ASTM E831-24

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Designation: E831 − 19 E831 − 24
Standard Test Method for
Linear Thermal Expansion of Solid Materials by
Thermomechanical Analysis
This standard is issued under the fixed designation E831; 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 Scope*
1.1 This test method determines the technical coefficient of linear thermal expansion of solid materials using thermomechanical
analysis techniques.
1.2 This test method is applicable to solid materials that exhibit sufficient rigidity over the test temperature range such that the
sensing probe does not produce indentation of the specimen.
1.3 The recommended lower limit of coefficient of linear thermal expansion measured with this test method is 5 μm/(m·°C). The
test method may be used at lower (or negative) expansion levels with decreased accuracy and precision (see Section 1112).
1.4 This test method is applicable to the temperature range from −120 °C to 900 °C. The temperature range may be extended
depending upon the instrumentation and calibration materials used.
1.5 The values stated in SI units are to be regarded as the standard. No other units of measurement are included in this standard.
1.6 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, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.7 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:
D696 Test Method for Coefficient of Linear Thermal Expansion of Plastics Between −30°C and 30°C with a Vitreous Silica
Dilatometer
D3386 Test Method for Coefficient of Linear Thermal Expansion of Electrical Insulating Materials (Withdrawn 2005)
E228 Test Method for Linear Thermal Expansion of Solid Materials With a Push-Rod Dilatometer
E473 Terminology Relating to Thermal Analysis and Rheology
This test method is under the jurisdiction of ASTM Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.10 on Fundamental,
Statistical and Mechanical Properties.
Current edition approved April 1, 2019May 1, 2024. Published April 2019May 2024. Originally approved in 1981. Last previous edition approved in 20142019 as
E831 – 14.E831 – 19. DOI: 10.1520/E0831-19.10.1520/E0831-24.
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.
The last approved version of this historical standard is referenced on www.astm.org.
*A Summary of Changes section appears at the end of this standard
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E831 − 24
E1142 Terminology Relating to Thermophysical Properties
E1363 Test Method for Temperature Calibration of Thermomechanical Analyzers
E2113 Test Method for Length Change Calibration of Thermomechanical Analyzers
E3142 Test Method for Thermal Lag of Thermal Analysis Apparatus
3. Terminology
3.1 Definitions—Thermal analysis terms in Terminologies E473 and E1142 shall apply to this test method, including coeffıcient
of linear thermal expansion, thermodilatometry, and thermomechanical analysis.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 mean coeffıcient of linear thermal expansion, (α ), n—the change in length, relative to the specimen length at ambient
m
temperature, accompanying a unit change in temperature identified by the midpoint temperature of the temperature range of
measurement.
4. Summary of Test Method
4.1 This test method uses a thermomechanical analyzer or similar device to determine the linear thermal expansion of solid
materials when subjected to a constant heating rate.
4.2 The change of the specimen length is electronically recorded as a function of temperature. The coefficient of linear thermal
expansion can be calculated from these recorded data.
5. Significance and Use
5.1 Coefficients of linear thermal expansion are used, for example, for design purposes and to determine if failure by thermal stress
may occur when a solid body composed of two different materials is subjected to temperature variations.
5.2 This test method is comparable to Test Method D3386 for testing electrical insulation materials, but it covers a more general
group of solid materials and it defines test conditions more specifically. This test method uses a smaller specimen and substantially
different apparatus than Test Methods E228 and D696.
5.3 This test method may be used in research, specification acceptance, regulatory compliance, and quality assurance.
6. Apparatus
6.1 Thermomechanical Analyzers (TMA)—The essential instrumentation required providing minimum thermomechanical analyti-
cal or thermodilatometric capability for this test method includes:
6.1.1 Rigid Specimen Holder, of inert, low coefficient of expansion material (≤0.5 μm/(m·°C)) to center the specimen in the furnace
and to fix the specimen to mechanical ground.
