Tensile Deformation of B19′ Martensite in Nanocrystalline NiTi Wires

Deformation mechanisms activated during tensile deformation of nanocrystalline NiTi wire in martensite state were investigated by combination of two experimental methods: (i) analysis of the evolution of martensite-variant microstructures in grains of deformed wire by TEM and (ii) analysis of the evolution of martensite texture by in situ synchrotron X-ray diffraction. The obtained results are linked to the activity of various twinning processes in martensite. It is concluded that martensite reorientation proceeds via motion of interdomain interfaces, gives rise to reoriented martensite with microstructure consisting of single (001) compound-twinned domain in each grain and results in sharp two-fiber texture of the martensite. The reorientation process leaves behind only very small unrecovered strains and very few dislocation defects in the austenitic microstructure of the deformed wire after unloading and heating. Plastic deformation of B19′ martensite proceeds via peculiar deformation mechanism which combines (100) deformation twinning with [100]/(011) dislocation slip based kinking. It gives rise to very special martensite variant microstructures consisting of deformation twin bands and kink bands containing martensite lattice aligned with [010] direction and characteristic two-fiber martensite texture. Reverse martensitic transformation of plastically deformed martensite upon unloading and heating leaves behind large unrecovered strains and high density of lattice defects in austenite. But there are also significant recoverable strains up to 10%. While the martensite matrix in grains of plastically deformed wire transforms into parent austenite matrix, (20-1) deformation twins transform into {114} austenite twins.


Introduction
Based on the pioneering work of Waitz [1] followed by frequent literature reports of (001) compound twins in the microstructure of nanocrystalline NiTi, it is now widely accepted in the SMA field that, while NiTi single crystals or large grain size polycrystals possess self-accommodated martensitic microstructures consisting of \011[ type-II twins (Fig. 1b), nanocrystalline NiTi alloys contain (001) compound twins (Fig. 1a). What yet needs to be find out, is how this (001) compound-twinned martensite-variant microstructure evolves during mechanical deformation-i.e., how conventional NiTi wires possessing nanocrystalline microstructure with (001) compound twins deform under mechanical loads. This motivated us to carry out research work focusing on deformation mechanisms activated during tensile deformation of nanocrystalline NiTi wires overviewed in this article.
Based on the results of experiments on single crystals and large grain-sized NiTi polycrystals, martensite reorientation was reported to proceed via detwinning of \011[ type-II twins [18,19]. These martensite twins created by the martensitic transformation during the stressfree cooling from the austenite form correspondent variant pairs (CVP) (Fig. 1b). The \011[ type-II twins enable formation and propagation of habit plane between the austenite and martensite. This view of thermally and stress induced B2-B19 0 martensitic transformation in NiTi is currently widely spread in the SMA field and frequently used in SMA modeling literature [16,17]. However, is this view correct for nanocrystalline NiTi alloys possessing (001) compound-twinned microstructure of self-accommodated martensite (Fig. 1a)? Results of our recent experiments involving TEM analysis of martensitic microstructures [9] and HEXRD analysis of textures [20] evolving during tensile tests suggest that it is not correct, since the (001) compound-twinned martensite in nanograined NiTi polycrystalline wires (Fig. 1a, b) responses differently to tensile loads than the \011[ type-II-twinned martensite (Fig. 1b).
The mechanism of plastic deformation of B19 0 martensite is understood even less than the mechanism of martensite reorientation. Plastic deformation of martensite is generally considered to proceed via dislocation slip [6,7], though experimental evidence suggesting activity of various deformation twinning modes during plastic deformation is abundant in the literature [2,6,8,9,12]. Recent TEM analyses of martensitic microstructures in plastically deformed NiTi wire [2,8,9] provide detailed experimental evidence on specific martensite twins observed in the microstructure of deformed nanocrystalline NiTi alloys. However, even if twins in the microstructure of deformed wire are known, it is very difficult to determine key deformation mechanism responsible for plastic deformation of B19 0 martensite just from the results of post-mortem TEM analysis. Observation of specific twin interfaces in martensite-variant microstructures of deformed wire does not automatically mean that a respective deformation twinning acts as a deformation mechanism.
To identify key deformation mechanism responsible for reorientation and plastic deformation of B19 0 martensite, one needs to employ additional experimental methods providing statistically relevant information on the activity of deformation twinning averaged over large number of grains. In situ X-ray (neutron) diffraction methods capable of evaluating lattice rotation accompanying twinning represent such methods. Since both martensite reorientation at low stresses and deformation twinning at high stresses are accompanied by discontinuous rotation of the martensite lattice, the orientation distribution of the martensite lattice (texture) evolves during the mechanical loading tests on NiTi polycrystal. The key is to establish a link between the activity of various deformation twinning modes activated during the deformation and texture evolution. It shall be mentioned that analysis of the evolution of 1D X-ray (neutron) diffraction patterns recorded during deformation (e.g., [13][14][15]) cannot be used for this purpose, since they  [1] in high-pressure torsion-processed and annealed nanocrystalline Ni-50.3 at.%Ti consisting of two (001) compound twin domains separated by interdomain interfaces (dashed line), b Microstructure observed by Nishida et al. [2] in solution annealed Ni-50 at.%Ti alloy consisting of \011[ type-II twins do not provide sufficient information on the lattice rotations accompanying the activity of deformation twinning modes.
This article focusses on the analysis of deformation mechanisms activated during tensile deformation of nanocrystalline NiTi wire in the martensite state until fracture based on the results of our recent TEM analysis local microstructures in grains [9] and texture analysis of orientation distribution within gage volume containing thousands of grains [20]. Key novelty of this work consists in evaluation of deformation mechanisms activated during the tensile test taking advantage of the synergy of both methods. Detailed information on both experimental methods can be found in original articles [9,20].

