ASTM E1877-21

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Designation: E1877 − 17 E1877 − 21
Standard Practice for
Calculating Thermal Endurance of Materials from
Thermogravimetric Decomposition Data
This standard is issued under the fixed designation E1877; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
1.1 This practice describes the determination of thermal endurance, thermal index, and relative thermal index for organic materials
using the Arrhenius activation energy generated for thermal decomposition measured by thermogravimetry.
1.2 This practice is generally applicable to materials with a well-defined thermal decomposition profile, profile upon heating,
namely a smooth, continuous mass change.
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.4 There is no ISO standard equivalent to this practice.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
D3045 Practice for Heat Aging of Plastics Without Load
E1641 Test Method for Decomposition Kinetics by Thermogravimetry Using the Ozawa/Flynn/Wall Method
E2550 Test Method for Thermal Stability by Thermogravimetry
This practice is under the jurisdiction of Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.10 on Fundamental, Statistical
and Mechanical Properties.
Current edition approved May 1, 2017March 1, 2021. Published June 2017May 2021. Originally approved in 1997. Last previous edition approved in 20152017 as
E1877 – 15.E1877 – 17. DOI: 10.1520/E1877-17.10.1520/E1877-21.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1877 − 21
E2958 Test Methods for Kinetic Parameters by Factor Jump/Modulated Thermogravimetry
3. Terminology
3.1 Definitions of Terms Specific to This Standard:
3.1.1 failure, n—change in some chemical, physical, mechanical, electrical or other property of sufficient magnitude to make it
unsuitable for a particular use.
3.1.2 failure temperature (T(Tf), ), n—the absolute temperature at which a material fails after a selected time.
f
3.1.3 thermal index (TI), n—the absolute temperature corresponding to a selected time-to-failure.thermal endurance value.
3.1.4 relative thermal index (RTI), n—the temperature corresponding to a selected time-to-failure when compared with that of a
control with proven thermal endurance characteristics.
3.1.4.1 Discussion—
The TI and RTI are considered to be the maximum temperature below which the material resists changes in its properties over a
selected period of time. In the absence of comparison data for a control material, a thermal endurance (time-to-failure) of 60 000 h
has been arbitrarily selected for measuring specific time period. TI and RTI.
3.1.4.2 Discussion—
In the absence of other comparison data for a control material, a thermal endurance (time-to-failure) of 20 000 h is arbitrarily
selected for measuring TI and RTI.
3.1.5 thermal endurance, endurance (tf), n—the time-to-failure corresponding to a selected temperature. Also known as thermal
lifetime or time-to-failure.
3.1.5.1 Discussion—
Also known as thermal lifetime or time-to-failure.
4. Summary of Practice
4.1 The Arrhenius activation energy obtained from other Test Methods (such as Test Methods E1641 and E2958, etc.) is used to
construct the thermal endurance curve of an organic material from which an estimate of lifetime at selected temperatures may be
obtained.
5. Significance and Use
5.1 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 practice is intended to provide an accelerated thermal endurance estimation in a fraction of the time require
for oven-aging tests. The primary product of this test method practice is the thermal index (temperature) for a selected estimated
thermal endurance (time) as derived from material decomposition.
5.4 Alternatively, the estimated thermal endurance (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 when
compared to a reference value for thermal endurance and thermal index obtained from electrical 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 lifetime
has been demonstrated. In many cases, multiple mechanisms occur during the decomposition of a material, with one mechanism
dominating over one temperature range, and a different mechanism dominating in a different temperature range. Users of this
practice are cautioned to demonstrate for their system that any temperature extrapolations are technically sound.
E1877 − 21
6. Calculation
6.1 The following values are used to calculate thermal endurance, estimated thermal life and failure temperature.index, and
relative thermal index.
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 anotherother methods (such as Test Methods E1641 and E2958, etc.).).
6.1.1.2 R = universal gas constant (= 8.31451(= 8.314 J/(mol K)),
6.1.1.3 β = heating rate (K/min),
NOTE 2—β 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 ttf = estimated thermal endurance (thermal life) for a constantwith an identified conversion (α) taken as the failure criterion
f
(min),(h),
6.1.1.6 TTf = failure absolute temperature taken as temperature for the point of constant conversion for β (K)(K/min) obtained
c
from Test Methods E2550 or E2958, (K),
6.1.1.7 RTI = Relative Thermal Indexrelative 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 areis exponentially dependent on the uncertainty of activation energy value used. Care should
be taken to use only the most precise values of E.
