Rubber Birefringence and Photoelasticity

The phenomenon of birefringence, discovered in 1669 by Erasmus Bartholin and later studied by Christian Huygens, is well known for its appearance in transparent crystalline solids. It is to be traced essentially to internal anisotropy of crystals for light propagation, so that under certain conditions a single wave front may give rise to multiple coherent waves which can cause double refraction or other phenomena such as the appearance of fringes varying in brightness and color due to interference of emerging wave fronts. Birefringence may be expressed as the difference of the velocities of propagation in various directions in the birefringent medium and particularly as the difference between the maximum and the minimum velocity or, alternatively, between the maximum and the minimum refractive index or even as the phase difference between emerging waves, given frequently as a number of wavelengths. While true double refraction phenomena may be observed with ordinary light when the difference n1−n2 between the refractive indexes is very high, the interference phenomena may be obtained only with polarized light, but may be observed even with very small differences between indexes. This is not the place to treat extensively general concepts like polarizer, analyzer, ordinary wave, extraordinary wave, uniaxial crystal, biaxial crystal, etc. which can be found in any good optics treatise. Birefringence is not in any way limited to crystalline media, possessing inherent structural anisotropy. It may also appear in bodies which are normally isotropic, when structural anisotropy is caused by external forces. Then birefringence is quantitatively dependent on force intensities, even if not always in an easily detectable way. This is called “accidental birefringence” or “stress-birefringence”. It was observed by Seebeck in 1813, and later studied in 1816 by Brewster for glass. It is observable in many transparent materials. Stress-birefringence is particularly conspicuous in macromolecular substances, including elastomers, vulcanized or not, where it is determined by the orientation of molecular links. This, of course, may not be ascribed altogether to stress, but sometimes also to partial crystallinity. Other phenomena of accidental birefringence may be observed in liquids or in solutions, especially of elastomers, when they are subjected to a velocity gradient, as when flowing through a capillary tube or, more commonly, when sheared between two coaxial cylinders.

Some Factors Which Determine the Flight of Aerological Sounding Balloons

Examination of Equations (8), which connect the external pressure and thus the altitude to the dilation of the balloon, shows that the most important factor with regard to the “limited” bursting height is the elongation at break of the envelope at temperatures of the order of −40° C and −60° C. The elasticity modulus of the material and the thickness of the envelope are therefore of little importance with respect to the bursting height. It must be remembered, however, that the thickness has an indirect influence because it increases the weight of the balloon proportionally, and possible irregularities in the envelope will be all the more harmful as the thickness decreases. As for the lift force, this remains practically constant during the ascent of the balloon. On the basis of experimental determinations, the elevated concentrations of ozone will not have a particularly harmful influence on the rubber envelope, even if it is of natural rubber, due to temperatures at high altitudes of less than −40° C, the high state of tension of the rubber, and the brief duration of the flight.

Accidental Factors Involved in the Fatigue Breakdown of Rubber Articles

Poor dispersion of compounding ingredients, and the presence of granules and of impurities which in some way get into vulcanized rubber and thereby disturb the normal distribution of stresses in an article and thus cause local stress concentration, are regarded as accidental factors in the fatigue breakdown of vulcanized rubber. This problem was studied by developing, by means of the photoelastic method, an adaptable schematic representation of the phenomena. Although only a qualitative evaluation of the local disturbance of the system of stresses caused by these factors is possible, in the particular case of granules, it has been found that the closer a granule is to the outside surface of the rubber article, the greater is the disturbance of the system of forces. Furthermore, the local stress concentration is greatest when there is no adhesion between the granules and the surrounding vulcanized rubber. Finally the stress concentration caused by a small cut or incision made at various locations on a rubber test-strip under tension is considered. This case has been included because fatigue cracks first become manifest in this form.

The Photoelastic Examination of Rubber Articles

After a short introduction to the photoelastic method and its applications to the examination of transparent planar structural models, some methods of examining plane models representing sections of actual rubber articles are indicated. In many cases it is advisable to place the model between parallel glass plates with their inner faces lubricated and at a distance apart equal to the thickness of the model itself. In other cases free models can be examined. In no case, however, is the law governing the birefringence of transparent materials within a range of small deformations, e.g., less than 1 per cent, equally applicable to greater deformations, e.g., up to 100 per cent. But in this range recourse can then be had to a law, based essentially on theoretical considerations and described by Treloar, which is an extension of the general law and which has been verified experimentally. Some special cases are considered where the law is of general application to the quantitative evaluation of the state of deformation at various points in a model under examination.