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A study on flow behavior of A-286 superalloy during hot deformation
Materials Chemistry and Physics 101 (2007) 153–157
A study on flow behavior of A-286 superalloy during hot deformation A.R. Salehi, S. Serajzadeh ∗ , N. Yazdipour Department of Materials Science and Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran Received 20 July 2005; received in revised form 11 January 2006; accepted 22 March 2006
Abstract The hot deformation behavior of A-286 superalloy has been characterized using hot compression experiments in the temperatures between 1000 and 1100 ◦ C and strain rates varying between 0.001 and 0.1 s−1 . In addition, hot workability of this alloy has been analyzed by employing flowlocalization parameter. The results show that both kinds of softening mechanism, dynamic recovery and dynamic recrystallization, occur during hot working, where at 1000 ◦ C the main mechanism is dynamic recovery and at higher temperatures and strain rate of 0.001–0.01 s−1 dynamic recrystallization takes place. Calculations demonstrates that this alloy mainly have a good workability for the utilized deformation conditions however, at temperatures around 1050 ◦ C critical conditions may be raised and flow localized region could be formed. © 2006 Elsevier B.V. All rights reserved. Keywords: Hot deformation; Superalloy; A-286; Workability
1. Introduction The IncoloyA-286 superalloy is an iron-base superalloy widely used in aeronautical and oil industries. Microstructure and mechanical properties of A-286 alloy is highly sensitive to metallurgical technology and thermo-mechanical processing. It is important to understand flow stress behavior and microstructural changes during hot working to achieve desired mechanical properties after deformation. This is because hot deformation behaviors of superalloys have been studied in several research works. Srinivasan et al. [1] have studied flow stress behavior of fine-grain IN718 in the temperature range of 871–1149 ◦ C and strain rates of 0.001–10 s−1 [1]. In a similar work, Garcia et al. [2] have investigated flow stress behavior of IN718 in the temperatures between 900 and 1177 ◦ C and the strain rates ranging between 0.005 and 5 s−1 . Nielsen et al. [3] and Zhang et al. [4] have developed constitutive relationships for describing flow stress behavior of IN718 as a function of deformation parameters such as temperature and strain rate. A few studies have also been carried out on the microstructure characterization and recrystallization behavior of superalloys and various empirical equations for prediction of grain size has been pro-
∗
Corresponding author. Tel.: +98 21 66165218; fax: +98 21 66005717. E-mail address: [email protected] (S. Serajzadeh).
0254-0584/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2006.03.012
posed [5,6]. Hale et al. [7] have studied discontinuous yielding in a nickel-base superalloy and calculated the activation energy for appearance dynamic strain aging. Modelling of microstructural changes during hot rolling have been conducted in several works [8–11]. Almroth et al. [8] have developed a mathematical model to express superalloys behavior in gas turbine hot part application while in the other research work they modeled flow behavior of IN792 in temperatures between 850 and 650 ◦ C where the material shows different visco-plastic behavior [9]. Yaguchi et al. [10] have developed constitutive equations for describing and modelling of flow stress behavior of IN738LC at different temperatures and strain rates. Yoo et al. [11] have predicted creep rate and creep rupture life for nickel-base superalloys. Where they have employed a Monte Carlo model for calculation of creep behavior. Despite of the excellent hot temperature properties of austenitic Fe–Ni alloy, A-286, and its extensive use in large forging parts such as gas turbine disks, its hot deformation behavior has been studied [12–14] however, more studies are still useful to understand flow stress behavior of this alloy under different working conditions. In the present study, flow behavior of A-286 superalloy has been examined. To do so, hot compression experiments in the temperatures ranging between 1000 and 1100 ◦ C and strain rates of 0.001–0.1 s−1 were performed. In addition, microstructural studies were performed to investigate the effect of deformation parameters on microstructures.
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A.R. Salehi et al. / Materials Chemistry and Physics 101 (2007) 153–157
Table 1 Chemical composition of the materials used in this study C Ni Cr Al Ti Si B P S Fe
0.04 24 15 0.3 2 0.5 0.003 0.02 0.02 Bal.
