Designation: E1877 − 17Standard 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, 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*1.1 This practice describes the determination of thermalendurance, thermal index, and relative thermal index 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. 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 safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.6 This international standard was developed in accor-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 Standards:2E1641 Test Method for Decomposition Kinetics by Thermo-gravimetry Using the Ozawa/Flynn/Wall MethodE2550 Test Method for Thermal Stability by Thermogravi-metryE2958 Test Methods for Kinetic Parameters by Factor Jump/Modulated Thermogravimetry3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 failure, n—change in some chemical, physical,mechanical, electrical or other property of sufficient magnitudeto make it unsuitable for a particular use.3.1.2 failure temperature (Tf), n—the temperature at which amaterial fails after a selected time.3.1.3 thermal index (TI), n—the temperature correspondingto a selected time-to-failure.3.1.4 relative thermal index (RTI), n—the temperature cor-responding to a selected time-to-failure when compared withthat of a control with proven thermal endurance characteristics.3.1.4.1 Discussion—The 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 thermalendurance (time-to-failure) of 60 000 h has been arbitrarilyselected for measuring TI and RTI.3.1.5 thermal endurance, n—the 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 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 thedetermination 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 product of this test method is1This 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 approved May 1, 2017. Published June 2017. Originallyapproved in 1997. Last previous edition approved in 2015 as E1877 – 15. DOI:10.1520/E1877-17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis 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 Trade (TBT) Committee.1the 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, the estimated thermal endurance of amaterial at selected failure time and temperature may beestimated when compared to a reference value for thermalendurance and thermal index obtained from electrical 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 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 thermalendurance, 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 1—E 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)),6.1.1.3 β = heating rate (K/min),NOTE 2—β may be obtained from Test Method E2550 and is typically5 K/min.6.1.1.4 TI = thermal index (K),6.1.1.5 tf= estimated thermal endurance (thermal life) for aconstant conversion (α) taken as the failure criterion (min),6.1.1.6 Tc= failure temperature taken as temperature for thepoint of constant conversion for β (K) obtained from TestMethods E2550 or E2958,6.1.1.7 RTI = Relative Thermal Index (K),6.1.1.8 σE = standard deviation in activation energy (J/mol)obtained from Test Methods E1641 and E2958, etc.,NOTE 3—The 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.6.1.1.9 TI = thermal index (K),6.1.1.10 σTI = standard deviation of the thermal index (K),6.1.1.11 σRTI = standard deviation of the relative thermalindex (K),6.1.1.12 σtf= standard deviation of the thermal endurance(min),6.1.1.13 tr= reference value for thermal endurance (min),and6.1.1.14 Tr= reference value for thermal index (K).6.2 Method 1 – Thermal Index:6.2.1 Using the 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 TIusing Eq 1.6.2.3 Select the thermal endurance (tf) and calculate itslogarithm.6.2.4 Substitute the values for E, R, tf, and β into Eq 1 toobtain the thermal index (TI) (1).3TI 5 $E ⁄ ~2.303 R!% ⁄ $log @100.4 tfβ R ⁄ E#10.463 E ⁄ RTc% (1)6.2.5 Determine the relative standard deviation (σTI/TI)using Eq 2.σTI ⁄ TI 60.19 σE⁄E (2)6.2.6 Report the thermal index (TI) and its relative standarddeviation (σTI/TI) along with the thermal endurance (tf).6.3 Method B – Thermal Endurance Curve:6.3.1 Arbitrarily select two or three temperatures in theregion of interest and calculate the corresponding logarithm ofthe thermal endurance (log[tf]) values at each temperatureusing Eq

[email protected]# 5 ~E ⁄ 2.303

[email protected] ⁄ 100.4 R β# 2 0.463 E ⁄ RTc(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 (log[tf] may be estimated from thisdisplay.6.3.4 The standard deviation in the thermal endurance (tf)may be estimated using Eq 4.σ

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[email protected]# 6σE ⁄ E (4)6.3.5 From the law of propagation of uncertainties (2):σtf⁄ tf5 2.303

[email protected]# σE ⁄ E (5)6.4 Method C – Relative Thermal Index:6.4.1 Relative Thermal Index may be determined from theactivation energy determined by thermogravimetry and thethermal index obtained by some other method (such aselectrical or mechanical tests) using Eq 6.RTI 5 E ⁄

