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Thermal cycling stability mechanism of Ti50.5Ni33.5Cu11.5Pd4.5 shape memory alloy with near-zero hysteresis
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ScienceDirect Scripta Materialia xxx (2015) xxx–xxx www.elsevier.com/locate/scriptamat
Thermal cycling stability mechanism of Ti50.5Ni33.5Cu11.5Pd4.5 shape memory alloy with near-zero hysteresis ⇑
X.L. Meng,a, H. Li,a W. Cai,a S.J. Haob and L.S. Cuib a
National Key Laboratory Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin 150001, People’s Republic of China b Materials Science and Engineering of China University of Petroleum, Peking 100000, People’s Republic of China Received 1 February 2015; revised 25 February 2015; accepted 26 February 2015
After 5000 thermal cycles, the change of the transformation temperature is less than 1 °C in a Ti50.5Ni33.5Cu11.5Pd4.5 alloy. Also, the hysteresis becomes smaller nearing zero. Using thermal dynamic calculations, the elastic energy is nearly unchanged during the thermal cycles, which means there is little addition of the irreversible energy. The transmission electron microscopy observations show that the irreversible defects such as dislocations are rare in the reciprocating phase transition processes. Both of these explain the high thermal stability mechanism. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ti–Ni–Cu–Pd alloy; Shape memory alloys (SMAs); Martensitic phase transformation; Thermodynamics; Transmission electron microscopy (TEM)
During the past decades, Ti–Ni shape memory alloys have been used as actuator materials because of their large output force and displacement [1,2]. However, the temperatures hystereses for phase transformation are greater than 30 °C in the vast majority of the Ti–Ni alloys, which makes it not possible to provide a fast enough response speed to satisfy the high sensitivity requirements in actuator drives. Also, over multiple thermal cycles during working status, the functional characteristics (such as the martensitic transformation temperature, temperature hystereses of phase transformation, etc.) suffer from attenuation, leading to poor stability. The martensite transformation starting temperature (Ms) decreases by about 30 °C and 40 °C in Ti–Ni and Cu–Al–Ni alloys after 10,000 cycles, respectively [3,4]. In these cases, the dislocations introduced during the martensitic transformation should be responsible for the decrease in Ms. And the instability of Ms during thermal cycling makes it difficult to realize a high precision control of the drive performance. Recently, a Ti50.2Ni34.4Cu12.3Pd3.1 alloy with a near-zero hysteresis has been designed based on the geometric nonlinear theory of martensite (GNLTM) [5]. When k2 (the middle eigenvalue of the phase transformation matrix) equals one, the alloy can display not only the ultra narrow hysteresis, but also high stability in thermal cycles [6–8].
⇑ Corresponding author. Tel.: +86 045186418649; e-mail: xlmeng@hit.
However, the mechanism of high thermal stability has not been further investigated so far. The aim of the present study is to examine the thermal stability in the Ti50.5Ni33.5Cu11.5Pd4.5 shape memory alloy with a near-zero hysteresis by means of transmission electron microscopy (TEM) observation and thermal dynamic calculation. Meanwhile, the mechanism of such a high thermal stability is also discussed. The alloys were prepared with high purity elements by melting 10 times in an argon atmosphere in a vacuum arc furnace. The samples were annealed in vacuum quartz tubes at 950 °C for 7.2 ks, and then water-quenched. The phase transformation temperatures were determined by the Perkin-Elmer diamond differential scanning calorimetry (DSC). X-ray diffraction (XRD) measurements were performed using an X’ Pert PRO MPD with Cu Ka radiation. An FEI TECNAI G2 20 STWIN 300 kV transmission electron microscope (TEM) equipped with a double-tilt cooling stage was used for microstructure observation at room temperature. In order to characterize the phase transformation hysteresis more precisely, the DSC tests with different scanning rates have been carried out. The effects of the heating/cooling rates on the hystereses (DTh) of the Ti50.5Ni33.5Cu11.5 Pd4.5 alloy are shown in Figure 1. The variation of the hystereses of the Ti50.5Ni49.5 and Ti50Ni37.5Cu12.5 alloys is also plotted in Figure 1 for comparison. Generally speaking, the hysteresis decreases when the heating/cooling
edu.cn http://dx.doi.org/10.1016/j.scriptamat.2015.02.030 1359-6462/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: X.L. Meng et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.02.030
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Figure 1. Effects of DSC scanning rates on the hystereses of the Ti50.5Ni49.5, Ti50Ni37.5Cu12.5 and Ti50.5Ni33.5Cu11.5Pd4.5 alloys.
