Devising Strain Hardening Models Using Kocks–Mecking Plots—A Comparison of Model Development for Titanium Aluminides and Case Hardening Steel
Abstract
:1. Introduction
2. Materials and Hot Compression Testing
3. Experimental Results
3.1. Hot Deformation Behavior
3.2. Microstructure Evolution
4. Microstructure-Based Strain Hardening Models for Hot Working
4.1. Derivation of Model Equations
4.2. Evaluation of Experimental Data and Parameters Identification
4.3. Determination of Model Parameters Common to Both Models
5. Final Calibration and Validation of the Model
6. Conclusions
- Kocks-Mecking plots reveal that in contrast to 25MoCrS4 steel the Ti–44.5Al–6.25Nb–0.8Mo–0.1B alloy neither shows a linear decrease of θ (i.e., no stage-III hardening) nor does it exhibit a plateau (stage IV hardening) or an inflection point (marking the onset of DRX) at all forming conditions.
- The information obtained from Kocks-Mecking plots should be taken into account in the development of strain hardening models. Otherwise, inconsistencies, e.g., with the Poliak-Jonas criterion, may result.
- Both models show a high accuracy. They may hence be used in finite element simulations of metal forming processes. For TNB-V4, however, the complex microstructure evolution, i.e., the recrystallization of the individual phases, the reorientation of the lamellar colonies and flow localization effects during deformation need to be taken into account in continuative work.
Acknowledgments
Author Contributions
Conflicts of Interest
References
- Appel, F.; Wagner, R. Microstructure and deformation of two-phase γ-titanium aluminides. Mater. Sci. Eng. Rep. 1998, 22, 187–268. [Google Scholar] [CrossRef]
- Dimiduk, D. Gamma titanium aluminide alloys—An assessment within the competition of aerospace structural materials. Mater. Sci. Eng. A 1999, 263, 281–288. [Google Scholar] [CrossRef]
- Kabir, M.R.; Chernova, L.; Bartsch, M. Numerical investigation of room-temperature deformation behavior of a duplex type γTiAl alloy using a multi-scale modeling approach. Acta Mater. 2010, 58, 5834–5847. [Google Scholar] [CrossRef]
- Mecking, H.; Kocks, U.F. Kinetics of flow and strain-hardening. Acta Metall. 1981, 29, 1865–1875. [Google Scholar] [CrossRef]
- Estrin, Y.; Mecking, H. A unified phenomenological description of work hardening and creep based on one-parameter models. Acta Metall. 1984, 32, 57–70. [Google Scholar] [CrossRef]
- Bergström, Y. A dislocation model for the stress-strain behaviour of polycrystalline α-Fe with special emphasis on the variation of the densities of mobile and immobile dislocations. Mater. Sci. Eng. 1970, 5, 193–200. [Google Scholar] [CrossRef]
- Baragar, D.L. The high temperature and high strain-rate behaviour of a plain carbon and an HSLA steel. J. Mech. Work. Technol. 1987, 14, 295–307. [Google Scholar] [CrossRef]
- Davenport, S.B.; Silk, N.J.; Sparks, C.N.; Sellars, C.M. Development of constitutive equations for modelling of hot rolling. Mater. Sci. Technol. 2013, 16, 539–546. [Google Scholar] [CrossRef]
- Rao, K.P.; Hawbolt, E.B. Development of constitutive relationships using compression testing of a medium carbon steel. J. Eng. Mater. Technol. 1992, 114, 116. [Google Scholar] [CrossRef]
- Cheng, L.; Xue, X.; Tang, B.; Kou, H.; Li, J. Flow characteristics and constitutive modeling for elevated temperature deformation of a high Nb containing TiAl alloy. Intermetallics 2014, 49, 23–28. [Google Scholar] [CrossRef]
- Laasraoui, A.; Jonas, J.J. Prediction of steel flow stresses at high temperatures and strain rates. Metall. Trans. A 1991, 22, 1545–1558. [Google Scholar] [CrossRef]
