Photo Elasticity

1Structures and Controls Lab - AE 461 Chasiotis I.

Measurement of Stress by Photoelasticity

References: M.M. Frocht, Photoelasticity, John Wiley and Sons, Boston, (1941)

A.J. Durrelli, Introduction to Photomechanics, Prentice-Hall, (1965)

Structures and Controls Lab - AE 461 Chasiotis I.

Photoelastic Experiment

Based on: When tractions are prescribed in a boundary value problem, the stress distribution is independent of material (properties), i.e. E and

Photoelasticity helps us visualize stresses inside an object

Objectives:

1. Introduce the use of photoelastic principles in stress analysis

2. Use the stress distribution in a polymer beam to find the material fringe constant

3. Measure the stress concentration in a notched polymer beam

Photoelastic Effect: Optical property of transparent materials in which the speed of light through the material is affected by the state of stress

How we use it: Pass light through a model of an engineering structure and measure the changes in the wave speed for a given applied load.


Use Photoelasticity to Find the Stress in the Object


Use Photoelasticity to Find the Stress in the Object


Definition of Light and Dark Fringes

Light and dark field isochromatics in a circular disk under diametric compression

Dark fringes fall between light fringes

High fringe density denotes high stress gradient (and perhaps stress concentration)


We Need Polarized Light

PLANE POLARIZED LIGHT

Light going through a polarizer is transmitted in one plane only


The Method Applies to Birefringent Materials

Gary Cloud, Experimental Techniques, 2008

Birefringent materials are those in which the index of refraction varies with the direction of polarization of the light passing through them.

The surface of the birefringent slab acts as a beam splitter, dividing the entering wave into two waves that are polarized in orthogonal directions called the principal axes of the refractive index.


The Plane Polariscope

Polarizer and Analyzer are crossed Dark fieldThe incident light that enters the model is split into two components that areorthogonally polarized and vibrate in the planes of 1 and 2


Isocromatics in the Object


Isocromatics Shadowed by Isoclinics



Circularly Polarized Light

The tip of the light vector traces a circular path with time forming a helixas it propagates along the z-axis

How do we create circularly polarized light?

Use a plane polarizer and a quarter wave plate


The Quarter Wave Plate


Crossing Quarter Wave Plates

Two parallel quarter plates shift the light plane by 90 Two crossing quarter plates shift the light plane by 0


The Circular Polariscope Dark Field

If analyzer is crossed Dark fieldIf analyzer is parallel Light field


Dark field Dark field Light field

Configurations of the Circular Polariscope






The Circular Polariscope ? FieldWHAT HAPPENS IF I PLACE AN OBJECT IN THE MIDDLE?

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The Circular Polariscope


The Circular Polariscope Light Field Arrangement

When light passes through the analyzer we have Light Field Arrangement

2 cos cos2

A k t

AmplitudeFrequency Phase shift

2 2 2 2Intensity: 4 cos cos2

I A k t Dark fields are generated when:

1. cos2(t)0 ; cannot be observed since is very high (~1012 Hz)2. cos2(/2)0

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The Circular Polariscope Light Field Arrangement

Condition for isochromatic fringes (light field)

2cos 0 1 2 0,1, 2,3,...2 2 2 n n

Question:

How does the applied STRESS affect ?1 2

Nft

: retardation of polarized light2

: material fringe constant (psi-in)

: thickness of model

N

fc

t


The Circular Polariscope Light vs. Dark Field

1 2 1 21 2 12 2fn t nt f

If we combine these relations:

For the material used in your experiment, obtain f as follows:

1 2

n

fslopet

Similarly, we find that for dark field:

1 2 1 2 f tm mt f In dark field, dark fringes correspond to integer fringe order In light field, dark fringes correspond to half fringe order

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Experimental Set-up for Bending Dark Field

fixed fixed

M M


Pure Bending

1-2=0 1 2 fm t

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Four Point Bending

1 2 fm t


Stress Concentration at a Circular Hole

Plate thickness = t

: 0 0r rr a r aBCs

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1-2=0

Stress Concentration


Stress Concentration

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Pre-Lab Assignment

For the isotropic photoelastic beam shown below (in a light-field polariscope), what is the highest fringe number? Locate the n = 0 fringe(s) and the highest fringe(s).

The fringes are denoted by the black lines. (Note: In a light-field polariscope, these are actually half-fringes, thus the need for (n+1/2) rather than n)


Pre-Lab Assignment

h = 1.5 in

h = 1.5 in

w = 0.25 in

Beam cross-section

0.125 in from highest fringe order to the edge of beam

Determine the fringe constant fs for the following beam with an applied moment of 12.00 in-lb at the ends. Note that the fringe pattern is symmetric about the neutral axis.

1 2 12 t nf

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Pre-Lab Assignment

Which would give a greater stress resolution in a photoelastic beam, a high fs or a low fs? Which is more applicable for sensitive experimental stress analysis? Explain.

1 2 12 t nf

1 2 t m

for

What purpose do the quarter wave plates serve in the experimental polariscope setup?


Pre-Lab AssignmentAround a circular hole the maximum stress is the nominal stress magnified by a factor of 3.0. If nfar = 2 (number of fringes seen in the far field):a) Derive the relationship between the stress concentration ratio to the number of near and far field fringes.b) How many fringe orders will be seen in the near field under this applied stress?

nnear

nfar

nom max

PP

1

1 212

tnf

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Other Examples


Other Examples


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Other Examples



Other Exampleshttp://www.flickr.com/photos/core-materials/3841043722/sizes/o/in/photostream/

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Other Examples

http://www.flickr.com/photos/core-materials/3840250573/sizes/o/in/photostream/


Other Examples

http://medlibrary.org/medwiki/Contact_mechanics

Documents

Photo Elasticity