Introduction

After full solution annealing, near equiatomic binary NiTi alloys show on cooling a one-stage thermoelastic martensitic transformation between the B2-structured austenite phase (A) and the B19′-structured martensite phase (M). With the presence of crystallographic defects (e.g., dislocation networks, coherent Ni4Ti3 precipitates), a thermoelastic transformation between the austenite phase and a rhombohedral R-phase has been frequently observed as an intermediate step before the formation of the final B19′ martensite phase during cooling [1, 2]. Dislocation networks and/or coherent Ni4Ti3 precipitates can be introduced by various thermomechanical treatments, such as post-deformation annealing [3], aging of Ni-rich NiTi alloys [4, 5] and thermomechanical cycling [6, 7]. Like the A ↔ M transformation, the A ↔ R transformation also shows shape memory effect and pseudoelasticity [8, 9]. Moreover, the A ↔ R transformation shows attractive properties, such as narrow thermal or stress hysteresis [10, 11], fast response to temperature change [1, 12, 13], as well as high functional stability during thermomechanical cycling [13–16]. Based on these unique properties, although the transformation strain is small (~1 %) [9, 17], various devices have been developed applying the A ↔ R transformation after proper structural design [18–22].

The R-phase transformation mechanism and the crystal structure of the R-phase have been well documented [1, 9, 23, 24]. However, there has been little discussion on how to control the R-phase transformation temperature, which is the crucial factor for practical applications. Some work has been carried out to investigate the evolution of the R-phase transformation temperatures with respect to annealing [3, 25], aging [26, 27], and thermal cycling conditions [7]. Unfortunately, to the best of our knowledge, the way to control the R-phase transformation temperatures has not been proposed. Moreover, frequently observed two- or multi-stage martensitic transformation may limit the practical application of the R-phase transformation, because the presence of B19′ martensite transformation will undermine the unique properties associated with the R-phase transformation (e.g., narrow hysteresis). Therefore, in order to fully utilize the potential of the A ↔ R transformation, the following two problems must be solved: (1) controlling the R-phase transformation temperatures and (2) separating the temperature domain of the R-phase and the B19′ martensite transformation.

This article reviews concisely our work on solving the above two problems [28–30], starting from investigating the effect of grain size on the transformation behavior of a Ti-50.8 at.% Ni alloy after low-temperature (523 K) aging treatment [30]. Afterward, an approach is proposed to control the R-phase transformation temperature and to suppress the B19′ martensite transformation by introducing nanoscaled Ni4Ti3 precipitates into the samples with micron-sized grains [28, 29].

Grain Refinement and Transformation Behavior

Multi-stage martensitic transformation has been frequently observed in solutionized Ni-rich NiTi alloys after aging treatment [26, 31–36]. Three-step transformations including two B19′ martensite transformations have been widely observed in Ni-rich NiTi alloys after aging at intermediate temperatures (673–823 K) [32–34]. After low-temperature aging, three-step transformations including two R-phase transformations were reported [26, 36]. The large-scale microstructural inhomogeneity, i.e., the different size and/or density of Ni4Ti3 precipitates between grain boundary region and grain interior, is considered as the main origin of the observed multi-stage martensitic transformation in aged Ni-rich NiTi polycrystals [32–34, 36]. The effect of grain boundaries, which is the main inducement for the inhomogeneous distribution of Ni4Ti3 precipitates in grains, has been emphasized [32, 36]. However, based on our knowledge, the influence of grain size on the aging microstructure and related multi-stage martensitic transformation has not been studied.

We focused on the transformation behavior of the samples with different grain size after low-temperature aging, because the nanoscaled Ni4Ti3 precipitates can be introduced by the low-temperature aging treatment [7, 26, 37]. The nanoscaled Ni4Ti3 precipitates can effectively improve the performance of NiTi alloys [37] as well as suppress the B19′ martensite transformation [26, 36].

In our work [30], a cold-deformed Ti-50.8 at.% Ni alloy was subjected to annealing at 973 K for different durations from 3 min to 24 h, in order to produce samples with different grain size. Figure 1 shows the microstructure of the annealed samples as captured by electron backscattered diffraction (EBSD) technique. Fully recrystallized equiaxed grains are obtained after annealing at 973 K for 3 min or longer. As indicated by the grain size distribution histograms, the main fraction of grains shifts to higher values with the increase in annealing time. The average grain size of the equiaxed grains increases from 5.6 to 21.7 µm with the increase in annealing time from 3 min to 24 h, as shown in Fig. 1i. All the annealed samples show identical transformation behavior with a single-stage A ↔ M transformation with the martensite transformation start temperature (M s) around 245 K [30].