- Godor, F.; Werner, R.; Lindemann, J.; Clemens, H.; Mayer, S. Characterization of the high temperature deformation behavior of two intermetallic TiAl–Mo alloys. Mater. Sci. Eng. A 2015, 648, 208–216. [Google Scholar] [CrossRef]
- Sellars, C.M.; McTegart, W.J. On the mechanism of hot deformation. Acta Metall. 1966, 14, 1136–1138. [Google Scholar] [CrossRef]
- Hensel, M.; Spittel, T. Ver- u. Entfestigung bei Warmumformung; Dt. Verl. für Grundstoffindustrie: Leipzig, Germany, 1982. [Google Scholar]
- He, X.; Yu, Z.; Liu, G.; Wang, W.; Lai, X. Mathematical modeling for high temperature flow behavior of as-cast Ti–45Al–8.5Nb–(W,B,Y) alloy. Mater. Des. 2009, 30, 166–169. [Google Scholar] [CrossRef]
- Pu, Z.J.; Wu, K.H.; Shi, J.; Zou, D. Development of constitutive relationships for the hot deformation of boron microalloying TiAl–Cr–V alloys. Mater. Sci. Eng. A 1995, 192–193, 780–787. [Google Scholar] [CrossRef]
- Deng, T.-Q.; Ye, L.; Sun, H.-F.; Hu, L.-X.; Yuan, S.-J. Development of flow stress model for hot deformation of Ti-47%Al alloy. Trans. Nonferr. Met. Soc. China 2011, 21, s308–s314. [Google Scholar] [CrossRef]
- Nobuki, M.; Hashimoto, K.; Takahashi, J.; Tsujimoto, T. Deformation of cast TiAl intermetallic compound at elevated temperatures. Mater. Trans. JIM 1990, 31, 814–819. [Google Scholar] [CrossRef]
- Fukutomi, H.; Nomoto, A.; Osuga, Y.; Ikeda, S.; Mecking, H. Analysis of dynamic recrystallization mechanism in γ-TiAl intermetallic compound based on texture measurement. Intermetallics 1996, 4, S49–S55. [Google Scholar] [CrossRef]
- Kim, H.Y.; Sohn, W.H.; Hong, S.H. High temperature deformation of Ti–(46–48)Al–2W intermetallic compounds. Mater. Sci. Eng. A 1998, 251, 216–225. [Google Scholar] [CrossRef]
- Fröbel, U.; Appel, F. Hot-workability of gamma-based TiAl Alloys during severe torsional deformation. Metall. Mater. Trans. A 2007, 38, 1817–1832. [Google Scholar] [CrossRef]
- Kim, H.Y.; Hong, S.H. Effect of microstructure on the high-temperature deformation behavior of Ti–48Al–2W intermetallic compounds. Mater. Sci. Eng. A 1999, 271, 382–389. [Google Scholar] [CrossRef]
- Semiatin, S.L.; Frey, N.; Thompson, C.R.; Bryant, J.D.; El-Soudani, S.; Tisler, R. Plastic flow behavior of Ti–48Al–2.5Nb–0.3Ta at hot-working temperatures. Scr. Metall. Mater. 1990, 24, 1403–1408. [Google Scholar] [CrossRef]
- Wiezorek, J.M.K.; Deluca, P.M.; Mills, M.J.; Fraser, H.L. Deformation mechanisms in a binary Ti-48 at % Al alloy with lamellar microstructure. Philos. Mag. Lett. 1997, 75, 271–280. [Google Scholar] [CrossRef]
- Schaden, T.; Fischer, F.D.; Clemens, H.; Appel, F.; Bartels, A. Numerical modelling of kinking in lamellar γ-TiAl based Alloys. Adv. Eng. Mater. 2006, 8, 1109–1113. [Google Scholar] [CrossRef]
- McQueen, H.; Ryan, N. Constitutive analysis in hot working. Mater. Sci. Eng. A 2002, 322, 43–63. [Google Scholar] [CrossRef]
- Kocks, U.F.; Mecking, H. A mechanism for static and dynamic recovery. In Strength of Metals and Alloys; Haasen, P., Gerold, V., Kostorz, G., Eds.; Pergamon Press: Oxford, UK, 1980; pp. 345–350. [Google Scholar]
- Jonas, J.J.; Quelennec, X.; Jiang, L.; Martin, É. The Avrami kinetics of dynamic recrystallization. Acta Mater. 2009, 57, 2748–2756. [Google Scholar] [CrossRef]
- Bambach, M.; Sizova, I.; Bolz, S.; Weiß, S. Development of a dynamic recrystallization model for a β-solidifying titanium aluminide alloy using kocks-mecking plots. In Proceedings of the 19st ESAFORM Conference on Material Forming, Nantes, France, 27–29 April 2016.
