1、Designation: D 4093 95 (Reapproved 2005)e1Standard Test Method forPhotoelastic Measurements of Birefringence and ResidualStrains in Transparent or Translucent Plastic Materials1This standard is issued under the fixed designation D 4093; the number immediately following the designation indicates the
2、year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.e1NOTEEditorial changes were made throughout in July 2005.INTRO
3、DUCTIONLight propagates in transparent materials at a speed, v, that is lower than its speed in vacuum, c. Inisotropic unstrained materials the index of refraction, n = c/v, is independent of the orientation of theplane of vibration of light. Transparent materials, when strained, become optically an
4、isotropic and theindex of refraction becomes directional. The change in index of refraction is related to strains. If nois the refractive index of unstrained material, the three principal indices of refraction, ni, become linearfunctions of strain:ni no= ( AijejUsing photoelastic techniques (initial
5、ly developed to measure stresses in transparent models) strainsin plastics can be assessed. In isotropic materials, two material constants, A and B, are sufficient todescribe their optomechanical behavior:Aij= A when i = j, andAij= B when i fi j.When light propagates through a region (where principa
6、l strains e1and e2are contained in the planeperpendicular to the direction of light propagation (see Fig. 1), the incoming vibration splits into twowaves vibrating in planes of e1and e2. The difference between the indexes of refraction n1= c/v1andn2= c/v2(or birefringence) is:n1 n2=(A B)(e1 e1)=k(e1
7、 e2)where k is a material property called the strain-optical constant. As a result of their velocitydifference, the waves vibrating along the two principal planes will emerge out of phase, their relativedistance, or retardation, d, given by:d =(n1 n2)t = kt(e1 e2)where t is the thickness of material
8、 crossed by the light. A similar equation, relating d to thedifference of principal stresses, s1and s2, can be written:d =(n1 n2)t = Ct(s1 s2)The objective of photoelastic investigation is to measure: (a) the azimuth, or direction of principalstrains, e1and e2(or stresses s1and s2), and (b) the reta
9、rdation, d, used to determine the magnitudeof strains. A complete theory of photoelastic effect can be found in the abundant literature on thesubject (an extensive bibliography is provided in Appendix X2).1. Scope1.1 This test method covers measurements of direction ofprincipal strains, e1and e2, an
10、d the photoelastic retardation, d,using a compensator, for the purpose of analyzing strains intransparent or translucent plastic materials. This test methodcan be used to measure birefringence and to determine thedifference of principal strains or normal strains when theprincipal directions do not c
11、hange substantially within the lightpath.1This test method is under the jurisdiction ofASTM Committee D20 on Plasticsand is the direct responsibility of Subcommittee D20.10 on Mechanical Properties.Current edition approved July 1, 2005. Published October 2005. Originallyapproved in 1982. Last previo
12、us edition approved in 2001 as D 4093 - 95 (2001)e1.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.1.2 In addition to the method using a compensator describedin this test method, other methods are in use, such as thegoniometric meth
13、od (using rotation of the analyzer) mostlyapplied for measuring small retardation, and expressing it as afraction of a wavelength. Nonvisual methods employing spec-trophotometric measurements and eliminating the human judg-ment factor are also possible.1.3 Test data obtained by this test method is r
14、elevant andappropriate for use in engineering design.1.4 The values stated in either SI units or inch-pound unitsare to be regarded as standard. The values stated in each systemmay not be exact equivalents; therefore, each system shall beused independently of the other. Combining values from thetwo
15、systems may result in nonconformance with the standard.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility
16、 of regulatory limitations prior to use.NOTE 1There is no known ISO equivalent to this test method.2. Referenced Documents2.1 ASTM Standards:2D 618 Practice for Conditioning Plastics for TestingD 638 Test Method for Tensile Properties of PlasticsD 882 Test Methods for Tensile Properties of Thin Plas
17、ticSheetingD 4000 Classification System for Specifying Plastic Mate-rialsE 691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test Method3. Terminology3.1 Definitions:3.1.1 compensatoran optical device used to measure re-tardation in transparent birefringent material
