Three-dimensional finite-element analysis of the quenching process of plain-carbon steel with phase transformation
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QUENCHING is widely used to produce a variety of mechanical parts such as machine, automobile, and aircraft components with high strength, hardness, wear resistance, etc. During the quenching process, various kinds of microstructures evolve, depending on the temperature field within the steel and its characteristics. The effective control of such phase transformations can lead to producing these steel parts with the better mechanical properties and microstructures required. Thus, mathematical modeling of the phase transformation has been important for accurately analyzing the quenching process. An earlier analytical equation for diffusional transformation under the isothermal condition was developed by Johnson and Mehl[1] and Avrami.[2,3] Together with this equation, Sheil’s additive rule[4] has been widely adopted to describe a nonisothermal cooling process like quenching. For handling diffusionless transformation, Koistinen and Marburger[5] proposed an empirical equation which can be used to predict the volume fraction of martensite after rapid quenching. Since numerical simulation has become an efficient tool in predicting the temperature and phase distributions in continuously cooled mechanical parts of plain-carbon steel, many researchers such as Brimacombe et al.,[6,7,8] Sjöström et al.,[9] Denis et al.,[10–13] and Inoue et al.[14,15,16] have paid significant attention to the modeling of phase transformation to improve the accuracy of such numerical simulations. In these research works, except for the Inoue group, the additive rule was employed in simulation of incubation time for computational simplicity. Most of their studies, however, did not consider SEONG-HOON KANG, Postdoctoral Candidate, and YONG-TAEK IM, Professor, are with the Computer Aided Materials Processing Laboratory, Department of Mechanical Engineering, ME3227, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea. Contact e-mail: [email protected] Manuscript submitted December 7, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS A
the diffusionless transformation of martensite and only focused on prediction of the temperature history and the pearlite volume fraction of a eutectoid steel cylinder with 0.79 wt pct C during cooling for the two-dimensional case. Recently, Wang[17,18] tried to predict the temperature histories and volume fraction of pearlite as well as that of martensite during the quenching. However, although diffusionless transformation of martensite was considered in his work, still, a simple problem such as a cylindrical specimen of eutectoid steel was solved using a two-dimensional finite-element (FE) program. In this study, a three-dimensional FE program was developed to predict the temperature history and volume fractions of various phases such as ferrite, pearlite, martensite, and retained austenite presented in the microstructure during the quenching process. Material properties depending on the temperature and carbon content, given from BISRA[19] and time-temperature-transformation (TTT) diagram
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