1、Designation: E1877 15Standard Practice forCalculating Thermal Endurance of Materials fromThermogravimetric Decomposition Data1This standard is issued under the fixed designation E1877; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision
2、, 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 practice describes the determination of thermalendurance, thermal index, and relative thermal index
3、 fororganic materials using the Arrhenius activation energy gener-ated by thermogravimetry.1.2 This practice is generally applicable to materials with awell-defined thermal decomposition profile, namely a smooth,continuous mass change.1.3 The values stated in SI units are to be regarded asstandard.
4、No other units of measurement are included in thisstandard.1.4 There is no ISO standard equivalent to this practice.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate
5、 safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E1641 Test Method for Decomposition Kinetics by Thermo-gravimetry Using the Ozawa/Flynn/Wall MethodE2550 Test Method for Thermal Stability by Thermogravi-me
6、tryE2958 Test Methods for Kinetic Parameters by Factor Jump/Modulated Thermogravimetry3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 failure, nchange in some chemical, physical,mechanical, electrical or other property of sufficient magnitudeto make it unsuitable for a particu
7、lar use.3.1.2 failure temperature (Tf), nthe temperature at which amaterial fails after a selected time.3.1.3 thermal index (TI), nthe temperature correspondingto a selected time-to-failure.3.1.4 relative thermal index (RTI), nthe temperature cor-responding to a selected time-to-failure when compare
8、d withthat of a control with proven thermal endurance characteristics.3.1.4.1 DiscussionThe TI and RTI are considered to be themaximum temperature below which the material resistschanges in its properties over a selected period of time. In theabsence of comparison data for a control material, a ther
9、malendurance (time-to-failure) of 60 000 h has been arbitrarilyselected for measuring TI and RTI.3.1.5 thermal endurance, nthe time-to-failure correspond-ing to a selected temperature. Also known as thermal lifetimeor time-to-failure.4. Summary of Practice4.1 The Arrhenius activation energy obtained
10、 from otherTest Methods (such as Test Methods E1641 and E2958, etc.) isused to construct the thermal endurance curve of an organicmaterial from which an estimate of lifetime at selected tem-peratures may be obtained.5. Significance and Use5.1 Thermogravimetry provides a rapid method for thedetermina
11、tion of the temperature-decomposition profile of amaterial.5.2 This practice is useful for quality control, specificationacceptance, and research.5.3 This test method is intended to provide an acceleratedthermal endurance estimation in a fraction of the time requirefor oven-aging tests. The primary
12、product of this test method isthe thermal index (temperature) for a selected estimatedthermal endurance (time) as derived from material decompo-sition.5.4 Alternatively, the estimated thermal endurance (time) ofa material may be estimated from a selected thermal index(temperature).5.5 Additionally,
13、the estimated thermal endurance of amaterial at selected failure time and temperature may be1This practice is under the jurisdiction of Committee E37 on Thermal Measure-ments and is the direct responsibility of Subcommittee E37.10 on Fundamental,Statistical and Mechanical Properties.Current edition
14、approved March 1, 2015. Published March 2015. Originallyapproved in 1997. Last previous edition approved in 2013 as E1877 13. DOI:10.1520/E1877-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandard
15、s 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 States1estimated when compared to a reference value for thermalendurance and thermal index obtained from el
16、ectrical ormechanical oven aging tests.5.6 This practice shall not be used for product lifetimepredications unless a correlation between test results and actuallifetime has been demonstrated. In many cases, multiplemechanisms occur during the decomposition of a material,with one mechanism dominating
17、 over one temperature range,and a different mechanism dominating in a different tempera-ture range. Users of this practice are cautioned to demonstratefor their system that any temperature extrapolations are tech-nically sound.6. Calculation6.1 The following values are used to calculate thermalendur
