Introduction

Shape-memory alloys (SMAs) are attractive class of functional materials with unique properties (e.g., shape-memory effect and superelasticity, SE) owing to their ability to undergo a thermoelastic martensitic transformation [1]. Very high strains, work outputs, and low hysteresis in actuation in addition to noise reduction and vibration damping are some outcomes of the SMAs [2–4]. They are also lightweight, frictionless, and easy to inspect [5–7]. Among the SMAs, NiTi alloys are the center of attention due to their good functional and mechanical properties [8, 9]. Thus, NiTi alloys have been used in numerous applications in many industries including automotive, aerospace, oil–gas [10], medical [11–13], construction, and seismic protection [11, 14].

However, the most studied NiTi system, near-equiatomic NiTi alloys, have certain disadvantages such as low transformation temperatures (TTs) (<100 °C) and strength (<700 MPa) [5, 15], which preclude their use in applications requiring high temperature and high strength. Hence, ternary alloying is employed to improve its shape-memory properties, where several NiTi–X (X = Pd, Hf, Pt, Zr) alloy systems have been investigated to date [16]. NiTiHf alloys are of high interest due to increased TTs and the lower cost of Hf compared to other precious metals [17] of Pd and Pt. However, there are also several disadvantages of Ni-lean NiTiHf alloys such as large thermal hysteresis (results in additional energy requirements and cycle time in actuator applications), poor thermal stability, brittleness, and low strength impeding their superelastic behavior [18]. All together, these shortcomings seriously limit the potential of Ni-lean NiTiHf alloys for practical applications. However, it has been recently demonstrated that precipitation-hardened Ni-rich NiTiHf alloys are promising alloys for high-temperature applications since they have high TTs, high strength, and low thermal hysteresis [19, 20].

Quaternary alloying can also be employed to alleviate the aforementioned limitations in the ternary alloys. Previously, shape-memory properties of Ni45.3Ti29.7Hf20Pd5 (at.%) were investigated as functions of aging temperature and time in polycrystalline [21] and single crystal [22–24] forms. It was shown that the [111]-oriented solutionized single crystals show superelastic behavior under extremely high stress levels (2.5 GPa) with low plastic deformation in addition to a very large damping capacity (44 J cm−3) due to a very wide mechanical hysteresis (>1200 MPa) [22]. The aged Ni45.3Ti29.7Hf20Pd5 polycrystalline has recoverable shape-memory strain of up to ~4 % under 1000 MPa, while [111]-oriented Ni45.3Ti29.7Hf20Pd5 single crystals exhibited ~2 % strain at stress levels as high as 1500 MPa [24].

Previously, shape-memory properties of a homogenized Ni45.3Ti39.7Hf10Pd5 (at.%) alloy system were reported [25], where transformation strain of up to 4.6 % and work output of up to 29 J cm−3 were obtained from strain–temperature responses. Ni45.3Ti39.7Hf10Pd5 showed a perfect superelastic behavior at 90 °C with recoverable strain of 4.3 %. It was also determined that the Ni45.3Ti39.7Hf10Pd5 alloy could develop two-way shape-memory strain of 1.6 % after thermal cycling under stress experiments [25]. In this study, in order to reveal the effects of Hf content on the shape-memory properties of NiTiHfPd alloys, the shape-memory behavior (including two-way shape-memory effect, TWSME) and superelastic responses of homogenized Ni45.3Ti34.7Hf15Pd5 and Ni45.3Ti29.7Hf20Pd5 (at.%) polycrystalline SMAs were investigated in compression, and they were compared to the homogenized Ni45.3Ti39.7Hf10Pd5 alloys.

