1、Designation: E831 12Standard Test Method forLinear Thermal Expansion of Solid Materials byThermomechanical Analysis1This standard is issued under the fixed designation E831; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year
2、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.This standard has been approved for use by agencies of the Department of Defense.1. Scope1.1 This test method determines the ap
3、parent coefficient oflinear thermal expansion of solid materials using thermome-chanical analysis techniques.1.2 This test method is applicable to solid materials thatexhibit sufficient rigidity over the test temperature range suchthat the sensing probe does not produce indentation of thespecimen.1.
4、3 The recommended lower limit of coefficient of linearthermal expansion measured with this test method is 5 m/(mC). The test method may be used at lower (or negative)expansion levels with decreased accuracy and precision (seeSection 11).1.4 This test method is applicable to the temperature rangefrom
5、 120 to 900 C. The temperature range may be extendeddepending upon the instrumentation and calibration materialsused.1.5 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.6 This test method is related to ISO 11359-2 but issignif
6、icantly different in technical detail.1.7 This standard does not purport to address all of thesafety problems, 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 li
7、mitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D696 Test Method for Coefficient of Linear Thermal Ex-pansion of Plastics Between 30C and 30C with aVitreous Silica DilatometerD3386 Test Method for Coefficient of Linear ThermalExpansion of Electrical Insulating Materials3E228 Test M
8、ethod for Linear Thermal Expansion of SolidMaterials With a Push-Rod DilatometerE473 Terminology Relating to Thermal Analysis and Rhe-ologyE1142 Terminology Relating to Thermophysical PropertiesE1363 Test Method for Temperature Calibration of Ther-momechanical AnalyzersE2113 Test Method for Length C
9、hange Calibration ofThermomechanical Analyzers2.2 ISO Standards:4ISO 11359-2 PlasticsThermomechanical Analysis(TMA)Part 2: Determination of Coefficient of LinearThermal Expansion and Glass Transition Temperature3. Terminology3.1 DefinitionsThermal analysis terms in TerminologiesE473 and E1142 shall
10、apply to this test method includingcoefficient of linear thermal expansion, thermodilatometry andthermomechanical analysis.3.2 Definitions of Terms Specific to This Standard:3.2.1 mean coeffcient of linear thermal expansion, (am)the change in length, relative to the specimen length at ambienttempera
11、ture, accompanying a unit change in temperatureidentified by the midpoint temperature of the temperature rangeof measurement4. Summary of Test Method4.1 This test method uses a thermomechanical analyzer orsimilar device to determine the linear thermal expansion ofsolid materials when subjected to a
12、constant heating rate.1This test method is under the jurisdiction ofASTM Committee E37 on ThermalMeasurements and is the direct responsibility of Subcommittee E37.10 on Funda-mental, Statistical and Mechanical Properties.Current edition approved March 1, 2012. Published April 2012. Originallyapprove
13、d in 1981. Last previous edition approved in 2006 as E831 06. DOI:10.1520/E0831-12.2For 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 pa
14、ge onthe ASTM website.3Withdrawn. The last approved version of this historical standard is referencedon www.astm.org.4Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO
15、 Box C700, West Conshohocken, PA 19428-2959, United States.4.2 The change of the specimen length is electronicallyrecorded as a function of temperature. The coefficient of linearthermal expansion can be calculated from these recorded data.5. Significance and Use5.1 Coefficients of linear thermal exp
16、ansion are used, forexample, for design purposes and to determine if failure bythermal stress may occur when a solid body composed of twodifferent materials is subjected to temperature variations.5.2 This test method is comparable to Test Method D3386for testing electrical insulation materials, but
17、it covers a moregeneral group of solid materials and it defines test conditionsmore specifically. This test method uses a smaller specimenand substantially different apparatus than Test Methods E228and D696.6. Apparatus6.1 Thermomechanical Analyzers (TMA)The essential in-strumentation required provi
18、ding minimum thermomechanicalanalytical or thermodilatometric capability for this test methodincludes:6.1.1 Rigid Specimen Holder, of inert, low expansivitymaterial (# 0.5 m/(m C) to center the specimen in thefurnace and to fix the specimen to mechanical ground.6.1.2 Rigid Expansion Probe, of inert,
