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Mechanical behavior of nanostructured TiNi shape memory alloy with different grain size
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 4 (2017) 4841–4845
www.materialstoday.com/proceedings
SMA 2016
Mechanical behavior of nanostructured TiNi shape memory alloy with different grain size Natalia Resninaa,b, Sergey Belyaeva,b, Vitali Piluginc, Diana Glazovaa* aSaint Petersburg State University, 7/9 Universitetskaya nab., Saint. Petersburg, 199034, Russia B.P. Konstantinov Petersburg Nuclear Physics Institute, NRC“Kurchatov Institute,” Orlova roshcha, Gatchina, 188300 Russia cM.N. Miheev Institute of Metal Physics of Ural Branch of Russian Academy of Sciences, st. S. Kovalevskoy 18, Ekaterinburg, 620990, Russia b
Abstract The influence of grain size on the deformation mechanisms of nanostructured Ti-50,2at.%Ni alloy during tension at two temperatures was studied. The deformation temperatures were chosen as 130 oC, at which TiNi phase was in the B2 phase; and 25 oC, at which the TiNi phase was in the R and/or B19’ phase depending on the grain size. The results showed that in the austenite B2 phase, the nanostructured TiNi alloy was unelastically deformed by dislocation slip and no pseudoelasticity behavior was observed. At a temperature of 25 oC, the reorientation of martensite crystals was found before the dislocation slip, as observed for coarse-grained TiNi alloy. The deformation mechanisms observed in the nanostructured Ti-50,2at.%Ni alloy were the same as those in the coarse-grain and a decrease in grain size did not have any additional effect on the mechanical behavior of the samples. It was found that in the samples of the Ti-50,2at.%Ni alloy with a grain size of 80 nm and less, the dependence of the yield stress on grain size was described by the Hall-Petch law. © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of The second conference “Shape memory alloys”. Keywords: Grain size; TiNi; mechanical properties; Hall-Petch law; deformation mechanisms.
1. Introduction It is well known that a decrease in grain size leads to variation in the mechanical and functional properties of shape memory alloys [1,2]. It is believed that a decrease in grain size prevents dislocation slip and improves the functional properties of shape memory alloys [3,4]. Usually, functional properties in nanostructured TiNi alloys are studied in the mode of bending because the samples have small sizes and it does not allow for the samples to be
* Corresponding author. Tel.: +7-905-273-2067; fax: +7-812-428-7079. E-mail address: [email protected] 2214-7853 © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of The second conference “Shape memory alloys”.
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subjected to tension. The samples are bent between two parallel plates or around the mandrel at a temperature at which the TiNi alloy is in the martensite state to give some preliminary deformation and then they are heated and subjected to thermal cycling through the temperature range of the phase transformation to study the one-way and two-way shape memory effects. However, this type of deformation results in a non-uniform stress distribution which does not allow the influence of grain size on the mechanisms of nanostructured TiNi alloy deformation to be studied. It is well known that shape memory alloys may be deformed by three mechanisms, depending on the deformation temperature: due to dislocation slip at a deformation temperature much higher than Af (finish temperature of the reverse martensitic transformation); by the formation of stress-induced martensite at temperatures close to transformation temperatures; and finally via martensite reorientation if the deformation temperature is less than Mf (finish temperature of the forward martensitic transformation [5]). Grain size determines the dislocation mobility as well as the martensitic transformation parameters and the formation of detwinned martensite [6] hence, variation in grain size should influence all the deformation mechanisms in nanostructured TiNi shape memory alloys. To elucidate the relation between the grain size and deformation mechanisms, it is necessary to study stressstrain diagrams obtained at different temperatures in tension of the nanostructured TiNi alloy with different grain sizes and this is the aim of this study. 2. Experimental procedure The Ti-50,2at.%Ni alloy samples were subjected to amorphization by high-pressure torsion (HPT) and postdeformation heating to different temperatures to obtain the nanocrystalline samples with different grain sizes. Plate samples with a bone shape (Fig. 1) were stamped out of discs with a diameter of 6 mm and thickness of 0.1 mm before post-deformation heating. The length of the samples was 5 mm, the gauge length was 1 mm and the width was 1 mm. After stamping, the samples were placed into the chamber of the differential scanning calorimeter “Mettler Toledo 822e” and heated up to different temperatures (359 oC, 365 oC, 380 oC, 550 oC) at a heating rate of 10 oC/min. For convenience, the samples are hereafter referred to as S0, S359, S365, S380, S550, where the number after the letter S indicates the heating temperature. After heating, all the samples were characterized by bimodal grain structure with 10 and 25 nm average grain sizes in sample S359 heated to 359 oC, and 270 and 550 nm average grain sizes in sample S550 that was heated to 550 oC. Further details about alloy structure, grain distribution and martensitic transformations are given in [7]. The mechanical properties were studied in the tensile mode using the testing machine “Lloyd 30k Plus” equipped with a video extensometer and a thermal chamber. The samples were placed in special grippers and installed into testing machine. The samples were subjected to tension with intermediate unloading at a speed of 0.01 mm/min up to failure. The deformation was carried out at two temperatures: 130 oC, at which all samples were in the austenite cubic B2 phase, and 25 oC, at which samples S359 and S365 contained rhombohedral R phases, sample S380 was in the rhombohedral R and monoclinic B19’ phases, and sample S550 was in the monoclinic B19’ phase.
