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Strain-induced crystallisation in natural rubber: a thermodynamically consistent model of the material behaviour using a multiphase approach

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Abstract

Strain-induced crystallisation (SIC) is the phenomenon of elastomers to experience a pronounced nonlinearity under large deformations of several hundred percentages of strain, which is advantageous for industrial applications due to the resulting positive properties such as increasing crack growth resistance and fatigue behaviour. The overall objective of the current study is the constitutive modelling of the material behaviour of natural rubber when stretched uniaxially. Initially, unfilled natural rubber is considered. Cyclic traction experiments in which crystallinity, elongation and stresses are simultaneously measured are found in the literature. The same vulcanisate is used to conduct additional experiments in the present laboratory. The experimental investigations focus on uniaxial tension tests, conducted with a variety of parameters such as time and stretch rate. The current work presents an approach to model the SIC phenomenon. The model considers thermoelasticity and crystallisation. The approach of the hybrid free energy is used to derive constitutive equations and to meet thermomechanical consistency. However, the effect of temperature is not the focus of the current work. Furthermore, the contribution of a mixing energy is represented in the free energy. The derivation of this mixing entropy is explained in detail by making use of different assumptions and approaches, e.g. the consideration of ideal mixtures. Here, a one-dimensional constitutive model for strain-crystallising rubber is developed, which can be extended with a micro-sphere approach (concept of representative directions) to a full thermodynamically consistent anisotropic model.

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Notes

  1. Phr is the abbreviation for parts per hundred, i.e. for 100 g NR 1.2 g sulphur is introduced.

  2. Changes in shape are also called conformation.

  3. Please note, that all values in the physical terms are specific values but the description ‘specific’ is not used continuously.

  4. The directional Helmholtz free energy per unit mass is defined as \({\hat{\psi }}_\alpha =\frac{{\hat{\varPsi }}_\alpha }{m_\alpha }\).

  5. The wording ‘entropy of mixing’ or ‘mixing entropy’ is used as an abbreviation for the total change in the entropy of a mixture.

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Authors and Affiliations

  1. Institute of Mechanics, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85579, Neubiberg, Germany

    Klara Loos, Ahmet B. Aydogdu, Alexander Lion & Michael Johlitz

  2. MICHELIN Technology Center, Clermont-Ferrand, France

    Jérôme Calipel

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Communicated by Johlitz, Laiarinandrasana and Marco.

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Loos, K., Aydogdu, A.B., Lion, A. et al. Strain-induced crystallisation in natural rubber: a thermodynamically consistent model of the material behaviour using a multiphase approach. Continuum Mech. Thermodyn. 32, 501–526 (2020). https://doi.org/10.1007/s00161-019-00859-y

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