Materials and methods

The arc melting method was used to fabricate the Ni45.3Ti34.7Hf15Pd5 and Ni45.3Ti29.7Hf20Pd5 (at.%) alloy ingots, starting with high-purity elemental constituents; [99.98 wt% Ni; 99.995 wt% Pd, 99.95 wt% Ti and 99.7 wt% Hf (excluding Zr, which is nominally 3 %)], Ni45.3Ti39.7Hf10Pd5, Ni45.3Ti34.7Hf15Pd5, and Ni45.3Ti29.7Hf20Pd5 alloys will be referred as NiTiPd–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf, respectively, throughout the text for brevity. The ingots were homogenized at 900 °C for 72 h in vacuum followed by a furnace cooling process. Compression samples (4 × 4 × 8 mm3) were electro-discharge machined from the homogenized ingots. Differential Scanning Calorimetry (DSC) technique was used to measure the TTs using a Perkin-Elmer Pyris 1 DSC with heating and cooling rates of 10 °C min−1 at stress-free condition. The TTs calculated by the intersection method of the three alloys under stress-free conditions are shown in Table 1.

Table 1 Transformation Temperatures of the NiTiPd–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf alloys obtained through DSC measurements
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Mechanical testing was conducted in an MTS Landmark servo hydraulic test platform with 100 kN load cell. The thermal cycling experiments were performed with 10 °C min−1 heating and cooling rates at constant stress, while SE experiments were performed with 8 × 10−4mm s−1 loading and 100 N s−1 unloading rates at constant temperature.

In the thermal cycling experiments, stresses ranging from 25 to 1000 MPa were applied in compression above the A f, and then the samples were cooled down below the M f and heated back above A f under the constant stress. On the other hand, in SE experiments, the specimens were loaded to a selected compressive strain and then unloaded at constant temperatures above A f. Transmission electron microscope (TEM) observations were conducted at room temperature (RT) in a JEOL 2010F instrument operated at 200 kV. The specimens for TEM observation were prepared by a twin-jet polishing technique using a solution of 20 % sulfuric acid and 80 % methanol at around −15 °C (258 K).

Results and discussion

Micro- and crystal structure of NiTiPd–15Hf and NiTiPd–20Hf alloys

Figure 1a shows the X-ray diffraction patterns of NiTiPd–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf alloys at RT. All the alloys consist of two phases, B2 austenite and B19′ martensite at room temperature. The crystal structure of NiTiPd–10Hf austenite was B2 cubic with a = 0.3063 nm, and the crystal structure of martensite is B19′ monoclinic with lattice parameters of a = 0.2985 nm, b = 0.4127 nm, c = 0.4732 nm, and β = 99.3°. For NiTiPd–15Hf, the crystal structure of the martensite was B19′ with lattice parameters of a = 0.3034 nm, b = 0.4109 nm, c = 0.4805 nm, and β = 100.9°, while the lattice parameter of B2 austenite phase was a = 0.3085 nm. On the other hand, the NiTiPd–20Hf had a B19′ martensite with lattice parameters of a = 0.3072 nm, b = 0.4128 nm, c = 0.4892 nm, and β = 102.6°, while the B2 austenite had a lattice parameter of a = 0.3121 nm. Thus, it can be concluded that as the Hf content increased, lattice parameters of the transforming phases are also increased in the current alloys. The volume of the B2 cubic structure of the austenite was expanded by 2.192 and 5.812 % as the Hf content was increased from 10 to 15 % and to 20 %, respectively.

Fig. 1
figure 1

a X-ray diffraction patterns for the NiTiPd–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf alloys. Bright-field TEM images of the b NiTiPd–15Hf alloy and c NiTiPd–10Hf alloy

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Figure 1b and c shows the bright-field TEM micrographs of the NiTiPd–15Hf and NiTiPd–10Hf alloys, respectively. The thickness of the martensite plates of NiTiPd–15Hf is lower than that in NiTiPd–10Hf. The internal twin of the NiTiPd–15Hf was found to be (001)B19′ compound twin which has also been observed in the NiTiPd–20Hf [21]. On the other hand, the internal twin of the NiTiPd–10Hf alloy was confirmed to be 〈011〉B19′ type II twin [25]. It is noted that the thickness of the (001)B19′ compound twin was thinner than that of the 〈011〉B19′ type II twin and higher density of twins was observed in the NiTiPd–15Hf alloy.

