1、Designation: E2769 15Standard 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 300C.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 Pract
7、ice 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 Th
8、ree-Point Bending(Withdrawn 2009)3E473 Terminology Relating to Thermal Analysis and Rhe-ologyE1142 Terminology Relating to Thermophysical PropertiesE1363 Test Method for Temperature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 Analyze
9、rsE2206 Test Method 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, st
10、ress, thermodilatometry, 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 Me
11、thod4.1 A specimen 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 resul
12、tingdeflection (strain) is measured under isothermal conditions.The elastic modulus is obtained from the linear portion of thedisplay of resultant strain versus applied stress.5. Significance and Use5.1 This test method provides a means of characterizing themechanical behavior of materials using ver
13、y small amounts 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, Statist
14、ical and Mechanical Properties.Current edition approved Oct. 1, 2015. Published October 2015. Originallyapproved in 2011. Last previous version approved in 2013 as E2769 13. DOI:10.1520/E2769-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at
15、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.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocke
16、n, PA 19428-2959. 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 rep
17、resentative 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 anddissipative element in a mechanically driven linear displac
18、e-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 minimum thermomechanicalanalytical or thermodilatometric capability
19、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 material30 m m-1K-1to support the test specimen in a three-pointbe
20、nding mode (see 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 outpu
21、tover a minimum 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 1527.2.5 Programmable weight or force transducer to generatea force program of 0.1 N min-1over the range
22、 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 and 300C to within60.1C.NOTE 3Other temperatures may
23、be used but shall be reported.7.2.7 Temperature programmer and furnace capable oftemperature programming the test specimen from 100 to300C at a linear rate of at least 20 6 1C min-1and holdingisothermally to within 61C.7.2.8 Means of sustaining an environment around the speci-men of inert gas at a p
24、urge rate of 50 mL min-16 5%.NOTE 4Typically, inert purge gases that inhibit specimen oxidationare greater than 99.9 % pure nitrogen, helium or argon. Dry gases arerecommended for all experiments unless the effect of moisture is part ofthe study.7.2.9 A data collection device to provide a means ofac
25、quiring, 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 required, it is convenient to have thecapability for continuous calculation and display of stress a
26、ndstrain 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 isothermal subambienttemperatures.7.4 Micrometer, calipers, film gage or other length-measuring d
27、evice capable of measuring 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 precisionan
28、d accuracy in this measurement.7.5 A steel beam reference material, 0.5 mm in thickness orgreater of approximately the same width and length as the testspecimen.8. Hazards8.1 Toxic or corrosive effluents, or both, may be releasedwhen heating some materials and could be harmful to person-nel and appa
29、ratus.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), width (b), and length (l),depending upon the modulus of the sample and length of thesupport span (L).NOTE 6Other sp
30、ecimen 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 allow overhanging oneach end of at least 10 % of the support span, that is l 1.2 L.NOTE 8For precise results, the surf
31、aces 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, such as in reinforcedcomposites, the direction of the reinforcing agent shall bereported relative to the specimen dimen
32、sions.9.3 Replicate determinations are required. Sufficient testspecimens for replicated determinations shall be prepared foreach sample.10. Calibration10.1 Calibrate the temperature measurement system of theapparatus according to Test Method E1363 using a heating rateof 1 6 0.1C min-1.10.2 Calibrat
33、e 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 Polymeric test specimens shall be conditioned at 23 62C and 50 6 10 % relative humidity for not less than 40 hprior to test a
34、ccording 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 support points of the flexure fixtureto three significant figures (see Fig. 2).NOTE 9For many apparatus, this will be 5.0
35、 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 supports of the flexurefixture, with the long axis of the specimen perpendicular to theloading nose and supports (see Fig.
36、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 specimen and pro-gram the temperature to the desired isothermal test temperature61C and equilibrate for 3 min.12.5 Preload
37、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 % up to 1.0 N while recording the appliedforce (or calculated stress) and specimen displacement (orcalculated strain) as a function of time
38、. 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 been reached, whichever occurs first. Oncemaximum force is achieved, terminate the force program andremove the load from the test speci
39、men. Cool the apparatus toambient temperature.E2769 153NOTE 11This method is not applicable for strains higher than 3 %.NOTE 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 specime
40、n.12.7 Perform a baseline determination similar to sections12.4 12.6 except that the test specimen is a steel beam of thesame 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
41、 deflection on the X-axis. The same X- and Y- axisscale sensitivities shall be used for both thermal curves.12.9 Using 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 str
42、ess (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 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 3.1
43、2.12 Method BUsing the resultant curve from 12.9,prepare a display of applied force on the Y-axis (or derivedstress) and 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 andr
44、eport the value of elastic modulus (E) at an identified pointwithin this linear region using Eq 3.13. Calculation13.1 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)wher
45、e: = 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, 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 (
46、see Fig. 1).14. Report14.1 Report the following information:14.1.1 Complete identification and description of the mate-rial tested including source, manufacturing code, fiber orreinforcing agents and their respective orientation, if known,and any thermal or mechanical pretreatment.14.1.2 Direction o
47、f 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 Support span length and
48、 support span-to-depth ratio.FIG. 3 Test Specimen GeometryE2769 15414.1.7 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 method used.15. Precision and Bias15.1 Precison:15.1.1 The precision of this method may be estimated fromth
49、e principle of “propagation of uncertainties” which indicatesthat the modulus relative standard deviation (E/E) is related tothe relative standard deviations of the measurements for force(F/F), beam width (b/b), beam thickness (d/d), support span(L/L) and beam displacement (D/D)byEq 4.EE 5 F F!21 L L!21 b b!21 3 d d!21 D D!2#12(4)Thus if all measurements are made witha1%precision, thatis F/F = L/L = b/b = d/d = D/D = 1 %, then:EE 5 1%!21 31%!21 1%!21 3 1%!21 1%!2#125 1 1 3
