Experimental investigation on electromechanical deformation of dielectric elasto

Lei Liu，Hualing Chen，∗，Bo Li，Junjie Sheng，Junshi Zhang，Chi Zhang，Yanjie Wang，Dichen Li

aState Key Laboratory for Strength and Vibration of Mechanical Structures，Xi’an Jiaotong University，Xi’an 710049，China

bSchool of Mechanical Engineering，Xi’an Jiaotong University，Xi’an 710049，China

cSchool of Aerospace，Xi’an Jiaotong University，Xi’an 710049，China

Experimental investigation on electromechanical deformation of dielectric elastomers under different temperatures

Lei Liua，b，Hualing Chena，b，∗，Bo Lia，b，Junjie Shenga，b，Junshi Zhanga，c，Chi Zhanga，b，Yanjie Wanga，b，Dichen Lia，b

aState Key Laboratory for Strength and Vibration of Mechanical Structures，Xi’an Jiaotong University，Xi’an 710049，China

bSchool of Mechanical Engineering，Xi’an Jiaotong University，Xi’an 710049，China

cSchool of Aerospace，Xi’an Jiaotong University，Xi’an 710049，China

A R T I C L E I N F O

Article history:

Accepted 20 April 2015

Available online 3 June 2015

Dielectric elastomer

Temperature effect

Pre-stretch

Chains alignment

Electromechanical deformation

Under an applied voltage，dielectric elastomers（DEs）produce an actuation strain that is nonlinear，partly because of the material properties.In this study，an experimental characterization is conducted to evaluate how the ambient temperature and pre-stretch affected the actuation performance.For DEs with a pre-stretch of 2×2，an increase of temperature from-10°to 80°results in a variation in the actuation strain of more than 1700%.Low pre-stretched DEs are more susceptible to temperature change；while highly pre-stretched DEs are relatively insensitive to temperature，because in this case the energy conversion was dominated by mechanical stretching，rather than thermal conduction，during the actuation.

©2015 The Authors.Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics.This is an open access article under the CC BY-NC-ND license（http://creativecommons.org/licenses/by-nc-nd/4.0/）.

Dielectricelastomers（DEs）aresoftactivematerialsthatexhibit a large strain response when they are subjected to an electrical excitation［1］.Because these characteristics resemble the properties of biological muscles，DEs have been investigated for biomimetic applications such as soft robots，artificial skin，tunable lenses，refreshable Braille displays，and nanostructured polymer systems in recent years［2-5］.

Dielectric elastomers display a high nonlinearity in their actuation，which is partly attributed to the material properties.Both the mechanical and the dielectric properties are sensitive to changes in the temperature and the degree of pre-stretch applied.Moreover，Liu et al.［6］theoretically predicted that as the temperature increases，the stretch of the dielectric elastomer is strengthened.An acrylic VHB polymer from 3M company is the most widely employed dielectric elastomer，but it shows strong stiffening in elasticity at large mechanical stretches［7］.Michel and Vu-Conga et al.［8，9］showed that the elastic modulus of DEs decreased by over two orders of magnitude when the temperature was increased from-50°C to 75°C.The dielectric constant is also sensitive to changes in the temperature，as shown in a series of experiments reported in the literature［10-12］.For instance，when the area expanded by four times，the dielectric constant dropped by 50%.Although the nonlinear properties have been reported separately，the above experiment focused on the characterization of individual factors，rather than considering the overall actuation performance during electromechanical coupling.The relationship between the temperature and the pre-stretch and their combined influence on the actuation remain unclear.We therefore present here a series of experiments on dielectric elastomers，measuring the voltageactuation strain when the material is under both thermal and mechanical loading.

