Electromechanical Fatigue Properties of Dielectric Elastomer Capacitive Sensors Based on Plantarflexion of the Human Ankle Joint

Wearable stretch sensors have potential applications across many fields including medicine and sports, but the accuracy of the data produced by the sensors over repeated uses is largely unknown due to a paucity of high-cycle fatigue (HCF) studies on both the materials comprising the sensors and the signal produced by the sensors. To overcome these limitations, using human physiologically-based parameters, stretch sensors were subjected to quasi-static testing and HCF with simultaneous capture of the signal. The strain produced by the sensor was then compared to the strain produced by testing instrument, and the results suggest that the output from the stretch sensors is strongly correlated with output from the testing instrument under quasi-static conditions; however, this correlation deteriorates under fatigue conditions. Such deterioration may be the result of several factors, including a mismatch between the material response to fatiguing and the signal response to fatiguing. From a materials perspective, the shape of the stress-life curve for the polymers comprising the sensors conforms to the Rabinowitz-Beardmore model of polymer fatigue. Based on these results, consideration of the material properties of a stretch sensor are necessary to determine how accurate the output from the sensor will be for a given application.

Fatigue life estimations were originally developed for metals. [1][2][3][4] Many of the fatigue life estimations for metals incorporate Basquin's equation (Eq. 1) to estimate high-cycle fatigue (HCF) behavior, 4 or the Coffin-Manson equation (Eq. 2) 1-3 to estimate low-cycle fatigue (LCF) behavior, and these equations were later extended for use with polymers. [5][6][7][8][9] Application of Basquin's equation to polymers is difficult due to the requirement that the loading be fully reversed. 4 For example, fully reversed loading of a stretch polymer would result in bending stress when in compression. Further, fatigue failure of some polymers can require tens of millions of cycles, and due to time constraints, many polymer fatigue tests are ended with runout rather than reaching the true failure cycle. Similarly, the Coffin-Manson equation may not be suitable for polymers due to their strain rate dependence and susceptibility to thermal fatigue. 7 To overcome these limitations, Opp et al. 7 developed one of the first fatigue models solely based on polymeric behavior. Their Combined Energy Model was based on the hysteresis energy of a polymer, and how the hysteresis energy could be transformed into other forms of energy such as occurs when heat is generated from the mechanical testing of a polymer. Based on the Combined Energy Model, nine fatigue behaviors were predicted for polymers: (1) loading frequency and fatigue life are inversely correlated-an increase in loading energy results in a decrease in fatigue life, (2) thicker polymers have shortened fatigue lives due to the increase in temperature facilitated by the increased cross-sectional area, (3) fatigue life is dependent upon the polymer itself, ambient temperature, and strain amplitude, (4) stress concentrations at the surface of a polymer allow for the radiation of heat, and may increase the fatigue life of the polymer, (5) polymers fail through either melt fracture or crack propagation, (6) resting of the polymer increases fatigue life by allowing the polymer to cool, (7) the waveform chosen for fatigue testing can affect the fatigue life of the polymer-a sinusoidal pattern results in an increase in the fatigue life vs a ramping waveform, (8) instability of the fatigue curve and failure at lower strain amplitudes can occur if the ambient temperature exceeds the glass transition temperature, and (9) if the glass transition temperature of the polymer is higher than the ambient temperature, the polymer will have an endurance limit. Conversely, if the ambient temperature is higher than the glass transition temperature, the polymer has no endurance limit. 7  8 and Rabinowitz and Beardmore 9 also investigated the fatigue behaviors of thermoplastic polymers and developed fatigue models to explain the processes occurring as polystyrene (PS), polymethylmethacrylate (PMMA), and polycarbonate (PC) are fatigued. Based on the fatiguing of polystyrene, a threez E-mail: selder@abe.msstate.edu phase fatigue-life model was developed. The first phase of the model is the short-life region (Region I) and is representative of thermoplastics fatigued at high stress amplitudes. 6,8 Region I is dominated by crazing resulting from repeated applications of high tensile stress. 