Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation

Summary

Experimental methods for investigation of solid state cooling processes and characterization of elastocaloric material properties of Shape Memory Alloys (SMA) are presented. A custom-built test rig has been designed for controlling and comprehensive monitoring of elastocaloric cooling processes. Furthermore, it provides a validation platform for thermomechanically coupled modeling approaches.

Abstract

Shape Memory Alloys (SMA) using elastocaloric cooling processes have the potential to be an environmentally friendly alternative to the conventional vapor compression based cooling process. Nickel-Titanium (Ni-Ti) based alloy systems, especially, show large elastocaloric effects. Furthermore, exhibit large latent heats which is a necessary material property for the development of an efficient solid-state based cooling process. A scientific test rig has been designed to investigate these processes and the elastocaloric effects in SMAs. The realized test rig enables independent control of an SMA's mechanical loading and unloading cycles, as well as conductive heat transfer between SMA cooling elements and a heat source/sink. The test rig is equipped with a comprehensive monitoring system capable of synchronized measurements of mechanical and thermal parameters. In addition to determining the process-dependent mechanical work, the system also enables measurement of thermal caloric aspects of the elastocaloric cooling effect through use of a high-performance infrared camera. This combination is of particular interest, because it allows illustrations of localization and rate effects — both important for efficient heat transfer from the medium to be cooled.

The work presented describes an experimental method to identify elastocaloric material properties in different materials and sample geometries. Furthermore, the test rig is used to investigate different cooling process variations. The introduced analysis methods enable a differentiated consideration of material, process and related boundary condition influences on the process efficiency. The comparison of the experimental data with the simulation results (of a thermomechanically coupled finite element model) allows for better understanding of the underlying physics of the elastocaloric effect. In addition, the experimental results, as well as the findings based on the simulation results, are used to improve the material properties.

Introduction

Solid state cooling processes based on ferroic materials have potential to be environmentally friendly alternatives to the conventional vapor compression based process. Ferroic materials may exhibit magnetocaloric, electrocaloric and elastocaloric effects ^1,2, as well as combinations of these effects, which are described as multicaloric material behavior ³. The different caloric effects in ferroic materials are currently being investigated as part of the German Science Foundation (DFG) Priority program SPP 1599 "Caloric Effects in Ferroic Materials: New Concepts for Cooling" ⁴. Shape Memory Alloys (SMA) which are investigated within this program show large elastocaloric effects, in particular Ni-Ti based alloys due to their large latent heats ⁵. The strain-induced phase transformation at high strain rates leads to significant temperature changes of the SMA, as shown in Figure 1. The adiabatic, exothermic phase transformation from austenite to martensite increases the SMA temperature. The endothermic transformation from martensite to austenite leads to a significant temperature decrease. These elastocaloric material properties can be used for solid-state cooling processes by applying a suitable mechanical loading and unloading cycle. Figure 2 shows a typical elastocaloric cooling cycle, following the Brayton cycle. The heat transfer between the heat source and the cold, unloaded SMA take place at low temperature levels. In the next phase, the SMA is in a contact-free state and the fast, adiabatic loading leads to a significant temperature increase of the SMA. The subsequent heat transfer between the hot SMA and the heat sink take place at constant strain of the SMA. Upon completion of the heat transfer, fast, adiabatic unloading leads to a significant temperature drop of the SMA below the temperature of the heat source, whereupon the next cooling cycle and the heat transfer with the heat source can start. The efficiency of the elastocaloric cooling process depends on the required mechanical work and the absorbed heat.

First, experiments monitoring the temperature field during tensile tests were performed by Shaw et al. ^6,7, with the objective to investigate the formation of local temperature peaks during tensile tests of SMA strips and wires at different rates. The applied experimental method combined the measurement of the mechanical parameters (stress, strain and strain rate) with simultaneous acquisition of temperature fields by means of thermographic measurements. During loading and unloading of a SMA specimen with a tensile testing machine, an infrared (IR) camera was used to acquire IR images of the SMA sample. This technique enables the investigation of the strain rate dependent formation of temperature peaks. The measurement of the temperature distribution on the sample is very important for the investigation of the elastocaloric effects and the determination of the cooling properties of the material. A local temperature measurement — by applying a contacting temperature measurement — is not sufficient in order to characterize the cooling properties of the material. A measurement of the temperature field was also used by Cui et al. ⁸ for the study of elastocaloric effects in Ni-Ti wires. Furthermore, Ossmer et al. ^9,10 showed that thermographic temperature measurements are also suitable for the investigation of elastocaloric effects in Ni-Ti based thin films, which required high frame rates of the IR camera for the investigation of adiabatic phase transformations at high strain rates. This technique allows for the investigation of elastocaloric quantities and the homogeneity of the temperature profile, which has a significant influence on the solid-state based heat transfer and the efficiency of elastocaloric processes.

