By George E. Totten, Lin Xie, Kiyoshi Funatani
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Additional resources for Modeling and Simulation for Material Selection and Mechanical Design (Dekker Mechanical Engineering)
All Rights Reserved. in the state of equilibrium between ferrite and austenite and the partition between ferrite and austenite does not occur after transformation. The ortho-equilibrium should be used when the transformation occurs at a relatively high temperature and the cooling rate is very slow. The paraequilibrium and the LE–NP should be used when the transformation occurs at a relatively low temperature as in rapid cooling. For the phase transformation in the continuous hot-rolling mill where the cooling rate is rapid, the para-equilibrium or the NP–LE should be used.
In order to calculate the temperature accurately, the prediction of transformation is particularly important. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. Figure 24 Finish rolling and coiling temperatures for experiments in production mill. 73mass%Mn steel hot rolled in a production mill. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. 73mass%Mn steel hot rolled in a production mill. As mentioned above, a mathematical model for predicting transformation of low-carbon steels during cooling while taking ferrite transformation into consideration has been developed because the principal transformation product in low-carbon steels is ferrite.
According to the classical nucleation theory, the nucleation rate, I, can be described by equation  DGÃ Ã I ¼ Nb Z exp À ð30Þ kT where N is the number of nucleation sites, bÃ is the rate of solute atoms arriving at the surface of new phase, Z (the Zeldovich factor) characterizes the annihilation of nucleation, T the temperature, k is the Boltzmann constant and DGÃ is the driving force for forming the nucleus with a critical size. Z and bÃ can be described by the following equations, respectively Z ¼ aTÀ1=2 ð31Þ bÃ ¼ bD ð32Þ where D is the diffusion coefficient of solute atoms, a the variable related to interfacial energy and b is the variable related to the nearest atomic distance.
Modeling and Simulation for Material Selection and Mechanical Design (Dekker Mechanical Engineering) by George E. Totten, Lin Xie, Kiyoshi Funatani