8 The second phase of the model, or the intermediate-life  region (Region II), is a sloped region representative of the linear relationship between stress (or strain) and the fatigue life. 8 In the third phase, or long-life region (Region III) of the model, the endurance limit of the polymer is achieved. 8 The Rabinowitz-Beardmore model 9 is based on the fatigue of PC and PMMA and identifies four stages of cyclic behavior which include: (1) an incubation stage includes the initial monotonic overloading that occurs with the first cycle and the subsequent cyclic softening of the polymer, (2) followed by a transition stage in which the peak stress begins to decline until (3) a stage of cyclic stability is reached, and ends with (4) the crack propagation stage which concludes with fracture of the polymer. 6,9,10 Following the initial monotonic overload, the polymer chains begin to disentangle during the transition stage, until the microstructure stabilizes in the third stage. 10 These stages can be identified by plotting the peak stress against the number of cycles (Fig. 1). 9 Despite the development of polymer fatigue life models, polymer fatigue testing studies still lag behind those of metals, 6 and of those studies, few studies have focused on modeling the fatigue behaviors of dielectric elastomeric polymers, such as those used in stretch sensors, due in part to how the differing microstructures of thermoplastics and elastomers respond to cyclic testing. Further confounding the issue: (1) the polymers utilized in stretch sensors may be mixed with a variety of additional materials including carbon nanotubes and fabrics, and (2) few fatigue studies performed on stretch sensors have focused on sensors utilizing capacitive sensing. [10][11][12][13][14][15] The microstructure of thermoplastic polymers is often comprised of entangled polymer chains; whereas, the microstructure of elastomers, such as the silicone used in stretch sensors, tend to be comprised of bonded cross-links. 16 In general, fatigue failure of thermoplastic polymers is initiated by crazes formed in the entangled chains during the repeated cycling. During crazing, voids begin to nucleate at localized defects in the material, typically normal to the principle strain direction, and as cycling continues, the voids coalesce, resulting in crack formation and propagation which decreases the elastic modulus causing failure of the thermoplastic polymer. 17,18 Conversely, a study of a cross-linked silicone-based dielectric elastomeric polymer subjected to 100,000 cycles found that over increasing cycles, the density of the cross-links in the silicone increased resulting in a concomitant increase the elastic modulus of silicone. 19 The increases in the cross-link density and the elastic modulus generally allows for increased cycling of elastomers in comparison to thermoplastics; however, repeated cycling of elastomers can result in polymer chain debonding and rearrangements and breakdown of the cross-links resulting in failure of the elastomer. 20 Stretch sensors have many potential applications especially in the medical, pharmaceutical, and athletic fields, 10, and interest in the use of not only stretch sensors, but wearable technologies in general, has continued to grow because of their potential use in telehealth applications. 10,[46][47][48][49][50][51][52][53][54] Despite the increased interest in the use of stretch sensors, fatigue testing standards for stretch sensors do not currently exist, 10,55 leading to the employment of variable methodologies in fatigue studies of stretch sensors. 10 Further, the fatigue testing of stretch sensors has the added complexity of not only determining the life of the materials comprising the sensors, but also the stability of the signal over time. 10 Fatigue studies of stretch sensors often focus on high amplitude, low-cycle fatigue (LCF), with the number of cycles varying for different studies. 11,12,26,27,[56][57][58][59][60][61][62][63][64] Stretch sensors used in pharmaceutical, medical, or athletic applications, however, would be expected to undergo low amplitude, high-cycle fatigue (HCF), but such HCF studies are lacking. 10 For example, a smart sock prototype that uses stretch sensors to measure the angle of the ankle joint is in development at Mississippi State University, and one of the goals for the prototype is its use to measure joint angles during athletic competitions. 22,24,25,65,66 If the sock prototype were worn over the course of a 20 game women's National Collegiate Athletic Association Division I (NCAA D1) soccer season, at least 178,200 steps would be taken exclusive of conference or national championship games, 67 which would subject the stretch sensors to recurrent HCF.
