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Acta Materialia 56 (2008) 1482–1490 www.elsevier.com/locate/actamat
Finite element simulation of quench distortion in a low-alloy steel incorporating transformation kinetics Seok-Jae Lee a, Young-Kook Lee b,* a
Research Institute of Iron and Steel Technology, Yonsei University, Seoul 120-749, Republic of Korea b Department of Metallurgical Engineering, Yonsei University, Seoul 120-749, Republic of Korea
Received 17 October 2007; received in revised form 22 November 2007; accepted 27 November 2007 Available online 22 January 2008
Abstract The uncontrolled distortion of steel parts has been a long-standing and serious problem for heat treatment processes, especially quenching. To get a better understanding of distortion, the relationship between transformation kinetics and associated distortion has been investigated using a low-alloy chromium steel. Because martensite is a major phase transformed during the quenching of steel parts and is influential in the distortion, a new martensite start (Ms) temperature and a martensite kinetics equation are proposed. Oil quenching experiments with an asymmetrically cut cylinder were conducted to confirm the effect of phase transformations on distortion. ABAQUS and its user-defined subroutines UMAT and UMATHT were used for finite element method (FEM) analysis. The predictions of the FEM simulation compare well with the measured data. The simulation results allow for a clear understanding of the relationship between the transformation kinetics and distortion. Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Finite element method; Martensitic transformation; Transformation kinetics; Distortion; Low-alloy steel
1. Introduction Heat-treating processes have traditionally been used to greatly enhance the mechanical properties of steel parts such as bearings, gears, shafts, etc. Unfortunately, heat treatments such as carburizing, quenching and tempering often cause excessive and uncontrolled distortion. This type of distortion is still a major issue in the production of quality parts. Many research groups have examined the causes of distortion and found that the phase transformations as well as thermal stresses that occur during the heat treatment play an important role. Denis et al. [1,2] have investigated the effects of stress on the phase transformation kinetics and transformation plasticity. Inoue et al. have studied the relation between phase transformations and residual stresses [3], as well as the
*
Corresponding author. Tel.: +82 2 2123 2831; fax: +82 2 312 5375. E-mail address:
[email protected] (Y.-K. Lee).
influence of transformation plasticity on the distortion of a carburized ring specimen [4]. Arimoto et al. [5] have explained the origin of distortion and the stress distribution in quenched cylinders by accounting for the phase transformation. Ju et al. [6] have studied the martensitic transformation plastic behavior during quenching. Because martensite is the major phase produced during the quenching of the steel parts, a reliable prediction of the martensitic transformation kinetics is indispensable for the computational simulators of the distortion such as HEARTS [7], SYSWELD [8], DEFORM-HT [9], DANTE [10] and COSMAP [11]. Koistinen and Marburger’s equation [12], dating from 1959, is still widely used for the prediction of martensite kinetics. Their equation was obtained by fitting the martensite volume fraction, measured by X-ray diffraction, as a function of temperature below the martensite start temperature (Ms) in various iron–carbon steels. Although the equation was originally developed using iron–carbon steels, many researchers have cited it without any modification
1359-6454/$34.00 Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.11.039
S.-J. Lee, Y.-K. Lee / Acta Materialia 56 (2008) 1482–1490
for low-alloy steels containing alloying elements such as chromium, nickel and molybdenum. In addition, the equation generates a C-curve shape for the martensite volume fraction plotted against the cooling temperature below Ms. In contrast, for most low-alloys steels the martensitic transformation kinetic curve exhibits a sigmoid shape. Although many researchers [1–6] have attempted to clarify the exact relationship between phase transformations and internal stress, few studies that clearly explain the interaction between transformation kinetics and distortion have been conducted. Therefore, the purpose of the present study was to investigate the relationship between transformation kinetics, focussing on martensitic transformation and distortion using an AISI 5120 steel, which is widely used for diverse automobile parts. In the present work the Ms point and a martensite kinetics equation for steel are proposed. The equation considers austenite grain size (AGS), chemistry and the shape of the kinetic curve. The Ms point and the equation were validated with experimental data from the literature. A finite element method (FEM) analysis was performed, using thermal and mechanical properties obtained from thermodynamic calculations and the literature. Quenching experiments using cut cylinders were conducted. The experimentally measured temperature and distortion data were used to explain the relationship between the transformation kinetics and distortion within the FEM simulations. 2. Transformation kinetics model 2.1. Diffusive transformation Dilatometric specimens of AISI 5120 steel were machined into small plates of 10 3 1 mm3 from a hot-rolled bar. Table 1 lists the chemical composition of AISI 5120 steel. The initial microstructure of the dilatometric specimen was a mixture of ferrite and pearlite produced by furnace cooling. The specimens were austenitized at 900 °C with heating rates ranging from 1 to 50 °C s1, and held for 10 min in a vacuum. The specimens were then cooled to room temperature at cooling rates from 1 to 50 °C s1 by blowing nitrogen gas. A dilatometer was used to measure contractions and expansions during the heating and cooling. The sensor force needed to hold a dilatometric specimen (7.9 kPa) was too small to produce plastic transformation phenomena. The cooled specimens were mechanically polished and etched using 2% Nital. A common differential formula to characterize the diffusive transformation was used in this study. Kirkaldy et al.
Table 1 Chemical compositions of AISI 5120 steel (wt.%) C
Mn
Si
Cr
P, S
Fe
0.21
0.89
0.24
1.25
