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 be havior of glassy polymers based on the thermally activated growth of d eformation zones (Somigliana dislocation loops). The Coulomb criterion of plasticity, sigma(c) = S - m sigma(n), is found as the critical th reshold 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 basical ly from chain spacing fluctuations in the polymer glass; the temperatu re dependences of both parameters are derived. Application to tensile and compressive tests under a confinement pressure P is developed, wit h 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 no rmal stress dependent term (exp D sigma(n)), which may have a decisive importance in a number of situations like multiaxial solicitations, s olid state polymer shaping, second phase effects in polymer blends, an d so on. Finally, a set of constant strain rate experiments is present ed on an unsaturated polyester resin crosslinked with styrene. Measure ments fit reasonably well with the predictions of the above model up t o similar to 50 K below the glass transition, at which collective mole cular motions invalidate its basic assumptions. The fit includes: (i) the Coulomb Criterion and its temperature dependence; and (ii) the dil ative and shear apparent activation volumes at yield at all pressures.