A unified approach to thermo-mechano-caloric-characterization of elastocaloric materials

This efficiency is based on the so-called material COP_mat, which is calculated by the ratio of released or absorbed latent heat H and mechanical work input W during a loading/unloading cycle, see equation (1) [34].

$$\begin{equation}CO{P_{{\text{mat}}}} = \frac{H}{W}.\end{equation} \tag{ 1 }$$

If one wants to determine the suitability of a given material for elastocalorics applications, it is hence important to experimentally characterize the following quantities:

The elastocalorically most relevant mechanical work input is given by the area of the mechanical stress/strain hysteresis. In addition, the value of plateau stresses and the resulting width of hysteresis are important features impacting the design of elastocaloric systems. These properties depend on a number of factors that need to be accounted for by systematic stress/strain experiments. Clearly, they vary from one material to another, but they also depend on loading conditions, e.g., strain rate and strain increment. Furthermore, material training carried out before application also has been shown to have a strong influence and needs to be characterized.

The latent heats released during mechanical loading and absorbed during unloading are essential for the potential heating and cooling powers of elastocaloric materials. High latent heats in materials lead to higher COPs, but they also determine the maximum temperature span during elastocaloric cycling [35]. From an experimental point of view, it is important for elastocalorics to account for, e.g., the load-dependencies of latent heats and the amount of latent heats due to application-specific partial transformations.

In addition to the efficiency-motivated work and heats, the observation of material temperatures during loading and unloading is of relevance because these temperatures constitute the basis for efficient heat transfer to an ambient medium, which is to be cooled or heated. Here, experimental aspects to be taken into account are, e.g. strain-rate dependency, adiabatic (max. and min.) temperature span, and also the homogeneity of temperature profiles.

From the above, it can be concluded that an assessment of a material's elastocaloric potential hence requires

• mechanical,
• thermal, and
• caloric characterization.

In particular due to the strong coupling of these effects and in order to account for elastocalorically relevant loading scenarios, it is desirable to perform these experiments in one setup while ideally using the same specimen. In the sequel, we will give a brief review of how the subject is currently being addressed, and then propose a novel method to characterize elastocaloric materials in a unified way.

A custom-built testing device tailored for experimental investigation of superelastic NiTi materials has been developed in [31, 45].

For the mechanical characterization, it uses a linear drive (Esr-Pollmeier-LM1418), with a load maximum of 1200 N, a maximum strain rate of 1 s⁻¹ and a maximum stroke of 280 mm. With an internal position decoder, a load cell (ME-Meßsysteme, KD40s) and a National Instruments CompactRIO real time data acquisition system running LabVIEW 2017, it allows for a large range of wires with different diameters to be tested from slow and isothermal to fast and adiabatic conditions. A particular custom-designed clamping mechanism enables quick exchange of various wires, while ensuring uni-axial alignment.

In order to monitor the temperature evolution during the loading/unloading processes of superelastic NiTi wires, a high-resolution IR camera system is installed as part of the test setup, see figure 1.

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The IR camera (Infratec, model IR 8380) is capable of measurements with a resolution of 0.1 K and a sample rate of up to 200 Hz when focused on the wire length, so even minor changes in temperature can be determined [48]. Prior to testing, the wire surface needs to be coated with a black paint providing an emission coefficient of 0.95 to enable quantitative measurements [49]. In order to visualize thermograms of distinct cycles, temperature data are extracted and subsequently averaged from pixels in a box around the wire.

Usually, caloric characterization of materials is carried out by DSC measurements [50]. A DSC device simultaneously heats and cools two small identical furnaces under temperature control. One of the furnaces is filled with a sample of the material under investigation, the other one is empty and serves as reference. Measuring the differential heat flux between the furnaces, one can determine specific heats and-during temperature-triggered phase transformations-also the associated latent heats along with start and finish temperatures of the transformations [44]. This is the standard way to investigate the behavior of, e.g., thermally- driven SMA actuators, with a thermally-induced, load-free transformation from twinned martensite to austenite. The elastocaloric effect, on the other hand, is triggered by the application and removal of mechanical loads and not by temperature changes. Furthermore, DSC measurements do not account for stress-induced transformation between austenite and detwinned martensite.

