1、Designation: E132 04 (Reapproved 2010)Standard Test Method forPoissons Ratio at Room Temperature1This standard is issued under the fixed designation E132; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A
2、 number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the Department of Defense.1. Scope1.1 This test method covers the determination of Poissons
3、ratio from tension tests of structural materials at room tem-perature. This test method is limited to specimens of rectan-gular section and to materials in which and stresses at whichcreep is negligible compared to the strain produced immedi-ately upon loading.1.2 The values stated in inch-pound uni
4、ts are to be regardedas standard. The values given in parentheses are mathematicalconversions to SI units that are provided for information onlyand are not considered standard.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsib
5、ility 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.2. Referenced Documents2.1 ASTM Standards:2E4 Practices for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mec
6、hanical TestingE8 Test Methods for Tension Testing of Metallic MaterialsE83 Practice for Verification and Classification of Exten-someter SystemsE111 Test Method for Youngs Modulus, Tangent Modulus,and Chord ModulusE1012 Practice for Verification of Test Frame and SpecimenAlignment Under Tensile and
7、 Compressive Axial ForceApplication3. Terminology3.1 Definitions:3.1.1 Poissons ratiothe negative of the ratio of trans-verse strain to the corresponding axial strain resulting from anaxial stress below the proportional limit of the material.3.1.2 DiscussionAbove the proportional limit, the ratio of
8、transverse strain to axial strain will depend on the averagestress and on the stress range for which it is measured and,hence, should not be regarded as Poissons ratio. If this ratio isreported, nevertheless, as a value of “Poissons ratio” forstresses beyond the proportional limit, the range of stre
9、ssshould be stated.3.1.3 DiscussionPoissons ratio will have more than onevalue if the material is not isotropic. Deviations from isotropyshould be suspected if the Poissons ratio, , determined by themethod described below differs significantly from that deter-mined when the ratio E/G of Youngs modul
10、us, E, to shearmodulus, G, is substituted in the following equation: 5 E/2G! 2 1 (1)where E and G must be measured with greater precision thanthe precision desired in the measurement of .4. Significance and Use4.1 When uniaxial force is applied to a solid, it deforms inthe direction of the applied f
11、orce, but also expands or contractslaterally depending on whether the force is tensile or compres-sive. If the solid is homogeneous and isotropic, and thematerial remains elastic under the action of the applied force,the lateral strain bears a constant relationship to the axial strain.This constant,
12、 called Poissons ratio, is an intrinsic materialproperty just like Youngs modulus and Shear modulus.4.2 Poissons ratio is used for design of structures where alldimensional changes resulting from application of force needto be taken into account, and in the application of thegeneralized theory of el
13、asticity to structural analysis.4.3 In this test method, the value of Poissons ratio isobtained from strains resulting from uniaxial stress only.5. General Considerations5.1 The accuracy of the determination of Poissons ratio isusually limited by the accuracy of the transverse strain mea-surements b
14、ecause the percentage errors in these measurementsare usually greater than in the axial strain measurements. Since1This test method is under the jurisdiction of ASTM Committee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.04 onUniaxial Testing.Current edition approved
15、 Sept. 1, 2010. Published April 2004. Originallyapproved in 1958. Last previous edition approved in 2004 as E132 04. DOI:10.1520/E0132-04R10.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volu
16、me information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.a ratio rather than an absolute quantity is measured, it is onlynecessary to know accurately the relative
17、 value of the calibra-tion factors of the extensometers.Also, in general, the values ofthe applied forces need not be accurately known. It is fre-quently expedient to make the determination of Poissons ratioconcurrently with determinations of Youngs modulus and theproportional limit.6. Apparatus6.1
18、ForcesForces shall be applied either by verified deadweights or in a testing machine that has been calibrated inaccordance with Practices E4.6.2 ExtensometersClass B-1 extensometers or better, asdescribed in Practice E83, shall be used except as otherwiseprovided in the product specifications.NOTE 1
19、If exceptions are provided in the product specification so thatextensometers of types other than those covered in Practice E83 are used,it may be necessary to apply corrections, for example, the correction forthe transverse sensitivity3of bonded resistance gages.6.2.1 It is recommended that at least
20、 two pairs of extensom-eters be usedone pair for measuring axial strain and the otherfor transverse strain, with the extensometers of each pairparallel to each other and on opposite sides of the specimen.Additional extensometers may be used to check on alignmentor to obtain better average strains in
21、 the case of unavoidablevariations in thickness. The extensometers should be placed onthe specimen with a free distance of at least one specimenwidth between any extensometer and the nearest fillet, and atleast two specimen widths between any extensometer and thenearest grip.NOTE 2Three possible arr
22、angements of extensometers, among themany that have been used, are shown in Fig. 1. Arrangement (a), Fig. 1,which requires only two pairs of extensometers, can be used if theconditions are very nearly ideal with respect to axiality of applied forceand constancy of cross-section within the length in
23、which the extensom-eters are placed. An additional pair of extensometers is used in arrange-ment (b) to provide some compensation for the effect of a uniformvariation in thickness in the axial direction. The other arrangement of threepairs of extensometers, arrangement (c), provides a check on align
24、ment.6.3 Alignment DevicesGrips and other devices for obtain-ing and maintaining axial alignment are shown in Test MethodsE8.7. Test Specimens7.1 Selection and Preparation of SpecimensSelect andprepare test specimens that are straight and uniform in thick-ness and representative of the material bein
