1、Designation: E111 17Standard 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 last revision.Anum
2、ber 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 U.S. Department of Defense.1. Scope*1.1 This test method covers the determination of Youngsmo
3、dulus, tangent modulus, and chord modulus of structuralmaterials, see Fig. 1. This test method is limited to materials inwhich and to temperatures and stresses at which creep isnegligible compared to the strain produced immediately uponloading and to 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, health, and e
6、nvironmental practices and deter-mine the applicability of regulatory limitations prior to use.1.5 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Sta
7、ndards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E6 Terminology Relating to Methods of Mechanical TestingE8/E8M Test Methods for Tension Testing of Metallic Ma-terialsE9 Test Methods of Co
8、mpression Testing of Metallic Mate-rials at Room TemperatureE21 Test Methods for ElevatedTemperatureTensionTests ofMetallic MaterialsE83 Practice for Verification and Classification of Exten-someter SystemsE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE1012 Practice for Ve
9、rification of Testing Frame and Speci-men Alignment Under Tensile and Compressive AxialForce Application2.2 General ConsiderationsWhile certain portions of thestandards and practices listed are applicable and should bereferred to, the precision required in this test method is higherthan that require
10、d in general testing.3. Terminology3.1 Definitions: Terms common to mechanical testing.3.1.1 The definitions of mechanical testing terms that ap-pear in Terminology E6 apply to this test method. These termsinclude initial tangent modulus, secant modulus, gauge length,yield strength, tensile strength
11、, stress-strain diagram, andextensometer.3.1.2 The terms accuracy, precision, and bias are used asdefined in Practice E177.3.1.3 In addition, the following common terms that appearin the Terminology E6 apply to this test method.3.1.4 chord modulusthe slope of the chord drawn betweenany two specified
12、 points on the stress-strain curve below theelastic limit of the material.3.1.5 elastic limit FL2, nthe greatest stress that a mate-rial is capable of sustaining without any permanent strainremaining upon complete release of the stress.3.1.5.1 DiscussionDue to practical considerations in de-terminin
13、g the elastic limit, measurements of strain using asmall force, rather than zero force, are usually taken as theinitial and final reference.3.1.6 indicated temperature, nthe temperature indicatedby a temperature measuring device using good pyrometricpractice.1This test method is under the jurisdicti
14、on of ASTM Committee E28 onMechanical Testing and is the direct responsibility of Subcommittee E28.04 onUniaxial Testing.Current edition approved July 15, 2017. Published September 2017. Originallyapproved in 1955. Last previous edition approved in 2010 as E111 04(2010). DOI:10.1520/E0111-04R102For
15、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 Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardC
16、opyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of Intern
17、ational Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.13.1.7 nominal temperature, nthe intended test tempera-ture.3.1.8 proportional limit FL2, nthe greatest stress that amaterial is capable of sustaining without deviation fr
18、omproportionality of stress to strain (Hookes law).3.1.9 tangent modulusthe slope of the stress-strain curveat any specified stress or strain.3.1.10 Youngs modulusthe ratio of tensile or compressivestress to corresponding strain below the proportional limit.4. Summary of Test Method4.1 A uniaxial fo
19、rce 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-straincurve, which ma
20、y 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 calculating compliance of stru
21、cturalmaterials 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 strain for a specified
22、 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 should be such as to conf
23、orm 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 grains relative to the dir
24、ection 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 the range in force va
25、lues, 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) ChordModulusE1111725.6 When
26、 the modulus determination is made at strains inexcess of 0.25 %, correction shall be made for changes incross-sectional area and gauge length, by substituting theinstantaneous cross section and instantaneous gauge length forthe original values.5.7 Compression results may be affected by barreling (s
27、eeTest Methods E9). Strain measurements should therefore bemade in the specimen region where such effects 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 Machines
28、In determining the suitability of atesting machine, the machine shall be calibrated under condi-tions approximating those under which the determination ismade. Corrections may be applied to correct for provensystematic errors.6.3 Loading FixturesLoading fixtures shall be properlydesigned and maintai
29、ned. The allowable bending as defined inPractice E1012 shall not exceed 5 %.NOTE 1 Grips and other devices for obtaining and maintaining axialalignment are shown in Test Methods E8/E8M and E9. Procedures forverifying the alignment are described in detail in Practice E1012.6.4 ExtensometersClass B-1
30、or better extensometers asdescribed in Practice E83 shall be used. Corrections may beapplied 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 arran
