1、Designation: E2113 18Standard Test Method forLength Change Calibration of Thermomechanical Analyzers1This standard is issued under the fixed designation E2113; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revisi
2、on. 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 calibration of the lengthchange (deflection) measurement or thermal expansion ofthermomechanical analy
3、zers (TMAs) within the temperaturerange from 150 C to 1000 C using the thermal expansion ofa suitable reference material.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.3 This standard does not purport to address all of th
4、esafety concerns, if any, associated with 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.1.4 This international standard was developed in accor
5、-dance with internationally recognized 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
6、 Standards:2E473 Terminology Relating to Thermal Analysis and Rhe-ologyE831 Test Method for Linear Thermal Expansion of SolidMaterials by Thermomechanical AnalysisE1142 Terminology Relating to Thermophysical PropertiesE1363 Test Method for Temperature Calibration of Thermo-mechanical AnalyzersE2161
7、Terminology Relating to Performance Validation inThermal Analysis and Rheology3. Terminology3.1 Specific technical terms used in this test method aredescribed in Terminologies E473, E1142, and E2161 includingcalibration, Celsius, coeffcient of linear thermal expansion,Kelvin, reference material, rep
8、eatability, reproducibility, andthermomechanical analysis.4. Summary of Test Method4.1 Thermomechanical analyzers (TMAs) or related devicesare commonly used to determine coefficient of linear thermalexpansion of solid materials (for example, Test Method E831).The test specimen is heated at a linear
9、rate over the temperaturerange of interest and the change in length (dimension) iselectronically recorded.4.2 Performance verification or calibration of the lengthchange measurement is needed to obtain accurate coefficient ofthermal expansion data.4.3 The thermal expansion of a reference material is
10、 re-corded using a thermomechanical analyzer. The recordedthermal expansion is compared to the known value of thereference material. The resultant ratio, a calibration coefficient,may then be applied to the determination of unknown speci-mens to obtain accurate results.5. Significance and Use5.1 Per
11、formance verification or calibration is essential to theaccurate determination of quantitative dimension change mea-surements.5.2 This test method may be used for instrument perfor-mance validation, regulatory compliance, research and devel-opment and quality assurance purposes.6. Apparatus6.1 Therm
12、omechanical Analyzer (TMA)The essential in-strumentation required to provide the minimum thermome-chanical analytical or thermodilatometric capability for this testmethod includes:6.1.1 A Rigid Specimen Holder, of inert, low expansivitymaterial 0.5 m m-1C-1 to center the specimen in thefurnace and t
13、o fix the specimen to mechanical ground.6.1.2 A Rigid Expansion Probe, of inert, low expansivitymaterial 0.5 m m-1C-1 which contacts the specimen withan applicable compressive or tensile force.1This test method is under the jurisdiction ofASTM Committee E37 on ThermalMeasurements and is the direct r
14、esponsibility of Subcommittee E37.10 onFundamental, Statistical and Mechanical Properties.Current edition approved June 1, 2018. Published June 2018. Originallyapproved in 2000. Last previous edition approved in 2013 as E2113 13. DOI:10.1520/E2113-18.2For referenced ASTM standards, visit the ASTM we
15、bsite, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United Sta
16、tesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Tr
17、ade (TBT) Committee.16.1.3 A Sensing Element, linear over a minimum of 2 mm,to measure the displacement of the rigid probe to within 610nm resulting from changes in length/height of the specimen.6.1.4 A Weight or Force Transducer, to generate a constantforce between 1 mN and 100 mN (0.1 g and 10 g)
18、appliedthrough the rigid probe to the specimen.6.1.5 A Furnace, capable of providing uniform controlledheating (cooling) of a specimen to a constant temperature or ata constant rate within the applicable temperature range of thistest method.6.1.6 A Temperature Controller, capable of executing aspeci
19、fic temperature program by operating the furnace over anysuitable temperature range between 150 C and 1000 C at arate of temperature change of 5 C/min constant to within 60.1C/min.6.1.7 A Temperature Sensor, that can be attached to, incontact with, or reproducibly positioned in close proximity tothe