NiTi Alloys and Samples
Two NiTi wires produced by Fort Wayne Metals in cold work state-superelastic FWM #1 wire (Ti-50.9 at.% Ni, 42% CW, diameter 0.1 mm) and shape memory FWM #5 (Ti-50.5 at.% Ni, 42% CW, diameter 0.1 mm) were heat treated by electropulse method [35] to prepare NiTi wire samples with recrystallized microstructure of desired grain size and functional properties. 50 mm long segments of cold-worked wire were crimped into two steel capillaries, prestressed to * 300 MPa, constrained at current length and subjected to the short pulse of controlled electric power [power density 160 W/mm 3 , pulse time 15 ms (shape memory wire) and 16 ms (superelastic wire)]. For given cold-worked wire and power density used in the heat treatment, the pulse time scales with the maximum temperature reached during the electropulse heating, which largely controls the microstructure and functional properties of the heat-treated wire. The ''16 ms NiTi #1 wire'' having fully recrystallized microstructure with mean grain size d = 500 nm, undergoes B2-R-B19 0 transformation upon cooling with characteristic transformation temperatures R s = -25°C, M s = -40°C, A f = -15°C. The ''15 ms NiTi #5 wire'' having grain size d = 250 nm undergoes B2-R-B19 0 transformation with characteristic transformation temperatures M s = 63°C, A f = 93°C.

Tensile Testing
Tensile tests were carried out using custom-made tensile testers for thin SMA wires consisting of a miniature load frame, environmental chamber, electrical conductive grips, load cell, linear actuator and position sensor, and closeloop Labview control program. The environmental chamber (Peltier elements, resistive elements, and liquid nitrogen vapors) enables to maintain homogeneous temperature around the thin wire from -100 to 200°C. The experiment started by gripping the wire into the tester, strain was set to zero in the austenitic state, and the wire was cooled to the test temperature under 10 MPa applied stress. Stressstrain-temperature-electric resistance of the wire was recorded during tensile tests. Figure 2 shows results of tensile tests until fracture at various temperatures and stress-temperature diagram characterizing functional behavior of 15 ms NiTi #5 ( Fig. 2a-c) and 16 ms NiTi #1 wire ( Fig. 2d-f). Stressstrain curves of superelastic and SME wires are different due to different M s temperatures. The 15 ms NiTi #5 SME wire was deformed in tension until 7% and 15% strain at 20°C in experiments focusing TEM analysis of martensite-variant microstructures because the microstructures can be at room temperature. Superelastic NiTi #1 wire was deformed in tension until fracture at -90°C in texture evolution experiment because it was part of broader research focusing deformation mechanisms in NiTi at various temperatures. Lattice defects generated by the tensile deformation were analyzed at room temperature after heating until 200°C [20,36].
Grain sizes of the 15 ms NiTi #5 (250 nm) (Fig. 3c) and 16 ms NiTi #1 (500 nm) wires are larger than grain size of the HPT-processed NiTi studied by Waitz (Fig. 1a). Nevertheless, the (001) compound-twinned microstructures are rather similar. The difference is that grains in our wires frequently contain not only two (001) compound twin domains ( Fig. 1a) but also multiple twin domains (Fig. 3c).
Tensile stress-strain responses of superelastic and SME NiTi wires are compared in Fig. 2. The responses are similar-stress-temperature diagrams are mainly shifted in temperature scale (transformation lines for B2-B19 0 transformation are shifted * 100°C in temperature). Plastic deformation line r Y of SME wire is shifted to higher stress due to smaller grain size of the 15 ms NiTi SME wire compared to 16 ms superelastic NiTi wire [35]. Note that the length of transformation plateau of the superelastic NiTi wire increases with increasing temperature (Fig. 2e), and unusually long plateaus are observed at temperatures around 100°C, at which transformation line r UP and plastic deformation line r Y meet. The reason is that the martensite stress that has been induced at high Stress-strain curves of two NiTi wires deformed in tension until fracture at various temperatures. a-c 15 ms NiTi #5 SME wire, d-f 16 ms NiTi #1 superelastic wire. Results of tensile tests (b, e) and stress-temperature diagrams constructed from the results of these tests (c, f) are shown to provide detailed information on tensile behavior of nanocrystalline superelastic and shape memory NiTi wires used in experiments reported in this work

Fig. 3
Martensitic microstructures evolving during tensile test on nanocrystalline NiTi #5 wire [9]. Stress-strain-temperature curves (a) recorded in tensile thermomechanical tests (black up to 7%, red up to 15%) with denoted stages in which TEM lamellas were cut from the deformed wires (solid circles). Although the TEM lamellae were cut at room temperature without stress, it is assumed that martensite variant microstructures shown by BF TEM images in Figs stress starts to deform plastically, as investigated and concluded in [37].