18、ance, estimated thermal life and failure temperature.6.1.1 The following definitions apply to 6.1 6.4:6.1.1.1 E = Arrhenius activation energy (J/mol),NOTE 1E may be obtained from another methods (such as TestMethods E1641 and E2958, etc.).6.1.1.2 R = universal gas constant (= 8.31451 J/(mol K),6.1.1
19、.3 = heating rate (K/min),NOTE 2 may obtained from Test Method E2550 and is typically 5K/min.6.1.1.4 TI = thermal index (K),6.1.1.5 a = Doyle approximation integral (taken from Table1),6.1.1.6 = constant conversion failure criterion,6.1.1.7 tf= estimated thermal endurance (thermal life) for aconstan
20、t conversion () taken as the failure criterion (min),6.1.1.8 Tc= failure temperature taken as temperature for thepoint of constant conversion for (K) obtained from TestMethod E2550,6.1.1.9 RTI = Relative Thermal Index (K),6.1.1.10 = standard deviation in activation energy (J/mol)obtained from Test M
21、ethods E1641 and E2958, etc.,NOTE 3The precision of the calculation in this practice are exponen-tially dependent on the uncertainty of activation energy value used. Careshould be taken to use only the most precise values of E.6.1.1.11 TI = thermal index (K),6.1.1.12 TI = standard deviation of the t
22、hermal index (K),6.1.1.13 RTI = standard deviation of the relative thermalindex (K),6.1.1.14 tf= standard deviation of the thermal endurance(min),6.1.1.15 tr= reference value for thermal endurance (min),and6.1.1.16 Tr= reference value for thermal index (K).6.2 Method 1 Thermal Index:6.2.1 Using the
23、activation energy (E) and failure tempera-ture (Tc), determine the value for E/RTc.6.2.2 Using the value of E/RTc, determine the value for theDoyle approximation intergral (a) by interpolation in Table 1.6.2.3 Select the thermal endurance (tf) and calculate itslogarithm.6.2.4 Substitute the values f
24、or E, R, log(tf), log(E/RTc) anda into Eq 1 to obtain the thermal index (TI) (3).3TI 5 E2.303 R log tf! 2 log$E R % 1a#! (1)6.2.5 Determine the relative standard deviation (TI/TI)using Eq 2.TITI1.2EE (2)6.2.6 Report the thermal index (TI) and its relative standarddeviation (TI/TI) along with the the
25、rmal endurance (tf).6.3 Method B Thermal Endurance Curve:3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.TABLE 1 Numerical Integration Constants (1, 2)3E/RT a8 5.36999 5.898010 6.415711 6.927612 7.432713 7.932314 8.427315 8.918216 9.405617 9.890018 10.37
26、1619 10.850720 11.327721 11.802622 12.275723 12.747124 13.217025 13.685526 14.152727 14.618728 15.083629 15.547430 16.010331 16.472232 16.933333 17.393634 17.853235 18.312036 18.770137 19.227638 19.684539 20.140840 20.596641 21.051942 21.506643 21.960944 22.414845 22.868246 23.321247 23.773848 24.22
27、6049 24.677950 25.129451 25.580652 26.031453 26.482054 26.932355 27.382356 27.831957 28.281458 28.730559 29.179460 29.6281E1877 1526.3.1 Arbitrarily select two or three temperatures in theregion of interest and calculate the corresponding logarithm ofthe thermal endurance (logtf) values at each temp
28、eratureusing Eq 3.logtf# 5 E2.303 RT!1logE R !# 2 a# (3)6.3.2 Prepare a display of logarithm of thermal enduranceon the ordinate versus the reciprocal of absolute temperature onthe abscissa (see Fig. 1).6.3.3 Alternative thermal indexes (TI) and associated loga-rithm of thermal endurance (logtf may
29、be estimated from thisdisplay.6.3.4 The standard deviation in the thermal endurance (tf)may be estimated using Eq 4.tftf5 1 2 0.052 E RT! 3 E E! (4)6.4 Method C Relative Thermal Index:6.4.1 Relative Thermal Index may be determined from theactivation energy determined by thermogravimetry and thetherm
30、al index obtained by some other method (such aselectrical or mechanical tests) using Eq 5.RTI 5 ERln tf# 2 lntr#1ERTr!# (5)6.4.2 The relative standard deviation of the relative thermalindex (RTI/RTI) is estimate from Eq 6 where the referencevalues of thermal endurance (tr) and corresponding referenc
31、etemperature (Tr) are considered to be exact.RTIRTI 5 1.4EE (6)7. Report7.1 Report the following information:7.1.1 The value, standard deviation (or relative standarddeviation), and source for each value used in the determination;7.1.2 Designation of the material under test, including thename of the
32、 manufacturer, the lot number, and supposedchemical composition when known; and7.1.3 The calculated thermal index (TI) and its relativestandard deviation (TI/TI) or relative thermal index (RTI) andits relative standard deviation (RTI/RTI) along with theidentified thermal endurance.7.1.3.1 ExampleTI
