ASTM E228-11(2016)
(Test Method)Standard Test Method for Linear Thermal Expansion of Solid Materials With a Push-Rod Dilatometer
Standard Test Method for Linear Thermal Expansion of Solid Materials With a Push-Rod Dilatometer
SIGNIFICANCE AND USE
5.1 Coefficients of linear thermal expansion are required for design purposes and are used, for example, to determine dimensional behavior of structures subject to temperature changes, or thermal stresses that can occur and cause failure of a solid artifact composed of different materials when it is subjected to a temperature excursion.
5.2 This test method is a reliable method of determining the linear thermal expansion of solid materials.
5.3 For accurate determinations of thermal expansion, it is absolutely necessary that the dilatometer be calibrated by using a reference material that has a known and reproducible thermal expansion. The appendix contains information relating to reference materials in current general use.
5.4 The measurement of thermal expansion involves two parameters: change of length and change of temperature, both of them equally important. Neglecting proper and accurate temperature measurement will inevitably result in increased uncertainties in the final data.
5.5 The test method can be used for research, development, specification acceptance, quality control (QC) and quality assurance (QA).
SCOPE
1.1 This test method covers the determination of the linear thermal expansion of rigid solid materials using push-rod dilatometers. This method is applicable over any practical temperature range where a device can be constructed to satisfy the performance requirements set forth in this standard.
Note 1: Initially, this method was developed for vitreous silica dilatometers operating over a temperature range of –180 to 900°C. The concepts and principles have been amply documented in the literature to be equally applicable for operating at higher temperatures. The precision and bias of these systems is believed to be of the same order as that for silica systems up to 900°C. However, their precision and bias have not yet been established over the relevant total range of temperature due to the lack of well-characterized reference materials and the need for interlaboratory comparisons.
1.2 For this purpose, a rigid solid is defined as a material that, at test temperature and under the stresses imposed by instrumentation, has a negligible creep or elastic strain rate, or both, thus insignificantly affecting the precision of thermal-length change measurements. This includes, as examples, metals, ceramics, refractories, glasses, rocks and minerals, graphites, plastics, cements, cured mortars, woods, and a variety of composites.
1.3 The precision of this comparative test method is higher than that of other push-rod dilatometry techniques (for example, Test Method D696) and thermomechanical analysis (for example, Test Method E831) but is significantly lower than that of absolute methods such as interferometry (for example, Test Method E289). It is generally applicable to materials having absolute linear expansion coefficients exceeding 0.5 μm/(m·°C) for a 1000°C range, and under special circumstances can be used for lower expansion materials when special precautions are used to ensure that the produced expansion of the specimen falls within the capabilities of the measuring system. In such cases, a sufficiently long specimen was found to meet the specification.
1.4 Computer- or electronic-based instrumentation, techniques, and data analysis systems may be used in conjunction with this test method, as long as it is established that such a system strictly adheres to the principles and computational schemes set forth in this method. Users of the test method are expressly advised that all such instruments or techniques may not be equivalent and may omit or deviate from the methodology described hereunder. It is the responsibility of the user to determine the necessary equivalency prior to use.
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.6 There is no ISO method equivalent to t...
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Designation: E228 − 11 (Reapproved 2016)
Standard Test Method for
Linear Thermal Expansion of Solid Materials With a Push-
Rod Dilatometer
This standard is issued under the fixed designation E228; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope 1.4 Computer- or electronic-based instrumentation,
techniques, and data analysis systems may be used in conjunc-
1.1 This test method covers the determination of the linear
tion with this test method, as long as it is established that such
thermal expansion of rigid solid materials using push-rod
a system strictly adheres to the principles and computational
dilatometers. This method is applicable over any practical
schemes set forth in this method. Users of the test method are
temperature range where a device can be constructed to satisfy
expressly advised that all such instruments or techniques may
the performance requirements set forth in this standard.
not be equivalent and may omit or deviate from the method-
NOTE 1—Initially, this method was developed for vitreous silica
ologydescribedhereunder.Itistheresponsibilityoftheuserto
dilatometers operating over a temperature range of –180 to 900°C. The
concepts and principles have been amply documented in the literature to
determine the necessary equivalency prior to use.
be equally applicable for operating at higher temperatures. The precision
1.5 The values stated in SI units are to be regarded as
and bias of these systems is believed to be of the same order as that for
silicasystemsupto900°C.However,theirprecisionandbiashavenotyet standard. No other units of measurement are included in this
been established over the relevant total range of temperature due to the
standard.
lack of well-characterized reference materials and the need for interlabo-
1.6 There is no ISO method equivalent to this standard.
ratory comparisons.