Also, latent heats and thermal output of the effect are typically dependent on the level of applied loads, which is also not captured by load-free DSC measurements. For these reasons, we subsequently suggest a method that can be integrated into the above device for thermo-mechanical characterization, and hence presents a number of advantages for the elastocaloric characterization of superelastic materials.

This novel approach is based on the idea of reproducing the exothermic temperature effects of the sample under loading by a direct Joule heating of the wire. After recording the temperature change during loading, a constant-amplitude electric current of the same duration as the loading process is applied to the wire. This leads to an increase in temperature, which will be simultaneously observed by the installed IR camera. The electrically induced temperature change is then matched with the elastocaloric temperature change by adjusting the electric power amplitude passing through the wire in an iterative process. Power amplitude and pulse duration subsequently allow for a quantitative determination of the energy during the process, which is a very good approximation to the latent heats from the mechanical loading process [46, 51].

To induce electric current and to measure the electric power input the former mechanical test setup is extended as shown in figure 2. A custom-built current source provides the current I_H to perform Joule heating. A resistor, R_S , is incorporated to account for the current-dependent voltage U_I . Additionally, a voltmeter is added to the setup to measure the voltage drop U_C over the investigated wire sample.

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Based on the electric parameters, the total electric power can be calculated according to equation (2). R_C stands for the total resistance of the clamps that needs to be taken into account. The value of R_S is chosen to be R_S = 0.22 Ω, the value of R_C is measured as R_C = 20 mΩ [51].

$$\begin{equation}{{\boldsymbol{P}}_{\boldsymbol{W}}} = {{\boldsymbol{I}}_{\boldsymbol{H}}}\cdot{{\mathbf{U}}_{\mathbf{C}}} - {\boldsymbol{I}}_{\boldsymbol{H}}^2\cdot{{\mathbf{R}}_{\mathbf{C}}} = \frac{{{{\boldsymbol{U}}_{\boldsymbol{I}}}}}{{{{\boldsymbol{R}}_{\boldsymbol{S}}}}}\cdot{{\mathbf{U}}_{\mathbf{C}}} - {\left( {\frac{{{{\boldsymbol{U}}_{\boldsymbol{I}}}}}{{{{\boldsymbol{R}}_{\boldsymbol{S}}}}}} \right)^2}\cdot{{\mathbf{R}}_{\mathbf{C}}}.\end{equation} \tag{ 2 }$$

As the procedure described above works very well for the loading-induced exothermic release of latent heats, the same Joule heating method obviously cannot be used to simulate the cooling of the wire as it happens during mechanical unloading. Therefore, in this case, mechanical unloading and Joule heating are performed simultaneously with the electric heat pulse used to compensate the endothermic temperature decrease due to the elastocaloric effect. The correct amount of Joule heating is determined by the criterion that the temperature level at the end of the unloading process is the same as at the start.

For both cases, loading and unloading alike, the specific latent heat $\Delta$ h of the material can then be calculated according to equation (3), with m being the mass of the investigated SMA wire.

$$\begin{equation}\Delta h = \frac{{{P_W}\cdot{t_{{\text{Pulse}}}}}}{m}.\end{equation} \tag{ 3 }$$

It is particularly important to point out that the above integration into the thermo-mechanical testing device allows for elastocaloric characterization in one single device with one sample. The device can also account for the effects of different sample geometries, i.e wire diameter or other shape factors for different sample types, as well as partial, application-oriented loading typically encountered in machines.

The focus of this work is on the validation of the described test setup and the illustration of the characterization routine. To this end, we show results with a number of different metallic materials to illustrate the variety of behaviors that can be captured. A full characterization of one particular material or the systematic study of influences of various parameters during testing will be addressed in subsequent publications.

Wire materials with diameters of 200 μm and 500 μm provided by Fort Wayne Metals, NiTi#3, and Ingpuls, binary Ni_50.9Ti_49.1 [52, 53], were used for the tests. Samples were consistently cut to a free length of 90 mm.

