1、Designation: E 111 04Standard Test Method forYoungs Modulus, Tangent Modulus, and Chord Modulus1This standard is issued under the fixed designation E 111; 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 (e) 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 of Youngsm
3、odulus, 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 problems associ
4、ated 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 This standard does not purport to add
5、ress 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 requirements prior to use.2. Referenced Documents2.1 ASTM Standards:3E 4 Practice
6、s for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechanical Test-ingE8 Test Methods for Tension Testing of Metallic MaterialsE9 Test Methods of Compression Testing of Metallic Ma-terials at Room TemperatureE21 Test Methods for Elevated Temperature Tension Testsof Met
7、allic MaterialsE83 Practice for Verification and Classification of Exten-sometersE 231 Method for Static Determination of Youngs Modu-lus of Metals at Low and Elevated TemperaturesE 1012 Practice for Verification of Specimen AlignmentUnder Tensile Loading2.2 General ConsiderationsWhile certain porti
8、ons of thestandards and practices listed are applicable and should bereferred to, the precision required in this test 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 a
9、verage ofmany observations made according to this method, preferablyby many observers) and the value determined.3.1.1.1 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
10、 even if one method is more precise than the other. See alsobias and precision.3.1.1.2 The accepted standard value is 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, st
11、atisticala constant or systematic error in testresults.3.1.2.1 Bias can exist between the accepted standard valueand 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 degre
12、e of mutual agreement amongindividual measurements made under prescribed like condi-tions.3.1.4 Youngs modulusthe ratio of tensile or compressivestress to corresponding strain below the proportional limit (seeFig. 1a).3.1.4.1 tangent modulusthe slope of the stress-straincurve at any specified stress
13、 or strain (see Fig. 1b).1This 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 June 1, 2004. Published July 2004. Originally approvedin 1955. Last previous edition app
14、roved in 1997 as E 111 97.2This test method is a revision of E 111 61 (1978), “Youngs Modulus at RoomTemperature” and includes appropriate requirements of E 231 69 (1975), “StaticDetermination of Youngs Modulus of Metals at Low and Elevated Temperatures”to permit the eventual withdrawal of the latte
15、r method. Method E 231 is under 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
16、, refer to the standards Document Summary page onthe ASTM website.1Copyright. (C) ASTM International, 100 Barr Harbour Dr. PO box C-700 West Conshohocken, Pennsylvania 19428-2959, United StatesCopyright by ASTM Intl (all rights reserved); Thu Mar 4 22:16:26 EST 2010Downloaded/printed byGuo Dehua (CN
17、IS) pursuant to License Agreement. No further reproductions authorized.3.1.4.2 chord modulusthe slope of the chord drawn be-tween any two specified points on the stress-strain curve (seeFig. 1c).3.2 For definitions of other terms used in this test method,refer to Terminology E6.4. Summary of Test Me
18、thod4.1 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 indicatedforce by the specimens original cross-sectional area. Theappropriate slope is then calculated from the stress-
19、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).5. Significance and Use5.1 The value of Youngs modulus is a material propertyuseful in design for calculati
20、ng 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 nonlinear elastic stress-strainbehavior, the value of tangent or chord modulus is useful inestimating the change in s
21、train 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 stress mode of interest.5.4 The accuracy and precision of apparatus, test specimens,and procedural steps shou
22、ld 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 may affect such deter-minations. These include (1) characteristics of the specimensuch as orientation of grain
23、s 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 testing, temperature,temperature variations, condition of test equipment, ratio oferror in applied force to
24、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-Strain Diagrams Showing Straight Lines Corresponding to (a) Youngs Modulus, (b) Tangent Modulus, and (c) ChordM
25、odulusE111042Copyright by ASTM Intl (all rights reserved); Thu Mar 4 22:16:26 EST 2010Downloaded/printed byGuo Dehua (CNIS) pursuant to License Agreement. No further reproductions authorized.5.6 When the modulus determination is made at strains inexcess of 0.25 %, correction should be made for chang
26、es incross-sectional area and gage length, by substituting theinstantaneous 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 effe
27、cts are minimal.6. Apparatus6.1 Dead WeightsCalibrated dead weights 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
28、approximating those under which the determination ismade. Corrections 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 MethodsE8andE9. It is essential that the loading fixtures be properl
29、ydesigned and maintained. Procedures for verifying the align-ment are described in detail in Practice E 1012. The allowablebending as defined in Practice E 1012 shall not exceed 5 %.6.4 ExtensometersClass B-1 or better extensometers asdescribed in Practice E83shall be used. Corrections may beapplied
30、 for proven systematic errors in strain and are notconsidered 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 othe
31、r than round sections, they shall be mounted at ends ofan axis 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 Youngsmodulu
32、s. The gage length shall be determined with an accu-racy consistent 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
33、length. This may, however, present problems inmaintaining specimen 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 sectio
34、n of the test specimen so thata variation of not more than 61.5C 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
35、differences in thermal expan-sion between specimen and extensometer 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 determ
36、ining Youngs modulus at low temperatures, anappropriate low-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
37、 welded or fastened to it to prevent leakage.For temperatures 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 wi
38、th liquid nitrogen to temperatureslower than 80C. Liquid nitrogen 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 effici
39、ent use of these coolants.When liquid hydrogen is used, special 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 cooli
40、ng.NOTE 2At low temperatures, when using a coolant bath, immersion-type extensometers are recommended.FIG. 2 Load-Deviation GraphE111043Copyright by ASTM Intl (all rights reserved); Thu Mar 4 22:16:26 EST 2010Downloaded/printed byGuo Dehua (CNIS) pursuant to License Agreement. No further reproductio
41、ns authorized.6.7 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 in place as they normallyare used.7. Test Specimens7.1 Selection and
42、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 shall be removed by a subsequent stress relief heattreatment which shall
43、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 length to cross section of compressionspecimens should be such as to avo
44、id buckling (see TestMethods E9).NOTE 3For examples of tension and compression specimens, see TestMethods E8andE9.7.3 For tension specimens, the center lines of the gripsections and of the threads of threaded-end specimens shall beconcentric with the center line of the gage section within closetoler
45、ances 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 sheet-type specimens,it may be necessary to provide small tabs or notches
46、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 0.025 mm ofeccentricity. This error increases to about 2.5 % per 0.025 mm fo
47、r 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 length of compression specimens shall bein accordance with Test Methods E
48、9, 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 used, the average cross-sectional area for the gage length should be use
49、din 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 properties. 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 ve
