1、Designation: E1877 15E1877 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
2、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 practice describes the determination of thermal endurance, thermal index, and relati
3、ve thermal index for organicmaterials using the Arrhenius activation energy generated by thermogravimetry.1.2 This practice is generally applicable to materials with a well-defined thermal decomposition profile, namely a smooth,continuous mass change.1.3 The values stated in SI units are to be regar
4、ded as standard. No other units of measurement are included in this standard.1.4 There is no ISO standard equivalent to this practice.1.5 This standard 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 est
5、ablish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.1.6 This international standard was developed in accordance with internationally recognized principles on standardizationestablished in the Decision on Principles for the Development
6、of International Standards, Guides and Recommendations issuedby the World Trade Organization Technical Barriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E1641 Test Method for Decomposition Kinetics by Thermogravimetry Using the Ozawa/Flynn/Wall MethodE2550 Test Method for
7、Thermal Stability by Thermogravimetry1 This practice is under the jurisdiction of Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.10 on Fundamental, Statisticaland Mechanical Properties.Current edition approved March 1, 2015May 1, 2017. Published March 2015
8、June 2017. Originally approved in 1997. Last previous edition approved in 20132015 asE1877 13.E1877 15. DOI: 10.1520/E1877-15.10.1520/E1877-17.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvol
9、ume information, refer to the standards Document Summary page on the ASTM website.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. Becauseit may not be technically possible to adeq
10、uately 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 appears at the end of this standardCopyright ASTM
11、International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1E2958 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, me
12、chanical, electrical or other property of sufficient magnitude to makeit unsuitable for a particular use.3.1.2 failure temperature (Tf), nthe temperature at which a material fails after a selected time.3.1.3 thermal index (TI), nthe temperature corresponding to a selected time-to-failure.3.1.4 relat
13、ive thermal index (RTI), nthe temperature corresponding to a selected time-to-failure when compared with that ofa control with proven thermal endurance characteristics.3.1.4.1 DiscussionThe TI and RTI are considered to be the maximum temperature below which the material resists changes in its proper
14、ties over aselected period of time. In the absence of comparison data for a control material, a thermal endurance (time-to-failure) of 60 000 hhas been arbitrarily selected for measuring TI and RTI.3.1.5 thermal endurance, nthe time-to-failure corresponding to a selected temperature. Also known as t
15、hermal lifetime ortime-to-failure.4. Summary of Practice4.1 The Arrhenius activation energy obtained from other Test Methods (such as Test Methods E1641 and E2958, etc.) is usedto construct the thermal endurance curve of an organic material from which an estimate of lifetime at selected temperatures
16、 maybe obtained.5. Significance and Use5.1 Thermogravimetry provides a rapid method for the determination of the temperature-decomposition profile of a material.5.2 This practice is useful for quality control, specification acceptance, and research.5.3 This test method is intended to provide an acce
17、lerated thermal endurance estimation in a fraction of the time require foroven-aging tests. The primary product of this test method is the thermal index (temperature) for a selected estimated thermalendurance (time) as derived from material decomposition.5.4 Alternatively, the estimated thermal endu
18、rance (time) of a material may be estimated from a selected thermal index(temperature).5.5 Additionally, the estimated thermal endurance of a material at selected failure time and temperature may be estimated whencompared to a reference value for thermal endurance and thermal index obtained from ele
19、ctrical or mechanical oven aging tests.5.6 This practice shall not be used for product lifetime predications unless a correlation between test results and actual lifetimehas been demonstrated. In many cases, multiple mechanisms occur during the decomposition of a material, with one mechanismdominati
20、ng over one temperature range, and a different mechanism dominating in a different temperature range. Users of thispractice are cautioned to demonstrate for their system that any temperature extrapolations are technically sound.6. Calculation6.1 The following values are used to calculate thermal end
21、urance, 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 Test Methods E1641 and E2958, etc.).6.1.1.2 R = universal gas constant (= 8.31451 J/(mol K),6.
22、1.1.3 = heating rate (K/min),NOTE 2 may be obtained from Test Method E2550 and is typically 5 K/min.6.1.1.4 TI = thermal index (K),6.1.1.5 a = Doyle approximation integral (taken from Table 1),6.1.1.6 = constant conversion failure criterion,6.1.1.5 tf = estimated thermal endurance (thermal life) for
23、 a constant conversion () taken as the failure criterion (min),6.1.1.6 Tc = failure temperature taken as temperature for the point of constant conversion for (K) obtained from TestMethodMethods E2550 or E2958,6.1.1.7 RTI = Relative Thermal Index (K),E1877 1726.1.1.8 E = standard deviation in activat
24、ion energy (J/mol) obtained from Test Methods E1641 and E2958, etc.,NOTE 3The precision of the calculation in this practice are exponentially dependent on the uncertainty of activation energy value used. Care shouldbe taken to use only the most precise values of E.6.1.1.9 TI = thermal index (K),6.1.