Fig. 1. Image of the sample used for tension tests on the millimeter scale paper.
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3. Results and Discussion Fig. 2 shows the stress-strain diagrams obtained at the temperatures of 130 oC (a) and 25 oC (b) during tension of the Ti-50,2at.%Ni alloy with different grain sizes. In all figures the value of grain size is equal to the average grain size (d) of the second mode of bimodal distribution (i.e. the highest average grain size). The stress-strain diagram obtained on tension of amorphous sample is shown at d = 0. Fig. 2a shows that if the grain size is 40 nm or less, the samples are deformed elastically a small plastic deformation is observed just before failure. An increase in grain size up to 80 nm results in observation of a plateau at a stress of 700 MPa and it may be assumed that this is caused by the appearance of martensitic crystals under stress (i.e. stress-induced martensite). If martensite appears on loading, it has to disappear on unloading due to the martensitic crystals being stable at temperatures higher than Af only under a stress [5]. In this case, the unloading should be non-linear and flag-shaped stress-strain curves must be found, as observed in Ni-rich TiNi alloys [5]. At the same time, Fig. 2a shows that unloading of S380 sample just after the plateau is elastic. Thus, it may be concluded that the plateau is not caused by the appearance of stress-induced martensite. An observation of a plateau is due to ordinary dislocation slip, and the pseudoelasticity effect is not observed in the Ti-50,2at.%Ni alloy. This is confirmed by the stress-strain curve measured in sample S550 with an average grain size of 500 nm. It is seen that the stress-strain curve is typical for deformation of coarse-grained equiatomic TiNi alloy in the austenite state; no evidence of pseudoelasticity behavior is found.
Fig. 2. Strain-stress diagrams obtained at temperatures of (a) 130 oC and (b) 25 oC during tension of the Ti-50,2at.%Ni alloy with different average grain sizes.
It is known that deformation of alloys containing the R and/or B19’ phases may be realized by two mechanisms: reorientation of the R or the B19’ crystals and dislocation slip. The yield stress for dislocation slip is higher than the stress for martensitic reorientation. In the TiNi alloy with coarse grains, two plateaus are usually observed in the stress-strain curve, as is found in sample S550 with an average grain size of 500 nm. The first plateau is due to the reorientation of the B19’ phase because this sample is fully in the B19’ phase at 25 oC; the second plateau is caused by ordinary dislocation slip. In S359, S365 samples with an average grain size of 25 and 40 nm, one small plateau is found at low stress (about 100 MPa); the other plateau is observed at high stress just before failure (Fig. 2b). According to the data published in [7], these two samples are in the R phase at room temperature; hence, the first small plateau may be due to the reorientation of the R phase, while the second plateau may be caused by plastic deformation or by the appearance of the B19’ phase under a stress. If the B19’ phase forms on loading then it should disappear on unloading and a non-linear recovery strain should be observed. At the same time, the data presented in Fig. 2b do not show non-linear strain recovery on unloading thus, the second plateau on the stress-stain curve is not due to the appearance of the B19’ phase: it is caused by dislocation slip. An increase in grain size up to 80 nm (sample S380) leads to a non-linear strain accumulation with an increase in stress larger than 300 MPa. At a temperature of 25 oC, sample S380 contains a mixture of R and B19’ phases [7], and the crystals of these phases are subjected to reorientation during deformation, making a contribution to the strain accumulation on loading. No
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Natalia Resnina et al./ Materials Today: Proceedings 4 (2017) 4841–4845
phase transition takes place on loading because the unloading of the samples is linear. Therefore, we have shown that in the austenite B2 phase, nanostructured TiNi alloys are unelastically deformed by dislocation slip, and no pseudoelasticity effect is observed. At a temperature of 25 oC at which the nanostructured samples contain the R and/or B19’ phases, the reorientation of the martensite crystals is found before the dislocation slip, as observed for coarse-grained TiNi alloys. The deformation mechanisms observed in the nanostructured Ti-50,2at.%Ni alloy are the same as in coarse-grained alloy; a decrease in grain size does not lead to any additional effect on the mechanical behavior of the samples. The stress-strain diagrams presented in Fig. 2 were used to determine the values of ultimate tensile strength, maximum strain up to failure, elastic modulus and plateau limit. The value of ultimate tensile strength and the maximum strain up to failure were measured as the stress and strain at which the sample failure was detected. The elastic modulus was estimated as the slope of the stress-strain curve during unloading. The plateau stress was determined as the stress at which the plateau started. The dependencies of these parameters on the average grain size are shown in Figs. 3 and 4.