Fig.1 shows the experimental setup.VHB 4910 film（3M company）with an original thickness of 1 mm was selected as the dielectric elastomer.The film was stretched to prescribed levels，whilebeingfixedtoarigidframetomaintainthemechanicalstrain load.Carbon grease（No.846，MG Chemicals）was then applied to the surface of the film，forming a circular pattern for actuation，as shown in Fig.1（a）.The circular configuration was characterized by its simpler structure and its response，which was tuned by varying the pre-stretch and the ratio of the electrode area to the passive area.These characteristics helped to reflect the effects of changing the temperature and the pre-stretch on the actuation performance more directly and conveniently.A lightweight copper marker was attached at the edge of the electrode area，and the displacement of this copper marker was traced and recorded by a laser sensor to illustrate the actuation.

Fig.1.Experimental setup.（a）Schematic sketch of the system，and（b）example of a DE actuator inside a heat chamber with a laser sensor.

Fig.2.（Color online）Responses of the DE actuation displacement，with an equal biaxial area pre-stretch of 2×2 at three different voltages of（a）3000 V，（b）4500 V，and（c）5600 V.The temperature range was-10°C to 80°C.The red cross shown in plot（c）denotes the electric breakdown.（d）Relative displacement vs.temperature.

Fig.3.（a）Relative displacement for different pre-stretches and（b）actuation displacement with two different pre-stretches of 4×4 under a voltage of 3000 V.（c）Effects of electrostatic，strain，and internal energy on the chain alignment.

As shown in Fig.1（a），the pre-stretched sheet was clamped by two heat resistant glasses of the same dimensions（inside diameter R of 30 mm）.The diameter of the electrode area r0was 10 mm.The dotted circle in Fig.1（a）represents the edge of the actuatedelectrodearea.Thewholedevicewasplacedwithinaconstant temperature chamber.Through the window of the chamber，the laser displacement sensor with sensitivity of 0.5µm（LK-G150/G10，Kenyence）recorded the actuation when a high voltage（from power source Model 610E，Trek）was applied.To eliminate the thermal expansion and cold shrinkage behavior of the membrane，the temperature in the chamber was maintained at a constant value for 30 min.

Time histories of the radial displacements are presented in Fig.2；2×2 means equal biaxial pre-stretching to 2 times the initial size.The displacement increased with time under a constant supplied voltage.This time-dependence was mainly attributed to two concurrent effects:（1）the viscoelastic creep deformation of the VHB film，and（2）when a constant voltage was applied，the elastomer thinned down，and in consequence the electric field increased.The temperature affected the actuation.Defining the displacementr at500sasthesteadystateforcomparison，r increased from 25.8µm to 458.7µm when the temperature was increased from-10°C to 80°C under a voltage of 3000 V.

Taking the actuation displacement at 20°C as the reference displacement r（T0）=r（20°C），we defined a relative displacement ΔR（T）=r（T）/r（T0）to evaluate the effects of the temperature，where T0and T are reference temperature and current temperature，respectively.As shown in Fig.2（d），the relative displacement was independent of the voltage.The results presented in Fig.2 demonstrated that changes in the ambient temperature significantly impacted the actuation of the VHB films.For example，as shown in Fig.2（d），when the temperature increased from 20°C to 30°C，a change that represents a common temperature range in practical applications，the strain for a pre-stretch 2×2 varied by approximately 45%.This variation suggests the possibility of using active feedback control strategies to sustain the electromechanical deformation.In any case，the temperature-actuation strain dependence offers sensing opportunities for VHB films to be applied as temperature sensors.

