experiment 4 theory

8/20/2019 Experiment 4 Theory

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GROUP M1 EXP: 4 IIT BOMBAY Page 1

EXPERIMENT 4

PHOTOELASTIC MEASUREMENT OF STRESS CONCENTRATION

FACTOR.

Objective: Determination of model Fringe Constant and Measurement of Stress

Concentration Factor.

APPARATUS USED:

1. Polariscope.

2. Test Specimen and clamping bolts. 3. Vernier Calliper.

THEORY:Te distribution of stresses in omogenous and isotropic material is independent of an! material

properties. Tis is te simple basis to determine te stress distribution in complicated real life

component troug a model stud!. "n te potoelasticit! te models are generall! made of

transparent materials #ic a$e birefringent properties upon loading. Tese include %po&!'

(raldite' and Columbia )ubber etc.

P!"#i$"ti%: . ( ligt #a$e tat is $ibrating in more tan one plane is referred to asunpolari*ed ligt. +igt emitted b! te sun' b! a lamp in te classroom' or b! a candle flame is

unpolari*ed ligt. "t is possible to transform unpolari*ed ligt into polari*ed ligt. Polari*ed ligt#a$es are ligt #a$es in #ic te $ibrations occur in a single plane. Te process of

transforming unpolari*ed ligt into polari*ed ligt is ,no#n as polari*ation. Te follo#ing figure

so#s a ligt #ic is plane polari*ed and propogating in te * direction . (n obser$er $ie#ingte ligt #a$e ead-on #ould see te #a$e #it its amplitude $ector restricted to a single plane'

#ic is called te plane of polarization. Tis plane is not necessaril! $ertical' as so#n in te

figure' but $ertical polari*ation is uite common. Polaroid/ sunglasses' for e&ample' emplo!$erticall! polari*ing media in bot lenses to bloc, te ori*ontall! polari*ed ligt tat is

reflected from suc ori*ontal surfaces as ig#a!s and la,es.


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Fig. 1 Plane polarized light .

&i#e'#i%(e%ce: "t is te optical propert! of a material a$ing t#o refracti$e inde& tatdepends on te polari*ation and propagation direction of ligt. Tese opticall! anisotropic

materials are said to be birefringent. Te birefringence is often uantified as te ma&imum

difference bet#een refracti$e indices e&ibited b! te material. Cr!stals #it as!mmetric cr!stal

structures are often birefringent' as #ell as plastics and composites under mecanical stress.

0en Polari*ed +igt its te loaded specimen of a birefringent material' te ligt is resol$ed

into t#o perpendicular planes #ic coincides #it te direction of te t#o principal stresses asso#n in figure 2. "n te loaded state' o#e$er' te orientation of a gi$en ligt amplitude $ector

#it respect to te principal stress a&es' and te magnitudes of te principal stresses' determine

te inde& of refraction for tat ligt #a$e.


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Fig 2. Birefringent material

)*"#te# +"ve P!"te: ( #a$eplate is an optical de$ice tat alters te polari*ation

state of a ligt #a$e tra$elling troug it.

Fig:3 uarter 0a$e Plate.


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• ( uarter-#a$e plate consists of a carefull! adusted tic,ness of a

birefringent material suc tat te ligt associated #it te larger inde& of

refraction is retarded b! 45 in pase 6a uarter #a$elengt7 #it respect to

tat associated #it te smaller inde&. Te material is cut so tat te optic

a&is is parallel to te front and bac, plates of te plate.• (n! linearl! polari*ed ligt #ic stri,es te plate #ill be di$ided into t#o

components #it different indices of refraction.

• 8ne of te useful applications of tis de$ice is to con$ert linearl! polari*ed

ligt to circularl! polari*ed ligt and $ice $ersa. Tis is done b! adusting

te plane of te incident ligt so tat it ma,es 95 angle #it te optic a&is.

• 0a$eplates are constructed out of a birefringent material 6suc as uart* or

mica7' for #ic te inde& of refraction is different for different orientations

of ligt passing troug it.

P!"#i,c-e: "t consists of a ligt source' polari*er' anal!*er and t#o uarter

#a$e plates. Tere are t#o t!pes of arrangements of te polariscope-

1. Plane Polariscope

2. Circular Polariscope.

1. P!"%e P!"#i,c-e- Te uarter #a$e plates are opticall! aligned #it a&es

of te polari*er and anal!*er. Tis arrangement is used to determine te

direction of principle stresses .

Fig. 4 Plane polariscope


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2. Ci#c*!"# P!"#i,c-e "n circular Polariscope ' a&is of te uarter #a$e

plates is at angle of 9 degrees to tat of polari*er and anal!*er. Tis

arrangement is used to measure te magnitude of te principle stresses at a

point.

