Annarasa, Vinotharan
(2021)
Modelling the mechanical response of elastomers: the roles of the network, the filler and the deformation history.
PhD thesis, University of Nottingham.
Abstract
The mechanical response of elastomers is influenced by a large range of factors including the elastomeric network, the deformation history (or Mullins effect) and the type and content of filler. The aim of this work is to develop modelling frameworks and models to capture the influences of these factors in selected elastomer systems. Several experimental studies were conducted to aid in the development and validation of the models.
The impact of the elastomer network on the mechanical response is explored using a set of soft custom-made cast ultraviolet light curable silicone-acrylate elastomers eventually intended for elastomer 3D printing. Five different compounds are explored, varying the silicone content from 30 to 70 wt%. Uniaxial tensile tests were performed on all of the compositions. The results from these tests suggest that varying the silicone content results in a systematic variation of the stress-strain response. To study the variation of the underlying network structure with the silicone content, an EdwardsVilgis (EV) strain energy function was fitted to the stress-strain data. By examining the evolution of EV parameters with respect to the proportion of silicone in the system, it was shown that: 1) the network density increases with increasing silicone content, 2) the limiting extensibility decreases with increasing silicone content, i.e., smaller deformations are possible, and 3) the slip-link mobility increases, i.e., there is more freedom for the motion of topological constraints. Simple functions were fitted to quantify the evolution of EV parameters with composition. Based on the evolution of these parameters, a model was proposed to tune the mechanical properties of this class of materials. As these materials were developed for 3D printing, a printability assessment was carried out. It was also shown that further optimisation of the printing process is necessary to achieve mechanical response identical to that of the cast material.
A phenomenological constitutive model was developed and validated to describe the impact of deformation history (or Mullins effect) on the mechanical response of an EPDM rubber compound. This model was inspired by recent experimental observations made on the uniaxial tensile cyclic stressstrain response. The third unloading-reloading loop after preconditioning was decomposed into elastic and viscous contributions. The viscous contribution was shown to form a master curve that was independent of the deformation history and only dependent on the effective network stretch. To the author’s knowledge, a constitutive model that incorporates a strain dependent viscosity has not been developed before. This model was shown to reasonably predict the stress in the third loop response, and provided an excellent prediction of the energy dissipated in this loop, making the model particularly useful for applications, such as vibration isolation where prediction of energy dissipation is vital. The initial loading case was underestimated by the model, and this is attributed to the time-dependent nature of the Mullins effect. The applicability of this model formulation to the deformation of CR and NBR rubber compounds was also explored. It was shown that the model was able to capture the response of NBR successfully but less so for CR. The failure was attributed to the inability of the strain energy function in capturing the upturn at small strains. Lastly, it was shown that the material requirement and the number of experiments required to parameterise the model can be reduced by utilising pseudo-cyclic tests.
An investigation on the impact of pre-deformation on the small strain dynamic response was also conducted. In this part of the study, the influence of filler type and filler content were explored in SBR compounds filled with three different filler types and amounts. A rheometer was used for both the quasi-static and the dynamic deformations. Uniaxial tensile tests were conducted for the pre-deformations, and oscillatory torsion was applied in the dynamic tests on the same specimens. Two test protocols were employed, and the Kraus model was used to study the small strain dynamic response (or Payne or Fletcher-Gent effect). The first protocol was concerned with the impact of pre-deformation on the small strain dynamic response. Prior to pre-deformation increasing the amount of filler and the surface area of the filler particles results in an increase in the storage modulus plateau at small strains G′ 0 . As increasing pre-deformation is applied, G′ 0 begins to decrease. Other parameters in the Kraus model, the strain γc at which half the van der Waals type interaction between aggregates are broken and the rate m at which it occurs, are approximately independent of pre-deformation, but are impacted by the filler type and content. The results indicate that it may be possible to control the stiffness, and to some extent the onset of the Payne effect (or Fletcher-Gent effect), by a combination of filler selection and pre-conditioning. To the author’s knowledge models describing the Payne effect have yet to incorporate the pre-deformation. To address this issue, an exponential function for G′ 0 is proposed to link it to the pre-deformation. In the second test protocol, alongside pre-deformation, a static tensile strain was also imposed. In the shear strain range explored, for any given static strain, the storage modulus G′ was independent of the shear strain. With increasing static strain, G′ 0 was seen to increase. For a given filler type, G′ 0 increased with increasing filler amount. However, unlike the first test protocol G′ 0 , the behaviour between different filler types is more complex.
Several models are presented in this work to describe the roles of the network, of the filler and of the deformation history on the mechanical response of elastomers. Although the models were developed for the materials used in this work, much of the modelling framework is applicable to a range of different materials. These models and the modelling framework supplement existing models in the prediction of the mechanical response of elastomers and are of value to engineers in the design process of elastomeric components. Owing to their physical nature, these models could also be leveraged by scientists to better understand the behaviour of elastomer network.
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