19、 low expansivitymaterial (#0.5 m/(m C) that contacts the specimen with anapplied compressive force.6.1.3 Sensing Element, linear over a minimum range of 2mm to measure the displacement of the rigid expansion probeto within 6 50 nm resulting from changes in length of thespecimen.6.1.4 Weight or Force
20、 Transducer, to generate a constantforce of 1 to 100 mN (0.1 to 10 g) that is applied through therigid expansion probe to the specimen.6.1.5 Furnace, capable of providing uniform controlledheating (cooling) of a specimen to a constant temperature or ata constant rate between 2 and 10 C/min within th
21、e applicabletemperatures range of between 150 and 1000 C.6.1.6 Temperature Controller, capable of executing a spe-cific temperature program by operating the furnace betweenselected temperature limits at a rate of temperature change of2 to 10 C/min constant to within 6 0.1 C/min or at anisothermal te
22、mperature constant to 6 0.5 C.6.1.7 Temperature Sensor, that can be attached to, in con-tact with, or reproducibly positioned in close proximity to thespecimen capable of indicating temperature to 6 0.5 C.6.1.8 A means of sustaining an environment around thespecimen of inert gas at a purge gas rate
23、of 10 to 50 mL/min.NOTE 1Typically, greater than 99 % pure nitrogen, argon, or heliumis used when oxidation in air is a concern. Unless effects of moisture areto be studied, use of dry purge gas is recommended and is essential foroperation at subambient temperatures.6.1.9 Data Collection Device, to
24、provide a means of acquir-ing, storing, and displaying measured or calculated signals, orboth. The minimum output signals required for thermome-chanical analysis are a change in linear dimension, temperatureand time.6.2 Cooling Capability, to sustain a subambient specimentemperature (if subambient m
25、easurements are to be made) or tohasten cool down of the specimen from elevated temperatures.6.3 Micrometer, or other length-measuring device with arange of up to 10 mm to determine specimen dimensions towithin 6 25 m.7. Test Specimens7.1 Specimens shall be between 2 and 10 mm in length andhave flat
26、 and parallel ends to within 6 25 m. Lateraldimensions shall not exceed 10 mm.NOTE 2Specimens of other dimensions may be used but dimensionsshall be reported.NOTE 3It has been found with some materials that this level offlatness and parallelness cannot be attained. Specimens that do not meetthese re
27、quirements may result in increased imprecision.7.2 The specimens are ordinarily measured as received.Where some heat or mechanical treatment is applied to thespecimen prior to test, this should be noted in the report.NOTE 4Some materials, particularly composites, may require heattreatment to conditi
28、on the specimen prior to test to relieve stresses ordistortions. Such heat treatment must be included in the report.8. Calibration8.1 Prepare the instrument for operation according to theprocedures in the manufacturers operation manual.8.2 Calibrate the temperature signal using Test MethodE1363.8.3
29、Calibrate the length change signal using Test MethodE2113 at the same heating rate as that to be used for the testspecimens. The observed expansion must be corrected for thedifference in expansion between the specimen holder and probeobtained from a blank run in which no sample or a specimen ofthe m
30、aterial of construction of the probe is run (see 10.1).9. Procedure9.1 Measure the initial specimen length in the direction ofthe expansion test to 6 25 m at 20 to 25 C.NOTE 5Direct readout of zero position and specimen length using theanalyzer sensing element, where available, with a sufficient ran
31、ge has beenfound to be an accurate means of length determination.9.2 Place the specimen in the specimen holder under theprobe. Place the specimen temperature sensor in contact withthe specimen or as near to the specimen as possible.9.3 Move the furnace to enclose the specimen holder. Ifmeasurements
32、at subambient temperature are to be made, coolthe specimen to at least 20 C below the lowest temperature ofinterest. The refrigerant used for cooling shall not come intodirect contact with the specimen.9.4 Apply an appropriate load force to the sensing probe toensure that it is in contact with the s
33、pecimen. Depending on thecompressibility of the specimen and the temperature range tobe investigated, a force of between 1 and 100 mN (0.1 to 10 g)is adequate. The actual incremental force, mass, or stress abovethat required to make contact with zero force shall be noted inthe report.E831 1229.5 Hea
34、t the specimen at a constant heating rate of 5 C/minover the desired temperature range and record the changes inspecimen length and temperature to all available decimalplaces.NOTE 6Other heating rates may be used but shall be noted in thereport.NOTE 7Normally, the expansion increases with the increa
