is unstrained

d γ :

austenite grain size

d α :

ferrite grain size after transformation of deformed austenite

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  1. the Department of Metallurgical Engineering, McGill University, H3A 2B2, Montreal, PQ, Canada

    Fulvio Siciliano Jr. (Research Associate) & John J. Jonas (Professor)

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  1. Fulvio Siciliano Jr.
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Siciliano, F., Jonas, J.J. Mathematical modeling of the hot strip rolling of microalloyed Nb, multiply-alloyed Cr-Mo, and plain C-Mn steels. Metall Mater Trans A 31, 511–530 (2000). https://doi.org/10.1007/s11661-000-0287-8

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