1、Designation: E2769 13Standard Test Method forElastic Modulus by Thermomechanical Analysis UsingThree-Point Bending and Controlled Rate of Loading1This standard is issued under the fixed designation E2769; the number immediately following the designation indicates the year oforiginal adoption or, in
2、the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method describes the use of linear controlled-rate-of-loading in three-poi
3、nt bending to determine the elasticmodulus of isotropic specimens in the form of rectangular barsusing a thermomechanical analyzer (TMA).NOTE 1This method is intended to provide results similar to those ofTest Methods D790 or D5934 but is performed on a thermomechanicalanalyzer using smaller test sp
4、ecimens. Until the user demonstratesequivalence, the results of this method shall be considered independentand unrelated to those of Test Methods D790 or D5934.1.2 This test method provides a means for determining theelastic modulus within the linear region of the stress-straincurves (see Fig. 1). T
5、his test is conducted under isothermaltemperature conditions from 100 to 300 C.1.3 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.4 There is no ISO standard equivalent to this test method.1.5 This standard does not purport to
6、 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 limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D618 Prac
7、tice for Conditioning Plastics for TestingD790 Test Methods for Flexural Properties of Unreinforcedand Reinforced Plastics and Electrical Insulating Materi-alsD5934 Test Method for Determination of Modulus of Elas-ticity for Rigid and Semi-Rigid Plastic Specimens byControlled Rate of Loading Using T
8、hree-Point Bending(Withdrawn 2009)3E473 Terminology Relating to Thermal Analysis and Rhe-ologyE1142 Terminology Relating to Thermophysical PropertiesE1363 Test Method for Temperature Calibration of Thermo-mechanical AnalyzersE2113 Test Method for Length Change Calibration of Ther-momechanical Analyz
9、ersE2206 Test Method for Force Calibration of Thermome-chanical Analyzers3. Terminology3.1 Definitions of technical terms used in this standard aredefined in Terminologies E473 and E1142 includinganisotropic, Celsius, expansivity, isotropic, proportional limit,storage modulus, strain, stress, thermo
10、dilatometer, thermome-chanical analysis, and yield point.3.2 Definitions of Terms Specific to This Standard:3.2.1 elastic modulus, nthe ratio of stress to correspond-ing strain within the elastic limit on the stress-strain curve (seeFig. 1) expressed in Pascal units.4. Summary of Test Method4.1 A sp
11、ecimen of rectangular cross section is tested inthree-point bending (flexure) as a beam. The beam rests on twosupports and is loaded by means of a loading nose midwaybetween the supports. A linearly increasing load (stress) isapplied to the test specimen of known geometry while theresulting deflecti
12、on (strain) is measured under isothermalconditions. The elastic modulus is obtained from the linearportion of the display of resultant strain versus applied stress.5. Significance and Use5.1 This test method provides a means of characterizing themechanical behavior of materials using very small amou
13、nts ofmaterial.5.2 The data obtained may be used for quality control,research and development and establishment of optimum1This test method is under the jurisdiction ofASTM Committee E37 on ThermalMeasurements and is the direct responsibility of Subcommittee E37.10 onFundamental, Statistical and Mec
14、hanical Properties.Current edition approved May 15, 2013. Published June 2013. Originallyapproved in 2011. Last previous version approved in 2011 as E2769 11. DOI:10.1520/E2769-13.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org
15、. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3The 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 19428-295
16、9. United States1processing conditions. The data are not intended for use indesign or predicting performance.NOTE 2This test method may not be suitable for anisotropic materials.6. Interferences6.1 Since small test specimen geometries are used, it isessential that the specimens be representative of
17、the materialbeing tested.6.2 This test method is not applicable for strains greater than3%.7. Apparatus7.1 The function of the apparatus is to hold a rectangulartest specimen (beam) so that the material acts as the elastic anddissipative element in a mechanically driven linear displace-ment system.