Additionally, experiments were performed on Ni_51.1Ti_48.9 ribbons with a cross section of 1.7 mm² and a free length of 90 mm in order to illustrate the possibilities of the test setup [47].

All test results shown were obtained by experiments performed in an air-conditioned room with a stationary temperature of 22 °C to ensure repeatability and comparability.

There are several training-related aspects of particular relevance to elastocalorics.

For stable behavior, NiTi materials typically require a training procedure, consisting of a number of loading/unloading cycles.

The mechanical data obtained during training of NiTi#3, performed for 50 cycles with a maximum strain of 8% and a strain rate of 5 × 10⁻³ s⁻¹ is shown in figure 3. Starting from the first cycle, a significant reduction in upper plateau stress is observed, as well as an increase of remanent strain after unloading. Over several training cycles, the shape of hysteresis also changes. The singular stress drops on the upper plateau give way to a considerably smoother behavior, and as the lower plateau stress remains at a similar level, the size of the hysteresis also decreases. It becomes clear that the necessary elastocaloric work input can be reduced significantly through training, and hence it will also have an effect on the material COP.

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However, training is not only of relevance for elastocalorics because of its effect on mechanical work. The second aspect becomes visible by inspection of IR thermograms. Here, one can clearly see individual phase fronts propagating through the wire during loading in the first cycles, see, e.g. figure 4. These phenomena are well known since the work by Shaw et al [54], and they are also the reason for the stress drops on the transformation plateaus. However, Schmidt et al [55], could show that there is a training effect of this temperature behavior as well, which manifests itself in an increasing homogenization of the phase transformation by forming more and more nucleation sites over the cycles. This explains the fact that the stress/strain hysteresis becomes smoother with increasing number of cycles, but it is also a desirable feature for elastocalorics. Figure 5 shows that the temperature evolution upon mechanical loading and unloading has become increasingly homogeneous over the cycles. This means that the heat transfer to the environment now becomes significantly more efficient because the entire wire participates in the process instead of the nucleation front location only.

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Another aspect that is noteworthy here is the difference in elastocaloric behavior due to different wire geometries and different training parameters. While figures 4 and 5 showed the behavior of a 200 μm wire, figure 6 shows the temperature evolution for a thicker wire of the same material, resulting in complete thermal stabilization during the training procedure of a NiTi#3 wire with a diameter of 500 μm [55]. The training procedure consists of 100 cycles with a maximum strain of 9% and a strain rate of 1 × 10⁻³ s⁻¹. Distinct transformation fronts are visible during the 1st and 5th cycle, but after 100 cycles of training, shown in figure 6(c), they have completely disappeared, and the wire exhibits a very homogeneous distribution, optimally suited for heat transfer to, e.g. surrounding air or fluid. Also, the homogenization can be seen in other sample geometries, like displayed for ribbon samples in [55].

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Once the material is trained, it is exposed to adiabatic loading conditions. These are relevant for elastocalorics, because they lead to the largest possible temperature changes.

Before conducting specific experiments, adiabatic strain rates for the specific samples need to be identified by mechanical and thermal investigation. Figure 7 shows the change in mechanical behavior of Ni_51.1Ti_48.9 ribbon samples with increasing strain rates from 5 × 10⁻⁵ s⁻¹ up to 1 × 10⁻¹ s⁻¹ due to the thermomechanical coupling. The faster the strain rate, the less time the ribbon has for heat exchange with the environment, leading to a saturation behavior in the adiabatic limit [47]. In order to subsequently ensure a full exchange of released latent heats with the environment, the constant position after loading and unloading, respectively, is held for 150 s.

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It can be seen that shape and slope of hysteresis change for different applied strain rates. Furthermore, the resulting work input is increasing with increasing strain rate. Simultaneously performed thermal characterization shows the dependency of temperature peaks in relation to different strain rates, as displayed in figure 8. At about the rate of 5 × 10⁻² s⁻¹, the temperature increase and decrease in the material is saturating around 20 K. Increasing the strain rate to 1 × 10⁻¹ s⁻¹ does not increase the temperature change any further, and the mechanical hystereses displayed in figure 7 are no longer distinguishable, hence the adiabatic limit is reached.