Previous studies have shown that mechanical pre-stretch contributes in several ways to the stabilization of DEs［13］.These findings motivated us to explore the influence of the prestretch on the thermal sensitivity of DEs.Fig.3（a）and 3（b）displays the actuation displacement for different pre-stretches.The relative displacement curve shown in Fig.3（a）indicated that large pre-stretches caused the actuation to be less sensitive to changes in the temperature.We interpreted this mechanism by considering the physics of the material.Dielectric elastomers deform under the principle of entropic elasticity.The application of a voltage or a mechanical stretch causes the molecular chains to align in terms of their polarization or deformation，as shown in Fig.3（c），so that the entropy in the material declines.The work done by voltage and mechanical load is then converted to electrostatic energy and strain energy.Increasing the temperature would disturb the chain alignment［14］，and would increase the internal energy，acting in opposition to the effects of the prestretch or the voltage as also presented in Fig.3（c）.Small prestretches contribute only small amounts of strain energy that fail to prevail over the thermal disturbances in the process of chain alignment.However，highly pre-stretched elastomers are able to overcome the thermal disturbance during the actuation，since the large mechanical force introduces a higher level of strain energy that dominates in the energy conversion.Therefore，for the highly pre-stretched films，the internal energy change within the temperature range shown in Fig.3（a）was negligible during the actuation.To confirm this interpretation，we increased the temperature beyond 80°C in the experiments.At these higher temperatures，the displacements began to decrease slowly，as shown in Fig.3（b）；these results demonstrated that the thermal energy prevailed，and suppressed the electrostatic energy.

As a member of macromolecular polymer，VHB films are of viscoelasticity.Under mechanical pre-stretching，VHB films stiffen，because the molecular chains reach their extension limit；this limits the viscoelasticity.However，under thermal heating，the polymer softens，and changes its viscosity accordingly.To understand the contribution of the viscoelasticity to the observed effect of lower temperature sensitivities at higher pre-stretches，a ramping voltage of 100 V/s was applied to investigate the displacement response.The results are shown in Fig.4，which illustrates a similar conclusion:the actuation strain in the low-pre-stretch state，as shown in Fig.4（a）and 4（b），was vulnerable to increases in the temperature，but the actuation strain was robust in the highly prestretched case，as shown in Fig.4（d）.Comparing Figs.3 and 4，it is clear that even when the constant voltage was replaced by a ramping voltage to amplify the viscoelastic effects，the principle of the lower temperature sensitivity at higher pre-stretches was not fundamentally changed.Note that there were some pulsations，as shown in Fig.4；these were mainly caused by the vibrations of the air compressor in our constant-temperature chamber.

Fig.4.Electromechanical displacement within the prescribed temperature range，under a ramping voltage of 100 V/s.

High pre-stretches produced a strong tautening in the elastomer and a slight relaxation in the stress，forcing the molecular chains to orient in the in-plane directions，consequently enabling the VHB films to have low sensitivity to the ambient temperatureunder electromechanical actuation.These tunable thermal sensitivity characteristics indicate the potential of the pre-stretched membranes for VHB film-based actuators or sensors.

In summary，in the present experiments，the electromechanical deformation of VHB films was affected by changes in the ambient temperature.For materials subjected to a pre-stretch level of 2×2，when the temperature increased from-10°C to 80°C，the displacement increased by 17.7 times；when the temperature increased beyond 80°C，the displacement decreased gradually.Furthermore，we found that the effects of the changes in temperature on the deformation were strongly dependent on the pre-stretch level.When the pre-stretch was increased while the temperature was increased in the range from-10°C to 80°C，the displacement increased only slowly，showing an insensitivity to the thermal environment.When the constant voltage was replaced by a ramping voltage to amplify the viscoelastic effects，the principle of the lower temperature sensitivity at higher pre-stretches was not fundamentally changed.These observations offer an insight into VHB film-based dielectric elastomer actuation for device design，mechanisms，and control strategies in the context of a varying ambient temperature.

Acknowledgment

This work was supported by the Major Program of National Natural Science Foundation of China（51290294）and the Doctoral Fund of Ministry of Education of China（20120201110030）.

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22 August 2014

∗at:State Key Laboratory for Strength and Vibration of Mechanical Structures，Xi’an Jiaotong University，Xi’an 710049，China.

E-mail address:hlchen@mail.xjtu.edu.cn（H.Chen）.

http://dx.doi.org/10.1016/j.taml.2015.05.007

2095-0349/©2015 The Authors.Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics.This is an open access article under the CC BY-NC-ND license（http://creativecommons.org/licenses/by-nc-nd/4.0/）.

*This article belongs to the Solid Mechanics