1、Designation: D4093 95 (Reapproved 2010)Standard Test Method forPhotoelastic Measurements of Birefringence and ResidualStrains in Transparent or Translucent Plastic Materials1This standard is issued under the fixed designation D4093; the number immediately following the designation indicates the year
2、 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 () indicates an editorial change since the last revision or reapproval.INTRODUCTIONLight propagates in transparent materials at a speed, v,
3、 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 anisotropic and theindex of refraction becomes directional. The c
4、hange 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= ( AijjUsing photoelastic techniques (initially developed to measure stresses in transparent models) strainsi
5、n 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 principal strains 1and 2are contained in the planeperpendicular to the d
6、irection of light propagation (see Fig. 1), the incoming vibration splits into twowaves vibrating in planes of 1and 2. The difference between the indexes of refraction n1= c/v1andn2= c/v2(or birefringence) is:n1 n2=(A B)(1 1)=k(1 2)where k is a material property called the strain-optical constant. A
7、s 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(1 2)where t is the thickness of material crossed by the light. A similar equation, relating d to thedifference of
8、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, 1and 2(or stresses s1and s2), and (b) the retardation, d, used to determine the magnitudeof strains. A complete theory of
9、photoelastic effect can be found in the abundant literature on thesubject (an extensive bibliography is provided in Appendix X2).1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.1. Scope1.1 This test method covers measurements of dire
10、ctionofprincipal strains, 1and 2, and 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 w
11、hen theprincipal directions do not change substantially within the lightpath.1.2 In addition to the method using a compensator describedin this test method, other methods are in use, such as thegoniometric method (using rotation of the analyzer) mostlyapplied for measuring small retardation, and exp
12、ressing 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 relevant andappropriate for use in engineering design.1.4 The values stated in either SI un
13、its 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 systems may result in nonconformance with the standard.1.5 This standard does not purport
14、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 of regulatory limitations prior to use.NOTE 1There is no known ISO equivalent to this tes
15、t method.2. Referenced Documents2.1 ASTM Standards:2D618 Practice for Conditioning Plastics for TestingD638 Test Method for Tensile Properties of PlasticsD882 Test Method for Tensile Properties of Thin PlasticSheetingD4000 Classification System for Specifying Plastic Materi-alsE691 Practice for Cond
16、ucting 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 materials.3.1.2 polarizerpolarizing element transmitting light vi-brating in one plane only.3.1.3 quarte
17、r-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 unit thickness, d/t.3.2.2 retardation, ddistance (nm) between two wavefronts resulting from passage
18、 of light through a birefringentmaterial. (Also called “relative retardations.”)3.2.3 strain, -strain (or deformation per unit length)could be permanent, plastic strain introduced in manufacturingprocess, or elastic strain related to the existing state of stress.Both types of strains will produce st
19、rain-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 of index of refraction (dimensionless).1This test method is under the jurisdiction ofASTM Committe
20、e D20 on Plasticsand is the direct responsibility of Subcommittee D20.10 on Mechanical Properties.Current edition approved Nov. 1, 2010. Published March 2011. Originallyapproved in 1982. Last previous edition approved in 2005 as D4093 - 95 (2005)1. DOI: 10.1520/D4093-95R10.2For referenced ASTM stand
21、ards, visit the ASTM website, www.astm.org, orcontact ASTM Customer 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 MaterialD4093 95 (2010)2k 5 n12 n
22、2!/122!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 strains photoelastically, two quantities aremeas
23、ured: (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. 3). A synchronousrotation of polarizers follows
24、 until light intensity becomes zeroat the observed location. The axes of the polarizers are thenparallel to direction of strains, revealing these directions.4.3 To suppress the directional sensitivity of the apparatus,the setup is changed, introducing additional filters.Acalibratedcompensator is int
25、roduced 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. 4).5. Significance and Use5.1 The observation and measurement of str
26、ains 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, and polymer stretchingcan be assessed and part exhibiting excessive str
27、ains 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 eliminate those speci-mens exhibiting abnormal internal strain level
28、(or defects). Forexample: Test Methods D638 (Note 8) and D882 (Note 11)recommend a polariscopic examination.5.4 The birefringence of oriented polymers can be related toorientation, shrinkage, etc. The measurements of birefringenceaid in characterization of these polymers.5.5 For many materials, ther
29、e 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 materialspecification before using this test method. Table 1 of Classi-fication System D4000 li
30、sts theASTM materials standards thatcurrently exist.6. Apparatus6.1 The apparatus used to measure strains is shown sche-matically 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 d
31、iffusershould provide a uniformly diffused light. To ensure adequatebrightness, minimum illumination required is 0.3 W/in.2(0.0465 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 t
32、o provide a color temperature no lower than 3150 K.There should be no visible nonuniformity, dark or bright spotson the diffuser 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-qui
33、red. The lamp shall be equipped with proper lenses toFIG. 2 Transmission Set-up of PolariscopeD4093 95 (2010)3ensure uniform illumination of the investigated object. At a distance of 2 ft (610 mm) from the lamp an area of 1 ft2(0.093FIG. 3 Reflection Set-up of PolariscopeFIG. 4 ApparatusFIG. 5 Direc
34、tion Measuring Set-upD4093 95 (2010)4m2) 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 of the pol
35、arizers 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 together to
36、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 be142 6 15
37、 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. The two qua
38、rter-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 retardation. The
39、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 characteris
40、tic 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 toprovide c
41、lear 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 the reta
42、rdation.The lead screw motion shall be controlled by a dial drum orcounter. Calibration of this compensator shall include theposition, as indicated by the drum or counter, where theretardation is zero and the number of division of drum orcounter d per unit of retardation. (The retardation per divisi
43、onis 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 isneeded. The offset retarder must be calibrated and positionedalong the axes of the compensator, between the
44、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 thoseinstances a monochromatic light can be obtained introducingwithin the light path, a filter transmitting
45、 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 (athalf-peak point) of 10 nm should be used.7. Test Specimen7.1 Sheet, film, or more generally, a constant-thic
46、kness 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 paint.5Alternatively, it is possible to place theexamined sheet specimen against a clean metal surface (pref-e
47、rably 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 containing a liquid selected to exhibitapproximately the same index of refraction as the tested item.This technique
48、is commonly used to examine three-dimensional shapes.7.3 If conditioning is required, Procedure A of PracticeD618 shall be used.8. Calibration and Standardization8.1 A periodic verification (every 6 months) is required toensure that the apparatus is properly calibrated. The followingpoints require v
49、erification: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-wave plate from its“indexed” position will produce an increase in the lightintensity transmitted.8.1.2 Verification of the Compensator:8.1.2.1 Examine the compensator in the polariscope andverify that its d = 0 point coincide
