Localized Plastic Deformation of Superelastic NiTi Wires in Tension

Tensile deformation of superelastic NiTi shape memory alloy wires at temperatures above austenite finish temperature proceeds via stress-induced martensitic transformation followed by plastic deformation of oriented martensite. While superelastic deformation tends to proceed in localized manner, plastic deformation of martensite is considered to be homogeneous. In this work, we have investigated strain localization patterns in tensile tests on superelastic NiTi wires deformed until fracture in wide temperature range from 10 to 400 °C using in situ digital image correlation analysis of local strains and analyzed lattice defects created during the deformation in TEM. We have found that plastic deformation of oriented martensite can be either homogeneous or localized, depending on the yield stress and strain hardening rate (on the Considere criterion for stability of tensile deformation). Plastic deformation of martensite proceeds via peculiar deformation mode involving combination of deformation twinning and dislocation-based kinking. Strain localization takes the form of either necking leading to wire fracture at 13–15% strain or via propagation of macroscopic deformation band fronts at constant stress. Regardless the deformation is homogeneous or localized, plastic strains at fracture reach ~ 50%. Strain localized within the propagating band front as large as ~ 40% was observed in tensile tests test on NiTi wires having specific microstructures (grain size ~ 230 nm) in a narrow temperature range (~ 10–60 °C).


Introduction
Plastic deformation of NiTi received so far much less attention than functional superelastic or shape memory behaviors which are due to martensitic transformation [1]. Plastic deformation of NiTi was investigated mainly from the point of view thermomechanical processing, as a mechanism of the hot forming and cold drawing used to fabricate NiTi products for engineering applications [2,3]. Recently, various methods of severe plastic deformation processing were applied to fabricate bulk NiTi [4,5] with enhanced functional properties approaching those of commercial cold worked/annealed thin nanocrystalline NiTi wires used in medical devices or as NiTi microactuators. On the other hand, NiTi alloys may deform plastically in service, for example, during superelastic [6] and actuator [7] cycling, when superelastic NiTi stent is crimped into delivery tube [8], during shape setting [9] or, generally, when deformed NiTi element is heated far above 100°C under external constraint [10]. Plastic deformation may also appear locally at stress concentrators-e.g., when cracks propagate during thermal actuation [11]. Plastic deformation frequently accompanies martensitic & Petr Š ittner sittner@fzu.cz 1 transformation, introduces irrecoverable strains, lattice defects, and internal stress into the austenitic microstructure [12] and affects functional thermomechanical properties of NiTi components. In this respect, deformation mechanisms responsible for plastic deformation of austenite [13,14] and martensite [15][16][17] phases in NiTi received much less attention than they deserve. It is very well known that NiTi has to be strengthened by cold work/annealing or Ti 3 Ni 4 precipitation annealing to be used in engineering applications. If this is done, transformation stress at room temperature is well separated from the yield stress for plastic deformation of martensite and cyclic thermomechanical responses are stable [1]. If transformation stress approaches yield stress, functional cyclic stress-strain-temperature responses of NiTi are not stable and lattice defects are generated during the mechanical as well as thermomechanical cycling [12]. This implies that plastic deformation of the martensite phase is a key issue in NiTi technology, even if it is not actively used in engineering applications.
When loaded in tension, NiTi wires, bars, and ribbons frequently start to deform in a localized manner via propagation of martensite band fronts (Lüders bands) [28][29][30] at constant external force. This does not apply only for the stress-induced martensitic transformation but also for martensite reorientation at low temperatures. Localized deformation via propagation of martensite band fronts was observed also in tensile tests at high temperatures, in which the stress-induced martensitic transformation is accompanied by significant plastic deformation [31].
Tensile deformation of NiTi in the plastic deformation range at high stresses is considered in the literature to be homogeneous. However, not every NiTi wire can be deformed plastically in tension up to large plastic strains. In fact, most of common superelastic or actuator NiTi wires with nanocrystalline microstructure fracture at 13-15% tensile strain, as superelastic NiTi wire with grain size * 215 nm in Fig. 1a. NiTi wires with larger grain size deform in homogeneous manner up to very large strains exceeding 50%.
We have recently observed that, in some experiments, plastic deformation of NiTi wires occurred via propagation of macroscopic deformation band fronts at constant stress, like in case of the stress-induced martensitic transformation. In this case, however, the deformation mechanism is not stress-induced martensitic transformation but plastic deformation of stress-induced or reoriented martensite. Very similar phenomenon was recently reported by Chen et al. [32], who investigated localized deformation of Ni 47 Ti 49 Nb 2 Fe 2 alloy in tensile test at -50°C. In this work, we report and discuss this phenomenon in detail.

