1、Designation: E2769 18Standard 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. Scope*1.1 This test method describes the use of linear controlled-rate-of-loading in three-po
3、int 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 s
4、pecimens. 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).
5、This test is conducted under isothermaltemperature conditions from 100 C 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 This standard does not purport to address all of thesafety concerns, if any, associated wi
6、th its use. It is theresponsibility of the user of this standard to establish appro-priate safety, health, and environmental 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
7、principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2D618 Practice for Condition
8、ing 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 Three-Point Bending
9、(Withdrawn 2009)3E473 Terminology Relating to Thermal Analysis and Rhe-ologyE1142 Terminology Relating to Thermophysical PropertiesE1363 Test Method for Temperature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 AnalyzersE2206 Test Meth
10、od for Force Calibration of Thermome-chanical Analyzers3. Terminology3.1 DefinitionsDefinitions of technical terms used in thisstandard are defined in Terminologies E473 and E1142 includ-ing anisotropic, Celsius, expansivity, isotropic, proportionallimit, storage modulus, strain, stress, thermodilat
11、ometry, ther-momechanical 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 specime
12、n of rectangular cross section is tested inthree-point bending (flexure) as a beam. The beam rests on twosupports and is loaded midway between the supports by meansof a loading nose. A linearly increasing load (stress) is appliedto the test specimen of known geometry while the resultingdeflection (s
13、train) is measured under isothermal conditions.The elastic modulus is obtained from the linear portion of thedisplay of resultant strain versus applied stress.1This test method is under the jurisdiction ofASTM Committee E37 on ThermalMeasurements and is the direct responsibility of Subcommittee E37.
14、10 onFundamental, Statistical and Mechanical Properties.Current edition approved June 1, 2018. Published June 2018. Originallyapproved in 2011. Last previous version approved in 2016 as E2769 16. DOI:10.1520/E2769-18.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact AST
15、M Customer Service at serviceastm.org. 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.*A Summary of Changes section appears at the end of this sta
16、ndardCopyright 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
17、International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.15. Significance and Use5.1 This test method provides a means of characterizing themechanical behavior of materials using very small amounts ofmaterial.5.2 The data
18、obtained may be used for quality control,research and development and establishment of optimumprocessing 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
19、 geometries are used, it isessential that the specimens be representative of 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
20、anddissipative element in a mechanically driven linear displace-ment system. 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 minimu
21、m thermomechanicalanalytical or thermodilatometric capability for this methodincludes: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 mate
22、rial30 m m-1K-1to support the test specimen in a three-pointbending mode (see Fig. 2). The radius of the supports shall notbe greater than 1 mm.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 Fi
23、g. 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 range of 5 mm to measure the displacement ofthe rigid compression probe (see 7.2.3) to within 60.1 m.7.2.5 Programmable weight or force transducer to generatea forc
24、e program of 0.1 N min-1over the range of 0.01 to 1.0 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 C and 300 C tow
25、ithin 60.1 C.NOTE 3Other temperatures may be used but shall be reported.7.2.7 Temperature programmer and furnace capable oftemperature programming the test specimen from 100 C to300 C at a linear rate of at least 20 6 1 C min-1and holdingisothermally to within 61 C.7.2.8 Means of sustaining an envir
26、onment around the speci-men of inert gas at a purge rate of 50 mL min-16 5%.FIG. 1 Stress-Strain Curve (Linear Region)E2769 182NOTE 4Typically, inert purge gases that inhibit specimen oxidationare greater than 99.9 % pure nitrogen, helium or argon. Dry gases arerecommended for all experiments unless
27、 the effect of moisture is part ofthe study.7.2.9 A data collection device to provide a means ofacquiring, storing, and displaying 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 r
28、equired, it is convenient to have thecapability for continuous calculation and display of stress andstrain resulting from 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
29、 isothermal subambienttemperatures.7.4 Micrometer, calipers, film gage or other length-measuring device capable of measuring length of 0.01 mm 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 w
30、ith which the test specimenthickness is measured. Care should be taken to ensure the best precisionand accuracy in this measurement.7.5 A high modulus (2 GPa) beam reference material, 0.5mm in thickness or greater of approximately the same widthand length as the test specimen.8. Hazards8.1 Toxic or
31、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 thickness or specimen depth (d),
32、 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 specimen shall be long enough to al
33、low 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 the specimen be anisotropic, suc
34、h 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. Calibration10.1 Calibrate the temperature m
35、easurement 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 E2206.11. Conditioning11.1 Polymeri
36、c 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 thedistance between the two sup
37、port points of the flexure fixtureto 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 5).12.3 Center the specimen on the suppo
38、rts of the flexurefixture, with the long axis of the specimen perpendicular to theloading 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 around the test speci
39、men 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.FIG. 2 Flexure Support GeometryE2769 18312.6 Apply a linearly increasing force at a rat
40、e of 0.1 N min-1 6 1 % up to the maximum applicable load while recordingthe applied force (or calculated stress) and specimen displace-ment (or calculated strain) as a function of time. Terminate thetest if the maximum strain reaches 30 mm m (3 %) or theproportional limit, the yield force, the ruptu
41、re force or themaximum force of the analyzer has been reached, whicheveroccurs first. Once maximum force is achieved, terminate theforce program and remove the load from the test specimen.Cool the apparatus to ambient temperature.NOTE 11This method is not applicable for strains higher than 3 %.NOTE
42、12If the specimen fails or ruptures, then use another specimenand repeat the test using forces that do not exceed the linear region asdefined by the failed or ruptured specimen.12.7 Perform a baseline determination similar to sections12.4 12.6 except that the test specimen is a high modulusbeam of t
43、he same nominal dimensions as the test specimen.12.8 For ease of interpretation, display the thermal curvesfrom sections 12.6 and 12.7 with stress or force on the Y-axisand strain or deflection on the X-axis. The same X- and Y- axisscale sensitivities shall be used for both thermal curves.12.9 Using
44、 the same Y-axis scale sensitivity, subtract thebaseline curve of 12.7 from the test specimen curve of 12.6.12.10 Method AUsing the resultant curve from 12.9,prepare a display of stress (see Eq 1) on the Y-axis and strain(see Eq 2) on the X-axis such as that in Fig. 1.12.11 Determinate the slope of
45、the linear portion of thecurve (that is, between the “upper limit of the toe” and the“proportional limit”). Report this slope as the elastic modulus(E) in bending according to Eq 3.12.12 Method BUsing the resultant curve from 12.9,prepare a display of applied force on the Y-axis (or derivedstress) a
46、nd deflection (or derived strain) on the X-axis. Deter-mine the linear portion of the curve (that is, between the “upperlimit of the toe” and the “proportional limit”) Determine andreport the value of elastic modulus (E) at an identified pointwithin this linear region using Eq 3.13. Calculation13.1
47、The elastic modulus is the ratio of stress 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 = forc
48、e, N,L = support span, mm, and = strain, dimensionless.NOTE 13Pa =Nm2, and MPa = N (mm)-2.strain 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 d
49、escription of the mate-rial tested including source, manufacturing code, fiber orFIG. 3 Test Specimen GeometryE2769 184reinforcing 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 modelnumber and location of the temperature sensor.14.1.5 Specimen dimensions including length, depth andwidth.14.1.6 Suppo
