Photoelasticity

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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.

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Photoelasticity

  1. 1. 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 2Hareesha N G, Asst Prof,DSCE, Blore
  2. 2. 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. 4/4/2014 3Hareesha N G, Asst Prof,DSCE, Blore
  3. 3. 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. 4/4/2014 4Hareesha N G, Asst Prof,DSCE, Blore
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  5. 5. • 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. 4/4/2014 6Hareesha N G, Asst Prof,DSCE, Blore
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  7. 7. • 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. 4/4/2014 8Hareesha N G, Asst Prof,DSCE, Blore
  8. 8. 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
  9. 9. 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 4/4/2014 10Hareesha N G, Asst Prof,DSCE, Blore
  10. 10. 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
  11. 11. 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 4/4/2014 12Hareesha N G, Asst Prof,DSCE, Blore
  12. 12. • 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. 4/4/2014 13Hareesha N G, Asst Prof,DSCE, Blore 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.
  13. 13. • 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. 4/4/2014 14Hareesha N G, Asst Prof,DSCE, Blore
  14. 14. • 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 4/4/2014 15Hareesha N G, Asst Prof,DSCE, Blore
  15. 15. 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. 4/4/2014 16Hareesha N G, Asst Prof,DSCE, Blore To illustrate this effect, consider the stressed model in the circular polariscope (arrangement A) shown in Fig.
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  18. 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. 4/4/2014 19Hareesha N G, Asst Prof,DSCE, Blore
  19. 19. 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. 4/4/2014 20Hareesha N G, Asst Prof,DSCE, Blore
  20. 20. 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 4/4/2014 21Hareesha N G, Asst Prof,DSCE, Blore
  21. 21. • 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. 4/4/2014 22Hareesha N G, Asst Prof,DSCE, Blore
  22. 22. 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 4/4/2014 23Hareesha N G, Asst Prof,DSCE, Blore
  23. 23. • 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 4/4/2014 24Hareesha N G, Asst Prof,DSCE, Blore

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