2. Experimental The chemical composition of the Incoloy A-286 alloy used in the investigation is listed in Table 1. The raw material was produced by vacuum melting process and it was hot forged in two stages to remove the casting structure. The microstructure after hot forgings is shown in Fig. 1. As it is observed the initial microstructure for hot deformation experiments consists of equiaxed austenite grains. The average grain diameter was measured as 40 m. It is worth noting that for determination of grain size, intercept method was utilized. Cylindrical specimens of 7 mm diameter and 11 mm height were machined out of the as-received stock and hot compression experiments were conducted under isothermal condition at constant true strain rates of 0.001, 0.01 and 0.1 s−1 and at temperatures of 1000, 1050 and 1100 ◦ C. All samples were heated up to 1200 ◦ C and hold for 15 min and then cooled to the deformation temperatures at which it was held for 3 min to eliminate the thermal gradient before deformation then the samples were deformed to total true strain of 0.7. After hot deformation the samples were quenched in water to capture microstructure of hot deformed material. Then microstructural studies were performed on the deformed the samples.
3. Results and discussion Stress–strain curves achieved at various temperatures and strain rates are presented in Fig. 2. It is observed that at lower strain rates i.e. 0.001 s−1 , the dominant flow softening process is “dynamic recrystallization” where stress–strain curves shows a peak stress at true strain of 0.25–0.35. However, at higher strain rates, i.e. 0.1 s−1 , the dominant softening mechanism is “dynamic recovery”. Fig. 3 shows the microstructures of the samples after deformation at 1050 ◦ C and strain rates of 0.001 and 0.01 s−1 . As it is seen from the figures for deformation at lower strain rate the microstructure consists of equiaxed grains
Fig. 2. True strain–true stress curves at different temperatures (a) strain rate of 0.001 s−1 , (b) strain rate of 0.1 s−1 .
which is representative of fully recrystallized structures but at higher strain rate the microstructure shows partially recrystallization conditions which is attributed to the higher strain rate and increasing the critical strain for onset of dynamic recrystallization and slower rate of recrystallization. Fig. 4 displays the microstructure of the sample deformed at 1000 ◦ C and strain rate of 0.1 s−1 . The microstructure consists of elongated grains with wavy-shape grain boundaries. It may be attributed the dynamic recrystallization occurring during hot working however, the grain boundary migration is restricted by the second phases that they are stable at temperatures around 1000 ◦ C. This causes stress–strain curve shows no recrystallization and also serrated grain boundaries will be formed during deformation as shown in Fig. 4. In order to study the deformation behavior of the employed alloy at elevated temperatures constitutive equations proposed by Sellars and Tegart [15] were used where relationship among strain rate, temperature and flow stress is expressed as below: Z = ε˙ exp
Fig. 1. Initial microstructure of process annealed A-286 superalloy.
Q RT
= AF (σ)
(1)
here Z, is Zener-Hollomon parameter, Q the apparent activation for hot deformation, A is a material constant and F(σ) is function
A.R. Salehi et al. / Materials Chemistry and Physics 101 (2007) 153–157
155
Fig. 5. ln(˙ε) vs. ln(sinh(ασ ss ))at different temperatures.
Fig. 3. Micro11structure of the sample deformed, (a) at temperature of 1050 ◦ C and strain rate of 0.001 s−1 , (b) at temperature of 1050 ◦ C and strain rate of 0.01 s−1 .
of flow stress which can be described as: F (σ) = Aσ n
for low stresses,
F (σ) = A exp (βσ)n
for high stresses,
F (σ) = A sinh (ασ)n
for all stress levels
(2)
Fig. 4. Microstructure of the sample deformed at temperature of 1000 ◦ C and strain rate of 0.1 s−1 .
