Introduction

It was clearly shown that the mechanical and functional properties of metals nanostructured using the severe plastic deformation approach are significantly higher than those of their micro- and submicro-grained counterparts [1, 2]. The same trend was also observed in Ti–Ni shape memory alloys where different nanostructures can be created in high-temperature B2-austenite phase as a result of post-deformation annealing (PDA) after severe deformation by high-pressure torsion [3–7], cold rolling (CR) [8–13], and cold drawing [14–16] techniques.

The structure formation features observed by transmission electron microscopy in cold-rolled and then annealed Ti–Ni alloys can be classified as a function of deformation intensity [11–13, 17]. In the range of moderate true strains (up to e = 0.3), a well-developed dislocation substructure forms. In the e = 0.5–1.2 strain range, this dislocation substructure is gradually replaced by a mixed amorphous and nanocrystalline structure, and when e ≥ 1.2, the structure is mainly amorphous. Similar trends are observed in the case of Ti–Ni alloys subjected to high-pressure torsion.

Note however that remnants of nanocrystalline structure are still present in the cold-rolled alloys after the highest applied strains of e = 2. In the high-pressure torsion-processed alloys, areas containing highly dislocated substructure and nanocrystalline structure are still observable after e  ~ 3, ~10, and even e ≥ 10 [5, 6, 18, 19], the latter possibly being a result of the cyclic amorphization–crystallization phenomena accompanying severe plastic deformation [ 20, 21].

During PDA, the above-mentioned structures undergo specific structural changes: in the highly dislocated substructure, recovery, polygonization (which includes subgrain formation and growth), and finally recrystallization occur; the grains of the deformation-induced nanocrystalline structure grow, the amorphous phase crystallizes, and the crystallized nano-sized grains grow alongside their deformation-induced counterparts [11–13, 15–17]. Note that individual groups of nano-sized subgrains can still be found in the latter case [5].

The observed nanostructure gradation into “nano-grains” and “nano-subgrains” is based on the well-understood difference between the nature of grains and subgrains: the term “grain” implies structure elements surrounded by high-angle boundaries (the misorientation angle >15°), whereas the term “subgrain” implies structure elements surrounded by low-angle dislocation boundaries, or subboundaries. The nature of the parent phase boundaries is an essential factor affecting the transformation and mechanical behavior of shape memory alloys. The low-angle boundaries (i.e., subgrain boundaries, subboundaries) are directly inherited by growing martensite crystals and serve as partially permeable barriers for dislocation slip, while high-angle boundaries (grain boundaries) are non-permeable barriers for both the martensite crystals and dislocations [22]. As concerned with the functional properties, an outstanding combination of high recovery stress and completely recoverable strain can be obtained in the case of B2-austenite structure consisting of nano-sized grains [11, 12, 17], while the best functional fatigue properties can be observed in the case of a mixed B2-austenite structure containing nano-sized grains and nano-sized subgrains [17]. The nanostructure containing exclusively nano-sized subgrains exhibits the lowest performance from the static and fatigue functional properties points of view [11, 12, 17].

Even though the described structure changes in deformed and annealed Ti–Ni alloys are obvious and logical, some discrepancies exist in their interpretation. For example, the term “nano-grain”, rather than the more accurate “nano-subgrain”, is frequently used when describing all nano-sized structure elements formed during PDA of Ti–Ni alloys after low-to-moderate deformation (e ≈ 0.5) [10, 23, 24], or even structures directly resulting from cold deformation of moderate intensity [ 24]. The same misleading appellation is also frequently used to describe the martensitic transformation features in nanostructured Ti–Ni alloys [ 25, 26].

The objective of this work is to illustrate, by means of quantitative transmission electron microscopy study, the difference in nanostructure types formed in Ti–Ni shape memory alloys subjected to CR and PDA and to determine the initial CR strain range for transition from one type to another.

Experimental

The Ti–50.26 at.%Ni alloy wire samples were homogenized at 700 °C (1 h), water-cooled, and thermomechanically treated: 0.9 and 2.5-mm-diameter wires (the latter only in the case of e = 0.3) were cold-rolled in several passes with a logarithmic strain ranging from e = 0.3–1.9. The samples of the deformed material were then annealed at 400 °C (1 h), and water-cooled to room temperature. Thin foils for electron microscopy study were prepared by electrolytical thinning of cut samples in HClO4 and CH3COOH solutions.

The following structure parameters taken from bright field (BF) and dark field (DF) images and selected area electron diffraction patterns (SAEDPs) were treated, using the statistical metallography procedures, to collect the following quantitative data:

  • BF images the average grain/subgrain size (AS) obtained by measuring an average distance between boundaries/subboundaries; i.e., any boundary is taken into consideration.

  • DF images (1) the visible surface areas occupied by nano-sized subgrains (F NSS) (not to be confused with their volume fractions), and (2) the average size of the individual regions occupied by the nano-sized subgrains (L NSS). The DF images were taken in each case from the most intensive part of the diffraction ring or arc.

