Modeling the effect of coating weight on the kinetics of iron enrichment in hot dip galvanneal coatings on interstitial-
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Modeling the Effect of Coating Weight on the Kinetics of Iron Enrichment in Hot Dip Galvanneal Coatings on Interstitial-Free Steel Sheets C.R. Xavier, U.R. Seixas, and P.R. Rios The coating weight is shown to have a significant effect on the isothermal kinetics of iron enrichment in hot dip galvanized coatings on interstitial-free (IF) steel sheets during a postcoating heat treatment that simulates galvannealing. A simple quantitative model is proposed to account for this effect and is found to give reasonable agreement with the experimental results obtained for the kinetics of iron enrichment for coating weights of 60 and 80 glm 2.
Keywords galvannealing, hot dip galvanized, IF steels
M~t
A simple model for the kinetics of coating iron enrichment in hot dip galvanized interstitial-free (IF) steels for isothermal galvannealing has been recently developed (Ref 1, 2). The model has been shown (Ref 1-3) to give good agreement with Xavier, Seixas, and Rios (Ref 3), Jordan, Goggins, and Marder (Ref 4), and Lin, Meshii, and Cheng (Ref 5) data. A detailed description of the model as well as its assumptions and applicability can be found in previous work (Ref 1, 2). The fundamental equation of the model is:
(Eq 4)
= A J= AkA(W s - W)
where M i s the total mass of the coating. Here one assumes that, as a first approximation, both the total mass of the coating, M, and the coating density remain constant. Noticing that MIA is the coating weight per unit of area, M A, and that W = I00 (mlMA) where m is the mass of iron per unit of area of the coating, Eq 4 can be written as:
kA
dW dt - k(Ws - W)
dmdt - MA (ms - m)
(Eq 5)
(Eq 1) Comparing Eq 1 and Eq 5 one can write:
where W is the coating iron content, Ws is a coating saturation iron content, and W0 is the initial coating iron content, all in mass%. Equation 1 can be integrated noting that for t = 0, W = W0, where W0 is the initial coating iron content: W = W0 + (WS - W0)(1 - exp (-kt))
k=
kA
(Eq 6a)
MA
(Eq 2) Ws = 100~--~s A
In the present work, the above model is modified to take into account the effect of the coating thickness on the kinetics of iron enrichment of the Fe-Zn coating. This can be accomplished by applying mass-transfer concepts in the derivation of Eq 1. The flux of mass per unit of area into the coating can be written:
(Eq 6b)
where m S is a certain saturation iron mass per unit of area of the coating. Integrating Eq 5 with m = m 0 at t = 0 gives:
m = m 0 + (m s - m0) 1 - exp J = kA(W s - W)
(Eq 7)
(Eq 3)
The mass of iron that flows through a certain area A of the interface between the steel and the coating must be equal to the increase in the mass of iron within the coating:
C.R. Xavier, U.R. Seixas, and P.R. Rios, Universidade Federal Fluminense, Escola de Engenharia Industrial Metalargica de Volta Redonda, Av. dos Trabalhadores, 420, Vila Santa Cecilia, Volta Redonda, RJ, 27260-740 Brasil.
596---Volume 6(5) October 1997
MA))
Table 1 Summary of parameters obtained by nonlinear curve fitting of Eq 7 to experiment
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