1、Designation: C 770 98 (Reapproved 2008)Standard Test Method forMeasurement of Glass StressOptical Coefficient1This standard is issued under the fixed designation C 770; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of la
2、st revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers procedures for determining thestress-optical coefficient of glass, which is used in photoelastic
3、analyses. In Procedure A the optical retardation is determinedfor a glass fiber subjected to uniaxial tension. In Procedure Bthe optical retardation is determined for a beam of glass ofrectangular cross section when subjected to four-point bending.In Procedure C, the optical retardation is measured
4、for a beamof glass of rectangular cross-section when subjected to uniaxialcompression.1.2 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 a
5、nd determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C 336 Test Method for Annealing Point and Strain Point ofGlass by Fiber ElongationC 598 Test Method for Annealing Point and Strain Point ofGlass by Beam BendingE 218 Method for Radiochem
6、ical Determination ofCesium-137 in Aqueous Solutions (ChloroplatinateMethod)33. Significance and Use3.1 Stress-optical coefficients are used in the determinationof stress in glass. They are particularly useful in determiningthe magnitude of thermal residual stresses for annealing orpre-stressing (te
7、mpering) glass.As such, they can be importantin specification acceptance.4. Apparatus4.1 Stressing Equipment and Polarimeter:4.1.1 Procedure A Figs. 1 and 2 illustrate a polarimeteremploying a quarter-wave plate and rotatable analyzer,4de-scribed in Test Method F 218. The quarter-wave plate shall be
8、designed for the wavelength of the light being used. Thepolarizing axes of the polarizer and analyzer shall be set atright angles to each other with each being located at an angleof 45 with the horizontal and vertical. The analyzer, however,shall be mounted in a rotatable mount having a scale gradua
9、tedon either side from 0 to 180. The quarter-wave plate shall befixed to give maximum extinction when the polarizer andanalyzer are crossed at right angles; that is, when its polarizingaxes are set at 45 and 135 to the horizontal and vertical. Inplace of the immersion cell E, a means of supporting a
10、ndloading a glass specimen shall be provided, either in air (Fig.3(a) or in an immersion liquid (Fig. 3(b). In this arrangementthe optical elements of the polarimeter between light sourceand telescope have been reversed and a large scale graduated in2-nm divisions is employed with the rotatable anal
11、yzer I.4.1.1.1 Fig. 3 illustrates the fiber-stressing and opticalarrangement used in Procedure A. Figure 3(a) shows the fibermounted vertically, positioned, and supported by two brasscollars with swivel handles so that the kilogram weight may beapplied to load the fiber.Alight shield having entrance
12、 and exitslits surrounds the fiber providing a degree of collimation to thelight passing through the fiber and also helping to eliminatestray light.4.1.1.2 In Fig. 3(b) the fiber is stressed while immersed in aliquid which matches the refractive index of the fiber. Thisarrangement provides more sati
13、sfactory viewing of the fiber.4.1.2 Procedure B:4.1.2.1 The apparatus for the beam-bending procedure isshown in Fig. 4(a). Radiation from a white-light source passesthrough the following components and in this sequence: adiffusing plate, an adjustable aperture, a polarizer whose axis isat 45 to the
14、vertical, the glass specimen, a Babinet compen-sator, a polarizer whose axis is at 90 to that of the firstpolarizer, and a telescope of modest power.1This test method is under the jurisdiction of ASTM Committee C14 on Glassand Glass Products and is the direct responsibility of Subcommittee C14.04 on
15、Physical and Mechanical Properties.Current edition approved April 1, 2008. Published December 2008. Originallyapproved in 1973. Last previous edition approved in 2003 as C 770 98 (2003).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceas
16、tm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Withdrawn. The last approved version of this historical standard is referencedon www.astm.org.4Goranson and Adams, “Measurement of Optical Path Differences,” Journal ofFrankl
17、in Institute, Vol 216, 1933, p. 475.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.4.1.2.2 The loading scheme is shown in Fig. 4(b). Metalfixtures shall be provided to subject the specimen to four-pointbending. A support span of 115
18、 mm and a moment arm, a, of45 mm are recommended. Dimensions within 5 % of thesevalues are acceptable. Symmetrical loading is essential, andrequires careful centering of the upper loading block. The knifeedges shall be finished to approximately 5-mm radius. Loadingcan be accomplished through a yoke,