1.7 This standard does not purport to address all of the
1.2 For this purpose, a rigid solid is defined as a material
safety concerns, if any, associated with its use. It is the
that, at test temperature and under the stresses imposed by
responsibility of the user of this standard to establish appro-
instrumentation, has a negligible creep or elastic strain rate, or
priate safety and health practices and determine the applica-
both, thus insignificantly affecting the precision of thermal-
bility of regulatory limitations prior to use.
length change measurements. This includes, as examples,
metals, ceramics, refractories, glasses, rocks and minerals,
2. Referenced Documents
graphites, plastics, cements, cured mortars, woods, and a
variety of composites.
2.1 ASTM Standards:
D696TestMethodforCoefficientofLinearThermalExpan-
1.3 The precision of this comparative test method is higher
sion of Plastics Between −30°C and 30°C with a Vitreous
than that of other push-rod dilatometry techniques (for
Silica Dilatometer
example, Test Method D696) and thermomechanical analysis
E220Test Method for Calibration of Thermocouples By
(forexample,TestMethodE831)butissignificantlylowerthan
Comparison Techniques
that of absolute methods such as interferometry (for example,
E289Test Method for Linear Thermal Expansion of Rigid
Test Method E289). It is generally applicable to materials
Solids with Interferometry
having absolute linear expansion coefficients exceeding 0.5
E473Terminology Relating to Thermal Analysis and Rhe-
µm/(m·°C) for a 1000°C range, and under special circum-
ology
stancescanbeusedforlowerexpansionmaterialswhenspecial
E644Test Methods for Testing Industrial Resistance Ther-
precautions are used to ensure that the produced expansion of
mometers
the specimen falls within the capabilities of the measuring
E831Test Method for Linear Thermal Expansion of Solid
system. In such cases, a sufficiently long specimen was found
Materials by Thermomechanical Analysis
to meet the specification.
E1142Terminology Relating to Thermophysical Properties
ThistestmethodisunderthejurisdictionofASTMCommitteeE37onThermal
Measurements and is the direct responsibility of Subcommittee E37.05 on Thermo-
physical Properties. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Sept. 1, 2016. Published September 2016. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1963. Last previous edition approved in 2011 as E228–11. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E0228-11R16. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E228 − 11 (2016)
3. Terminology the derivative of the expansion curve when plotted versus
temperature, at the temperature T. It has a rather limited utility
3.1 Definitions—The following terms are applicable to this
for engineering applications, and therefore it is more common
test method and are listed in Terminologies E473 and E1142:
to use the average coefficient of thermal expansion, than the
coeffıcient of linear thermal expansion, thermodilatometry,and
instantaneous one.
thermomechanical analysis.
3.3 Symbols:
3.2 Definitions of Terms Specific to This Standard:
3.2.1 dilatometer—a device that measures the difference in
α = mean or average coefficient of linear thermal
m
linear thermal expansion between a test specimen and its own
expansion over a temperature range, µm/(m·°C),
-1 -1
parts adjacent to the sample.
K ,or°C
3.2.1.1 Discussion—Thermomechanical analyzers (TMA),
α = expansivity or instantaneous coefficient of linear
T
instruments used in thermal analysis, are often also character-
thermal expansion at temperature T, µm/(m·°C).
