1、Designation: E111 04 (Reapproved 2010)Standard Test Method forYoungs Modulus, Tangent Modulus, and Chord Modulus1This standard is issued under the fixed designation E111; the number immediately following the designation indicates the year of originaladoption or, in the case of revision, the year of
2、last revision.Anumber in parentheses indicates the year of last reapproval.Asuperscriptepsilon () 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 method2covers the determination
3、 of Youngsmodulus, tangent modulus, and chord modulus of structuralmaterials. This test method is limited to materials in which andto temperatures and stresses at which creep is negligiblecompared to the strain produced immediately upon loading andto elastic behavior.1.2 Because of experimental prob
4、lems associated with theestablishment of the origin of the stress-strain curve describedin 8.1, the determination of the initial tangent modulus (that is,the slope of the stress-strain curve at the origin) and the secantmodulus are outside the scope of this test method.1.3 The values stated in SI un
5、its are to be regarded asstandard. No other units of measurement are included in thisstandard.1.4 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 pra
6、ctices and determine the applica-bility of regulatory requirements prior to use.2. Referenced Documents2.1 ASTM Standards:3E4 Practices for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechanical TestingE8 Test Methods for Tension Testing of Metallic MaterialsE9 Test M
7、ethods of Compression Testing of Metallic Ma-terials at Room TemperatureE21 Test Methods for Elevated Temperature Tension Testsof Metallic MaterialsE83 Practice for Verification and Classification of Exten-someter SystemsE231 Method for Static Determination of Youngs Modulusof Metals at Low and Elev
8、ated Temperatures4E1012 Practice for Verification of Test Frame and SpecimenAlignment Under Tensile and Compressive Axial ForceApplication2.2 General ConsiderationsWhile certain portions of thestandards and practices listed are applicable and should bereferred to, the precision required in this test
9、 method is higherthan that required in general testing.3. Terminology3.1 Definitions:3.1.1 accuracythe degree of agreement between an ac-cepted standard value of Youngs modulus (the average ofmany observations made according to this method, preferablyby many observers) and the value determined.3.1.1
10、.1 Increased accuracy is associated with decreased biasrelative to the accepted standard value; two methods with equalbias relative to the accepted standard value have equal accu-racy even if one method is more precise than the other. See alsobias and precision.3.1.1.2 The accepted standard value is
11、 the value of Youngsmodulus for the statistical universe being sampled using thismethod. When an accepted standard value is not available,accuracy cannot be established.3.1.2 bias, statisticala constant or systematic error in testresults.3.1.2.1 Bias can exist between the accepted standard valueand
12、a test result obtained from this test method, or between twotest results obtained from this test method, for example,between operators or between laboratories.3.1.3 precisionthe degree of mutual agreement amongindividual measurements made under prescribed like condi-tions.1This test method is under
13、the jurisdiction of ASTM Committee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.04 onUniaxial Testing.Current edition approved Sept. 15, 2010. Published January 2011. Originallyapproved in 1955. Last previous edition approved in 2004 as E111 04. DOI:10.1520/E0111-04R
14、102This test method is a revision of E111 61 (1978), “Youngs Modulus at RoomTemperature” and includes appropriate requirements of E231 69 (1975), “StaticDetermination of Youngs Modulus of Metals at Low and Elevated Temperatures”to permit the eventual withdrawal of the latter method. Method E231 is u
15、nder thejurisdiction of ASTM-ASME Joint Committee on Effect of Temperature on theProperty of Metals.3For referenced ASTM standards, 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 Do
16、cument Summary page onthe ASTM website.4Withdrawn. Last approved version of this historical standard is referenced onwww.astm.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.4 Youngs modulusthe ratio of tensile or compressive
17、stress to corresponding strain below the proportional limit (seeFig. 1a).3.1.4.1 tangent modulusthe slope of the stress-straincurve at any specified stress or strain (see Fig. 1b).3.1.4.2 chord modulusthe slope of the chord drawn be-tween any two specified points on the stress-strain curve (seeFig.
