A thermodynamically-based constitutive theory for amorphous glassy polymers at finite deformations

In this work, a fully thermomechanical coupling constitutive theory is developed for amorphous glassy polymers to explain and predict their complex temperature- and rate-related nonlinear behavior during finite deformations. The foundation for the theory is the original kinematic and thermodynamic framework derived by Bouvard et al. (2013), in which internal state variables with clear physical significance are applied to describe the deformation mechanism of polymers. In contrast to the viewpoint of Bouvard et al. (2013), in the proposed model, we further divide the entanglements into two kinds of molecular microstructures, “permanent entanglements” and “dynamic entanglements”, and describe how their evolution during deformation is regarded as the internal mechanism for the material's macroscopic mechanical properties. Further, a series of new constitutive equations related to “dynamic entanglements” are proposed, which account for the strain softening caused by the dissociation of “dynamic entanglements”, reflect the influence of temperature on the dissociation rate of “dynamic entanglements” and include the effect of rate-dependent glass transition temperature ( θ g ) on the microstructure. The equations related to “permanent entanglements” are also illustrated, which are improved based on the the work of Ames et al. (2009). The predictive capacity of the proposed thermomechanical coupling constitutive theory has been numerically realized by writing a user subroutine for finite element program. Taking polycarbonate (PC) as an example, the simulations are compared with experimental results for compression, shear, tension, and creep at different temperatures and strain rates. It is demonstrated that our proposed constitutive model with a more detailed physical meaning can well reproduce nonlinearity before yield, yield peak, strain softening, hardening and unloading behavior for amorphous glassy polymers under different stress states.