The current smart sock prototype utilizes StretchSENSE™ Stretch FABRIC sensors to capture movement data; however, production of these sensors has ceased, and the potential of using FlexSense stretch sensors (Parker Hannifin, Minneapolis, MN, USA) in the smart sock prototype is currently being explored. FlexSense dielectric elastomer stretch sensors contain a strip of conductive carbon ink encapsulated in a silicone film inserted between two electrodes. As the sensor is stretched, the film thins and increases its area producing an increase in capacitance which is output as a stretch percentage. 68, 69 Currently, the number of times a dielectric sensor can be used before its performance degrades is poorly understood; therefore, to assess the fatigue properties of not only the materials comprising the FlexSense sensors, but also the stability of the signal over time, the sensors were subjected to HCF with simultaneous capture of the signal output as the sensor is fatigued. Additionally, the potential of applying the Rabinowitz-Beardmore model 9 to explain the fatigue behavior of dielectric elastomeric polymers, such as those used in the FlexSense stretch sensors, will also be explored.

Experimental
The dimensions of the FlexSense sensors are 139 mm long × 16 mm wide × 0.66 mm thick with a gauge length of 100 mm (Fig. 2). Output from the sensor is given as percentage stretch; therefore, fully stretching the sensor its gauge length of 100 mm produces an output of 100% stretch. Each FlexSense sensor is equipped with a microchip that transmits data to a computer via a mini B to USB cable. The interface provided with the sensors allows the sampling rate to be changed and the stretch percentage to be zeroed. Output includes the time (s), total stretch percentage, and tared stretch percentage.
Quasi-static tests.-Initial characterization of the electromechanical properties of the FlexSense sensors were assessed through quasi-static testing at one of three strain rates: 0.02 s −1 , 0.05 s −1 , or 0.08 s −1 . Three FlexSense sensors were tested in tension for each strain rate using an Instron 5869 electromechanical testing system equipped with a 100 N load cell. Output from the sensor was also simultaneously collected for each tensile test at a sampling rate of 50 Hz. All tests were performed at ambient temperature. Results from the quasi-static tests were then used to create stress-strain curves for the material and to assess the linearity of the signal through correlation of the strain and stretch percentage. The stretch percentage data were initially decimated by a factor of 2, and the Shapiro-Wilk test for normality (α = 0.05) was then used to test the null hypothesis that strain and stretch percentage for each strain rate are normally distributed. Results of the Shapiro-Wilk test show that the strain and stretch percentage for each strain rate are not normally distributed (p < 0.05, reject the null hypothesis, the data do not have a normal distribution); therefore, the correlation between the strain and stretch percentage for each strain rate were tested using a two-tailed Spearman's Rank Correlation Coefficient test. 70 All data and statistical analyses were performed using OriginPro Version 2022 (OriginLab Corporation, Northampton, MA, USA).
To further assess the material properties of the FlexSense sensors, five dog bone coupons (3.32 mm long × 0.63 mm thick, with a gauge length of 19 mm) were stamped out of the conductive area of the sensors for tensile testing (Fig. 3). The dog bone coupons were tested using a MACH-1 Micromechanical System equipped with a 10 kg load cell. All tests were performed at ambient temperature at a strain rate of 0.05 s −1 .
Fatigue tests.-HCF fatigue tests were performed on FlexSense sensors using an MTS 858 table top material testing system equipped with a 1.0 kN load cell. All fatigue tests were performed at ambient temperature, using a sinusoidal waveform, under displacement control. Displacement was based on the mean 25°of plantarflexion for the human ankle joint. 71 Prior to the start of the fatigue test, each sensors was manually tensioned in the MTS 858 until approximately 12 mm of displacement was reached. At this point, all measurements were zeroed, and the test began. Maximum displacement for all tests was set at approximately 13 mm. The initial tensioning plus the maximum displacement allowed for a total stretch of 25 mm.
To protect the microchip at the end of the sensor, and allow for data collection from the sensors during the fatigue tests, eyehooks were attached to the ends of two 12″ long 1″ × 2″ vertically-oriented pine boards. The eyehooks were placed approximately one inch from the top edges of the boards. Each board was centered in the grips of the MTS 858, and the sensors were then attached to the eyehooks (Fig. 4).