Reconstruction of Martensite-Variant Microstructures in Grains of Deformed Wire by TEM
When polycrystalline NiTi wire transforms from austenite to martensite, each austenite grain (Fig. 3b) decomposes into a complex martensite-variant microstructure. It is essential that recrystallized grains of a virgin NiTi wire are free of internal strain and dislocation defects, so these are not later confused with lattice defects and internal strain created during the tensile deformation. The grains have to be large enough ([ 20 nm) so they do not overlap in the * 50-nm-thick TEM lamella but small enough so that the gage volume created by the lamella cutting through roughly spherical grain consumes large portion of the grain volume. Martensite-variant microstructures within grains can be reconstructed by post-mortem selected area electron diffraction (SAED) with dark-field (DF) image analysis method (''SAED-DF imaging method'') in TEM (see Appendix A in [9]). This method is based on tilting the TEM lamella into a low-index zone, in which all observed interface planes within selected grain are aligned with the electron beam.  Martensitic microstructures evolving during tensile deformation of 15 ms NiTi #5 SME wire deformed were analyzed by the SAED-DF method in [9]. Key results are summarized in Figs. 3, 4, 5, and 6. Lattice defects created by tensile deformation of superelastic 16 ms NiTi #1 at room temperature ( Fig. 16) until fracture were analyzed in [36]. TEM lamella was cut from the subsurface layers of deformed wire (10 lm below the surface, wire axis in the lamella plane) by focused ion beam (FIB) using a FEI Quanta 3D FIB-SEM microscope. TEM observations were performed using a FEI Tecnai TF20 X-twin transmission electron microscope equipped with a field emission gun operated at 200 keV using a double tilt specimen holder. The projections of wire axis are denoted by thick arrows in all TEM micrographs. The observed TEM diffraction patterns were indexed using the lattice parameters of the parent B2 cubic austenite phase (a 0 = 0.301 nm) and product monoclinic B19 0 martensite (a = 0.289 nm, b = 0.412 nm, c = 0.462 nm, and b = 96.8°). Figure 3 summarizes results of the analysis of the evolution of martensite-variant microstructures in NiTi #5 SME wire deformed up to 7% (15%) strain, unloaded and heated above the A f temperature. Reconstructed martensitevariant microstructures of reoriented ( Fig. 4) and plastically deformed (Fig. 5) martensites are presented in detail, separately. When the wire was cooled from 150°C to room temperature, the austenite (Fig. 3c) transformed into selfaccommodated B19 0 martensite with microstructure in grains consisting of multiple (001) compound-twinned domains (Fig. 3c). The characteristic laminate of (001) compound twins could be observed only if twin planes are aligned with the electron beam.
When the wire was deformed via martensite reorientation up to 7% strain (black curve in Fig. 3), the self-accommodated microstructure became converted into single (001) compound-twinned laminate in each grain (Fig. 3c). This microstructure is analyzed in detail in Fig. 4. Dark field images (Fig. 4e, f) using diffraction spots belonging to the blue and magenta lattices in Fig. 4d clearly show the (001) compound twin laminate filling nearly whole grain. Many grains, however, contained relict martensite domains (white domains in Fig. 4b), which were not converted during the martensite reorientation within the plateau range. Martensite reorientation proceeds via motion of interdomain interfaces and partial detwinning of persisting (001) compound twin domains (Sect. ''Reorientation of Martensite''). Upon unloading and heating, the reoriented martensite retransformed back to the parent austenite without leaving any significant unrecovered strains and lattice defects in the austenitic microstructure of the deformed wire.
When the wire was deformed into the plastic deformation range up to 15% strain (red curve in Fig. 3), the observed microstructure consisted of multiple deformation bands and peculiar dislocation contrast (Figs. 3e, 5, 6). It will be concluded (see Sect. ''Plastic Deformation of B19 0 Martensite by Kwinking'') that the B19 0 martensite deforms plastically via a peculiar deformation mechanism which combines (100) deformation twinning with [100](001) dislocation slip based kinking in martensite. Since this new deformation mechanism combines twinning with kinking, it was called ''kwinking'' [38]. Upon unloading and heating, reverse martensitic transformation takes place leaving large unrecovered strains and high density of {114} austenite twins in the fully austenitic microstructure [36].
Results of detailed analysis of martensite-variant microstructures in plastically deformed martensite are presented in Figs. 5, 6. Frequently, these microstructures consist of nearly parallel bands formed by (100) deformation twins and (20-1) deformation twins. Wedge microstructures (Fig. 5) were frequently observed in grains oriented with (001) martensite plane normal oriented along the load axis. Practically all grains observed in the TEM lamella contain deformation bands, although their amount varies significantly from grain to grain. Since analysis requires tilting the TEM lamella into the unique [010] zone in which all interfaces are parallel to electron beam, one cannot make a low magnification overview of microstructures in multiple neighboring grains.
Example of analysis of wedge multiband microstructures is shown in Fig. 5. Selected grain had to be rotated into [010] low-index zone (unique in monoclinic structure) to analyze martensite-variant microstructure in it. When this is done by tilting the lamella, the grain becomes completely dark (Fig. 5b), in spite of the presence of multiple martensite variants in it (Fig. 5a). The composite diffraction pattern (Fig. 5c), consisted of seven misoriented diffraction patterns in [010] zone colored in Fig. 5d. Selected interfaces are characterized by lines and prisms in Fig. 5m-r (twin plane and lattice misorientation). All bands were created from the yellow matrix lattice but not all bands are (20-1) or (100) twins. Lattice misorientations and interface planes frequently deviate from exact twinning geometry-these interfaces are kwink band interfaces [38]. In some cases, band interfaces do not display twin relationship at all-two martensite lattices are only rotated (Fig. 5r)-these are kink band interfaces. There are also interfaces between two impinging bands. Deformation bands display uneven contrast, frequently with fringes along (001) planes, not necessarily (001) compound twins. In fact, plastically deformed martensite is largely detwinned from (001) compound twins.
A thin TEM lamella was prepared to analyze selected band interfaces by HRTEM (Fig. 6). Selected grain containing multiband band microstructure is characterized by composite diffraction pattern (Fig. 6b, c) consisting of ten colored martensite diffraction patterns. The reconstructed martensite-variant microstructure is shown in Fig. 6d. HRTEM images of selected interfaces found in this microstructure are shown in Fig

