The phenomenology of plastic deformation in glassy polymers is described, and a theory based on a molecular model for such deformation is presented and contrasted with other published theories. A phenomenological yield criterion is presented which is consistent with the theory. It is shown that the theory is in very good accord with experimental results on the temperature dependence of the plastic shear resistance of a large group of glassy polymers with widely different molecular structures. Finally, the formation and growth of shear deformation bands is described, based purely on the mechanics of localization processes in inelastically deforming continua.
PHENOMENOLOGY OF PLASTIC DEFORMATION OF POLYMERSlasticity of a solid is usually associated with certain P w e l l defined deformation behavior such as: a) a sharp bend in the stress-strain curve for constant strain rate to give large increments of strain for small changes in stress, b) a strong and highly non-linear dependence of the strain rate for small increments of stress, and c) permanence of distortions upon removal of the applied stresses. Under favorable conditions, when care is taken to suppress fracture, glassy polymers can undergo deformations below the glass transition temperature which satisfy the above-described behavior. Figure 1 shows a series of stress-strain curves demonstrating yielding in prestrained glassy polyethylene terephthalate (PET) sheet, re-strained along axes making different angles with the initial draw direction of the sheet (1). Figure 1 shows, as in the case of polycrystalline metals, that the stress or strain where plastic flow initiates is not always exactly determinable and often requires setting down somewhat arbitrary criteria. Figure 2 stress is much less than 0.01 of the shear modulus, the polymer is linearly viscoelastic. At stresses exceeding this level, the response becomes non-linear, and the shear strain rate appears to asymptotically become infinite as the stress approaches an athermal limit, in direct correspondence with the familiar plastic behavior of polycrystalline metals (2).
We investigate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate associated with a massive spinor field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. In order to do that, we use the generalized Abel-Plana summation formula. As we shall see, this procedure allows us to extract from the vacuum expectation values the contribution coming from the unbounded spacetime and to explicitly present the boundary induced parts. As regards the boundary induced contribution, two distinct situations are examined: the vacuum average effects inside and outside the spherical shell. The asymptotic behaviour of the vacuum densities is investigated near the sphere centre and near the surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in the global monopole geometry, the sphere induced expectation values are exponentially suppressed. We discuss, as a special case, the fermionic vacuum densities for the spherical shell on the background of the Minkowski spacetime. Previous approaches to this problem within the framework of the QCD bag models have been global and our calculation is a local extension of these contributions.
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