18、1c).3.2 For definitions of other terms used in this test method,refer to Terminology E6.4. Summary of Test Method4.1 A uniaxial force is applied to the test specimen and theforce and strain are measured, either incrementally or continu-ously. The axial stress is determined by dividing the indicatedf
19、orce by the specimens original cross-sectional area. Theappropriate slope is then calculated from the stress-straincurve, which may be derived under conditions of eitherincreasing or decreasing forces (increasing from preload tomaximum applied force or decreasing from maximum appliedforce to preload
20、).5. Significance and Use5.1 The value of Youngs modulus is a material propertyuseful in design for calculating compliance of structuralmaterials that follow Hookes law when subjected to uniaxialloading (that is, the strain is proportional to the applied force).5.2 For materials that follow nonlinea
21、r elastic stress-strainbehavior, the value of tangent or chord modulus is useful inestimating the change in strain for a specified range in stress.5.3 Since for many materials,Youngs modulus in tension isdifferent from Youngs modulus in compression, it shall bederived from test data obtained in the
22、stress mode of interest.5.4 The accuracy and precision of apparatus, test specimens,and procedural steps should be such as to conform to thematerial being tested and to a reference standard, if available.5.5 Precise determination of Youngs modulus requires dueregard for the numerous variables that m
23、ay affect such deter-minations. These include (1) characteristics of the specimensuch as orientation of grains relative to the direction of thestress, grain size, residual stress, previous strain history,dimensions, and eccentricity; (2) testing conditions, such asalignment of the specimen, speed of
24、 testing, temperature,temperature variations, condition of test equipment, ratio oferror in applied force to the range in force values, and ratio oferror in extension measurement to the range in extensionvalues used in the determination; and (3) interpretation of data(see Section 9).FIG. 1 Stress-St
25、rain Diagrams Showing Straight Lines Corresponding to (a) Youngs Modulus, (b) Tangent Modulus, and (c) ChordModulusE111 04 (2010)25.6 When the modulus determination is made at strains inexcess of 0.25 %, correction should be made for changes incross-sectional area and gage length, by substituting th
26、einstantaneous cross section and instantaneous gage length forthe original values.5.7 Compression results may be affected by barreling (seeTest Methods E9). Strain measurements should therefore bemade in the specimen region where such effects are minimal.6. Apparatus6.1 Dead WeightsCalibrated dead w
27、eights may be used.Any cumulative errors in the dead weights or the dead weightloading system shall not exceed 0.1 %.6.2 Testing MachinesIn determining the suitability of atesting machine, the machine shall be calibrated under condi-tions approximating those under which the determination ismade. Cor
28、rections may be applied to correct for provensystematic errors.6.3 Loading FixturesGrips and other devices for obtain-ing and maintaining axial alignment are shown inTest MethodsE8 and E9. It is essential that the loading fixtures be properlydesigned and maintained. Procedures for verifying the alig
29、n-ment are described in detail in Practice E1012. The allowablebending as defined in Practice E1012 shall not exceed 5 %.6.4 ExtensometersClass B-1 or better extensometers asdescribed in Practice E83 shall be used. Corrections may beapplied for proven systematic errors in strain and are notconsidere
30、d as a change in class of the extensometer. Either anaveraging extensometer or the average of the strain measuredby at least two extensometers arranged at equal intervalsaround the cross section be used. If two extensometers are usedon other than round sections, they shall be mounted at ends ofan ax
31、is of symmetry of the section. If a force-strain recorder,strain-transfer device, or strain follower is used with theextensometer, they shall be calibrated as a unit in the samemanner in which they are used for determination of Youngsmodulus. The gage length shall be determined with an accu-racy con
32、sistent with the precision expected from the modulusdetermination and from the extensometer.NOTE 1The accuracy of the modulus determination depends on theprecision of the strain measurement. The latter can be improved byincreasing the gage length. This may, however, present problems inmaintaining sp
33、ecimen tolerances and temperature uniformity.6.5 Furnaces or Heating DevicesWhen determiningYoungs modulus at elevated temperature, the furnace orheating device used shall be capable of maintaining a uniformtemperature in the reduced section of the test specimen so thata variation of not more than 6