18、Displacements (deflections) are generated using acontrolled loading rate applied to a specimen in a three-pointbending configuration.7.2 Thermomechanical AnalyzerThe essential instrumen-tation required to provide the minimum thermomechanicalanalytical or thermodilatometric capability for this method
19、includes:7.2.1 A rigid specimen holder of inert low expansivitymaterial 30 m m-1K-1to center the specimen in the furnaceand to fix the specimen to mechanical ground.7.2.2 Arigid flexure fixture of inert low expansivity material30 m m-1K-1to support the test specimen in a three-pointbending mode (see
20、 Fig. 2).7.2.3 A rigid knife-edge compression probe of inert lowexpansivity material 30 m m-1K-1that contacts the speci-men with an applied compressive force (see Fig. 1). The radiusof the knife-edge shall not be larger than 1 mm.7.2.4 Deflection sensing element, having a linear outputover a minimum
21、 range of 5 mm to measure the displacement ofthe rigid compression probe (see 7.2.3) to within 60.1 m.FIG. 1 Stress-Strain Curve (Linear Region)FIG. 2 Flexure Support GeometryE2769 1327.2.5 Programmable weight or force transducer to generatea force program of 0.1 N min-1over the range of 0.01 to 1.0
22、 Nthat is applied to the specimen through the rigid compressionprobe (see 7.2.3).7.2.6 Temperature sensor, that can be reproducibly posi-tioned in close proximity to the specimen to measure itstemperature with the range between 100 and 300 C to within60.1 C.NOTE 3Other temperatures may be used but s
23、hall be reported.7.2.7 Temperature programmer and furnace capable oftemperature programming the test specimen from 100 to300 C at a linear rate of at least 20 6 1Cmin-1and holdingisothermally to within 61 C.7.2.8 Means of sustaining an environment around the speci-men of inert gas at a purge rate of
24、 50 mL min-16 5%.NOTE 4Typically, inert purge gases that inhibit specimen oxidationare 99.9+ % pure nitrogen, helium or argon. Dry gases are recommendedfor all experiments unless the effect of moisture is part of the study.7.2.9 A data collection device to provide a means ofacquiring, storing, and d
25、isplaying measured or calculatedsignals, or both. The minimum output signals required are achange in linear dimension change, applied force, temperatureand time.7.2.10 While not required, it is convenient to have thecapability for continuous calculation and display of stress andstrain resulting from
26、 the measurements of dimension changeand force.7.3 Auxiliary instrumentation considered necessary or use-ful in conducting this method includes:7.3.1 Cooling capability to provide isothermal subambienttemperatures.7.4 Micrometer, calipers, film gage or other length-measuring device capable of measur
27、ing length of 0.01 to20 mm with a precision of 60.001 mm (61 m).NOTE 5Propagation of uncertainties shows that the largest source oferror in this determination is the accuracy with which the test specimenthickness is measured. Care should be taken to ensure the best precisionand accuracy in this meas
28、urement.8. Hazards8.1 Toxic or corrosive effluents, or both, may be releasedwhen heating some materials and could be harmful to person-nel and apparatus.9. Test Specimens9.1 The test specimens used in this test method are ordinar-ily in the form of rectangular beams with aspect ratios of 1:3:12for t
29、hickness or specimen depth (d), width (b), and length (l),depending upon the modulus of the sample and length of thesupport span (L).NOTE 6Other specimen and support dimensions may be used but caremust be taken that the support length to specimen thickness ratio (L/d)begreater than 10.NOTE 7The spec
30、imen shall be long enough to allow overhanging oneach end of at least 10 % of the support span, that is l 1.2 L.NOTE 8For precise results, the surfaces need to be smooth andparallel. Twisting of the specimen will diminish precision.9.2 This test method assumes that the material is isotropic.Should t
31、he specimen be anisotropic, such as in reinforcedcomposites, the direction of the reinforcing agent shall bereported relative to the specimen dimensions.9.3 Replicate determinations are required. Sufficient testspecimens for replicated determinations shall be prepared foreach sample.10. Calibration1
32、0.1 Calibrate the temperature measurement system of theapparatus according to Test Method E1363 using a heating rateof 1 6 0.1 C min-1.10.2 Calibrate the deflection display of the apparatus ac-cording to Test Method E2113.10.3 Calibrate the force display of the apparatus accordingto Test Method E220
33、6.11. Conditioning11.1 Polymeric test specimens shall be conditioned at 23 62 C and 50 6 10 % relative humidity for not less than 40 hprior to test according to Procedure A of Practice D618, unlessotherwise specified and reported.12. Procedure12.1 Measure the test length (L) of the test specimen as
