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Purpose

The purpose of this experiment is to determine and calibrate the optical coefficient of a sample of

photoelastic. This is to be done so by done so by measuring the location of the fringe orders using a

polariscope, and then applying as per theory.

Theory

When using transparent non-crystalline materials, one can analyze the stress by using the photoelastic

method. When stress free, non crystalline materials are isotropic, but when a stress is applied, it then

becomes anisotropic. By using photostress, analyzing experimental stress becomes achievable because

one now has a visible picture of the overall surface stress distribution. It also gives reliable quantitative

values for the magnitude and direction of the stress.

Consider a material coated with a photoelastic material, which is then subjected to an external load. The

strain developed in the sample due to the external load is the same as the photoelastic material. There

is a retardation between the two polarized beams of light shown in the x and y direction at each pointon the material tested.

( )  [1]

Variables:   is the retardation (in)

λ  is the wavelength of white light   

  is the sensitivity of the material or Photoelastic coefficient

  is the fringe order

  is the thickness of the coating

Where  is the fringe value given the by equation,

 

 

Which stems from the equation below rearranged from equation [1], yielding principal strain difference:

( )

 

Therefore leaving the final equation being

( )   [2]

To find the principal stress difference,

( )

  [3]

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When polarized light is shone through the photoelastic coated material while also subjected to external

stress, the waves split and propagate at different speeds along the direction of principal stress. This

causes the polarized waves to be out of phases with each other. At points where the direction of the

polarized beam and the principal stress are parallel,, the light emerging from the photoelastic coating

will be the same as the incident light. On the other hand, dark fringes are observed in the plane

polariscope, called isoclinic. The fringe order of light along the beam can be determined by aligning the

isoclinic to the point of interest.

To compensate because the point of interest falls between the fringes, Tardy compensation and

absolute compensation are used.

Absolute compensation measures the photoelastic signal at the point of interest by using entering a

calibrated value equal in size, but opposite in sign into the light path. When the photoelastic signal is

cancelled to read zero at the point of interest, the recognized fringe value is eliminated.

Tardy compensation on the other hand lets the fringe order to be seen by aligning the polarizer with the

direction of principal stress and quarter wave plates at 45°. The tardy compensator analyzer can be

rotated if the fringe orders are initially between points of interest, so that they can be moved onto the

point analyzed. This experiment measured fringe order with reference to the first fringe order.

Apparatus

  Loading Frame

  Cantilever Beam with a photoelastic coating

  Precision dead load

  portable polariscope

Figure 1: Lab Setup

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Procedure

1) 

Measure the cross sectional geometry of the beam used in the experiment. Also measure

the distance between the markings along the beam. (FIGURE 1)

2) 

Calculate the maximum allowable load determined by the maximum allowable stress.

3) 

Measure the beam and coating thickness.

4) 

Apply the maximum amount of load.

5) 

Record the fringe location at each point marked along the beam.

a. 

For the polariscope, the purple fringe order is used and moved to the desired

location using the scale on the plariscope.

b. 

For the compensator, the dial was moved until the dark fringe order was positioned

at the marked location.

c. 

The value displayed on the counter is read and adjusted using the calibration chart

for fringe order.

6) 

Repeat step 5, this time using two pounds less. Stop recording data after measurements at

the 6 pound load is taken.

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Observations

Table1: Fringe location for Serial Number 397

Load Fringe for

Location 1

Fringe for

Location 2

Fringe for

Location 3

Fringe for

Location 4

Fringe for

Location 5

- Null Tardy Null Tardy Null Tardy Null Tardy Null Tardy

14 1.17 64 1.42 74 1.68 88 1.96 102 2.16 113

12 1.02 57 1.22 65 1.44 75 1.69 86 1.97 95

10 0.89 48 1.05 57 1.23 65 1.46 69 1.64 80

8 0.74 40 0.86 47 1.00 52 1.18 57 1.36 64

6 0.62 31 0.69 33 0.77 39 0.91 46 1.04 50

Table2: Fringe location for Serial Number 450

Load Fringe for

Location 1

Fringe for

Location 2

Fringe for

Location 3

Fringe for

Location 4

Fringe for

Location 5- Null Tardy Null Tardy Null Tardy Null Tardy Null Tardy

14 54 1.16 64 1.36 75 1.56 85 1.88 95 2

12 45 10 54 1.22 61 1.36 71 1.54 82 1.75

10 30 0.6 45 10 55 1.2 64 1.38 72 1.54

8 29 0.4 33 0.68 40 0.9 53 1.14 57 1.26

6 14 0.1 19 0.2 20 0.4 29 0.6 37 0.8