6.1.2 Rigid Expansion Probe, of inert, low coefficient of expansion material (≤0.5 μm/(m·°C)) that contacts the specimen with an
applied compressive force.
6.1.3 Sensing Element, linear over a minimum range of 2 mm 2 mm to measure the displacement of the rigid expansion probe
readable to within 650 nm resulting from changes in length of the specimen.
6.1.4 Weight or Force Transducer, to generate a constant force of 1 mN to 100 mN (0.1 g to 10 g) that is applied through the rigid
expansion probe to the specimen.
6.1.5 Furnace, capable of providing uniform controlled heating (cooling) of a specimen to a constant temperature or at a constant
rate between 2 °C/min and 10 °C/min within the applicable temperatures range of between –150 °C and 1000 °C.1000 °C.
6.1.6 Temperature Controller, capable of executing a specific temperature program by operating the furnace between selected
temperature limits at a rate of temperature change of 2 °C/min to 10 °C/min constant to within 60.1 °C/min or at an isothermal
temperature constant to 60.5 °C.
E831 − 24
6.1.7 Temperature Sensor, that can be attached to, in contact with, or reproducibly positioned in close proximity to the specimen
capable of indicating temperature readable to 60.5 °C.
6.1.8 A means of sustaining an environment around the specimen of inert gas at a purge gas rate of 10 mL/min to 50
50 mL mL/min.⁄min.
NOTE 1—Typically, greater than 99 % pure nitrogen, argon, or helium is used when oxidation in air is a concern. Unless effects of moisture are to be
studied, use of dry purge gas is recommended and is essential for operation at subambient temperatures.
6.1.9 Data Collection Device, to provide a means of acquiring, storing, and displaying measured or calculated signals, or both.
The minimum output signals required for thermomechanical analysis are a change in linear dimension, temperature and time.
6.2 Cooling Capability, to sustain a subambient specimen temperature (if subambient measurements are to be made) or to hasten
cool down of the specimen from elevated temperatures.
6.3 Micrometer, or other length-measuring device with a range of up to 10 mm to determine specimen dimensions to within 625
μm.mm, readable to 625 μm, to determine specimen dimensions.
7. Test Specimens
7.1 Specimens shall be between 2 mm and 10 mm in length and have flat and parallel ends to within 625 μm. Lateral dimensions
shall not exceed 10 mm.
NOTE 2—Specimens of other dimensions may be used but dimensions shall be reported.
NOTE 3—It has been found with some materials that this level of flatness and parallelness cannot be attained. Specimens that do not meet these
requirements may result in increased imprecision.
7.2 The specimens are ordinarily measured as received. Where some heat or mechanical treatment is applied to the specimen prior
to test, this should be noted in the report.
NOTE 4—Some materials, particularly composites, may require heat treatment to condition the specimen prior to test to relieve stresses or distortions. Such
heat treatment must be included in the report.
8. Calibration
8.1 Prepare the instrument for operation according to the procedures in the manufacturer’s operation manual.
8.2 Calibrate the temperature signal using Test Method E1363. at the same heating rate as that used for the test specimen (see
section 9.5). (See Appendix X1).
8.3 Calibrate the length change signal using Test Method E2113 at the same heating rate as that to be used for the test specimens.
The observed expansion must be corrected for the difference in expansion between the specimen holder and probe obtained from
a blank run in which no sample or a specimen of the material of construction of the probe is run (see 10.1).
NOTE 5—Calibration or calibration verification of all signals is recommended at last annually.
9. Procedure
9.1 Measure the initial specimen length in the direction of the expansion test to 625 μm at 20 °C to 25 °C.
NOTE 6—Direct readout of zero position and specimen length (L) using the analyzer sensing element, where available, with a sufficient range has been
found to be an accurate means of length determination.
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9.2 Place the specimen in the specimen holder under the probe. Place the specimen temperature sensor in contact with the
specimen or as near to the specimen as possible.
