Heterogeneous Dynamics and Polymer Plasticity

Abstract

We extend a model that has been proposed for describing mechanical properties of glassy polymers and that takes into account the heterogeneous nature of the dynamics. We describe their nonlinear mechanical properties, up to a few 10% deformation. We propose that the elastic energy stored in the volume ∼ ξ3 of dynamical heterogeneities effectively reduces the free energy barriers present for internal relaxation. It allows to calculate yield stresses of order a few 10 MPa, which are consistent as compared to experimental data without additional adjustable parameters than the scale ξ. The model is solved in 3D by numerical simulations with spatial resolution the scale of dynamical heterogeneities. We show that the prediction of our model as regards to yield behavior is consistent with the value of 3–5 nm for the scale for dynamical heterogeneities. Yield appears as the result of an acceleration of the dynamics of subunits with intermediate relaxation times which relax under stress before subunits with very long relaxation. Our simulations describe the onset of plastic behavior and the reorganization at the scale of dynamical heterogeneities. We predict the appearance of shear bands on a scale of a few tens of nanometers at yield and beyond.

Brittle‐ductile transition in uniaxial compression of polymer glasses

“…The popular Eyring's idea of stress‐induced activation meets an obvious challenge. In order to explain yielding, all previous theoretical treatments assume the stress to be always available to lower the activation energy barrier. Unfortunately, the Eyring style argument cannot answer when a glassy polymer ceases to be ductile.…”

Weak nonlinearities in viscoelastic mechanical properties of polymers near their glass transition: Local versus macroscopic laws for stress-induced acceleration of the mechanical response

“…Many studies have focused on upscaling the mechanical response of disordered materials as it is encountered in many different systems (granular media [1], foams [2], networks [3], and polymers [4,5]) and situations (elasticity fracture [6] and yield stress [7]). Many nonintuitive behaviours have been reported, particularly in the nonlinear regime.…”

Thermalized formulation of soft glassy rheology

“…The different trends shown in panel (c) may arise because currently available SGR theories lack any "facilitation" mechanism. Mechanical facilitation is the speedup of yielding that occurs in heterogeneous systems when zones have a broad distribution of stresses [42]. Zones that carry stresses much higher than the average value σ yield faster because their environments cannot maintain local mechanical equilibrium (i.e.…”

“…cannot force-balance such large stresses), and zones that carry very low stresses may similarly yield faster when σ is large. The net effect is homogenization of the yielding dynamics and of systems' relaxation in the postyield, plastic-flow regime [39][40][41][42]. It would be interesting in future work to add mean-field facilitation (or a comparable stress-diffusion mechanism [43]) to SGR theory.…”