The signal from the sensor was also captured simultaneously with the fatigue test. After the displacement was manually tensioned to 12 mm on the MTS, the signal produced by the sensor was also tared allowing the displacement recorded by the MTS to be directly compared to the stretch percentage recorded by the sensor (i.e., 13 mm of displacement equals 13% stretch). A sampling rate of 200 Hz was used for all tests.
Two HCF tests were performed at a cycling rate of 2.5 Hz. This rate was based the average self-selected step frequency used by some athletes when running at various speeds. 72 To test the limits of the sensors, three tests were also performed with a cycling rate of 10 Hz.
Data from the HCF tests were used to create stress-life curves, while the signal data was linearly interpolated to the correct number of cycles. The strain, calculated from the displacement recorded by the MTS, and the proportion of the peak stretch percentage output by the sensor were then compared. Signal peaks were found in the raw, non-interpolated data using the top 10 function available in OriginPro Version 2022. The peaks found using this function are returned in the order in which they are found, rather than ranked, but, due the large number of lines of signal data collected at 200 Hz, an excess number of peaks were returned for each dataset. To equilibrate the number of signal peaks to the number of fatigue cycles, linear interpolation was applied to the peaks. For a more direct comparison of the strain and stretch, the stretch percentage was converted to strain, and the resulting proportion was then scalable with the strain calculated from the displacement measured by the displacement transducer/actuator of the MTS 858. Because the peaks do not form a normal distribution, a two-tailed Mann-Whitney test, which is also known as the Wilcoxon Rank Sum test, was applied to the peak stretch and peak strain datasets to determine if the two datasets have the same distribution (H 0 : no difference exists between the distributions of the two samples; H A : a difference exists between the distributions of the two samples). 70

Results
Quasi-static tests.-The stress-strain loading curves exhibit a viscoelastic loading response. At the strain rates employed, strainrate dependency of the materials cannot be determined as all of the curves lie atop one another (Fig. 5a). Based on the results of the Spearman Rank Correlation Coefficient test, the strain and stretch percentage are strongly correlated (coefficient of 1) for all strain rates (Figs. 5b-5d).
To determine if the conductive ink strip exhibited a different response, the dog bone coupons were tested. Of the five tests performed, data from dog bone coupon 2.1 were not included in the  analysis because the coupon slipped from the top grip of the MACH 1 during testing. The remaining four dog bone coupons tested also exhibit a viscoelastic loading response (Fig. 6).
Fatigue tests.-Of the two fatigue tests performed at a cycling rate of 2.5 Hz, one test ran for 450,000 cycles, while the second was truncated after 250,000 cycles due to an issue with the MTS 858. As the signal recorded for the initial 20,000 cycles of the FlexSense sensor tested to 450,000 cycles were sampled at a rate of only 10 Hz, these initial cycles have been removed from all analyses involving the stretch percentage.
An averaged stress-life curve for the sensors cycled at 2.5 Hz is presented in Fig. 7. Note that the stresses decrease into negative values as a result of the size of the load cell; however, the pattern of the stress does provide insight into the fatigue behavior of the materials comprising the sensor. In particular, the stress is increased as cycling begins, but begins to decline following the initial cycle before transitioning to steady-state stress at approximately 150,000 cycles.
Linearly interpolated signal data are presented in Figs. 8a and 8b. No drops in signal are visible on the 450,000-cycle plot; however, the signal is briefly dropped five times before stabilizing after 50,000 cycles on the 250,000-cycle plot. The distribution of the peak strain calculated from the actuator for the 450,000-cycle dataset remains fairly tight about the mean (std. dev. = 0.0007), but the distribution  Similarly, the distribution of the peak actuator-based strain for the 250,000-cycle dataset remains fairly close to the mean (std. dev. = 0.0006) while the peak sensor-based strain is highly scattered (std. dev. = 0.3) (Fig. 9). Based on the results of the Mann-Whitney tests, the distribution of the peak actuator-based strain and the distribution of the sensor-based strain are statistically significantly different for both the 450,000-cycle (asymptotic p = 0) dataset and the 250,000cycle dataset (asymptotic p = 0); therefore, the null hypothesis is rejected. The distributions are not equal.