Materials and Methods
Polycrystalline NiTi wires produced by Fort Wayne Metals Co. (FWM #1, Ti-50.9 at.% Ni, 40.8% cold work) with diameter of 100 lm and length of * 23 mm were used in this work. When properly annealed, these wires display B2-B19' thermally and stress-induced martensitic phase transformation. Instead of using conventional heat treatment in environmental furnace, we used short pulse heat treatment with controlled parameters of electric power 125 W (power normalized on 100 mm length of the wire) for different pulse time (PT) in milliseconds. Depending on the used pulse time, the heat-treated wires display different austenitic microstructures (grain size), transformation temperatures, and functional stress-strain response in tensile test at room temperature (Fig. 1a). The short pulse of heat treatment enables preparation of wire samples with extraordinary repeatability of austenitic microstructure and functional superelastic properties. Short heating followed by slower cooling in air prevents the growth of precipitates and extensive surface oxidation. Most of the experiments in this work was performed on 14 ms NiTi wire. The 125 W/ 14 ms pulse heat treatment results in recrystallization of cold worked microstructure of the wire yielding defect-free austenite grains * 215 nm in diameter (Fig. 2d). To determine the martensitic transformation temperatures, the sample was subjected to heating and cooling in the temperature range of ? 100°C to -150°C with a cooling rate of 3°C min -1 in TA DSC 25 differential scanning calorimeter. The results are summarized in Table 1.
In-house designed and built thermomechanical tester used for tensile thermomechanical testing of NiTi wires consists of loading frame, replaceable sample environmental chambers, electrically conductive grips with active water cooling, a load cell with 45 N tension and compression capacity, and a linear actuator controlled with position magnetic sensor with precision class of ± 10 lm/ m. While environmental chamber based on Peltier elements enables controlling of temperature in the range of -40°C to 200°C, high-temperature chamber was used to control test temperature from room temperature up to 600°C. The electrically conductive grips were used in insitu electric resistance measurements during tensile testing. The stress-strain-temperature tests were controlled and data were acquisitioned via National Instruments cRIO systems and close-loop Labview control system A 20 MPx digital camera mounted with lens allowing of maximal FOV about 37.5 9 37.5 mm was used for in-situ evaluation of local surface strains.
Thermomechanical testing in tension was carried out as follows. The wire sample was permanently gripped into two stainless steel capillaries before it was clamped into tester holding grips. This allows for avoiding potential problems with twisting the specimen prior to loading, sliding out of the grips, thermal gradients at sample ends, and defining the length of the sample. Strain was set to zero always in the austenitic state and tensile tests were performed at constant temperatures in the range of 10-400°C in position control regime with strain rate of 0.001 s -1 . Noncontact strain measurement by Digital Image Correlation (1D-DIC) was performed to evaluate local strains evolving during the test. A fine random pattern of waterbased color was sprayed on the wire samples with an airbrush gun for tracking of surface strains.
The tested superelastic NiTi wires were analyzed in Scanning Electron Microscope (SEM) TESCAN FERA3 GM microscope. TEM lamellae for microstructure observations in deformed wires were cut from the surface layer parallel to the wire axis by focused ion milling (FIB) using and FEI Quanta 3D FIB-SEM microscope with Ga ion source. The lamella was observed in a FEI Tecnai TF20 X-twin transmission electron microscope equipped with a field emission gun operated at 200 keV using a double tilt sample holder. Defect microstructures created by tensile deformation in single grains were analyzed using selected area electron diffraction (SAED) with dark-field (DF) imaging (SAED-DF method) [33].

