Elastocaloric cooling processes: The influence of material strain and strain rate on efficiency and temperature span Open Access

Solid state cooling technologies based on ferroic materials may have the potential to become an environmentally friendly alternative to conventional vapor compression based technology. Ferroic materials show magnetocaloric, electrocaloric, and elastocaloric effects.^1–3 The magnetocaloric effect was the first caloric effect in ferroic materials, which has been investigated in a systematic manner.⁴ Several magnetocaloric cooling devices have already been developed.⁵ The most promising magnetocaloric device concept up to now is the active magnetocaloric regenerator.⁶ In addition to magnetocaloric devices, first prototypes of electrocaloric cooling systems have also been designed.^7–9 Elastocaloric cooling is a novel ferroic cooling technology; however, a number of scientific test systems have already been developed^10–12 to investigate the elastocaloric effect under process conditions.

Ni-Ti based shape memory alloys (SMA’s), used in these systems as elastocaloric cooling medium, show a very high potential in comparison with other SMA’s.^2,13 The advantages of Ni-Ti based alloys are the large latent heats of up to 22 J/g and a small work input, which is required to activate these heats.^2,14 The binary Ni-Ti alloys show already good elastocaloric properties although these alloys have not been optimized for elastocaloric cooling. The main application area for these alloys is the medical field.^15,16 Novel ternary and quaternary Ni-Ti based alloys have been developed to meet the specific material requirements for elastocaloric cooling.^17–20 The developed alloys show a small mechanical hysteresis as well as low transformation strains,^20,21 which reduce the mechanical work and increase the efficiency. In addition, the functional and structural fatigue of the materials have been improved.^19,21

The efficiency of elastocaloric cooling devices does not only depend on the material properties but also the thermodynamic process control has a significant influence on the process efficiency.^22–25 The Brayton cycle has already been investigated experimentally^11,26 for which the process efficiency as well as the cooling power can be influenced by controlling the contact time.^27,28 However, advanced thermodynamic cycles with combined adiabatic isothermal process control hold the potential to be more efficient²³ than the Brayton cycle. This has already been documented for magnetocaloric cooling systems.²⁹ A further process parameter, influencing the efficiency and the cooling power, is the applied maximum material strain, which will be discussed in this paper. This parameter enables a control of the phase transformation and the release of latent heats. These investigations require a scientific test setup, which enables the independent control of the process parameters.

Figure 1 shows the developed scientific test setup, which enables comprehensive investigations of elastocaloric materials and cooling processes. The system is set up in two levels. The upper level includes a linear direct drive to load and unload the elastocaloric material with a maximum continuous force of 1200 N and a maximum speed of 3 m/s. The load cell as well as the position measurement system of the linear direct drive enables strain and stress measurements. The lower level of the setup includes the heat transfer system. A second linear direct drive moving orthogonally to the linear direct drive in the upper level switch the position of the heat sink and the heat source relative to the SMA position. A pneumatic cylinder brings the heat sink as well as the heat source into contact with the SMA sample. Two PT-100 temperature sensors measure the core temperature of the heat sink and the heat source. In addition, a load cell measures the contact force between SMA and heat sink/source. The setup is equipped with a high resolution infrared camera, which enables a continuous temperature field measurement of heat sink, heat source, and SMA sample. The control of the experimental setup allows for independent setting of process parameters like SMA strain, SMA strain rate, contact time, contact force, as well as contact phase. Furthermore, the setup can be used for material training and elastocaloric material characterization. A more detailed description of the setup is given in the work of Schmidt et al.¹¹ 

The investigated material is an elastocalorically optimized quaternary Ni₄₅Ti_47.25Cu₅V _2.75 alloy, which has been developed at Ruhr-Universität Bochum.¹⁸ The sample has a cross section of 1.254 mm² and a length of 90 mm. A training procedure was applied prior to the material characterization in order to stabilize the material. The sample has been cycled for 100 mechanical cycles at a strain rate of 5 × 10⁻⁴ s⁻¹ and a maximum strain of 5%. At this strain, the material is maximally transformed. With this we mean the degree of phase transformation at the end of the loading plateau, which has been determined based on the stress increase at the end of the loading plateau during an isothermal cycle. During the training, the material shows mechanical, thermal, and caloric stabilization effects, which have been discussed in the work of Schmidt et al.³⁰ Within 30 cycles, the material is stabilized with a remanent strain of 0.35%. After stabilization, the elastocaloric material properties can be determined.

The material is characterized at four different strains from 2% to 4.65% and eight different strain rates from 5 × 10⁻⁵ s⁻¹ to 1 × 10⁻¹ s⁻¹. 4.65% is the maximum reversible strain based on the applied training procedure. The characterization can be divided in four steps and is comparable with the Brayton cycle. After loading of the SMA during the first step, the maximum strain is kept constant for 180 s (step two) until thermal equilibration with the environment is reached. In the third step, the sample is unloaded followed by a 180 s waiting period at constant minimum strain (step four). Figure 2 shows the mechanical material behavior at four different strains and two different strain rates for the previously described experiment. This diagram includes the two extrema, quasi-isothermal behavior at a strain rate of 5 × 10⁻⁵ s⁻¹, and adiabatic behavior at a strain rate of 1 × 10⁻¹ s⁻¹. It is obvious that high strain rates lead to significantly larger hysteresis areas compared to low strain rates, which is due to the thermomechanically coupled material behavior.^14,31 The hysteresis area influences the efficiency of the process. Assuming work recovery during unloading, the area of the mechanical hysteresis represents the applied mechanical work. The variation of the maximum strain at high strain rates shows a significant increase of the transformation stress with increasing strain. This behavior is caused by the strain dependency of the temperature change.