The strain–temperature responses

The load biased shape-memory responses of the NiTiPd–15Hf alloy as a function of stress are shown in Fig. 2. Compressive stresses ranging from 25 to 1000 MPa were applied in austenite and kept constant during the thermal cycling. No irrecoverable strain was observed up to a stress level of 600 MPa.

Fig. 2
figure 2

The strain–temperature response of the NiTiPd–15Hf alloy as a function of stress from 25 to 1000 MPa

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Figure 3 shows that the shape-memory responses of the NiTiPd–20Hf alloy as a function of compressive stress ranging from 25 to 1000 MPa were applied. Irrecoverable strain was observed after 700 MPa.

Fig. 3
figure 3

The strain–temperature response of the NiTiPd–20Hf alloy as a function of stress from 25 to 1000 MPa

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Figure 4a shows the transformation strain values as functions of applied stress, extracted from the thermal cycling experiments shown in Figs. 2 and 3. Total strain was measured between the cooling and heating curves at M s, as shown in Fig. 2b. As the applied stress is increased, the total strain is also increased and then saturated as the selection of preferred variants of martensite saturated at intermediate stress levels. Beyond the plateau, with further increase in stress, transformation strain started to decrease due to plastic deformation.

Fig. 4
figure 4

a Transformation strain as a function of stress and b C–C relationship in NiTiPd–10Hf, c C–C relationship in NiTiPd–15Hf, and d C–C relationship in NiTiPd–20 alloys

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Transformation strain was calculated by mathematically subtracting the irrecoverable strain from the total strain. Transformation strains were 0.3, 3.5, and 3 % under 25, 500, and 1000 MPa, respectively, for NiTiPd–15Hf, while transformation strains of 0, 2.2, and 2 % were observed in NiTiPd–20Hf under 25, 500, and 1000 MPa, respectively. For NiTiPd–10Hf, the transformation strains were 0.8, 4.6, and 5 % under 25, 500, and 1000 MPa, respectively [25]. It is clear that as the Hf content increased in the alloys, the transformation strains were decreased, which is in good agreement with the previously reported data for NiTiHf alloys [26].

The change of TTs (e.g., M s and A f) with applied stress in the strain–temperature responses (Figs. 2 and 3) are plotted in Fig. 4b, c, and d for the NiTiPd–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf, respectively. It was found that Clausius–Clapeyron (C–C) slopes were 8.5, 11.8, and 15 MPa °C−1 for M s in the NiTiPd–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf alloys, respectively. The C–C relationship is formulated as [27]

$$ \frac{\Delta \sigma }{\Delta T} = -_{{}} \frac{\Delta H}{{T_{\text{o}} \, \varepsilon_{\text{tr}} }}, $$

where ∆σ is the difference between critical stresses, ∆T is the temperature difference, ∆H is the transformation enthalpy, T o is the equilibrium temperature, and ε tr is the reversible strain. Assuming that the ∆H and T o are comparable in these alloys, there is a good agreement between the C–C slopes and the transformation strains, ε tr of the current alloys where the C–C slopes are inversely proportional to ε tr.

Figure 5 shows the thermal hysteresis and irrecoverable strain values as a function of applied stress obtained from the strain–temperature responses. Figure 2b shows the calculation methods of TTs, the thermal hysteresis, and the irrecoverable strain. The irrecoverable strain was not observed up to 500, 600, and 700 MPa in NiTiPd–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf alloys, respectively. [25]. As the stress was increased to 1000 MPa, irrecoverable strains of 2.5, 1.3, and 1.8 % were measured for NiTiPd–10Hf alloy [25], NiTiPd–15Hf, and NiTiPd–20Hf alloys, respectively.