Experimental Results
Superelastic NiTi wires are typically subjected to (i) cyclic tensile loading-unloading at constant temperature up to stresses just beyond the end of the transformation plateau or (ii) thermal cycling under low constant applied stress. The reason is that the reversible stress-strain and straintemperature responses in such czclic closed loop tests are mainly of interest for application development. The only activated deformation mechanism in such tests is martensitic transformation and there is a strong desire to avoid plastic deformation during thermomechanical cycling. Nevertheless, results of many experiments reported in the literature suggest that plastic deformation cannot be avoided since it accompanies martensitic transformation proceeding under applied stress [6,7,12,18,25]. In our previous research on superelastic NiTi wires possessing a wide range of microstructures [19,31,34], we realized that very important experimental information is missed, if the wires are not deformed into the plastic range, as common in the material engineering research (Figs. 1, 2). Figure 1a shows results of a series of tensile tests at room temperature until fracture on superelastic NiTi wires having range of microstructures created by electropulse treatment with parameters 125 W/100 mm for times 0-20 ms. Similar results were already reported in [34] Fig. 1a shows results of the same tests repeated again 5 years later using different testing equipment. The earlier results were reproduced very well. The cold worked NiTi wire displays elastic deformation up to fracture at * 2 GPa. With increasing pulse time, tensile strain due to stress-induced martensitic transformation increases up to 10% in case of 7 ms NiTi wire ( Fig. 1). Starting from the 8 ms NiTi wire, tensile deformation of wires becomes localized in martensite band fronts propagating at constant stress in the transformation plateau range (Fig. 1b, c). While the wires with grain size of B 215 nm fractured at * 13-15% (Fig. 1b), those with larger grain size deformed homogeneously up to * 55-65% strain (Fig. 1c). The yield stress for plastic deformation decreased and strain hardening rate in the plastic range increased with increasing grain size. We decided to investigate systematically tensile deformation of the 14 ms NiTi wire with grain size 215 nm. It shows localized superelastic deformation with negligible unrecovered strain upon tensile superelastic cycling at room temperature (Fig. 2a). Upon tensile loading beyond the end of the plateau, the wire fractured at 13-15% strain (Fig. 2b). It was found that necking starts by a dynamic event registered by 1D-DIC method and evidenced on the stress-strain curve as sudden drop of tensile stress * 50 MPa. When we looked at the fractured wires more   (Fig. 2c), it became clear that the fracture happened after heavy plastic deformation localized within a neck at 13-15% strain (Fig. 1a). However, strain localization was hardly detected by the in situ 1D-DIC measurement (despite of the used high frame rate 120 s -1 ). This means that large plastic deformation within the neck must have occurred extremely fast. NiTi wires with larger grain size, which deformed homogeneously beyond yield stress (Fig. 1a), fractured also via necking but much later in the test at * 55% strain. In this case, however, there was no stress drop and strain localization prior fracture was easily detected by the in situ 1D-DIC measurement. The experiment thus confirmed the earlier reported result [34] that the sharp change from the low to the high ductility of superelastic NiTi wires is due to macroscopic instability of tensile deformation and necking the conditions for which are given by the Considere criterion [35] (Eq. 1).
It shall be pointed out that Considere criterion is only applicable to strain rate and temperature insensitive materials tested under quasi-static loading conditions, which is perfectly true for tensile tests on NiTi wire deforming plastically in martensite.

Localized Deformation of Superelastic NiTi Wires During Tensile Testing
To further investigate strain localization and necking at 13-15% strain, the experiment in Fig. 2 was performed again at slightly lower temperature 10°C (Fig. 3), which to our benefit slightly slowed down the dynamics of the necking process so it can be interrupted (Fig. 3). The deformation was stopped at 13% strain just after the necking started but before the wire could fracture. The wire sample was unloaded and heated under 25 MPa constant stress up to 60°C to evaluate strain recovery upon heating. The results of the performed 1D-DIC observation show that the wire deformed locally up to * 15% strain at z-positions 6-18 mm, before strain started to localize into neck at z = 10 mm, where local strain exceeded 20% when the loading was stopped. Reverse martensitic transformation occurred partially during the unloading but mainly during the subsequent heating under 25 MPa stress in the range 10-40°C (Fig. 3a). Reverse martensitic transformation occurred everywhere in the wire including within the neck. Roughly * 10% strain was recovered on unloading and heating both within the neck and out of it. Local unrecovered strains out of the neck in LS1 and LS2 points were 1% and 3.3%, respectively (Fig. 3c), and 11% within the neck (LS3 point in Fig. 3c). Time evolution of local strains during 5 stages of the tensile test can be seen in Fig. 3d. Clearly, majority of unrecovered plastic strains is localized with the neck.
In order to obtain more detailed information on the deformation mechanism activated within the neck, four TEM lamellae were cut from the deformed and heated NiTi wire. Three lamellae were cut from within the neck region (B, C, D) and fourth one from the part of the wire out of the neck (A), as shown in Fig. 4b. The aim was to observe and analyze lattice defects created by tensile deformation in the parts of the wire, where the deformation was localized into neck. It was found that the deformed and heated wire (Fig. 4a) is austenitic everywhere within the neck and out of it. This is natural as the wire is superelastic and it was heated after unloading to recover all residual martensite (Fig. 4a). The lattice defects in austenite (Fig. 4A-D) are relicts of the deformation process activated during the plastic deformation in martensite which remained in the austenitic microstructure after the reverse transformation on unloading and heating. Out of the neck (Fig. 4A), the microstructure contained mainly slip dislocations and isolated deformation bands in some grains. Within the neck ( Fig. 4B-D), the microstructure contained slip dislocations and deformation bands, the density of which increased from the edge of the neck toward its center (from B to D).