The stress and strains and proportion were not calculated for the sensors cycled at 10 Hz, as the signal was dropped for all sensors tested. Further, to check the possibility that the cycling rate was causing the lack of correlation between the peak displacement and peak stretch percentage, four FlexSense sensors were tested at a cycling rate of 0.5 Hz for 500 cycles. The sampling rate for the sensor was kept at 200 Hz; however, of the four sensors tested, only two actually sampled at 200 Hz (Samples 1b and 3). Similar to the results of the sensors cycled at 2.5 Hz, the distribution of the actuator-based strain and the distribution of the sensor-based strain are statistically significantly different at a cycling rate 0.5 Hz (asymptotic p = 0 for both samples) (Fig. 10). Sample 1b had a calculated correlation coefficient of 0.07, and a correlation coefficient of 0.04 was found for sample 3. The peak strain as measured by both sensors was highly scattered. Sample 1b returned a standard deviation of 0.2 for the peak stress percentage vs a standard deviation of 0.002 for the peak displacement. Similarly, a standard deviation of 0.3 was calculated for the sensor-based strain of sample 3, while a standard deviation of 0.002 was returned for the actuatorbased strain.

Discussion
FlexSense sensors performed well during quasi-static testing, producing the expected viscoelastic loading curve. The viscoelastic loading response was also found when the conductive ink strip was tested. At quasi-static loading rates, the strain and stretch percentage exhibited strong correlation, suggesting that the sensor can accurately measure the stretch percentage during the application of slow, steady non-reversed tensile loading; however, the correlation between the strain and stretch percentage broke down during the fatigue tests. Fatigue testing of dielectric elastomer actuators has shown that an increase in the number of cycles results in decreased permittivity of the actuators, 19 but the strain measured by the MTS 858 and the stretch percentage measured by the FlexSense sensor were uncorrelated from the initial cycle and continued throughout the fatigue testing. Why this breakdown occurred is unclear, but several possibilities exist. The first possibility is related to the set-up of the fatigue tests (Fig. 4). When the sensors were first attached to the set-up, they remained straight; however, when the mini B to USB cable was attached to the microchip, a slight angle was formed, and the sensors may have been sensitive enough to read this angle as part of the displacement. A second possibility is that the full 25 mm of stretch for each cycle resulted in early onset plastic deformation of the conductive carbon ink creating a permanently increased conductive path which was translated into higher capacitance. 73,74 Another possibility is expansion of the precut attachment holes in the silicone allowing for extra stretch of the sensor that results in an increased stretch percentage. These holes would be expected to be localized areas of stress concentration; however, visual inspection of the sensors revealed no expansion or pull-out at the attachment sites. Inhomogeneity in the elasticity of the materials may also be a possibility to explain to the mismatch between the displacement and  stretch percentage. 75,76 Although both exhibited a viscoelastic loading response in quasi-static testing, the rate of recovery between the conductive ink strip and the silicone encapsulant may vary; therefore, full relaxation of the materials in the fatigue cycle valley may not have been achieved before the next cycle began resulting in the presence of residual strain in the material which contributed to the scatter of the stretch percentage. Future fatigue tests should incorporate a ramp waveform with a holding step at the maximum displacement. A holding step will provide both the material and signal extra recovery time and help to discern if the increase in peak stretch vs the strain results from hysteresis effects associated with the material constituents of the sensor. The conductive ink strip may not initially stretch as quickly as the silicone encapsulant resulting creating the scatter in the stretch percentage values. Without further investigation, the exact cause of the discrepancy between the displacement and stretch percentage will remain unknown. Also, the development of standard fatigue testing methods for both the material and electrical constituents of dielectric elastomer sensors would help to counter some of the issues that were found during the fatigue tests.
