Photo Elasticity

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. 

If A is an integer multiple of tt, then the total wave is linearly polarized in the AxX + Ayf direction. Otherwise, the wave is elliptically polarized with the special case of circular polarization when Ax = Ay. Although Jones calculus cannot represent unpolarized light in a simple way, Jones realized that all of the information in polarized light can be represented by a complex Jones vector, J = or 2 x 1 matrix, where ( ) = ln zl + vf) + Bx + ey)/2. 

Optical elements can be represented by 2 x 2 matrices, wbicb act from the left by matrix multiplication on J to produce a new vector representing the light leaving the element. The leading phase term e is not needed to describe relative phase shifts and is usually dropped for simplicity. From this description, the intensity of light is calculated by taking tbe modulus of tbe complex inner product of the Jones vector I = J J, where is the complex-conjugate transpose. 

The power of the technique is that a complex chain of optical elements can be described using a few basic elements 

The Jones vector represents light polarized in the x-direction S(0) rotates polarization by angle 0 

---

Polarization modulation ellipsometers use a photo-elastic modulator to modulate the state of polarization of the incident beam. Polarizer and analyzer are fixed during the measurement. Eourier analysis of the time dependent signal gives the ellipse-... 

In the last decades, the modeling of both compacted particulates and flowing particle assemblies under loads and under flow conditions has been advanced by DEM, first developed by Cundall (46) for two-dimensional compacted-disk assemblies in 1971. The origins of DEM are in the field of molecular dynamics (MD), where the motions of individual molecules are tracked under the influence of an external force (e.g., electrostatic) field (47). Experimental results such as those with model photo-elastic assemblies just discussed have also assisted the development of the DEM simulation models. 

Both these concerns were addressed by the development of modified IR techniques. In the technique of Subtractively Normalised Fourier Transform IR Spectroscopy (SNIFTIRS) or Potential Difference IR (SPAIRS or PDIR) [37], the increased stability and sensitivity of Fourier Transform IR is exploited, allowing usable spectra to be obtained by simple subtraction and ratioing of spectra obtained at two potentials without the need for potential modulation or repeated stepping. A second technique which does not call for potential modulation, but actually modulates the polarisation direction of the incoming IR beam is termed Photo-elastically Modulated Infra-Red Reflectance Absorption Spectroscopy (PM-IRRAS) this was applied to the methanol chemisorption problem by Russell and co-workers [44], and Beden s assignments verified, including the potential-induced shift model for COads. 

Qualitative information concerning the distribution and zones of concentration of stresses in the various areas of flow and the different dies considered was obtained by birefidngence. Like many other authors [37-39], we shall assume that the photo-elastic law, which expresses the relation between the optical tensor and stress tensor, is linear for the experiments performed here. Thus, at least in principle, this relation may be used to obtain an experimental measurement of stresses at all points of the flow [37, 38,40, see also chapter III.l in this book]. 

Fig. 2 Schematic of the dynamic photo elasticity setup (Xu and Rosakis)...

A schematic setup of the photo-elasticity technique is given in Fig. 2. Two sheets of a circular polarizer were placed on both sides of the specimen. An Innova Sabre argon-ion pulsed laser... 

Through the photo-elastic facility, the early stages of the damage pattern were recorded. Fig. 9 shows the experimental fringe pattern and the numerical contour plots of maximum shear stress at about 42 ps after impact. Note the clear shock wave pattern in both cases. This implies that the crack propagates at a velocity above the shear wave speed of the core material Homalite, and is therefore inter-sonic. 

A crystal exposed to a stress S will show a change of its impermeability. The photo-elastic (or elasto-optic) constants, P. p are defined by... 

Equation (9.8) states that the stress field close to the crack tip has a particular form. This can be revealed using the photo-elastic effect. The refractive indices tt and 2 in the directions of the principal stresses and [Pg.270]

The report of the inquiry [111] criticised the design and fabrication of the alterations made to the original pontoon. The actual cause of the accident was the failure of some tie bars in the detail around the jacking points. The failure was due to brittle fracture which initiated from severe notches such as a small radius curve at the fillet between the spade end and the shank of the tie bar. Weld defects and fatigue cracks were also present in tie bars subsequently recovered from the sea bed. The tie bars had been flame cut to shape and had weld repairs visible to the eye. There had been no post welding heat treatment of the steel. The steel complied with the original specification but tests showed low Charpy V notch impact values. Photo elastic tests indicated a stress concentration factor of 7 at the fillet between the spade end and the shank. The fracture was initiated in the opinion of the inquiry tribunal by the low ambient temperature of around 3°C. 

Mechanical Photo-elastic effect Conservation of moment Friction heat Piezo- electricity Magnetostriction Pressure-induced explosion... 

PM-IRRAS exploits the different attenuation of s- and p-polarized light by adsorbed species at a reflective (electrode) surface to annul the unchanging contributions to the infrared signal at the detector from the solvent, window, and so on, and produces an absolute rather than difference spectrum at a particular potential. In this approach, a photo-elastic modulator is employed to modulate the polarization state of the incident infrared ray between s- and p-states. On the basis of Greenler s theory [81, 82], this polarization modulation gives rise to an AC signal at the detector, which is proportional (/p —7s)-the difference in intensity of the two polarizations. Since, in principle, /p is absorbed... 

These experiments show that the photo-elastic effect in films of a ladder polymer is of a complex molecular and supermolecular nature. The appearance of mesomorphic properties in these films, never observed previously, is due... 

FIGURE 18 The basic operation of an acousto-optic device is to reduce the intensity of a transmitted beam by diffraction from a refractive index grating that is generated, via the photo-elastic effect, by the RF power supplied to the transducer. The device depicted is used for Q-switching and cavity dumping. If configured as a resonator for the acoustic wave, it serves as a mode-locker. 

The distribution of stresses can be clearly revealed in photo-elastic models of joint assemblies made from a transparent material that becomes doubly refractive when subjected to stress. If a beam of polarised white light is shone through a stressed component, coloured lines appear when the object is viewed through a second polarisation filter as a result of interference effects. These lines indicate areas of equal stress. If stress levels are increased, the sequence of coloured lines is repeated. The photographs below show specimen components made from clear acrylic or polycarbonate joined by different methods. In the side view of a bolted coimecfion under load, the stress peaks around the bolt appear very clearly (Fig. 13). 

Figure 13 Stress patterns in photo elastic models Bolted connection under load. For easier understanding please refer to the colour section.

Figure 14 Stress patterns in photo elastic models thin and thick-layer rigid adhesive bonds (See colour plate section for colour photographs.)...

If the fibre is subjected to any kind of strain or stress, there is a change in refractive index, and consequently there is an induced phase difference between different polarisation directions (this phenomenon is called photo-elastic effect). The change in the refractive index due to stress or strain is also known as induced refractive index (Fidanboylu and Efendioglu, 2009). 

---