This presentation gives an information about: photoelasticity, covering syllabus of Unit-3, of Experimental stress analysis subject for BE course under Visvesvaraya Technological University (VTU), Belgaum.

2. 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
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3. 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.
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4. 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.
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6. • 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.
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8. • 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.
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9. 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.
4/4/2014 9Hareesha N G, Asst Prof,DSCE, Blore

10. 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
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11. 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.
4/4/2014 11Hareesha N G, Asst Prof,DSCE, Blore

12. 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
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13. • 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.
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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.

14. • 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.
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15. • 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
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16. 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.
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To illustrate this effect, consider the
stressed model in the circular
polariscope (arrangement A) shown in
Fig.

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19. 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.
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20. 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.
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21. 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
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22. • 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.
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23. 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
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24. • 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
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