20、 specimen to provide an indication of the specimen/furnacetemperature to within 60.1 C.6.1.8 A means of sustaining an environment around thespecimen of an inert purge gas at a rate of 10 mL/min to 50 65 mL/min.NOTE 1Typically, 99.9+ % pure nitrogen, helium or argon isemployed, when oxidation in air
21、is a concern. Unless effects of moistureare to be studied, use of dry purge gas is recommended and is essential foroperation at subambient temperatures.6.1.9 A Data Collection Device, to provide a means ofacquiring, storing, and displaying measured or calculatedsignals, or both. The minimum output s
22、ignals required aredimension (length) change, temperature, and time.6.2 Micrometer, calipers or other length measurement de-vice capable of measuring linear dimensions up to 10 mm withreadability of 625 m.6.3 While not required, the user may find useful softwarethat performs the calculations describ
23、ed in this test method.6.4 Thermal expansion reference material of 8 mm 6 2mmlength, the linear coefficient of expansion of which is known to60.1 m m-1C-1. The coefficient of thermal expansion shouldbe between 9 m m-1C-1and 40 m m-1C-1.6.4.1 In the absence of primary or secondary referencematerials,
24、 high purity aluminum or platinum may be usedalong with the values for coefficient of thermal expansionpresented in Table 1.NOTE 2The linear expansion of high purity aluminum, commonlysupplied by instrument manufactures, is useful as a working referencematerial. Coefficient of thermal expansion valu
25、es for pure aluminum arepresented in Table 1 along with those for platinum.7. Test Specimen7.1 Specimens shall be between 6 mm and 10 mm in lengthand have flat and parallel ends to within 625 m. LateralTABLE 1 Thermal Expansion CoefficientsAAluminumBCDEFPlatinumGHIJTemperature, CMean Coefficient of
26、Linear Thermal Expansion,m/(m C)Mean Coefficient of Linear Thermal Expansion,m/(m C)1100 12.331000 11.87900 11.26800 11.08700 10.75600 10.45550 35.3 10.31500 33.2 10.18450 31.8 10.05400 30.5 9.92350 29.2 9.80300 27.8 9.67250 26.8 9.64200 26.2 9.45150 25.5 9.38100 24.5 9.1850 23.6 9.010 22.6 8.8550 2
27、0.9 8.59100 18.8 8.19150 7.37AMean coefficient of linear thermal expansion values are calculated for 50 C from the indicated temperature except in the case of platinum where values are for 100C of the indicated temperature for the range of 200 to 700 C.BNix, F. C., and MacNair, D., “The Thermal Expa
28、nsion of Pure Metals: Copper, Gold, Aluminum, Nickel, and Iron,” Physical Review, Vol 60, 1941, pp. 597605.CSimmons, R. O., and Balluffi, R. W., “Measurements of Equilibrium Vacancy Concentrations in Aluminum,” Physical Review, Vol 117, 1960, pp. 5231.DFraser, D. B., and Hollis Hallet, A. C., “The C
29、oefficient of Linear Expansion and Gruneisen of Cu, Ag, Au, Fe, Ni, and Al from 4K to 300K,” Proceedings of the 7thInternational Conference on Low-Temperature Physics, 1961, pp. 689692.EAltman, H. W., Rubin, T., and Johnson, H. L., Ohio State University, Cryogenic Laboratory Report OSU-TR-26427 (195
30、4) AD 26970.FHidnert, P., and Krider, H. S., “Thermal Expansion of Aluminum and Some Aluminum Alloys,” Journal of Research National Bureau of Standards, Vol 48, 1952, pp.209220.GNix, F. C., and MacNair, D., “The Thermal Expansion of Pure metals. II: Molybdenum, Palladium, Silver, Tantalum, Tungsten,
31、 Platinum, and Lead,” Physical Review,Vol61, 1942, pp. 7478.HWhite, G. K., “Thermal Expansion of Platinum at Low Temperature,” Journal of Physics, Vol 2F, 1972, pp. L30L31.IHahn, T. A., and Kirby, R. K., “Thermal Expansion of Platinum from 293 to 1900 K,” American Institute of Physics Conference Pro
32、ceedings, 3, 1972, pp. 8795.JKirby, R. K., “Platinum A Thermal Expansion Reference Material,” Thermal Conductivity 24/Thermal Expansion 12, Technomic Publishing, Lancaster, PA 1997, pp.655661.E2113 182dimensions shall be between 3 mm and 9 mm. Other lengthsand widths may be used but shall be noted i
33、n the report.8. Calibration8.1 Perform any calibration procedures described in themanufacturers operations manual.8.2 Calibrate the temperature sensor using Test MethodE1363.9. Procedure9.1 Measure the initial specimen length in the direction ofthe expansion test to within 625 m at 23 6 2 C.9.2 Plac
34、e the specimen on the specimen holder under theprobe and adjust so that no load is applied. Place the specimentemperature sensor within 2 mm but not touching the testspecimen.9.3 Move the furnace to enclose the specimen holder. Ifmeasurements at subambient temperatures are to be made, coolthe test s
