ASTM_E_111_-_04_2010.pdf

Designation:E11104(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 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 U.S.Department of Defense.1.Scope1.1 This test method2covers the determination 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 problems 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 units 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 practices 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 Methods of Compression Testing of Metallic Mate-rials at Room TemperatureE21 Test Methods for Elevated Temperature Tension Tests ofMetallic MaterialsE83 Practice for Verification and Classification of Exten-someter SystemsE231 Method for Static Determination of Youngs Modulusof Metals at Low and Elevated Temperatures(Withdrawn1985)4E1012 Practice for Verification 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 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.3.1.1.1 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 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 a test result obtained from this test method,or between twotest results obtained from this test method,for example,between operators or between laboratories.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 Sept.15,2010.Published January 2011.Originallyapproved in 1955.Last previous edition approved in 2004 as E111 04.DOI:10.1520/E0111-04R102This 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 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,refer to the standards Document Summary page onthe ASTM website.4The last approved version of this historical standard is referenced onwww.astm.org.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 3.1.3 precisionthe degree 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-strain curveat any specified stress or strain(see Fig.1b).3.1.4.2 chord modulusthe slope of the chord drawn be-tween any