ASTM D4093-95
(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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Designation: D 4093 – 95 An American National Standard
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 D 4093; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
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 5 c/v, is independent of the orientation of the
plane of vibration of light. Transparent materials, when strained, become optically anisotropic and the
index of refraction becomes directional. The change in index of refraction is related to strains. If n
o
is the refractive index of unstrained material, the three principal indices of refraction, n , become linear
i
functions of strain:
n − n 5( A e
i o ij j
Using photoelastic techniques (initially developed to measure stresses in transparent models) strains
in plastics can be assessed. In isotropic materials, two material constants, A and B, are sufficient to
describe their optomechanical behavior:
A 5 A when i 5 j, and
ij
A 5 B when i � j.
ij
When light propagates through a region (where principal strains e and e are contained in the plane
1 2
perpendicular to the direction of light propagation (see Fig. 1), the incoming vibration splits into two
waves vibrating in planes of e and e . The difference between the indexes of refraction n 5 c/v and
1 2 1 1
n 5 c/v (or birefringence) is:
2 2
n − n 5 (A − B)(e − e ) 5 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:
d5 (n − n )t 5 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
d5 (n − n )t 5 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 normal strains when the principal directions do not change
substantially within the light path.
1.1 This test method covers measurements of direction of
1.2 In addition to the method using a compensator described
principal strains, e and e , and the photoelastic retardation, d,
1 2
in this test method, other methods are in use, such as the
using a compensator, for the purpose of analyzing strains in
goniometric method (using rotation of the analyzer) mostly
transparent or translucent plastic materials. The test method
applied for measuring small retardation, and expressing it as a
can be used to determine the difference of principal strains or
fraction of a wavelength. Nonvisual methods employing pho-
This test method is under the jurisdiction of ASTM Committee D-20 on Plastics toelectric conversion and eliminating the human judgement
and is the direct responsibility of Subcommittee D20.10 on Mechanical Properties.
factor are also possible.
Current edition approved Oct. 10, 1995. Published December 1995. Originally
1.3 Test data obtained by this test method is relevant and
published as D 4093 – 82. Last previous edition D 4093 – 93.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
D 4093
FIG. 1 Propagation of Light to a Strained Transparent Material
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. Birefringence can also result from optical anisotropy
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)
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
D 618 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.
D 638 Test Method for Tensile Properties of Plastics
C 5 ~n 2 n !/~s 2s ! (2)
D 882 Test Methods for Tensile Properties of Thin Plastic
1 2 1 2
Sheeting
4. Summary of Test Method
D 4000 Classification System for Specifying Plastic Mate-
3 4.1 To analyze strains photoelastically, two quantities are
rials
measured: (a) the directions of principal strains and (b) the
E 691 Practice for Conducting an Interlaboratory Study to
4 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:
rotation of polarizers follows until light intensity becomes zero
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.
the setup is changed, introducing additional filters. A calibrated
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.
tion in the calibrated compensator is then equal and opposite in
3.2 Definitions of Terms Specific to This Standard:
sign to the retardation in the investigated specimen (see Fig. 4).
3.2.1 birefringence—retardation per unit thickness, d/t.
3.2.2 retardation, d—distance (nm) between two wave
5. Significance and Use
fronts resulting from passage of light through a birefringent
5.1 The observation and measurement of strains in transpar-
material. (Also called “relative retardations.”)
ent or translucent materials is extensively used in various
3.2.3 strain, e-strain (or deformation per unit length)—
modeling techniques of experimental stress analysis.
could be permanent, plastic strain introduced in manufacturing
5.2 Internal strains induced in manufacturing processes such
as casting, molding, welding, extrusion, and polymer stretching
can be assessed and part exhibiting excessive strains identified.
Annual Book of ASTM Standards, Vol 08.01.
Such measurements can lead to elimination of defective parts,
Annual Book of ASTM Standards, Vol 08.02.
Annual Book of ASTM Standards, Vol 14.02. process improvement, control of annealing operation, etc.
D 4093
FIG. 2 Transmission Set-up of Polariscope
FIG. 3 Reflection Set-up of Polariscope
5.3 When testing for physical properties, polariscopic ex- 6. Apparatus
amination of specimens is required, to eliminate those speci-
6.1 The apparatus used to measure strains is shown sche-
mens exhibiting abnormal internal strain level (or defects). For
matically in Fig. 4. It consists of the following items:
example: Test Methods D 638 (Note 8) and D 882 (Note 11)
6.1.1 Light Source:
recommend a polariscopic examination.
6.1.1.1 Transmitted-Light Set-Up—An incandescent lamp
5.4 The birefringence of oriented polymers can be related to
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
modifications that take precedence when adhering to the
ensure that the specimen temperature will not change more
specification. Therefore, it is advisable to refer to that material
than 2°C during the test. The incandescent lamp must be
specification before using this test method. Table 1 of Classi-
selected to provide a color temperature no lower than 3150 K.
fication System D 4000 lists the ASTM materials standards that
There should be no visible nonuniformity, dark or bright spots
currently exist.
