Stress relaxation, dynamics and plasticity of transient polymer networks

TL;DR

This paper introduces a comprehensive theoretical framework for transient polymer networks that unifies microscopic and macroscopic behaviors, explaining stress relaxation, plasticity, and deformation dynamics in such materials.

Contribution

The paper develops a novel rate-based model linking microscopic crosslink dynamics with macroscopic elastic behavior in transient polymer networks.

Findings

Model accurately predicts stress relaxation in thermoplastic elastomers.

The theory explains stress overshoot phenomena during strain ramping.

Results align well with experimental data on vitrimer networks.

Abstract

We propose a theoretical framework for dealing with a transient polymer network undergoing small deformations, based on the rate of breaking and re-forming of network crosslinks and the evolving elastic reference state. In this framework, the characteristics of the deformed transient network at microscopic and macroscopic scales are naturally unified. Microscopically, the breakage rate of the crosslinks is affected by the local force acting on the chain. Macroscopically, we use the classical continuum model for rubber elasticity to describe the structure of the deformation energy, whose reference state is defined dynamically according to when crosslinks are broken and formed. With this, the constitutive relation can be obtained. We study three applications of the theory in uniaxial stretching geometry: for the stress relaxation after an instantaneous step strain is imposed, for the stress overshoot and subsequent decay in the plastic regime when a strain ramp is applied, and for the cycle of stretching and release. We compare the model predictions with experimental data on stress relaxation and stress overshoot in physically bonded thermoplastic elastomers and in vitrimer networks.