34、1.5C for temperatures up to andincluding 900C, and not more than 63.0C for temperaturesabove 900C, occurs. (Heating by self-resistance is not ac-cepted.) Minimize temperature variations and control changeswithin the allowable limits, since differences in thermal expan-sion between specimen and exten
35、someter parts may causesignificant errors in apparent strain. An instrumented samplerepresentative of the real test will demonstrate that the setupmeets the above capabilities.6.6 Low-Temperature Baths and Refrigeration EquipmentWhen determining Youngs modulus at low temperatures, anappropriate low-
36、temperature bath or refrigeration system isrequired to maintain the specimen at the specified temperatureduring testing. For a low-temperature bath, the lower tensionrod or adapter may pass through the bottom of an insulatedcontainer and be welded or fastened to it to prevent leakage.For temperature
37、s to about 80C, chipped dry ice may be usedto cool an organic solvent such as ethyl alcohol in thelow-temperature bath. Other organic solvents having lowersolidification temperatures, such as methylcyclohexane orisopentane, may be cooled with liquid nitrogen to temperatureslower than 80C. Liquid nit
38、rogen may be used to achieve atesting temperature of 196C. Lower testing temperaturesmay be achieved with liquid hydrogen and liquid helium, butspecial containers or cryostats are required to provide forminimum heat leakage to permit efficient use of these coolants.When liquid hydrogen is used, spec
39、ial precautions must betaken to avoid explosions of hydrogen gas and air mixtures. Ifrefrigeration equipment is used to cool the specimens with airas the cooling medium, it is desirable to have forced aircirculation to provide uniform cooling.NOTE 2At low temperatures, when using a coolant bath, imm
40、ersion-type extensometers are recommended.FIG. 2 Load-Deviation GraphE111 04 (2010)36.7 Temperature measuring, controlling, and recording in-struments shall be calibrated periodically against a secondarystandard, such as a precision potentiometer. Lead-wire errorshould be checked with the lead wires
41、 in place as they normallyare used.7. Test Specimens7.1 Selection and Preparation of SpecimensSpecial careshall be taken to obtain representative specimens which arestraight and uniform in cross section. If straightening of thematerial for the specimen is required, the resultant residualstresses sha
42、ll be removed by a subsequent stress relief heattreatment which shall be reported with the test results.7.2 DimensionsThe recommended specimen length (andfillet radius in the case of tension specimens) is greater than theminimum requirements for general-purpose specimens. Inaddition, the ratio of le
43、ngth to cross section of compressionspecimens should be such as to avoid buckling (see TestMethods E9).NOTE 3For examples of tension and compression specimens, see TestMethods E8 and E9.7.3 For tension specimens, the center lines of the gripsections and of the threads of threaded-end specimens shall
44、 beconcentric with the center line of the gage section within closetolerances in order to obtain the degree of alignment required.If pin-loaded sheet-type specimens are used, the centers of thegripping holes shall be not more than 0.005 times the width ofthe gage section from its center line. For sh
45、eet-type specimens,it may be necessary to provide small tabs or notches forattaching the extensometer.NOTE 4The effect of eccentric loading may be illustrated by calcu-lating the bending moment and stress thus added. For a standard 12.5-mmdiameter specimen, the stress increase is 1.5 % for each 0.02
46、5 mm ofeccentricity. This error increases to about 2.5 % per 0.025 mm for a 9-mmdiameter specimen and to about 3.2 % per 0.025 mm for a 6-mm diameterspecimen.7.4 The length of the reduced section of tension specimensshall exceed the gage length by at least twice the diameter ortwice the width. The l
47、ength of compression specimens shall bein accordance with Test Methods E9, and all specimens shallhave a uniform cross-sectional area throughout the gage length.NOTE 5If a general-purpose tension specimen such as those shown inTest Methods E8, having a small amount of taper in the reduced sectionis
48、used, the average cross-sectional area for the gage length should be usedin computing stress.7.5 For compression specimens, the ends shall be flat,parallel and perpendicular to the lateral surfaces as specified inTest Methods E9.7.6 This test method is intended to produce intrinsic mate-rials proper
49、ties. Therefore, the specimen needs to be free ofresidual stresses, which may require an annealing procedure atTm/3 for 30 min to relieve the stresses in the material (whereTmis the melting point of the material in K). The proceduremust be mentioned in the report section. If the intent of the testis to verify the performance of a product, the heat treatmentprocedure may be omitted. Record the condition of the materialtested, including any heat treatment, in the test report.8. Procedure8.1 For most loading systems and test spec