Fig. 1
figure 1

Microstructure captured by EBSD and the histogram of grain size distribution of a Ti-50.8 at.% Ni alloy after annealing at 973 K for a and d 3 min; b and e 10 min; c and f 1 h; g and h 24 h. i The average grain size as a function of annealing time (Adapted after [30])

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After annealing at 973 K for different durations, all the annealed samples were further subjected to aging treatment at 523 K for 24 h. Figure 2 shows the transformation behavior of the aged samples, as characterized by both differential scanning calorimetry (DSC) and electrical resistance. The sample with average grain size of 21.7 µm shows a two-stage R-phase transformation, followed by a one-stage B19′ martensite transformation. The R-phase transformations with higher and lower temperatures are denoted as A ↔ R1 and A ↔ R2, respectively. The two-stage R-phase transformation is also revealed by the electrical resistance measurement, as shown in Fig. 2b, a two-step increase of the electrical resistance is observed in the samples with average grain size of 15.3 µm.

Fig. 2
figure 2

a DSC charts of a Ti-50.8 at.% Ni alloy with different grain size (obtained by annealing at 973 K for different durations) after aging at 523 K for 24 h (adapted after [30]). Electrical resistance curves of the Ti-50.8 at.% Ni alloy with average grain size of b 15.3 and c 5.6 µm after aging at 523 k for 24 h

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As indicated in Fig. 2a, the volume fraction of the A ↔ R1 transformation gradually increases, while the volume fraction of the A ↔ R2 transformation gradually decreases with the decrease in grain size. Although only the A ↔ R1 transformation is detected by DSC in the sample with average grain size of 5.6 µm, a two-step increase of the electrical resistance is observed (Fig. 2c), as the electrical resistance measurement provides a higher resolution on characterizing the transformation behavior. However, the second step, which relates to the A ↔ R2 transformation, is very small, indicating that only a small amount of material undergoes A ↔ R2 transformation in the aged sample with average grain size of 5.6 µm. Figure 2a also shows that the B19′ martensite transformation is gradually suppressed with the decrease in grain size, in terms of both transformation temperature and transformation heat.

The above findings indicate that the grain size can indeed affect the aging microstructure and related transformation behavior. This phenomenon can be understood based on the different precipitation behavior in grain boundary region and grain interior. It is generally accepted that, as compared with the grain interior, grain boundaries favor the formation of precipitates during aging treatment [32, 36]. As illustrated in Fig. 3a, as compared with the grain interior, the grain boundary region contains a higher density of precipitates, leading to a more intense Ni depletion in the matrix in the vicinity of grain boundaries. The R-phase transformation temperature depends strongly on the Ni concentration in the matrix [5, 36], and decreases rapidly with the increase in the Ni content. Therefore, A ↔ R1 transformation with a higher transformation temperature occurs in the grain boundary region, while the A ↔ R2 transformation takes place in the grain interior.

Fig. 3
figure 3

Schematic illustration of the aging-induced microstructure and related transformation in the samples with a coarse grains and b fine grains

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As shown in Fig. 3, the volume fraction of grain interior decreases for smaller grain size, so that less and less material undergoes the A ↔ R2 transformation. On the other hand, the volume fraction of grain boundary region, which contains a higher density of precipitates, gradually increases with the decrease in grain size, so that more and more material undergoes the A ↔ R1 transformation. The presence of coherent Ni4Ti3 precipitates gives rise to a strain field around the precipitates [38, 39], which can suppress the B19′ martensite transformation [1, 2]. As compared with the grain interior, the B19′ martensite transformation is more suppressed in the grain boundary region, as it contains a higher density of precipitates. Therefore, since the volume fraction of grain boundary region increases with the decrease in grain size, the gradual suppression of B19′ martensite transformation is provoked in samples with smaller grains.

Control of the R-phase Transformation and Related Mechanical Properties

The above findings inspired us to think about what will happen if grains are further refined. In our work [28, 29], a cold-deformed Ti-50.8 at.% Ni thin wire (50 µm in diameter) was subjected to recrystallization annealing at 873 K for 30 min. Fully recrystallized equiaxed grains are observed, as indicated by the EBSD map shown in Fig. 4. An average grain size of 1.7 µm was manually determined using the line intercept method. After annealing at 873 K for 30 min, the Ti-50.8 at.% Ni wire was further subjected to aging treatment at 523 K for different durations (from 1 to 500 h). Nanoscaled Ni4Ti3 precipitates were revealed using high-resolution transmission electron microscopy [28, 29]. Based on this observation, we can conclude that a Ti-50.8 at.% Ni alloy with micron-sized grains (average grain size 1.7 µm) and nanoscaled Ni4Ti3 precipitates was produced.