Fig. 5
figure 5

Thermal hysteresis and irrecoverable strain as functions of applied stress extracted from the strain–temperature response of the NiTiPd–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf alloys (data for NiTiPd–10Hf were taken from [25] for comparison)

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For NiTiPd–10Hf, the temperature hysteresis was almost constant (66 °C) up to 700 MPa. This was followed by a dramatic increase in hysteresis to 113 °C as the applied stress was increased to 1000 MPa [25]. The thermal hysteresis of the NiTiPd–15Hf was 39 and 66 °C under 25 and 500 MPa, respectively. Then, it increased to 105 °C under 1000 MPa. In the NiTiPd–20Hf, the hysteresis cannot be detected at 25 MPa, while it was increased from 48 °C to above 150 °C as the applied stress increased from 500 to 1000 MPa. Consequently, the increase of the Hf content resulted in lower initial temperature hysteresis, and the progress of the thermal hysteresis with stress was different.

The evolution of the thermal hysteresis in the current alloys can be analyzed in two regions as before (pre-saturation region) and after (post-saturation region) saturation stress. The saturation stress could be defined as the stress at which transformation strain stops increasing and starts either saturating or decreasing as shown in Fig. 4a. For instance, the saturation stress was 500 MPa for the NiTiPd–10Hf alloy, while it was 700 MPa for the NiTiPd–15Hf and NiTiPd–20Hf alloys. The thermal hysteresis in the NiTiPd–10Hf alloy was almost constant up to the saturation stress of 500 MPa where it increased progressively even before the saturation stress in the NiTiPd–15Hf and NiTiPd–20Hf alloys. After plastic deformation occurred (shown as increased irrecoverable strain in Fig. 5), hysteresis increased abruptly in all the alloys. It is known that the hysteresis is a result of dissipation mechanisms in SMAs [8, 28]. In SMAs, the three main energy dissipation mechanisms can be expressed as (i) friction between transforming phases or in-compatibility, (ii) friction between martensite variants and (iii) dislocation generation [29]. Friction during detwinning can also be added to the list.

When the stress is low initially, the difference between thermal hysteresis of the two alloys should be independent of possible effects associated with the applied stress. The thermal hysteresis was 72, 41, and 17 °C at 100 MPa for NiTiPd–10Hf, NiTiHf–15Hf, and NiTiPd–20Hf alloys, respectively.

This initial difference in the hysteresis could be related to the compatibility between the transforming phases of the alloys. It has been reported that there is a close relationship between hysteresis and lattice compatibility that depends on the lattice parameters of the transforming phases in SMAs. When the interphase of the transforming phases is more compatible, a lower hysteresis is expected [30–32]. A sign of the compatibility between the transforming phases is the middle eigen value λ 2 of a selected matrix of the phase transformation between crystal structures based on the Non-Linear Geometric Theory of Martensite (NLGTM) [30]. According to the theory, the closer the middle Eigen value is to 1, the less hysteresis is expected in SMAs [31, 33–37]. Using the parameters for B2 to B19′ transformation [38], λ 2 values were calculated to be 0.9077, 0.8870, and 0.8747 for the NiTiHf–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf, respectively. It is clear that there is an inverse relation between the middle Eigen values and the initial temperature hysteresis in the currently studied NiTiHfPd alloys. Moreover, the λ 2 values are not even close to 1, which is the sign of incompatible microstructures, in the alloys. Thus, the compatibility between the transforming phases could not be the only reason alone in explaining the initial hysteresis differences in the current alloys. The difference in the dissipation energy at low stress could be attributed to difference in internal twinning characteristics (Fig. 1b, c) and/or formation of partial self accommodated martensite structures.