The cooling efficiency of the material can be determined by calculating the required work based on the stress/strain measurements as well as the heat (which can be determined taking into account the temperature change and the heat capacity of the material). However, the experimental method does not enable the investigation of the elastocaloric material under process condition. This includes a heat transfer between the SMA and a heat source, which has a significant influence on the efficiency of the cooling effect.

The material characterization of cooling process conditions and the investigation of elastocaloric cooling processes require a test rig enabling solid-state based heat transfer, which cannot be investigated by any existing commercial system. To this end, a novel testing platform has been developed. The test rig is set up in two levels as shown in Figure 3. The upper level allows for basic elastocaloric material characterization and initial training procedures, similar to the previously described method (see Figure 4). The setup is equipped with a linear direct drive capable of loading and unloading the SMA at strain rates up to 1 sec^-1 (see Figure 5). The linear direct drive enables the investigation of samples with a cross section of up to 1.8 mm², while the typical sample length is 90 mm. The advantage of a linear direct drive is the high velocity and the high acceleration — in contrast to ball screw drives which are typically used for tensile tests. Furthermore, a load cell, as well as the integrated position measurement system of the linear drive, provides mechanical measurement data. A high-resolution IR camera (1,280 x 1,024 pixels) is used to measure the temperature profile of the SMA with up to 400 Hz (in the required temperature range). The use of a microscope lens with a resolution of 15 µm/pixel enables the investigation of local temperature effects. The lower level of the test rig contains a mechanism that allows for alternating conductive heat transfer between the SMA and the heat source/heat sink (see Figures 6 and 7). The linear direct drive in the lower level switches between the heat source to the SMA and from the SMA to the heat sink, whereas a pneumatic cylinder lifts and lowers the heat source/sink (see Figure 8). Each actuator can be controlled independently allowing for investigation of different cooling process variations. The comprehensive measurement system enables measurements of mechanical parameters: actuator position, actuator velocity, SMA loading force, contact force between SMA and heat source/sink during heat transfer as well as thermal parameters (i.e., temperatures inside the heat source/sink, temperature distribution on the surface of the SMA and the heat source/sink). A more detailed description of the scientific testing platform is given in Schmidt et al. ¹¹.

Figure 5. Scheme of the upper level of the test rig. A linear direct drive for loading and unloading of the SMA sample with integrated position measurement system; a load cell for measuring of tensile forces, as well as a high-resolution IR camera (1,280 x 1,024 pixels) for temperature profile acquisitions.

Figure 7. Scheme of the lower level of the test rig. A linear direct drive for switching between heat sink and heat source; a pneumatic cylinder to make contact between the SMA sample and the heat source/sink; temperature sensors have been integrated in the heat sink/source to measure the core temperature of the blocks. A compression load cell for measuring the contact force between the SMA and the heat source/sink is integrated in the heat transfer mechanism and not visible in this scheme.

The test rig allows for the investigation of different alloy compositions and sample sizes as well as geometries (ribbons, wires). Furthermore, the setup enables comprehensive investigations of elastocaloric materials and cooling processes. The previously described experiments can be performed and the execution will be described step-by-step in the protocol section of this manuscript.

Material stabilization:

Stable material behavior is important for the use of elastocaloric materials in cooling systems. To this end, a mechanical stabilization procedure is applied. During this procedure the material passes mechanical loading and unloading cycles and performs a phase transformation from austenite to martensite. The material stabilization shows a strong rate dependency. High loading rates lead to a temperature change of the material, which is caused by the latent heat of the phase transformation. This temperature change has a similar influence on the material stabilization, as do mechanical training cycles at various temperatures ^12-15. In addition to the well-known mechanical ¹³ and caloric ¹⁶ stabilization, a thermal material stabilization can be observed with the designed setup by applying thermography ¹⁷.