rates decrease in the DSC measurements. Therefore, the DSC with a fast scanning rate is considered to be inadequate to capture near-zero hysteresis values due to the inherent delay of the measurement signal. It has been found that the results of the alternating current potential drop (ACPD) technique and DSC are different when testing the same alloy. And ACPD was used for the characterization of the near-zero hysteresis behavior [5]. For all three kinds of alloys, the hystereses decrease linearly with the slower heating/cooling rates. By linear fitting, it can be seen that when the scan rate gets close to zero, the hysteresis is 1.7 °C in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy, as shown in Figure 1. This means the intrinsic hysteresis can be reflected by the slower heating/cooling rate, which is near the equilibrium of the cooling condition. The inherent delay of the measurement signal can be overcome, and thus, the hysteresis can be detected most accurately by using this method. Effects of the thermal cycles on the transformation temperatures of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy are shown in Figure 2. Both the martensitic transformation peak temperature (Mp) and the reverse transformation peak temperature (Ap) of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy remain almost constant when the number of cycles increased and a perfect thermal cycling stability is observed as shown in Figure 2a and b. After 5000 thermal cyclings, the changes in Mp and Ap are 1 °C and 0.8 °C respectively. In Figure 2c, the phase transformation temperatures are shown as a function of the number of the thermal cycles. With the increase in the cycle number, Ms rises monotonously, and the reverse transformation starting temperature (As) decreases slightly in the initial
circulations, and thereafter both level out. In Ti–Ni alloys, both Ms and As decrease rapidly in the first 20 cycles, and then the trend of decrease begins to level out [3]. Figure 3a–c shows the bright-field images of the martensite structure after 0, 1000 and 5000 thermal cycles of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy respectively. Mainly the type of twin martensites (B19) parallel to each other in the grain interior, present a single configuration morphology (singlepair). By contrast with the TEM photo of the untreated sample, only a few dislocations are generated in the sample after 1000 thermal circulations. In the following thermal cycles, there is no significant increase in the number of dislocations, as shown in Figure 3c. This is different from the phenomenon observed in Ti–Ni and Cu–Al–Ni alloys [3,4]. In those alloys, the dislocation density rapidly increased with increasing thermal cyclings. Regarding the present alloy after 5000 cycles, the dislocation density is lower than that in the Ti–Ni alloys after 5 cycles [9]. This may be the reason for the good stability presented in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy from the view of microstructure change. Through thermodynamic calculation, it can be found that dislocations introduced in the process of thermal cycling are related to the elastic energy. Figure 4 shows the change in the elastic energy in the martensite variants with the increase of the thermal cycles. The elastic energy is derived from [10]: Ms Mf DS 2 The entropy results from:
DGel ¼
DS ¼
DH T0
ð1Þ
ð2Þ
DH is the enthalpy of martensitic transformation, determined by the DSC measurement. The equilibrium temperature T0 is the midpoint between Af and Ms: M s þ Af 2 Thus the following formula is deduced:
T0 ¼
DGel ¼
Ms Mf DH M s þ Af
ð3Þ
ð4Þ
Mf and Af are the finishing temperatures of the martensitic and reverse transformations, respectively. Here the frictional energy in the process of the phase transition is taken into account. The frictional energy is related to the interface hindered motion inside the
Figure 2. DSC curves of (a) heating and (b) cooling processes of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy during thermal cycle. (c) The shift of martensite start (Ms), finish (Mf) and austenite start (As), finish (Af) temperatures.
Please cite this article in press as: X.L. Meng et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.02.030
X.L. Meng et al. / Scripta Materialia xxx (2015) xxx–xxx
3
Figure 3. Bright-field images of martensite after (a) 0 thermal cycle, (b) 1000 thermal cycles and (c) 5000 thermal cycles of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy.