6.1.1.9 σlog[TItf = thermal index (K),] = standard deviation of the logarithm of thermal endurance with tf in h,
6.1.1.10 σTI = standard deviation of the thermal index (K),
6.1.1.11 σRTI = standard deviation of the relative thermal index (K),
6.1.1.12 σttf = standard deviation of the thermal endurance (min),(h),
f
6.1.1.13 ttr = reference time value for thermal endurance (min),(h), and
r
6.1.1.14 TTr = reference value for thermal index (K).
r
6.2 Method 1A – Thermal Index:
6.2.1 Using the Obtain activation energy (E) and determined previously (for example, see Test Method E1641). Obtain the failure
temperature (TTf ), determine ) from a thermal curve determined at heating rate (β = 300 K/h = 5 K/min) (see Test Method
c
E1641the value for ). Select the thermal endurance (Etf/)RT (typically .20 000 h).
c
6.2.2 Using the value of E/RT , determine the value for TI using Eq 1.
c
6.2.3 Select the thermal endurance (t ) and calculate its logarithm.
f
E1877 − 21
6.2.2 Substitute the values for E,R,ttf, , and β into Eq 1 to obtain the thermal index (TI) (1, 2).
f
TI 5 E ⁄ 2.303 R ⁄ log 100.4 tf β R ⁄ E 10.463 E ⁄ R Tf (1)
$ ~ !% $ @ # %
TI 5 $E ⁄ ~2.303 R!% ⁄ $log @100.4 t β R ⁄ E#10.463 E ⁄ R T % (1)
f c
NOTE 4—See derivation in Appendix X3.
6.2.3 Determine the thermal index relative standard deviation (σTI/TI) using Eq 2.
σTI ⁄ TI 5 σE⁄E (2)
σTI ⁄ TI'60.19 σE⁄E (2)
6.2.4 Report the thermal index (TI) and its relative standard deviation (σTI/TI) along with the and thermal endurance (ttf ).
f
6.3 Method B – Thermal Endurance Curve:
6.3.1 Arbitrarily select two or three temperatures (Tr) in the region of interest and calculate the corresponding logarithm of the
thermal endurance (log[ttf ]) values in hours at each temperature using Eq 3. with β expressed in units of K/h.
f
log tf , h 5 E ⁄ 2.303 R Tr 1log E ⁄ 100.4 R β 2 0.463 E ⁄ RTf (3)
@ # ~ ! @ #
log t 5 E ⁄ 2.303 R T 1log E ⁄ 100.4 R β 2 0.463 E ⁄ RT (3)
@ # ~ ! @ #
f c c
-1
NOTE 5—β shall be in units of K h .
6.3.2 Prepare a display of logarithm of thermal endurance on(log[tf, the ordinate h]) versus the reciprocal of absolute temperature
on(Tr the abscissa ]) (see Fig. 1).
6.3.3 Alternative thermal indexes (TI) and associated logarithm of thermal endurance (log[ttf, ] h]) may be estimated from this
f
display.
6.3.4 The standard deviation in the logarithm of the thermal endurance (ttf ) may be estimated using Eq 4.
f
σlog tf , h ⁄ log tf , h 5σE ⁄ E (4)
@ # @ #
σlog@t # ⁄ log@t #'6σE ⁄ E (4)
f f
6.3.5 From the law of propagation of uncertainties (2):
σt ⁄ t 5 2.303 log@t # σE ⁄ E (5)
f f f
6.4 Method C – Relative Thermal Index:
6.4.1 Relative Thermal Index thermal index (RTI) for an alternative thermal endurance (tf(RTI)) may be determined from the
activation energy determined by thermogravimetry (E) and the reference thermal index (TI at tf(RTI)) obtained by some other
method (such as electrical or mechanical tests) using Eq 65.
RTI 5 TI ⁄ 2.303 RTI ⁄ E log tf RTI ⁄tf TI 11 (5)
$~~ ! @ ~ ! ~ !#! %
RTI 5 E ⁄ R@ln @t # 2 ln@t #1E ⁄ ~R T !# (6)
f r r
NOTE 6—See derivation in Appendix X3.
7. Report
7.1 Report the following information:
7.1.1 The value, standard deviation (or relative standard deviation), and source for each value used in thefor this determination;
The boldface numbers in parentheses refer to a list of references at the end of this standard.
E1877 − 21
FIG. 1 Thermal Endurance Curve

E1877 − 21
7.1.2 Designation of the material under test, including the name of the manufacturer, the lot number, and supposed chemical
composition when known; and
7.1.3 The calculated thermal index (TI) and its relative standard deviation (σTI/TI) or relative thermal index (RTI) and its relative
standard deviation (σRTI/RTI) along with the identified thermal endurance.
7.1.3.1 Example:
TI 60 000 hr 5 45366 K 180 6 6 ° C
~ ! ~ !
TI~20 000 h!5 45666 K~180 6 6 °C!
7.1.4 The specific dated version of this practice that is used.
8. Precision and Bias
8.
...