18、s.3.1.2 polarizerpolarizing element transmitting light vi-brating in one plane only.3.1.3 quarter-wave platea transparent filter providing arelative retardation of14 wavelength throughout the transmit-ting area.3.2 Definitions of Terms Specific to This Standard:3.2.1 birefringenceretardation per uni
19、t thickness, d/t.3.2.2 retardation, ddistance (nm) between two wavefronts resulting from passage of light through a birefringentmaterial. (Also called “relative retardations.”)3.2.3 strain, e-strain (or deformation per unit length)could be permanent, plastic strain introduced in manufacturingprocess
20、, or elastic strain related to the existing state of stress.Both types of strains will produce strain-birefringence in mostpolymers. Birefringence can also result from optical anisotropydue to crystalline orientation.3.2.4 strain-optical constant, kmaterial property, relatingthe strains to changes o
21、f index of refraction (dimensionless).k 5 n12 n2!/e12e2!3.2.5 stress-optical constant, Cmaterial property relatingthe stresses to change in index of refraction. C is expressed inm2/N or Brewsters (1012m2/N). C is usually temperature-dependent.C 5 n12 n2!/s12s2!4. Summary of Test Method4.1 To analyze
22、 strains photoelastically, two quantities aremeasured: (a) the directions of principal strains and (b) theretardation, d, using light paths crossing the investigatedmaterial in normal or angular incidence.4.2 The investigated specimen or sample is introducedbetween the polarizers (see Fig. 2 and Fig
23、. 3). A synchronousrotation of polarizers follows until light intensity becomes zeroat the observed location. The axes of the polarizers are thenparallel to direction of strains, revealing these directions.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer
24、Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.FIG. 1 Propagation of Light in a Strained Transparent MaterialD 4093 95 (2005)e124.3 To suppress the directional sensitivity of the apparatus,the setup is
25、changed, introducing additional filters.Acalibratedcompensator is introduced and its setting adjusted until lightintensity becomes zero at the observed location. The retarda-tion in the calibrated compensator is then equal and opposite insign to the retardation in the investigated specimen (see Fig.
26、 4).5. Significance and Use5.1 The observation and measurement of strains in transpar-ent or translucent materials is extensively used in variousmodeling techniques of experimental stress analysis.5.2 Internal strains induced in manufacturing processes suchas casting, molding, welding, extrusion, an
27、d polymer stretchingcan be assessed and part exhibiting excessive strains identified.Such measurements can lead to elimination of defective parts,process improvement, control of annealing operation, etc.5.3 When testing for physical properties, polariscopic ex-amination of specimens is required, to
28、eliminate those speci-mens exhibiting abnormal internal strain level (or defects). Forexample: Test Methods D 638 (Note 8) and D 882 (Note 11)recommend a polariscopic examination.5.4 The birefringence of oriented polymers can be related toorientation, shrinkage, etc. The measurements of birefringenc
29、eaid in characterization of these polymers.5.5 For many materials, there may be a specification thatrequires the use of this test method, but with some proceduralmodifications that take precedence when adhering to thespecification. Therefore, it is advisable to refer to that materialFIG. 2 Transmiss
30、ion Set-up of PolariscopeFIG. 3 Reflection Set-up of PolariscopeD 4093 95 (2005)e13specification before using this test method. Table 1 of Classi-fication System D 4000 lists theASTM materials standards thatcurrently exist.6. Apparatus6.1 The apparatus used to measure strains is shown sche-matically
31、 in Fig. 4. It consists of the following items:6.1.1 Light Source:6.1.1.1 Transmitted-Light Set-UpAn incandescent lampor properly spaced fluorescent tubes covered with a diffusershould provide a uniformly diffused light. To ensure adequatebrightness, minimum illumination required is 0.3 W/in.2(0.046
32、5 W/cm2). Maximum light source power is limited toensure that the specimen temperature will not change morethan 2C during the test. The incandescent lamp must beselected to provide a color temperature no lower than 3150 K.There should be no visible nonuniformity, dark or bright spotson the diffuser
33、surface, when no specimen is inserted in theapparatus.6.1.1.2 Reflection-Light SourceFor the reflection set-upan incandescent, reflector-equipped projection lamp is re-quired. The lamp shall be equipped with proper lenses toensure uniform illumination of the investigated object. At adistance of 2 ft
34、 (610 mm) from the lamp an area of 1 ft2(0.093m2) should be illuminated, with no visible dark or bright spots.The lamp power should be at least 150 W.6.1.2 PolarizerThe polarizing element shall be keptclean. The ratio of the transmittance of polarizers with theiraxes parallel, to the transmittance o