here n, A, A , A , α and β are material constants. Regarding to the wide variation of flow stress in A-286, for the employed deformation conditions. “Hyperbolic-sine” was used for expressing constitutive equations. For calculation of α-value, an iterative scheme has been utilized. Different values for “α” have been generated and then “n”-value was determined for various temperatures. It was observed that for the value of α = 0.0012, “n” is almost independent of temperature and its mean value is equal to “6.84”. Fig. 5 presents ln(˙ε) versus ln(sinh(ασ ss )) at different temperatures. In addition, to calculate the activation energy for hot deformation, the following equation was employed: Q ∂(ln(˙ε)) . (3) =− R ∂(1/T ) σss Fig. 6 shows ln(˙ε) versus 1/T at different steady state stresses. The mean activation energy was calculated as 795 kJ/mol for the steady state stresses span between 75 and 150 MPa. The amount of calculated activation energy is much larger than the selfdiffusion of iron in lattice. The similar results have been reported for the other superalloys [16,17]. For the case of UDIMET 720 nickel based superalloy, the mean activation energy was calculated as 1552 kJ/mol [16]. As it is observed the calculated activation energies both in this work or the published ones are much larger than the self-diffusion of Ni, Fe. This offers that the hot deformation behavior is controlled by two or more mechanisms. For example some alloys elements such as chromium raise the effective diffusion rate in the lattice as well as the presence of the second phases increases critical shear stress for dislocation glide. These factors increase hot deformation activation energy or in other words, the resistance to plastic deformation is increased. Strain rate sensitivity is an important material property, which can affect workability of metals. Fig. 7 shows variation of flow
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A.R. Salehi et al. / Materials Chemistry and Physics 101 (2007) 153–157
Fig. 6. ln(˙ε) vs. 1/T at different steady-state stresses.
stress at the true strain of 0.3 as a function of strain rate at different temperatures. The slope of these curves gives strain rate sensitivity. As it is observed the strain rate sensitivity varies in the temperatures between 1000 and 1100 ◦ C where it changes from 0.105 at 1000 ◦ C to 0.15 at 1100 ◦ C. Fig. 8 shows the dependence of strain rate sensitivity on temperature. Increasing in strain rate
Fig. 8. Variation of strain rate sensitivity vs. temperature.
sensitivity may be attributed to occurring dynamic recrystallization at higher temperatures that produces higher strain rate sensitivity [18]. The other important factor affecting hot deformation behavior is the strain-hardening rate, γ, which is described as below: 1 dσ γ= . (4) σ dε ε˙ Utilizing the achieved stress–strain curves and numerical differentiation, strain-hardening rate has been calculated for different deformation conditions. In order to determine this parameter central difference scheme was employed as below: γi =
1 σi+1 − σi−1 σi εi+1 − εi−1
(5)
here γ i is the strain-hardening rate at the ith strain increment. Table 2 shows γ max calculated under various temperatures and strain rates. It should be noted that for the case of compression test work-hardening coefficient would be positive if the material experiences negative work hardening. In order to estimate workability of metal and alloys under hot deformation condition, flow-localization parameter, “FLP” has been proposed [18]. This Table 2 Maximum strain-hardening rate under different deformation conditions Strain rate (s−1 )
Fig. 7. Variation of flow stress at true strain of 0.3 with strain rate in different temperatures.
0.001 0.01 0.1
Temperature (◦ C) 1100
1050
1000
0.386 0.212 ≤0
0.188 1.12 ≤0
0.124 <0 0.012
A.R. Salehi et al. / Materials Chemistry and Physics 101 (2007) 153–157
