A Kinetics Model for Martensite Transformation in Plain Carbon and Low-Alloyed Steels
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INTRODUCTION
MARTENSITE is an important steel microstructure that contributes greatly to the final mechanical properties of steel after heat treatment because of its high strength and hardness. To predict steel microstructures accurately that result from the decomposition of austenite, a reliable kinetics model of martensite transformation is necessary. This model needs to calculate the volume fraction of martensite quantitatively and accurately as a function of temperature below martensite start (Ms) temperature. The martensite transformation is a time-independent (diffusionless) transformation, and the amount of martensite produced depends on the degree of undercooling below the Ms temperature. Research over the last 60 years has shown that the degree of undercooling below Ms temperature acts as a driving force to form martensite. Many investigations have related data about the amount of undercooling and the amount of martensite formed these relationships into various empirical kinetics models to predict the martensite transformation quantitatively in different types of steels.[1–7] The most well-known and widely used empirical model is one proposed by Koistinen and Marburger[5] VM ¼ 1 exp½K ðMs TÞ
½1
where VM is the volume fraction of martensite, T is the temperature in Kelvin, Ms is the martensite start temperature, and K is a constant. Koistinen and Marburger determined the value of the constant from plots of retained austenite obtained by X-ray analysis at
SEOK-JAE LEE, Research Assistant Professor, is with the Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea. Contact e-mail: [email protected] CHESTER J. VAN TYNE, FIERF Professor, is with the Advanced Steel Processing and Products Research Center, Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, CO 80401. Manuscript submitted July 15, 2010. Article published online September 8, 2011 422—VOLUME 43A, FEBRUARY 2012
room temperature after undercooling down to 194 K (–79 °C) in four carbon steels that had different carbon contents (i.e., 0.37, 0.50, 0.81, and 1.10 wt pct C). From their analysis, the value of 0.011 was found for the constant (i.e., KKM = 0.011). The term ‘‘KM model’’ will be used when this value for the constant is used in Eq. [1]. For more than 60 years, Eq. [1] has been used widely to model martensite transformation in steels. The KM model has been used not only in the metallurgical research field but also in the field of mechanics (primarily by the finite-element method) to calculate the overall volume change of martensite during the heat-treatment processes of various steels. The KM model was derived by considering only the undercooling effect on martensite formation. However, the undercooling degree below Ms temperature is not the only factor that can affect martensite transformation. Several studies on the effect of prior austenite grain size (PAGS) on martensite transformation have been reported.[8–12] The PAGS affects M
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