35、pecimen to at least 20 C below the lowest tempera-ture of interest.NOTE 3The refrigerant used for cooling shall not come into directcontact with the specimen.9.4 Apply an appropriate load force to the sensing probe toensure that it is in contact with the specimen. A force between1 mN and 50 mN (0.1
36、g and 5 g) is adequate. The actualincremental force, mass or stress above that required to makecontact with the zero force shall be noted in the report.9.5 Heat the specimen at a rate of 5 6 0.1 C/min over thedesired temperature range and record the change in specimenlength and temperature to all av
37、ailable decimal places.NOTE 4Other heating rates may be used but shall be noted in thereport.NOTE 5For best results, specimen temperature gradients should besmall. High heating rates, large specimen size and low specimen thermalconductivity may lead to large specimen temperature gradients.9.6 Determ
38、ine the measurement instrument baseline byrepeating steps 9.2 9.5 using the same test parameters butwithout a test specimen. The measured change of length (L)of the specimen should normally be corrected by curvesubtraction for this baseline (that is, the probe is placed on theempty specimen holder)
39、especially for low expansion materi-als.9.7 Select a temperature change range (T) from a smoothportion of the thermal curve in the desired temperature range.Then obtain the L for this temperature range as depicted inFig. 1.9.8 Record the change in length (L) for the test specimenover a corresponding
40、 change in temperature (T). See Fig. 1.NOTE 6For the best calibration results, values for T should rangebetween 50 C and 100 C.10. Calculation10.1 Calculate the mean coefficient of linear thermal expan-sion for the desired temperature range and calibration coeffi-cient retaining all available signif
41、icant figures.k 5 LT/L (1)where: = mean coefficient of linear thermal expansion for thereference material at the midpoint of the T range, inm m-1C-1,k = calibration coefficient, dimensionless,L = length of the reference material at room temperature,in m,L = change in length of the reference material
42、 due toheating, in m, andT = temperature difference over which the change in speci-men length is measured, in C.NOTE 7The mean coefficient of linear thermal expansion describedhere is an approximation to the traditional coefficient of linear thermalexpansion where the reference length is taken at th
43、e test temperature ofinterest. This approximation creates a bias on the order of about 0.015 %.10.2 The true length change (Lt) of an unknown may bederived by multiplication of the observed length change (Lo)by the calculation coefficient (k).Lt5 kLo(2)11. Report11.1 A complete description of the Re
44、ference Material usedincluding dimensions of the specimen and any physical,mechanical or thermal pre-treatment and orientation withrespect to the original part (if cut to size).11.2 A complete description of the thermomechanical ana-lyzer being calibrated.11.3 A complete description of the experimen
45、tal conditionsincluding temperature range of test, heating rate, purge gastype and flow rate.11.4 The calibration coefficient value determined the mid-point of the temperature range of calibration. For example:k = 1.001 at 100 C.11.5 The specific dated version of this test method used.12. Precision
46、and Bias12.1 Precision:12.1.1 Precision of the calibration constant value may beestimated by the propagation of uncertainties method fromestimates of the precision of the respective components of thecalculation using:kk5FSLLD21SLLD21STTD2G12(3)where:k = calibration coefficient, dimensionless,k = imp
47、recision in the measurement of k, dimensionless,L = length of the reference material, in mm,L = imprecision in the measurement of L,inmm,L = change in specimen length due to heating, in m,L = imprecision of the measurement of L,inm,T = temperature difference over which the change inspecimen length i
48、s measured, in C, andT = imprecision of the measurement of T,inC.E2113 18312.1.2 For example, if:L = 8.00 mm,L = 25 m = 0.025 mm,L = 18.8 m,L = 0.10 m,T = 100.0 C, andT = 0.10 C.kk5FS0.10 m18.8 mD21S0.025 mm8.00 mmD21S0.10 C100.0 CD2G12(4)k/k 5 0.005319!210.003125!210.001000!2#12 (5)k/k 5 0.00002829
49、! 1 0.000009766! 1 0.000001000!#125 0.000039056#12 (6)k/k 5 0.006249 (7)Or expressed as percent:k/k 5 0.6249 % (8)12.1.3 Intralaboratory precision measurements confirm therelationship in 12.1.1.12.1.4 An interlaboratory test involving eight laboratoriesand six instrument models was conducted in 1985.3Analuminum calibration material, 8.0 mm in length was testedover a 100 C temperature range.12.1.5 RepeatabilityThe standard deviatio
