A physically-based model for strain-induced crystallization in natural rubber. Part II: Derivation of the mechanical model

Abstract

Despite the numerous experimental investigations performed over the past century and more intensively in the last fifteen years, strain-induced crystallization in natural rubber still remains hardly understood in its precise mechanisms, limiting most of constitutive equations to phenomenological approaches. The present Part II of our work aims to develop a physically-motivated constitutive equation which qualitatively reproduces phenomena observed during deformation. Firstly, the amorphous network is assumed to deform in an equal-force manner, resulting in a representative chain encompassing the inhomogeneity of cross-linking into the chain-length distribution. Then, as proposed in Part I, crystallization and melting conditions are considered, based on classical thermodynamics and on the entangled nature of the polymer network. Finally, a semi-crystallized chain is defined, accounting for both the inhomogeneity of the amorphous phase and the heterogeneity due to the presence of a crystalline phase. This chain is included in a modified full-network model, initially dedicated to amorphous networks. It leads to a constitutive equation which qualitatively reproduces the mechanical response of natural rubber.