25、1.10 TI = standard deviation of the thermal index (K),6.1.1.11 RTI = standard deviation of the relative thermal index (K),6.1.1.12 tf = 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).
26、6.2 Method 1 Thermal Index:6.2.1 Using the activation energy (E) and failure temperature (Tc), determine the value for E/RTc.6.2.2 Using the value of E/RTc, determine the value for the Doyle approximation intergral (aTI) by interpolation using Eq 1 inTable 1.6.2.3 Select the thermal endurance (tf) a
27、nd calculate its logarithm.6.2.4 Substitute the values for E,R, log(tf), log(, E/RTc) and a into Eq 1 to obtain the thermal index (TI) (31).3TI 5 E$2.303 R log tf ! 2 log$E R % 1a#% (1)TI 5$E 2.303 R!% $log 100.4 tf R E#10.463 E R Tc% (1)6.2.5 Determine the relative standard deviation (TI/TI) using
28、Eq 2.TITI1.2EE (2)TI TI60.19 EE (2)6.2.6 Report the thermal index (TI) and its relative standard deviation (TI/TI) along with the thermal endurance (tf).6.3 Method B Thermal Endurance Curve:6.3.1 Arbitrarily select two or three temperatures in the region of interest and calculate the corresponding l
29、ogarithm of thethermal endurance (logtf) values at each temperature using Eq 3.logtf# 5E2.303 R T!1logE R !# 2a! (3)logtf# 5E 2.303 R Tc!1logE 100.4 R # 20.463 E RTc (3)6.3.2 Prepare a display of logarithm of thermal endurance on the ordinate versus the reciprocal of absolute temperature on theabsci
30、ssa (see Fig. 1).6.3.3 Alternative thermal indexes (TI) and associated logarithm of thermal endurance (logtf may be estimated from thisdisplay.6.3.4 The standard deviation in the thermal endurance (tf) may be estimated using Eq 4.tftf 51 2 0.052 E R T! 3 E E! (4)logtf# logtf#6E E (4)6.3.5 From the l
31、aw of propagation of uncertainties (2):tf tf 52.303 logtf# E E (5)6.4 Method C Relative Thermal Index:6.4.1 Relative Thermal Index may be determined from the activation energy determined by thermogravimetry and the thermalindex obtained by some other method (such as electrical or mechanical tests) u
32、sing Eq 56.RTI 5ERln tf# 2lntr#1ER Tr!# (6)RTI 5E Rln tf# 2lntr#1E R Tr!# (6)6.4.2 The relative standard deviation of the relative thermal index (RTI/RTI) is estimate from Eq 6 where the reference valuesof thermal endurance (tr) and corresponding reference temperature (Tr) are considered to be exact
33、.RTIRTI 51.4EE (6)7. Report7.1 Report the following information:7.1.1 The value, standard deviation (or relative standard deviation), and source for each value used in the determination;7.1.2 Designation of the material under test, including the name of the manufacturer, the lot number, and supposed
34、 chemicalcomposition when known; and3 The boldface numbers in parentheses refer to a list of references at the end of this standard.E1877 173FIG. 1 Thermal Endurance CurveE18771747.1.3 The calculated thermal index (TI) and its relative standard deviation (TI/TI) or relative thermal index (RTI) and i
35、tsrelative standard deviation (RTI/RTI) along with the identified thermal endurance.7.1.3.1 ExampleExample:TI60 000 hr!545366K180 66C!TI (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 calculat
36、ions depend on the precision and bias of the kinetic data used in them. To providean example of the precision expected, thermal index was calculated by the procedure in this practice using data forpoly(tetrafluoroethylene) from the interlaboratory study conducted to develop the precision and bias st
37、atement for Test MethodE1641. Extreme values of thermal life were calculated using an arbitrarily chosen value for temperature of 600 K and the extremevalues of E corresponding to the 95 % confidence level from that interlaboratory study. The resulting calculated extreme valueswere 9 years and 3700