Martensite Texture Evolving During Tensile Deformation Evaluated by In Situ HEXRD Method
Although we have analyzed martensitic microstructures within multiple grains in several TEM lamellae cut from the deformed wire [9] and proposed deformation mechanisms for martensite reorientation and plastic deformation based on the results, we could not be sure that these deformation mechanisms are really representative for tensile deformation of the martensitic NiTi wire. To confirm this, we needed statistically relevant experimental evidence for activity of each deformation mechanism during the tensile test. This evidence was obtained by the analysis of the experimentally determined evolution of martensite texture using theoretical framework allowing for qualitative texture simulation based on the discontinuous lattice rotations associated with twinning in martensite described in Appendix A in [20] and outlined in Sect. ''Theoretical Prediction of Martensite Texture Evolution from Calculated Discontinuous Lattice Rotations Due to Twinning in Martensite.'' In situ synchrotron X-ray diffraction measurements were carried out on the ID15A beamline at ESRF Grenoble, using 64.2 keV beam energy (wavelength 0.19312 Å ) and a beam size of 150 9 150 lm 2 . A Pilatus3 X CdTe 2 M detector (active area of 253.7 (W) 9 288.8 (H) mm 2 and pixel size of 172 9 172 lm 2 ) was used to collect Debye-Scherrer ring patterns, with the sample-to-detector distance being 587.618 mm. The MITTER wire tester was installed on the beamline so that the gage volume was placed into the wire center. The NiTi wire sample was cooled to test temperature T = -90°C, and tensile test was run in position control until fracture. Since the exposure time for each diffraction measurement was only 0.2489 s, continuous data acquisition was employed throughout the whole experiment.
Python module FabIO [39] was used to read raw 2D diffraction images in cbf format (cif binary files), and the pyFAI library [40] was used to calibrate the experimental setup and perform azimuthal integration of sequential diffraction images. To this end, the recorded CeO 2 standard ring pattern was used to calibrate the beam center, sampleto-detector distance, and detector tilt (roll, pitch, and yaw). An azimuth (g) range from 21°to 201°on each image (detector) plane was analyzed due to the space limitations stemming from the instrumentation setup. 2D diffraction images were regrouped into 2048 bins along radial (2h) coordinates with 2h spacing from 0.34562°to 18.12745°to include main reflections. All ring patterns were segmented into Dg = 2°slices such that each recorded 2D diffraction pattern yields 111 radially integrated 1D diffraction spectra of 2h versus total X-ray intensity. Thus, each 1D diffraction spectrum provides orientation-specific information on the microstructure within the gage volume within ± 1°a ngle around the corresponding azimuth angle. The set of 1D diffraction spectra from the CeO 2 standard was used to determine the azimuth-dependent instrumental contribution to profile line broadening.
To evaluate the texture from X-ray diffraction patterns, Rietveld refinement of the whole set of 111 radially integrated 1D diffraction spectra obtained by sequencing Debye-Scherrer ring patterns was performed. This was undertaken using the General Structure and Analysis System (GSAS-II) [41] with a modified script from GSAS-II scriptable routines [42]. As a general methodology, spectrum-related parameters such as Gaussian and Lorentzian peak profile terms (determined from the CeO 2 standard) reflecting the instrumental contribution to profile line broadening were fixed while the scale factor and background coefficients were refined. For spectrum-phase-related parameters, peak shift (to lattice parameters) due to macroscopic strain (D ij values) was fitted to represent hydrostatic/elastic strain. Deformation-induced peak broadening was evaluated with the generalized microstrain model [43,44].
A generalized spherical-harmonic description of texture was implemented [45]. It is known that intensity variation along a Debye-Scherrer ring (i.e., corresponding to a {hkl} reflection) is in proportion to pole intensity of the orientation sphere imposed on a sample. Given that no sample rotation was applied and viewing along the axial (loading) direction (AD), each Debye-Scherrer ring results in pole figure coverage, which is represented as a pair of centrosymmetric curved lines with an interspacing of 2h on the {hkl} pole figure [46]. As we know that the wire possesses an initial fiber texture along the AD direction, the sample was oriented perpendicularly to the beam. The AD direction was placed in the center of the pole figure by setting the sample goniometer angle Phi = 90°. This allows cylindrical symmetry to be imposed in such a way as to improve effective pole figure coverage. A harmonic order of 6 was used with an order increment up to 10, such that higher orders did not result in additional significant improvement of the refinement.
Texture was further processed in MTex [47] after exporting the pole figure data of the first intense reflections of both phases derived from the texture model. MTex provides five types of orientation distribution functions (ODF) to model texture components in polycrystalline materials, which appear as preferred orientations with a certain variance. We used unimodal ODF defined through an unimodal bell-shaped function centered at each sample orientation on SO(3) with defined halfwidth (or standard deviation). A kernel function is required to define the specific form of the unimodal ODF. The de la Vallée Poussin kernel (default function in MTex), which represents a well localized, non-negative radially symmetric function on SO(3), was used with a halfwidth of 10°. Pole figures (PF) and inverse pole figures (IPF) were interpreted as multiples of random distribution (mrd). In situ texture evolution experiment starts by evaluating texture of the wire in austenite at room temperature (Fig. 7). The wire sample was gripped into the tester at room temperature, strain was set to zero, diffraction pattern was recorded, and the texture of the wire in austenite state was later evaluated from this pattern. Then the wire was cooled under low stress 10 MPa stress to the test temperature T = -90°C, and the texture of the wire in martensite state (Fig. 7) was evaluated again. It is essential to remember that the AD IPF shows the orientation of the wire axis (AD Direction) in the monoclinic martensite lattice. Since there are multiple variously oriented Fig. 9 Transformation and deformation twins in the B19 0 monoclinic martensite. There are 12 lattice correspondence variants of martensite phase fulfilling lattice correspondence between the cubic B2 austenite and B19 0 monoclinic martensite (Table A1 in Appendix A in [20]). Each LCV variant may undergo transformation twinning. The most important transformation twin of the B19 0 martensite in nanocrystalline NiTi is the (001) compound twin presented in (a, b) consisting of two LCV variants V9 and V10 (Table A1)  Results of the texture evolution experiment are presented by showing sequence of AD IPFs determined in 18 strain states during the tensile test (Fig. 8). The stressstrain curve displays five deformation stages, in which various deformation mechanisms are activated. Stage I-elastic deformation of self-accommodated martensite, stage II-reorientation of martensite, stage III-apparent elastic deformation of oriented martensite, stage IV-early plastic deformation, and stage V-late plastic deformation and fracture. A complication is that the wire deformed in the stage II in localized manner. Hence, the four-fiber texture of self-accommodated martensite was changed into twofiber texture of reoriented martensite in a step-wise manner between the strain states 2-3. This two-fiber texture of reoriented martensite then evolved only slightly in stages II and III, the intensity of the left fiber increased, and that of the right fiber decreased. When the wire was loaded into the plastic deformation range (stages IV and V), the twofiber texture evolved further so that the intensity of the left fiber decreased and that of the right fiber increased and    Table A1 in Appendix A in [20]), texture of ideal single fiber-textured martensite polycrystal will be simulated by four poles in AD IPF and four rings in 45°IPF and TD IPF (Fig. A7 in Appendix A [20]). Each pole corresponds to three LCV variants equally oriented with respect to the load axis (triplets T1-T4 in Fig. 10 Figure 10 shows how the martensite lattice is rotated by the activation of each twinning system. Out of these transformation twins, only the (001) compound twins (Fig. 9a, b) are formed by two LCV martensite variants, all other twins are always between one LCV variant and a transformation twin. Note that even (100) twining rotates the martensite lattice out of the set of 12 LCV lattices (Fig. 9c). Hence, when simulating the texture of self-accommodated martensite, we predict, in addition to poles T1-T4, also poles from all possible transformation twins. Since the orientation of the rotated lattice of martensite twins, however, is not far from the predicted poles T1-T4, the predicted texture is only slightly modified considering all transformation twins introduced in Fig. 11a.
To simulate martensite reorientation at low tensile stress, we assume that all twinning systems in Fig. 10 providing tensile strain into the load axis are activated, except of (001) twinning, which we know that it is suppressed, and (20-1) deformation twinning, which requires very high stress. The resulting texture of reoriented martensite is shown in Fig. 11b. To simulate plastic deformation, we resume activity of (001) compound twinning (detwinning) and (20-1) deformation twinning of the reoriented martensite. Additionally, we allow (100) twinning of already (20-1) twinned lattice which simulates the rolling over mechanism discussed in Sect. ''Plastic Deformation of B19 0 Martensite by Kwinking.'' The resulting simulated texture of plastically deformed martensite is shown in Fig. 11c. The simulated and experimentally determined texture of self-accommodated (Fig. 11a), reoriented (Fig. 11b), and plastically deformed (Fig. 11c) martensite is mutually compared by overlapping experimentally determined AD IPFs with theoretically predicted martensite poles.