- Konovalov, S.; Henke, T.; Jansen, U.; Hardjosuwito, A.; Lohse, W.; Bambach, M.; Prahl, U. Test case gearing component. In Integrative Computational Materials Engineering: Concepts and Applications of a Modular Simulation Platform; Schmitz, G.J., Prahl, U., Eds.; John Wiley & Sons: Weinheim, Germany, 2012. [Google Scholar]
- Semiatin, S.L.; Frey, N.; El-Soudani, S.M.; Bryant, J.D. Flow softening and microstructure evolution during hot working of wrought near-gamma titanium aluminides. Metall. Mater. Trans. A 1992, 23, 1719–1735. [Google Scholar] [CrossRef]
- Lohmar, J.; Bambach, M. Influence of different interpolation techniques on the determination of the critical conditions for the onset of dynamic recrystallization. Mater. Sci. Forum 2013, 762, 331–336. [Google Scholar] [CrossRef]
- Xiong, W.; Lohmar, J.; Bambach, M.; Hirt, G. A new method to determine isothermal flow curves for integrated process and microstructural simulation in metal forming. Int. J. Mater. Form. 2015, 8, 59–66. [Google Scholar] [CrossRef]
- Bolz, S.; Oehring, M.; Lindemann, J.; Pyczak, F.; Paul, J.; Stark, A.; Lippmann, T.; Schrüfer, S.; Roth-Fagaraseanu, D.; Schreyer, A.; et al. Microsturcture and mechanical properties of a forged β-solidifying γ-TiAl alloy in different heat treatment conditions. Intermetallics 2015, 58, 71–83. [Google Scholar] [CrossRef]
- Fujiwara, T.; Nakamura, A.; Hosomi, M.; Nishitani, S.; Shirai, Y.; Yamaguchi, M. Deformation of polysynthetically twinned crystals of TiAl with a nearly stoichiometric composition. Philos. Mag. A 1990, 61, 591–606. [Google Scholar] [CrossRef]
- Schwaighofer, E.; Clemens, H.; Lindemann, J.; Stark, A.; Mayer, S. Hot-working behavior of an advanced intermetallic multi-phase γ-TiAl based alloy. Mater. Sci. Eng. A 2014, 614, 297–310. [Google Scholar] [CrossRef]
- Bariani, P.F.; Negro, T.D.; Bruschi, S. Testing and modelling of material response to deformation in bulk metal forming. CIRP Ann. Manuf. Technol. 2004, 53, 573–595. [Google Scholar] [CrossRef]
- Bambach, M. Implications from Poliak—Jonas criterion for the construction of flow stress models incorporating dynamic recrystallization. Acta Mater. 2013, 61, 6222–6233. [Google Scholar] [CrossRef]
- Luton, M.; Sellars, C. Dynamic recrystallization in nickel and nickel-iron alloys during high temperature deformation. Acta Metall. 1969, 17, 1033–1043. [Google Scholar] [CrossRef]
- Beynon, J.H.; Sellars, C.M. Modelling microstructure and its effects during multipass hot rolling. ISIJ Int. 1992, 32, 359–367. [Google Scholar] [CrossRef]
- Sellars, C.M. Modelling of structural evolution during hot working processes. In Proceedings of the International Symposium on Annealing Processes: Recovery, Recrystallisation and Grain Growth, Sheffield, UK, 8–12 September 1986; pp. 167–187.
- Sandström, R.; Lagneborg, R. A model for hot working occurring by recrystallization. Acta Metall. 1975, 23, 387–398. [Google Scholar] [CrossRef]
- Sommitsch, C.; Mitter, W. On modelling of dynamic recrystallisation of fcc materials with low stacking fault energy. Acta Mater. 2006, 54, 357–375. [Google Scholar] [CrossRef]
- Cingara, A.; McQueen, H.J. New formula for calculating flow curves from high temperature constitutive data for 300 austenitic steels. J. Mater. Process. Technol. 1992, 36, 31–42. [Google Scholar] [CrossRef]
Evolution of ρ | Flow Stress | θ(σ) | Curvature | Form/Reference |
---|---|---|---|---|
None (linear course) | [4] | |||
Concave up/concave down | [42] [43] | |||
Concave up | [11] | |||
- | N.A. | concave down for C ≥ 1 | [44] | |
- | N.A. | | linear (stage III)/linear (stage IV)/concave down | [38] |
Model Part | 25MoCrS4 Steel | TNB |
---|---|---|
Strain hardening | | |
Critical strain | (Equation (3), s. Figure 3) | |
Peak strain | (Equation (2), s. Figure 3) | |
Steady state stress | (Equation (4), s. Figure 3) | |
Peak stress | (Equation (5), s. Figure 3) | |
Steady state stress | (Equation (6), s. Figure 3) | |
DRX kinetics | ||
Flow stress |
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Bambach, M.; Sizova, I.; Bolz, S.; Weiß, S. Devising Strain Hardening Models Using Kocks–Mecking Plots—A Comparison of Model Development for Titanium Aluminides and Case Hardening Steel. Metals 2016, 6, 204. https://doi.org/10.3390/met6090204
Bambach M, Sizova I, Bolz S, Weiß S. Devising Strain Hardening Models Using Kocks–Mecking Plots—A Comparison of Model Development for Titanium Aluminides and Case Hardening Steel. Metals. 2016; 6(9):204. https://doi.org/10.3390/met6090204
Chicago/Turabian StyleBambach, Markus, Irina Sizova, Sebastian Bolz, and Sabine Weiß. 2016. "Devising Strain Hardening Models Using Kocks–Mecking Plots—A Comparison of Model Development for Titanium Aluminides and Case Hardening Steel" Metals 6, no. 9: 204. https://doi.org/10.3390/met6090204