Fig. 3. Dependencies of (a) ultimate tensile strength, (b) maximum strain up to failure and (c) Elastic modulus on average grain size in the Ti50,2at.%Ni alloy.
Fig. 3a shows the dependencies of ultimate tensile strength on average grain size measured at two temperatures. The dependence σmax(d) measured at 25 oC is non-monotonic. The existence of nanograins in the samples results in hardening of the alloy: the ultimate strength increases compared to the stress at which the amorphous samples were broken. The increase in average grain size from 25 to 80 nm leads to a significant decrease in ultimate strength from 840 MPa to 580 MPa. Further increases in grain size result in an increase in the strength up to 990 MPa. The dependence σmax(d) measured at 130 oC is monotonic and the strength decreases from 1300 MPa to 640 MPa with increasing average grain size. Fig. 3b shows the dependence of maximum strain up to failure on average grain size. The dependence εmax(d) does not depend on deformation temperature. An increase in grain size from 0 to 40 nm does not influence the maximum strain, which equals 12–15 %. An increase in a grain size to 80 nm leads to a significant increase in maximum strain to 40 %. Further increases in grain size to 500 nm result in an increase in the maximum strain up to 75–80 %. Fig. 3c shows the dependence of the elastic modulus on average grain size. At a temperature of 25 oC, the samples were in different phases, which might have an additional effect on the elastic modulus. This is why the E(d) curve was obtained using the stress-strain curves measured at a deformation temperature of 130 oC. It is seen that the dependence of the elastic modulus on grain size is nonlinear and decreases from 20.3 GPa in the amorphous sample to 8.8 GPa in the sample with an average grain size of 500 nm. Fig. 4a shows dependencies of stress limit on grain size found at a temperature of 130 oC. An increase in grain size leads to a decrease in yield limit during deformation in the austenite state (at a temperature of 130 oC) due to the dislocation movement becoming easier with grain growth. It is known that the dependence of yield limit on average grain size in polycrystalline materials usually follows the Hall-Petch law, so it is assumed that the dependence of yield limit on average grain size obtained in the nanostructured Ti-50,2at.%Ni alloy at a temperature of 130 oC may be approximated by the Hall-Petch relationship. Fig. 4b shows the dependence of yield limit on a d-1/2 value: the Hall-Petch law is observed in the samples with a grain size of 80 nm and less. The yield limit measured in the
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sample with 500 nm average grain size is located below the line described by the Hall-Petch law. This may be due to the bimodal structure of the alloy and deformation of the sample by different mechanisms in different grains, which significantly affects the stress for dislocation slip. Therefore, the results of the study have shown that a decrease in grain size in the Ti-50,2at.%Ni alloy results in the same effect as in ordinary alloys. It prevents dislocation slip and results in an increase in ultimate and yield stresses and a decrease in strain up to failure. No additional effects of the grain size on the deformation mechanisms or mechanical behavior of the nanostructured alloy were found.
Fig. 4. (a) Dependencies of plateau limits on average grain size in the Ti-50,2at.%Ni alloy and (b) Approximation of the dependence of yield limit on average grain size in the Ti-50,2at.%Ni alloy using the Hall-Petch relationship.
