A physical model of the pressure dependence and biaxial mechanical properties of solid polymers

We give here a model for the pressure dependent, biaxial mechanical behavior of glassy polymers based on the thermally activated growth of deformation zones (Somigliana dislocation loops). The Coulomb criterion of plasticity, σ_c = S ? mσ_n, is found as the critical threshold needed to propagate Somigliana loops, in the same way as yield in crystals is found as the stress to move Volterra dislocation loops. While S is the shear strength, it is proposed that m follows basically from chain spacing fluctuations in the polymer glass; the temperature dependences of both parameters are derived. Application to tensile and compressive tests under a confinement pressure P is developed, with the aim to derive the pressure dependent (biaxial) strain-rate law. In particular, the pressure effect on dislocation density, that is, on plasticity defect nucleation, is shown to have a definite role in the plasticity of these solids. It introduces in the strain-rate law a normal stress dependent term (exp Dσ_n), which may have a decisive importance in a number of situations like multiaxial solicitations, solid state polymer shaping, second phase effects in polymer blends, and so on. Finally, a set of constant strain rate experiments is presented on an unsaturated polyester resin crosslinked with styrene. Measurements fit reasonably well with the predictions of the above model up to ～50 K below the glass transition, at which collective molecular motions invalidate its basic assumptions. The fit includes: (i) the Coulomb Criterion and its temperature dependence; and (ii) the dilative and shear apparent activation volumes at yield at all pressures.