A Modified Approach to Modeling of Diffusive Transformation Kinetics from Nonisothermal Data and Experimental Verificati
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INTRODUCTION
In steels or other metallic materials with the diffusional phase transformation, the isothermal transformation diagrams (also known as Time–Temperature–Transformation (TTT) diagrams) describe the relationship between the holding time and transformed phase fraction at a given soaking temperature. TTT diagrams are easily described by the famous Johnson–Mehl–Avrami– Kolmogorov (JMAK) models and have been widely used in industry as a guide for heat treatment process to predict the final microstructure.[1] However, lots of actual heat treatment processes are not only isothermal, while the parts have to undergo complex cooling or heating paths. In the past decades, many generalized models were proposed to predict the transformation kinetics with the arbitrary thermal histories. In those cases, the additivity rule based on isothermal data[2–6] was usually adopted to describe the nucleation and grain growth kinetics during nonisothermal cooling process, see Eq. [1],
XIANGJUN CHEN, Student, is with the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, China, and also with the School of Engineering, Deakin University, Geelong, VIC 3217, Australia. NAMIN XIAO, Associate Professor, and DIANZHONG LI, Professor, are with the Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, China. Contact e-mail: [email protected] MINGHUI CAI and BERNARD F. ROLFE, Associate Professors, are with the School of Engineering, Deakin University. GUANGYAO LI, Professor, and GUANGYONG SUN, Associate Professor, are with the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University. Contact e-mail: [email protected] Manuscript submitted January 10, 2016. METALLURGICAL AND MATERIALS TRANSACTIONS A
m X Dti 1
si
¼ 1;
½1
where si is the TTT incubation time or the time required to reach the specified fraction of transformation at the temperature Ti ; Dti is the small time increment; and m is the number of calculation time steps in the simulation process. Under an isothermal condition, the JMAK model is generally used to describe the nucleation and grain growth of phase transformation,[5] F ¼ 1 expðb tn Þ
½2
Considering the influence of incubation time, a modified formula of JMAK equation has been expressed by Hawbolt[7] in the following equation, F ¼ 1 exp½b ðt ts Þn ;
½3
where F is the phase volume fraction, t is the elapsed time from the beginning of the transformation, and ts is the real start time of phase transformation, i.e., the incubation time for isothermal transformation. Commonly, the parameter b is dependent of the transformed temperature, composition of the parent phase, and grain size,[8] while n is related to the mechanism of nucleation and grain growth of phase transformation which is also affected by the temperature or transformation types.[9] For the purposes of this paper, it will be assumed (Cahn Hypothesis[10]) that b and n are the functions of temperat
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