Effect of Test Temperature on the Localized Deformation of Superelastic NiTi Wires in Tension
To evaluate the effect of temperature on the strain localization in tension, series of tensile tests until fracture was performed on 14 ms NiTi wire within the temperature range from 10 to 400°C (Fig. 5). The deformation via stress-induced martensitic transformation is localized in Lüders bands from 10°C up to temperature as high as 350°C (Fig. 5a). Electric resistance of the wire was evaluated during the tensile test. It brings supplementary evidence on the volume fraction of martensite evolving during the test. For a given strain value, the higher is the electric resistance, the larger volume fraction of martensite is in the wire [19]. Figure 5b shows temperature dependence of upper plateau stress and strength evaluated from stressstrain curves. Figures 5c, d shows temperature dependence of strains localized within the moving Lüders band fronts, which are of main concern in this work.
Strain localization patterns evaluated by in situ 1D-DIC method are shown in Fig. 6. In tensile tests at low temperatures (characterized by stress-strain curve at 10°C in Fig. 6a), the inelastic tensile deformation starts by stressinduced martensitic transformation within the plateau range, the stress-induced martensite deforms elastically beyond the end of the plateau. When yield stress is exceeded, strain localizes in a neck and the wire fractures at 13-15% strain. In tensile tests at higher temperatures 60-80°C (Fig. 6b, c), upper plateau stress increases with increasing temperature. When stress reaches the yield stress, there is a second plateau-strain localizes again into macroscopic deformation band fronts propagating along the wire at constant stress. Strain localized within the propagating band fronts in the second plateau can be small but also very large-it reaches 35% [macro-strain evaluated from stress-strain curve (Figs. 5c)] or 43% [local strain evaluated by 1D-DIC (Figs. 5d)] in tensile test at 60°C. Since the deformation mechanism activated within the second plateau is plastic deformation of martensite via kwinking, we use terms ''kwink band'' and ''kwink band front'' when referring to macroscopic deformation band fronts propagating in the second plateau. In tensile tests at still higher temperatures 100-300°C (Figs. 5d, 6d-g), transformation plateau due to stress-induced martensitic transformation (first plateau) became unusually long (* 15% strain). The wires fractured due to strain localization in necks forming right beyond the end of the plateau at 10-20% strain. In tensile tests at highest test temperatures above 300°C, stress did not increase with increasing temperature anymore. At temperatures higher than 350°C, ductility became very low, since strain started to localize in a neck at very low strains (Fig. 6h, i). There was little space for Lüders band propagation since the strain localization started just after the band was nucleated and quickly resulted in necking within the nucleated band.

Localized Plastic Deformation of Martensite via Kwinking
The localized plastic deformation taking place via propagation of deformation band fronts was further analyzed in the tensile thermomechanical loading test in Fig. 7. We repeated the tensile test on 14 ms NiTi wire at 60°C again but instead of deforming the wire until fracture, we unloaded it at 30% strain and heated under 25 MPa constant stress up to 150°C and cooled to the room temperature (Fig. 7). It was found that the reverse martensitic transformation proceeded partially on unloading and partially on heating. On unloading, strain reversal proceeded homogeneously in the parts of the wire that deformed  plastically within the kwink band (homogeneous) and in localized manner in parts of the wire out of the neck. The strain recovered on unloading and heating was about * 10% within the kwink band as well as out of it, but unrecovered strains were very different (Fig. 7c). The strain reversal on heating was homogeneous both within the neck and out of it. TEM lamellae were cut from the material within the kwink band (B) and out of it (A) (Fig. 8). Lattice defects in the microstructure created by tensile deformation were analyzed. Out of the kwink band ( Fig. 8c-A), the microstructure contains only slip dislocations and isolated deformation bands. Within the kwink band ( Fig. 8c-B), the microstructure contains very high density of deformation bands with islands of heavily deformed crystalline material mixed with nearly amorphous lattice. The microstructure in Fig. 8c-B is quite similar to the microstructure observed within the center of the neck (Fig. 4-3). Fig. 8 support the view that the material within the macroscopic deformation band experienced very large plastic deformation, while that out of the band was only slightly plastically deformed (see also diffraction patterns). The large plastic deformation must have occurred while the deformation band front moved along the wire (Fig. 7d). However, it is difficult to learn anything about this deformation mechanism just from the bright field TEM images in Fig. 8A, B. Therefore, microstructures observed within a single grain outside (Fig. 9) and inside ( Fig. 10) of the deformation band were analyzed by the SAED-DF method in TEM [22].