parameter can be expressed as follows: γ (for shear band formation). (6) m This parameter is calculated in different temperatures and strain rates using Eq. (6). It can be found that at higher strain rates and low temperatures the possibility of occurring flow localizations is quite high and the material has a poor workability at this range. For example critical conditions may arise at hot deformation around 1050 ◦ C and strain rates of 0.01 s−1 where the work-hardening coefficient has a high value of “1.12” and on the other hand strain rate sensitivity has a rather low value of order of 0.12. Under these conditions, flowlocalization parameter is 9.24, which means that severe shear band regions will be formed during hot deformation. Therefore, an accurate control on temperature and strain rate should be applied to ensure producing a sample with the homogenous microstructure. FLP =
4. Conclusion Hot compression experiments have been performed on A-286 superalloy. The experiments were conducted in the temperatures between 1000 and 1100 ◦ C and strain rates of 0.001, 0.01 and 0.1 s−1 . By means of stress–strain curves the flow stress behavior and workability of this alloys have been studied. The results show that: 1. Both kinds of dynamic softening mechanisms may take place in A-286 superalloy. Dynamic recovery occurs at lower temperatures while dynamic recrystallization mainly occurs at 1100 ◦ C and strain rates of 0.001 and 0.01 s−1 . 2. The mean hot deformation activation energy is 795 kJ/mol, which shows high resistance of this alloy to hot deformation in the utilized deformation conditions. 3. The strain rate sensitivity of the alloy is not constant for the employed temperature range and it changes from 0.105 at 1000 ◦ C to 0.152 at 1100 ◦ C. Therefore, it is expected that at higher temperatures the workability would be improved. 4. Calculation of flow-localization parameter shows that at temperatures between 1000 and 1050 ◦ C and strain rate of
157
0.01 s−1 , the possibility of formation of severe flow-localized region is quite possible. Acknowledgement The first author (AS) wants to express his appreciation to the Turbine Machine M.E. Company for the financial support and the raw materials used in this research. References [1] R. Srinivasan, V. Ramnarayan, U. Deshpande, V. Jain, I. Weiss, Met. Trans. A 24A (1993) 2061. [2] C.I. Garcia, G.D. Wang, D.E. Camus, E.A. Loria, A.J. DeArdo, in: E.A. Loria (Ed.), Superalloys 718, 625, 706 and Various Derivatives, TMS, Warrendale, PA, 1994, p. 293. [3] D.R. Nielsen, S.W. Thompson, C.J. VanTyne, M.C. Mataya, in: E.A. Loria (Ed.), Superalloys 718, 625, 706 and Various Derivatives, TMS, Warrendale, PA, 1989, p. 119. [4] J.M. Zhang, Z.Y. Gao, J.Y. Zhuang, Z.Y. Zhang, Met. Mater. Trans. A 30A (1999) 2701. [5] J.M. Zhang, Z.Y. Gao, J.Y. Zhuang, Z.Y. Zhong, Mater. Proc. Tech. 88 (1999) 244–250. [6] J.M. Zhang, Z.Y. Gao, J.Y. Zhuang, Z.Y. Zhong, Mater. Proc. Tech. 101 (2000) 25–30. [7] C.L. Hale, W.S. Rollings, W.L. Weaver, Mater. Sci. Eng. A 300 (2001) 153–164. [8] P. Almroth, M. Hasselqvist, S. Sj¨ostr¨om, K. Simonsson, Comp. Mater. Sci. 25 (2002) 305–315. [9] P. Almroth, M. Hasselqvist, K. Simonsson, S. Sj¨ostr¨om, Comp. Mater. Sci. 29 (2004) 437–445. [10] M. Yaguchi, M. Yamamoto, T. Ogata, Int. J. Plasticity 18 (2002) 1111–1131. [11] Y.S. Yoo, C.Y. Jo, C.N. Jones, Mater. Sci. Eng. A (2002) 22–29. [12] K.J. Ducki, K. Rodak, M. Hetma´nczyk, D. Kuc, Mater. Chem. Phys. 81 (2003) 490–492. [13] K.J. Ducki, K. Rodak, M. Hetma´nczyk, D. Kuc, Mater. Chem. Phys. 81 (2003) 493–495. [14] K. Kusabiraki, Y. Takasawa, T. Ooka, ISIJ Int. 35 (1995) 542–547. [15] C.M. Sellars, W.J.Mc. Tegart, Acta Metal. 14 (1966) 1136. [16] H. Monajati, M. Jahazi, S. Yue, A.K. Taheri, Met. Mater. Trans. 36A (2005) 895–905. [17] S.L. Semiatin, D.S. Weaver, P.N. Fagin, M.G. Glavicic, J.R. Gotez, N.D. Frey, P.C. Kramb, M.M. Antony, Met. Mater. Trans. 35A (2004) 679–693. [18] S.L. Semiatin, J.J. Jonas, Formability and Workability of Metals, Plastic Instability and Flow Localization, American Society of Metals, Metals Park, OH, 1984.