Figure 4. (a) Elastic energy stored in the martensite variants as a function of the number of thermal cycles in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy. (b) The linear fitting curves of the elastic energy stored in the martensite variants as a function of 100 thermal cycles in the Ti50.5Ni33.5Cu11.5Pd4.5 and Ti50.5Ni49.5 alloys.
transforming variants and the interaction with defects. So the total elastic energy is composed of the reversible elastic energy and the irreversible elastic energy. The reversible elastic energy results from the accommodation of the volume change. Hence, it basically remains unchanged. However, the irreversible energy is mainly due to the consumption of the frictional energy, and it will increase with the increased dislocations introduced during the thermal cycling. It can be seen from Figure 4a that in the initial 100 cycles the elastic energy of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy increases modestly. This suggests that there are a few dislocations induced in the initial circulations. It is consistent with the slight change in Ms along with the addition of the thermal cycles. Then the elastic energy stays in the range of 0.09–0.1 J/g. The induction of dislocations becomes fewer with the following more thermal cyclings. Through linear fitting, it can be found that the slope in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy is much smaller than that in the Ti50.5Ni49.5 alloy as shown in Figure 4b. For comparison, after 100 thermal cycles, the elastic energy the Ti50.5Ni49.5 alloy sharply increases from 0.1511 J/g to 0.234 J/g. The amplitude of the variation is larger than that in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy after 5000 thermal cyclings (from 0.0735 J/g to 0.0917 J/g). This also implies that after thermal cycles, the dislocations introduced in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy are far less than those in the Ti50.5Ni49.5 alloy. Generally speaking, the dislocations have two effects on the martensitic transformation: (1) When the dislocation density is low, the dislocations can help the martensitic nucleation [11–13]. (2) The high dislocation density may strengthen the matrix, which is unfavorable for the shear
of the martensitic transformation, and therefore blocks the martensite phase transformation. The degree of supercooling has to be increased to complete the martensite phase transformation, causing a reduction of Ms. As mentioned above, the results of the thermal dynamic calculation imply a slight increase in the dislocation density in Ti50.5Ni33.5Cu11.5Pd4.5 alloy quantificationally. TEM observation manifests the dislocations induced through thermal cycling are very few in the present Ti50.5Ni33.5Cu11.5Pd4.5 alloy. The martensitic transformation is from cubic to orthorhombic in the present Ti50.5Ni33.5Cu11.5Pd4.5 alloy, therefore there are six variants of martensite. The deformation matrixes for these variants are listed in Table 1. We determine from the deformation matrixes that k2 = 1.0014, close to 1. The crystal symmetry and geometric compatibilities between martensite and austenite are excellent in the present alloy [14]. Thus, dislocations may not be needed to coordinate the phase transformation in this case. This leads to few dislocations introduced. The effect of the matrix strengthening will not be brought in such low dislocation density. In the present study, the stress field around a small amount of dislocations may be beneficial to the martensitic nucleation, and reduce the phase transformation driving force. Its macroscopic reflection is a tiny advance in Ms, meanwhile the hysteresis is getting smaller. Compared with the present Ti50.5Ni33.5Cu11.5Pd4.5 alloy, even a few thermal cycles can import a mass of dislocations in Ti–Ni alloys, leading to a significant reduction in Ms. In summary, we find that the Ti50.5Ni33.5Cu11.5Pd4.5 alloy exhibits an excellent thermal stability even after 5000 thermal cycles, and the hysteresis tends to be smaller. TEM observation shows there are very few dislocations
Please cite this article in press as: X.L. Meng et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.02.030
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X.L. Meng et al. / Scripta Materialia xxx (2015) xxx–xxx
Table 1. Shape-strain matrices for six variants in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy.a Variant(i) 1
Ui 0
Variant(i) 1
0:948 0 0 0 1:031 0:03 A 0 0:03 1:031 0 1 0:948 0 0 @ 0 1:031 0:03 A 0 0:03 1:031
4
5
0 3 a
1 1:031 0 0:03 @ 0 0:948 0 A 0:03 0 1:031
1 1:031 0 0:03 0 0:948 0 A 0:03 0 1:031 0 1 1:031 0:03 0 @ 0:03 1:031 0 A 0 0 0:948
@
@
2
Ui 0
0 6
1 1:031 0:03 0 @ 0:03 1:031 0 A 0 0 0:948
Input parameters for B2 phase, a = 0.3037 nm, for B19 martensite, a = 0.2879 nm, b = 0.43 nm, c = 0.4556 nm.