In the pre-saturation region, the gradual increase in the thermal hysteresis in the NiTiPd–15Hf and NiTiPd–20Hf alloys can be attributed to the increase in the friction between the martensite variants due to increased transformation strain by growing martensite plates. Since the strain was increased, the friction between strain carrying martensite plates also increased resulting in progressively increased hysteresis. On the other hand, the thermal hysteresis of the NiTiPd–10Hf alloy was almost constant in this region in spite of the increasing transformation strain. The difference in the progress of thermal hysteresis in this pre-saturation region could stem from the observed difference in the twinning types of the alloys. The 〈011〉B19′ type II twin was observed in NiTiPd–10Hf, while (001)B19′ compound twinning was observed in NiTiPd–15Hf and NiTiPd–20Hf alloys. Compound twins are thinner when they are compared with the type II twins (as shown in Fig. 1), and this may result in more interfaces and increased friction. Furthermore, it is more difficult to detwin the compound twins which increase the friction during propagation and selection of martensite variants. Previously, the mobility of the (001)-type compound twins in a Ni49.8Ti42.2Hf8 alloys was reported to be less than 〈011〉 type II twins in an equiatomic Ni50Ti50 [39]. Thus, the compound twins in NiTiPd–15Hf and NiTiPd–20Hf alloys may cause larger internal friction during the motion of the phase fronts during generation of transformation strain due to the limited mobility, resulting in progressively increasing dissipation and hysteresis with increasing stress.

In all the alloys, an abrupt increase of the thermal hysteresis in the post-saturation region (>700 MPa) was observed. In this region, the increase in the hysteresis can be mainly attributed to the plastic deformation, which is manifested by the open loops (irrecoverable strain) at the end of the thermal cycles in Fig. 2 and Fig. 3. As the plastic deformation was occurred in the material, the dissipation of energy was increased and so thus the thermal hysteresis.

Isothermal stress–strain behavior

Figure 6 shows the stress–strain responses of the NiTiPd–15Hf alloy at 15 °C. The alloy was in martensite phase (since 15 °C was lower than Mf of 35 °C as shown in Table 1). The specimen was incrementally loaded and unloaded at this temperature up to strain of 8 % and compressive stress of 2100 MPa. The initial linear part of the stress–strain curve shows predominantly elastic deformation of martensite followed by and re-orientation of martensite variants monitored as a plateau-like region. At the end of this region, it could be expected that the material is fully re-oriented. Following the plateau-like region, primarily elastic deformation of martensite is observed. In addition to the elastic deformation, further re-orientation and detwinning of martensite could be expected even though they are less favorable by the applied stress [40], while dislocation slip and deformation twinning of the martensite might also occur [41].

Fig. 6
figure 6

Stress–strain response of the NiTiPd–15Hf at 15 °C

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At the last stage, plastic deformation becomes more dominant at the second “yield” point. In this region, dislocation processes and/or deformation twinning are expected to dominate the deformation response [40]. Therefore, it is expected that bulk plastic deformation of martensite occurs at relatively high stresses of more than 2 GPa, which is beneficial for biomedical or other industrial applications requiring high strength.

In order to investigate the morphology of re-oriented martensite, TEM observation was conducted at room temperature for NiTiPd–15Hf after the compression tests as shown in Fig. 6. Figure 7a shows a bright-field image of re-oriented martensite variants. Thicker re-oriented martensite plates were frequently observed as compared to the thermally induced martensite (Fig. 1b). The thick martensite variant is considered to be a favorable variant under stress. The selected area diffraction pattern obtained from the interface between the martensite plates A and B in Fig. 7a is shown in Fig. 7b. The twinning in the martensite plates was revealed as (001)B19′ compound twin. The boundary between the plates A and B is determined to be {111}B19′-type boundary [42]. Although the plates A and B are {111}B19′ type I twin related, the boundary of the plates is not completely parallel to the twinning plane, {111}B19′, since the plates contain the (001)B19′ compound twins that cause crystal rotations in the plates. The boundary slightly rotates from the (111)A(M) plane to the (\( \bar{1}\bar{1} \)1)A(T) plane in the plate A and from the (111)B(M) plane to the (\( \bar{1}\bar{1} \)1)B(T) plane in the plate B as can be seen in Fig. 7b.