Discussion
The stress-strain curve of the NiTi #1 wire deformed in martensite state at -90°C until fracture displays five stages (Fig. 8). Tensile deformation of NiTi in martensite state is assumed in the literature to proceed at first via detwinning of \011[ type-II twins in the reorientation plateau at low stress (stage II) and later followed by plastic deformation via combination of dislocation slip and twinning in martensite at high stress in stages IV and V. The self-accommodated and reoriented martensites are assumed to deform elastically in stages I and III. This state-of-theart view of NiTi deformation, although it is widely spread in the literature, is not consistent with the results of TEM and X-ray diffraction studies on nanocrystalline NiTi wire presented above.

Reorientation of Martensite
The four-fiber texture of self-accommodated B19 0 martensite changed into two-fiber texture of reoriented martensite between the strain states 2-3 of the tensile test (Fig. 8). This sharp change is due to the localized tensile deformation of the wire in the reorientation plateau. The texture of the reoriented martensite displays only two fibers-one strong fiber near (-103) plane normal direction on the left and one weak fiber near (103) plane normal direction on the right of the AD IPF (Fig. 8). This two-fiber texture varies only slightly with stress increasing in stage III (strain states [4][5][6][7][8], the intensity of the left fiber increases and right fiber decreases due to partial detwinning of (001) compound twins (see detailed analysis in [9]). At the same time, grains filled with single domain of (001) compound twins are observed in the microstructure of reoriented martensite by TEM (Figs. 3, 4, 5). The (001) compound twins do not disappear completely even during the plastic deformation of martensite (Fig. 5), though their amount in the microstructure of plastically deformed wire is much less.
One can easily understand from the orientation dependence of the transformation strain of B19 0 martensite (Fig. 12a) that martensite oriented with (-103) plane normal direction provides maximum strain into the load axis. If we assume that only martensite variants providing large tensile strain into the load axis form during the reorientation in tension within the abstraction of ideal \ hkl[ fiber-textured polycrystal, we would arrive to the conclusion that only martensite variants represented by the pole T2 near the (-103) plane normal direction remain in the microstructure of reoriented martensite. Comparing with the experimentally determined texture (Fig. 8) and microstructure (Fig. 4), however, this is evidently not the case. Clearly, there are two fibers in AD IPF and (001) compound twins remain in the microstructure of reoriented martensite.
The experimentally observed intensity distribution in AD IPF of reoriented martensite (Figs. 8, 11b) confirms that martensite variants with (-103) plane normal direction oriented into the load axis become dominant in the microstructure of reoriented martensite (left fiber centered at (-103) plane normal direction becomes strong and fibers near (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) and (120) plane normal directions disappear after tensile deformation within the reorientation plateau). But why there is that second weak fiber near (103) plane normal direction on the right side of the AD IPF of the reoriented martensite (Fig. 8), if the respective martensite variants covered by the T1 pole provide small compressive transformation strain -1.2% into the load axis (Fig. 10)? This is in agreement with the TEM observation of (001) compound twins in the reoriented martensite (Fig. 4). The increase of the intensity of the left fiber and decrease of the right fiber (Fig. 8) can be explained by the disappearance of relict domains combined with partial detwinning of (001) compound twins. A question, thus, appears why detwinning providing theoretically very large tensile strains into the load axis did not occur during the martensite reorientation in stage II and during further deformation in the stage III. There must be a reason for this.

Mechanism of Martensite Reorientation
Let us briefly discuss the martensite reorientation process based on the observed texture change between the selfaccommodated and reoriented martensites using the abstraction of ideal \hkl[ fiber-textured polycrystal. Looking at Fig. 10c, e, f, martensite reorientation process shall be associated with the activity of the \011[ type-II, {0-11} type-I, and/or {-1-11} type-I twinning during the tensile loading in the stage II. On the other hand, CVP laminates of those twins were never observed in the microstructure of the self-accommodated martensite by TEM. Self-accommodated martensite is (001) compound twinned. Hence, detwinning of CVPs containing \011[ type-II twins widely considered in the literature as a mechanism of the martensite reorientation process [18,19] does not apply for nanocrystalline NiTi wires. Nevertheless, the martensite lattice rotated during the reorientation from fibers near T4 poles towards fibers near T2 and T1 poles. This can only be accomplished only via \011[ type-II, {0-11} type-I, and/or {-1-11} type-I twinning. Therefore, we deduce that these misorientations must exist within the interdomain interfaces separating two neighboring (001) compound-twinned domains (Fig. 13). The interdomain interfaces move during the reorientation process (reorientation proceeding via shrinking of unsuitably oriented domains). We assume that interdomain interfaces move at low stress, based on the arguments similar to those expressed in the analysis of mobile twin interfaces in NiMnGa [48].
On the other hand, this mechanism still does not explain the observed lack of detwinning of (001) compound twins in stages II and III. Critical stress for detwinning is low [6], Schmid factor is near 0.5 in majority of grains (Fig. 12c), yet the grains of reoriented martensite remain (001) compound twinned up to the yield point. Mechanics of tensile deformation of NiTi polycrystalline aggregate containing such (001) laminated grains was analyzed in [9] and concluded that detwinning of (001) compound twins was suppressed by constraints on the cooperative deformation of grains via a single deformation mechanism in polycrystalline environment (see Appendix C in [9]). Since the reoriented martensite is (001) compound twinned, the use of the word ''detwinning'' as a synonym for ''martensite reorientation'' is not appropriate for nanocrystalline NiTi wires loaded in tension.