33、(60 000 hr) = 453 6 6 K (180 6 6C)7.1.4 The specific dated version of this practice that is used.8. Precision and Bias48.1 The precision and bias of these calculations depend onthe precision and bias of the kinetic data used in them. Toprovide an example of the precision expected, thermal indexwas c
34、alculated by the procedure in this practice using data forpoly(tetrafluoroethylene) from the interlaboratory study con-ducted to develop the precision and bias statement for TestMethod E1641. Extreme values of thermal life were calculatedusing an arbitrarily chosen value for temperature of 600 K and
35、the extreme values of E corresponding to the 95 % confidencelevel from that interlaboratory study. The resulting calculatedextreme values were 9 years and 3700 years for this material.9. Keywords9.1 Arrhenius activation energy; Arrhenius pre-exponentialfactor; kinetic parameters; relative thermal in
36、dex; thermaldecomposition; thermal endurance; thermal life; thermogravi-metric analysis4Supporting data have been filed at ASTM International Headquarters and maybe obtained by requesting Research Report RR:E37-1024. ContactASTM CustomerService at serviceastm.org.E1877 153FIG.1ThermalEnduranceCurveE
37、1877 154APPENDIX(Nonmandatory Information)X1. EXAMPLE CALCULATIONSX1.1 Example Calculations for the Values Determined inThis StandardX1.1.1 Example data obtained from Test Method E1641includes:X1.1.1.1 E = 320 kJ/mol = 320 000 J/molX1.1.1.2 E = 24 kJ/mol = 24 000 J/molX1.1.1.3 R = 8.31451 J/(mol K)X
38、1.1.1.4 = 5.0 K/minX1.1.2 Example data obtained from Test Method E2550includes:X1.1.2.1 Tc= 783 KX1.1.2.2 Tc=6KX1.1.3 Arbitrarily selected:X1.1.3.1 tf= 60 000 hr = 3 600 000 min = 6.8 yrX1.1.3.2 Tr= 683 KX1.1.3.3 tr= 100 000 hr = 6 000 000 min = 11 yrX1.2 Example Calculations for Thermal Index (TI)X
39、1.2.1 Determine the value for E/RT from values inX1.1.1.1, X1.1.1.3, and X1.1.2.1:ERT 5 320 000 J mol!8.31451 J/ mol K! 3783 K#5 49.1532X1.2.2 Using the value of E/RT from X1.2.1, determine thevalue for a by interpolation in Table 1:a 5 24.7471X1.2.3 Substitute values from X1.1.1.1, X1.1.1.3, X1.1.1
40、.4,X1.1.3.1, and X1.2.2 into Eq 1:TI 5 E2.303 R $log tf# 2 logE R !#1a%!5 $320 000 J mol 2.303 3 8.314 J mol K!%$log 3.6 3 106min#2log320 000 J mol 8.31451 J mol K! 35 Kmin#224.74715 $16 712 K%$6.5563 2 log 7697.39 min# 2 24.7471%5 16 712 K$6.5563 2 3.8863 2 24.7471%5 16 712 K27.4171TI 5 609.5 K 5 3
41、36.3 CX1.3 Example Calculation for the Imprecision in Ther-mal IndexX1.3.1 Substituting values from X1.1.1.2 and X1.1.1.3 intoEq 2:TI 51.2 EE51.2 324 000 Jmol320 000 Jmol50.090X1.4 Example Calculation for Thermal EnduranceX1.4.1 Substituting the values from X1.1.1.1, X1.1.1.3,X1.1.1.4, X1.1.3.2, and
42、 X1.2.2 into Eq 3:logtf# 5 E2.303 RT#1logE R # 2 a5 320 000 Jmol2.303 3 683 K!1log320 000 J mol 8.31451 J mol K!#224.7471 35 Kmin5 24.46801log7697.39# 2 24.74715 24.468013.8863 2 24.7471logtf# 5 3.6072tf5 4048 min 3 hr/60 min! 5 67.46 hrX1.5 Example Calculation of the Imprecision in ThermalEndurance
43、 (tf)X1.5.1 Substituting value from X1.1.1.1, X1.1.1.2,X1.1.1.3, X1.1.3.2, and X1.2.2 into Eq 4:tftf5 1 1 0.052 E RT! 3 EE5 1 1 0.052 3 320 000 J mol!8.31451 J mol K 3 683 K!324 000 Jmol320 000 Jmol5 1 1 2.930! 30.0755 3.930 30.0755 0.29X1.6 Example Calculation of Relative Thermal IndexX1.6.1 Substi
44、tuting values from X1.1.1.1, X1.1.1.3,X1.1.3.1, X1.1.3.2, and X1.1.3.3 into Eq 5:RTI 5 ER$ln tf# 2 lntr#1ERTr#%5 320 00 Jmol 8.31451JmolK$ln 3 600 000 min#2ln6 000 000 min#1320 000 Jmol K8.31451 J mol K 3 683 K!5 38 487 K15.0964 2 15.6073 1 56.3706!5 38 487 K55.85975 689 KX1.7 Example Calculation of
45、 the Standard Deviation ofRelative Thermal IndexX1.7.1 Substituting values from X1.1.1.1 and X1.1.1.2 intoEq 6:RTIRTI 51.4 324 000 Jmol320 000 Jmol50.105E1877 155REFERENCES(1) Toop, D. J., “Theory of Life Testing and Use of ThermogravimetricAnalysis to Predict the Thermal Life of Wire Enamels,” IEEE
46、Transactions on Electrical Insulation, Vol EI-6, No. 1, 1971, pp. 214.(2) Flynn, J. H., “The Isoconversional Method for Determination ofEnergy of Activation at Constant Rates Corrections for the DoyleApproximation,” Journal of Thermal Analysis, Vol 27, 1983, pp.95102.(3) Krizanovsky, L., and Mentlik
47、, V., “The Use of Thermal Analysis toPredict the Thermal Life of Organic Electrical Insulating Materials,”Journal of Thermal Analysis, Vol 13, 1978, pp. 571580.ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this stan
48、dard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be revie
49、wed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your commen