19、 which rests in a V-groovein the upper loading block, and a weight pan as shown.However, any convenient loading scheme at the center of theupper block may be used.4.1.2.3 A Babinet compensator is positioned so as to pro-duce vertical fringes (Fig. 4(c). The neutral fringe must fallnear the center of
20、 the support span. Recommended fringespacing is 1000 6 200 nm of retardation per centimeter. Inactual practice the compensator is placed very close to thespecimen inside the loading yoke.4.1.2.4 A telescope is mounted in a rotating collar equippedwith an angular scale which can be read to 0.1 by a v
21、ernier.The cross hairs in the eyepiece are used to measure the tiltangle of the neutral fringe as shown in Fig. 4(c). An 80-mmobjective lens and 103 eyepiece are adequate components forthe telescope.4.1.2.5 The adjustable aperture is set at the smallest diam-eter that permits suitable viewing. As wi
22、th the fiber apparatus,this provides some collimation and helps to eliminate straylight.4.1.3 Procedure C:4.1.3.1 Polarimeter as described in Test Method F 218.4.1.3.2 Force application frame, shown in Fig. 5 mustinclude:a) A strain-gage load cell and load cell indicator, capable ofmeasuring the for
23、ce applied within 1 % accuracy.b) Hydraulic or mechanical means of applying constantforce and maintaining the force during the measuring time.c) Swivel-mounted loading blocks, offering at least twodegrees of swivel freedom, to avoid the loading on the edge.4.2 Micrometer Caliper, for measuring speci
24、men dimen-sions to 0.0025 mm (0.0001 in.).4.3 Weights that are known to an accuracy of 61%.5. Test Specimen5.1 Procedure A:5.1.1 Select a mass of the glass to be tested that has goodoptical quality with no heavy cords or striae. By conventionallamp-working methods, draw 0.6 to 0.9 m (2 to 3 ft) of f
25、iberfrom the glass, sufficient to provide five specimens 76 to 102mm (3 to 4 in.) long with taper (variation in diameter along thelength) less than 0.025 mm (0.001 in.) and diameters in therange 0.635 mm (0.025 in.) to 0.760 mm (0.030 in.). Thedifference in mutually perpendicular diameters at any po
26、intalong the specimen length shall be less than 0.0076 mm(0.0003 in.).FIG. 1 PolarimeterFIG. 2 Orientation of Polarimeter in Standard PositionC 770 98 (2008)25.1.2 Bead both ends of each specimen by holding the endin a flame with the fiber vertical until a bead of two to threefiber diameters forms.5
27、.1.3 Anneal the specimens together so as to remove mostof the lamp-working stress (Annex A2).5.2 Procedure B:5.2.1 Select a mass of glass to be tested that has good opticalquality with no heavy cords or striae. By conventional grindingmethods, prepare a beam of rectangular cross section. Thewidth of
28、 the beam shall be within the range 20 to 30 mm (0.8to 1.2 in.), the thickness within the range 6 to 10 mm (0.25 to0.40 in.), and the length within the range 120 to 130 mm (4.75to 5.10 in.). Use a fine grind for the upper and lower surfaces(as the beam sits on the loading fixture) and polish the vie
29、wingsurfaces. The ends need not be finished and a simple saw cutwill suffice. The four major surfaces shall be flat and parallel towithin 0.050 mm (0.002 in.).5.2.2 Before final finishing, fine anneal the glass (AnnexA2) to such a degree that when the specimen is placed in thefixture unloaded there
30、is very little curvature to the portion ofthe neutral fringe that appears within the specimen.5.3 Procedure C:5.3.1 The thickness of the specimen (see Fig. 6) should beno less than 5 mm (316 in.).(a) Fiber in Air (Top View, Optical Elements)(b) Fiber ImmersedALight Source JTelescopeCOptical cell and
31、 index liquid KBrass collarsEPolarizer PPulley systemGQuarter-wave plate SShield and slitsIRotatable analyzerFIG. 3 Optical and Fiber-Stressing Polarimeter ArrangementC 770 98 (2008)3(a) Beam Stressing and Polarimeter Arrangement(b) Beam Loading Scheme (c) View of Babinet Compensator Fringe Pattern
32、Through Stressed BeamaMoment arm FYoke and weight panALight Source GBabinet compensatorBAdjustable aperature HPolarizerCPolarizer ITelescope and angular scaleDBeam LLoadELoading fixtures uTile angle of neutral fringeFIG. 4 Optical and Mechanical Details for Beam Method(a) Load Cell(b) Swivel(c) Pres
33、sure Plate(d) Specimen(e) Spherical Washer(f) Axial BearingFIG. 5 Force Application FrameC 770 98 (2008)45.3.2 The width should be no less than 10 mm (38 in.).5.3.3 The length of the specimen should be larger than 43width, but not longer than 603 thickness, to avoid bucklingfailures.5.3.4 Both ends
34、must be ground flat and parallel, within 0.1mm (0.004 in.).6. Procedure6.1 Procedure A:6.1.1 Mount the fiber specimen vertically by the beaded endin the test fixture so that approximately the midlength is in thepolariscope light beam and the fiber image is clearly in focus.6.1.2 Adjust the light shi