9.3 Move the furnace to enclose the specimen holder. If measurements at subambient temperature are to be made, cool the
specimen to at least 20 °C below the lowest temperature of interest. The refrigerant used for cooling shall not come into direct
contact with the specimen.
9.4 Apply an appropriate load force to the sensing probe to ensure that it is in contact with the specimen. Depending on the
compressibility of the specimen and the temperature range to be investigated, a force of between 1 mN and 100 mN (0.1 g to 10
g) is adequate. The actual incremental force, mass, or stress above that required to make contact with zero force shall be noted
in the report.
9.5 Heat the specimen at a constant heating rate of 5 °C/min over the desired temperature range and record the changes in
specimen length and temperature to all available decimal places.
NOTE 7—Other heating rates may be used but shall be noted in the report.report (see Appendix X1).
NOTE 8—Normally, the expansion increases with the increase in temperature as shown in the schematic diagram of Fig. 1. An abrupt change in slope of
the expansion curve indicates a transition of the material from one state to another.
NOTE 9—For best results, specimen temperature gradients should be small. High heating rates, large specimen sizes, and low specimen thermal
conductivity may lead to large specimen temperature gradients. The effects of specimen temperature gradients may be compensated for by correction
found through the use of suitable reference materials whose size and thermal conductivity are close to that of the test specimen.
9.6 Measure the measurement instrument baseline by repeating 9.3 through 9.5 using the same test parameters but without a test
specimen, that is, with the probe in contact with the specimen holder. The measured ΔL for the specimen should normally be
corrected for this instrument baseline, especially for low expansion specimens.
10. Calculation
10.1 Calculate the mean coefficient of linear thermal expansion rounded to the nearest 0.1 μm/(m·°C) for a desired temperature
range as follows:
FIG. 1 Specimen Expansion Versus Temperature
E831 − 24
ΔL ×k
sp
α 5 (1)
m
L ×ΔT
where:
α = mean coefficient of linear thermal expansion, μm/(m·°C),
m
k = calibration coefficient, from Test Method E2113,
L = specimen length at room temperature, m,
L = specimen length at the lower limit of the temperature change, μm,
L = specimen length at the higher limit of the temperature change, μm,
ΔL = change of specimen length, μm, = L – L (=ΔL in Fig. 1),
sp 2 1
ΔT = temperature difference over which the change in specimen length is measured, °C, and
ΔT = temperature difference over which change in specimen length is measured, °C, = T – T (=ΔT in Fig. 1),
2 1
T = midpoint temperature of the temperature range ΔT.
T = midpoint temperature of the temperature range (T + T ) / 2,
2 1
T = lower limit of the temperature change, °C, and
T = higher limit of the temperature change, °C.
NOTE 10—For low-expansion specimens, ΔL should be corrected for the expansion of the sample holder displaced by the specimen.
ΔL ~or ΔL !5 ΔL 1L ΔT α 2 ΔL (2)
sp ref obs holder blank
where:
ΔL = measured change in length, μm,
obs
α = mean coefficient of linear thermal expansion for holder, μm/(m·°C), and
holder
ΔL = change of baseline due to heating, μm.
blank
If the holder is composed of vitreous silica, α = 0.52 6 0.02 μm/(m·°C) from 20 °C to 700 °C.
holder
10.2 Select a 100 °C temperature range (ΔT) from a smooth portion of the thermal curves in the desired temperature range
symmetrically around the temperature of interest; then obtain ΔL as depicted in Fig. 1. The α shall not be calculated from a
m
temperature range in which a transition point is noted.
NOTE 11—Other ranges of temperature (for example, 50 °C) may be used but shall be reported.
NOTE 12—Values for ΔT generally range between 50 °C and 100 °C. Values less than 50 °C may lead to poor precision; values greater than 100 °C100 °C
may mask small change in the expansion coefficient.
11. Report
11.1 The report shall include the following:
11.1.1 A complete description of the test specimen including specimen orientation with respect to the original part or the direction
of the oriented fiber fillers if a composite material is used, any dimensions, and spe
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