A study on flow behavior of A-286 superalloy during hot deformation A.R. Salehi, S. Serajzadeh ∗ , N. Yazdipour Department of Materials Science and Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran Received 20 July 2005; received in revised form 11 January 2006; accepted 22 March 2006
Abstract The hot deformation behavior of A-286 superalloy has been characterized using hot compression experiments in the temperatures between 1000 and 1100 ◦ C and strain rates varying between 0.001 and 0.1 s−1 . In addition, hot workability of this alloy has been analyzed by employing flowlocalization parameter. The results show that both kinds of softening mechanism, dynamic recovery and dynamic recrystallization, occur during hot working, where at 1000 ◦ C the main mechanism is dynamic recovery and at higher temperatures and strain rate of 0.001–0.01 s−1 dynamic recrystallization takes place. Calculations demonstrates that this alloy mainly have a good workability for the utilized deformation conditions however, at temperatures around 1050 ◦ C critical conditions may be raised and flow localized region could be formed. © 2006 Elsevier B.V. All rights reserved. Keywords: Hot deformation; Superalloy; A-286; Workability
1. Introduction The IncoloyA-286 superalloy is an iron-base superalloy widely used in aeronautical and oil industries. Microstructure and mechanical properties of A-286 alloy is highly sensitive to metallurgical technology and thermo-mechanical processing. It is important to understand flow stress behavior and microstructural changes during hot working to achieve desired mechanical properties after deformation. This is because hot deformation behaviors of superalloys have been studied in several research works. Srinivasan et al. [1] have studied flow stress behavior of fine-grain IN718 in the temperature range of 871–1149 ◦ C and strain rates of 0.001–10 s−1 [1]. In a similar work, Garcia et al. [2] have investigated flow stress behavior of IN718 in the temperatures between 900 and 1177 ◦ C and the strain rates ranging between 0.005 and 5 s−1 . Nielsen et al. [3] and Zhang et al. [4] have developed constitutive relationships for describing flow stress behavior of IN718 as a function of deformation parameters such as temperature and strain rate. A few studies have also been carried out on the microstructure characterization and recrystallization behavior of superalloys and various empirical equations for prediction of grain size has been pro-
∗
Corresponding author. Tel.: +98 21 66165218; fax: +98 21 66005717. E-mail address: [email protected] (S. Serajzadeh).
0254-0584/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2006.03.012
posed [5,6]. Hale et al. [7] have studied discontinuous yielding in a nickel-base superalloy and calculated the activation energy for appearance dynamic strain aging. Modelling of microstructural changes during hot rolling have been conducted in several works [8–11]. Almroth et al. [8] have developed a mathematical model to express superalloys behavior in gas turbine hot part application while in the other research work they modeled flow behavior of IN792 in temperatures between 850 and 650 ◦ C where the material shows different visco-plastic behavior [9]. Yaguchi et al. [10] have developed constitutive equations for describing and modelling of flow stress behavior of IN738LC at different temperatures and strain rates. Yoo et al. [11] have predicted creep rate and creep rupture life for nickel-base superalloys. Where they have employed a Monte Carlo model for calculation of creep behavior. Despite of the excellent hot temperature properties of austenitic Fe–Ni alloy, A-286, and its extensive use in large forging parts such as gas turbine disks, its hot deformation behavior has been studied [12–14] however, more studies are still useful to understand flow stress behavior of this alloy under different working conditions. In the present study, flow behavior of A-286 superalloy has been examined. To do so, hot compression experiments in the temperatures ranging between 1000 and 1100 ◦ C and strain rates of 0.001–0.1 s−1 were performed. In addition, microstructural studies were performed to investigate the effect of deformation parameters on microstructures.
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A.R. Salehi et al. / Materials Chemistry and Physics 101 (2007) 153–157
Table 1 Chemical composition of the materials used in this study C Ni Cr Al Ti Si B P S Fe
0.04 24 15 0.3 2 0.5 0.003 0.02 0.02 Bal.
2. Experimental The chemical composition of the Incoloy A-286 alloy used in the investigation is listed in Table 1. The raw material was produced by vacuum melting process and it was hot forged in two stages to remove the casting structure. The microstructure after hot forgings is shown in Fig. 1. As it is observed the initial microstructure for hot deformation experiments consists of equiaxed austenite grains. The average grain diameter was measured as 40 m. It is worth noting that for determination of grain size, intercept method was utilized. Cylindrical specimens of 7 mm diameter and 11 mm height were machined out of the as-received stock and hot compression experiments were conducted under isothermal condition at constant true strain rates of 0.001, 0.01 and 0.1 s−1 and at temperatures of 1000, 1050 and 1100 ◦ C. All samples were heated up to 1200 ◦ C and hold for 15 min and then cooled to the deformation temperatures at which it was held for 3 min to eliminate the thermal gradient before deformation then the samples were deformed to total true strain of 0.7. After hot deformation the samples were quenched in water to capture microstructure of hot deformed material. Then microstructural studies were performed on the deformed the samples.
