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Hot deformation and dynamic recrystallization of NiTi intermetallic compound
Accepted Manuscript Hot deformation and dynamic recrystallization of NiTi intermetallic compound H. Mirzadeh, M.H. Parsa PII: DOI: Reference:
S0925-8388(14)01408-X http://dx.doi.org/10.1016/j.jallcom.2014.06.063 JALCOM 31479
To appear in:
Journal of Alloys and Compounds
Received Date: Revised Date: Accepted Date:
24 April 2014 10 June 2014 11 June 2014
Please cite this article as: H. Mirzadeh, M.H. Parsa, Hot deformation and dynamic recrystallization of NiTi intermetallic compound, Journal of Alloys and Compounds (2014), doi: http://dx.doi.org/10.1016/j.jallcom. 2014.06.063
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Hot deformation and dynamic recrystallization of NiTi intermetallic compound H. Mirzadeha,c ∗, M.H. Parsa a,b,c a
School of Metallurgy and Materials Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran
b
Center of Excellence for High Performance Materials, School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran
c
Advanced Metalforming and Thermomechanical Processing Laboratory, School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran
Abstract The hot deformation behavior of a binary nitinol alloy with chemical composition of 50.5 at% Ni – 49.5 at% Ti was studied using the hot compression flow curves corresponding to the temperature range of 700 to 1000 °C under strain rate of 0.1 s-1. The typical single-peak dynamic recrystallization (DRX) behavior was seen in the resultant flow curves. The strain hardening rate analysis was used to reveal if DRX occurred. The effect of the Zener-Hollomon parameter (Z) on the characteristic points of flow curves was studied using the power law relations. The normalized critical stress and strain for initiation of DRX were respectively found to be 0.98 and 0.73. A power law constitutive equation, which relates the peak stress to Z with a Z exponent of 0.15, was proposed to characterize the hot working response of the investigated material.
Keywords: NiTi shape memory alloy; High-temperature deformation; Dynamic recrystallization; Strain hardening rate.
∗
Corresponding author. Tel.: +982182084127; Fax: +982188006076. E-mail addresses: [email protected] (H. Mirzadeh), [email protected] (M.H. Parsa)
1
1. Introduction Developed by the Naval Ordnance Laboratory (NiTiNOL) in Maryland, NiTi alloys are considered to be indispensable materials for many engineering and biomedical applications because of their unique functional properties, namely the shape memory effect and superelasticity (Pseudoelasticity), and also because of their biocompatibility, mechanical properties, and corrosion resistance [1-3]. The memory properties of these alloys are generally obtained with 49.3 to 51 at% Ni. Higher amount of Ni makes the alloy extremely hard and brittle [1]. For NiTi ordered intermetallic compound, the crystal structures of high temperature austenite phase and low temperature martensite phase are B2 type ordered structure and monoclinic structure, respectively [1,3]. The as-cast NiTi ingot is not ductile enough and does not show significant shape memory effect or superelasticity. Therefore, the cast ingots are generally subjected to hot working operations to break the cast structure, to improve mechanical properties and also to reduce cross section to facilitate further processing [1]. Hot working, through its related phenomena such as dynamic recovery (DRV) and dynamic recrystallization (DRX), is important in obtaining a suitable microstructure, which in turn influences the mechanical and functional properties of the material and hence its applicability. To improve the properties of the material, the parameters of the forming process must be controlled carefully. The understanding of the microstructural behavior is therefore required [4-6], together with the constitutive relation describing material flow [7-12]. There are some research works on hot deformation of binary NiTi alloys with 55 at% Ni [13], 49.8 at% Ni [14], and 50.9 at% Ni [15], which generally indicate the occurrence of DRX in these materials. However, the relations between the important points of hot deformation flow curves and the critical conditions for initiation of DRX have received 2
less attention. In the current work, the hot compression behavior of NiTi intermetallic compound with chemical composition of 50.5 at% Ni – 49.5 at% Ti with emphasis on the mentioned issues will be studied. Moreover, an appropriate constitutive equation to characterize the hot working behavior of this material will be proposed.