-1 -1
ized as dilatometers, due to their ability to determine linear
K ,or°C
thermal expansion characteristics. Typically, they employ
L = originallengthofspecimenattemperature T,mm
0 0
specimens much smaller than dilatometers; however, TMA L = length of specimen at temperature T,mm
1 1
L = length of specimen at temperature T,mm
systems with sufficiently large specimen size capability have
2 2
L = length of specimen at a particular temperature T,
been shown to measure thermal expansion accurately. When
i i
mm
using the small TMA specimen size, this utilization of TMA
∆L = change in length of specimen between any two
equipment should be limited to testing only very high expan-
temperatures T and T , T and T , etc., µm
sion materials, such as polymers, otherwise the data obtained 1 2 0 1
(∆L/L ) = expansion
may be substantially in error. Conversely, some dilatometers
T = temperature at which initial length is L,°C
0 0
can perform some of the TMA functions, but the two devices
T,T = two temperatures at which measurements are
1 2
should not be considered equivalent or interchangeable in all
made, °C
applications.
T = temperature at which length is L,°C
i i
3.2.2 linearthermalexpansion, ∆L/L —thechangeinlength
∆T = temperature difference between any two tempera-
relative to the initial length of the specimen accompanying a
tures T and T , T and T , etc., °C
2 1 1 0
change in temperature, between temperatures T and T ,
m = measured expansion of the reference material
0 1
expressed as: t = true or certified expansion of the reference mate-
rial
∆L L 2 L
1 0
5 (1)
s = assumed or known expansion of the parts of the
L L
0 0
dilatometer
3.2.2.1 Discussion—It is a dimensionless quantity, but for
A = numerical calibration constant
practical reasons the units most often used are µm/m, (m/
-6 -6
m)·10 , (in./in.)·10 , ppm or percent (%).
4. Summary of Test Method
3.2.3 mean (average) coeffıcient of linear thermal
4.1 This test method uses a single push-rod tube type
expansion, α —the ratio between the expansion and the
m
dilatometer to determine the change in length of a solid
temperature difference that is causing it. It is referred to as the
material relative to that of the holder as a function of
average coefficient of thermal expansion for the temperature
temperature. A special variation of the basic configuration
range between T and T .
0 1
known as a differential dilatometer employs dual push rods,
1 ∆L
where a reference specimen is kept in the second placement at
α 5 (2)
m
L ∆T
all times and expansion of the unknown is determined relative
3.2.3.1 Discussion—Most commonly, it is expressed in
to the reference material rather than to the specimen holder.
-1
µm/(m °C) or °C , and it is determined for a sequence of
4.2 The temperature is controlled either over a series of
temperature ranges, starting with 20°C by convention, being
steps or at a slow constant heating or cooling rate over the
presented as a function of temperature. In case the reference
entire range.
temperature differs from 20°C, the specific temperature used
for reference has to be indicated in the report. 4.3 The linear thermal expansion and the coefficients of
linearthermalexpansionarecalculatedfromtherecordeddata.
3.2.4 thermal expansivity (instantaneous coeffıcient of ther-
mal expansion), α —identical to the above, except that the
T
5. Significance and Use
derivative replaces the finite differences of Eq 2. The thermal
expansivityisrelatedtothelengthchangeforaninfinitesimally 5.1 Coefficientsoflinearthermalexpansionarerequiredfor
narrow temperature range, at any temperature T (essentially a design purposes and are used, for example, to determine
“tangent” point), and is defined as follows: dimensional behavior of structures subject to temperature
changes,orthermalstressesthatcanoccurandcausefailureof
1 dL
α 5 (3)
S D
a solid artifact composed of different materials when it is
T
L dT
0 T
subjected to a temperature excursion.
3.2.4.1 Discussion—It is expressed in the same units as the
average coefficient of thermal expansion. In terms of physical 5.2 This test method is a reliable method of determining the
meaning, the instantaneous coefficient of thermal expansion is linear thermal expansion of solid materials.
E228 − 11 (2016)
5.3 For accurate determinations of thermal expansion, it is the sample holder and the push-rod(s) shall be made of the
absolutelynecessarythatthedilatometerbecalibratedbyusing same material, having been proven to exhibit thermal expan-
areferencematerialthathasaknownandreproduciblethermal sion characteristics within 61% of each other. Illustrations of
expansion. The appendix contains information relating to typical tube and rod-type configurations are given in Fig. 1.It
reference materials in current general use. is often practiced to configure specimen holders that are not
shaped as a tube, but serve the same structural purpose.This is
5.4 The measurement of thermal expansion involves two
an acceptable practice, as long as the shape is mechanically
parameters: change of length and change of temperature, both
stable and is not prone to reversible configurational changes
of them equally important. Neglecting proper and accurate
(such as twisting, etc.) upon heating and cooling.
temperature measurement will inevitably result in increased
uncertainties in the final data.
