Birefringence, stress induced

Gent, A.N. Stress-induced birefringence of swollen polymer networks. Macromolecules 2, 262-265 (1969). 

The relationship between the measured relative retardation (R) and the stress-induced birefringence (An) is given by R = fAn (2), in which t is the sample thickness. The stress optical coefficient C is defined by An = Ct (2), in which t is the true stress (t = f/A f is the force in newtons per square millimeter, and A is the cross-sectional area of the network sample). This coefficient is thus simply the slope of the line in a plot of An versus t. Finally, the optical configuration parameter An is defined by... 

For a brittle glassy polymer like PMMA, the results for both sharp and blunted cracks are reproducible and show negligible scattering. The sharp cracks give a lower estimation of the toughness but this is not only related to a notch root effect. In the case of a blunt crack with notch radius of 250 micrometers, stress induced birefringence related to plasticity is observed... 

Microscopy. The polarized optical micrographs of thin films of HX-205 and F-185 neat resins were obtained using a Zeiss ultraphot microscope equipped with a polarizer and an analyzer. Thin films, approximately 100 microns thick, were prepared by thln-sectlonlng the resin sheet with a razor blade at room temperature. The domains were observable because of light scattering as a result of refractive Index mismatch between the rubber domain and the epoxy matrix, as well as to stress-induced birefringence produced by the thermal stress Imposed on the domains. 

Schneider and Vedam (1970), Yu and Cardona (1971) and Galkiewicz and Tauc (1971) studied stress-induced birefringence of a-Se and a-As2S3 respectively (Table 4.2). a-Se exhibits hysteresis effects. 

The stress-induced birefringence is used to characterize striae five different quality levels are distinguished depending on the optical path difference caused by the striae. The path difference is measured with white light and given in nm. The standard quality may have striae causing a maximum optical path difference of less than 60 nm. For applications with very strict striae requirements the stress optical method is not sensitive enough in these cases... 

The disks are between crossed linear polarizers, and stress-induced birefringence results in the picture shown the white streaks are force chains. 

Stress-induced birefringence or photoelasticity (Figure 2.4) has been an important technique for studying granular materials since 1950s [176-178,193, 194,207-214]. It can be used to visualize and measure forces in 2D packings. 

In 1815, David Brewster discovered birefringence in glass and many ordinary materials like ice, human hair, and wax [224]. In 1816, he discovered stress-induced birefringence and suggested its use as a dynamometer to measure force, as it is commonly used today [225]. He outlined the basic relationships between stress and birefringence, and in 1853, James Clerk Maxwell [226] consolidated his observations into the stress-optic law for 2D stress states. 

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