Fig. 7
figure 7

a Bright-field image obtained at room temperature for the NiTiPd–15Hf alloy deformed at 15 °C and b selected area diffraction pattern taken from the interfaces between the martensite plates A and B in (a). Subscripts M and T indicate matrix and (001)B19′ compound twin, respectively

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In Fig. 8, compressive stress–strain responses of NiTiPd–15Hf are shown at 60 and 90 °C. At 60 °C, full recovery was not observed since the test temperature was below A f. Upon heating above A f temperature, the retained strain was completely recovered as shown by the heating (strain-temperature) curve in Fig. 8a.

Fig. 8
figure 8

Stress–strain responses of NiTiPd–15Hf at a 60 and b 90 °C

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In Fig. 8b, the sample was incrementally (by 1 %) loaded up to 5 % strain at 90 °C, above A f. Almost fully reversible superelastic response was observed even when a stress level of nearly 1400 MPa was applied. When the sample was loaded to 5 % strain and unloaded, irrecoverable strain of 0.3 % was observed. The transformation strain was determined to be 3.1 %. Stress hysteresis, calculated between the loading and unloading curves at 2.5 % (as shown in Fig. 8b), was determined as 635 MPa at 90 °C.

Figure 9 shows the stress–strain behaviors of the NiTiPd–20Hf alloy at 200 °C, which are above A f. As the material was loaded to 2 %, a transformation strain of 0.7 % was obtained at 200 °C. The stress hysteresis calculated at 1 % was 260 MPa at 200 °C. As the compressive strain of 3 % was applied, a full recovery was not realized due to high hardening and plastic deformation.

Fig. 9
figure 9

Stress–strain responses of NiTiPd–20Hf at 200 °C

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Two-way shape-memory effect

It is known that TWSME behavior can be observed in SMAs upon generation of anisotropic internal stress by dislocation networks or nucleation sites for martensite by interfaces such as precipitates or retained martensite after certain “training” procedures such as thermal cycling [43, 44], stress cycling [45], or variant re-orientation during isothermal deformation [46, 47].

Figure 10 shows the strain–temperature responses of the NiTiPd–15Hf under 5 MPa after various training conditions. A small stress of 5 MPa was applied to keep the sample in contact with the compression grips during thermal cycling tests. The initial thermal cycling of the material (T-0) did not result in significant strain since the applied stress of 5 MPa was not enough to favor any preferred martensite variants. TWSME after thermal cycling under 700 MPa (T-1) and 1000 MPa (T-2), as shown in Fig. 2, yielded in compressive strain.

Fig. 10
figure 10

The constant stress–strain–temperature responses of the as-homogenized and trained Ni45.3Ti39.7Hf15Pd5 and NiTiPd–20Hf alloys at 5 MPa

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The TWSME strain in T-1 was 0.6 %, while thermal hysteresis was 45 °C. At T-2, the TWSME strain was 0.5 % and the temperature hysteresis was decreased to 40 °C. It is clear that the TWSME was decreased after the T-2 condition since significant dislocation generation was observed when the bias stress increased from 700 to 1000 MPa as shown in Fig. 2. The decrease in the thermal hysteresis in the T-2 condition can stem from the less volume of transformed material due to increased irrecoverable strain. Moreover, as the material hardens due to plastic deformation, it becomes more difficult to form new defects and dislocations resulting in decreased energy dissipation.

In NiTiPd–20Hf, TWSME strain in T-1 was 0.8 % with a thermal hysteresis of 35 °C. In T-2, TWSME strain was 0.85 % and the temperature hysteresis was decreased to 30 °C, similar to NiTiPd–15Hf alloy. It is clear that there is a huge elastic energy storage (monitored as a larger difference between M s and M f in Fig. 10b) during the transformation in the T-2 case, which could be a result of hard propagation of phase fronts due to generated dislocations after the strain–temperature response at 1000 MPa (Fig. 3b). In comparison, it should be recalled that the NiTiPd–10Hf alloy could develop two-way shape-memory strain of 1.6 % without an intense training process [25], owing to larger internal stress and/or larger volume of favored martensite plates resulting in higher TWSME strain compared to the other alloys.

