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Research Papers

A New Constitutive Equation to Predict Single Peak Flow Stress Curves

[+] Author and Article Information
E. Shafiei

Graduate Student
e-mail: e.shafiei@aut.ac.ir

R. Ebrahimi

Assoc. Professor
Department of Materials Science
and Engineering
Shiraz University
Shiraz, 71345/1585, Iran
e-mail: ebrahimy@shirazu.ac.ir

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received January 1, 2012; final manuscript received October 10, 2012; published online January 23, 2013. Assoc. Editor: Joost Vlassak.

J. Eng. Mater. Technol 135(1), 011006 (Jan 23, 2013) (4 pages) Paper No: MATS-12-1001; doi: 10.1115/1.4023186 History: Received January 01, 2012; Revised October 10, 2012

In this study a new constitutive equation, using the extrapolation of dynamic recovery (DRV) flow stress curve and kinetic equation for dynamic recrystallization (DRX), has been developed. This model is expressed in terms of characteristic points such as critical stress, critical strain, DRX steady state stress, and DRV saturation stress. Moreover, this analysis was done for the stress-strain curves under hot working condition for Ti-IF steel, but it is not dependent on the type of material and can be extended for any condition that a single peak dynamic recrystallization occurs. The results indicate that the stress-strain curves predicted by this model are in a good agreement with experimentally measured ones at all deformation conditions.

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References

McQueen, H. J., and Rayan, N. D., 2002, “Constitutive Analysis in Hot Working,” Mater. Sci. Eng., A, 322, pp. 43–63. [CrossRef]
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Ebrahimi, R., Zahiri, S. H., Najafizadeh, A., 2006, “Mathematical Modeling of the Stress-Strain Curves of Ti-IF Steel at High Temperature,” J. Mater. Process. Tech., 171, pp. 301–306. [CrossRef]
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Ebrahimi, R., and Solhjoo, S., 2007, “Characteristic Points of Stress-Strain Curves at High Temperature,” Int. J. Iron Steel Soc. Iran, 4, pp. 24–27.
Laasraouli, A., and Jonas, J. J., 1991, “Prediction of Steel Flow Stresses at High Temperatures and Strain Rates,” Metall. Trans. A, 22, pp. 1545–1557. [CrossRef]
Imbert, C. A. C., and McQueen, H. J., 2001, “Peak Strength, Strain Hardening and Dynamic Restoration of A2 and M2 Tool Steels in Hot Deformation,” Mater. Sci. Eng., A, 313, pp. 88–103. [CrossRef]
Ebrahimi, R., 2003, “Hot and Warm Deformation of IF Steel,” Ph.D thesis, Isfahan University of Technology, Isfahan, Iran.
Jonas, J. J., Quelennec, X., Jiang, L., and Martin, E., 2009, “The Avrami Kinetics of Dynamic Recrystallization,” Acta Mater., 57, pp. 2748–2756. [CrossRef]

Figures

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Fig. 1

Schematic representation of flow stress curves at high temperature

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Fig. 2

Variations of strain hardening rate versus stress up to the peak stress

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Fig. 3

Plot for calculation of MC-Queen constant

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Fig. 4

Extrapolation of DRV flow curve, drop of flow stress and predicted flow curve for Ti-IF steel at temperature of 1050 °C and strain rate of 1 S−1

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Fig. 5

Comparison of measured and predicted stress-strain curves of Ti-IF steel

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Fig. 6

Variation of mean error of flow stress with true strain under different deformation conditions

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