3. Results and discussion Stress–strain curves achieved at various temperatures and strain rates are presented in Fig. 2. It is observed that at lower strain rates i.e. 0.001 s−1 , the dominant flow softening process is “dynamic recrystallization” where stress–strain curves shows a peak stress at true strain of 0.25–0.35. However, at higher strain rates, i.e. 0.1 s−1 , the dominant softening mechanism is “dynamic recovery”. Fig. 3 shows the microstructures of the samples after deformation at 1050 ◦ C and strain rates of 0.001 and 0.01 s−1 . As it is seen from the figures for deformation at lower strain rate the microstructure consists of equiaxed grains
Fig. 2. True strain–true stress curves at different temperatures (a) strain rate of 0.001 s−1 , (b) strain rate of 0.1 s−1 .
which is representative of fully recrystallized structures but at higher strain rate the microstructure shows partially recrystallization conditions which is attributed to the higher strain rate and increasing the critical strain for onset of dynamic recrystallization and slower rate of recrystallization. Fig. 4 displays the microstructure of the sample deformed at 1000 ◦ C and strain rate of 0.1 s−1 . The microstructure consists of elongated grains with wavy-shape grain boundaries. It may be attributed the dynamic recrystallization occurring during hot working however, the grain boundary migration is restricted by the second phases that they are stable at temperatures around 1000 ◦ C. This causes stress–strain curve shows no recrystallization and also serrated grain boundaries will be formed during deformation as shown in Fig. 4. In order to study the deformation behavior of the employed alloy at elevated temperatures constitutive equations proposed by Sellars and Tegart [15] were used where relationship among strain rate, temperature and flow stress is expressed as below: Z = ε˙ exp
Fig. 1. Initial microstructure of process annealed A-286 superalloy.
Q RT
= AF (σ)
(1)
here Z, is Zener-Hollomon parameter, Q the apparent activation for hot deformation, A is a material constant and F(σ) is function
A.R. Salehi et al. / Materials Chemistry and Physics 101 (2007) 153–157
155
Fig. 5. ln(˙ε) vs. ln(sinh(ασ ss ))at different temperatures.
Fig. 3. Micro11structure of the sample deformed, (a) at temperature of 1050 ◦ C and strain rate of 0.001 s−1 , (b) at temperature of 1050 ◦ C and strain rate of 0.01 s−1 .
of flow stress which can be described as: F (σ) = Aσ n
for low stresses,
F (σ) = A exp (βσ)n
for high stresses,
F (σ) = A sinh (ασ)n
for all stress levels
(2)
Fig. 4. Microstructure of the sample deformed at temperature of 1000 ◦ C and strain rate of 0.1 s−1 .
here n, A, A , A , α and β are material constants. Regarding to the wide variation of flow stress in A-286, for the employed deformation conditions. “Hyperbolic-sine” was used for expressing constitutive equations. For calculation of α-value, an iterative scheme has been utilized. Different values for “α” have been generated and then “n”-value was determined for various temperatures. It was observed that for the value of α = 0.0012, “n” is almost independent of temperature and its mean value is equal to “6.84”. Fig. 5 presents ln(˙ε) versus ln(sinh(ασ ss )) at different temperatures. In addition, to calculate the activation energy for hot deformation, the following equation was employed: Q ∂(ln(˙ε)) . (3) =− R ∂(1/T ) σss Fig. 6 shows ln(˙ε) versus 1/T at different steady state stresses. The mean activation energy was calculated as 795 kJ/mol for the steady state stresses span between 75 and 150 MPa. The amount of calculated activation energy is much larger than the selfdiffusion of iron in lattice. The similar results have been reported for the other superalloys [16,17]. For the case of UDIMET 720 nickel based superalloy, the mean activation energy was calculated as 1552 kJ/mol [16]. As it is observed the calculated activation energies both in this work or the published ones are much larger than the self-diffusion of Ni, Fe. This offers that the hot deformation behavior is controlled by two or more mechanisms. For example some alloys elements such as chromium raise the effective diffusion rate in the lattice as well as the presence of the second phases increases critical shear stress for dislocation glide. These factors increase hot deformation activation energy or in other words, the resistance to plastic deformation is increased. Strain rate sensitivity is an important material property, which can affect workability of metals. Fig. 7 shows variation of flow
156
A.R. Salehi et al. / Materials Chemistry and Physics 101 (2007) 153–157
Fig. 6. ln(˙ε) vs. 1/T at different steady-state stresses.