induced. The results of the thermodynamic calculation indicate the increment of the irreversible elastic energy (caused by the introduction of dislocations) is very little. Only a few dislocations are introduced during the thermal cycling, which is the main reason for the excellent thermal cycling stability in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy. The work was supported by Natural Science Foundation of China (No. 51171052 and No. 51322102), 973 projects of China (2011CB012904 and 2012CB619400), Doctoral Program Foundation of Institutions of Higher Education of China (20112302130006) and the Fundamental Research Funds for the Central Universities (HIT. BRET III 201201).
[1] S. Miyazaki, Y. Ohmi, K. Otsuka, Y. Suzuki, J. Phys. (Fr.) 43 (1982), C4-255-260. [2] S. Miyazaki, K. Otsuka, ISIJ Int. 29 (1989) 353–377. [3] T. Tadaki, Y. Nakata, K. Shimizu, Trans. JIM 28 (1987) 883–890. [4] Y. Nakata, T. Tadaki, K. Shimizu, Trans. JIM 26 (1985) 646–652.
[5] R. Zarnetta, R. Takahashi, M.L. Young, A. Savan, Y. Furuya, S. Thienhaus, B. Maaß, M. Rahim, J. Frenzel, H. Brunken, Y.S. Chu, V. Srivastava, R.D. James, I. Takeuchi, G. Eggeler, A. Ludwig, Adv. Funct. Mater. 20 (2010) 1917– 1923. [6] R. Delville, D. Schryvers, Z.Y. Zhang, R.D. James, Scr. Mater. 60 (2009) 293–296. [7] Y.T. Song, X. Chen, V. Dabade, T.W. Shield, R.D. James, Nature 502 (2013) 85–88. [8] V. Srivastava, X. Chen, R.D. James, Appl. Phys. Lett. 97 (2010) 014101. [9] S. Miyazaki, Y. Igo, K. Otasuka, Acta Metall. 34 (1986) 2045–2051. [10] J. Rodrı´guez-Aseguinolaza, I. Ruiz-Larrea, M.L. No´, A. Lo´pez-Echarri, J.S. Juan, Acta Mater. 56 (2008) 6283–6290. [11] H. Knapp, U. Dehlinger, Acta Metall. 4 (1956) 289–297. [12] T. Fukuda, T. Saburi, K. Doi, S. Nenno, Mater. Trans. JIM 33 (1992) 271–277. [13] A. Ibarra, D. Caillard, J. San Juan, M.L. No´, Appl. Phys. Lett. 90 (2007) 101907. [14] J. Cui, Y.S. Chu, O.O. Famodu, Y. Furuya, J. Hattricksimpers, R.D. James, A. Ludwig, S. Thienhaus, M. Wuttig, Z.Y. Zhang, I. Takeuchi, Nat. Mater. 5 (2006) 286–290.
