Micro-and Macro-viscohyperelastic Behavior Of Carbon Black Filled Rubbers

Carbon black filled rubber is a typical visco-hyperelastic composite, its mechanicalbehaviors are affected by the dispersion, dimension and content of the filled particles, andremarkably influenced by temperature, strain rate and loading time. Furthermore, due tothe viscoelastic properties of the rubber material, hysteresis loss results in temperaturerise in rubber material during deformation, especially loaded with cyclic deformation. Inthis thesis, we studied the hyperelasticity, viscoelasticity and visco-hyperelasticalconsititutive models of the filled rubber, and the thermorheological characteristics andrelationship between hysteresis loss and dynamical properties were also investigated.Moreover, the effect of carbon black content on the mechanical behaviors of filled rubberwas explored, and a micro-mechanical analysis method was developed. The main worksand achievements are listed as follows.1. Properties of nature rubber, mechanism of carbon black enhancement, mainmechanical properties of filled rubber, and the recent advanced constitutive models forrubber material and the influence factors of the viscoelastic behaviors of filled rubberswere briefly reviewed.2. Accurate material parameters of hyperelastic constitutive models are critical forstructural finite element calculation of rubber components. The prediction performancesof six often used hyperelastic models and the model selection strategies were explored inthe case of incompletion of the three basic types of mechanical tests, and finally a modelselection strategy was developed. That is, in the case of complete data under ST, PT andET tests, Ogden model (N=3) is the first choice, and the Yeoh and Arruda-Boyce modelare the substitutive ones. If there are only two types of basic tests available, ET test ispreferred, and the Ogden model (N=3) is the best model that can precisely predict thethird deformation mode. The Arruda-Boyce model provides most excellent prediction forPT and ET deformation based on the ST test data only.3. The influence of carbon black content on the Mullins effect, break strength, creep,stress relaxation and dynamical behavior of filled rubbers were experimentally studied. Itis shown that adding carbon black into rubber material can effectively improve its initialmodulus, break strength and exacerbate its stress softening and viscoelastic property.4. The thermorheological property of filled rubber was studied. Temperature sweep and frequency sweep DMA tests were performed to investigate the frequency dependentglass transition temperature and to identify the thermorheological nature of the material.The test data show that master curves of dynamical properties can be created byhorizontal shifts alone and cover a frequency range of21decades, verifying the material’sthermorheological simplicity. Such simplicity is also confirmed by the van Gurp-Palmenplot and the Cole-Cole plot. Moreover, the temperature dependence of the shift factors iswell modeled by both WLF equation and Arrhenius equation.5. Three classic viscoelastic constitutive models and their corresponding fractionalderivative models were theoretically derived. The results show that, the classic models areinaccurate to describe the viscoelastic behaviors in a wide range of time and frequency,while the fractional derivative models overcome these shortages. However, the fractionalderivative Maxwell and Kelvin-Vogit model can only usable to describe dynamicbehaviors at high and low frequency range, down and up to the loss peak. For thefractional derivative Zener model, it is enough to fit experimental curves in a widefrequency range with four parameters, but the loss modulus, loss factor for the fractionalZener model are symmetric which is not observed for real polymers. A modifiedfractional derivative Zener model was developed to capture the unsymmetric behaviors ofreal viscoelastic materials, and its capability was vertified by experimental data.6. The influence of loading frequency, pre-strain and temperature on the Payne effectof filled rubbers were experimentally studied. It is shown that the frequency has slightinfluence on the Payne effect of the filled rubbers, and the pre-strains over50%caninfluence the Payne effect, while the Payne effect is influenced remarkably bytemperature. Furthermore, the Kraus model was used to capture the Payne effect of thefilled rubbers, the model is in good agreement with experimental data.7. Cyclic compressive loadings and cyclic extension loadings were applied to filledrubbers, the strain and frequency dependence of the stress-strain behavior and hysteresisloss of the filled rubbers were experimentally investigated. The results show that, thestress-strain curves of filled rubber subjected to cyclic loading were hysteresis loops, andthe area of the loop increased with increasing frequency and strain amplitude. Accordingto the linear viscoelasticity, a model was developed to calculate the energy dissipatedduring testing. Due to the hysteresis loss, obvious temperature rise on the surface of thespecimen was observed. Take the energy loss as an internal heat source, a controlequation to calculate the transient temperature field of rubber cylinder under dynamicalcompression was given. The calculated temperature rises agree with the teste data. 8. Three dimensional RVE models of filled rubber were developed based on therandom sequential absorption (RSA) algorithm, and the multiscale visco-hyperelasticmechanical behaviors of filled rubber were modeled. The simulation results show that thecarbon black improves the modulus and strength of the filled rubbers, which is due to themicromechanical stress concentration near the randomly distributed carbon blackparticles. The degree of stress concentration increases with the increase in carbon blackcontent and the strain rate. In addition, the stiffness of filled rubbers increases with strainrate, while the hysteresis loss increases first and then decreases with the increasing strainrate.