Modeling the viscoelastic-viscoplastic behavior of glassy polymer membrane with consideration of non-uniform sub-chains in entangled networks

Glassy polymers are common engineering materials and usually work in a linear elastic stage. However, some functional glassy polymers, such as perfluorinated sulfonic acid (PFSA) membranes, face more complicated working conditions: varied temperature, humidity, and long-term loading, where the viscoelastic behavior has a huge impact on their durability. The early studies on the constitutive model of glassy polymers focus on the elastic-plastic behavior, especially yielding and strain hardening, while showing limitations in predicting the time-dependent viscoelastic response of the PFSA membrane at complex conditions. This paper establishes a viscoelastic-viscoplastic (VE-VP) constitutive model of glassy polymers based on the non-uniform length distribution of entangled molecular chains. During loading, heating and hydration, the prior activation of short entangled chains is the precondition of the viscoelastic response of the material in the small deformation stage. To distinguish activated molecular chains from others, a calculation method of chain activation is established based on the energy conservation criterion and applied to monitor the activation state of the entangled chain network. For the verification of the model, uniaxial tensile, stress relaxation, and dynamic thermomechanical tests are conducted. The present model shows great accuracy in predicting the VE-VP behavior of the PFSA membrane, with the error less than 8% in the stress relaxation tests, providing a new perspective of constitutive modeling for glassy polymers.