Photoelasticity Polariscope

8/12/2019 Photoelasticity Polariscope

1/19

Structures 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)


Photoelastic Experiment

Based on: When tractions are prescribed in a boundary value problem, the stressdistribution 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 oflight 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.


2/19


Use Photoelasticity to Find the Stress in the Object


Use Photoelasticity to Find the Stress in the Object


3/19


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


4/19


The Method Applies to BirefringentMaterials

Gary Cloud, Experimental Techniques, 2008

Birefringent materials are those in which

the index of refraction varies with the

direction of polarization of the light passingthrough them.

The surface of the

birefringent slab acts as a

beam splitter, dividing the

entering wave into two waves

that are polarized inorthogonal directions called

the principal axes of the

refractive index.


The Plane Polariscope

Polarizer and Analyzerare crossed Dark field

The incident light that enters the model is split into two components that are

orthogonally polarized and vibrate in the planes of1 and2


5/19


Isocromatics in the Object


Isocromatics Shadowed by Isoclinics

Gary Cloud, Experimental Techniques,

2008


6/19


Circularly Polarized Light

The tip of the light vector traces a circular path with time forming a helix

as it propagates along the z-axis

How do we create circularly polarized light?

Use a plane polarizerand a quarter wave plate


The Quarter Wave Plate


7/19


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 field

If analyzer is parallel Light field


8/19


Dark field Dark field Light field

Configurations of the Circular Polariscope




9/19




The Circular Polariscope ? Field

WHAT HAPPENS IF I PLACE AN OBJECT IN THE MIDDLE?


10/19


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


11/19


12/19


Experimental Set-up for Bending Dark Field

fixed fixed

M M


Pure Bending

1-2=0

1 2 fmt


13/19


Four Point Bending

1 2 mt


Stress Concentration at a Circular Hole

Plate thickness = t

: 0 0r rr a r aBCs


14/19


1-2=0

Stress Concentration


Stress Concentration


15/19


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 21

2

t

nf


16/19


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 stressanalysis? Explain.

1 21

2

t

nf

1 2

t

mf

or

What purpose do the quarter wave plates serve in the experimentalpolariscope setup?


Pre-Lab Assignment

Around 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 2

1

2

tn

f


17/19


18/19


Other Examples

Gary Cloud, Experimental Techniques, 2009


Other Examples

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


19/19

Documents

Photoelasticity Polariscope