Tensile Deformation of B19′ Martensite in Nanocrystalline NiTi Wires

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/mm³, 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′ 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′ transformation with characteristic transformation temperatures M_s = 63 °C, A_f = 93 °C.

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 close-loop 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. Stress–strain–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). Stress–strain 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′ transformation are shifted ~ 100 °C in temperature). Plastic deformation line σ^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 σ^UP and plastic deformation line σ^Y meet. The reason is that the martensite stress that has been induced at high stress starts to deform plastically, as investigated and concluded in [37].

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. Reconstructed microstructures are characterized by (i) “composite diffraction pattern” providing information on orientations of all martensite-variant lattices within the SAED volume (multiple color coded overlapping diffraction patterns) and (ii) color map visualizing location, size, and orientation of each martensite variant within the grain (Figs. 3, 4, 5, 6) determined through DF imaging. Martensite-variant microstructures in grains evolve during tensile test. Microstructures observed in all grains in a TEM lamella are characteristic for given stage of the tensile test (see Fig. 5 in [9]). The analyzed martensite variant microstructures in grains are qualitatively similar, if they are viewed in proper low-index zone axis. This is consequence of the activated deformation mechanisms. Lattice defects created by tensile deformation in martensite state are additionally observed in the austenite state on the TEM lamella heated above the A_f temperature (dislocations and austenite twins).

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 µm 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 (a₀ = 0.301 nm) and product monoclinic B19′ martensite (a = 0.289 nm, b = 0.412 nm, c = 0.462 nm, and β = 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 martensite-variant 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 self-accommodated B19′ 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′ Martensite by Kwinking”) that the B19′ 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. 6e–i. While (001) compound twin interface (Fig. 6e) is atomically sharp, (20-1) deformation twin (Fig. 6g) shows irregular wavy interfaces [see white rectangle in (g)]. Most of the observed interfaces are actually (20-1) kwinks with lattice misorientations and interface plane slightly deviating from the twinning geometry. Results of detailed HRTEM analysis of kwink interfaces in this microstructure will be reported separately. The interface analyzed in Figs. 6k–m is kink band interface. The blue and magenta lattices in (Fig. 6m) are only slightly rotated around the [010] zone axis. Kink band interface is roughly parallel to the (100) lattice planes of the matrix.

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 × 150 μm². A Pilatus3 X CdTe 2 M detector (active area of 253.7 (W) × 288.8 (H) mm² and pixel size of 172 × 172 μm²) 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 CeO₂ standard ring pattern was used to calibrate the beam center, sample-to-detector distance, and detector tilt (roll, pitch, and yaw). An azimuth (η) 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 (2θ) coordinates with 2θ spacing from 0.34562° to 18.12745° to include main reflections. All ring patterns were segmented into Δη = 2° slices such that each recorded 2D diffraction pattern yields 111 radially integrated 1D diffraction spectra of 2θ versus total X-ray intensity. Thus, each 1D diffraction spectrum provides orientation-specific information on the microstructure within the gage volume within ± 1° angle around the corresponding azimuth angle. The set of 1D diffraction spectra from the \({\text{CeO}}_{2}\) 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 \({\text{CeO}}_{2}\) 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 (\({\text{D}}_{\text{ij}}\) 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 2θ 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 martensite lattices in self-accommodated microstructure, there are multiple fibers in AD IPF of martensite. Whole projections of martensite AD IPFs are shown in Fig. 7, later on, only half of the AD IPFs are shown to save space. The intensity of fibers in AD IPF, 45° IPF, and TD IPF (transverse direction) are cross related. The poles in AD IPF correspond to arcs in 45° IPF (45° vs. load axis) and TD IPF (transverse direction). The maxima in 45° IPF and TD IPF appear at directions, where the arcs cross each other.

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 stress–strain 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 two-fiber 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 two-fiber texture evolved further so that the intensity of the left fiber decreased and that of the right fiber increased and moved rightwards and settled close to pole (101). Evolution of the martensite texture during the tensile test will be discussed in Sect. “Discussion” based on the theoretical framework outlined in Sect. “Theoretical Prediction of Martensite Texture Evolution from Calculated Discontinuous Lattice Rotations Due to Twinning in Martensite”.

The experimentally determined texture of the wire in austenite state (Fig. 7) is approximated by a simplified texture of ideal single <111>_A fiber-textured austenite polycrystal having all grains equally oriented with <111> direction along the wire axis (representative sample direction \(\overrightarrow {s}\)) and random distribution of crystal orientations in radial directions. The texture of such idealized polycrystal is characterized by <111> pole in AD IPF and rings in 45° IPF and TD IPF. In response to cooling or mechanical loading, this ideal single <111> _A fiber-textured model austenite polycrystal undergoes B2 = > B19′ martensitic transformation. Assuming that 12 lattice correspondent variants (LCV) of monoclinic martensite may be created from the <111>-oriented austenite lattice and austenite and martensite lattices obey the B2-B19′ lattice correspondence (see 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). Since the real austenite wire shows spread of crystal lattice orientations around the <111> direction, there are fibers (intensity surrounding poles) in AD IPFs. See Figs. A5 and A6 in Appendix A [20] for more detailed explanation why this four-fiber martensite texture forms on cooling from the <111>_A fiber textured austenite.

However, these 12 LCV martensite variants may undergo wide range of transformation and deformation twinning including (001) and (100) compound twinning, {011} Type I, {111} Type I, {-1-11} Type I, and <011> Type-II transformation twinning and (20-1) plastic deformation twinning. 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′ 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.

The four-fiber texture of self-accommodated B19′ 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 4–8), 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′ 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 (1-20) 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.

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.