2. Experimental details 2.1. Casting and sample preparation Commercial purity titanium plates and nickel pellets were used as raw materials. Since the transformation temperatures of NiTi alloys, regarding their functional properties, are extremely sensitive to the chemistry and contaminants [1], the NiTi ingot with a chemical composition of 50.5 at% Ni – 49.5 at% Ti was cast using a Vacuum induction melting (VIM) furnace. To refine the microstructure, this is followed by vacuum arc remelting (VAR). The cast ingot was slightly hot rolled at 950 °C with a reduction of 5%. Afterwards, the homogenization treatment was performed at 950 °C for 14 hours using a vacuum furnace. The homogenized ingot (~ 100L × 15 W × 12T mm3) was shape rolled at 950 °C to obtain a square cross section of 10 × 10 mm2. Specimens with height of 12 mm and diameter of 8 mm were prepared by machining for hot compression tests.
2.2. Hot compression A universal testing machine equipped with an electrical resistance furnace was used for hot compression testing of samples at temperatures of 700, 800, 900, and 1000 °C under strain rate of 0.1 s-1. The specimens were deformed up to true strain of 0.7 and then they were quenched in water. For all samples, variations of flow stress with strain during hot compression test were recorded from start of deformation to the end of straining.
3
3. Results and discussion 3.1. Flow curves Flow curves obtained at different deformation conditions are shown in Fig. 1. All curves exhibit typical single peak DRX behavior with a broad peak followed by a gradual fall towards a steady state stress. In the single peak behavior, new cycles of DRX initiate before completion of the first cycle. Therefore, after completion of the first DRX cycle, other DRX cycles are incomplete. This means that different grains will be at different stages of the DRX process at any point of time. The flow curve will represent the averaged flow stress of grains at different stages of recrystallization in the form of a broad peak. Fig. 1 also shows that the flow stress decreases with increasing deformation temperature. This may be attributed to the increase in the rate of restoration processes and decrease in the strain hardening rate. Moreover, the critical, peak, and steady state strains decrease with increasing deformation temperature. Since the formation of DRX nuclei becomes easier at higher deformation temperatures, the critical strain for initiation of DRX decreases. Moreover, the mobility of grain boundaries increases with increasing deformation temperature and hence the rate of DRX increases. Therefore, both the peak and steady state strains decrease with increasing deformation temperature [7].
3.2. Work hardening rate analysis It has been shown that the onset of DRX can also be detected from inflections in plots of the strain hardening rate against stress [16-18]. Therefore, the onset of DRX was detected from the inflections in plots of the work hardening rate (θ) versus σ (before the
4
peak point of flow curves) as shown in Fig. 2a. The θ-σ curves (Fig. 2a) show inflection points, which is evident from the appearance of a global minimum in − dθ / dσ versus σ curves (Fig. 2b). These observations are considered as signs for the occurrence of
DRX. In each curve of Fig. 2a, the work hardening rate (θ) linearly decreases with the flow stress. After that, the curves gradually change to another linear line and then drop towards θ = 0 at peak stress. Afterwards, the work hardening rate becomes negative and then again tends to θ = 0 at steady-state stress. This is better shown in Fig. 2c and these results are consistent with the general DRX behavior [18-20].
3.3. Characteristic points of DRX flow curves The characteristic points of flow curves were detected from − dθ / dσ versus σ (based on their minimums to find the critical stress for initiation of DRX, σ C , as shown in Fig. 2b), θ-σ (to find the peak stress, σ P , and steady-state stress, σ S , as shown in Fig. 2c), θ-
ε (to find the peak strain ε P and steady-state strain ε S , as shown in Fig. 2d), and ln θ -
ε curves (based on their inflection points to find the critical strain for the onset of DRX, ε C ) and subsequently were plotted in Fig. 3. More information on analysis and preparation of hot deformation flow curves can be found elsewhere [7,20,21]. Regression analysis of these curves (using an equation of the form of y=ax based on the expected relations between the characteristic points) showed that σ C = 0.98σ P ,
ε C = 0.73ε P , σ S = 0.86σ P , and ε S = 6.5ε P . Therefore, the normalized critical stress and strain can be expressed as σ C / σ P = 0.98 and ε C / ε P = 0.73 , respectively. While the DRX process starts when the strain becomes equal to 0.73ε P , however, the high value for normalized critical stress shows that the flow hardening or softening from the 5
critical point to the peak point is negligible. At the onset of steady state flow ( ε S = 6.5ε P ), as a result of the balance between work hardening and restoration processes, the flow stress reaches to the value of 0.86σ P . This implies that the restoration processes can effectively soften the alloy during hot working. The obtained value of normalized critical strain is also consistent with the previous studies (mainly on steels) which have reported a value in the range of 0.3 to 0.9 [7].