The strain and the strain rate dependency of the achieved temperature drop during sample unloading are shown in Figure 3(a). With increasing strain as well as strain rate, the temperature change of the sample increases. At maximum strain and strain rate, a temperature drop of 18.4 K below the ambient temperature (T₀) of 295 K could be measured. A saturation effect of the temperature change can be observed at strain rates above 5 × 10⁻² s⁻¹, which indicates that the adiabatic limit is reached. The temperature change of the sample has been determined based on infrared measurements. The mean temperature change on the SMA surface has been taken into account for the determination. The ΔT-strain rate-diagram (Figure 3(a)) shows that the strain dependency of the temperature change increases with increasing strain rate, a trend, which is related to the transition from isothermal to adiabatic phase transformation. At adiabatic conditions, a large dependency of the ΔT on the maximum applied strain can be observed. The strain variation is directly correlated to a variation of the material transformation and the associated usage of latent heats. The increasing latent heat results in higher adiabatic temperature changes and the previously described rise of the transformation stress.

The coefficient of performance (COP) of the material is shown in Figure 3(b). The applied work can be described by the area inside the hysteresis curve of a force displacement diagram. The absorbed heat is calculated based on the temperature change of the material after unloading (ΔT = T_o − T_c) and the specific heat capacity (c = 0.46 J/g K) of the material. The COP shows an inverse dependency on applied strain in comparison to the temperature change. However, the strain rate dependency is equivalent to the strain rate dependency of the temperature change. Based on these results and under the assumption of a Brayton like cooling cycle, the material should be transformed adiabatically to achieve a good cooling performance. Furthermore, to increase the COP, small strain amplitudes should be applied and if a large temperature span is required, the material should be loaded up to the maximum strain. Larger maximum strains lead to a more homogeneous temperature distribution of the sample after adiabatic unloading, as shown in Figure 4. The material shows a localized phase transformation, which starts at the clamps. With increasing strain, the number of transformation bands increases and results in a homogeneous temperature distribution of the sample.

The COP and the adiabatic temperature change are important parameters to validate the cooling properties of elastocaloric materials. However, a comparison with other materials and cooling systems is still difficult. The COP of a cooling system strongly depends on the temperature span at which the system operates. A more general approach is the evaluation of the material efficiency in comparison to the COP of a Carnot cycle (T_c/T₀ − T_c), operating at the equivalent temperature spans. Figure 5 shows the efficiency of the NiTiCuV alloy at the four different strains and a strain rate of 1 × 10⁻¹ s⁻¹ as well as the Carnot efficiency at equivalent temperature spans. The assumed ambient temperature for the Carnot cycle (T₀) is 295 K equivalent to the ambient temperature during the experiments. The comparison shows that with increasing strain and the resulting larger temperature change, the deviation between material COP and Carnot COP is becoming smaller. The ratio of material COP to Carnot COP shows that at maximum strain, more than 50% of the Carnot efficiency can be reached. However, small strains of 2% result in material COP to Carnot COP ratio of slightly more than 30%. This trend can be linked to the hysteretic effects in the mechanical material behavior. The quasi-isothermal hysteresis area (cf. Figure 2) describes the irreversible losses of the material, which do not contribute to a temperature change. The adiabatic hysteresis curve includes the additional amount of work required to change the temperature of the material. Comparing the relation of irreversible contributions to the work input with temperature dependent work input, the irreversible contributions have a larger proportion at small strains as at large strains. This results in a small material COP to Carnot COP ratio.

This work showed that the variation of strain and strain rate has a significant influence on the cooling properties of elastocaloric materials. The highest material COP of 14.9 has been measured at a strain rate of 1 × 10⁻² s⁻¹ and 2% strain. The largest temperature change of 18.4 K and a COP of 7.9 have been measured at a strain rate of 5 × 10⁻² s⁻¹ and 4.65% strain. These results can be interpreted such that low strains increase the efficiency and high strains increase the temperature span. The calculation of the Carnot COP at the respective temperature span of the material showed the opposite. The irreversible mechanical losses of the material are more dominant at small strains than at high strains. At a strain of 4.65%, the material is maximally transformed and reaches 51% of the Carnot efficiency; Ossmer et al.²⁶ investigated NiTiFe thin films, which show a Carnot efficiency of 60% at fully transformed material and a temperature change of 16 K. The larger temperature change of the material at large strain amplitudes will also lead to a higher cooling power of an elastocaloric cooling device, which is a further important process parameter of a cooling process, beside the COP. However, lowering the strain amplitude could be considered in designing elastocaloric cooling devices. The major advantage of low strain amplitudes is the significant increase of material lifetime,³² which is one of the key challenges for elastocaloric cooling up to now. However, for an efficient heat transfer, the maximum strain should be above 3%, at smaller strains, the temperature distribution of the sample shows significant inhomogeneities, which lead to an inefficient heat transfer. An additional possibility to increase the functional fatigue resistivity of the material is to further improve the structural fatigue behavior, as shown by Chluba et al.¹⁹ in SMA thin films.

The authors would like to acknowledge the support of the German Research Foundation (DFG: Deutsche Forschungsgemeinschaft) through priority Program No. 1599 “Caloric effects in ferroic materials: New concepts for cooling” (Project Nos. SCHU2217/2-1, SE704/2-1, SCH2217/3-2, SE704/2-2). They would also like to thank André Wieczorek, Jan Frenzel, and Gunther Eggeler from the Chair for Materials Science and Engineering (Ruhr-Univerität Bochum) for providing the Ni-Ti-Cu-V alloys.