Microstructures in
Microstructure out of the band (Figs. 8c-A and 9) contains slip dislocations and few deformation bands in a wedge arrangement. When selected grain (Fig. 9a) is tilted into\110[A low index zone (Fig. 9b), it becomes dark in the BF image, because both austenite matrix and deformation bands within the grain diffract strongly. Diffraction patterns taken from the SAED areas denoted in (Fig. 9b) show three differently oriented austenite diffraction patterns in the \110[ A low index austenite zone (Fig. 9c,d) b Fig. 5  corresponding to austenite matrix (red) and two {114} twins (green, blue). There is also a single martensite diffraction pattern in \010[ zone (Fig. 9g,  h) corresponding to few residual martensite plates (magenta). Microstructure in the selected grain was reconstructed using the analysis of DF images using reflection from each Fig. 7 1D-DIC analysis of local strain evolution in tensile test on 14 ms NiTi wire at 60°C in which kwink band front propagation was observed (Fig. 6b). The wire was deformed till 30% strain, followed by unloading and stress free heating up to 150°C. a Stress-strain temperature record of the test, b 1D-DIC record of the test, c evolution of macroscopic strain and local strains in points LS1, LS2, and LS3 (defined in b) during the test, d spatially distributed local strains in selected times I-V (defined in b) during the test. Strain response on unloading is localized out of the deformation band and homogeneous within the band. Notice that strain localized within the propagating deformation band front reaches 40%. Total strain within the band reaches 57%, out of which * 8% was recovered on unloading and heating (see local strain in point LS1 in (c)). Total strain out of the band is only * 13% and most of it is recovered on unloading and heating (see local strain in point LS3 in (c))] individual lattice (Fig. 9e, f, i, j). All denoted austenite twin planes and austenite/martensite interface planes are aligned with the electron beam. The resulting microstructure of the grain is presented in Fig. 9l, orientation of individual austenite and martensite twins in Fig. 9d. For more detailed information on the use of SEAD-DF method [33] to reconstruct the microstructure within a single grain of plastically deformed NiTi wires, see Refs. [19,21,33]. Microstructure within the deformation band (Figs. 8c-B and 10) contains mixture of crystalline and nearly amorphous lattices and high density of deformation bands. Individual grains can be hardly resolved in the TEM lamella and display ring diffraction pattern suggesting nearly amorphous structure. Nevertheless, there are also small grains containing high density of thin bands and crystalline diffraction patterns. One of such grains (Fig. 10) was oriented into the \110[ A low index zone (Fig. 10b) and diffraction pattern taken form the SAED area denoted in Fig. 10b) was analyzed as belonging to the austenite matrix and two {114} austenite twins (Fig. 10c, d). The austenite twins are not continuous bands anymore, but mutually interconnected fragments, and the microstructure contains significant amount of martensite phase apparently all belonging to a single martensite lattice orientation (Fig. 10h, i). Reconstruction of this refined microstructure (Fig. 10j) is problematic due to the fragmentation by the kwinking and high density of lattice defects [22,27]. Kwinking deformation leads not only to localized deformation via necking and fracture at 13-15% strain but also to localized plastic deformation within moving macroscopic band fronts. Macroscopic band fronts propagating at constant stress beyond the onset of plastic deformation in tensile tests are hence called ''kwink band fronts'' to simplify further discussion.

Effect of Austenitic Microstructure on the Localized Tensile Deformation of Superelastic NiTi Wires
NiTi wires with ultrafine, partially recrystallized microstructure (6-14 ms in Fig. 1a) fail via necking and fracture at 13-15% strain. With pulse time increasing from 14 ms (grain size * 215 nm) to 15 ms (grain size * 250 nm), a sharp transition occurs from the necking at 13-15% strain towards plastic deformation in a strain hardening manner up to * 60% strain of NiTi wires with large grain size (pulse time [ 15 ms). This sharp transition depends not only on the wire microstructure ( Fig. 1a) but also on the test temperature (Figs. 5, 6).
To investigate the temperature and microstructure dependence of this peculiar transition from necking at 13-15% strain towards ductile plastic deformation up to * 60% strain, NiTi wires with different microstructures 14, 14.2, 14.4, and 14.6 ms were deformed in tensile tests at test temperatures of 0, 20, 40, and 60°C (Fig. 11). It appeared that plastic deformation of the wire proceeds in localized manner via propagation of kwink band fronts only for specific combinations of test temperature and microstructure (pulse time). There were even two successive kwink bands propagating along the wire (e.g., 14.4 ms at 60 C in Fig. 11). The wire in this test thus displayed loss of the stability of the tensile deformation four times (19 Lüders band, 29 kwink band, 19 final neck). Strain localization patterns observed in individual tests show large variability. Strain localized within the moving front can be estimated from the change of color across the front in Fig. 11. Main conclusion from Fig. 11 is that the localization of plastic deformation of martensite via kwinking in this range is extremely sensitive to the test temperature and austenitic microstructure of the wire (Fig. 12).