35、eld or aperture so that the slits arein the line of sight when viewing the fiber through thetelescope.6.1.3 Rotate the polarimeter analyzer until a bright area orline is visible, centered in the fiber cross section and parallel toits sides (the “image” of the light source that the cylindricalfiber “
36、lens” tends to form).6.1.4 Rotate the analyzer until the bright line becomesdarkest or reaches extinction. Record the retardation indicatedon the polarimeter scale either in degrees or nanometres.Repeat five times to obtain an average “zero” scale reading, r0. Normally, this will be near the scale z
37、ero for a relativelyunstressed fiber and may be in the direction of rotation whichindicates vertical tension. Since 180 of rotation covers aretardation of one full wavelength each angular degree corre-sponds to 3.03 nm, if light of a wavelength of 546 nm is used.6.1.5 Add a 10 N (2.25 lb) weight to
38、the fiber loadingsuspension of the test fixture. Rotate the analyzer in the tensiondirection (Annex A1) until extinction again occurs and recordthe retardation indicated. Repeat this rotation about five timesand obtain an average scale reading, r .6.1.6 Remove the fiber, measure, and record to the n
39、earest0.0025 mm (0.0001 in.) the average diameter, d (average ofdiameters parallel and perpendicular to light path) at theposition where retardation was measured.6.1.7 Repeat this procedure with the other fiber specimens.6.2 Procedure B:6.2.1 With the specimen removed from the polarimeter, setthe re
40、ference cross hair on and parallel to the black neutralfringe. Simultaneously set the angle to zero on the rotatablereference scale.6.2.2 Place the specimen on the metal loading support andthen position the upper loading block. After careful position-ing, engage the loading yoke and weight pan. Reco
41、rd thecombined weight of the upper block, yoke, weight pan, andcoupling fixtures which is load L1. This must be known to anaccuracy of 61%.6.2.3 Measure the angle of tilt (Annex A1) of the neutralfringe caused by the load L1and record this angle as u1.6.2.4 Add a 10 N (2.25 lb) weight. Record the to
42、tal load L2and measure and record the resulting angle u2.6.2.5 Increase the load in 10 or 20 N steps, measuring andrecording the resulting associated tilt angles, u, until a maxi-mum load of about 70 N (15.7 lb) is reached.6.2.6 Plot the tangent of the tilt angle, u, as a function ofload as shown in
43、 Fig. 7. Draw the best straight line through thedata and determine the average slope, S (Annex A3).6.3 Procedure C:6.3.1 Place the specimen in the testing frame.5Carefullycenter the specimen, placing it between the load-cell and thecompression plates. Place heavy paper or low-modulus plasticfilm 0.1
44、 to 0.5 mm thick (0.005 to 0.02 in.) between thepressure platens and the ground face of the specimen, to avoidchipping of the flat ends.6.3.2 Place the test frame between the polarizer and ana-lyzer sections of the polarimeter.5Working drawings of test frames are available from Strainoptic Technolog
45、ies,Inc., North Wales, PA.FIG. 6 Compression SpecimenFIG. 7 Typical Plot of Tilt Angle versus LoadC 770 98 (2008)56.3.3 Maintain a small pre-load (approximately 10 % of theexpected total force F) and observe the strain pattern. If anonuniform field is observed (one side gray, the other black; ora bl
46、ack fringe within the specimen), then realign the specimenor remachine the ends to avoid bending due to application offorce on one side only.6.3.4 Calculate the maximum force, Fmax, to be applied. Theforce should be sufficient to produce at least 20 MPa (2900 psi)compression stress:Fmax520A (1)where
47、:A = specimen cross-section area (mm2).Fmax= force, N.6.3.5 Measure the retardation R0at the center of thespecimen, using thickness, t, as the optical path.6.3.6 Apply the force in five equal increments and measurethe retardation, r at each increment. The retardation r can bemeasured (in nm) using a
48、 suitable compensator. The retarda-tion r can also be measured using analyzer rotation a. Theretardation is calculated from the rotation angle a, using:r5la/180 (2)where:l = wavelength of light (nm)a = analyzer rotation (degrees)The wavelength of white light shall be taken as 565 nm.6.3.7 Prepare a
49、table of test results.6.3.8 Plot the test results from 6.3.6. Establish a best-fitstraight line and determine slope, S, in nm/N.7. Calculation7.1 Procedure A Calculate the stress-optical coefficient,K, for each specimen, as follows (see Annex A4):K57.8l/180r2 r0!d 10213m/mPa! (3)where:d = average fiber diameter (cm),r = average of scale retardation readings, andr0= average of zero scale retardation readings, degrees.7.2 Procedure B Calculate the stress-optical coefficient,K, for the test beam as follows:K51.67 Ct3S 10215am/mPa! (4)whe