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In order to investigate the efficiency of elastocaloric materials, latent heats also need to be determined along with the mechanical work from the hysteresis area. The measurements shown in the following were performed using the novel method introduced above.

Figure 9 illustrates the experimental procedure to determine the latent heat during loading of NiTi#3 with a maximum strain of 6.5%, covering complete phase transformation [46]. In figure 9(a), (upper part), mechanical strain (black) and different applied electric power pulses (colored) are displayed over time.

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The lower part, figure 9(b) displays the temperature change of the sample due to elastocaloric loading (black) and the resulting temperature changes during applied power pulses (colored).

During the experiment, four different electric power inputs were used to match the elastocaloric temperature change. The temperature variation from different electric power inputs clearly shows the amplitude of the red curve to be chosen too low and the light blue too high. The green curve perfectly matches the one from the mechanical loading experiment, and the corresponding latent heat for the investigated NiTi#3 in figure 9 can be determined as h_A→M = 15.4 J g⁻¹.

In the next step, this procedure is repeated for the unloading process, shown in figure 10. Figure 10(a) again displays the mechanical strain (black) and different applied power pulses (colored) while (b) displays the comparison of elastocaloric temperature change (black) and the electrically induced compensation of temperature (colored).

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The aim of this experiments is to compensate the elastocaloric cooling effect due the endothermic nature of the reverse martensite-austenite transformation. If the applied electric pulse power is not sufficient, see the red curve in figure 10(b), the temperature after the experiment is lower than the start temperature, and we observe a subsequent temperature increase until equilibrium with the environment is reached. On the other hand, application of overly high-power values leads to too high a temperature after unloading, and the reverse equilibration takes place, as the light blue curve shows. The correct power can be identified from end and start temperature being equal after the unloading process, shown in blue, and leads to a latent heat of h_M→A = 14.0 J g⁻¹. Note that the latent heat due to unloading is slightly lower, which can be expected due to the lower stress level of the hysteretic reverse transformation.

As a validation, the obtained values for latent heats are compared to different published DSC-based experimental results, e.g. Frenzel et al [35] performed a systematic study of various NiTi-based-alloys, resulting in latent heats of 9 J g⁻¹ up to 28 J g⁻¹ for binary NiTi. Shaw et al [44] cite latent heats in a range of 15–20 J g⁻¹. Performing DSC measurements on SMA thin film material, Brüderlin et al [57] also measured latent heats of 15 J g⁻¹.

These examples show that the latent heats determined by the proposed joule heating method fit right into the representative range for binary NiTi.

In elastocaloric applications, operation parameters may vary, and it is important to understand how this affects work, heats, and efficiency. To this end, a series of partial loading experiments was performed in order to show the process-depending mechanical and thermal behavior during complete and partial transformations. Figure 11 displays the stress/strain behavior and resulting hysteresis curves of multiple tests with a strain rate of 1 × 10⁻¹ s⁻¹ performed with Ni_50.9Ti_49.1. The tests were performed starting from a change in strain of 1% up to 6.5% in increments of 0.5%. After loading, a holding time of 10 s was added. The corresponding maximum temperatures prior to unloading are shown in figure 12. It can be seen that these temperatures scale linearly with the applied strain level.

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In contrast to DSC measurements, the effect of partial transformation on latent heats can also be investigated with the novel test setup. Figure 13 displays the determination of latent heat on unloading with a maximum Δ of 6%. In comparison, figure 14 shows the process with a maximum Δ of 3%.

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The tests performed with varying maximum strains show a decrease in released latent heat with decreasing maximum strain. For the applied Δ = 6%, a latent heat of h_M→A,6% = 14.5 J g⁻¹ is observable, for Δ = 3% the latent heat decreases to h_M→A,3% = 6.8 J g⁻¹.

Combining these results with area calculations from corresponding mechanical partial loading/unloading experiments, it will be possible to also calculate efficiencies for partial cycles and get a better estimate for machine operation under such circumstances.