Comparison with Literature Results
Results of in situ neutron (x-ray) texture experiments focusing reorientation of B19 0 martensite in NiTi were reported in Refs. [12,22,23,[28][29][30]. Unfortunately, some authors used a different notation of martensite lattice parameters (monoclinic angle c and a \ c \ b) from that commonly used in crystallographic analysis of lattice defects in NiTi observed by TEM. We used this latter notation (monoclinic angle b and a \ b \ c). However, taking these different notations into account, the experimentally observed textures of reoriented martensite are similar to our results.
Two-fiber textures of the martensite reoriented in tension were observed in synchrotron X-ray texture evolution studies on thin nanocrystalline NiTi wires [22,23]. The interpretation was, however, quite different since detwinning of \011[ type-II twins was considered as the deformation mechanism of martensite reorientation [22]. This, however, contradicts the results of TEM observations evidencing lack of \011[ type-II twin laminates in the self-accommodated microstructure of martensite and presence of (001) compound twin laminates in reoriented martensite (Fig. 3). On the other hand, we cannot exclude activity of \011[ type-II twinning within the interdomain boundaries moving during the reorientation process. The observation of a single (-130) fiber (the weak intensity of the minor fiber was not admitted) at the yield stress was explained by conversion of \011[ type-II-twinned laminate to single-martensite variant followed by rigid body rotation of the martensite lattice during the martensite reorientation in [23]. That is again inconsistent with the observation of (001) compound twin laminates in reoriented martensite (Fig. 3). Moreover, it contradicts the character of the observed two-fiber texture of the reoriented martensite. The advantage of having both TEM and texture Fig. 14 (20-1) deformation twin is a prototype kwink. The (20-1) deformation twin is unique in that it displays very large twinning transformation shear (Fig. 9d) and brings about unrecovered strain. According to [49], the monoclinic lattice has to go through a complex pathway involving shear and shuffle to reach the twin configuration. Alternatively, same twin configuration can be reached by combination of (100) deformation twinning and kinking via coordinated [100](001) dislocation slip in martensite [38]. Shape strains and twin-orientation relationships are equal, the difference lies in local nature of the interface. The (20-1) kwink interface is not atomically sharp due to the randomness of [100](001) slip as can be seen in the HRTEM image on the right Fig. 15 Visualization of the rotation of martensite lattice and tensile strain in \111 [ A direction along the wire axis due to (001) and (100) compound twinning, (20-1) kwinking and kinking. The yellow lattice corresponds to martensite lattice fully oriented under tensile loading. It respects lattice correspondence to the austenite and monoclinic distortion of the martensite. The light blue lattice denotes austenite to which tensile strains relate. The dark blue lattice is the twinned martensite lattice within the bands. The (20-1) kwink combines (100) twin and kink. The red line shows a segment of a (001) plane that preserves its area under the action of all considered deformation mechanisms. Axial strains with respect to austenite (e tr ) and fully oriented martensite (De) are denoted on the top (Color figure online) results for analysis of deformation mechanism is evident from the above discussion.
Neutron texture experiments on bulk NiTi rods deformed [28][29][30] provided four-fiber texture of self-accommodated martensite and one broad fiber texture of reoriented martensite covering wide range of crystal directions around (010) pole ((001) in our notation). This is different from our observation of sharp two-fiber textures around the two redicted poles (Fig. 11b). Such texture can be rationalized by considering that bulk NiTi rods with large grains display less sharp austenite texture in comparison to the heavily hot-drawn and cold-drawn thin NiTi wires. Recall that the model prediction applies only for \111[ textured polycrystal and cannot be applied to the results obtained on such less textured polycrystals. Mutual comparison is, thus, difficult. Moreover, bulk NiTi rods with large grains might not contain (001) compound twins in the self-accommodated microstructure but \011[ type-II twins. As textures would be four-fiber type for both laminates, results of TEM observations of twins in microstructure of bulk NiTi rods would be needed for meaningful comparison with our results.

Plastic Deformation of B19 0 Martensite by Kwinking
When the wire was deformed further into the plastic deformation range in stage IV and V, martensite texture evolved further (strain states 8-12-18 in Fig. 8). While the intensity of the major T2 fiber near the (-103) plane normal direction decreased that of the minor T1 fiber near the (103) plane normal direction increased and shifted to the right towards the (101) normal direction. Results of TEM analysis of microstructure in plastically deformed wire (Figs. 3,5) show multiple (20-1) and (100) deformation twin and kink bands. Both results suggest that plastic deformation of martensite is due to massive reorientation of its monoclinic lattice which cannot be brought about by conventional dislocation slip only.