38、years for this material.9. Keywords9.1 Arrhenius activation energy; Arrhenius pre-exponential factor; kinetic parameters; relative thermal index; thermaldecomposition; thermal endurance; thermal life; thermogravimetric analysisAPPENDIX(Nonmandatory Information)X1. EXAMPLE CALCULATIONSX1.1 Example Ca
39、lculations for the Values Determined in This StandardX1.1.1 Example data obtained from Test Method E1641 includes: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)X1.1.1.4 = 5.0 K/minX1.1.2 Example data obtained from Test Method E2550 includes
40、:X1.1.2.1 Tc = 783 KX1.1.2.2 Tc = 6 KX1.1.3 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 yr4 Supporting data have been filed at ASTM International Headquarters and may be obtained by requesting Research Report R
41、R:E37-1024. Contact ASTM CustomerService at serviceastm.org.E1877 175X1.2 Example Calculations for Thermal Index (TI)X1.2.1 Determine the value for E/RT from values in X1.1.1.1, X1.1.1.3, and X1.1.2.1:ERT 5320 000 Jmol!8.31451 J/ mol K!3783 K#549.1532E RT 5320 000 Jmol!8.31451 Jmol K!783 K#549.1532X
42、1.2.2 Using the value of E/RT from X1.2.1, determine the value for a by interpolation in Table 1:a 524.7471X1.2.2 Substitute values from X1.1.1.1, X1.1.1.3, X1.1.1.4, X1.1.3.1, and X1.2.2X1.2.1 into Eq 1:TI 5 E2.303 R $log tf# 2logE R !#1a%!5 $320 000 Jmol 2.303 3 8.314 Jmol K!%$log 3.6 3 106 min#2l
43、og320 000 Jmol 8.31451 Jmol K!35 Kmin#224.74715 $16 712 K%$6.5563 2 log 7697.39 min#224.7471%5 16 712 K$6.5563 2 3.8863 2 24.7471%5 16 712 K27.4171TI 5 609.5 K5336.3 CTI 5 hE 2.303 Rjhlog f100.4 tf R Eg10.463ERTj5 h320 000 J mol21 2.303 3 8.314 J mol21 K21jhlog f100.4 3 3 600 00 min 3 5 K min21 3 8.
44、314 J mol21 K21 320 000 J mol21g10.463349.1532j5 h16 713 Kjhlog f46 953g122.758j5 h16 713 Kjh4.672122.758j5 h16 713 Kjh27.430j5 609.3 K5.336.1CX1.3 Example Calculation for the Imprecision in Thermal IndexX1.3.1 Substituting values from X1.1.1.2X1.1.1.1 and X1.1.1.3X1.1.1.2 into Eq 2:TI 51.2 EE51.232
45、4 000 Jmol320 000 Jmol50.090TITI 560.19 EE50.19324 000 Jmol21320 000 Jmol2150.014Expressing as a percent:5 0.0143100%5 61.4%E1877 176X1.4 Example Calculation for Thermal EnduranceX1.4.1 Substituting the values from X1.1.1.1, X1.1.1.3, X1.1.1.4, X1.1.3.2, and X1.2.2X1.2.1 into Eq 3:logftfg 5 sE 2.303
46、 R Td1logfE 100.4 R g 20.463 ERT5 s320 000 J mol21 2.303 3 8.314 J mol21 K21 3 683 Kd1logf320 000 J mol21 100.4 3 8.314 J mol21 K21 3 5 K mol21g20.463349.15325 24.4701logf76.672g222.7585 24.47011.885222.7585 3.597Taking the antilog:logtf# 5 E2.303 R T#1logE R # 2a5 320 000 Jmol2.303 3 683 K!1log320
47、000 Jmol 8.31451 Jmol K!#224.747135Kmin5 24.46801log7697.39#224.74715 24.468013.8863224.7471logtf# 5 3.6072tf 5 4048 min3hr/60 min!567.46 hrtf 53954 min3hr 60 min!566 hrX1.5 Example Calculation of the Imprecision in Thermal Endurance (tf)X1.5.1 Substituting value from X1.1.1.1, X1.1.1.2, X1.1.1.3, X
48、1.1.3.2, and X1.2.2X1.2.1 into Eq 4:tftf 5 110.052 E R T! 3EE5 110.052 3 320 000 Jmol!8.31451 Jmol K 3 683 K!324 000 Jmol320 000 Jmol5 112.930!30.0755 3.93030.0755 0.29logtf#logtf# 6EE 24 kJ mol21320 kJ mol21 60.075E1877 177X1.5.2 From Eq 5:tftf 5 2.303 logtf#3EE5 2.30333.596324 kJmol320 kJmol5 0.62Expressing as percent:5 0.623100 %5 662 %X1.6 Example Calculation of Relative Thermal IndexX1.6.1 Substituting values from X1.1.1.1, X1.1.1.3, X1.1.3.1, X1.1.3.2, and X1.1.3.3 into Eq 56:RTI 5 ER$ln tf# 2lntr#1ERTr#%5 320 00 Jmol 8.31451JmolK$ln 3 600 000 min#2ln6 000 000 min#1320 000 Jmol K8.31451
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