Material characterization:

After an initial mechanical training procedure, the material shows stable mechanical, thermal and caloric behavior allowing the elastocaloric material properties to be characterized. Therefore, mechanical cycling at different rates is performed whereas, in contrast to the training procedure, the elastocaloric characterization includes a holding phase after loading and unloading. For the duration of the holding phase the SMA strain is kept constant until an ambient temperature level is reached again. This type of experiment is required in order to determine the lowest achievable temperature after unloading, starting from ambient temperature levels, as well as the material efficiency. Rate dependent formation of local temperature peaks can be observed, with higher rates leading to an increasingly homogeneous temperature distribution. Furthermore, by increasing the strain rate the temperature change equally increases until adiabatic conditions are achieved. The material efficiency can be determined by calculating the required mechanical work, based on a force-displacement diagram of an adiabatic experiment, as well as the absorbable heat, based on the mean temperature change of the material during unloading and the heat capacity of the sample.

Elastocaloric cooling process:

The investigation of the cooling efficiency of SMAs under process conditions requires the heat transfer between the SMA cooling medium and a heat source, as well as a heat sink. For this purpose, the SMA is in contact with a solid-state heat source (following adiabatic unloading) and a heat sink (following adiabatic loading). The efficiency of the process strongly depends on the process control and the thermal boundary conditions. The comprehensive investigation of the cooling process requires a variation of the control parameters in order to determine the most efficient process control. The individual influence of the parameters (contact time, SMA strain, SMA strain rate, contact phase (contact during the loading/unloading phase or following) and contact force) on the process performance has to be investigated. Furthermore, the influence of the changing thermal boundary condition by increasing number of cooling cycles has to be taken into account.

Model validation:

The development of a thermomechanically coupled material model, capable of reproducing the mechanical and thermal material behavior during cooling cycle, is crucial for the development of a novel cooling technology. The model allows for material and process optimization by reduced experimental and material development effort. The validation requires an initial isothermal tensile test of a stabilized material to generate the required mechanical material input data (elastic modulus of the austenite and the martensite phase, the width of the mechanical hysteresis as well as the transformation strain). The validation of the model takes place on the basis of tensile tests at different rates. The required caloric input data for the model can be determined by differential scanning calorimetry (DSC) following the mechanical experiments. The DSC measurements have to be performed after the mechanical test in order to measure the caloric material properties of a stabilized sample.

Protocol

1. Sample Preparation

1. Measure the SMA ribbon with calipers and determine the cross section of the sample.
2. Prepare the sample for IR measurements by coating the ribbon with a thin layer of high emissivity (ε=0.96) paint.
   Caution: The paint is classified as an irritant. Gloves, safety glasses and mouth protection must be worn during the processing of the paint.

2. Material Stabilization (Training)

Note: Initial mechanical cycling leads to a mechanical and thermal material stabilization. The investigation of the stabilization effect, and the training procedure itself, requires the use of the actuator and the sensors mounted in the upper level of the test rig as well as the IR camera.