4. Conclusions Summarizing the data, the following conclusions may be drawn: 1. In the austenite B2 phase, the nanostructured Ti-50,2at.%Ni alloy is unelastically deformed by dislocation slip and no pseudoelasticity effect is observed. 2. At a temperature of 25 oC at which the nanostructured samples contain the R and/or B19’ phases, reorientation of the martensite crystals is found before dislocation slip, as observed for coarse-grained TiNi alloys. 3. The deformation mechanisms observed in the nanostructured Ti-50,2at.%Ni alloy are the same as in the coarse-grained alloy; a decrease in grain size does not lead to any additional effect on the mechanical behavior of the samples. 4. The Hall-Petch law is observed in the samples with grain sizes of 80 nm and less. The yield limit measured in the sample with 500 nm average grain size is located below the line described by the Hall-Petch law. Acknowledgements The study has been carried out through the financial support of Saint-Petersburg State University (project numbers 0.37.177.2014, 6.37.147.2014) References [1] R. Z. Valiev, D. V. Gunderov, A. V. Lukyanov, V. G. Pushin, J. Mater. Sci. 47 (2012) 7848–7853. [2] D. Gunderov, N. Kuranova, A. Lukyanov, V. Makarov, E. Prokofiev, A. Pushin, Rev. Adv. Mater. Sci. 25 (2010) 58-66. [3] V. Brailovski, S. Prokoshkin, K. Inaekyan, V. Demers, J. Alloys Compd. 509 (2011) 2066-2075. [4] I. Khmelevskaya, S. Prokoshkin, V. Brailovski, K. Inaekyan, V. Demers, I. Gurtovaya, A. Korotitskiy, S. Dobatkin, Advances in Science and Technology (Proc. Int. Conf. CIMTEC). 59 (2008) 156-161. [5] V. Brailovski, S. Prokoshkin, P. Terriault, F. Trochu, Shape memory alloys: Fundamental, Modeling and Applications, ETS Publ., Montreal, 2003. [6] T. Waitz, T. Antretter, F.D. Fischer, H.P. Karnthaler. Mater. Sci. Technol. 24 (2008) 934-940. [7] N. Resnina, S. Belyaev, V. Zeldovich, V. Pilyugin, N. Frolova, D. Glazova, Thermochim. Acta 627 (2016) 20-30.
ScienceDirect Materials Today: Proceedings 4 (2017) 4841–4845
www.materialstoday.com/proceedings
SMA 2016
Mechanical behavior of nanostructured TiNi shape memory alloy with different grain size Natalia Resninaa,b, Sergey Belyaeva,b, Vitali Piluginc, Diana Glazovaa* aSaint Petersburg State University, 7/9 Universitetskaya nab., Saint. Petersburg, 199034, Russia B.P. Konstantinov Petersburg Nuclear Physics Institute, NRC“Kurchatov Institute,” Orlova roshcha, Gatchina, 188300 Russia cM.N. Miheev Institute of Metal Physics of Ural Branch of Russian Academy of Sciences, st. S. Kovalevskoy 18, Ekaterinburg, 620990, Russia b
Abstract The influence of grain size on the deformation mechanisms of nanostructured Ti-50,2at.%Ni alloy during tension at two temperatures was studied. The deformation temperatures were chosen as 130 oC, at which TiNi phase was in the B2 phase; and 25 oC, at which the TiNi phase was in the R and/or B19’ phase depending on the grain size. The results showed that in the austenite B2 phase, the nanostructured TiNi alloy was unelastically deformed by dislocation slip and no pseudoelasticity behavior was observed. At a temperature of 25 oC, the reorientation of martensite crystals was found before the dislocation slip, as observed for coarse-grained TiNi alloy. The deformation mechanisms observed in the nanostructured Ti-50,2at.%Ni alloy were the same as those in the coarse-grain and a decrease in grain size did not have any additional effect on the mechanical behavior of the samples. It was found that in the samples of the Ti-50,2at.%Ni alloy with a grain size of 80 nm and less, the dependence of the yield stress on grain size was described by the Hall-Petch law. © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of The second conference “Shape memory alloys”. Keywords: Grain size; TiNi; mechanical properties; Hall-Petch law; deformation mechanisms.
1. Introduction It is well known that a decrease in grain size leads to variation in the mechanical and functional properties of shape memory alloys [1,2]. It is believed that a decrease in grain size prevents dislocation slip and improves the functional properties of shape memory alloys [3,4]. Usually, functional properties in nanostructured TiNi alloys are studied in the mode of bending because the samples have small sizes and it does not allow for the samples to be
* Corresponding author. Tel.: +7-905-273-2067; fax: +7-812-428-7079. E-mail address: [email protected] 2214-7853 © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of The second conference “Shape memory alloys”.