35、f the polarizers with theiraxes perpendicular to each other (or in crossed position),should not be less than 500. A glass-laminated construction ofpolarizers is recommended. The polarizers must be mechani-cally or electrically coupled to insure their mutually perpen-dicular setting while rotated tog
36、ether to measure directions. Agraduated scale must be incorporated to indicate the commonrotation of polarizers to a fixed reference mark.6.1.3 Quarter-Wave PlatesTwo quarter-wave plates arerequired in the procedure described below (see 9.2):6.1.3.1 The retardation of each quarter-wave plate shall b
37、e142 6 15 nm, uniform throughout its transmission area. Thedifference in retardation between the two quarter-wave platesshould not exceed 65 nm.6.1.3.2 The quarter-wave plates will be indexed, to permittheir insertion in the field of the apparatus with their axes at 45to the polarizers direction. Th
38、e two quarter-wave plates shallhave their axes crossed (that is, their optical axes perpendicularto each other), thus insuring that the field remains at maximumdarkness when both quarter-wave plates are inserted (see Fig.5).6.1.4 CompensatorThe compensator is the essentialmeans of measuring retardat
39、ion. The following types of com-pensators can be used:6.1.4.1 Linear Compensator3In the linear compensatorthe retardation in the compensator is linearly variable along itslength. A graduated scale shall be attached to the compensatorbody in such a manner that slippage cannot occur. Thecalibration ch
40、aracteristic of the compensator shall include theposition along its length (as indicated by the scale) of the linewhere the retardation is zero and the number of divisions d perunit retardation (usually one wavelength). (The retardation perdivision is D=l/d.) The scale density shall be sufficient to
41、provide clear visibility for observing 1 % of the useful range ofthe compensator.6.1.4.2 Uniform Field Compensator4The uniform fieldcompensator is usually constructed from two optical wedgesmoved by means of a lead screw, the amount of relative motionbeing linearly related to the total thickness and
42、 the retardation.The lead screw motion shall be controlled by a dial drum orcounter. Calibration of this compensator shall include the3Also known as “Babinet” compensator.4Also known as “Babinet-Soleil” compensator.D 4093 95 (2005)e14position, as indicated by the drum or counter, where theretardatio
43、n is zero and the number of division of drum orcounter d per unit of retardation. (The retardation per divisionis D=l/d.)6.1.4.3 Compensators have a limited range of measuredretardation. In case the retardation in the sample exceeds therange of the compensator used, insertion of an offset retarder i
44、sneeded. The offset retarder must be calibrated and positionedalong the axes of the compensator, between the analyzer andthe sample.6.1.5 FilterMonochromatic light is required to performvarious operations in photoelasticity and some operationscannot be successfully accomplished using white light. In
45、 thoseinstances a monochromatic light can be obtained introducingwithin the light path, a filter transmitting only light of thedesired wave length. To best correlate with observation inwhite light, a narrow band-pass filter with peak transmittanceat 570 6 6 nm and a maximum transmitted band-width (a
46、thalf-peak point) of 10 nm should be used.7. Test Specimen7.1 Sheet, film, or more generally, a constant-thickness itemcan be examined using a transmission set-up. For use inreflection, a reflecting surface must be provided. This can beaccomplished by painting one side of the specimen withaluminum p
47、aint.5Alternatively, it is possible to place theexamined sheet specimen against a clean metal surface (pref-erably aluminum) or an aluminum-painted surface.7.2 Examination of complex surfaces or shapes sometimesrequires the use of an immersion liquid. The examined item isplaced inside a tank contain
48、ing a liquid selected to exhibitapproximately the same index of refraction as the tested item.This technique is commonly used to examine three-dimensional shapes.7.3 If conditioning is required, Procedure A of PracticeD 618 shall be used.5Krylon aluminum aerosol can spray paint was found satisfactor
49、y.FIG. 4 ApparatusFIG. 5 Direction Measuring Set-upD 4093 95 (2005)e158. Calibration and Standardization8.1 A periodic verification (every 6 months) is required toensure that the apparatus is properly calibrated. The followingpoints require verification:8.1.1 Verification of Polariscope:8.1.1.1 Verify that the polarizers remain in “crossed” posi-tion. A small deviation of one of the polarizers produces anincrease in the light intensity transmitted.8.1.1.2 Verify that the quarter-wave plates are properlycrossed. A small deviation of one quarter-