1. Start motor controller program and check the loaded settings. Change the settings to position mode and command mode. Verify the motor is in active mode.
2. Set the target position in the motor controller program to 0 µm and click on the "operation enable" button — at this position the distance between the clamps is 90 mm.
3. Place the sample between clamps of the experimental setup and use a special designed alignment tool to align the sample.
4. Tighten clamps using a mounting aid in order to avoid bending load on load cell and sample. Use a torque wrench for tightening the screws to ensure a reproducible clamping force (tightening torque: 20 Nm).
5. Check current motor position and make sure that the motor is at start position (0 µm).
6. Start the IR camera software and load the calibration for a 50 mm lens combined with a close-up lens. Choose an image size of 1,280 x 100 pixels and a temperature range of -20 °C to 50 °C. Position the camera by using the motor focus unit and confirm the whole sample is in the field of view of the camera.
   Note: The IR camera, in combination with the chosen lens system, has a focal length (f) of 50 mm, an aperture of f/2 and a minimum pixel size of 60 µm at a working distance of 200 mm.
7. Open the control program for training and material characterization and set the control parameters (displacement, velocity, holding time, maximum and minimum force, number of cycles and camera frame rate).
   1. Set the start position (0 µm) and choose the target position (4,500 µm) so that the material undergoes a complete phase transformation.
   2. Set the linear direct drive velocity (velocity loading/ unloading) to meet the desired strain rate. Select a strain rate of 5 x 10^-4 sec^-1 (actuator velocity of 45 µm/sec) for cooling process related training.
      1. Determine the linear direct drive velocity (v) based on the chosen strain rate () and the initial sample length (l₀) of 90 mm (v = ∙l₀)
   3. Set the holding time to 0 sec.
   4. Set the number of cycles to 1 for the first cycle with a new sample.
   5. Set the sample-specific minimum and maximum force level to avoid compressive load and tensile overload (minimum load 1 MPa, maximum load 800 MPa).
   6. Choose an IR camera acquisition rate of 50 msec/frame (20 frames per second).
   7. Click on the start button to load the settings.
8. Open the IR camera software, choose a file name and allocate 5,000 frames.
   1. Switch from internal to external trigger source and start the data acquisition mode.
9. Open the control program and press the start experiment button.
10. Data visualization
    1. Once the experiment is finished, load the data into the data processing software and visualize it in terms of force/displacement, stress/strain, force/time and position/time diagrams.
    2. Load the IR data into the IR camera software and evaluate the time resolved temperature profiles. Define a measurement area which covers the surface of the SMA ribbon and plot the mean maximum and minimum temperature of the sample vs. time.
11. Repeat steps 2.6 to 2.9 until the material shows stable mechanical behavior and adapt the start position to compensate for residual strains.
    1. After the first 10 cycles, increase the number of cycles per experiment to 10 and proceed with the experiments until stable material behavior is reached.

3. Material Characterization

Note: The material characterization requires the use of the actuator and the sensors mounted in the upper level of the test rig as well as the IR camera. During the characterization procedure the sample is loaded and unloaded at different rates while performing a holding period after loading and unloading.

1. If the SMA ribbon has been unclamped and the control system of the test rig has been switched off after the training, repeat steps 2.1 to 2.6 and clamp the sample again. If this was not the case, proceed as follows.
2. Open the control program for training and material characterization and set the control parameters (displacement, velocity, holding time, number of cycles and camera frame rate).
   1. Set the start position so that the sample is under zero load and set the target position equivalent to the target position of the training (4,500 µm).
   2. Set the linear direct drive velocity (velocity loading/unloading) to meet the desired strain rate. Choose a strain rate of 1 x 10^-1 sec^-1 (actuator velocity of 9,000 µm/sec) which leads to an adiabatic phase transformation for samples with a cross section of 0.75 mm x 1.4 mm or larger.
   3. Set the holding time to 180 sec, which is sufficient for the sample to reach the initial temperature level.
      Note: The holding time has to be verified after the experiment by calculating a thermal equilibration time constant (τ) and a holding time smaller than 4 x τ has to be increased before the next characterization experiment starts.
   4. Set the number of cycles to 1.
   5. Set the sample-specific minimum and maximum force level to avoid compressive load and tensile overload (minimum load 1 MPa, maximum load 800 MPa).
   6. Choose an IR camera acquisition rate of 5 msec/frame (200 frames per second).
   7. Click on the start button to load the settings.
3. Open the IR camera software, choose a file name and allocate 80,000 frames.
   1. Switch from internal to external trigger source and start the data acquisition mode.
4. Open the control program and press the start experiment button.
5. Load the IR data into the IR camera software. Plot mean maximum and minimum sample temperatures vs. time. Export the data and calculate the thermal equilibration time constant with the data processing software ^10,11.
6. Adapt the holding time, if necessary, based on the calculated thermal equilibration time constant.
7. Repeat steps 3.2 to 3.5 and vary the strain rate from 5 x 10^-5 sec^-1 to 1 x 10^-1 sec^-1, as well as the strain from 2% to a maximum strain of 5% (maximum strain is equivalent to the maximum strain during training).
8. Investigation of local temperature peaks:
   Note: The material shows a rate-dependent localization effect of the elastocaloric effect. Careful study of these effects requires a high special resolution of the SMA temperature profile. For this purpose, the lens of the IR Camera has to be replaced by a microscope lens. The microscope lens has an aperture of 3.0, a magnification of 1X and a pixel size of 15 µm at a working distance of 195 mm.
   1. Switch the light off, remove all heat sources from the field of view of the IR camera and change the lens.
   2. Change the camera calibration settings and load a microscope lens calibration within the temperature range of 20 °C to 50 °C and an image size of 500 x 250 pixels. Use the motor focus unit to focus the sample.
   3. Perform a tensile test at a strain rate of 1 x 10^-1 sec^-1 (9,000 μm/sec), follow the steps described in section 2: Material stabilization.
9. Data Visualization
   1. Load the mechanical data into the data processing software and visualize it in terms of force/displacement, stress/strain, force/time and position/time diagrams.
   2. Load the IR data into the IR camera software and evaluate the time resolved temperature profiles. Define a measurement area which covers the surface of the SMA ribbon and plot the mean maximum and minimum temperature of the sample vs. time.

