A Simple Mathematical Model for Establishing Isothermal Transformation Kinetics from Continuous Cooling Data
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the steel industry, the final microstructure is one of the critical factors, which is directly related to the mechanical properties of products. This leads to a
JEONG MIN KIM is with the Division of Materials Science and Engineering, Hanyang University, Seoul 04763, Republic of Korea; and also with the Center for Energy Materials Research, Korea Institute of Science and Technology, Seoul 02792, Republic of Korea. MINWOO KANG and SEUNG-HYUN HONG are with the Metallic Materials Research Lab., Automotive Research and Development Division, Hyundai Motor Group, Hwaseong, Gyeonggi 18280, Republic of Korea. NAM HOON GOO is with the R&D Center, Hyundai Steel Company, Dangjin, Chungnam 31719, Republic of Korea. JAE-HYEOK SHIM is with the Center for Energy Materials Research, Korea Institute of Science and Technology. Contact e-mail: [email protected] YOUNG-KOOK LEE is with the Department of Materials Science and Engineering, Yonsei University, Seoul 03722, Republic of Korea. KYUNG JONG LEE is with the Division of Materials Science and Engineering, Hanyang University. Manuscript submitted March 03, 2020.
METALLURGICAL AND MATERIALS TRANSACTIONS A
significant interest in constructing a precise phase transformation model for predicting the microstructural evolution of steel during production. The traditional method for constructing phase transformation model starts with the data of isothermal transformation kinetics.[1–4] The reaction parameters n and k of the following Johnson–Mehl–Avrami (JMA) equation can be extracted by fitting ti X data from isothermal measurements of transformation at various temperatures: X ¼ 1 exp ktni ½1 where X is a normalized fraction, which is the ratio of the actual fraction to the equilibrium fraction of transformation and ti is the time required to obtain the fraction X. Combining extracted reaction parameters with the additivity rule,[1–6] phase transformation behavior during continuous cooling can be calculated as follows: Zttot
dt ¼1 ti ðX; TÞ
½2
0
where ttot is the time required to obtain the fraction X under continuous cooling condition. T is the temperature. Therefore, ttot can be calculated from Eq. [2] for arbitrary cooling patterns, only if ti(X, T) is known from isothermal tests. However, the problem of the traditional method is that isothermal measurements cannot always be performed easily.[7] For some steels, especially with low austenite stabilizing element or carbon content, time required for the start of phase transformation, i.e., the incubation time, is too short. In this case, phase transformation can partly occur during cooling process before reaching target isothermal temperature, resulting in the loss of the transformation information at the beginning period. To overcome this problem, a method for establishing isothermal transformation kinetics from continuous cooling data was first proposed by Rios.[6] Rios[6] proposed the following relationship between isothermal time and phase transformation kinetics during continuous cooling: ti ðX; TÞ ¼
@TX @q
½3
where
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