Strain-Induced Optical Birefringence

The speed of sound through a medium is a function of applied strain. The relationship is governed by the acoustoelastic coefficient. Stress states with unequal principle stresses (i.e., nonhydrostatic) have the effect of introducing anisotropic acoustic behavior to otherwise isotropic materials. This effect is similar to strain-induced optical birefringence (covered in the next section). The advantage is that ultrasonic birefringence can be measured in optically opaque materials. 

There are three ways of measuring ultrasonic birefringence. To measure stress in an entire specimen, one may measure the time of flight of ultrasonic waves as a function of propagation direction. For smaller sections of sample, shear wave velocities are measured as a function of the orientation of the plane of oscillation of the shear wave. Surface stress can be ultrasonically measured using the velocity of Rayleigh waves as a function of direction. Any of these methods will yield the direction of principle stress and relative stress intensities between samples of identical materials. To find actual values of stress, one must know the value of the acoustoelastic coefficient of the material. An experimental setup for measuring bulk acoustoelastic coefficients has been reported by Koshti.  

Strain-induced optical birefringence is a rapid and powerful technique for transparent isotropic materials. Not only is it possible for one to see residual strains introduced as a result of processing, but inclusions that are invisible to the naked eye can be seen by their associated strain fields. This technique is extremely fast. The product can be conveyed between two crossed polarizers, allowing a single inspector to inspect the output of a small factory. This technique is capable of resolving stresses of as little as 55 MPa (8 kpsi) in Pyrex glass. 

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An example of a relevant optical property is the birefringence of a deformed polymer network [246]. This strain-induced birefringence can be used to characterize segmental orientation, both Gaussian and non-Gaussian elasticity, and to obtain new insights into the network chain orientation (see Chapter 8) necessary for strain-induced crystallization [4,16,85,247,248]. 

Methods to study crystallization of deformed elastomers include x-ray diffraction [207,208,263-265], optical birefringence [266,267], infrared or Raman spectroscopy, electron microscopy [268], dilatometry [269, 270], NMR [271], and mechanical measurements [193,262,272]. Strain-induced crystallization is manifested in the latter by both greater hysteresis (Fig. 23) and a longer time for stress decay (Fig. 24). However, the shape of the stress-strain curve during extension does not obviously reveal the onset of crystallization [207,208,262]. 

BirGfring6nC6 of Polymer Networks. Elastomeric polymer networks deserve special mention because their cross-linked structure gives them unique physical properties, unlike those of other polymers. Covalently bonded networks are insoluble in any solvent, even in those that dissolve their precursor polymers. Optical techniques such as strain-induced birefringence allow the development of structure-property relationships as well as the study of their optical properties. Here we review some of the classical theories as well as some of the latest developments in the field. 

The transverse strain-induced wavelength sensitivity of FBGs in silica optical fibres is low. For instance, in lateral compression, the changes in fibre birefringence are smaller than 10 This level of birefringence corresponds to wavelength separations much smaller than the typical bandwidth of an FBG. However, we have shown in Section 10.3.1 that the sensitivity factor is a function of the two principal transverse strains and axial strain, which are normally unknown. The needs are apparent for multi-axial measurements of strain and temperature. 

Figure 2. Experimentally determined flow-induced birefringence vs. strain rate for atactic polystyrene. The maximum value of birefringence is 1.15 x 10, which corresponds to an optical retardation of 27 nm for a cell depth of 1.8 mm 0.1% solution. Mu, 5.5 X 10 in decahydronaphthalene).

Commonly known as the Kerr Effect, this is the best known electro-optic phenomenon. Although initially studied in glasses by John Kerr (J) in 1875, who considered the birefringence to be related to electrically induced strain in the material, it is now used widely to follow the alignment due to orientation and deformation of macro-particles in solution and suspension (2—4). It owes its origin to anistropy of the refractive indices associated with the major geometric axes of the molecules. 

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