4. Elastocaloric Cooling Process

Note: The investigation of elastocaloric cooling processes requires the use of actuators and sensors in the upper and lower level of the setup as well as the IR camera. These experiments include a variation of the control parameters in order to optimize the process performance.

1. If the SMA ribbon has been unclamped and the test rig has been switched off after the material characterization, repeat steps 2.1 to 2.5 and clamp the sample again. If this was not the case, proceed as follows.
2. Start the IR camera software and load the calibration for the 50 mm lens with close-up lens. Choose an image size of 1,280 x 1,024 pixels and a temperature range of -20 °C to 50 °C. Position the camera by using the motor focus unit and make sure that the entire sample is in the field of view of the camera.
   Note: The IR camera in combination with the chosen lens system has a focal length (f) of 50 mm, an aperture of f/2 and a minimum pixel size of 60 µm at a working distance of 200 mm.
3. Open the control program for elastocaloric cooling processes and set the control parameters (displacement of linear direct drive one (upper level), velocity of linear direct drive one and two, contact time, maximum and minimum force, contact phase, number of cycles and camera frame rate).
   1. Set the start position of the linear direct drive for SMA loading and unloading, so that the sample is under zero load and set the target position equivalent to the target position of the training (4,500 µm).
   2. Set the velocity (velocity loading/unloading) of the linear direct drive for loading and unloading of the SMA to meet a strain rate of 1 x 10^-1 sec^-1 (9,000 µm/sec). Set the velocity of the linear direct drive in the lower level of the setup to 100 mm/sec.
   3. Set the contact time to 6 sec.
      Note: The contact time determines the duration of the heat transfer and can be set to any value above 10 msec.
   4. Choose the contact after loading/unloading mode.
      Note: The contact phase influences whether the loading and unloading is adiabatic (contact after loading/unloading) or combined with a heat transfer to the heat sink/source (contact during loading/unloading).
   5. Set the number of cycles to 40.
   6. Set the sample-specific minimum and maximum force level to avoid compressive load and tensile overload (minimum load 1 MPa, maximum load 800 MPa).
   7. Choose an IR camera acquisition rate of 20 msec/frame (50 frames per second). Click on the start button to load the settings.
4. Open the IR camera software, choose a file name and allocate 50000 frames. Switch from internal to external trigger source and start the data acquisition mode.
5. Open the control program and press the start experiment button.
6. Data visualization
   1. Once the experiment is finished load the data into the data processing software and visualize the following data: force/displacement, stress/strain, temperature/time (temperature of the heat sink/source), force/time, contact force/ time and position of the linear actuators/time.
   2. Load the IR data into the IR camera software and evaluate the time resolved temperature profiles. Define three measurement areas which cover the surface of the SMA sample as well as the surface of the heat sink and the heat source. Export the time resolved mean, maximum and minimum temperature data of the defined measurement areas and load them into the data processing software.
   3. Visualize the IR data in a temperature/time diagram.
7. Repeat the experiment under variation of the parameters: strain, contact time and contact phase.

5. Model Validation

Note: The validation of thermo-mechanically coupled material models requires experiments adhering to material stabilization or material characterization. Use a Ni-Ti wire with a cross section of 0.6 mm to perform the experimental investigations.