  • SAEDP the fraction of various types of SAEDP: N I (mainly nano-sized subgrains), N II (nano-sized subgrains and grains), and N III (mainly nano-sized grains). To ensure more representative statistics, the SAEDPs produced in this study were completed by the SAEDPs obtained in our earlier works on binary Ti–Ni alloys of different compositions but subjected to identical thermomechanical treatments. This methodology is deemed adequate since SAEDPs keep their particular features up to the recrystallization temperature, the latter occurring in this alloy in the 450–550 °C temperature range, depending on the alloy’s composition and thermomechanical history [11, 12, 27]. The selected area diameter was 1 μm.

The histograms of the AS and L NSS distributions were built using the linear intercept method: 508–542 linear intercepts for AS and 60–127 linear intercepts for L NSS, both in the 5–10 random independent fields range per treatment. As for F NSS, it was calculated using the point-counting method with 2251–2844 points in the 8–13 random independent fields range per treatment. From the histograms, the average parameter value and its confidence interval with a 95 % probability were calculated. The N I, N II, and N III fractions were determined by a direct classification of 11–22 SAEDPs per treatment.

Results and Discussion

To perform this study, the CR strain range of e = 0.3–1.9 is chosen to cover a large spectrum of deformation-induced structures: from the highly dislocated substructure to the mixed amorphous and nanocrystalline structure. The PDA temperature of 400 °C is then selected to ensure the best direct visibility of nanostructure elements. Note that the structures formed as a result of such a PDA allow an unambiguous assessment of the preceding deformation-induced structure formation processes. Indeed, the nano-sized subgrains form as a result of polygonization of a highly dislocated substructure resulting from the low-to-moderate deformation intensities, whereas the nano-sized grains are the result of two simultaneous processes: crystallization of the amorphized material and growth of the deformation-refined nano-sized grains.

The main phase under consideration is B2-austenite. Other phases, which can simultaneously be observed at room temperature, either inherit B2-austenite substructure and misorientations (B19′ and R martensites) or affect its transformation kinetics upon cooling and heating (Ti3Ni4 phase).

Before presentation and discussion of the results, an important terminological assumption is proposed. Since a clear source of the discrepancies in the nanostructure elements interpretation is the plural meaning of the commonly used term “nanocrystalline structure” or NCS, we propose to reserve this term to designate nano-sized grain structure only, while applying different term, “nanosubgrained structure” or NSS, to designate nano-sized subgrain substructure. (Moreover, if the size of the regions consisting of nano-subgrains exceeds 100 nm [13, 28], these regions should be regarded as submicrocrystalline.)

The results of the statistical investigation of the nanostructure parameters are considered below in the following sequence: BF image, then DF image, and finally, SAEDP parameters.

The typical BF nanostructure images are presented in Fig. 1a–d. It can be seen that the nanostructures observed after different CR strains, but subjected to identical annealing conditions, are visually hardly distinguishable on these images. Only in the case of the lowest initial CR strain, e = 0.3 (Fig. 1a), the regions with high dislocation density are observed more frequently, and, sometimes, they look like regions of an incompletely recovered dislocation substructure. In other words, one cannot conclude on whether these are grains (high-angle grain boundaries) or subgrains (low-angle subboundaries). The only conclusion that can be drawn from the results of the statistical analysis presented in Fig. 3a is that when CR strain increases from 0.3 to 1.0, the grain/subgrain size decreases from ~45 to ~35 nm gradually and becomes stable at higher strains.

Fig. 1
figure 1

Typical nanostructures in cold-rolled and annealed at 400 °C (1 h) Ti–50.26 at.%Ni alloy. Initial CR strain: a, e e = 0.3; b, f 0.75; c, g 1.5; d, h 1.9. a–d bright field, e–h dark field images

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Typical DF nanostructure images are presented in Fig. 1e–h. Two types of bright structure elements are observable there: (1) individual grain-like elements which do not border on other bright elements and (2) bright regions which themselves represent a group of many (at least, two) neighboring grain-like structure elements. In accordance with the definitions given above, the first type of the DF image-observed features should be considered as grains, and the structure consisting of such grains described as NCS. Conversely, the second type of the DF image-features should be considered as regions containing closely oriented nano-sized subgrains (a polygonized, or subgrained, dislocation substructure, or NSS).

The examples of DF images of Ti–50.26%Ni alloy annealed at 400 °C (1 h) after CR (e = 0.3–1.9) are presented in Fig. 1e–h to illustrate a gradual replacement of NSS by NCS with increasing CR strain. This visual impression is confirmed by the results of the statistical analysis of the DF images in Fig. 3b and showing a significant decrease in the NSS area fraction when CR strain increases from 0.3 to 1.9. This replacement of NSS by NCS is accompanied by a permanent decrease in the average size of NSS regions which transits from a submicro- to a nanoscale range (Fig. 3c). The subgrain and grain sizes were not measured from the DF images because not all the subboundaries and grain boundaries were clearly visible. The following important observation should be emphasized: NSS does not vanish even when the highest CR strain of e = 1.9 is applied, whereas the NCS is already observable even for the lowest CR strain of e = 0.3.