Discussion
There are three problems with analysis of plastic deformation of commercial superelastic NiTi wires with nanocrystalline microstructure. First problem is that these wires tend to fracture just beyond the yield stress at * 13-15% strain and, therefore, plastic deformation of commercial nanocrystalline NiTi wires loaded in tension cannot be studied. Second problem is that grain size of the best performing nanocrystalline NiTi wires is too small and contains lattice defects persisting from cold work and, therefore, detailed analysis of martensite variant microstructures and lattice defects in grains generated during plastic deformation cannot be investigated by TEM. Third problem is that, even if superelastic NiTi wires with larger grain size deform plastically up to large strains, they deform plastically in the martensite state, and when researchers want to analyze lattice defects created by the tensile deformation in TEM lamellae cut from deformed wire, they find very complex microstructure containing mixtures of austenite phase with residual martensite bands. Lattice defects in such microstructures are very difficult to analyze and mainly interpret in terms of deformation mechanism, since one never sees whole grain in the TEM lamella. Hence, the deformation mechanism activated during plastic deformation cannot be studied by TEM on superelastic NiTi wires. These three issues were overcome in our recent work [22,25] by performing tensile tests on NiTi SME wires with optimized grain size-small enough that the wire still shows excellent superelasticity but large enough so the martensite variant microstructures in polycrystal grains created by the tensile deformation can be reconstructed. Dislocations and austenite twins in austenite created by the deformation in martensite were observed in TEM at 200°C [25]. Based on the analysis of the observed martensite variant microstructures [22], it was concluded that nanocrystalline NiTi wires deform plastically in martensite by the kwinking deformation involving combination of deformation twinning with dislocation slip-based kinking [27].
Since the martensite in 14 ms superelastic NiTi wire plastically deformed by kwinking undergoes reverse martensitic transformation on unloading and heating, we could not analyze the martensite variant microstructures in this deformed wire by TEM. However, we can analyze lattice defects inherited into the austenite phase during the reverse martensitic transformation on unloading and heating, particularly to the {114} austenite twins (Figs. 9, 10). It was shown in [22] that (20-1) deformation twins forming wedge microstructures with (100) deformation twins in plastically deformed martensite undergo reverse martensitic transformation into wedges made of {114} austenite twins (see Fig. 11 in [22]). The observation of {114} austenite twin wedges in the microstructure of plastically deformed superelastic NiTi wire thus serves as experimental evidence for plastic deformation of martensite by kwinking. Number of {114} austenite twins in the microstructure of plastically deformed superelastic NiTi wire increases while size of twins (lengths and thickness of deformation bands) decreases with increasing plastic strain which leads to refinement of the austenitic microstructure down to nanoscale [19].

Fracture of NiTi Wires via Necking
Experimental results (Figs. 1, 2, 3, 4) prove that nanocrystalline NiTi wires with grain size B 215 nm fail via localized plastic deformation of martensite by kwinking which leads to necking that proceeds very fast and leads to wire fracture at * 13-15% strain. Strain localization and necking area consequence of the instability of tensile deformation of martensite by kwinking, the conditions for which are expressed by Considere criterion (Eq. 1). The reason is that the material deforming by kwinking beyond the yield stress displays very low strain hardening rate even at very high stresses. Few related observations, however, shall be pointed out in this respect: (i) yield stress sharply decreases with increasing grain size of the austenitic microstructure (Fig. 1a) as well as with increasing test temperature [19] (Fig. 5), (ii) strain hardening rate increases with increasing strain in the range 15-30% in case of NiTi wires with large grains size (wires 14-15 ms in Fig. 1a), (iii) strain hardening rate increases with increasing grain size as well as with increasing test temperature [34], and (iv) necking proceeds very fast because kwinking deformation is nearly strain rate insensitive [25]. These observations are characteristic for kwinking deformation. Yield stress and strain hardening rate (depending on the austenitic microstructure and test temperature) control the stability of tensile deformation. Conventionally, Considere criterion is used to determine the strain at which the strain localization (neck or deformation band) appears. Since strain hardening rate of conventional metals continuously decreases with increasing strain, conventional metal undergoes necking. In case of NiTi wires with small grains size (NiTi wires \ 14 ms in Fig. 1a), strain hardening rate is probably relatively low until fracture and given the high yield stress, this leads to necking and fracture at 13-15% strain. In case of NiTi wires with medium grains size (NiTi wires 14-15 ms in Fig. 1a), strain hardening rate is constant after the onset of yielding over a stress plateau (its length changes with temperature and microstructure) and later increases with increasing strain. Because of that, localization of tensile deformation into moving kwink band fronts becomes possible and preferable over necking.