3.4. Constitutive analysis Constitutive equations were used to calculate the activation energy and hot deformation constants of NiTi alloy. The power law description of flow stress can be expressed as Z = ε exp( Q / RT ) = Aσ q , where Z is the Zener-Hollomon parameter, Q is the
deformation activation energy, A and q are apparent material constants, R is the universal gas constant, and T is the absolute temperature. The reported values of selfdiffusion activation energies for nickel and beta titanium are 279.7 kJ/mol and 251.2 kJ/mol, respectively [22]. It has been shown that in creep and hot deformation studies, the self-diffusion activation energy can be used as the deformation activation energy to calculate Z [23]. Therefore, the average value of Q = (279.7+251.2)/2 = 265.45 kJ/mol was considered here. The values of 250.74 kJ/mol [13], 261 kJ/mol [14], and 230 kJ/mol [24] have also been reported for hot deformation activation energy of binary NiTi alloys with different chemical compositions, which are more or less consistent with the value of about 265 kJ/mol considered here. The description of flow stress by equation Z = Aσ q is incomplete, because no strain for determination of flow stress is specified. Therefore, characteristic stresses such as steady state or peak stresses may be used for this purpose. Since the steady state stress 6
may not be precisely attained, it is usual to use the peak stress [21]. Taking natural logarithm from the equation Z = Aσ Pq results to ln Z = ln A + q ln σ P . Therefore, the slope of the plot of ln Z against ln σ P can be used for obtaining the values of q and A. The corresponding plot is shown in Fig. 4 and the linear regression of the data results in the values of q = 6.59 and A = 0.00188. Therefore, the appropriate constitutive equation to characterize the hot deformation behavior of the investigated NiTi alloy can be expressed as Z = ε exp(31928 / T ) = 0.00188σ P6.59 or equivalently σ P = 2.59 × Z 0.15 , where the peak stress is expressed in MPa. The Z exponent of 0.15 for the peak stress is comparable to values of 0.13 [25], 0.147 [26], and 0.18 [20] for AISI 304L stainless steel, medium carbon microalloyed steel, and 17-4 PH stainless steel, respectively. As shown in Fig. 5, the peak strain was also plotted on a logarithmic scale with respect to Z based on the power relation of ε P = B × Z m or equivalently ln ε P = ln B + m ln Z . The linear regression of the data results in the equation of ε P = 0.022 × Z 0.053 . Therefore, based on ε C = 0.73ε P , the onset of DRX can also be expresses by ε C = 0.016 × Z 0.053 .
4. Conclusions
(1) The stress-strain curves of the NiTi alloy, in the range of deformation conditions used in this study, exhibited typical single peak DRX behavior with a broad peak followed by a gradual fall towards a steady state stress. (2) The normalized critical stress and strain for initiation of DRX were found to be 0.98 and 0.73, respectively. While the DRX process starts when the normalized strain becomes equal to 0.73, however, the high value of 0.98 for normalized critical stress shows that the flow hardening or softening from the critical point to the peak point is negligible in the investigated NiTi alloy. 7
(3) At the onset of steady state flow (normalized strain of about 6.5), as a result of the balance between work hardening and restoration processes, the normalized flow stress reaches to the value of 0.86. This implies that the restoration processes can effectively soften the alloy during hot working. (4) The Z exponents for the peak stress and peak strain were determined as 0.15 and 0.053, respectively. (5) The constitutive equation of Z = ε exp(31928 / T ) = 0.00188σ P6.59 can be used to express the hot working characteristics of the investigated alloy, in which the peak stress is expressed in MPa.
