ASTM D4093-95(2001)e1
(Test Method)Standard Test Method for Photoelastic Measurements of Birefringence and Residual Strains in Transparent or Translucent Plastic Materials
Standard Test Method for Photoelastic Measurements of Birefringence and Residual Strains in Transparent or Translucent Plastic Materials
SCOPE
1.1 This test method covers measurements of direction of principal strains, E 1 and E2 , and the photoelastic retardation, [delta], using a compensator, for the purpose of analyzing strains in transparent or translucent plastic materials. The test method can be used to determine the difference of principal strains or normal strains when the principal directions do not change substantially within the light path.
1.2 In addition to the method using a compensator described in this test method, other methods are in use, such as the goniometric method (using rotation of the analyzer) mostly applied for measuring small retardation, and expressing it as a fraction of a wavelength. Nonvisual methods employing photoelectric conversion and eliminating the human judgement factor are also possible.
1.3 Test data obtained by this test method is relevant and appropriate for use in engineering design.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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e1
Designation: D 4093 – 95 (Reapproved 2001)
Standard Test Method for
Photoelastic Measurements of Birefringence and Residual
Strains in Transparent or Translucent Plastic Materials
This standard is issued under the fixed designation D4093; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
e NOTE—Symbol in X3.1 was changed editorially. Also, certain equations were re-formatted throughout the standard in
December 2001.
INTRODUCTION
Light propagates in transparent materials at a speed, v, that is lower than its speed in vacuum, c. In
isotropic unstrained materials the index of refraction, n = c/v, is independent of the orientation of the
planeofvibrationoflight.Transparentmaterials,whenstrained,becomeopticallyanisotropicandthe
index of refraction becomes directional. The change in index of refraction is related to strains. If n
o
istherefractiveindexofunstrainedmaterial,thethreeprincipalindicesofrefraction, n,becomelinear
i
functions of strain:
n − n = ( A e
i o ij j
Usingphotoelastictechniques(initiallydevelopedtomeasurestressesintransparentmodels)strains
in plastics can be assessed. In isotropic materials, two material constants, A and B, are sufficient to
describe their optomechanical behavior:
A = A when i = j, and
ij
A = B when i fi j.
ij
Whenlightpropagatesthrougharegion(whereprincipalstrains e and e arecontainedintheplane
1 2
perpendicular to the direction of light propagation (see Fig. 1), the incoming vibration splits into two
wavesvibratinginplanesof e and e .Thedifferencebetweentheindexesofrefraction n = c/v and
1 2 1 1
n = c/v (or birefringence) is:
2 2
n − n =(A − B)(e − e )= k(e − e )
1 2 1 1 1 2
where k is a material property called the strain-optical constant. As a result of their velocity
difference, the waves vibrating along the two principal planes will emerge out of phase, their relative
distance, or retardation, d, given by:
d =(n − n )t = kt(e − e )
1 2 1 2
where t is the thickness of material crossed by the light. A similar equation, relating d to the
difference of principal stresses, s and s , can be written:
1 2
d =(n − n )t = Ct(s − s )
1 2 1 2
The objective of photoelastic investigation is to measure: (a) the azimuth, or direction of principal
strains, e and e (or stresses s and s ), and (b) the retardation, d, used to determine the magnitude
1 2 1 2
of strains. A complete theory of photoelastic effect can be found in the abundant literature on the
subject (an extensive bibliography is provided in Appendix X2).
1. Scope using a compensator, for the purpose of analyzing strains in
transparent or translucent plastic materials. The test method
1.1 This test method covers measurements of direction of
can be used to determine the difference of principal strains or
principal strains, e and e , and the photoelastic retardation, d,
1 2
normal strains when the principal directions do not change
substantially within the light path.
ThistestmethodisunderthejurisdictionofASTMCommitteeD20onPlastics
1.2 Inadditiontothemethodusingacompensatordescribed
and is the direct responsibility of Subcommittee D20.10 on Mechanical Properties.
in this test method, other methods are in use, such as the
Current edition approved Oct. 10, 1995. Published December 1995. Originally
published as D4093–82. Last previous edition D4093–93. goniometric method (using rotation of the analyzer) mostly
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 4093
FIG. 1 Propagation of Light to a Strained Transparent Material
applied for measuring small retardation, and expressing it as a 3.2.2 retardation, d—distance (nm) between two wave
fraction of a wavelength. Nonvisual methods employing pho- fronts resulting from passage of light through a birefringent
toelectric conversion and eliminating the human judgement material. (Also called “relative retardations.”)
factor are also possible. 3.2.3 strain, e-strain (or deformation per unit length)—
1.3 Test data obtained by this test method is relevant and could be permanent, plastic strain introduced in manufacturing
appropriate for use in engineering design. process, or elastic strain related to the existing state of stress.