NOTE 2—The tube and the push-rod beyond the specimen, while
parallel to each other, are expected to have identical thermal gradients
5.5 The test method can be used for research, development,
along them, thereby identical thermal expansion. This is a critical factor,
specification acceptance, quality control (QC) and quality
as differences in net expansion between the tube and the push-rod will
assurance (QA).
appear very much like expansion produced by the specimen. To a limited
extent, calibration (see Section 9) can be used to account for these
6. Interferences
differences in the thermal expansion of the two parts, however, it is noted
that this is one of the most fundamental of all practical limitations for
6.1 Materials Considerations:
dilatometers.Tominimizethiseffect,thetubeandthepush-rodshallbein
6.1.1 The materials of construction may have substantial
close proximity of each other and heated slowly enough to prevent
impact on the performance of the dilatometer. It is imperative
substantial thermal gradients that occur radially.
thatregardlessofthematerialsused,stepsbetakentoascertain
7.1.2 Test Chamber, composed of:
that the expansion behavior is stabilized, so that repeated
7.1.2.1 Furnace, Cryostat, or Bath, used for heating or
thermal cycling (within the operating range of the device)
cooling the specimen uniformly at a controlled rate over the
causes no measurable change.
temperature range of interest, and able to maintain the tem-
6.2 General Considerations: perature uniform along the sample during its heating, cooling,
6.2.1 Inelastic creep of a specimen at elevated temperatures or just equilibrating.
can often be prevented by making its cross section sufficiently
NOTE 3—Extreme care must be exercised in using furnaces for high
large.
temperatures, to prevent interaction with the dilatometer’s parts or with
6.2.2 Avoid moisture in the dilatometer, especially when
the specimen. In many instances, it is necessary to protect the specimen
and the dilatometer from oxidation and in some cases this may be
used at cryogenic temperatures.
accomplished with the use of a muffle tube. If it is necessary, the furnace,
6.2.3 Means to separate the bath from the specimen are
in such cases, shall contain provisions to provide inert atmosphere or
required when the dilatometer is immersed in a liquid bath.
vacuum environment, as well as provisions to protect against air back-
6.2.4 Support or hold the specimen in a position so that it is
streaming on cooling.
stable during the test without unduly restricting its free
NOTE 4—Unless it is absolutely necessary to have the specimen tested
in vacuum, measurements of thermal expansion in vacuum are not
movement.
recommended due to extreme thermal gradients, thermal lags, etc.
6.2.5 Thespecimenholderandpush-rodshallbemadefrom
betweenvariouscomponentsofthedilatometerandthespecimen,thatare
the same material. The user must not practice uncontrolled
caused by the very poor heat transfer that occurs in the absence of a gas.
substitutions (such as when replacing broken parts), as serious
7.1.2.2 Temperature Controller(orcircuitrywithequivalent
increase of the uncertainties in the measured expansion may
function) capable of executing a specific temperature program
result.
byoperatingthefurnace(s)betweenselectedtemperaturelimits
6.2.6 A general verification of a dilatom
...
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. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E228 − 11 E228 − 11 (Reapproved 2016)
Standard Test Method for
Linear Thermal Expansion of Solid Materials With a Push-
Rod Dilatometer
This standard is issued under the fixed designation E228; 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.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope
1.1 This test method covers the determination of the linear thermal expansion of rigid solid materials using push-rod
dilatometers. This method is applicable over any practical temperature range where a device can be constructed to satisfy the
performance requirements set forth in this standard.
NOTE 1—Initially, this method was developed for vitreous silica dilatometers operating over a temperature range of –180 to 900°C. The concepts and
principles have been amply documented in the literature to be equally applicable for operating at higher temperatures. The precision and bias of these
systems is believed to be of the same order as that for silica systems up to 900°C. However, their precision and bias have not yet been established over
the relevant total range of temperature due to the lack of well-characterized reference materials and the need for interlaboratory comparisons.
