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Birefringence of non-linear viscoelastic-plastic polymers

The observation of photoelastic-plastic states of stress is well known as one of the valuable methods of experimental stress analysis in an infinitesimal elastic-plastic deformation. Photorheology is a comparatively new method for the measurement of non-steady inelastic deformation. Several investigations have been reported of birefringent properties in the elastic-plastic or in the viscoelastic-plastic region. In these, however, the birefringence relations are regarded as empirical or semi-empirical. A birefringence relation for a non-linear viscoelastic-plastic polymer is deduced mathematically from the view-point of continuum mechanics. The birefringent effect is the product of the principal strain difference and a scalar function of the invariants of the elastic and the viscoplastic strains.