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Natalia Resnina et al./ Materials Today: Proceedings 4 (2017) 4841–4845
subjected to tension. The samples are bent between two parallel plates or around the mandrel at a temperature at which the TiNi alloy is in the martensite state to give some preliminary deformation and then they are heated and subjected to thermal cycling through the temperature range of the phase transformation to study the one-way and two-way shape memory effects. However, this type of deformation results in a non-uniform stress distribution which does not allow the influence of grain size on the mechanisms of nanostructured TiNi alloy deformation to be studied. It is well known that shape memory alloys may be deformed by three mechanisms, depending on the deformation temperature: due to dislocation slip at a deformation temperature much higher than Af (finish temperature of the reverse martensitic transformation); by the formation of stress-induced martensite at temperatures close to transformation temperatures; and finally via martensite reorientation if the deformation temperature is less than Mf (finish temperature of the forward martensitic transformation [5]). Grain size determines the dislocation mobility as well as the martensitic transformation parameters and the formation of detwinned martensite [6] hence, variation in grain size should influence all the deformation mechanisms in nanostructured TiNi shape memory alloys. To elucidate the relation between the grain size and deformation mechanisms, it is necessary to study stressstrain diagrams obtained at different temperatures in tension of the nanostructured TiNi alloy with different grain sizes and this is the aim of this study. 2. Experimental procedure The Ti-50,2at.%Ni alloy samples were subjected to amorphization by high-pressure torsion (HPT) and postdeformation heating to different temperatures to obtain the nanocrystalline samples with different grain sizes. Plate samples with a bone shape (Fig. 1) were stamped out of discs with a diameter of 6 mm and thickness of 0.1 mm before post-deformation heating. The length of the samples was 5 mm, the gauge length was 1 mm and the width was 1 mm. After stamping, the samples were placed into the chamber of the differential scanning calorimeter “Mettler Toledo 822e” and heated up to different temperatures (359 oC, 365 oC, 380 oC, 550 oC) at a heating rate of 10 oC/min. For convenience, the samples are hereafter referred to as S0, S359, S365, S380, S550, where the number after the letter S indicates the heating temperature. After heating, all the samples were characterized by bimodal grain structure with 10 and 25 nm average grain sizes in sample S359 heated to 359 oC, and 270 and 550 nm average grain sizes in sample S550 that was heated to 550 oC. Further details about alloy structure, grain distribution and martensitic transformations are given in [7]. The mechanical properties were studied in the tensile mode using the testing machine “Lloyd 30k Plus” equipped with a video extensometer and a thermal chamber. The samples were placed in special grippers and installed into testing machine. The samples were subjected to tension with intermediate unloading at a speed of 0.01 mm/min up to failure. The deformation was carried out at two temperatures: 130 oC, at which all samples were in the austenite cubic B2 phase, and 25 oC, at which samples S359 and S365 contained rhombohedral R phases, sample S380 was in the rhombohedral R and monoclinic B19’ phases, and sample S550 was in the monoclinic B19’ phase.
Fig. 1. Image of the sample used for tension tests on the millimeter scale paper.
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3. Results and Discussion Fig. 2 shows the stress-strain diagrams obtained at the temperatures of 130 oC (a) and 25 oC (b) during tension of the Ti-50,2at.%Ni alloy with different grain sizes. In all figures the value of grain size is equal to the average grain size (d) of the second mode of bimodal distribution (i.e. the highest average grain size). The stress-strain diagram obtained on tension of amorphous sample is shown at d = 0. Fig. 2a shows that if the grain size is 40 nm or less, the samples are deformed elastically a small plastic deformation is observed just before failure. An increase in grain size up to 80 nm results in observation of a plateau at a stress of 700 MPa and it may be assumed that this is caused by the appearance of martensitic crystals under stress (i.e. stress-induced martensite). If martensite appears on loading, it has to disappear on unloading due to the martensitic crystals being stable at temperatures higher than Af only under a stress [5]. In this case, the unloading should be non-linear and flag-shaped stress-strain curves must be found, as observed in Ni-rich TiNi alloys [5]. At the same time, Fig. 2a shows that unloading of S380 sample just after the plateau is elastic. Thus, it may be concluded that the plateau is not caused by the appearance of stress-induced martensite. An observation of a plateau is due to ordinary dislocation slip, and the pseudoelasticity effect is not observed in the Ti-50,2at.%Ni alloy. This is confirmed by the stress-strain curve measured in sample S550 with an average grain size of 500 nm. It is seen that the stress-strain curve is typical for deformation of coarse-grained equiatomic TiNi alloy in the austenite state; no evidence of pseudoelasticity behavior is found.