References
[1] S.K. Bhaumik, Trans. Indian. Inst. Met. 61 (2008) 435-445. [2] M.A. Meyers, K.K. Chawla, Mechanical behavior of materials, second ed., Cambridge University Press, 2009. [3] K. Otsuka, X. Ren, Prog. Mater. Sci. 50 (2005) 511-678. [4] J. Jia, K. Zhang, L. Liu, F. Wu, J. Alloys Compd. 600 (2014) 215-221. [5] X. Xia, Q. Chen, J. Li, D. Shu, C. Hu, S. Huang, Z. Zhao, J. Alloys Compd. 610 (2014) 203-211. [6] F. Yang, F. Kong, Y. Chen, S. Xiao, J. Alloys Compd. 589 (2014) 609-614. [7] H. Mirzadeh, A. Najafizadeh, ISIJ Int. 53 (2013) 680-689. [8] B. Li, Q. Pan, Z. Yin, J. Alloys Compd. 584 (2014) 406-416. [9] J. Guoa, S. Zhao, R. Murakami, R. Dinga, S. Fan, J. Alloys Compd. 566 (2013) 6267. [10] J. Jia, K. Zhang, L. Liu, F. Wu, J. Alloys Compd. 600 (2014) 215-221. 8
[11] L. Zhang, X. Qu, X. He, D. Rafi-ud, M. Qin, H. Zhu, J. Alloys Compd. 512 (2012) 39-46. [12] B. Li, Q. Pan, Z. Yin, J. Alloys Compd. 584 (2014) 406-416. [13] K. Dehghani, A.A. Khamei, Mater. Sci. Eng. A 527 (2010) 684-690. [14] M. Morakabati, S. Kheirandish, M. Aboutalebi, A. Karimi Taheri, S.M. Abbasi, Mater. Sci. Eng. A 528 (2011) 5656-5663. [15] S.Y. Jiang, Y.Q. Zhang, Y. Zhao, Trans. Nonferrous Met. Soc. China 23 (2013) 140-147. [16] N.D. Ryan, H.J. McQueen, Can. Metall. Q. 29 (1990) 147-162. [17] E.I. Poliak, J.J. Jonas, Acta Mater. 44 (1996) 127-136. [18] H. Mirzadeh, A. Najafizadeh, Mater. Des. 31 (2010) 1174-1179. [19] H. Mirzadeh, J.M. Cabrera, A. Najafizadeh, P.R. Calvillo, Mater. Sci. Eng. A 538 (2012) 236-245. [20] H. Mirzadeh, A. Najafizadeh, M. Moazeny, Metall. Mater. Trans. A 40 (2009) 2950-2958. [21] H. Mirzadeh, A. Najafizadeh, M. Moazeny, Mater. Sci. Tech. 26 (2010) 501-504. [22] D.A. Porter, K.E. Easterling, Phase Transformations in Metals and Alloys, second ed., Chapman & Hall, 1992. [23] H. Mirzadeh, J.M. Cabrera, A. Najafizadeh, Acta Mater. 59 (2011) 6441-6448. [24] S.Y. Jiang, Y.Q. Zhang, Y. Zhao, J. Cent. South. Univ. 20 (2013) 24-29. [25] H. Mirzadeh, M.H. Parsa, D. Ohadi, Mater. Sci. Eng. A 569 (2013) 54-60. [26] H. Mirzadeh, J.M. Cabrera, J.M. Prado, A. Najafizadeh, Mater. Sci. Eng. A 528 (2011) 3876-3882.
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Figure Captions
Fig. 1: Flow curves obtained at different deformation conditions. Fig. 2: Work hardening rate analyses. It should be noted that third order polynomials were fitted to the θ-σ curves (until the peak point corresponding to θ = 0) to get smoother − dθ / dσ -σ curves. Fig. 3: Plots used to derive the relations among the various characteristic points of flow curves. Fig. 4: Plot used to derive the constitutive equation for hot deformation of NiTi alloy. Fig. 5: Plot used to obtain the dependence of the peak strain on Z.
