The rheological behavior of polymers in the neighborhood of the glass transition is investigated in the framework of the free volume theory of nonlinear viscoelastic behavior. Free volume theory as normally applied above the glass transition is modified to account for the effect of the residual volume of vacancies below the glass transition; this modification is accomplished by modeling the changes in the state of the polymer as the sum of viscoelastic changes and a random disturbance deriving from the thermal collisions between molecule segments. The changes in mechanical properties in passing across the glass transition follow from the freezing‐in of relaxation mechanisms and of free volume; the model, which also incorporates a time‐dependent coefficient of thermal expansion under isobaric conditions, does not require additional parameters other than those characterizing the rubbery state. The pressure dependence of the glass transition is found to be in qualitiative agreement with measurements on PVAc, while the ratio of the glassy and rubbery heat capacities is found to coincide with the ratio of the equilibrium bulk compliances in the glassy and rubbery domains.

The problem of crack propagation through a material possessing nonlinearly viscoelastic material response is considered, including the influence of stress-induced free-volume changes on the rheology, as well as the formation of voids as material failure is approached. This particular material response is confined to a thin layer along the crack propagation axis, while the bulk of the material behaves in a linearly viscoelastic manner, thus simulating the situation arising in the growth of a crazeled crack, or the failure of a bonded joint with a thin adhesive layer strained uniformly across its thickness. The nonlinear material behavior thus governs simultaneously the stress and strain distribution at the crack tip as well as the crack speed solely in dependence on the applied load (stress intensity factor). Only quasi-static motion is considered, the velocities being understood to be “reduced” by temperature according to a time-temperature superposition principle. Comparisons with a model based on linearly viscoelastic considerations and rate-insensitive properties of the damaged material are presented.

Three different rheological models are applied to the study of transient and residual thermal stresses in amorphous polymers cooled across the glass transition. The models differ mainly in their treatments of the nonequilibrium (time-dependent) portion of the morphological changes in the polymer and their influence on the relaxation process. The interstitial volume between polymer chains (free volume) is found to play an important role in the residual stresses; they are affected by the relative time scale of thermal diffusion and thermoviscoelastic relaxation/creep. This result has implications for injection molded parts of different section dimensions and for extrusion products. This fact must also be accounted for in determining the thermomechanicalproperties in the glass transition range. The step cooling ofPVAc spheres (1 and 20 mm dia.) and a cylinder (20 mm dia.) have been considered; most of the results presented apply to the sphere(s). Residual stresses can vary by as much as 100percent depending on whether the interstitial molecular (free) volume is counted or not. It is also demonstrated that residual stresses can be higher than an elastic analysis based on the glassy properties would suggest; thus the “stressfree temperature” is found to be significantly above the glass transition.

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