1.4 This standard does not purport to address all of the Both types of strains will produce strain-birefringence in most
safety concerns, if any, associated with its use. It is the polymers.Birefringencecanalsoresultfromopticalanisotropy
responsibility of the user of this standard to establish appro- due to crystalline orientation.
priate safety and health practices and determine the applica- 3.2.4 strain-optical constant, k—material property, relating
bility of regulatory limitations prior to use. the strains to changes of index of refraction (dimensionless).
k 5 ~n 2 n !/~e 2e !
1 2 1 2
2. Referenced Documents
3.2.5 stress-optical constant, C—material property relating
2.1 ASTM Standards:
the stresses to change in index of refraction. C is expressed in
D618 Practice for Conditioning Plastics and Electrical
2 −12 2
m /N or Brewsters (10 m /N). C is usually temperature-
Insulating Materials for Testing
dependent.
D638 Test Method for Tensile Properties of Plastics
C 5 ~n 2 n !/~s 2s !
D882 Test Methods for Tensile Properties of Thin Plastic 1 2 1 2
Sheeting
4. Summary of Test Method
D4000 Classification System for Specifying Plastic Mate-
4.1 To analyze strains photoelastically, two quantities are
rials
measured: (a) the directions of principal strains and (b) the
E691 Practice for Conducting an Interlaboratory Study to
retardation, d, using light paths crossing the investigated
Determine the Precision of a Test Method
material in normal or angular incidence.
4.2 The investigated specimen or sample is introduced
3. Terminology
between the polarizers (see Fig. 2 and Fig. 3). A synchronous
3.1 Definitions:
rotationofpolarizersfollowsuntillightintensitybecomeszero
3.1.1 compensator—an optical device used to measure re-
at the observed location. The axes of the polarizers are then
tardation in transparent birefringent materials.
parallel to direction of strains, revealing these directions.
3.1.2 polarizer—polarizing element transmitting light vi-
4.3 To suppress the directional sensitivity of the apparatus,
brating in one plane only.
thesetupischanged,introducingadditionalfilters.Acalibrated
3.1.3 quarter-wave plate—a transparent filter providing a
compensator is introduced and its setting adjusted until light
relative retardation of ⁄4 wavelength throughout the transmit-
intensity becomes zero at the observed location. The retarda-
ting area.
tioninthecalibratedcompensatoristhenequalandoppositein
3.2 Definitions of Terms Specific to This Standard:
signtotheretardationintheinvestigatedspecimen(seeFig.4).
3.2.1 birefringence—retardation per unit thickness, d/t.
5. Significance and Use
5.1 Theobservationandmeasurementofstrainsintranspar-
Annual Book of ASTM Standards, Vol 08.01.
ent or translucent materials is extensively used in various
Annual Book of ASTM Standards, Vol 08.02.
Annual Book of ASTM Standards, Vol 14.02. modeling techniques of experimental stress analysis.
D 4093
FIG. 2 Transmission Set-up of Polariscope
FIG. 3 Reflection Set-up of Polariscope
5.2 Internalstrainsinducedinmanufacturingprocessessuch modifications that take precedence when adhering to the
ascasting,molding,welding,extrusion,andpolymerstretching specification. Therefore, it is advisable to refer to that material
canbeassessedandpartexhibitingexcessivestrainsidentified. specification before using this test method. Table 1 of Classi-
Such measurements can lead to elimination of defective parts, ficationSystemD4000liststheASTMmaterialsstandardsthat
process improvement, control of annealing operation, etc. currently exist.
5.3 When testing for physical properties, polariscopic ex-
6. Apparatus
amination of specimens is required, to eliminate those speci-
mens exhibiting abnormal internal strain level (or defects). For 6.1 The apparatus used to measure strains is shown sche-
example: Test Methods D638 (Note 8) and D882 (Note 11) matically in Fig. 4. It consists of the following items:
recommend a polariscopic examination. 6.1.1 Light Source:
5.4 Thebirefringenceoforientedpolymerscanberelatedto 6.1.1.1 Transmitted-Light Set-Up—An incandescent lamp
orientation, shrinkage, etc.The measurements of birefringence or properly spaced fluorescent tubes covered with a diffuser
aid in characterization of these polymers. should provide a uniformly diffused light. To ensure adequate
5.5 For many materials, there may be a specification that brightness, minimum illumination required is 0.3 W/in.
requires the use of this test method, but with some procedural (0.0465 W/cm ). Maximum light source power is limited to
D 4093
ensure that the specimen temperature will not change more polarizers is recommended. The polarizers must be mechani-
than 2°C during the test. The incandescent lamp must be cally or electrically coupled to insure their mutually perpen-
selected to provide a color temperature no lower than 3150 K. dicular setting while rotated together to measure directions. A
There should be no visible nonuniformity, dark or bright spots graduated scale must be incorporated to indicate the common
FIG. 4 Apparatus
FIG. 5 Direction Measuring Set-up
on the diffuser surface, when no specimen is inserted in the rotation of polarizers to a fixed reference mark.
apparatus.