From a materials perspective, the shape of the stress-life curve conforms to the Rabinowitz-Beardmore model (Figs. 1 and 7). 9 In the stress-life curve, an initial monotonic overload at the first cycle (Stage 1) is followed by a gradual decline in the peak stress (Stage 2) until a period of cyclic stability is reached at approximately 150,000 cycles (Stage 3). Stage 4 of the model is not reached, and the material failure mode remains unknown. Elastomeric materials may have extensive fatigue lives due to not only an increase in crosslinking density with repeated cycling, 19 but also the formation of sideways cracks orthogonal to the initial cracks that form normal to the strain direction. These sideway cracks dissipate energy needed to drive the crack tip forward. 77  In general, the stress-life curve also resembles a stress-relaxation curve (Fig. 7). When considered in terms of stress-relaxation, the transition stage (stage 2) of the Rabinowitz-Beardmore model 9 is representative of cyclic softening that continues until the polymer chains are disentangled or broken, and the stress reaches a steadystate plateau as predicted by stage 3 of the model. 9,10 How the material properties affect the signal properties remains unclear, but viscoelastic stretch sensors that were used to measure activities of daily living, subsequent to subjection of HCF, exhibited drift in their output over time potentially due to the retention of a modicum of strain with each cycle. 78 Further, the shape of the peak stress in the stress-life curve suggests that the Rabinowitz-Beardmore model curve 9 may be general enough to apply to all polymers, not just thermoplastics, provided that the model is adapted to account for elastomeric phenomena such as cross-link density, polymer chain debonding, polymer chain rearrangement, and cross-link breakdown. 19,20 In broad terms, nano-to microstructurally small crack incubation may begin with the initial monotonic overload and transition stages, and continue until long crack propagation results in failure of the material 5,9,79 but, as Opp et al. 7 have noted, these results may depend on the polymer being tested, and more studies assessing the effect of fatigue on the microstructure of the dielectric elastomer sensors is needed to determine the times needed to incubate and propagate the cracks.
Hopefully, this study will serve as a step towards creating standardized fatigue testing methods for dielectric stretch sensors, but several limitations to this study should be noted. As aforementioned, the offset of the sensor from the grips during fatigue testing may not be ideal (Fig. 4). Determining a way to place the sensor directly within the grips while still protecting the microchip and cabling may improve the output. Additionally, when measuring the signal during HCF, bypassing the provided software, and measuring the capacitance with a dedicated instrument such as an LCR meter could result in a more accurate measurement of the signal and improve the correlation between the capacitance of the sensor and the strain as measured by the MTS 858. Future studies may also consider measuring the thermal response of the sensors to repeated cycling and how this response effects the output. More insight into the effects of the thermal response and the effects of material properties, such as cyclic softening, on the capacitance could be elucidated by allowing the sensor to recover from the initial fatigue testing, and then restarting the cycling of the sensor to determine if the polymer has reached the steady state plateau of the Rabinowitz-Beardmore model curve, 9 and may also help to determine if the capacitance has stabilized or if the signal is still scattered or has drifted. Finally, capturing the unloading (relaxation) curve of the sensor during quasi-static testing would provide additional insights into both the behavior of the material comprising the sensor and the signal response to both loading and unloading. Future studies incorporating these improvements would help to determine if the discrepancy between the material response to fatigue and the signal response to fatigue is a result of a mismatch between the material properties of the conductive strip and the material properties of the silicone encapsulation. If such a mismatch is found, pre-straining of the stretch sensors prior to their application may be considered.

Conclusions
Based on the results of the HCF tests, consideration of the material properties of a stretch sensor are necessary to determine how accurate the output from the sensor will be for a given application, especially under repeated cycling. While the output from the FlexSense sensors performed well under quasi-static conditions, the accuracy of the output declined under HCF. Materialistically, the shape of the stress-life curve produced by fatiguing the stretch sensors conformed to the Rabinowitz-Beardmore model of polymer fatigue; whereby, the material underwent cyclic softening and transitioned to a steady state. 9 The signal, however, exhibited a wide scatter in values. Scattering of the signals may be an artifact of the set-up used during the fatigue test, but this decline may also be a result of differing material responses of the conductive ink strip and the silicone encapsulation comprising the sensors to cyclic loading. Further fatigue testing of stretch sensors is needed to determine the exact cause of the scattering of the signals during HCF, and would also help to determine whether the prestraining of stretch sensors would decrease the scatter leading to the collection of accurate data.