1、Designation: E2769 15E2769 16Standard 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
2、 or, in 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 Scope*1.1 This test method describes the use of linear controlled-rate-of-loadi
3、ng in three-point bending to determine the elasticmodulus of isotropic specimens in the form of rectangular bars using a thermomechanical analyzer (TMA).NOTE 1This method is intended to provide results similar to those of Test Methods D790 or D5934 but is performed on a thermomechanical analyzerusin
4、g smaller test specimens. Until the user demonstrates equivalence, the results of this method shall be considered independent and unrelated to thoseof Test Methods D790 or D5934.1.2 This test method provides a means for determining the elastic modulus within the linear region of the stress-strain cu
5、rves(see Fig. 1). This test is conducted under isothermal temperature conditions from 100 to 300C.1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.1.4 There is no ISO standard equivalent to this test method.1.5 This standar
6、d does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM S
7、tandards:2D618 Practice for Conditioning Plastics for TestingD790 Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating MaterialsD5934 Test Method for Determination of Modulus of Elasticity for Rigid and Semi-Rigid Plastic Specimens by Controlled Rate
8、of Loading Using Three-Point Bending (Withdrawn 2009)3E473 Terminology Relating to Thermal Analysis and RheologyE1142 Terminology Relating to Thermophysical PropertiesE1363 Test Method for Temperature Calibration of Thermomechanical AnalyzersE2113 Test Method for Length Change Calibration of Thermom
9、echanical AnalyzersE2206 Test Method for Force Calibration of Thermomechanical Analyzers3. Terminology3.1 DefinitionsDefinitions of technical terms used in this standard are defined in Terminologies E473 and E1142 includinganisotropic, Celsius, expansivity, isotropic, proportional limit, storage mod
10、ulus, strain, stress, thermodilatometry, thermomechani-cal analysis, and yield point.3.2 Definitions of Terms Specific to This Standard:3.2.1 elastic modulus, nthe ratio of stress to corresponding strain within the elastic limit on the stress-strain curve (see Fig.1) expressed in Pascal units.1 This
11、 test method is under the jurisdiction ofASTM Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.10 on Fundamental,Statistical and Mechanical Properties.Current edition approved Oct. 1, 2015April 1, 2016. Published October 2015April 2016. Originally approved i
12、n 2011. Last previous version approved in 20132015 asE2769 13.15. DOI: 10.1520/E2769-15.10.1520/E2769-16.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standard
13、s Document Summary page on the ASTM website.3 The last approved version of this historical standard is referenced on www.astm.org.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. B
14、ecauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.*A Summary of Changes section ap
15、pears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States14. Summary of Test Method4.1 Aspecimen of rectangular cross section is tested in three-point bending (flexure) as a beam. The beam rests on two supportsa
16、nd is loaded midway between the supports by means of a loading nose. A linearly increasing load (stress) is applied to the testspecimen of known geometry while the resulting deflection (strain) is measured under isothermal conditions. The elastic modulusis obtained from the linear portion of the dis
17、play of resultant strain versus applied stress.5. Significance and Use5.1 This test method provides a means of characterizing the mechanical behavior of materials using very small amounts ofmaterial.5.2 The data obtained may be used for quality control, research and development and establishment of
18、optimum processingconditions. The data are not intended for use in design 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 is essential that the specimens be representative of the mate
19、rial beingtested.6.2 This test method is not applicable for strains greater than 3 %.7. Apparatus7.1 The function of the apparatus is to hold a rectangular test specimen (beam) so that the material acts as the elastic anddissipative element in a mechanically driven linear displacement system. Displa
20、cements (deflections) are generated using acontrolled loading rate applied to a specimen in a three-point bending configuration.7.2 Thermomechanical AnalyzerThe essential instrumentation required to provide the minimum thermomechanical analyticalor thermodilatometric capability for this method inclu
21、des:7.2.1 Arigid specimen holder of inert low expansivity material 30 m m-1 K-1 to center the specimen in the furnace and to fixthe specimen to mechanical ground.7.2.2 A rigid flexure fixture of inert low expansivity material 30 m m-1 K-1 to support the test specimen in a three-pointbending mode (se
22、e Fig. 2).7.2.3 A rigid knife-edge compression probe of inert low expansivity material 30 m m-1 K-1 that contacts the specimen withan applied compressive force (see Fig. 1). The radius of the knife-edge shall not be larger than 1 mm.FIG. 1 Stress-Strain Curve (Linear Region)E2769 1627.2.4 Deflection
23、 sensing element, having a linear output over a minimum range of 5 mm to measure the displacement of the rigidcompression probe (see 7.2.3) to within 60.1 m.7.2.5 Programmable weight or force transducer to generate a force program of 0.1 N min-1 over the range of 0.01 to 1.0 N thatis applied to the
24、specimen through the rigid compression probe (see 7.2.3).7.2.6 Temperature sensor, that can be reproducibly positioned in close proximity to the specimen to measure its temperaturewith the range between 100 and 300C to within 60.1C.NOTE 3Other temperatures may be used but shall be reported.7.2.7 Tem
25、perature programmer and furnace capable of temperature programming the test specimen from 100 to 300C at alinear rate of at least 20 6 1C min-1 and holding isothermally to within 61C.7.2.8 Means of sustaining an environment around the specimen of inert gas at a purge rate of 50 mL min-1 6 5 %.NOTE 4
26、Typically, inert purge gases that inhibit specimen oxidation are greater than 99.9 % pure nitrogen, helium or argon. Dry gases arerecommended for all experiments unless the effect of moisture is part of the study.7.2.9 A data collection device to provide a means of acquiring, storing, and displaying
