Photoelasticity

UNIT-3: Photo-elasticity: • Nature of light, Wave theory of light

• optical interference , Stress optic law,

• effect of stressed model in plane and circular polariscopes,

• Isoclinics & Isochromatics,

• Fringe order determination

• Fringe multiplication techniques,

• Calibration photoelastic model materials

08 Hours

4/4/2014 2 Hareesha N G, Asst Prof,DSCE, Blore

Nature of Light • Huygens (1629—1695) attempted to explain the optical effects

associated with thin films, lenses and prisms with a wave theory. • In this theory, light is considered as a transverse disturbance in a

hypothetical medium, of zero mass, called the ether. • At the same time Newton (1642—1727) proposed his corpuscular

theory, in which light is visualized as a stream of small but swift particles (corpuscles) emanating from shining bodies in all directions, travelling at the speed of light.

• The next major step in the evolution of the theory of light was due to Maxwell (1831—1879), who presented the electromagnetic wave theory.

• Here light is an electromagnetic disturbance, propagating through space, represented by two vectors (electric and magnetic) mutually perpendicular and perpendicular to the direction of wave propagation.

• The most recent theory is the wave-mechanic or quantum theory, which is a combination of the first two theories.

• The photo-elastic effect can be conveniently explained by adopting either the wave theory or the electromagnetic theory.


WAVE THEORY OF LIGHT

• Electromagnetic radiation is predicted by Maxwell's theory to be a transverse wave motion which propagates with an extremely high velocity.

• Associated with the wave are oscillating electric and magnetic fields which can be described with electric and magnetic vectors E and H.

• These vectors are in phase, perpendicular to each other, and at right angles to the direction of propagation.

• A simple representation of the electric and magnetic vectors associated with an electromagnetic wave at a given instant of time is illustrated in Fig.



• All types of electromagnetic radiation propagate with the same velocity in free space, approximately 3 x 108 m/s.

• The parameters used to differentiate between the various radiations are wavelength and frequency.

• The two quantities are related to the velocity by the relationship

λf=c

where λ = wavelength

f= frequency

c = velocity of propagation

• The electromagnetic spectrum has no upper or lower limits.

• The radiations commonly observed have been classified in the broad general categories shown in Fig.



• Light is usually defined as radiation that can affect the human eye.

• From Fig. it is evident that the visible range of the spectrum is a small band centered about a wavelength of approximately 550 nm.

• The limits of the visible spectrum are not well defined because the eye ceases to be sensitive at both long and short wavelengths; however, normal vision is usually in the range from 400 to 700 nm.

• Within this range the eye interprets the wavelengths as the different colors.

• Light from a source that emits a continuous spectrum with near equal energy for every wavelength is interpreted as white light.

• Light of a single wavelength is known as monochromatic light.


Effects of a stressed model in a plane polariscope • Consider a plane-stressed model inserted into the field of a plane

polariscope with its normal coincident with the axis of the polariscope, as illustrated in Fig.

• Note that the principal-stress direction at the point under consideration in the model makes an angle α with the axis of polarization of the polarizer.


Effects of a stressed model in a plane polariscope

• We know that a plane polarizer resolves an incident light wave into components which vibrate parallel and perpendicular to the axis of the polarizer.

• The component parallel to the axis is transmitted, and the component perpendicular to the axis is internally absorbed.

• Since the initial phase of the wave is not important , the plane-polarized light beam emerging from the polarizer can be represented by the simple expression


Effects of a stressed model in a plane polariscope • After leaving the polarizer, this plane-polarized light wave enters the

model, as shown in Fig.

• Since the stressed model exhibits the optical properties of a wave plate (Doubly refracting material), the incident light vector is resolved into two components E1 and E2 with vibrations parallel to the principal stress directions at the point.


Effects of a stressed model in a plane polariscope • Thus

• Since the two components propagate through the model with different velocities ( c > v1 > v2), they develop phase shifts Δ1 and Δ2 with respect to a wave in air.

• The waves upon emerging from the model can be expressed as

where


• After leaving the model, the two components continue to propagate without further change and enter the analyzer in the manner shown in Fig.