Fig. 4
figure 4

Microstructure captured by EBSD of a cold-deformed Ti-50.8 at.% Ni thin wire after annealing at 873 K for 30 min

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The transformation behavior of the aged samples was characterized using DSC and electrical resistance measurements, as shown in Fig. 5 [28]. The annealed sample shows a normal A ↔ M transformation with M s at 227 K. With the increase in aging time, the B19′ martensite transformation is significantly suppressed by the precipitation process. After annealing at 523 K for 4 h or longer, no distinguishable B19′ martensite transformation peak is detected by DSC both during cooling and heating, as shown in Fig. 5a. Only a small hysteresis is revealed by the electrical resistance measurement on cooling and heating (Fig. 5b) in the samples aged for 4 h or longer, indicating that only a small volume fraction of B19′ martensite is formed. The hysteresis between cooling and heating electrical resistance curves maintains unchanged even after cooling down to 14 K [28]. The R-phase transformation start temperature (R s) determined by DSC is presented as a function of aging time in Fig. 6. R s increases monotonously from 258 to 311 K with the increase in aging time from 1 to 500 h. The above findings show that controlling the R-phase transformation temperatures by aging time and suppressing the thermally induced B19′ martensite transformation can be achieved by introducing nanoscaled Ni4Ti3 precipitates in the sample with micron-sized grains.

Fig. 5
figure 5

a DSC and b electrical resistance curves of a T-50.8 at.% Ni alloy with an average grain size of 1.7 µm (obtained by annealing at 873 K for 30 min) after aging at 523 K for different durations. The shadowed area visualizes the variation of hysteresis of the transformation to B19′ martensite phase [28]

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Fig. 6
figure 6

Effect of aging time on the R-phase transformation start temperature (R s) of a Ti-50.8 at. % Ni alloy with an average grain size of 1.7 µm after aging at 523 K for different durations (Adapted after [28])

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The work output, which describes the capacity of actuators, associated with the A ↔ R transformation is evaluated for samples in the form of a single wire. As shown in Fig. 7a, the NiTi thin wires were firstly loaded to a pre-set stress of 200, 300, and 400 MPa, respectively, at 353 K. Afterward, the samples were subjected to thermal cycling between 353 and 273 K, and the strain-temperature response was recorded. The recoverable strain (ε) of the third cycle was used to calculate the specific work output (W) via the following equation:

$$W = \frac{{\varepsilon \times \sigma_{\text{constant}} }}{\rho },$$
(1)

where \(\sigma_{\text{constant}}\) represents the pre-set external stress (200, 300, and 400 MPa) and ρ is the density of NiTi alloys (6.45 g cm−3). The work output associated with A ↔ R transformation under different external stresses as a function of aging time is summarized in Fig. 7b. The sample subjected to a higher external stress shows a higher work output. Under the same external stress, the work output varies slightly with the increase in aging time. However, the working temperature increases monotonously with the increase in aging time. As shown in Fig. 7c, the start temperature of A → R transformation under different external stresses (\(R_{\text{s}}^{\sigma }\)) gradually increases with the increase in aging time, indicating a controllable working temperature of the R-phase transformation under external stresses.

Fig. 7
figure 7

a Representative cyclic strain-temperature response under different external stresses of a Ti-50.8 at.% Ni alloy (with an average grain size of 1.7 µm) after aging at 523 K for 500 h; b specific work output associated with the A → R transformation under different external stresses; c the A → R transformation start temperature under different external stresses (\(R_{\text{s}}^{\sigma }\)); d working windows of the A → R transformation under the external stress of 400 MPa (\(T_{\text{window}}^{\sigma 400}\)) as a function of aging time. Inset in (d) shows an example of how to determine the working window. (Adapted after [29])

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Figure 5 shows that the thermally induced B19′ martensitic transformation can be significantly suppressed by introducing nanoscaled Ni4Ti3 precipitates in the sample with micron-sized grains. However, the B19′ martensite transformation can occur with the assistance of external stress. As shown in the inset in Fig. 7d, with an external stress of 400 MPa, the R-phase transformation of the sample aged for 500 h starts at 327 K (\(R_{\text{s}}^{\sigma 400}\)), with further cooling, the B19′ martensite transformation occurs at 248 K (\(M_{\text{s}}^{\sigma 400}\)). The temperature interval between the R-phase and B19′ martensite transformation under a fixed stress is defined as the working window \(T_{\text{window}}^{\sigma }\) for A ↔ R transformation, which describes to what extend the influence from B19′ martensite can be avoided. The working window under an external stress of 400 MPa (\(T_{\text{window}}^{\sigma 400} = R_{\text{s}}^{\sigma 400} - M_{\text{s}}^{\sigma 400}\)) as a function of aging time is presented in Fig. 7d. \(T_{\text{window}}^{\sigma 400}\) increases from 57 to 81 K with the increase in aging time from 4 to 24 h. With further increase in aging time from 24 to 500 h, \(T_{\text{window}}^{\sigma 400}\) remains essentially constant and varies between 78 and 83 K.