Mechanism of Plastic Deformation of Martensite
To interpret the observed evolution of the martensite texture in terms of activated deformation mechanisms, let us consider discontinuous rotations of the martensite lattice during the tensile deformation of the ideal two-fiber-textured martensite polycrystal associated with (i) detwinning of (001) compound twins (Fig. 10a), (ii) (100) deformation twinning (Fig. 10b), and (iii) (20-1) deformation twinning (Fig. 10g). The (20-1) deformation twinning is unique among the observed twinning modes in B19 0 martensite in three aspects. First, it is the only twinning system which can further reorient the optimally oriented martensite lattice (Fig. 10g) so that large tensile strain is obtained ( Fig. 12a, b). Second, it requires much higher critical stress that any other twinning systems [6]. Third, it gives rise to intrinsically unrecoverable strains, since it is assisted by the coordinated [100](001) dislocation slip in martensite [38]. Moreover, the [100](001) dislocation slip displays maximized Schmid factor for the martensite orientation along the (-103) plane normal direction (Fig. 12a-c).
The onset of plastic deformation manifested by appearance of (100) and (20-1) deformation twins in the microstructure of deformed wire gives rise to families of lattice correspondent martensite reflections (Fig. 6b) in diffraction patterns. The reflections denoted by ellipses are reflections from martensite lattice planes in deformation bands corresponding to a single austenite lattice plane. Since reflections corresponding to (100) twinning are always present in composite diffraction patterns of plastically deformed martensite, it appears that (100) deformation twinning is essential for its plastic deformation (see Fig. 5 in [9]). (100) deformation twinning indeed plays crucial role in the theoretical description [38] of plastic deformation of martensite by kwinking (Figs. 14, 15).
In texture evolution experiment (Fig. 8), plastic deformation is manifested by gradual change of the texture character-the intensity of the left fiber starts to decrease while that of the right fiber starts to increase and it moves rightwards. This texture evolution can be rationalized by lattice rotations due to (20-1) deformation twinning (Fig. 10g), (100) deformation twinning (Fig. 10b), and detwinning of (001) compound twins (Fig. 10a). The (20-1) deformation twinning provides very large tensile twinning strains (e tw = 19.6%) into the load axis direction and rotates the sample orientation from the solid cyan pole T2 near (-103) plane normal direction towards the dotted cyan pole near (101) orientation on the right side of the AD IPF (see Fig. A10 in Appendix A in [20] for detailed explanation).
Although  deformation twins were frequently observed in the microstructure of plastically deformed NiTi in the literature [2,6,9], general agreement on its atomic mechanism is still lacking in the literature. Ezaz et al. [49] proposed atomistic model for the (20-1) deformation twinning considering combination of homogeneous shear and shuffle (Fig. 14). Gao et al. [50] developed a theoretical framework that can be used to identify deformation twinning systems in the B19 0 martensite in NiTi, the activity of which leads to unrecoverable strains. In this framework, the (20-1) twin is generated through a ''nontransformation pathway'' giving rise to intrinsically irrecoverable mechanical twin in the monoclinic phase. Seiner et al. [38] treat the (20-1) deformation twin as a kwink, which combines (100) deformation twinning with [100](001) dislocation slip-based kinking (Fig. 14). Both (20-1) twin and (20-1) kwink give rise to same shape strains and same twin-orientation relationships. The difference is in the mechanism of creation and consequently in the local nature of the twin interface. The (20-1) kwink interface is not locally planar due to the randomness of [100](001) dislocation slip which assists in its creation [38].
However, besides the (20-1) deformation twin bands, there are also (100) deformation twin bands, kink bands, and more general kwink bands all sharing common [010] martensite axis within grains of NiTi wire deformed into the plastic range (Figs. 5, 6). This together with the observation of families of diffraction spots in composite diffraction patterns of plastically deformed martensite introduced above (Fig. 6b) represents experimental evidence for extensive kwinking deformation within the volume covered by the SAED area. Under no circumstances, these diffraction spots can be associated with 12 LCV martensite variants possibly forming from the austenite phase. In fact, most of the bands are not (20-1) twins but kwinks combining (100) deformation twinning and dislocation-based kinking. Lattice rotations from the martensite matrix towards the lattices within deformation bands explain the experimentally observed texture evolution (Fig. 8).
The [100](001) dislocation slip in martensite may also affect texture evolution as in any plastically deforming metal [6]. On the other hand, there is no experimental evidence for massive [100](001) dislocation glide in conventional sense during plastic deformation of B19 0 . It is due to the low symmetry of the monoclinic martensite phase, this slip system cannot operate alone during the plastic deformation of NiTi wire in tension. Conventional After deformation, the wire was unloaded and stress free heated up to 200°C. The BF images, SAED patterns, and STEM images were taken from wire deformed up to gradually increasing total strains. Although the figure shows lattice defects in austenitic microstructure, plastic deformation that generated these defects occurred in martensite. It is clear that the austenitic microstructure becomes gradually refined down to nanoscale. Number of diffraction spots in the diffraction pattern and their azimuthal spreading increase with increasing strain due to the increasing amount of austenite twins and misorientations among the austenite lattices present within the SAED area. See [36] for details on the observed lattice defects slip is also suppressed within the deformation-banded microstructure. Hence, we do not consider conventional slip in our analysis. We assume that [100](001) dislocation slip in martensite plays important role the plastic twinning deformation mechanism in the B19 0 martensite via kwinking [38]. An alternative view of kwinking deformation as [100](001) slip kinking mediated by (100) twinning is martensite (Fig. 15) may be even closer to the reality.
All deformation modes acting within each grain yield integrally tensile strains with respect to the (001) twinned domain of reoriented martensite. They include detwinning of (001) twins, (100) deformation twinning, kink banding, kwink banding, and [100]/(011) dislocation slip. All these deformation mechanisms rotate (twin) the martensite lattice around the [010] crystal direction (Fig. 15). This explains observation of bands and wedges in the microstructure of plastically deformed martensite (Figs. 5, 6) which can be analyzed only if each grain is tilted into the [010] zone in TEM [9]. As concerns the evolution of martensite texture during the plastic deformation (strain states 8-18 in Fig. 8), this explains why orientation distribution changes during the tensile deformation only within the [010] zone (i.e., why poles in AD IPFs denoting sample direction s ! move only in the (010) plane).
Although the (20-1) twinning strain is very large, it is still limited (19.6% in tension along the wire axis). Hence, we need to assume either massive dislocation slip or multiple twinning to explain plastic deformation of the wire up to 50-70% strain. We believe that the latter is happening. A rolling over deformation twinning mechanism was proposed in [9] to explain large plastic strains. The martensite lattice already rotated by the (20-1) deformation twinning into the (101) pole on the right side of the AD IPF (Fig. 10g) may undergo (100) deformation twinning (Fig. 10b), which produces 11.9% tensile strain into the load axis and rotates the martensite lattice back to the left side of the AD IPF, where it is again susceptible to the (20-1) deformation twinning under tensile stress. The (20-1) and (100) deformation twinning can, thus, roll over to achieve very large tensile strains.
Finally, the experiment shows that the plastically deformed martensite (Fig. 5) transforms back to the austenite upon the unloading and heating (Fig. 16). We still do not know how exactly the reverse transformation proceeds. There is experimental evidence in the literature suggesting that the (20-1) twins created during plastic deformation of B19 0 martensite are converted into {114} austenite twins upon the reverse martensitic transformation on unloading and heating [51]. We have shown that wedgeshaped martensitic microstructures frequently observed in plastically deformed martensite transform into wedge-shaped austenitic microstructures observed upon unloading and heating (Fig. 11 in [9]).
We propose that repeated kwinking deformation of the same crystal volume, as introduced for rolling over  and (100) deformation twinning (kwinking), leads to appearance of finer and finer kwink bands within the microstructure in grains of the wire deformed up to large tensile strains. This martensite microstructure reverse transforms upon unloading and heating into austenite microstructure containing large number of {114} austenite twins (Fig. 16). It is evident that NiTi wire is capable of deforming via kwinking in martensite at very high stress (* 1 GPa) with steady hardening up to very large plastic strain (* 50%) and that kwinking refines the austenitic microstructure of the wire down to nanoscale.