Work output

In Fig. 11, work output levels for the NiTiPd–10Hf, NiTiPd–15Hf, and NiTiPd–20Hf alloys are shown as a function of applied stress. The work output can be expressed as the mathematical product of the reversible strain and applied stress obtained from the strain–temperature responses. As the applied stress increased, the work output also increased due to an increment in reversible strain and stress.

Fig. 11
figure 11

Work output and transformation strain values as a function of applied compressive stress for the NiTiPd-20Hf, NiTiPd–15Hf and NiTiPd–10Hf alloys

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In the NiTiPd–10Hf alloy, work output was 0.2 J cm−3 under 25 MPa and reached a maximum value of 29 J cm−3 under 700 MPa [25]. As for the current alloys, the work output was 0.075 J cm−3 under 25 MPa and reached a maximum value of 30 J cm−3 under 1000 MPa in the NiTiPd–15Hf alloy. The work output values were 5 and 20 J cm−3 at the compressive stress levels of 100 and 1000 MPa, respectively, in NiTiPd–20Hf. As the applied stress increased further to 1000 MPa, the work output decreased to 25 J cm−3 due to a lower reversible strain of only 2.5 % [25].

In comparison, the NiTiPd–10Hf alloy has nearly comparable work output to a previously studied extruded Ni45.3Ti29.7Hf20Pd5 alloy, which is capable of 32–35 J cm−3 [21]. Binary NiTi alloys can generally provide work outputs of 10–20 J cm−3 [48], while Ni-rich NiTiHf alloys can produce around 18–20 J cm−3 [19, 20]. Finally, NiTiPd and NiTiPt alloys can yield work outputs of 9–15 J cm−3 at temperatures above 150 °C [49, 50]. However, it should be noted that the upper temperature capability is limited in NiTiHfPd alloys compared to more conventional ternary NiTi–X (X = Hf, Pd, Pt) high-temperature SMAs. High work output levels were realized in the NiTiHfPd alloys owing to high stress capability and good transformation strain.

Conclusions

The shape-memory properties of Ni45.3Ti34.7Hf15Pd5 and Ni45.3Ti29.7Hf20Pd5 polycrystalline SMAs were investigated through evaluation of the strain–temperature response (shape-memory behavior) and isothermal stress–strain responses (superelastic behavior). The Ni45.3Ti34.7Hf15Pd5 alloy exhibited shape-memory response with 3.8 % maximum transformation strain at 700 MPa, while 2.6 % maximum strain was possible in the Ni45.3Ti29.7Hf20Pd5 at the same stress level. The Ni45.3Ti34.7Hf15Pd5 and Ni45.3Ti29.7Hf20Pd5 alloys exhibited two-way shape-memory strains of 0.6 and 0.8 %, respectively, after thermal cycling experiments under 700 MPa. In Ni45.3Ti34.7Hf15Pd5, superelastic response with transformation strain of 3.1 % was observed at 90 °C with nearly complete recovery of applied strain of 5 % at a stress level of 1400 MPa. In Ni45.3Ti29.7Hf20Pd5, high hardening was observed in the stress–strain behavior at a high temperature of 200 °C, resulting in a limited superelasticity. The maximum work outputs of Ni45.3Ti34.7Hf15Pd5 and Ni45.3Ti29.7Hf20Pd5 were of 30 and 20 J cm−3, respectively, achieved at a stress level of 1000 MPa. As the Hf content was increased, the transformation strain was decreased and the volume of crystal structures was expanded. The differences between the evolutions of the thermal hysteresis with the applied stress were linked to the difference in twinning types. A progressively increasing hysteresis with the applied stress in the strain–temperature response was observed in the compound twinned Ni45.3Ti34.7Hf15Pd5 and Ni45.3Ti29.7Hf20Pd5 alloys in contrast to type II twinned Ni45.3Ti39.7Hf10Pd5 alloy.