With the decrease in the applied stress, an increase in the working window is expected. The \({\text{d}}\sigma /{\text{d}}T\) value, as described by the Clausius–Clapeyron-type relation between the critical stress and temperature for stress-induced martensitic transformation [40], is higher for a stress-induced R-phase transformation (13–18 MPa K−1 [10, 14, 41]) than for a stress-induced B19′ martensite transformation (5–8 K MPa−1 [10, 41, 42]). Therefore, with the decrease of the applied external stress, the stress-induced B19′ martensite transformation shifts to lower temperatures faster than the stress-induce R-phase transformation, as illustrated in Fig. 8. As a result, the working window increases with the decrease in the applied stress, i.e., \(T_{\text{window}}^{\sigma 2}\) is larger than \(T_{\text{window}}^{\sigma 1}\), provided that \(\sigma 1\) is larger than \(\sigma 2\). The large working windows ensure that the sample can work safely in the A ↔ R transformation state, without the interference from the B19′ martensite transformation.

Fig. 8
figure 8

Schematic illustration of the variation of the working window with respect to the change of applied stress. \(T_{\text{window}}^{\sigma 1}\) and \(T_{\text{window}}^{\sigma 2}\) represent the working window at a higher and lower applied stress, respectively. SIM and SIR stand for stress-induced B19′ martensite and stress-induced R-phase transformation, respectively

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When the shape recovery from the R-phase and/or B19′ martensite phase is impeded, a recovery stress can be generated during heating, due to the reverse transformation [12, 43]. As compared with the M → A (or M → R) transformation, the R → A transformation can be beneficially used to produce recovery stress with a higher recovery rate (e.g., 17 MPa K−1 [12]). The recovery stress associated with the R → A transformation was measured via the following procedure: (1) loading the sample to a strain of 1.2 % at a temperature 20 K below the R-phase transformation finish temperature (R f, determined from DSC results in Fig. 5a); (2) unloading the sample to 0 MPa, leaving some residual strain due to the R-phase reorientation [12]; and (3) fixing the clamps after unloading and increasing the temperature up to 373 K. The stress-temperature response was recorded, as shown in Fig. 9a. \(A_{\text{s}}^{\varepsilon }\) and \(A_{\text{f}}^{\varepsilon }\) represent the start and finish temperature of the R → A transformation under the constrained condition.

Fig. 9
figure 9

a Representative constrained cyclic stress-temperature response of the Ti-50.8 at.% Ni alloy (with an average grain size of 1.7 µm) after aging at 523 K for different durations; b maximum recovery stress and recovery stress rate as a function of aging time; c the reverse transformation (R → A) temperatures under constrained condition (\(A_{\text{s}}^{\varepsilon }\), \(A_{\text{f}}^{\varepsilon }\)) as a function of aging time (Adapted after Ref. [29])

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With the increase in aging time from 4 to 500 h, the maximum recovery stress gradually increases from 252 to 374 MPa, as presented in Fig. 9b. The observed recovery stress rate increases from 8.3 to 11.5 MPa K−1 with the increase in aging time from 4 to 24 h. With further increase in aging time from 24 to 500 h, the recovery stress rate varies between 10.6 and 12.4 MPa K−1, as shown in Fig. 9b. Although the observed recovery stress rate is lower than the previously reported value (17 MPa K−1 [12]), it is much higher than the recovery stress rate associated with the B19′ martensite transformation. Most importantly, the actuating temperature range, which is defined as the temperature range between \(A_{\text{s}}^{\varepsilon }\) and \(A_{\text{f}}^{\varepsilon }\), gradually shifts to higher temperatures with the increase in aging time, as shown in Fig. 9a, c. While also both \(A_{\text{s}}^{\varepsilon }\) and \(A_{\text{f}}^{\varepsilon }\) monotonously increase with the increase in aging time (Fig. 9c), indicating that the working temperature range, in which the A → R transformation produces high recovery force, can be controlled by aging time.

Conclusions

The work on improving the applicability of the R-phase transformation is concisely reviewed. After investigating the effect of grain size on the aging microstructure and related transformation behavior of a Ti-50.8 at. % Ni alloy after low-temperature (523 K) aging treatment, an approach is proposed to (1) control the R-phase transformation temperatures and (2) separate the temperature domain of the R-phase and B19′ martensite transformations, which are the two crucial issues limiting the application of the R-phase transformation. This approach consists in introducing nanoscaled Ni4Ti3 precipitates in a Ti-50.8 at.% Ni alloy with micron-sized grains (average grain size of 1.7 µm). As a result, the A ↔ R transformation shows a high recovery stress and a high work output with a large working window. Moreover, the transformation temperature of the A ↔ R transformation under both constant stress and constrained strain conditions can be controlled by aging time. This indicates that the R-phase transformation can be efficiently used in appropriate devices.