3.1. Mechanical behaviorsFigure 1 (a) shows the stress–strain curves of the NiTi alloys with an applied strain of 7% at various temperatures. The NiTi alloys are tensile tested at approximately the isothermal hysteresis loop area (with a low strain rate of 1 × 10−4 s−1). In the present case, the stress linearly increases with strain at low strain level (ε = 1%) increasing, corresponding to the elastic response of the austenite phase. When the critical stress (σt) for stress-induced martensitic transformation is reached, a large transformation strain (Δ ε) occurs at almost constant stress over the transformation plateau (the determination method of σt and Δ ε will be shown in Fig. 4(a)). Then the produced martensite phase is elastically deformed. After stress is released, the total strain can be fully recovered, indicating complete superelastic deformation in NiTi alloy. However, a little residual strain is observed at 313 K and 321 K, separately, which can be attributed to the dislocations generated by the stress-induced martensite transformation and remnant martensite stabilized by the dislocation strain field at higher temperatures. It is worth noting that the flat “plateau” appears in the loading and unloading processes of the stress-strain curves, typically indicating the positive/reverse stress-induced MT. The “plateau” gradually moves to the higher stress with increasing temperature. As shown in Fig. 1(b), the critical transformation stress (σt) linearly increases with a slope of in the loading and in the unloading process, separately. Figure 1(c) shows the variation of isothermal hysteresis loop area for loading-unloading cycles. It is worth noting that the NiTi binary alloy shows three phases (B2, R, and ) based on the phase composition diagram, where the R phase is an intermediate transitional phase.[32] The stress-induced martensite transformation (A–M) undergoes the B2-R–B19 phase change process, while the reverse phase transformation (M–A) from back to B2 is a single step process. The intrinsic two-step phase transformation and asymmetric phase transformation path on the phase diagram determine that the NiTi shape memory alloy has hysteresis during the phase transformation.[33] Like the behavior of the critical stress, the hysteresis loop area increases with temperature increasing. Both of them show that more input work is needed to induce the martensite transformation at higher temperature. It is worth noting that the hysteresis loop area turns to decrease at 321 K, which may be related to the insufficient phase transformation for the applied strain of 7% at higher temperature. Based on the stress-strain curves in Fig. 1(a), the Young’s modulus is evaluated and shown in Fig. 1(d). The Young modulus is strongly temperature dependent and decreases with temperature decreasing, showing the softening of the trend towards the transition temperature (Af = 283 K). It is reported that the Young moduli of both the martensite phase and austenite phase are temperature dependent and softened toward the transition temperatures for NiTi shape memory alloys. This is attributed to the shear phonon softening of the austenite phase and martensite phase in the vicinity of the transition temperature.[34–36] Quantitatively, the austenite phase of this NiTi alloy exhibits the softening (approximately ) with temperature decreasing.
3.2. Elastocaloric propertiesFigure 2(a) shows the isothermal stress–strain curves (with a low strain rate of 1 × 10−4 s−1) for different strain levels of 1%–7% at 291 K. The critical stress (σt) is reached at an applied strain of about 1%. Then the transformation plateau extends with increasing the applied strain. When the applied strain reaches to 7%, the stress-induced martensite transformation is completed and the produced martensite phase is elastically deformed. After the stress is released, the total strain could be fully recovered for all the applied strain levels, indicating an ideal superelastic deformation in NiTi alloy. The critical stress reaches to about 480 MPa with an applied maximum strain of 2% and then gradually decreases to 420 MPa when the applied maximum strain increases to 7%. The generation of internal stress with increasing strain is favorable for the formation of the stress-induced martensite phase, leading to the gradual degradation of the critical stress.[28] We also observe that the area of the stress hysteresis loop between the loading and unloading curve increases with strain increasing, showing that the fraction of martensite phase increases with strain increasing.
In order to measure the adiabatic temperature change, an increased strain rate of 5 × 10−3 s−1 is used in the tensile test (Fig. 2(b)) and the temperature changes are shown in Fig. 2(c). The temperature change increases correspondingly with the strain increasing, which is attributed to the increase of the martensite volume fraction. When the applied strain increases to 7%, the temperature change () reaches to its maximum value of 30 K upon loading due to the release of heat during the forward MT. During holding, the temperature change value recovers to the room temperature as a result of heat exchange between the sample and environment, and then decreases to −19 K upon unloading () due to the absorption of heat during reverse MT. Finally, the temperature change value recovers again to the room temperature during further holding due to the heat exchange.
