Recent Advances in Photoelastic Applications

8/12/2019 Recent Advances in Photoelastic Applications

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Recent Advances in Photoelastic Applications

Anand Asundi

School of Mechanical and Aerospace Engineering

Nanyang Technological University

Singapore

email:[email protected]

Abstract:

Photoelasticity is one of the oldest methods for eperimental stress analysis! "ut has "een overshado#ed "y the

$inite Element Method for engineering applications over the past t#o%three decades. &o#ever! certain ne# and

novel developments and applications have revived the use of photoelasticity. Among them are image processing for

fringe analysis! polarimetric fi"er optic sensors! infra'red photoelasticity! lo# cost dynamic photoelasticity and

photoelastic applications in stereolithography. This paper #ill! after a "rief introduction to photoelasticity! highlight

some of these advances and developments.

Introduction:

As the name implies! photoelasticity #as developed to apply optical (photo) principles to solve engineering

pro"lems of elasticity. The method relies on the "irefringence property ehi"ited "y transparent plastics. *n

particular! the phenomenon of stress (or load ) induced "irefringence is utili+ed #here the material "ecomes

"irefringence under the influence of eternal loading. The phenomenon #as first o"served "y ,avid -re#ster in the

early nineteenth century in glass and he foresa# the potential of this for stress analysis. &o#ever! glass #as far from

the ideal material although photoelasticity of glass () has generated great interest. The techni/ue #as !ho#ever !

systematically developed into a via"le eperimental stress analysis tool only in the second /uarter of this century.

0or1s "y 2o1er and $ilon (3)! $rocht (4) and 5essop and &arris (6 ) are particularly note#orthy in this regard. Thepotential of 4', stress analysis #as also developed "y 7ppel (8) and &etenyi (9) and to this day remains one of the

very fe# eperimental methods for 4', stress analysis. 0ith this "ac1ground! photoelastictiy found #idespread

application in many industrial applications. *n particular! determination of stress concentration () in front of notchesand holes #as and still is one of the premier forte of photoelasticity in design of machine elements.

*n the past t#o decades! photoelasticity has "een overrun "y the $inite Element Method ($EM). The simplicity and

"lac1 "o nature of $EM #as particularly inviting to designers #ho did not have toget their hands dirty. &o#ever!#hile one cannot ignore the po#er of $EM! one has to reali+e the limitations of the method in it "eing as good as the

model used. *ndeed! critics of photoelasticity did mention that photoelasticity re/uires a "irefringent model to "e

used instead of the actual structure. The same applies to $EM since it relies on a numerical model of the actual

structure and loading to generate the stress and displacement distri"ution patterns. A ne# school of thought is the


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use of hy"rid methods #here advantages of "oth eperimental and numerical methods are eploited. Nevertheless!

recent needs such as continuous on'line monitoring of structures! residual stresses in glass (plastics) and

microelectronics material ! rapid prototype products and dynamic visuali+ation of stress #aves have "rought

photoelasticity into the limelight once again. This paper #ill highlight some of these advances and developments in

photoelasticity.

Photoelastic basics:

The principles of photoelasticity can "e succinctly elucidated "y the follo#ing t#o la#s:

. $or stress ( or strain ) induced "irefringence! the normally incident polari+ed light is split

into t#o components along the principal stress directions in a plane perpendicular to the

direction of light propagation and are transmitted only along these planes through themodel.

. The velocities of light transmission along these directions is directly proportional to the

intensities of the respective principal stresses.

These la#s imply that the input linearly polari+ed light emerges as an elliptical polari+ed light #here the degree of

ellipticity depends on the principal stress directions and the magnitudes of the principal stresses. *n particular "y

invo1ing Ma#ell;s Stress 7ptic


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!i"ure 1: #che$atic of rossed Plane Polariscope

a pair of polarisers! termed the polariser and analy+er! #ith crossed polari+ation ais on either side of the model.

?irtually any light source can "e utili+ed and currently !!3....

$rom figure ! this condition is satisfied #hen either principal stress direction coincides #ith the ais of polari+ation

of the polari+er. These dar1 lines or points are the I#IN lines! and provide information on direction of

principal stresses throughout the model.


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2% sin /2 =& i%e% = 2 N#here N > !!3 ....

$rom e/n. ()! this condition is satisfied #hen

/ 2 = N = d ( 1- 2) / f(*)

These are the I#+R,AI frin"es! lines of constant principal stress difference. *ndeed! since is

#avelength dependent! these fringes have "een referred to as isochromatics ' lines of the same colour. *f the incident

light is monochromatic dar1 and "right fringes #ill "e o"served. 2onventional photoelasticity used "lac1 and #hite

fringes for processing since they #ere easily distinguisha"le "y the human operator. 0hite light illumination #asused principally to identify the +ero order ( N>) fringe #hich is "lac1 #hile higher order fringes are coloured.