1.2 For this purpose, a rigid solid is defined as a material that, at test temperature and under the stresses imposed by
instrumentation, has a negligible creep or elastic strain rate, or both, thus insignificantly affecting the precision of thermal-length
change measurements. This includes, as examples, metals, ceramics, refractories, glasses, rocks and minerals, graphites, plastics,
cements, cured mortars, woods, and a variety of composites.
1.3 The precision of this comparative test method is higher than that of other push-rod dilatometry techniques (for example, Test
Method D696) and thermomechanical analysis (for example, Test Method E831) but is significantly lower than that of absolute
methods such as interferometry (for example, Test Method E289). It is generally applicable to materials having absolute linear
expansion coefficients exceeding 0.5 μm/(m·°C) for a 1000°C range, and under special circumstances can be used for lower
expansion materials when special precautions are used to ensure that the produced expansion of the specimen falls within the
capabilities of the measuring system. In such cases, a sufficiently long specimen was found to meet the specification.
1.4 Computer- or electronic-based instrumentation, techniques, and data analysis systems may be used in conjunction with this
test method, as long as it is established that such a system strictly adheres to the principles and computational schemes set forth
in this method. Users of the test method are expressly advised that all such instruments or techniques may not be equivalent and
may omit or deviate from the methodology described hereunder. It is the responsibility of the user to determine the necessary
equivalency prior to use.
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.6 There is no ISO method equivalent to this standard.
1.7 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 and health practices and determine the applicability of regulatory
limitations prior to use.
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
E220 Test Method for Calibration of Thermocouples By Comparison Techniques
This test method is under the jurisdiction of ASTM Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.05 on
Thermophysical Properties.
Current edition approved April 1, 2011Sept. 1, 2016. Published April 2011September 2016. Originally approved in 1963. Last previous edition approved in 20062011 as
E228 – 06.E228 – 11. DOI: 10.1520/E0228-11.10.1520/E0228-11R16.
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.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E228 − 11 (2016)
E289 Test Method for Linear Thermal Expansion of Rigid Solids with Interferometry
E473 Terminology Relating to Thermal Analysis and Rheology
E644 Test Methods for Testing Industrial Resistance Thermometers
E831 Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis
E1142 Terminology Relating to Thermophysical Properties
3. Terminology
3.1 Definitions—The following terms are applicable to this test method and are listed in Terminologies E473 and E1142:
coeffıcient of linear thermal expansion,thermodilatometry, and thermomechanical analysis.
3.2 Symbols:
-1 -1
α = mean or average coefficient of linear thermal expansion over a temperature range, μm/(m·°C), K , or °C
m
-1 -1
α = expansivity or instantaneous coefficient of linear thermal expansion at temperature T, μm/(m·°C). K , or °C
T
L = original length of specimen at temperature T , mm
0 0
L = length of specimen at temperature T , mm
1 1
L = length of specimen at temperature T , mm
2 2
L = length of specimen at a particular temperature T , mm
i i
ΔL = change in length of specimen between any two temperatures T and T , T and T , etc., μm
1 2 0 1
(ΔL/L ) = expansion
T = temperature at which initial length is L , °C
0 0
T , T = two temperatures at which measurements are made, °C
1 2
T = temperature at which length is L , °C
i i
ΔT = temperature difference between any two temperatures T and T , T and T , etc., °C
2 1 1 0
m = measured expansion of the reference material,
t = true or certified expansion of the reference material,
s = assumed or known expansion of the parts of the dilatometer,
A = numerical calibration constant
3.2 Definitions of Terms Specific to This Standard:
3.2.1 dilatometer—a device that measures the difference in linear thermal expansion between a test specimen and its own parts
adjacent to the sample.
3.2.1.1 Discussion—
Thermomechanical analyzers (TMA), instruments used in thermal analysis, are often also characterized as dilatometers, due to
their ability to determine linear thermal expansion characteristics. Typically, they employ specimens much smaller than
dilatometers; however, TMA systems with sufficiently large specimen size capability have been shown to measure thermal
expansion accurately. When using the small TMA specimen size, this utilization of TMA equipment should be limited to testing
only very high expansion materials, such as polymers, otherwise the data obtained may be substantially in error. Conversely, some
dilatometers can perform some of the TMA functions, but the two devices should not be considered equivalent or interchangeable
in all applications.