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Research Highlights
•
Hot deformation behavior and dynamic recrystallization (DRX) in NiTi alloy
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The normalized critical stress and strain for initiation of DRX of 0.98 and 0.72
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The hot deformation activation energy of 265 kJ/mol for calculation of Z
•
A power law constitutive equation for the peak stress with a Z exponent of 0.15
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Graphical abstract
17
S0925-8388(14)01408-X http://dx.doi.org/10.1016/j.jallcom.2014.06.063 JALCOM 31479
To appear in:
Journal of Alloys and Compounds
Received Date: Revised Date: Accepted Date:
24 April 2014 10 June 2014 11 June 2014
Please cite this article as: H. Mirzadeh, M.H. Parsa, Hot deformation and dynamic recrystallization of NiTi intermetallic compound, Journal of Alloys and Compounds (2014), doi: http://dx.doi.org/10.1016/j.jallcom. 2014.06.063
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Hot deformation and dynamic recrystallization of NiTi intermetallic compound H. Mirzadeha,c ∗, M.H. Parsa a,b,c a
School of Metallurgy and Materials Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran
b
Center of Excellence for High Performance Materials, School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran
c
Advanced Metalforming and Thermomechanical Processing Laboratory, School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran
Abstract The hot deformation behavior of a binary nitinol alloy with chemical composition of 50.5 at% Ni – 49.5 at% Ti was studied using the hot compression flow curves corresponding to the temperature range of 700 to 1000 °C under strain rate of 0.1 s-1. The typical single-peak dynamic recrystallization (DRX) behavior was seen in the resultant flow curves. The strain hardening rate analysis was used to reveal if DRX occurred. The effect of the Zener-Hollomon parameter (Z) on the characteristic points of flow curves was studied using the power law relations. The normalized critical stress and strain for initiation of DRX were respectively found to be 0.98 and 0.73. A power law constitutive equation, which relates the peak stress to Z with a Z exponent of 0.15, was proposed to characterize the hot working response of the investigated material.
Keywords: NiTi shape memory alloy; High-temperature deformation; Dynamic recrystallization; Strain hardening rate.
∗
Corresponding author. Tel.: +982182084127; Fax: +982188006076. E-mail addresses: [email protected] (H. Mirzadeh), [email protected] (M.H. Parsa)
1
1. Introduction Developed by the Naval Ordnance Laboratory (NiTiNOL) in Maryland, NiTi alloys are considered to be indispensable materials for many engineering and biomedical applications because of their unique functional properties, namely the shape memory effect and superelasticity (Pseudoelasticity), and also because of their biocompatibility, mechanical properties, and corrosion resistance [1-3]. The memory properties of these alloys are generally obtained with 49.3 to 51 at% Ni. Higher amount of Ni makes the alloy extremely hard and brittle [1]. For NiTi ordered intermetallic compound, the crystal structures of high temperature austenite phase and low temperature martensite phase are B2 type ordered structure and monoclinic structure, respectively [1,3]. The as-cast NiTi ingot is not ductile enough and does not show significant shape memory effect or superelasticity. Therefore, the cast ingots are generally subjected to hot working operations to break the cast structure, to improve mechanical properties and also to reduce cross section to facilitate further processing [1]. Hot working, through its related phenomena such as dynamic recovery (DRV) and dynamic recrystallization (DRX), is important in obtaining a suitable microstructure, which in turn influences the mechanical and functional properties of the material and hence its applicability. To improve the properties of the material, the parameters of the forming process must be controlled carefully. The understanding of the microstructural behavior is therefore required [4-6], together with the constitutive relation describing material flow [7-12]. There are some research works on hot deformation of binary NiTi alloys with 55 at% Ni [13], 49.8 at% Ni [14], and 50.9 at% Ni [15], which generally indicate the occurrence of DRX in these materials. However, the relations between the important points of hot deformation flow curves and the critical conditions for initiation of DRX have received 2
less attention. In the current work, the hot compression behavior of NiTi intermetallic compound with chemical composition of 50.5 at% Ni – 49.5 at% Ti with emphasis on the mentioned issues will be studied. Moreover, an appropriate constitutive equation to characterize the hot working behavior of this material will be proposed.
2. Experimental details 2.1. Casting and sample preparation Commercial purity titanium plates and nickel pellets were used as raw materials. Since the transformation temperatures of NiTi alloys, regarding their functional properties, are extremely sensitive to the chemistry and contaminants [1], the NiTi ingot with a chemical composition of 50.5 at% Ni – 49.5 at% Ti was cast using a Vacuum induction melting (VIM) furnace. To refine the microstructure, this is followed by vacuum arc remelting (VAR). The cast ingot was slightly hot rolled at 950 °C with a reduction of 5%. Afterwards, the homogenization treatment was performed at 950 °C for 14 hours using a vacuum furnace. The homogenized ingot (~ 100L × 15 W × 12T mm3) was shape rolled at 950 °C to obtain a square cross section of 10 × 10 mm2. Specimens with height of 12 mm and diameter of 8 mm were prepared by machining for hot compression tests.