Please cite this article in press as: X.L. Meng et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.02.030
ScienceDirect Scripta Materialia xxx (2015) xxx–xxx www.elsevier.com/locate/scriptamat
Thermal cycling stability mechanism of Ti50.5Ni33.5Cu11.5Pd4.5 shape memory alloy with near-zero hysteresis ⇑
X.L. Meng,a, H. Li,a W. Cai,a S.J. Haob and L.S. Cuib a
National Key Laboratory Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin 150001, People’s Republic of China b Materials Science and Engineering of China University of Petroleum, Peking 100000, People’s Republic of China Received 1 February 2015; revised 25 February 2015; accepted 26 February 2015
After 5000 thermal cycles, the change of the transformation temperature is less than 1 °C in a Ti50.5Ni33.5Cu11.5Pd4.5 alloy. Also, the hysteresis becomes smaller nearing zero. Using thermal dynamic calculations, the elastic energy is nearly unchanged during the thermal cycles, which means there is little addition of the irreversible energy. The transmission electron microscopy observations show that the irreversible defects such as dislocations are rare in the reciprocating phase transition processes. Both of these explain the high thermal stability mechanism. Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Ti–Ni–Cu–Pd alloy; Shape memory alloys (SMAs); Martensitic phase transformation; Thermodynamics; Transmission electron microscopy (TEM)
During the past decades, Ti–Ni shape memory alloys have been used as actuator materials because of their large output force and displacement [1,2]. However, the temperatures hystereses for phase transformation are greater than 30 °C in the vast majority of the Ti–Ni alloys, which makes it not possible to provide a fast enough response speed to satisfy the high sensitivity requirements in actuator drives. Also, over multiple thermal cycles during working status, the functional characteristics (such as the martensitic transformation temperature, temperature hystereses of phase transformation, etc.) suffer from attenuation, leading to poor stability. The martensite transformation starting temperature (Ms) decreases by about 30 °C and 40 °C in Ti–Ni and Cu–Al–Ni alloys after 10,000 cycles, respectively [3,4]. In these cases, the dislocations introduced during the martensitic transformation should be responsible for the decrease in Ms. And the instability of Ms during thermal cycling makes it difficult to realize a high precision control of the drive performance. Recently, a Ti50.2Ni34.4Cu12.3Pd3.1 alloy with a near-zero hysteresis has been designed based on the geometric nonlinear theory of martensite (GNLTM) [5]. When k2 (the middle eigenvalue of the phase transformation matrix) equals one, the alloy can display not only the ultra narrow hysteresis, but also high stability in thermal cycles [6–8].
⇑ Corresponding author. Tel.: +86 045186418649; e-mail: xlmeng@hit.
However, the mechanism of high thermal stability has not been further investigated so far. The aim of the present study is to examine the thermal stability in the Ti50.5Ni33.5Cu11.5Pd4.5 shape memory alloy with a near-zero hysteresis by means of transmission electron microscopy (TEM) observation and thermal dynamic calculation. Meanwhile, the mechanism of such a high thermal stability is also discussed. The alloys were prepared with high purity elements by melting 10 times in an argon atmosphere in a vacuum arc furnace. The samples were annealed in vacuum quartz tubes at 950 °C for 7.2 ks, and then water-quenched. The phase transformation temperatures were determined by the Perkin-Elmer diamond differential scanning calorimetry (DSC). X-ray diffraction (XRD) measurements were performed using an X’ Pert PRO MPD with Cu Ka radiation. An FEI TECNAI G2 20 STWIN 300 kV transmission electron microscope (TEM) equipped with a double-tilt cooling stage was used for microstructure observation at room temperature. In order to characterize the phase transformation hysteresis more precisely, the DSC tests with different scanning rates have been carried out. The effects of the heating/cooling rates on the hystereses (DTh) of the Ti50.5Ni33.5Cu11.5 Pd4.5 alloy are shown in Figure 1. The variation of the hystereses of the Ti50.5Ni49.5 and Ti50Ni37.5Cu12.5 alloys is also plotted in Figure 1 for comparison. Generally speaking, the hysteresis decreases when the heating/cooling
edu.cn http://dx.doi.org/10.1016/j.scriptamat.2015.02.030 1359-6462/Ó 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: X.L. Meng et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.02.030
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X.L. Meng et al. / Scripta Materialia xxx (2015) xxx–xxx
Figure 1. Effects of DSC scanning rates on the hystereses of the Ti50.5Ni49.5, Ti50Ni37.5Cu12.5 and Ti50.5Ni33.5Cu11.5Pd4.5 alloys.