The value is not equal to the value at each strain level (1%–7%) (Fig. 2(c)), indicating the elastocaloric irreversibility () between the forward and reverse MTs. Analogous elastocaloric irreversibility was also reported in other NiTi alloys.[31,34] We also calculate the elastocaloric irreversibilities derived from the friction dissipation () by using the following equation[28]
where the density (
ρ) is
, and the specific heat (
) is measured to be
for the NiTi alloy. The
value is the stress hysteresis area of the isothermal test. The irreversible entropy change (
) is obtained from the stress hysteresis area of the stress–strain curve under the isothermal condition (Fig.
2(a)) since the stress hysteresis under the adiabatic condition additionally includes the thermodynamic work needed to perform the cooling cycle with self-heating and self-cooling of the material.
[28] The obtained
values are plotted in Fig.
2(d). They are consistent with the measured
values, which confirms that the friction dissipation contributes to the elastocaloric irreversibility.
Figure 3 shows the measured temperature changes of NiTi alloys in a wider temperature range of 286 K–321 K, which is required for almost all practical solid-state cooling applications. Large temperature changes of 20 K∼30 K upon loading and −13 K∼-19 K upon unloading are observed with an applied strain of 7% in the measured temperature range. The maximum temperature change () values are 30 K upon loading and −19 K upon unloading at 291 K, respectively, which are even higher than the measured Δ T values of some other reported NiTi alloys (such as the poly-crystalline NiTi wires,[15,31] the trained poly-crystalline NiTi wires,[28] the NiTi single crystal,[23,29] and the NiTi thin film[30]).
Based on the Clausius–Clapeyron equation, the stress-induced entropy change () can be calculated from ,[1] where T is the ambient temperature in Kelvin, is the specific heat (), is the specific volume of is the transformation strain, and is the critical transformation stress dependence on temperature (shown in Fig. 1(b)). As a result, large values of for loading and for unloading process are obtained in the measured temperature range of 286 K–321 K (Fig. 4(b)), respectively, which are higher than those of some other poly-crystalline NiTi alloys.[28,31] So the above high temperature changes can be attributed to these large entropy changes. In the NiTi single crystals, a larger theoretical value of is reported in the [148] orientation, in which the transformation strain () is calculated by using the lattice deformation theory (LDT).[23] The value is the potential attainable transformation strain. So the measured temperature drop (−14 K) is not higher than our results (shown in Fig. 3).
As mentioned above, the COPmater is expressed as the ratio of cooling power (Q) to input work (W) (),[11,15] where is the theoretical temperature change under the adiabatic condition, which is a potentially attainable value. In the following, the COPmater value is approximately estimated () by using the measured temperature change (). Based on the adiabatic stress–strain curves at room temperature (Fig. 2(b)), the input work (W) in the unloading process is calculated by integrating the area enclosed by the loading and the unloading curve.[11,15] With a density of and heat capacity of , the COPmater value is estimated at different strain levels (ε = 1%–7%) and shown in Fig. 5. The COPmater values show an inverse dependency on the applied strain level. When the applied strain level is ε = 1%, the obtained COPmater value is 11.7. With increasing the applied strain level, the COPmater values decrease. Smaller strain amplitudes should be used to increase the COPmater values. Analogous results were reported in NiFeGa magnetic shape memory alloy.[35] However, larger strain should be loaded up to obtain high temperature change. So, a moderate strain level will be adopted in the actual cooling application.
The tensile cycling test is performed 1000 times with a high strain rate (5 × 10−3 s−1) at 300 K. The values of the first cycle are 29 K upon loading and −17 K upon unloading, respectively, under a large strain level of 7% (Figs. 6(a) and 6(b)), which is consistent with the above results of other samples. With increasing the cycle numbers, the value gradually decreases and then gradually stabilizes at 23 K upon loading and −6 K upon unloading when the cycle number is over 200. The decrease of with increasing cycle number is also observed in some other elastocaloric materials,[11,31] which is attributed to the accumulation of dislocations with increasing cycles. In Figs. 6(c) and 6(d), we observe the decrease of the critical stress of martensitic transformation, the area of hysteresis loop and the transformation strain, which confirms the accumulation of defects with increasing cycles. The initially formed dislocations and remnant martensite, in turn, suppress the dislocation generation in the subsequent long-term cycles, which leads to the stabilization of the temperature changes.[28,29,36] However, it is still not enough to evaluate the elastocaloric stability (long-term stress cycles on the order of 106 would be needed). In the next work, the microstructural modification by doping (Cu, Co, etc.) or incorporating the ductile second phase into grain boundaries, and mechanically training pretreatment of elastocaloric materials are expected to enhance mechanical and elastocaloric stability. Moreover, the compression, instead of tension, will restrain the fatigue crack growth and lead to a longer life span.