35、se intemperature as shown in the schematic diagram of Fig. 1. An abruptchange in slope of the expansion curve indicates a transition of thematerial from one state to another.NOTE 8For best results, specimen temperature gradients should besmall. High heating rates, large specimen sizes, and low speci
36、men thermalconductivity may lead to large specimen temperature gradients. Theeffects of specimen temperature gradients may be compensated for bycorrection found through the use of suitable reference materials whosesize and thermal conductivity are close to that of the test specimen.NOTE 9Intralabora
37、tory testing indicates that no detectable increase inimprecision is observed for specimen sizes from 2 to 10 mm in length, forheating rates from 2 to 10 C/min, and for thermal conductivities from 0.2to 400 W/(mC) if only one parameter is changed.9.6 Measure the measurement instrument baseline by re-
38、peating 9.3 through 9.5 using the same test parameters butwithout a test specimen, that is, with the probe in contact withthe specimen holder. The measured DL for the specimen shouldnormally be corrected for this instrument baseline, especiallyfor low expansion specimens.10. Calculation10.1 Calculat
39、e the mean coefficient of linear thermal expan-sion rounded to the nearest 0.1 m/(mC) for a desiredtemperature range as follows:am5DLsp3 kL 3DT(1)where:am= mean coefficient of linear thermal expansion,m/(mC),k = calibration coefficient, from Test Method E2113,L = specimen length at room temperature,
40、 m,DLsp= change of specimen length, m,DT = temperature difference over which the change inspecimen length is measured, C, andT = midpoint temperature of the temperature range DT.NOTE 10For low-expansion specimens, DL should be corrected forthe expansion of the sample holder displaced by the specimen
41、.DLspor DLref! 5DLobs1 L DT aholder2DLblank(2)where:DLobs= measured change in length, m,aholder= mean coefficient of linear thermal expansion forholder, m/(mC), andDLblank= change of baseline due to heating, m.If the holder is composed of vitreous silica, aholder= 0.52 60.02 m/(mC) from 20 to 700 C.
42、10.2 Select a DT from a smooth portion of the thermalcurves in the desired temperature range symmetically aroundthe temperature of interest; then obtain DL as depicted in Fig.1. The amshall not be calculated from a temperature range inwhich a transition point is noted.NOTE 11Values for DT generally
43、range between 50 and 100 C.Values less than 50 C may lead to poor precision; values greater than 100C may mask small change in the expansion coefficient.11. Report11.1 The report shall include the following:11.1.1 Designation of the material, including the name ofthe manufacturer and information on
44、lot number and chemicalcomposition when known,11.1.2 Specimen orientation with respect to the original partor the direction of the oriented fiber fillers if a compositematerial is used,11.1.3 Method of test specimen preparation,11.1.4 Dimensions of the specimen,11.1.5 Description of the thermomechan
45、ical analysis appa-ratus, including manufacturer and model number,11.1.6 Purge gas and cooling medium, if used,11.1.7 The midpoint temperature (T) and the temperaturerange (DT) at which the coefficient of linear thermal expansionhas been determined,11.1.8 Average value of the coefficient of linear t
46、hermalexpansion in m/(mC) as determined from three specimens,11.1.9 Expansion curves obtained, and11.1.10 The specific dated version of this test method used.12. Precision and Bias512.1 Precision of thermal expansion measurements dependson the length of the specimen, the temperature range ofinterest
47、, and the change in the specimen length. Maximumimprecision in the calculated coefficient of linear thermal5Supporting data have been filed at ASTM International Headquarters and maybe obtained by requesting Research Report RR:E37-1000.FIG. 1 Specimen Expansion Versus TemperatureE831 123expansion ma
48、y be estimated from the imprecisions in theindividual measurements by the following equation.da/am5 dDL/ 6DL!21 dL/L!21 dDT/DT!2#1/2(3)where:am= mean coefficient of linear thermal expansion, m/(mC),da= imprecision in the measurement of a, m/(mC),DL = change of specimen length due to heating, m,dDL =
49、 imprecision in the measurement of DL, m,L = specimen length at room temperature, m,dL = imprecision in the measurement of L, m,DT = temperature difference over which the change inspecimen length is measured, C, anddDT = imprecision in the measurement of DT, C.12.1.1 Example:L 5 8 mm (4)dL 5625 m (5)DL 5 60 m (6)dDL 561 m (7)DT 5 100 C (8)dDT 560.5 C (9)da/am5 1 m/60 m!21 25 3 1026m/ 8 3 1023m!21 0.5 C/100 C!2#1/2(10)or expressed as percent:da/am561.8% (11)12.1.2 Intralaboratory
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