2.2. Hot compression A universal testing machine equipped with an electrical resistance furnace was used for hot compression testing of samples at temperatures of 700, 800, 900, and 1000 °C under strain rate of 0.1 s-1. The specimens were deformed up to true strain of 0.7 and then they were quenched in water. For all samples, variations of flow stress with strain during hot compression test were recorded from start of deformation to the end of straining.
3
3. Results and discussion 3.1. Flow curves Flow curves obtained at different deformation conditions are shown in Fig. 1. All curves exhibit typical single peak DRX behavior with a broad peak followed by a gradual fall towards a steady state stress. In the single peak behavior, new cycles of DRX initiate before completion of the first cycle. Therefore, after completion of the first DRX cycle, other DRX cycles are incomplete. This means that different grains will be at different stages of the DRX process at any point of time. The flow curve will represent the averaged flow stress of grains at different stages of recrystallization in the form of a broad peak. Fig. 1 also shows that the flow stress decreases with increasing deformation temperature. This may be attributed to the increase in the rate of restoration processes and decrease in the strain hardening rate. Moreover, the critical, peak, and steady state strains decrease with increasing deformation temperature. Since the formation of DRX nuclei becomes easier at higher deformation temperatures, the critical strain for initiation of DRX decreases. Moreover, the mobility of grain boundaries increases with increasing deformation temperature and hence the rate of DRX increases. Therefore, both the peak and steady state strains decrease with increasing deformation temperature [7].
3.2. Work hardening rate analysis It has been shown that the onset of DRX can also be detected from inflections in plots of the strain hardening rate against stress [16-18]. Therefore, the onset of DRX was detected from the inflections in plots of the work hardening rate (θ) versus σ (before the
4
peak point of flow curves) as shown in Fig. 2a. The θ-σ curves (Fig. 2a) show inflection points, which is evident from the appearance of a global minimum in − dθ / dσ versus σ curves (Fig. 2b). These observations are considered as signs for the occurrence of
DRX. In each curve of Fig. 2a, the work hardening rate (θ) linearly decreases with the flow stress. After that, the curves gradually change to another linear line and then drop towards θ = 0 at peak stress. Afterwards, the work hardening rate becomes negative and then again tends to θ = 0 at steady-state stress. This is better shown in Fig. 2c and these results are consistent with the general DRX behavior [18-20].
3.3. Characteristic points of DRX flow curves The characteristic points of flow curves were detected from − dθ / dσ versus σ (based on their minimums to find the critical stress for initiation of DRX, σ C , as shown in Fig. 2b), θ-σ (to find the peak stress, σ P , and steady-state stress, σ S , as shown in Fig. 2c), θ-
ε (to find the peak strain ε P and steady-state strain ε S , as shown in Fig. 2d), and ln θ -
ε curves (based on their inflection points to find the critical strain for the onset of DRX, ε C ) and subsequently were plotted in Fig. 3. More information on analysis and preparation of hot deformation flow curves can be found elsewhere [7,20,21]. Regression analysis of these curves (using an equation of the form of y=ax based on the expected relations between the characteristic points) showed that σ C = 0.98σ P ,
ε C = 0.73ε P , σ S = 0.86σ P , and ε S = 6.5ε P . Therefore, the normalized critical stress and strain can be expressed as σ C / σ P = 0.98 and ε C / ε P = 0.73 , respectively. While the DRX process starts when the strain becomes equal to 0.73ε P , however, the high value for normalized critical stress shows that the flow hardening or softening from the 5
critical point to the peak point is negligible. At the onset of steady state flow ( ε S = 6.5ε P ), as a result of the balance between work hardening and restoration processes, the flow stress reaches to the value of 0.86σ P . This implies that the restoration processes can effectively soften the alloy during hot working. The obtained value of normalized critical strain is also consistent with the previous studies (mainly on steels) which have reported a value in the range of 0.3 to 0.9 [7].