31、ged at equal intervalsaround the cross section shall be used. If two extensometers areused on other than round sections, they shall be mounted atends of an axis of symmetry of the section. If a force-strainrecorder, strain-transfer device, or strain follower is used withthe extensometer, they shall
32、be calibrated as a unit in the samemanner in which they are used for determination of Youngsmodulus. The gauge length shall be determined with anaccuracy consistent with the precision expected from themodulus determination and from the extensometer.NOTE 2The accuracy of the modulus determination dep
33、ends on theprecision of the strain measurement. The latter can be improved byincreasing the gauge length. This may, however, present problems inmaintaining specimen tolerances and temperature uniformity.6.5 Furnaces or Heating DevicesWhen determiningYoungs modulus at elevated temperature, the furnac
34、e orheating device used shall be capable of maintaining a uniformindicated temperature in the reduced section of the testspecimen so that a variation of not more than 61.5C fornominal temperatures up to and including 900C, and not morethan 63.0C for temperatures above 900C, occurs. (Heatingby self-r
35、esistance shall not be used.) Minimize indicatedtemperature variations and control changes within the allow-able limits. An instrumented sample representative of the realtest may be used demonstrate that the setup meets the abovecapabilities.NOTE 3Differences in thermal expansion between specimen an
36、dextensometer parts can cause significant errors in apparent strain.6.6 Low-Temperature Baths and Refrigeration EquipmentWhen determining Youngs modulus at temperatures belowroom temperature, an appropriate low-temperature bath orrefrigeration system shall be used to maintain the specimen atthe nomi
37、nal temperature during testing. For a low-temperaturebath, the lower tension rod or adapter may pass through thebottom of an insulated container and be welded or fastened toit to prevent leakage.NOTE 4For nominal temperatures to about 80C, chipped dry icethat cools an organic solvent such as ethyl a
38、lcohol in the low-temperaturebath is suitable. Other organic solvents having lower solidificationtemperatures, such as methylcyclohexane or isopentane, cooled withliquid nitrogen are useful at temperatures lower than 80C. Liquidnitrogen can be used to achieve a nominal temperature of 196C. Lowernomi
39、nal temperatures are possible with liquid hydrogen and liquid helium,with special containers or cryostats to minimize heat leakage and to permitefficient use of these coolants. Liquid hydrogen can produce explosivemixtures of hydrogen gas and air. If refrigeration equipment is used tocool the specim
40、ens with air as the cooling medium, it is desirable to haveforced air circulation to provide uniform cooling.6.6.1 At low temperatures, when using a coolant bath,immersion-type extensometers should be used.6.7 Temperature measuring, controlling, and recording in-struments shall be calibrated periodi
41、cally 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 Preparation of SpecimensSpecial careshall be taken to obtain representative specimens that arestraight and u
42、niform in cross section. If straightening of thematerial for the specimen is required, then resultant residualstresses shall be removed by a subsequent stress relief anneal-ing procedure that shall be reported with the test results.7.2 DimensionsThe specimen length (and fillet radius inthe case of t
43、ension specimens) should be greater than theminimum requirements for general-purpose specimens. Inaddition, the ratio of length to cross section of compressionspecimens should be such as to avoid buckling (see TestMethods E9).NOTE 5For examples of tension and compression specimens, see TestMethods E
44、8/E8M and E9.7.3 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 gauge section within closetolerances in order to obtain the degree of alignment required.If pin-loaded sheet-type specimens are use
45、d, the centers of thegripping holes shall be not more than 0.005 times the width ofthe gauge section from its center line. For sheet-typespecimens, small tabs or notches for attaching the extensom-eter may be used.NOTE 6The effect of eccentric loading can be illustrated by calculat-ing the bending m
46、oment 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 for a 9-mmdiameter specimen and to about 3.2 % per 0.025 mm for a 6-mm diameterspecimen.E1111737.4 The length of the r
47、educed section of tension specimensshall exceed the gauge length by at least twice the diameter ortwice the width. The length of compression specimens shall bein accordance with Test Methods E9, and all specimens shallhave a uniform cross-sectional area throughout the gaugelength.7.4.1 If a general-
48、purpose tension specimen such as thoseshown in Test Methods E8/E8M, having a small amount oftaper in the reduced section is used, the average cross-sectionalarea for the gauge length should be used in computing stress.7.5 For compression specimens, the ends shall be flat,parallel and perpendicular t
49、o the lateral surfaces as specified inTest Methods E9.7.6 The specimen shall be free of residual stresses. Thespecimen may be subjected to an annealing procedure torelieve the residual stresses. If the intent of the test is to verifythe performance of a product, the annealing procedure may beomitted. Report the condition of the material tested, includingany annealing procedure.NOTE 7An annealing procedure at Tm/3 for 30 min to relieve thestresses in the material (where Tmis the melting point of the material inK) has been used su