In addition, however, there is the strain rate sensitivity which likely plays a very important role. When plastically deforming material is strain rate sensitive, a considerable delay in necking occurs [36]. Very large strain rate sensitivity is a condition for superplastic behavior of metals achieved through suppression of necking. When the material is strain rate insensitive, as NiTi martensite deforming via kwinking, strain localization via necking, or Lüders band front propagation is promoted. The apparent lack of experimental observation of necks by 1D-DIC method in tensile tests on nanocrystalline NiTi wires (Figs. 1b) is due to the fact that the strain rate within the growing neck is extremely high, which is only possible, if kwinking deformation is strain rate insensitive process, as confirmed experimentally [25].
Strain localization patterns recorded in tensile tests on NiTi wires with slightly different microstructures within the range of 14-15 ms at different temperatures (Fig. 11) provide detailed information on the strain localization behavior under critical conditions, where the necking changes into kwink band front propagation (Figs. 1a, 5a). Whether plastic deformation by kwinking will be localized in a neck leading to wire fracture at * 13-15% strain or in mobile deformation band fronts enabling large plastic deformation up to * 60% strain depends on the constitutive stress-strain behavior of NiTi via kwinking, as will be discussed in section ''Localized tensile deformation of superelastic NiTi wires by kwinking.''  At ambient temperatures (T = 50-80°C), the wire deforms plastically up to very large strains (* 50%) via propagation of kwink band fronts (Fig. 6b, c),. At higher temperature around 140°C, stress-induced martensitic transformation proceeds in very long plateaus (Fig. 6e) because martensitic transformation within the Lüders bands propagating at these conditions is accompanied by plastic deformation [31]. However, since upper plateau strain increases with increasing temperature at these high temperatures, stress-induced martensitic transformation must be activated. Ductility, however, becomes again limited to 13-15% strain. In tensile tests at highest temperatures 300-400°C (Fig. 6g), the wire deforms plastically at 1200 MPa stress and ductility decreases from 12 to * 3% strain only. Stress-induced martensitic transformation is thus most likely involved in tensile deformation beyond the yield stress up to very high test temperatures. However, at temperature above 350°C (Fig. 6h, i), ductility becomes very limited since strain localizes within the volume where first Lüders bands appear. In can be deduced from these results that yield stress for dislocation slip in austenite exceeds 1150 MPa at 400°C. Because of that, massive activity of dislocation slip in austenite at temperatures T \ 300°C can be safely excluded as a sole deformation mechanism. On the other hand, plastic deformation occurs within the moving Lüders band front, where martensite was stress induced. Dislocation slip in austenite can be involved in this plastic deformation process. Nevertheless, deformation mechanism of the 14 ms NiTi wire at elevated temperatures cannot be deduced from experiments reported in this work. The reader is referred to article [24], in which deformation mechanism of superelastic NiTi wire deforming at elevated temperature is thoroughly discussed based on the results of the analysis of texture evolution in austenite and martensite phases during the tensile tests at elevated temperatures.

Localized Tensile Deformation of Superelastic NiTi Wires by Kwinking
It was explained in section ''Fracture of NiTi wires via necking'' that nanocrystalline NiTi wires tend to fail via localized plastic deformation of martensite by kwinking leading to fast necking and fracture at * 13-15% strain. However, even more interesting is the large plastic deformation of martensite proceeding within the moving kwink band fronts, in which up to 40% strain is localized (Figs. 6b, 7, 8). Observation of {114} austenite twins within the band microstructure (Figs. 8,9,10) proves that the martensite deforms within the moving fronts by kwinking.
The prerequisite for this unusual strain localization phenomenon is the specific yield stress and strain hardening rate, which are adjusted by the test temperature and wire microstructure (Fig. 11). The mechanism which controls the magnitude of strain localized within the propagating band front (length of the stress plateau) is proposed as follows. Assume that the NiTi wire is capable of deforming at roughly constant stress beyond the onset of plastic deformation (the material displays stress-strain response similar to that of 15 ms NiTi wire (Fig. 1a)). In other words, let us assume that the strain hardening rate is low and constant beyond the onset of plastic deformation and further increases later in the test. This would give rise to a stress plateau (similar to 15 ms NiTi wire (Fig. 1a)), the length of which defines the amount of plastic strain to be potentially localized within the moving band front. Very important is the increase of the strain hardening rate somewhere beyond the end of this plateau. If this is absent, the wire fractures via necking at 13-15% strain, which is what happens in tensile tests on 14 ms NiTi wire at test temperatures lower than 50°C (Fig. 11) or in NiTi wires with smaller grain sizes (Fig. 1a, b).