rates decrease in the DSC measurements. Therefore, the DSC with a fast scanning rate is considered to be inadequate to capture near-zero hysteresis values due to the inherent delay of the measurement signal. It has been found that the results of the alternating current potential drop (ACPD) technique and DSC are different when testing the same alloy. And ACPD was used for the characterization of the near-zero hysteresis behavior [5]. For all three kinds of alloys, the hystereses decrease linearly with the slower heating/cooling rates. By linear fitting, it can be seen that when the scan rate gets close to zero, the hysteresis is 1.7 °C in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy, as shown in Figure 1. This means the intrinsic hysteresis can be reflected by the slower heating/cooling rate, which is near the equilibrium of the cooling condition. The inherent delay of the measurement signal can be overcome, and thus, the hysteresis can be detected most accurately by using this method. Effects of the thermal cycles on the transformation temperatures of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy are shown in Figure 2. Both the martensitic transformation peak temperature (Mp) and the reverse transformation peak temperature (Ap) of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy remain almost constant when the number of cycles increased and a perfect thermal cycling stability is observed as shown in Figure 2a and b. After 5000 thermal cyclings, the changes in Mp and Ap are 1 °C and 0.8 °C respectively. In Figure 2c, the phase transformation temperatures are shown as a function of the number of the thermal cycles. With the increase in the cycle number, Ms rises monotonously, and the reverse transformation starting temperature (As) decreases slightly in the initial
circulations, and thereafter both level out. In Ti–Ni alloys, both Ms and As decrease rapidly in the first 20 cycles, and then the trend of decrease begins to level out [3]. Figure 3a–c shows the bright-field images of the martensite structure after 0, 1000 and 5000 thermal cycles of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy respectively. Mainly the type of twin martensites (B19) parallel to each other in the grain interior, present a single configuration morphology (singlepair). By contrast with the TEM photo of the untreated sample, only a few dislocations are generated in the sample after 1000 thermal circulations. In the following thermal cycles, there is no significant increase in the number of dislocations, as shown in Figure 3c. This is different from the phenomenon observed in Ti–Ni and Cu–Al–Ni alloys [3,4]. In those alloys, the dislocation density rapidly increased with increasing thermal cyclings. Regarding the present alloy after 5000 cycles, the dislocation density is lower than that in the Ti–Ni alloys after 5 cycles [9]. This may be the reason for the good stability presented in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy from the view of microstructure change. Through thermodynamic calculation, it can be found that dislocations introduced in the process of thermal cycling are related to the elastic energy. Figure 4 shows the change in the elastic energy in the martensite variants with the increase of the thermal cycles. The elastic energy is derived from [10]: Ms Mf DS 2 The entropy results from:
DGel ¼
DS ¼
DH T0
ð1Þ
ð2Þ
DH is the enthalpy of martensitic transformation, determined by the DSC measurement. The equilibrium temperature T0 is the midpoint between Af and Ms: M s þ Af 2 Thus the following formula is deduced:
T0 ¼
DGel ¼
Ms Mf DH M s þ Af
ð3Þ
ð4Þ
Mf and Af are the finishing temperatures of the martensitic and reverse transformations, respectively. Here the frictional energy in the process of the phase transition is taken into account. The frictional energy is related to the interface hindered motion inside the
Figure 2. DSC curves of (a) heating and (b) cooling processes of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy during thermal cycle. (c) The shift of martensite start (Ms), finish (Mf) and austenite start (As), finish (Af) temperatures.
Please cite this article in press as: X.L. Meng et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.02.030
X.L. Meng et al. / Scripta Materialia xxx (2015) xxx–xxx
3
Figure 3. Bright-field images of martensite after (a) 0 thermal cycle, (b) 1000 thermal cycles and (c) 5000 thermal cycles of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy.
Figure 4. (a) Elastic energy stored in the martensite variants as a function of the number of thermal cycles in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy. (b) The linear fitting curves of the elastic energy stored in the martensite variants as a function of 100 thermal cycles in the Ti50.5Ni33.5Cu11.5Pd4.5 and Ti50.5Ni49.5 alloys.