6.1.3 Quarter-Wave Plates—Two quarter-wave plates are
6.1.1.2 Reflection-Light Source—For the reflection set-up required in the procedure described below (see 9.2):
an incandescent, reflector-equipped projection lamp is re-
6.1.3.1 The retardation of each quarter-wave plate shall be
quired. The lamp shall be equipped with proper lenses to
142 6 15 nm, uniform throughout its transmission area. The
ensure uniform illumination of the investigated object. At a
difference in retardation between the two quarter-wave plates
distanceof2ft(610mm)fromthelampanareaof1ft (0.093
should not exceed 65 nm.
m )shouldbeilluminated,withnovisibledarkorbrightspots.
6.1.3.2 The quarter-wave plates will be indexed, to permit
The lamp power should be at least 150 W.
theirinsertioninthefieldoftheapparatuswiththeiraxesat45°
6.1.2 Polarizer—The polarizing element shall be kept
to the polarizers direction. The two quarter-wave plates shall
clean. The ratio of the transmittance of polarizers with their
havetheiraxescrossed(thatis,theiropticalaxesperpendicular
axes parallel, to the transmittance of the polarizers with their
toeachother),thusinsuringthatthefieldremainsatmaximum
axes perpendicular to each other (or in crossed position), darkness when both quarter-wave plates are inserted (see Fig.
should not be less than 500.Aglass-laminated construction of 5).
D 4093
6.1.4 Compensator—The compensator is the essential 8. Calibration and Standardization
means of measuring retardation. The following types of com-
8.1 A periodic verification (every 6 months) is required to
pensators can be used:
ensure that the apparatus is properly calibrated. The following
6.1.4.1 Linear Compensator —In the linear compensator
points require verification:
the retardation in the compensator is linearly variable along its
8.1.1 Verification of Polariscope:
length.Agraduated scale shall be attached to the compensator
8.1.1.1 Verify that the polarizers remain in “crossed” posi-
body in such a manner that slippage cannot occur. The
tion. A small deviation of one of the polarizers produces an
calibration characteristic of the compensator shall include the
increase in the light intensity transmitted.
position along its length (as indicated by the scale) of the line
8.1.1.2 Verify that the quarter-wave plates are properly
where the retardation is zero and the number of divisions d per
crossed. A small deviation of one quarter-wave plate from its
unit retardation (usually one wavelength). (The retardation per
“indexed” position will produce an increase in the light
division is D= l/d.) The scale density shall be sufficient to
intensity transmitted.
provideclearvisibilityforobserving1%oftheusefulrangeof
8.1.2 Verification of the Compensator—:
the compensator.
8.1.2.1 Examine the compensator in the polariscope and
6.1.4.2 Uniform Field Compensator —The uniform field
verify that its d=0 point coincides with the calibration
compensator is usually constructed from two optical wedges
reported.
movedbymeansofaleadscrew,theamountofrelativemotion
8.1.2.2 Using monochromatic light (filter), verify that the
being linearly related to the total thickness and the retardation.
spacing of interference fringes, D, coincides with the calibra-
The lead screw motion shall be controlled by a dial drum or
tionreport.If listhewavelengthofmonochromaticlightused,
counter. Calibration of this compensator shall include the
it should be verified that d = l/D.
position, as indicated by the drum or counter, where the
retardation is zero and the number of division of drum or
9. Procedure
counter d per unit of retardation. (The retardation per division
9.1 Measuring Direction of Principal Strains:
isD= l/d.)
9.1.1 Insert the specimen between the polarizers and align a
6.1.5 Filter—Monochromatic light is required to perform
characteristicreferencedirectionofthespecimen(forexample:
various operations in photoelasticity and some operations
edge, axis of symmetry, base) with the reference of the
cannotbesuccessfullyaccomplishedusingwhitelight.Inthose
instrument.
instances a monochromatic light can be obtained introducing
9.1.2 Set the polariscope in the direction measuring set-up.
within the light path, a filter transmitting only light of the
Thequarter-waveplatesmustberemovedortheiraxesaligned
desired wave length. To best correlate with observation in
with the polarizers (see Fig. 5).
white light, a narrow band-pass filter with peak transmittance
9.1.3 Observe the light intensity at the point (s) (or the
at 570 6 6 nm and a maximum transmitted band-width (at
region) where measuring is to be performed. Rotate polarizers
half-peak point) of 10 nm should be used.
(synchronized together) until a minimum of light intensity
emerges and the point (s) (or the region) appear dark or black.
7. Test Specimen
9.1.4 Read on the dial the angle indicating the directions of
the polarizer axes which are also the direction of principal
7.1 Sheet,film,o
...
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