3.4. Constitutive analysis Constitutive equations were used to calculate the activation energy and hot deformation constants of NiTi alloy. The power law description of flow stress can be expressed as Z = ε exp( Q / RT ) = Aσ q , where Z is the Zener-Hollomon parameter, Q is the
deformation activation energy, A and q are apparent material constants, R is the universal gas constant, and T is the absolute temperature. The reported values of selfdiffusion activation energies for nickel and beta titanium are 279.7 kJ/mol and 251.2 kJ/mol, respectively [22]. It has been shown that in creep and hot deformation studies, the self-diffusion activation energy can be used as the deformation activation energy to calculate Z [23]. Therefore, the average value of Q = (279.7+251.2)/2 = 265.45 kJ/mol was considered here. The values of 250.74 kJ/mol [13], 261 kJ/mol [14], and 230 kJ/mol [24] have also been reported for hot deformation activation energy of binary NiTi alloys with different chemical compositions, which are more or less consistent with the value of about 265 kJ/mol considered here. The description of flow stress by equation Z = Aσ q is incomplete, because no strain for determination of flow stress is specified. Therefore, characteristic stresses such as steady state or peak stresses may be used for this purpose. Since the steady state stress 6
may not be precisely attained, it is usual to use the peak stress [21]. Taking natural logarithm from the equation Z = Aσ Pq results to ln Z = ln A + q ln σ P . Therefore, the slope of the plot of ln Z against ln σ P can be used for obtaining the values of q and A. The corresponding plot is shown in Fig. 4 and the linear regression of the data results in the values of q = 6.59 and A = 0.00188. Therefore, the appropriate constitutive equation to characterize the hot deformation behavior of the investigated NiTi alloy can be expressed as Z = ε exp(31928 / T ) = 0.00188σ P6.59 or equivalently σ P = 2.59 × Z 0.15 , where the peak stress is expressed in MPa. The Z exponent of 0.15 for the peak stress is comparable to values of 0.13 [25], 0.147 [26], and 0.18 [20] for AISI 304L stainless steel, medium carbon microalloyed steel, and 17-4 PH stainless steel, respectively. As shown in Fig. 5, the peak strain was also plotted on a logarithmic scale with respect to Z based on the power relation of ε P = B × Z m or equivalently ln ε P = ln B + m ln Z . The linear regression of the data results in the equation of ε P = 0.022 × Z 0.053 . Therefore, based on ε C = 0.73ε P , the onset of DRX can also be expresses by ε C = 0.016 × Z 0.053 .
4. Conclusions
(1) The stress-strain curves of the NiTi alloy, in the range of deformation conditions used in this study, exhibited typical single peak DRX behavior with a broad peak followed by a gradual fall towards a steady state stress. (2) The normalized critical stress and strain for initiation of DRX were found to be 0.98 and 0.73, respectively. While the DRX process starts when the normalized strain becomes equal to 0.73, however, the high value of 0.98 for normalized critical stress shows that the flow hardening or softening from the critical point to the peak point is negligible in the investigated NiTi alloy. 7
(3) At the onset of steady state flow (normalized strain of about 6.5), as a result of the balance between work hardening and restoration processes, the normalized flow stress reaches to the value of 0.86. This implies that the restoration processes can effectively soften the alloy during hot working. (4) The Z exponents for the peak stress and peak strain were determined as 0.15 and 0.053, respectively. (5) The constitutive equation of Z = ε exp(31928 / T ) = 0.00188σ P6.59 can be used to express the hot working characteristics of the investigated alloy, in which the peak stress is expressed in MPa.
References
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Figure Captions
Fig. 1: Flow curves obtained at different deformation conditions. Fig. 2: Work hardening rate analyses. It should be noted that third order polynomials were fitted to the θ-σ curves (until the peak point corresponding to θ = 0) to get smoother − dθ / dσ -σ curves. Fig. 3: Plots used to derive the relations among the various characteristic points of flow curves. Fig. 4: Plot used to derive the constitutive equation for hot deformation of NiTi alloy. Fig. 5: Plot used to obtain the dependence of the peak strain on Z.
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Research Highlights
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Hot deformation behavior and dynamic recrystallization (DRX) in NiTi alloy
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The normalized critical stress and strain for initiation of DRX of 0.98 and 0.72
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The hot deformation activation energy of 265 kJ/mol for calculation of Z
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A power law constitutive equation for the peak stress with a Z exponent of 0.15
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Graphical abstract
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