transforming variants and the interaction with defects. So the total elastic energy is composed of the reversible elastic energy and the irreversible elastic energy. The reversible elastic energy results from the accommodation of the volume change. Hence, it basically remains unchanged. However, the irreversible energy is mainly due to the consumption of the frictional energy, and it will increase with the increased dislocations introduced during the thermal cycling. It can be seen from Figure 4a that in the initial 100 cycles the elastic energy of the Ti50.5Ni33.5Cu11.5Pd4.5 alloy increases modestly. This suggests that there are a few dislocations induced in the initial circulations. It is consistent with the slight change in Ms along with the addition of the thermal cycles. Then the elastic energy stays in the range of 0.09–0.1 J/g. The induction of dislocations becomes fewer with the following more thermal cyclings. Through linear fitting, it can be found that the slope in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy is much smaller than that in the Ti50.5Ni49.5 alloy as shown in Figure 4b. For comparison, after 100 thermal cycles, the elastic energy the Ti50.5Ni49.5 alloy sharply increases from 0.1511 J/g to 0.234 J/g. The amplitude of the variation is larger than that in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy after 5000 thermal cyclings (from 0.0735 J/g to 0.0917 J/g). This also implies that after thermal cycles, the dislocations introduced in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy are far less than those in the Ti50.5Ni49.5 alloy. Generally speaking, the dislocations have two effects on the martensitic transformation: (1) When the dislocation density is low, the dislocations can help the martensitic nucleation [11–13]. (2) The high dislocation density may strengthen the matrix, which is unfavorable for the shear
of the martensitic transformation, and therefore blocks the martensite phase transformation. The degree of supercooling has to be increased to complete the martensite phase transformation, causing a reduction of Ms. As mentioned above, the results of the thermal dynamic calculation imply a slight increase in the dislocation density in Ti50.5Ni33.5Cu11.5Pd4.5 alloy quantificationally. TEM observation manifests the dislocations induced through thermal cycling are very few in the present Ti50.5Ni33.5Cu11.5Pd4.5 alloy. The martensitic transformation is from cubic to orthorhombic in the present Ti50.5Ni33.5Cu11.5Pd4.5 alloy, therefore there are six variants of martensite. The deformation matrixes for these variants are listed in Table 1. We determine from the deformation matrixes that k2 = 1.0014, close to 1. The crystal symmetry and geometric compatibilities between martensite and austenite are excellent in the present alloy [14]. Thus, dislocations may not be needed to coordinate the phase transformation in this case. This leads to few dislocations introduced. The effect of the matrix strengthening will not be brought in such low dislocation density. In the present study, the stress field around a small amount of dislocations may be beneficial to the martensitic nucleation, and reduce the phase transformation driving force. Its macroscopic reflection is a tiny advance in Ms, meanwhile the hysteresis is getting smaller. Compared with the present Ti50.5Ni33.5Cu11.5Pd4.5 alloy, even a few thermal cycles can import a mass of dislocations in Ti–Ni alloys, leading to a significant reduction in Ms. In summary, we find that the Ti50.5Ni33.5Cu11.5Pd4.5 alloy exhibits an excellent thermal stability even after 5000 thermal cycles, and the hysteresis tends to be smaller. TEM observation shows there are very few dislocations
Please cite this article in press as: X.L. Meng et al., Scripta Mater. (2015), http://dx.doi.org/10.1016/j.scriptamat.2015.02.030
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X.L. Meng et al. / Scripta Materialia xxx (2015) xxx–xxx
Table 1. Shape-strain matrices for six variants in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy.a Variant(i) 1
Ui 0
Variant(i) 1
0:948 0 0 0 1:031 0:03 A 0 0:03 1:031 0 1 0:948 0 0 @ 0 1:031 0:03 A 0 0:03 1:031
4
5
0 3 a
1 1:031 0 0:03 @ 0 0:948 0 A 0:03 0 1:031
1 1:031 0 0:03 0 0:948 0 A 0:03 0 1:031 0 1 1:031 0:03 0 @ 0:03 1:031 0 A 0 0 0:948
@
@
2
Ui 0
0 6
1 1:031 0:03 0 @ 0:03 1:031 0 A 0 0 0:948
Input parameters for B2 phase, a = 0.3037 nm, for B19 martensite, a = 0.2879 nm, b = 0.43 nm, c = 0.4556 nm.
induced. The results of the thermodynamic calculation indicate the increment of the irreversible elastic energy (caused by the introduction of dislocations) is very little. Only a few dislocations are introduced during the thermal cycling, which is the main reason for the excellent thermal cycling stability in the Ti50.5Ni33.5Cu11.5Pd4.5 alloy. The work was supported by Natural Science Foundation of China (No. 51171052 and No. 51322102), 973 projects of China (2011CB012904 and 2012CB619400), Doctoral Program Foundation of Institutions of Higher Education of China (20112302130006) and the Fundamental Research Funds for the Central Universities (HIT. BRET III 201201).
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