Fig. 2. Strain-stress diagrams obtained at temperatures of (a) 130 oC and (b) 25 oC during tension of the Ti-50,2at.%Ni alloy with different average grain sizes.
It is known that deformation of alloys containing the R and/or B19’ phases may be realized by two mechanisms: reorientation of the R or the B19’ crystals and dislocation slip. The yield stress for dislocation slip is higher than the stress for martensitic reorientation. In the TiNi alloy with coarse grains, two plateaus are usually observed in the stress-strain curve, as is found in sample S550 with an average grain size of 500 nm. The first plateau is due to the reorientation of the B19’ phase because this sample is fully in the B19’ phase at 25 oC; the second plateau is caused by ordinary dislocation slip. In S359, S365 samples with an average grain size of 25 and 40 nm, one small plateau is found at low stress (about 100 MPa); the other plateau is observed at high stress just before failure (Fig. 2b). According to the data published in [7], these two samples are in the R phase at room temperature; hence, the first small plateau may be due to the reorientation of the R phase, while the second plateau may be caused by plastic deformation or by the appearance of the B19’ phase under a stress. If the B19’ phase forms on loading then it should disappear on unloading and a non-linear recovery strain should be observed. At the same time, the data presented in Fig. 2b do not show non-linear strain recovery on unloading thus, the second plateau on the stress-stain curve is not due to the appearance of the B19’ phase: it is caused by dislocation slip. An increase in grain size up to 80 nm (sample S380) leads to a non-linear strain accumulation with an increase in stress larger than 300 MPa. At a temperature of 25 oC, sample S380 contains a mixture of R and B19’ phases [7], and the crystals of these phases are subjected to reorientation during deformation, making a contribution to the strain accumulation on loading. No
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Natalia Resnina et al./ Materials Today: Proceedings 4 (2017) 4841–4845
phase transition takes place on loading because the unloading of the samples is linear. Therefore, we have shown that in the austenite B2 phase, nanostructured TiNi alloys are unelastically deformed by dislocation slip, and no pseudoelasticity effect is observed. At a temperature of 25 oC at which the nanostructured samples contain the R and/or B19’ phases, the reorientation of the martensite crystals is found before the dislocation slip, as observed for coarse-grained TiNi alloys. The deformation mechanisms observed in the nanostructured Ti-50,2at.%Ni alloy are the same as in coarse-grained alloy; a decrease in grain size does not lead to any additional effect on the mechanical behavior of the samples. The stress-strain diagrams presented in Fig. 2 were used to determine the values of ultimate tensile strength, maximum strain up to failure, elastic modulus and plateau limit. The value of ultimate tensile strength and the maximum strain up to failure were measured as the stress and strain at which the sample failure was detected. The elastic modulus was estimated as the slope of the stress-strain curve during unloading. The plateau stress was determined as the stress at which the plateau started. The dependencies of these parameters on the average grain size are shown in Figs. 3 and 4.
Fig. 3. Dependencies of (a) ultimate tensile strength, (b) maximum strain up to failure and (c) Elastic modulus on average grain size in the Ti50,2at.%Ni alloy.