[email protected] @tf# 2

[email protected]#1E ⁄ ~RTr!# (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 manufacturer, the lot number, and supposedchemical composition when known; and7.1.3 The calculated thermal index (TI) and its relativestandard deviation (σTI/TI) or relative thermal index (RTI) andits relative standard deviation (σRTI/RTI) along with theidentified thermal endurance.7.1.3.1 Example:TI~60 000 hr! 5 45366K~180 6 6 ° C!7.1.4 The specific dated version of this practice that is used.3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.E1877 − 172FIG.1ThermalEnduranceCurveE1877 − 1738. 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 calculated 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 andthe 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 index; thermaldecomposition; thermal endurance; thermal life; thermogravi-metric analysisAPPENDIX(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 σE = 24 kJ/mol = 24 000 J/molX1.1.1.3 R = 8.31451 J/(mol K)X1.1.1.4 β = 5.0 K/minX1.1.2 Example data obtained from Test Method E2550includes:X1.1.2.1 Tc= 783 KX1.1.2.2 σTc=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)X1.2.1 Determine the value for E/RT from values inX1.1.1.1, X1.1.1.3, and X1.1.2.1:E ⁄ RT 5 ~320 000 J ⁄ mol! ⁄ @8.31451 J ⁄ ~mol K!783 K# 5 49.1532X1.2.2 Substitute values from X1.1.1.1, X1.1.1.3, X1.1.1.4,X1.1.3.1, and X1.2.1 into Eq 1:TI 5 hE ⁄ 2.303 Rj⁄hlog f100.4 tfβ R ⁄ Eg10.463E⁄RTj5 h320 000 J mol21⁄ 2.303 3 8.314 J mol21K21j⁄hlog f100.4 3 3 600 00 min 3 5Kmin213 8.314 J mol21K21⁄ 320 000 J mol21g10.463349.1532j5 h16 713 Kj⁄hlog f46 953g122.758j5 h16 713 Kj⁄h4.672 1 22.758j5 h16 713 Kj⁄h27.430j5 609.3 K 5.336.1°CX1.3 Example Calculation for the Imprecision in Ther-mal IndexX1.3.1 Substituting values from X1.1.1.1 and X1.1.1.2 intoEq 2:σTI⁄TI 560.19 σE⁄E50.19 324 000 J⁄mol21⁄320 000 J⁄mol2150.014Expressing as a percent:5 0.014 3100%561.4%X1.4 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 X1.2.1 into Eq 3:logftfg 5 sE ⁄ 2.303 RTd1logfE ⁄ 100.4 R βg 2 0.463 E⁄RT5 s320 000 J mol21⁄ 2.303 3 8.314 J mol21K213 683 Kd1logf320 000 J mol21⁄ 100.4 3 8.314 J mol21K213 5 K mol21g20.463349.15325 24.4701logf76.672g 2 22.7585 24.47011.8852 22.7585 3.5974Supporting data have been filed at ASTM International Headquarters and maybe obtained by requesting Research Report RR:E37-1024. ContactASTM CustomerService at

[email protected] − 174Taking the antilog:tf5 3954 min 3 ~hr ⁄ 60 min! 5 66 hrX1.5 Example Calculation of the Imprecision in ThermalEndurance (tf)X1.5.1 Substituting value from X1.1.1.1, X1.1.1.2,X1.1.1.3, X1.1.3.2, and X1.2.1 into Eq 4:σ

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[email protected]# 6σE⁄E 24 kJ mol21⁄320 kJ mol21 60.075X1.5.2 From Eq 5:σtf⁄tf5 2.303

[email protected]#3σE⁄E5 2.303 33.596 324 kJ⁄mol⁄320 kJ⁄mol5 0.62Expressing as percent:5 0.62 3100 %5662 %X1.6 Example Calculation of Relative Thermal IndexX1.6.1 Substituting 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 6:RTI 5 E⁄Rhfln ftfg 2 lnftrg1E⁄RTrgj5 320 00 J⁄mol⁄8.31451 J⁄mol Khln f3 600 000 ming 2 lnf6 000 000 ming1320 000 J⁄mol K⁄s8.31451 J ⁄ mol K 3 683 Kdj5 38 487 K⁄s15.0964 2 15.6073 1 56.3706d5 38 487 K⁄55.85975 689 KREFERENCES(1) Krizanovsky, L., and Mentlik, V., “The Use of Thermal Analysis toPredict the Thermal Life of Organic Electrical Insulating Materials,”Journal of Thermal Analysis, Vol 13, 1978, pp. 571–580.(2) Skoog, D. A., West, D. M., Holler, F. J., Crouch, S. R., Fundamentalsof Analytical Chemistry, Thompson Brooks/Cole, 8th ed, 2004, pp.127–133.(3) Xu, J. J., and Kaminski, C. A., “Temperature Index of ElectricalInsulations by mTGA,” Journal of Testing and Evaluation, Vol 42,2014, pp. 1366–1376.(4) Toop, D. J., “Theory of Life Testing and Use of ThermogravimetricAnalysis to Predict the Thermal Life of Wire Enamels,” IEEETransactions on Electrical Insulation, Vol EI-6, No. 1, 1971, pp. 2–14.(5) 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.95–102.SUMMARY OF CHANGESCommittee E37 has identified the location of selected changes to this standard since the last issue (E1877 – 15)that may impact the use of this standard. (Approved May 1, 2017.)(1) Section 6.1.1.5 – replace table 1 with the Xu approximation(3).(2) Section 6.2.4 – replace Eq. 1 with Xu approximation (3).(3) Section 6.2.5 – Revise Eq. 2(4) Section 6.3.1 – Revise Eq. 3(5) Section 6.3.5 – Revise Eq. 4(6) Section 6.4.2 – Delete this section(7) Appendix X1 – Revise example calculations to reflectchanges in the body of the standard.ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. 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 respons