2olour imaging and processing is no# "eing revived #ith the ready access to digital colour imaging and image

processing. Nevertheless! regions of high fringe gradient might still call for gray level processing.

The standard plane Polariscope #ill thus sho# "oth the isoclinics and isochromatics intert#ined. $rom a stress

analysis point of vie# this is /uite inconvenient. ?isuali+ation of only isoclinics can "e achieved "y reducing the

num"er of isochromatics "y applying a smaller load or using a material #ith a high material fringe constant.

?isuali+ation of isochromatics alone can "e achieved "y using a circular Polariscope #hich in addition to the plane

Polariscope elements ! has t#o opposing /uarter #ave plates on either side of the model. $igure 3 sho#s typicalisochromatics around an inclusion and a crac1 at a "imaterial interface.


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!i"ure 2 Isochro$atics at the interface of a bi$aterial .ith an inclusion and a crac

&aving o"tained the isochomatics! the net stage is the analysis for stress determination. Photoelasticity! as

mentioned a"ove provides the direction of principal stress at every point and the magnitude of principal stressdifference. -y themselves! these are not sufficient for a complete 3', stress analysis. &o#ever! in most engineering

applications! maimum stresses occur at "oundaries #here one of the principal stress components is 1no#n a priori.

&ence the separation of stresses is trivial. At other locations additional data is re/uired either through another

eperiment ( o"li/ue incidence method (=)) or "y numerical means ( shear difference method (=)). $urthermore!

from the considerations of e/n. (4)! only the dar1 fringes #ere evaluated and points in "et#een #ere graphically

etrapolated. $ractional fringe order determination #ould greatly assist in this etrapolation and various schemes

have "een proposed for the same #ith the Tardy method (=) the traditional favourite.


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Advances and Applications

1% A o. ost 0i"ital Polariscope ()

A typical schematic of a current Polariscope is sho#n in fig. 4. 0hile the optical elements are essentially the same!

changes in the illumination and imaging systems have "een /uite novel and interesting. 2urrent light sources that

have found favour for their versatility are the


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!i"ure 3% Isochro$atics usin" "reen and oran"e 405s respectivel

$urthermore! the


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(a)

(b)

!i"ure 6 0i"ital 0na$ic Photoelasticit usin" (a) a 40 (b) a aser diode

*n the a"ove eamples the light sources emit in the visi"le region. This is the norm for traditional photoelasticity.&o#ever in the microelectronics industry the material commonly used is silicon #hich is opa/ue to visi"le radiation

"ut "irefringent in the near infra'red. *n this case an infra'red


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!i"ure 6(c) Infra-red 0i"ital 0na$ic Photoelasticit

*n all these eamples! each frame had to "e individually recorded at the preset time delay follo#ing impact. 0hile

this #ould "e accepta"le for eperiments #hich are repeata"le! in other eamples such as crac1 propagation studiesthis approach #ould not "e suita"le. To overcome this deficiency! a


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(a)

(b)

!i"ure 7%8 (a) #che$atic of 40 based ran9 #chardin #ste$

(b) Isochro$atic due to i$pact of a si$pl supported bea$

2% I$a"e Processin" in Photoelasticit


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The current trend of digital imaging of photoelastic fringe patterns also augurs #ell for image processing to

delineate the re/uired information from the fringe patterns. The three "asic image processing techni/ues as applied

to fringe patterns in eperimental mechanics ' fractional fringe method! $ast $ourier Transform method and the

Phase Shift Method! have also "een applied to photoelastic fringes. &o#ever! unli1e other interferomteric methods

#here! in general a"solute fringe orders are not necessary as long as the fringe sign is availa"le! in photoelasticity!the a"solute fringe order and the fringe sign are essential. 7f the three methods the phase'shift method has the most

potential particularly in respect of fringe sign determination. &o#ever! the starting fringe order has still to "eassigned manually. The advent of colour image processing can possi"ly overcome this pro"lem as only the +ero

order fringe is "lac1 and should "e readily identifia"le! if present.

The phase shift method as applied to photoelasticity is not as simple as it appears. The principle is "ased on the

Tardy method. 0hereas the traditional Tardy method #as applied for single point determination ' since only dar1fringes #ere "eing analy+ed! digital Tardy method can ma1e use of all the gray levels present. &o#ever! for the

Tardy method to "e applied! the points "eing analy+ed should fall on the isoclinc corresponding to the currentpolari+ation ais of the polariser. The isoclinics are not necessarily straight lines and identifying the corresponding

points for use can "e /uite cum"ersome. Solutions to this are availa"le "y recording more than the re/uired num"er

of images compared to the traditional phase'shift methods (4). &o#ever! for lines of symmetry (6)! the method

can "e readily applied in the traditional sense. Phase shifting is achieved "y rotating the analy+er through e/ui '

angles ! noting that the fringe pattern is repeated every = degree rotation of the analy+er. $igure sho#s the

isochromatics in a tensile plate #ith a hole and the corresponding fringe order distri"ution along the hori+ontal line

of symmetry. Note that the hole is rightly identified.

