Strain-induced crystallisation in natural rubber: a thermodynamically consistent model of the material behaviour using a
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O R I G I NA L A RT I C L E
Klara Loos · Ahmet B. Aydogdu · Alexander Lion · Michael Johlitz · Jérôme Calipel
Strain-induced crystallisation in natural rubber: a thermodynamically consistent model of the material behaviour using a serial connection of phases Received: 23 April 2020 / Accepted: 2 November 2020 © The Author(s) 2020
Abstract A thermodynamically consistent concept to model the strain-induced crystallisation phenomenon using a multiphase approach is discussed in Loos et al. (CMAT 32(2):501–526,2020). In this follow-up contribution, the same mechanical framework is used to construct a second model that sets the same three phases in a serial connection, demonstrating an alternative to the former parallel connection of phases. The hybrid free energy is used to derive the constitutive equations. The evaluation of the Clausius–Duhem inequality ensures thermomechanical consistency. The model is based on a one-dimensional derivation that extends with the concept of representative directions to a three-dimensional anisotropic model. After the step-by-step derivation, the performance of the model is analysed in detail, including its comparison to the well-known Flory model, its evaluation for infinite fast and slow excitations, its simulation of uniaxial cycles and its validation via relaxation experiments. Finally, the model is compared comprehensively to the former parallel model showing their equivalent reason for existence. Keywords Strain-induced crystallisation · Natural rubber · Nonlinear continuum mechanics · Constitutive modelling · Thermodynamical consistency · Anisotropic modelling · Concept of representative directions 1 Introduction and state of the art High deformations of natural rubber (NR) result in a change of the molecular orientation of its network. Since its discovery in 1925 by Katz [33], the phenomenon of strain-induced crystallisation (SIC) in NR has become the focus of experimental and modelling investigations. Although SIC is a challenging subject due to its complex thermodynamics, polymer physics and sophisticated kinetics, SIC is a rewarding subject for academic research and industrial applications. It is motivated by the beneficial influence of SIC on the mechanical material characteristics such as NR’s superior crack growth resistance and excellent tensile properties [2,54]. The main application made from NR is vehicle tires, where 60 - 70 % of the world’s NR production is utilised. The kinetics of SIC is a highly investigated topic shown with a large number of recent publications and conference contributions. Several studies focus on different aspects during the crystallisation process, such as the nucleation of crystals and their orientation, whereas others focus on different materials and loading conditions [3]. The crystallisation process during the loading of natural rubber is measured in situ with synchrotrons using wideangle X-ray scattering (WAXS) since the beginning of 2000 [60,61]. Huneau published an overview of different Communicated by Andreas Öchsner. K. Loos (B) ·
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