Strain Hardening in Polymer Glasses: Limitations of Network Models

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While traditional entropic network models can be fit to the total stress, their underlying assumptions are inconsistent with simulation results. There is a substantial energetic contribution to the stress that rises rapidly as segments between entanglements are pulled taut. The thermal component of stress is less sensitive to entanglements, mostly irreversible, and directly related to the rate of local plastic arrangements. Entangled and unentangled chains show the same strain hardening when plotted against the microscopic chain orientation rather than the macroscopic strain.Comment: 4 pages, 3 figure

Viscoplasticity and large-scale chain relaxation in glassy-polymeric strain hardening

A simple theory for glassy polymeric mechanical response which accounts for large scale chain relaxation is presented. It captures the crossover from perfect-plastic response to strong strain hardening as the degree of polymerization $N$ increases, without invoking entanglements. By relating hardening to interactions on the scale of monomers and chain segments, we correctly predict its magnitude. Strain activated relaxation arising from the need to maintain constant chain contour length reduces the $N$ dependence of the characteristic relaxation time by a factor $\sim \dot\epsilon N$ during active deformation at strain rate $\dot\epsilon$. This prediction is consistent with results from recent experiments and simulations, and we suggest how it may be further tested experimentally.Comment: The theoretical treatment of the mechanical response has been significantly revised, and the arguments for coherent relaxation during active deformation made more transparen

Strain Hardening of Polymer Glasses: Entanglements, Energetics, and Plasticity

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only observed in shape recovery of deformed samples when heated above the glass transition. While short chains do not form an entangled network, they exhibit partial shape recovery, orientation, and strain hardening. Stresses for all chain lengths collapse when plotted against a microscopic measure of chain stretching rather than the macroscopic stretch. The thermal contribution to the stress is directly proportional to the rate of plasticity as measured by breaking and reforming of interchain bonds. These observations suggest that the correct microscopic theory of strain hardening should be based on glassy state physics rather than rubber elasticity.Comment: 15 pages, 12 figures: significant revision