D 4093
FIG. 4 Apparatus
FIG. 5 Direction Measuring Set-up
on the diffuser surface, when no specimen is inserted in the required in the procedure described below (see 9.2):
apparatus. 6.1.3.1 The retardation of each quarter-wave plate shall be
6.1.1.2 Reflection-Light Source—For the reflection set-up 142 6 15 nm, uniform throughout its transmission area. The
an incandescent, reflector-equipped projection lamp is re- difference in retardation between the two quarter-wave plates
quired. The lamp shall be equipped with proper lenses to should not exceed 65 nm.
ensure uniform illumination of the investigated object. At a 6.1.3.2 The quarter-wave plates will be indexed, to permit
distance of 2 ft (610 mm) from the lamp an area of 1 ft (0.093 their insertion in the field of the apparatus with their axes at 45°
m ) should be illuminated, with no visible dark or bright spots. to the polarizers direction. The two quarter-wave plates shall
The lamp power should be at least 150 W. have their axes crossed (that is, their optical axes perpendicular
6.1.2 Polarizer—The polarizing element shall be kept to each other), thus insuring that the field remains at maximum
clean. The ratio of the transmittance of polarizers with their darkness when both quarter-wave plates are inserted (see Fig.
axes parallel, to the transmittance of the polarizers with their 5).
axes perpendicular to each other (or in crossed position), 6.1.4 Compensator—The compensator is the essential
should not be less than 500. A glass-laminated construction of means of measuring retardation. The following types of com-
polarizers is recommended. The polarizers must be mechani- pensators can be used:
cally or electrically coupled to insure their mutually perpen- 6.1.4.1 Linear Compensator —In the linear compensator
dicular setting while rotated together to measure directions. A the retardation in the compensator is linearly variable along its
graduated scale must be incorporated to indicate the common
rotation of polarizers to a fixed reference mark.
6.1.3 Quarter-Wave Plates—Two quarter-wave plates are Also known as “Babinet” compensator.
D 4093
length. A graduated scale shall be attached to the compensator 8.1.1.2 Verify that the quarter-wave plates are properly
body in such a manner that slippage cannot occur. The crossed. A small deviation of one quarter-wave plate from its
calibration characteristic of the compensator shall include the “indexed” position will produce an increase in the light
position along its length (as indicated by the scale) of the line intensity transmitted.
where the retardation is zero and the number of divisions d per 8.1.2 Verification of the Compensator—:
unit retardation (usually one wavelength). (The retardation per 8.1.2.1 Examine the compensator in the polariscope and
division is D5l/d.) The scale density shall be sufficient to verify that its d5 0 point coincides with the calibration
provide clear visibility for observing 1 % of the useful range of reported.
the compensator. 8.1.2.2 Using monochromatic light (filter), verify that the
6.1.4.2 Uniform Field Compensator —The uniform field spacing of interference fringes, D, coincides with the calibra-
compensator is usually constructed from two optical wedges tion report. If l is the wavelength of monochromatic light used,
moved by means of a lead screw, the amount of relative motion it should be verified that d 5l/D.
being linearly related to the total thickness and the retardation.
9. Procedure
The lead screw motion shall be controlled by a dial drum or
9.1 Measuring Direction of Principal Strains:
counter. Calibration of this compensator shall include the
9.1.1 Insert the specimen between the polarizers and align a
position, as indicated by the drum or counter, where the
characteristic reference direction of the specimen (for example:
retardation is zero and the number of division of drum or
edge, axis of symmetry, base) with the reference of the
counter d per unit of retardation. (The retardation per division
instrument.
is D5l/d.)
9.1.2 Set the polariscope in the direction measuring set-up.
6.1.5 Filter—Monochromatic light is required to perform
The quarter-wave plates must be removed or their axes aligned
various operations in photoelasticity and some operations
with the polarizers (see Fig. 5).
cannot be successfully accomplished using white light. In those
9.1.3 Observe the light intensity at the point (s) (or the
instances a monochromatic light can be obtained introducing
region) where measuring is to be performed. Rotate polarizers
within the light path, a filter transmitting only light of the
(synchronized together) until a minimum of light intensity
desired wave length. To best correlate with observation in
emerges and the point (s) (or the region) appear dark or black.
white light, a narrow band-pass filter with peak transmittance
9.1.4 Read on the dial the angle indicating the directions of
at 570 6 6 nm and a maximum transmitted band-width (at
the polarizer axes which are also the direction of principal
half-peak point) of 10 nm should be used.
strains at the point with respect to the reference direction.
7. Test Specimen
9.1.5 In polarizing microscopes the polarizer and analyzer
remain fixed while the specimen stage rotates. The polarizer in
7.1 Sheet, film,
...
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