Pre-stretching for performance improvement of soft polymeric thermal actuators - Rezaeyan, Hamid (Nanyang Technological University, 2022)
Thermal polymeric actuators are among the most promising polymeric actuators due to their several superiorities. They induce the highest level of stress among polymeric actuators, where induced stress is one of the key indicators in evaluating actuation performance. Thermal polymeric actuators are simple and low cost requiring only heat energy for their actuation. The current challenges with prevalent application of thermal polymeric actuators are their small induced strain and slow response. Finding innovative solutions to tackle these challenges would allow us to take advantage of the superiorities of a thermal polymeric actuator. Polymers with capability of inducing a large range of thermal deformation are of particular interest. A pre-stretched rubber band can thermally deform one to two orders of magnitude larger than a virgin rubber without stretching. After preliminary screening of potential candidates, VHB4910, an acrylic elastomer which is a rubber, was selected as a thermal polymeric actuator to study the effect of pre-stretching on the range of thermal deformation. VHB4910 is a mechanically isotropic elastomer with a large range of elasticity. Without pre-stretching, a virgin VHB4910 showed only 0.6% thermal strain within a working temperature of 26°C to 100°C, which is far below the strain range of a biological muscle (20-40%). With pre-stretching, the range of thermal strain of VHB4910 significantly increased to 29.7%, reaching the middle strain range of the biological muscle. Pre-stretching also decreased the thickness of a VHB4910 significantly, thus improving its thermal response. Pre-stretching is indeed an innovative, simple, and practical approach to simultaneously solve the small strain and slow response limitations of a thermal polymeric actuator. Pre-stretching converts the usual small thermal expansion of a virgin VHB4910 to a unique large thermal contraction with an increase in temperature. Pre-stretching resulted in a significant increase in the average linear coefficient of thermal expansion α from 81×10-6 °C-1 of the virgin VHB4910 film to -4024×10-6 °C-1 of the 4 times equi-biaxial pre-stretched film, i.e. a 4868% increase in the magnitude of thermal deformation in the stretch direction. Pre-stretching by 4 times equi-biaxial stiffened a VHB4910 film by 911.9%, and thus increased the magnitude of thermally induced stress by 12,831%, and accelerated the response time by 3.4 times through thickness reduction. Testing with 11 actuation thermal cycles, the stress relaxation ratio, the creep ratio, and the coefficient of variation were observed to be less than or equal to 2.3%, 0.1%, and 1.1%, respectively. For long term testing, its actuation window had only 9.5% variation within 21 days. These indicate that a pre-stretched film is reversible and stable with force and temperature variations over a long period. Predicting the unique thermomechanical behavior of rubbers, in particular the thermal contraction of a pre-stretched VHB4910, is of high interest. To date, the development of a constitutive model for rubbers faces three main challenges, namely i) a highly non-linear stress-strain-temperature behavior of rubbers, ii) evolution of material constants with pre-stretching, and iii) describing a large negative coefficient of thermal expansion of a pre-stretched VHB4910 in the stretch direction. More importantly, there is no theoretical basis for the existing formulations and models to describe the thermal contraction of a pre-stretched VHB4910. This investigation developed a 3D thermomechanical constitutive model from first principle to address specifically the large negative coefficient of thermal expansion of a pre-stretched VHB4910 in the stretch direction. This model could link the unique thermomechanical behavior of a pre-stretched VHB4910 to the changes in its microstructure. The practical application of a generalized model for rubbers from the virgin state all the way to the pre-stressed state has to address the challenges associated with the modeling of the highly non-linear behavior of rubbers. For thermal actuator, the stress-strain history prior to stretching is of no relevance. Experimental investigation indicates that the responses of a pre-stretching film were rather linear. As such, by employing a local linearization approximation around the pre-stretched state, i.e. shifting the frame of reference to the pre-stretched state, a greatly simplified 3D local linearized thermomechanical model was obtained. Thus, this local linearization with reference to the pre-stretched state avoided the challenges stated previously in the modeling of the highly non-linear thermomechanical behavior of rubbers. As this linearized 3D model requires the same usual conventional constants, (but with rather unusual large in-plane thermal contraction described by large negative thermal coefficient of expansion), it allows the conventional approaches to be used to model a pre-stretched VHB4910 film’s thermomechanical behavior, including the use of a commercial finite element package. For demonstration purpose, a 2 times radially pre-stretched VHB4910 film was used for the fabrication of a cone shape actuator prototype. It had non-uniform stress and strain distributions, which were totally different from the uniform stress and strain distributions of an equi-biaxial stretching film for obtaining the material constants. As such, it is also an excellent demonstrator to be employed for the validation of the linearized 3D thermomechanical constitutive model. Experimentally, the cone-shape actuator, under a loading of 101g resulted in a displacement of 12.5mm at 30°C; a temperature increase from 30°C to100°C could induce a decrease of displacement of 2.1 ± 0.1mm. These results represent a significant mechanical and thermal strain range. The predicted trends of displacements simulated by the Solid Mechanics Module of Comsol Multiphysics 5.3 Software were consistent with experimental observations. Without considering the initial pre-stress before loading and using the reference initial load analysis (i.e. the same initial simulated and experimental load before temperature changes), the largest discrepancy was at the lowest loading value of 41g, i.e. 27.4% at 50°C. As the load increases, the discrepancies become less significant, with the smallest discrepancy of -1.04% for 81g weight at 50°C. With the reference initial displacement analysis (i.e. using the same simulated and experimental initial displacements before temperature changes), better agreements between numerical predictions and experimental observations were achieved, with the largest discrepancy of -18.8% for 41g weight at 100°C. To account for the existence of pre-stress due to pre-stretching, the pre-stress before any mechanical or temperature loading was assumed to be approximately equal to the stress caused by the difference between the simulated and experimentally measured displacements for the smallest applied load of 41g at 30°C. This pre-stress was calculated to be 30.4kPa at room temperature. By considering the pre-stress/pre-strain due to the initial applied pre-stretch and using the reference initial displacement analysis (i.e. the same initial simulated and experimental displacement before temperature changes), the most accurate prediction was achieved, with the largest discrepancy of -14.3% for 41g weight at 70°C. Comparing with the two previous sets of analyses, theoretically this set of analyses reflected most appropriately the behavior of the prototype. Taking into consideration the rather large thermo-mechanical deformations causing significant strains, the geometrical nonlinearity and the non-uniform stress and strain distributions of this cone shape actuator prototype, and the challenges for measuring the various material constants accurately, the overall agreements obtained between experimental observations and simulations are respectable. Indeed, this development represents the very first attempt in the development of a 3D local linearized thermomechanical model for a pre-stretched rubber film allowing ease and accurate simulation of its large deformation. In summary, this investigation reveals that pre-stretching resulted in a unique and significant enhancement in mechanical and thermal actuation performance of a VHB4910 film. Pre-stretching totally changed the thermomechanical behavior of VHB4910 from a small thermal expansion to a large thermal contraction on heating, caused a remarkable increase in the material stiffness, and a decrease in thermal response time. A cone-shape prototype demonstrated the promising thermal actuation performance of a pre-stretched VHB4910 for driving a uniaxial motion. The developed 3D local linearized thermomechanical model for a pre-stretched film could successfully and accurately describe the increase in displacement with an increase in load and/or temperature.