27、 measured or calculated signals, or both.The minimum output signals required are a change in linear dimension change, applied force, temperature and time.7.2.10 While not required, it is convenient to have the capability for continuous calculation and display of stress and strainresulting from the m
28、easurements of dimension change and force.7.3 Auxiliary instrumentation considered necessary or useful in conducting this method includes:7.3.1 Cooling capability to provide isothermal subambient temperatures.7.4 Micrometer, calipers, film gage or other length-measuring device capable of measuring l
29、ength of 0.01 to 20 mm with aprecision of 60.001 mm (61 m).NOTE 5Propagation of uncertainties shows that the largest source of error in this determination is the accuracy with which the test specimen thicknessis measured. Care should be taken to ensure the best precision and accuracy in this measure
30、ment.7.5 A steel high modulus (2 GPa) beam reference material, 0.5 mm in thickness or greater of approximately the same widthand length as the test specimen.8. Hazards8.1 Toxic or corrosive effluents, or both, may be released when heating some materials and could be harmful to personnel andapparatus
31、.FIG. 2 Flexure Support GeometryE2769 1639. Test Specimens9.1 The test specimens used in this test method are ordinarily in the form of rectangular beams with aspect ratios of 1:3:12 forthickness or specimen depth (d), width (b), and length (l), depending upon the modulus of the sample and length of
32、 the supportspan (L).NOTE 6Other specimen and support dimensions may be used but care must 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 on each end of at least 10 % of the support span, that is l 1.2
33、 L.NOTE 8For precise results, the surfaces need to be smooth and parallel. 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 b
34、e reported relative to the specimen dimensions.9.3 Replicate determinations are required. Sufficient test specimens for replicated determinations shall be prepared for eachsample.10. Calibration10.1 Calibrate the temperature measurement system of the apparatus according to Test Method E1363 using a
35、heating rate of1 6 0.1C min-1.10.2 Calibrate the deflection display of the apparatus according to Test Method E2113.10.3 Calibrate the force display of the apparatus according to Test Method E2206.11. Conditioning11.1 Polymeric test specimens shall be conditioned at 23 6 2C and 50 6 10 % relative hu
36、midity for not less than 40 h priorto test according to Procedure A of Practice D618, unless otherwise specified and reported.12. Procedure12.1 Measure the test length (L) of the test specimen as the distance between the two support points of the flexure fixture tothree significant figures (see Fig.
37、 2).NOTE 9For many apparatus, this will be 5.0 mm.12.2 Measure the width (b) and thickness (d) of the specimen midway along its length to three significant figures (see Fig. 3).(See Note 5).FIG. 3 Test Specimen GeometryE2769 16412.3 Center the specimen on the supports of the flexure fixture, with th
38、e long axis of the specimen perpendicular to the loadingnose and supports (see Fig. 2).NOTE 10The typical rectangular test beam is tested flat wise on the support span, with the applied force through its thinnest dimension.12.4 Place the furnace around the test specimen and program the temperature t
39、o the desired isothermal test temperature 61Cand equilibrate for 3 min.12.5 Preload the test specimen with 0.01 N 6 1 % of full scale. Set the displacement-axis signal to be zero.12.6 Apply a linearly increasing force at a rate of 0.05 N min-1 6 1 % up to 1.0 N while recording the applied force (orc
40、alculated stress) and specimen displacement (or calculated strain) as a function of time. Terminate the test if the maximum strainreaches 30 mmm (3 %) or the proportional limit, the yield force, the rupture force or the maximum force of the analyzer has beenreached, whichever occurs first. Once maxi
41、mum force is achieved, terminate the force program and remove the load from the testspecimen. Cool the apparatus to ambient temperature.NOTE 11This method is not applicable for strains higher than 3 %.NOTE 12If the specimen fails or ruptures, then use another specimen and repeat the test using force
42、s that do not exceed the linear region as definedby the failed or ruptured specimen.12.7 Perform a baseline determination similar to sections 12.4 12.6 except that the test specimen is a steel high modulus beamof the same nominal dimensions as the test specimen.12.8 For ease of interpretation, displ
43、ay the thermal curves from sections 12.6 and 12.7 with stress or force on the Y-axis andstrain or deflection on the X-axis. The same X- and Y- axis scale sensitivities shall be used for both thermal curves.12.9 Using the same Y-axis scale sensitivity, subtract the baseline curve of 12.7 from the tes
44、t 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 Eq2) on the X-axis such as that in Fig. 1.12.11 Determinate the slope of the linear portion of the curve (that is, between the “upper limit of the toe” and
45、 the “proportionallimit”). 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 derived stress) anddeflection (or derived strain) on the X-axis. Determine the linear portion o
46、f the curve (that is, between the “upper limit of the toe”and the “proportional limit”) Determine and report the value of elastic modulus (E) at an identified point within this linear regionusing Eq 3.13. Calculation13.1 The elastic modulus is the ratio of stress with respect to strain within the el
47、astic limit of the stress-strain curve (Fig. 1).It is calculated using Eq 3.stress55 3 F L!2 b d2! (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, dimensionless.NOTE 13Pa5Nm2strain55
48、6 D d!L2! (2)elastic modulus5E 5 5 F L3!4 b d3 D! (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 material tested including source, manufacturing code, fiber or reinforcingag
49、ents and their respective orientation, if known, and any thermal or mechanical pretreatment.E2769 16514.1.2 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 model number and location of the temperature sensor.14.1.5 Specimen dimensions including length, depth and width.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
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