The main types of SAEDPs are presented in Fig. 2. These three SAEDP types are characterized as follows:

Fig. 2
figure 2

SAEDP types in nanostructured Ti–Ni alloys: a, b Type I; c, d Type II; e, f Type III (see detailed description in the text). Examples of typical B2, R and B19′ reflections are indicated by arrows. A set of overlapping arc reflections embraced by the square bracket in (b) consists of 110B19′, 002B19′, \( 11\bar{1}_{{{\text{B19}^{\prime}}}} \), 330R, 110B2, \( 3\bar{3}0_{\text{R}} \), 020B19′, 111B19′, sequentially

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Type I (Fig. 2a, b): arc-shaped fragmented or non-fragmented B2-phase reflections with low-angle (<15°) azimuthal broadening (mainly NSS). These reflections can be accompanied by rare individual B2-phase point reflections from NCS distributed along a ring (Fig. 2b). Reflections of other phases (R, B19′), which preserve an orientation relationship with B2-austenite, possess the same shape.

Type II (Fig. 2c, d): arc-shaped intensive B2-phase reflections with high-angle (>15°) azimuthal broadening superposed on point reflections scattered along a ring (mixed NSS+NCS). Note that the arc-shaped reflections observed in this study, as well as in many other studies, indicate a rolling texture, which is {111}B2 in most cases. However, it should be emphasized that a decision on the nature of the related reflecting structure elements, whether they are grains or subgrains, can be taken only after examination of the corresponding DF images.

Type III (Fig. 2e, f): more or less uniform point ring (mainly NCS).

The examples of SAEDPs of Ti–50.26 at.%Ni alloy annealed at 400 °C (1 h) after CR strain ranging from e = 0.3–1.9 illustrate a continuous transition from NSS to NCS when CR strain increases (Fig. 2b–f). The SAEDPs presented in Fig. 2b–d, f correspond to the areas shown in Fig. 1a–d, respectively. Figure 2a presents Type I SAEDP free of the superposed B19′-martensite reflections (it belongs to equiatomic Ti–Ni alloy annealed at 300 °C (1 h) after CR (e = 0.3) [11]).

The mentioned regularity follows from the results of the statistical analysis of the SAEDPs presented in Fig. 3d, which clearly shows a transition from the SAEDP Type I through the SAEDP Type II to the SAEDP Type III, with CR strain increasing from 0.3 to 1.9.

Fig. 3
figure 3

Nanostructure parameters after PDA versus initial CR strain: a average subgrain/grain size in BF images (AS), b visible fraction of DF image area occupied by NSS (F NSS), c average size of NSS region evaluated from DF images (L NSS), d fraction of a given SAEDP type (N). a–c for Ti-50.26 %Ni alloy after PDA at 400 °C (1 h); d summarized data for Ti-50.26 %Ni alloy after PDA at 400 °C (1 h), and Ti-50.0 and Ti-50.7 %Ni alloys after PDA at 200–450 °C, 1 h). Combined data for e = 0.75 and 1.0 are shown in d at e = 1.0, and for e = 1.2 and 1.5 in d at e = 1.5

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The parallel analysis of the BF, DF, and SAEDP images allows us to confirm that the structures, resulting either from cold deformation of Ti–Ni SMA with low-to-moderate strains (0.3–0.5) or obtained during annealing after such deformations, cannot be regarded as truly nanocrystalline, i.e., consisting of nano-sized grains exclusively. If they are considered directly after deformation, these structures represent a mixture of highly dislocated, nanocrystalline and amorphized regions. When they are observed after PDA, these structures represent a mixture of nanosubgrained and nanocrystalline structures. (The latter definition is only valid if the annealing temperature is low enough to avoid recrystallization or growth of the nanosized grains and subgrains beyond the nanometric scale.)

Conclusions

In conclusion, the results of the statistical analysis unambiguously indicate that

  1. (1)

    There are two types of nanostructures formed in Ti–Ni shape memory alloys as a result of PDA after cold deformation: (a) a nanosubgrained structure which consists of closely oriented subgrains separated by low-angle dislocation boundaries (subboundaries) formed as a result of polygonization of the initially highly dislocated substructure; (b) a nanocrystalline structure, which consists of grains separated by high-angle boundaries (grain boundaries) formed as a result of growth of the deformation-induced nano-grains and of the nano-grains formed as a result of crystallization of the amorphous phase.

  2. (2)

    The formation of specific nanostructures during PDA depends on the initial cold work intensity (case of CR): when CR logarithmic thickness reduction increases from e = 0.3 to 1.9, the nanosubgrained structure gradually transforms to the nanocrystalline structure. After CR of low-to-moderate intensity (e = 0.3,…,0.5), the structure is mainly nanosubgrained. After CR of moderate-to-high intensity (e = 0.5,…,1.0), the structure is mixed (nanosubgrained+nanocrystalline). Finally, after high-intensity, or severe, CR (e = 1,…,2), the structure is mainly nanocrystalline.

  3. (3)

    The PDA after CR in the applied CR strain range does not result in the formation of “pure” nanosubgrained or nanocrystalline structures. Traces of the nanocrystalline structure are already observed for the true strains as low as e = 0.3, whereas traces of the nanosubgrained structure are still present for the true strains as high as e = 2.