• Since the vertical components are internally absorbed in the analyzer, they have not been shown in Fig.


The light components E1’ and E'2 are resolved when they enter the analyzer into horizontal components E1’’ and E"2 and into vertical components.

• The horizontal components transmitted by the analyzer combine to produce an emerging light vector Eax, which is given by

Using in the above equation,

we get,

• It is interesting to note in the above Eqn that, the average angular phase shift (Δ2+Δ1)/2 affects the phase of the light wave emerging from the analyzer but not the amplitude.


• Since the intensity of light is proportional to the square of the amplitude of the light wave, the intensity of the light emerging from the analyzer of a plane polariscope is given by


Effects of a stressed model in a circular polariscope (Dark Field, Arrangement A)

• When a stressed photo-elastic model is placed in the field of a circular polariscope with its normal coincident with the z axis, the optical effects differ significantly from those obtained in a plane polariscope.


To illustrate this effect, consider the stressed model in the circular polariscope (arrangement A) shown in Fig.

4/4/2014 Hareesha N G, Asst Prof,DSCE, Blore 17

4/4/2014 Hareesha N G, Asst Prof,DSCE, Blore 18

Effect of Principal-Stress Directions • When 2α = nπ, where n = 0, 1, 2,..., sin2 2α = 0 and extinction

occurs. • This relation indicates that, when one of the principal-stress

directions coincides with the axis of the polarizer (α = 0, π /2, or any exact multiple of π /2) the intensity of the light is zero.

• Since the analysis of the optical effects produced by a stressed model in a plane polariscope was conducted for an arbitrary point in the model, the analysis is valid for all points of the model.

• When the entire model is viewed in the polariscope, a fringe pattern is observed; the fringes are loci of points where the principal-stress directions (either or a2) coincide with the axis of the polarizer.

• The fringe pattern produced by the sin2 2α term in Eq. is the isoclinic fringe pattern.

• Isoclinic fringe patterns are used to determine the principal-stress directions at all points of a photo-elastic model.


Effect of Principal-Stress Difference

• When Δ/2 = nπ, where n = 0, 1, 2, 3,..., sin2 (Δ /2) = 0 and extinction occurs.

• When the principal-stress difference is either zero (n = 0) or sufficient to produce an integral number of wavelengths of retardation (n = 1, 2, 3,...), the intensity of light emerging from the analyzer is zero.

• When a model is viewed in the polariscope, this condition for extinction yields a second fringe pattern where the fringes are loci of points exhibiting the same order of extinction (n = 0,1, 2, 3,...).

• The fringe pattern produced by the sin2 (Δ /2) term in Eq. is the isochromatic fringe pattern.


Isoclinics

• The human eye is very sensitive to minima in light intensity.

• From Eqn

it is seen that either one of two conditions will prevent light that passes through a given point in the specimen from reaching the observer, when a plane polariscope is used. The first condition is that


• Since α is the angle that the maximum principal normal stress makes with the polarizing direction of the analyzer, this result indicates that all regions of the specimen where the principal-stress directions are aligned with those of the polarizer and analyzer will be dark.

• The locus of such points is called an isoclinic because the orientation, or inclination, of the maximum principal normal stress direction is the same for all points on this locus.

• By rotating both the analyzer and polarizer together (so that they stay mutually crossed), isoclinics of various principal-stress orientations can be mapped throughout the plane.


Isochromatics

• The locus of points for which this condition is met is called an

isochromatic, because (except for n = 0) it is both stress and wavelength dependent.

• Recall from Eqn. (7) that


• Therefore, points along an isochromatic in a plane polariscope satisfy the condition

• The number n is called the order of the iso-chromatic.

• If monochromatic light is used, then the value of Δ is unique, and very crisp isochromatics of very high order can often be photographed.

• However, if white light is used, then (except for n = 0), the locus of points for which the intensity vanishes is a function of wavelength.

• For example, the locus of points for which red light is extinguished is generally not a locus for which green or blue light is extinguished, and therefore some combination of blue and green will be transmitted wherever red is not.

• The result is a very colorful pattern, to be demonstrated by numerous examples in class using a fluorescent light source


Engineering

Photoelasticity