!i"ure 7% Phase shiftin" in Photoelasticit

ecently! a novel phase un#rapping algorithm (8) has "een proposed and eperimentally verified. The method is

"ased on modulation ordering and relies on the intensity modulation in the piels on the "oundary of the phase

un#rapped areas. -oth the discrete phase distri"ution and the intensity modulation are calculated and a preliminary"inary control mas1 is set'up "y analy+ing the histograms of the intensity modulation. The "inary mas1 is used to

roughly identify valid and invalid areas and control the limits of the su"se/uent phase un#rapping and phase

interpolation operations. The path of the phase un#rapping is determined on the ordering result of the intensity

modulation ma1ing the algorithm very ro"ust. $igure = displays the results at various stages in the process. The five

frame algorithm for phase shifting is adopted (fig. =(a))! from #hich the #rapped phase is determined (fig = (")).having set'up the "inary mas1 the phase un#rapping process is initiated. $ig. =(c) sho#s an intermediate stage in the

un#rapping process. Note that the phase un#rapping process successfully circumvents the hole. the final gray scale

map is sho#n in fig. = (d).


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!i"ure A robust phase un.rappin" al"orith$

*% Polari$etric !iber ptic #train #ensors (P!##) (18)

esearch and development in fi"er optic sensors #ith applications amongst others as continuos monitoring system

for advanced materials and structures! has "een gro#ing tremendously in past fe# years. The sensors can "e "roadly

classed into three categories ' intensity sensors! interferometric sensors and polarimetric sensors. The intensitysensors rely on changes in transmitted intensity due to eternal pertur"ations to measure the desired /uantities.

0hile "eing /uite rugged! they can in some cases "e /uite unrelia"le. The micro '"end sensor is one of the sensors

that fall in this category. *nterferometric sensors have very high sensitivity since they are "ased on interference

"et#een light traversing a reference fi"er and that going through the test piece. The high sensitivity implies carefuleperimentation and sometimes may not "e suita"le for engineering applications. The Polarimetric sensors fall in

"et#een these t#o etremes.


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(a)

(b)

!i"ure (a) #che$atic of Polari$etric !iber ptic #train #ensor

(b) Response correspondin" to different debond len"ths%

changes the input polari+ation "ased on the eternal loading. A standard Polariscope setting can then "e used to

analy+e the output intensity. The small si+e of the fi"er implies that the stress at a single point is "eing measured.

The length of the fi"er #hich is under stress corresponds to the thic1ness. Thus unli1e conventional photoelasticity!

these sensors measure point#ise stresses averaged over the length of the fi"er. *n a general situation the result #ould

"e /uite meaninglessD ho#ever in the contet of damage detection they could prove informative. ,amage in

composite is caused through various mechanisms! such as fi"er'matri de"onding! delamination and fi"er "rea1age.

Each of these mechanisms involves transfer of stresses from the damaged area to other areas resulting in a change in

load "earing contri"ution from the undamaged sections. An optical fi"er located in any of these layers #ould alsogive a different response as compared to the undamaged laminate. This #ould affect the state of polari+ation at the

eit #hich is "eing monitored. 0hen the damage reaches critical proportion a threshold response #ould "e received

re/uiring the component or part to "e ta1en out of service for repairs or replacement. Thus a continuous monitoring

system results.


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3% Photoelasticit in Rapid Prototpin"

apid prototyping using stereolithography is a fairly ne# process of generating three dimensional prototypes from a

li/uid polymer #ithout the use of traditional tools and %or molding techni/ues. The process is to firstly create the

three'dimensional model in the computer. Each layer of this three dimensional model is then #ritten using a laser

"eam onto a li/uid photopolymer. Each layer can "e any#here from .8 mm to mm. The laser "eam polymeri+es

the resin and the uneposed part is removed prior to the eposure of the net layer. A resin prototype of thecomputer model is thus generated. Since the resin normally used in this process is epoy! it #ould "e "ut natural to

evaluate the stress! "oth residual and load induced! using the photoelastic method. This area is still in its infancy#ith the choice of resin "eing one of the topics "eing investigated. Nevertheless! the potential for this eists and has

"een demonstrated.

6% onclusions

*n this paper! some developments in photoelasticity and its applications have "een highlighted. The method has seen

some revival in the past fe# years #ith digital imaging and image processing and ne# light sources "ecoming

readily availa"le. Also ne# application areas such as real time strain sensing and residual stress measurement in

sterolithographic manufactured prototypes have emerged.

Recent Advances in Photoelastic Applications

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