A Mathematical Model for Amorphous Polymers Based on Concepts of Reptation Theory

Abstract

Mechanical behaviors of amorphous polymers have been investigated in all aspects from macroscopic thermodynamics to molecular dynamics in past five decades. Most models either have too complex mathematics or can only explain mechanical behaviors of specific materials under certain defined conditions. In this article, a mathematical model is proposed to understand mechanical behaviors of amorphous polymers with aid of the concepts of reptation theory. This new model is capable to match most experimental results of different amorphous polymers for a wide range of time and temperature effect from rubber zone to glassy zone. Above glass transitional temperature, the model shows hyperelastic behavior. Below glass transitional temperature, elastic–viscoplastic properties can be obtained. In the proposed model, no yielding surface is assumed. Hyperelasticity and Mullin's effect are illustrated in a different way without assuming strain energy function in advance. Yielding stress is controlled by Young's moduli, defect density, and defect velocity of molecular chains. Anisotropic plasticity is simply controlled by anisotropic Young's moduli. Therefore, no additional anisotropic parameters are needed to define anisotropic yielding surface. Strain rate, temperature, and hydrostatic pressure effects on yielding stress are through their effect on Young's moduli. Linear elastic, hyperelastic, viscoelastic, and viscoplastic models are put into one single equation, which makes the mathematical structure very easy to understand and easy to use. This model is validated by comparing with five existed experimental data. Proposed model also shares some features similar to the old well‐known large deformation models for amorphous polymers. POLYM. ENG. SCI., 59:2335–2346, 2019. © 2019 Society of Plastics Engineers

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