stress at the true strain of 0.3 as a function of strain rate at different temperatures. The slope of these curves gives strain rate sensitivity. As it is observed the strain rate sensitivity varies in the temperatures between 1000 and 1100 ◦ C where it changes from 0.105 at 1000 ◦ C to 0.15 at 1100 ◦ C. Fig. 8 shows the dependence of strain rate sensitivity on temperature. Increasing in strain rate
Fig. 8. Variation of strain rate sensitivity vs. temperature.
sensitivity may be attributed to occurring dynamic recrystallization at higher temperatures that produces higher strain rate sensitivity [18]. The other important factor affecting hot deformation behavior is the strain-hardening rate, γ, which is described as below: 1 dσ γ= . (4) σ dε ε˙ Utilizing the achieved stress–strain curves and numerical differentiation, strain-hardening rate has been calculated for different deformation conditions. In order to determine this parameter central difference scheme was employed as below: γi =
1 σi+1 − σi−1 σi εi+1 − εi−1
(5)
here γ i is the strain-hardening rate at the ith strain increment. Table 2 shows γ max calculated under various temperatures and strain rates. It should be noted that for the case of compression test work-hardening coefficient would be positive if the material experiences negative work hardening. In order to estimate workability of metal and alloys under hot deformation condition, flow-localization parameter, “FLP” has been proposed [18]. This Table 2 Maximum strain-hardening rate under different deformation conditions Strain rate (s−1 )
Fig. 7. Variation of flow stress at true strain of 0.3 with strain rate in different temperatures.
0.001 0.01 0.1
Temperature (◦ C) 1100
1050
1000
0.386 0.212 ≤0
0.188 1.12 ≤0
0.124 <0 0.012
A.R. Salehi et al. / Materials Chemistry and Physics 101 (2007) 153–157
parameter can be expressed as follows: γ (for shear band formation). (6) m This parameter is calculated in different temperatures and strain rates using Eq. (6). It can be found that at higher strain rates and low temperatures the possibility of occurring flow localizations is quite high and the material has a poor workability at this range. For example critical conditions may arise at hot deformation around 1050 ◦ C and strain rates of 0.01 s−1 where the work-hardening coefficient has a high value of “1.12” and on the other hand strain rate sensitivity has a rather low value of order of 0.12. Under these conditions, flowlocalization parameter is 9.24, which means that severe shear band regions will be formed during hot deformation. Therefore, an accurate control on temperature and strain rate should be applied to ensure producing a sample with the homogenous microstructure. FLP =
4. Conclusion Hot compression experiments have been performed on A-286 superalloy. The experiments were conducted in the temperatures between 1000 and 1100 ◦ C and strain rates of 0.001, 0.01 and 0.1 s−1 . By means of stress–strain curves the flow stress behavior and workability of this alloys have been studied. The results show that: 1. Both kinds of dynamic softening mechanisms may take place in A-286 superalloy. Dynamic recovery occurs at lower temperatures while dynamic recrystallization mainly occurs at 1100 ◦ C and strain rates of 0.001 and 0.01 s−1 . 2. The mean hot deformation activation energy is 795 kJ/mol, which shows high resistance of this alloy to hot deformation in the utilized deformation conditions. 3. The strain rate sensitivity of the alloy is not constant for the employed temperature range and it changes from 0.105 at 1000 ◦ C to 0.152 at 1100 ◦ C. Therefore, it is expected that at higher temperatures the workability would be improved. 4. Calculation of flow-localization parameter shows that at temperatures between 1000 and 1050 ◦ C and strain rate of
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