Fig ! "irc#lar Polarisope

I,c!i%ic,: Te +oci of te points in te specimen along #ic te principal stresses are in te

same direction.

I,c/#0"tic,: +oci of te points along #ic te difference bet#een t#o principle stresses is

constant.

Plane Polariscope so#s bot isocromatic and isoclinic fringes but te circular polariscope

so#s onl! te isocromatic fringes.

For isocromatic lines

;1- ;2 < n=f ;

0ere '

;1 and ;2 are t#o principle stresses.

>< Fringe 8rder

f ;


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PROCEDURE:

Procedure ?sed:-

1. Ta,e te rectangular specimen 6#itout ole7 of gi$en geometr!. +oad it

graduall!. >ote te fringe order and corresponding load.6 load $alue #e canfind out b! using te gauge attaced to te instrument.7

2. +oad $alue is in Pounds. Con$ert it into > b! using te relation as follo#s:

1 Pound< @4.93=.A1B >

3. ?se te relation f ; < @;1B > and ;1 < P( 6( is cross section area of

specimen 7 for calculations.9. >o#' #e are using specimen #it one ole and loading it graduall!. >ote

do#n fringe order near point ( of te ole and corresponding load.. (t point (' te minimum principle stress is *ero' as inner surface of ole is

load free. 8nl! ma&imum principle stress is non-*ero.6 ;17 Tus' te stressconcentration factor is gi$en b!'

t < @Stress at point (B @($g. StressB< >= f ; ; a$g.

0ere'

; a$g


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Sample Load corresponding

to frst transition to

PURPLE

Isochromatic ringecolour (N=1)

Load corresponding to

second transition to

PURPLE Isochromatic

ringe colour (N=)

!RE!(mm")

Sample

1

60 lb 130 lb 33.5 *10=335

Sample

30 lb 70 lb (35.3-10.2)*10=251

Sample

#

50 lb 100 lb (42.78-

10.1)*10=326.8

SAMPLE CALCULATIONS :

CASE :1

For Plate $ith no hole

;1 < P(

P


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Tis $alue #ould be used in furter calculations for finding e&perimental SCF.

CASE 2:

For plate $ith one hole

a7 For >


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8ne ole >


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8ne ole >


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T#o oles' >


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T#o oles ' >


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LOAD =130 POUNDS=578.34N A!A=335mm2

ANAL"#$%AL S#!SS=1247N6mm" ANS"S

!SUL#=12471N6mm"

PL!E ,I- +NE -+LE

8 t= #0 9 #170(a) : #442(a)" 9 1;2(a)"#


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SRESS ISRI*UI+N ,I- +NE -+LE

LOAD=70 POUND=311.41 N A!A=251 mm&2

ANAL"#$%AL S#!SS=' *m+al ,e,,=2.366*1.24=2.935 N6mm"

ANS"S !SUL#=3#2516mm"

PL!E ,I- -REE -+LES


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SRESS ISRI*UI+N ,I- RELIE& -+LE

LOAD=50 POUND=222.44 N A!A=326.8 mm&2

ANS"S !SUL#=14#2326mm"

SRESS ISRI*UI+N ,I- RELIE& -+LE

LOAD=100 POUND=444.88 N A!A=326.8 mm&2

ANS"S !SUL#=#2;5 6mm"

CONCLUSION :


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1. Te teoretical stress concentration $alues #ere found to matc #it ans!s $alues.

2. Tere #as a small difference bet#een te teoretical and e&perimental $alues due to

errors. Te sources of error are mentioned as follo#s:-due to inerient defect in te birefringent component during manufacturing suc as

residual stresses.

-"n e&periment #e considered te load to be acting around te region of clamping but inans!s 'te load #as uniforml! distributed across te cross section.-Te birefringent propert! depends upon temperature so tere migt be $ariation in

propert! as te component #as ta,en out of te free*er and subected to room

temperature

-Tere migt be error in loading te component.- Manual errors ma! be tere in identif!ing and distinguising te fringe patterns.

-Te instrument #as a$ing a least count of 14lb #ic is ig so te measuring

instrument ma! introduce error in identif!ing te correct load.

3. (s stress is a geometric propert! and depends upon dimension of component ' ence an!

. component a$ing same dimensions but different material can be used for e&perimental

. stress determination in original component.

9. For te case of a unia&ial load ' te isocromatic fringes #ere found to be s!mmetricalabout te $ertical a&is .

Re'e#e%ce,:

1.###.!perp!sics.p!.astr.gsu.edu

2.%&perimental stress anal!sis Names # Pilips

3.0i,ipedia
http://www.hyperphysics.phy.astr.gsu.edu/http://www.hyperphysics.phy.astr.gsu.edu/

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