Abstract
An indigenous, non-linear, and coupled finite element (FE) program has been developed to predict the temperature field and phase evolution during heat treatment of steels. The diffusional transformations during continuous cooling of steels were modeled using Johnson–Mehl–Avrami–Komogorov equation, and the non-diffusion transformation was modeled using Koistinen–Marburger equation. Cylindrical quench probes made of AISI 4140 steel of 20-mm diameter and 50-mm long were heated to 1123 K (850 °C), quenched in water, and cooled in air. The temperature history during continuous cooling was recorded at the selected interior locations of the quench probes. The probes were then sectioned at the mid plane and resultant microstructures were observed. The process of water quenching and air cooling of AISI 4140 steel probes was simulated with the heat flux boundary condition in the FE program. The heat flux for air cooling process was calculated through the inverse heat conduction method using the cooling curve measured during air cooling of a stainless steel 304L probe as an input. The heat flux for the water quenching process was calculated from a surface heat flux model proposed for quenching simulations. The isothermal transformation start and finish times of different phases were taken from the published TTT data and were also calculated using Kirkaldy model and Li model and used in the FE program. The simulated cooling curves and phases using the published TTT data had a good agreement with the experimentally measured values. The computation results revealed that the use of published TTT data was more reliable in predicting the phase transformation during heat treatment of low alloy steels than the use of the Kirkaldy or Li model.
Similar content being viewed by others
Abbreviations
- A e1 :
-
Pearlite transformation start temperature in K (°C)
- A e3 :
-
Ferrite transformation start temperature in K (°C)
- b :
-
Constant of JMAK equation
- B s :
-
Bainite transformation start temperature in K (°C)
- c :
-
Specific heat (J/kg K)
- G :
-
Austenite grain size (ASTM No.)
- h :
-
Heat transfer coefficient (W/m2 K)
- I :
-
Reaction term (Integral part) in Kirkaldy model and Li model
- k :
-
Thermal conductivity (W/m K)
- M s :
-
Martensite transformation start temperature in K (°C)
- n :
-
Exponent of JMAK equation
- n x , n y :
-
Direction cosines of the outward normal vector
- Q :
-
Activation energy for diffusion reaction, (cal/mol)
- q :
-
Heat flux (W/m2)
- R :
-
Universal gas constant (cal/K mol)
- T :
-
Temperature, in K (°C)
- t :
-
Time (s)
- X :
-
Volume fraction of phases
- \( \rho \) :
-
Density (kg/m3)
- \( \dot{q} \) :
-
Rate of heat generation (W/m3)
- [C]:
-
Capacitance matrix
- [K]:
-
Element stiffness matrix
- {\( \dot{T} \)}:
-
First derivative of the temperature, T
- {F}:
-
Force vector
- ΔH :
-
Enthalpy of phase transformation (J/m3)
- ΔT :
-
Degree of undercooling, in K (°C)
- Δt :
-
Time step (s)
- ΔX :
-
Fraction of phase transformed over Δt
- τ :
-
Isothermal transformation time, (s)
- A:
-
Austenite
- B:
-
Bainite
- eqb:
-
Equilibrium
- F:
-
Ferrite
- f:
-
Finish of transformation
- M:
-
Martensite
- P:
-
Pearlite
- q:
-
Quenchant
- s:
-
Start of transformation
- true:
-
True
References
L. Huiping, Z. Guoqun, N. Shanting and H.Chuanzhen: Mater. Sci. Eng. A, 2007, vol. 452–453, pp. 705–14.
S.H. Kang and Y.T. Im: J. Mater. Process. Technol., 2007, vol. 192–193, pp. 381-90.
M. Eshraghi Kakhki, A. Kermanpur and M.A. Golozar: Model. Simul. Mater. Sci. Eng., 2009, vol. 17, 045007.
S. Denis, D. Farias, and A. Simon: ISIJ Int., 1992, vol. 32, pp. 316-25.
D. Homberg: Acta Mater., 1996, vol. 44, pp. 4375-85.
R. Thomas, M. Ganesa-Pillai, P.B. Aswath, K.L. Lawrence, and A. Haji-Sheikh: Metall. Mater. Trans. A, 1998, vol. 29A, pp. 1485-98.
P.R. Woodard, S. Chandrasekar, and H.T.Y. Yang: Metall. Mater. Trans. B, 1999, vol. 30B, pp. 815-22.
S. Serajzadeh: J. Mater. Process. Technol., 2004, vol. 146, pp. 311-17.
S.H. Kang and Y.T. Im: Metall. Mater. Trans. A, 2005, vol. 36A, pp. 2315-25.
P. Carlone, G.S. Palazzo and R. Pasquino: Comput. Math. Appl., 2010, vol. 59, pp. 585-94.
W.P. Oliveira, M.A. Savi, P.M.C.L. Pacheco, and L.F.G. de Souza: Mech. Mater., 2010, vol. 42, pp. 31-43.
J.S. Kirkaldy, D. Venugopalan, in: A.R. Marder, J.I. Goldstein, (Eds.), Phase Transformations in Ferrous Alloys, AIME, 1983, Warrendale, PA, pp. 125-48.
B. Buchmayr and J.S. Kirkaldy: J. Heat Treat., 1990, vol. 8, pp. 127-36.
D.F. Watt, L. Coon, M. Bibby, J. Goldak and C. Henwood: Acta. Metall., 1998, vol. 36, pp. 3029-35.
T.C. Nguyen and D.C. Weckman: Metall. Mater. Trans. B, 2006, vol. 37B, pp. 275-92.
P. Akerstrom and M. Oldenburg: J. Mater. Process. Technol., 2006, vol. 174, pp. 399-406.
V.M. Li, David V. Niebuhr, Lemmy L. Meekisho, and David G. Atteridge: Metall. Mater. Trans. B, 1998, vol. 29B, pp. 661-72.
T.S. Prasanna Kumar: Numer. Heat Transfer Part B, 2004, vol. 45, pp. 541-63.
T.S. Prasanna Kumar, and H.C. Kamath: Metall. Mater. Trans. B, 2004, vol. 35B, pp. 575–85.
K. Babu and T.S. Prasanna Kumar: Metall. Mater. Trans. B, 2010, vol. 41B, pp. 214-24.
K. Babu and T.S. Prasanna Kumar: J. Heat Trans-T ASME, 2011, vol. 133, 071501 (8 pages).
K. Babu and T.S. Prasanna Kumar: Int. Heat Mass Transf., 2011, vol. 54, pp. 106-17.
D.P. Koistinen, and R.E. Marburger: Acta Metall., 1959, vol. 7, pp. 59-60.
C.H. Gur, and J. Pan: Handbook of Thermal Process Modeling of Steels, Taylor & Francis Group, New York, 2008.
C.Y. Kung and J.J. Rayment: Metall. Trans. A, 1982, vol. 13A, pp. 328-31.
S.J. Lee and Y.K. Lee: Mater. Des., 2008, vol. 29, pp. 1840-44.
K. Babu and T.S. Prasanna Kumar: ICTPMCS’10 ID No. C02, 2010, Shanghai, China.
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript submitted November 7, 2013.
Rights and permissions
About this article
Cite this article
Babu, K., Prasanna Kumar, T.S. Comparison of Austenite Decomposition Models During Finite Element Simulation of Water Quenching and Air Cooling of AISI 4140 Steel. Metall Mater Trans B 45, 1530–1544 (2014). https://doi.org/10.1007/s11663-014-0069-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11663-014-0069-0