Fig. 3a shows the dependencies of ultimate tensile strength on average grain size measured at two temperatures. The dependence σmax(d) measured at 25 oC is non-monotonic. The existence of nanograins in the samples results in hardening of the alloy: the ultimate strength increases compared to the stress at which the amorphous samples were broken. The increase in average grain size from 25 to 80 nm leads to a significant decrease in ultimate strength from 840 MPa to 580 MPa. Further increases in grain size result in an increase in the strength up to 990 MPa. The dependence σmax(d) measured at 130 oC is monotonic and the strength decreases from 1300 MPa to 640 MPa with increasing average grain size. Fig. 3b shows the dependence of maximum strain up to failure on average grain size. The dependence εmax(d) does not depend on deformation temperature. An increase in grain size from 0 to 40 nm does not influence the maximum strain, which equals 12–15 %. An increase in a grain size to 80 nm leads to a significant increase in maximum strain to 40 %. Further increases in grain size to 500 nm result in an increase in the maximum strain up to 75–80 %. Fig. 3c shows the dependence of the elastic modulus on average grain size. At a temperature of 25 oC, the samples were in different phases, which might have an additional effect on the elastic modulus. This is why the E(d) curve was obtained using the stress-strain curves measured at a deformation temperature of 130 oC. It is seen that the dependence of the elastic modulus on grain size is nonlinear and decreases from 20.3 GPa in the amorphous sample to 8.8 GPa in the sample with an average grain size of 500 nm. Fig. 4a shows dependencies of stress limit on grain size found at a temperature of 130 oC. An increase in grain size leads to a decrease in yield limit during deformation in the austenite state (at a temperature of 130 oC) due to the dislocation movement becoming easier with grain growth. It is known that the dependence of yield limit on average grain size in polycrystalline materials usually follows the Hall-Petch law, so it is assumed that the dependence of yield limit on average grain size obtained in the nanostructured Ti-50,2at.%Ni alloy at a temperature of 130 oC may be approximated by the Hall-Petch relationship. Fig. 4b shows the dependence of yield limit on a d-1/2 value: the Hall-Petch law is observed in the samples with a grain size of 80 nm and less. The yield limit measured in the
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sample with 500 nm average grain size is located below the line described by the Hall-Petch law. This may be due to the bimodal structure of the alloy and deformation of the sample by different mechanisms in different grains, which significantly affects the stress for dislocation slip. Therefore, the results of the study have shown that a decrease in grain size in the Ti-50,2at.%Ni alloy results in the same effect as in ordinary alloys. It prevents dislocation slip and results in an increase in ultimate and yield stresses and a decrease in strain up to failure. No additional effects of the grain size on the deformation mechanisms or mechanical behavior of the nanostructured alloy were found.
Fig. 4. (a) Dependencies of plateau limits on average grain size in the Ti-50,2at.%Ni alloy and (b) Approximation of the dependence of yield limit on average grain size in the Ti-50,2at.%Ni alloy using the Hall-Petch relationship.
4. Conclusions Summarizing the data, the following conclusions may be drawn: 1. In the austenite B2 phase, the nanostructured Ti-50,2at.%Ni alloy is unelastically deformed by dislocation slip and no pseudoelasticity effect is observed. 2. At a temperature of 25 oC at which the nanostructured samples contain the R and/or B19’ phases, reorientation of the martensite crystals is found before dislocation slip, as observed for coarse-grained TiNi alloys. 3. The deformation mechanisms observed in the nanostructured Ti-50,2at.%Ni alloy are the same as in the coarse-grained alloy; a decrease in grain size does not lead to any additional effect on the mechanical behavior of the samples. 4. The Hall-Petch law is observed in the samples with grain sizes of 80 nm and less. The yield limit measured in the sample with 500 nm average grain size is located below the line described by the Hall-Petch law. Acknowledgements The study has been carried out through the financial support of Saint-Petersburg State University (project numbers 0.37.177.2014, 6.37.147.2014) References [1] R. Z. Valiev, D. V. Gunderov, A. V. Lukyanov, V. G. Pushin, J. Mater. Sci. 47 (2012) 7848–7853. [2] D. Gunderov, N. Kuranova, A. Lukyanov, V. Makarov, E. Prokofiev, A. Pushin, Rev. Adv. Mater. Sci. 25 (2010) 58-66. [3] V. Brailovski, S. Prokoshkin, K. Inaekyan, V. Demers, J. Alloys Compd. 509 (2011) 2066-2075. [4] I. Khmelevskaya, S. Prokoshkin, V. Brailovski, K. Inaekyan, V. Demers, I. Gurtovaya, A. Korotitskiy, S. Dobatkin, Advances in Science and Technology (Proc. Int. Conf. CIMTEC). 59 (2008) 156-161. [5] V. Brailovski, S. Prokoshkin, P. Terriault, F. Trochu, Shape memory alloys: Fundamental, Modeling and Applications, ETS Publ., Montreal, 2003. [6] T. Waitz, T. Antretter, F.D. Fischer, H.P. Karnthaler. Mater. Sci. Technol. 24 (2008) 934-940. [7] N. Resnina, S. Belyaev, V. Zeldovich, V. Pilyugin, N. Frolova, D. Glazova, Thermochim. Acta 627 (2016) 20-30.