The observation of 40% strain localized within the kwink band front moving under 1 GPa engineering stress (14 ms, 60°C in Fig. 11) means that the microstructure within the kwink band has to resist 1500 MPa stress due to the change of the cross section of the wire at * 50% total strain. This is indeed the case, notice that, while the kwink band front moves in this test, the wire does not deform within the kwink band. Nevertheless, when the kwink band extends over whole length of the wire, stress further increases and wire fractures since the stress of 1500 MPa approaches the maximum true stress the strengthened material can withstand without additional strain localization and necking.
However, strain localized within the band can be much smaller than 40%. It depends on the wire microstructure and test temperature (Figs. 11, 12). The wire deforms homogeneously after the kwink band extends over whole length of the wire. Figure 12 shows strains localized with the moving band fronts in dependence on the test temperature and wire microstructure evaluated from tests in Fig. 11 and some additional tensile tests. Strain-maxima form a band in temperature-microstructure space which probably continues toward larger grain sizes and lower temperatures. Chen et al. [32] observed localized deformation in Ni 47 Ti 49 Nb 2 Fe 2 alloy in tensile test at low temperature -50°C, since that alloy had microstructure with larger grain size. On the other hand, observation of kwink band fronts in tensile test at temperatures above 100°C is less likely, since kwinking deformation is suppressed at high temperatures.
Kwink band front propagation mode is observed in tensile tests only within a narrow temperature (* 10-60°C) and microstructure (grain size * 230 nm) interval. Due to this narrow temperature-microstructure interval, kwink band front propagation mode can be easily overlooked. In fact, we missed the kwink band front propagation mode in our earlier work [34], since tensile tests on 14 ms NiTi wire were not performed at temperatures between 20 and 100°C (see Fig. 6 in [34]).
Very important for strain localization in kwink band fronts is also the already mentioned strain rate insensitivity of the kwinking deformation. As the kwink band front propagates along the wire in the tensile test on 14 ms NiTi wire at 60°C, local strain rate within the moving band front (Figs. 7, 8) temporarily increases to strain rate 0.03 s -1 evaluated experimentally by the 1D-DIC method. Compare with the constant macroscopic strain rate 0.001 s -1 prescribed in the experiment. Local stress in the material gradually increases across the moving front, as the cross section of the wire decreases but the the material within the band hardens via the kwinking deformation. However, if the stress required for kwinking would increase with increasing strain rate, kwink band front would not be able to propagate. While in case of necking, the strain rate insensitivity of kwinking deformation leads to very fast neck growth (section ''Fracture of NiTi wires via necking''), in case of kwink band front propagation, it enables motion of fronts, in which very large strain (* 40%) is localized.

Conclusions
Tensile deformation of superelastic NiTi wires with nanocrystalline microstructure was investigated by tensile tests until fracture in wide temperature range from 10 to 400°C. Strain localization during tensile tests was characterized by in situ digital image correlation method and lattice defects in austenitic microstructure created during the tensile test were characterized by post-mortem TEM analysis.
Following conclusions were drawn from the performed experiments: 1. Tensile deformation at low stresses at which stressinduced martensitic transformation takes place (at test temperatures 10-300°C) is homogeneous in NiTi wires having small grain size (0-7 ms NiTi wires) and localized in mobile Lüders band fronts in wires with larger grain size (8-20 ms NiTi wires). 2. Plastic deformation of martensite at high stresses can be either localized or homogeneous in dependence on the test temperature and virgin austenitic microstructure of the wire (grain size) affecting the stability of macroscopic tensile deformation controlled by the yield stress and strain hardening rate through the Considere criterion. 3. Plastic deformation of martensite (homogeneous or localized) occurs via peculiar kwinking deformation mechanism involving combination of deformation twinning in martensite with dislocation slip-based kinking. 4. Localized plastic deformation of martensite proceeds either as necking leading to fracture at 13-15% strain or as propagation of macroscopic deformation band fronts at constant stress leading potentially to very large plastic strains at fracture in the range 20-60%. 5. The propagation of macroscopic deformation band fronts in plastic deformation range was observed only in tensile tests test on NiTi wires having specific microstructures (grain size * 230 nm) in a narrow temperature range (* 10-60°C). 6. Magnitude of the plastic strain localized within the moving macroscopic deformation band fronts varied in the range of 0-40% in dependence on wire microstructure and test temperature. 7. Low strain rate sensitivity of the kwinking mechanism of plastic deformation of martensite facilitates fast necking upon tensile loading beyond the yield stress and enables motion of macroscopic deformation band fronts with extremely large localized strains during tensile deformation of NiTi wires.
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