34、thedistance between the two support points of the flexure supportgeometry to three significant figures (see Fig. 2).NOTE 9For many apparatus, this will be 5.0 mm.12.2 Measure the width (b) and thickness (d) of the speci-men midway along its length to three significant figures (seeFig. 3). (See Note
35、5).12.3 Center the specimen on the supports, with the long axisof the specimen perpendicular to the loading nose and supports(see Fig. 2).NOTE 10The typical rectangular test beam is tested flat wise on thesupport span, with the applied force through its thinnest dimension.12.4 Place the furnace arou
36、nd the test specimen and pro-gram the temperature to the desired isothermal test temperature61 C and equilibrate for 3 min.12.5 Preload the test specimen with 0.01 N 6 1 % of fullscale. Set the displacement-axis signal to be zero.12.6 Apply a linearly increasing force at a rate of0.05 N min-16 1 % u
37、p to 1.0 N while recording the appliedforce (or calculated stress) and specimen displacement (orcalculated strain) as a function of time. Terminate the test if themaximum strain reaches 30 mm/m (3 %) or the proportionallimit, the yield force, the rupture force or the maximum forceof the analyzer has
38、 been reached, whichever occurs first. Oncemaximum force is achieved, terminate the force program andremove the load from the test specimen. Cool the apparatus toambient temperature.NOTE 11This method is not applicable for strains higher than 3 %.NOTE 12If the specimen fails or ruptures, then use an
39、other specimenand repeat the test using forces that do not exceed the linear region asdefined by the failed or ruptured specimen.E2769 13312.7 Method APrepare a display of stress (see Eq 1)ontheordinate and strain (see Eq 2) on the abscissa such as that inFig. 1.12.8 Determinate the slope of the lin
40、ear portion of the curve(that is, between the “upper limit of the toe” and the “propor-tional limit”). Report this slope as the elastic modulus (E)inbending according to Eq 3.12.9 Method BPrepare a display of applied force on theordinate (or derived stress) and deflection (or derived strain) onthe a
41、bscissa. Determine the linear portion of the curve (that is,between the “upper limit of the toe” and the “proportionallimit”) Determine and report the value of elastic modulus (E)at an identified point within this linear region using Eq 3.13. Calculation13.1 The elastic modulus is the ratio of stres
42、s with respect tostrain within the elastic limit of the stress-strain curve (Fig. 1).It is calculated using Eq 3.stress 5 53 FL!2 bd2!(1)where: = stress, MPa,b = beam width, mm,d = beam thickness, mm,D = beam displacement, mm,E = elastic modulus, MPa,F = force, N,L = support span, mm, and = strain,
43、dimensionless.NOTE 13Pa5Nm2strain 5 56 Dd!L2!(2)elastic modulus 5 E 55FL3!4 bd3D!(3)NOTE 14E is the slope of the stress versus strain curve (see Fig. 1).14. Report14.1 Report the following information:14.1.1 Complete identification and description of the mate-rial tested including source, manufactur
44、ing code, fiber orreinforcing agents and their respective orientation, if known,and any thermal or mechanical pretreatment.14.1.2 Direction of cutting and loading of the specimen,including preload force or deflection.14.1.3 Conditioning procedure.14.1.4 Description of the instrument used, including
45、modelnumber and location of the temperature sensor.14.1.5 Specimen dimensions including length, depth andwidth.14.1.6 Support span length and support span-to-depth ratio.14.1.7 Method (A or B) used.14.1.8 The elastic modulus and temperature of test.14.1.9 The specific dated version of this test meth
46、od used.15. Precision and Bias15.1 An interlaboratory test will be conducted in2015 2020 to develop a detailed precision and bias statementfor this test method. Anyone wishing to participate in thisinterlaboratory test may contact the ASTM International StaffManager for Committee E37.FIG. 3 Test Spe
47、cimen GeometryE2769 13415.2 Within laboratory relative standard deviation deter-mined in a single laboratory was found to be 65 % for a meanmodulus of 13.2 GPa.16. Keywords16.1 elastic modulus; modulus of elasticity; stress; strain;thermomechanical analysisASTM International takes no position respec
48、ting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard 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 sta
49、ndard is subject to revision at any time by the responsible technical committee and must be reviewed every five years 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, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your vie