1. Perform an isothermal tensile test at a strain rate of 5 x 10^-5 sec^-1 and a strain of 5%, proceed by performing the steps described in Section 2.
2. Once the experiment is finished, load the data into the data processing software and visualize the stress/strain measurement. Calculate the elastic modulus of the austenite and the martensite phase, the transformation strain as well as the width of the hysteresis. The aforementioned data function as mechanical input data for the model ⁷.
3. Perform further tensile tests at strain rates of 1 x 10^-4 sec^-1, 5 x 10^-4 sec^-1, 1 x 10^-3 sec^-1, 5 x 10^-3 sec^-1, 1 x 10^-2 sec^-1, 5 x 10^-2 sec^-1, 1 x 10^-1 sec^-1 to generate validation data for the model.
4. If the experiments are completed take the sample out of the test system and perform a differential scanning calorimetric measurement (DSC) ¹⁸ to determine the caloric material properties (latent heats of the phase transformation and specific heat capacity of the material) of the stabilized material.
   Note: The DSC measurements provide caloric input data for the thermo-mechanically coupled model.
5. Start the simulation of the tensile tests described in step 5.3.
   1. Implement custom model for shape memory alloys into commercially available finite element software:
      1. Select Geometry node and choose Interval to draw 1D wire geometry.
      2. Select Parameters node to define model parameters identified from mechanical tests in step 5.2.
      3. Right-click Definitions node and select Variables to create a Variables node. Select Variables node and define algorithm for determining the transition probabilities derived from statistical thermodynamics ¹⁹.
      4. Select Add Physics and add Coefficient Form PDE or General Form PDE to define set of one-dimensional partial differential equations describing the behavior of superelastic Shape Memory Alloy, consisting of the stationary momentum balance, the balance of internal energy and kinetic equations of phase transformation ²⁰.
   2. Select Initial Values sub-node to set the initial temperature of the wire to the environment temperature.
      1. Select Dirichlet Boundary Condition to prescribe mechanical boundary conditions for applying a strain following the experimental procedure described in section 2, for the strain-rates in step 5.3, constraining the displacement of one end of the wire and prescribing the displacement of the other end.
      2. Select Dirichlet Boundary Condition to set thermal boundary conditions to constant temperature because of the massive clamps compared to the thin wire.
         Note: Standard settings of the finite element software do not lead to a converging solution.
      3. Select sub-nodes of Solver Configuration to modify standard settings (e.g., absolute and relative tolerances and damping coefficient of the nonlinear, iterative Newton-Raphson solver) and click "Compute" to run solver.
6. Data Analysis
   1. Load the experimental and simulation results into the data analysis software and visualize the mechanical and thermal data.
   2. Compare the experimental and simulation results, respective mechanical (stress/strain response) and thermal (special resolved temperature evolution of the sample) material behavior.

Results

Material stabilization (Training):

Figure 9 shows a stress/strain diagram of 50 training cycles. The investigated sample is a Ni-Ti ribbon with a cross section of A = 1.45 mm². The applied strain rate of 1 x 10^-3 sec^-1 leads to a mean temperature increase of ΔT = 12.2 K. The temperature increase has a significant influence on the stabilization effect ^12-

Discussion

The presented scientific test rig enables comprehensive investigation of elastocaloric materials and cooling processes by performing the experiments described in the protocol section. Precise alignment of the sample before clamping is crucial for all the experiments. Bad alignment can potentially lead to early material failure. Furthermore, the maximum applied strain has significant influence on the material lifetime, whereas the required strain to reach a complete phase transformation depends on the alloy composition. T...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Linear direct drives	ESR-Pollmeier	ML 1418-U5-W1	SMA loading/unloading; heat transfer
Pneumatic cylinder	Festo	ADNGF-40 574031	Contact between heat source/sink and SMA
Inductive position measurement system	AMO	LMKA-1101.1NN-1.0-0
Tension and compression load cell	Futek	LCF451; FSH02241	SMA force
Compression load cell	Futek	LTH300; FSH00297	Contact force
IR camera	Infra Tec	Image IR 9360; M91129	1,280 x 1,024 pixels; Maximum frame rate 3,200 Hz
Real-Time Controller	National Instruments	NI CompactRIO-9074	Data acquisiton and control system
Camera varnish	Tetenal	105202