Comparison with Literature Results
Cai et al. [23] observed a similar texture evolution in their in situ synchrotron X-ray texture experiment on thin shape memory NiTi wire deformed in tension at room temperature from the 5% and 30% applied strain. The texture evolution, particularly the appearance of (110) fiber at large strains (Fig. 2 in [23]), was ascribed to the activity of (2-10) twinning ((20-1) deformation twinning in our notation) which is in accord with our interpretation. However, this explanation was not based on the analysis of the lattice rotations associated with the deformation twinning but merely relied on the existing literature evidence for the activity of (20-1) deformation twinning in plastic deformation of B19 0 martensite [2,8].
Stebner et al. [28][29][30], who performed neutron texture analysis of bulk hot-extruded NiTi bars deformed in tension and compression, observed decrease of the intensity of the broad [010] fiber ([001] in our notation) and its spreading towards the [110] direction ([101] in our notation) between 10 and 20% tensile strains. This texture evolution, in spite of being different from ours (Fig. 8), might have the same origin. The reason for the difference might be that the austenite texture of hot-extruded NiTi bars [28][29][30] is much weaker than the texture of the thin NiTi wire (see pole figures in Fig. 3 in [30]). The interpretation of the texture evolution during the tensile loading offered in [30] is different from ours, particularly in that the authors considered activity of multiple twinning systems and significant involvement of conventional dislocation slip during the plastic deformation. In a contrast, we consider only plastic deformation mechanisms which move the martensite lattice orientations within the [010] zone: detwinning of (001) compound twins, (20-1) deformation twinning, (100) deformation twinning, [100](001) dislocation slip, [100](001) kink banding, and the rolling over  and (100) deformation twinning in the late stages of the tensile test. All these deformation mechanism rotate the martensite lattice within the [010] zone, as observed in TEM studies [9]. Benafan et al. [52,53], who performed in situ neutron texture evolution experiments on bulk NiTi samples involving plastic deformation in tension (Fig. 4 in [53]) suggested that the (110) fiber ((101) fiber associated with the (20-1) deformation twinning in our notation) disappears on unloading at 14% strain (although at larger strains). This would mean that (20-1) deformation twins tends to detwin on unloading. Similar ''reversible (20-1) deformation twinning'' was reported also by Chen et al. [54], though the reported effect is small. Such reversible (20-1) deformation twinning apparently contradicts the above presented ideas on kwinking deformation and poses a challenge for further studies.

Conclusions
Deformation processes activated during tensile deformation of nanocrystalline NiTi wire in low-temperature martensite state were investigated by in situ synchrotron X-ray diffraction texture evolution studies combined with TEM analysis of martensite-variant microstructures in deformed wire.
Nanocrystalline \111[ A fiber textured NiTi wire in the self-accommodated martensite state contains martensitevariant microstructure consisting of multiple (001) compound-twinned domains in grains and displays four-fiber martensite texture.
Upon tensile loading in the reorientation plateau, this microstructure and texture evolve into microstructure of reoriented martensite characterized by single (001) compound-twinned domain in each grain and sharp two-fiber texture. It is concluded that martensite reorientation proceeds via motion of interdomain interfaces. Reorientation strains are nearly recoverable on unloading and heating. Martensite reorientation in the studied wire leaves behind very small unrecovered strains and very few dislocation defects in the austenitic microstructure of the deformed wire. Since the reoriented martensite is (001) compound twinned, martensite reorientation shall not be called ''detwinning.'' Upon tensile loading further into the plastic deformation range, very special martensite variant microstructures consisting of deformation twin bands and kink bands within the detwinned matrix are observed by TEM in grains of plastically deformed martensite and two-fiber texture of reoriented martensite gradually changes with increasing tensile strain into a different two-fiber texture of plastically deformed martensite. It is concluded that plastic deformation of B19 0 martensite proceeds via peculiar deformation mechanism consisting in (100) deformation twinning combined with [100]/(011) dislocation slip based kinking, which we call kwinking. Reverse martensitic transformation taking place upon unloading and heating leaves large unrecovered strains and high density of lattice defects in austenite. Significant strains up to 10% are recovered on unloading and heating. While the martensite matrix transforms into parent austenite, (20-1) deformation twins transform into {114} austenite twins. Plastic deformation of the NiTi wire by this deformation mechanism can proceed at high stresses * 1 GPa up to plastic strains * 50% at fracture and refines the austenitic microstructure of the wire down to nanoscale.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/.