25、g tested.7.2 DimensionsThe recommended specimen configura-tion has a tested length of at least five times the tested width,and a length between the grips of at least seven times the testedwidth. The tested width itself is at least equal to the testedthickness. The radius of the fillets of a standard
26、 rectangularspecimen is not less than the minimum width of the specimen.The width shall be constant over the entire length where theextensometers are placed and for an additional distance at eachend equal to at least this width, unless otherwise provided inthe product specifications.7.3 Stress Relie
27、fThis test method is intended to produceintrinsic materials properties. Therefore, the specimen needs tobe free of residual stresses, which may require an annealingprocedure at Tm/3 for 30 min (Tmis the melting point of thematerial in K). If the intent of the test is to verify theperformance of a pr
28、oduct, the heat treatment procedure may beomitted. Record the condition of the material tested, includingany heat treatment, in the test report.8. Procedure8.1 Measurement of SpecimensAll surfaces on the rectan-gular specimen shall be flat. Opposite surfaces across the widthand thickness shall be pa
29、rallel within 0.001 in. (0.025 mm) and0.0001 in. (0.0025 mm) respectively. Specimen thickness shallbe measured to within 0.001 in. (0.025 mm) and width shall bemeasured to within 0.0001 in. (0.0025 mm) at three locationsand an average determined.NOTE 3For thin sheet, a survey of thickness variation
30、by moresensitive devices, such as a pneumatic or electric gage, may be needed todetermine thickness with the required accuracy.8.2 AlignmentProcedures for verifying the alignment aredescribed in detail in Practice E1012. The allowable bending asdefined in Practice E1012 shall not exceed 5 %.8.3 Reco
31、rd simultaneous measurements of applied force andstrain.8.4 Speed of TestingThe speed of testing shall be lowenough to make the thermal effects of adiabatic expansion orcontraction negligible, yet high enough to make creep negli-gible. In applying forces with dead weights, avoid temporaryoverloading
32、 due to inertia of the weights.8.5 Applied ForcesThe applied forces shall correspond tostresses that are within the linear portion of the stress-straincurve, that is, less than the proportional limit. The precision ofthe value of Poissons ratio obtained will depend on thenumber of data pair of longi
33、tudinal and transverse strain taken(see Fig. 2).8.6 Strain ReadingsRead all extensometers at the sameapplied force.3Perry, C. C., and Lissner, H. R., The Strain Gage Primer, McGraw-Hill BookCo., New York, NY, 1955, pp. 141146.NOTE 1Each symbol indicates the location of a pair of extensometerson oppo
34、site sides of the specimen.FIG. 1 Three Possible Arrangements of ExtensometersE132 04 (2010)28.7 TemperatureRecord the temperature. Avoid changesin temperature during the test.9. Evaluation of Data9.1 Plot the average longitudinal strain, l, indicated by thelongitudinal extensometers and the average
35、 transverse strain,t, indicated by the transverse extensometers, against theapplied force, P, as shown in Fig. 2. Draw a straight linethrough each set of points, and determine the slopes, dl/dP,and dt/dP, of these lines. Calculate Poissons ratio as follows: 5 dt/dP!/dl/dP! (2)9.2 The errors introduc
36、ed by drawing a straight line throughthe points can be reduced by applying the method of leastsquares.4,5, 6The value of Poissons ratio thus obtained shouldcoincide with that obtained for a single large force incrementbetween stresses below the proportional limit.NOTE 4For the method of least square
37、s, random variations in the dataare considered as variations in strain. In determining the stress range(force range) for which data should be used in the calculations, it is helpfulto examine the data using the strain deviation method described in TestMethod E111. Due to possible small offsets at ze
38、ro applied force and smallvariations in establishing the load path in the specimen during the firstsmall increment of force application, the readings at zero applied forceand the first small increment of force application are typically not includedin the calculations, and the line is not constrained
39、 to pass through zero.10. Report10.1 Report the following information:10.1.1 Specimen MaterialSpecimen material, alloy, heattreatment, mill batch number, grain direction, and other rel-evant material information.10.1.2 Specimen ConfigurationSketch of the specimenconfiguration or reference to the spe
40、cimen drawing.10.1.3 Specimen DimensionsActual measured dimen-sions for the specimen.10.1.4 Test FixtureDescription of the test fixture or refer-ence to fixture drawings.10.1.5 Testing Machine and ExtensometersManufacturer,model, serial number, and force range of the testing machineand the extensome
41、ters.10.1.6 Speed of TestingTest rate and mode of control.10.1.7 TemperatureTest temperature.10.1.8 Stress-Strain DiagramStress-strain diagram show-ing both longitudinal and transverse strain with scales, speci-men number, test data, rate, and other pertinent information.10.1.9 Poissons RatioValue a
42、nd method to determine thevalue in accordance with Section 9.11. Precision and Bias11.1 Elastic properties such as Poissons ratio, shear modu-lus and Youngs modulus are not determined routinely and aregenerally not specified in materials specifications. Precisionand bias statements for this test met
43、hod are therefore notavailable.12. Keywords12.1 axial strain; longitudinal strain; Poissons ratio; stress-strain diagram; transverse strainASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this s
44、tandard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years
45、andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee
46、, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2
47、959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standa
48、rd may also be secured from the ASTM website (www.astm.org/COPYRIGHT/).4Youden, W. J., Statistical Methods for Chemicals, John Wiley and Sons, Inc.,New York, NY, Chapter 5, 1951, pp. 4049.5Natrella, M. G., “Experimental Statistics,” National Bureau of StandardsHandbook 91, U.S. Dept. of Commerce, Chapter 5.6Bowker, A. H., and Lieberman, G. J., Engineering Statistics,Prentice-Hall,Inc., Englewood Cliffs, NJ, 1959, Chapter 9.FIG. 2 Plot of Average Strains versus Applied Force forDetermination of Poissons RatioE132 04 (2010)3
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