3.2.2 linear thermal expansion, ΔL/L —the change in length relative to the initial length of the specimen accompanying a
change in temperature, between temperatures T and T , expressed as:
0 1
ΔL L 2 L
1 0
5 (1)
L L
0 0
3.2.2.1 Discussion—
-6 -6
It is a dimensionless quantity, but for practical reasons the units most often used are μm/m, (m/m)·10 , (in./in.)·10 , ppm or
percent (%).
3.2.3 mean (average) coeffıcient of linear thermal expansion, α —the ratio between the expansion and the temperature
m
difference that is causing it. It is referred to as the average coefficient of thermal expansion for the temperature range between T
and T .
1 ΔL
α 5 (2)
m
L ΔT
3.2.3.1 Discussion—
E228 − 11 (2016)
-1
Most commonly, it is expressed in μm/(m °C) or °C , and it is determined for a sequence of temperature ranges, starting with 20°C
by convention, being presented as a function of temperature. In case the reference temperature differs from 20°C, the specific
temperature used for reference has to be indicated in the report.
3.2.4 thermal expansivity (instantaneous coeffıcient of thermal expansion), α —identical to the above, except that the derivative
T
replaces the finite differences of Eq 2. The thermal expansivity is related to the length change for an infinitesimally narrow
temperature range, at any temperature T (essentially a “tangent” point), and is defined as follows:
1 dL
α 5 (3)
S D
T
L dT
0 T
3.2.4.1 Discussion—
It is expressed in the same units as the average coefficient of thermal expansion. In terms of physical meaning, the instantaneous
coefficient of thermal expansion is the derivative of the expansion curve when plotted versus temperature, at the temperature T.
It has a rather limited utility for engineering applications, and therefore it is more common to use the average coefficient of thermal
expansion, than the instantaneous one.
3.3.4 dilatometer—a device that measures the difference in linear thermal expansion between a test specimen and its own parts
adjacent to the sample.
3.3.4.1 Discussion—
Thermomechanical analyzers (TMA), instruments used in thermal analysis, are often also characterized as dilatometers, due to
their ability to determine linear thermal expansion characteristics. Typically, they employ specimens much smaller than
dilatometers; however, TMA systems with sufficiently large specimen size capability have been shown to measure thermal
expansion accurately. When using the small TMA specimen size, this utilization of TMA equipment should be limited to testing
only very high expansion materials, such as polymers, otherwise the data obtained may be substantially in error. Conversely, some
dilatometers can perform some of the TMA functions, but the two devices should not be considered equivalent or interchangeable
in all applications.
3.3 Symbols:
-1 -1
α = mean or average coefficient of linear thermal expansion over a temperature range, μm/(m·°C), K , or °C
m
-1 -1
α = expansivity or instantaneous coefficient of linear thermal expansion at temperature T, μm/(m·°C). K , or °C
T
L = original length of specimen at temperature T , mm
0 0
L = length of specimen at temperature T , mm
1 1
L = length of specimen at temperature T , mm
2 2
L = length of specimen at a particular temperature T , mm
i i
ΔL = change in length of specimen between any two temperatures T and T , T and T , etc., μm
1 2 0 1
(ΔL/L ) = expansion
T = temperature at which initial length is L , °C
0 0
T , T = two temperatures at which measurements are made, °C
1 2
T = temperature at which length is L , °C
i i
ΔT = temperature difference between any two temperatures T and T , T and T , etc., °C
2 1 1 0
m = measured expansion of the reference material
t = true or certified expansion of the reference material
s = assumed or known expansion of the parts of the dilatometer
A = numerical calibration constant
4. Summary of Test Method
4.1 This test method uses a single push-rod tube type dilatometer to determine the change in length of a solid material relative
to that of the holder as a function of temperature. A special variation of the basic configuration known as a differential dilatometer
employs dual push rods, where a reference specimen is kept in the second placement at all times and expansion of the unknown
is determined relative to the reference material rather than to the specimen holder.
4.2 The temperature is controlled either over a series of steps or at a slow constant heating or cooling rate over the entire range.
4.3 The linear thermal expansion and the coefficients of linear thermal expansion are calculated from the recorded data.
E228 − 11 (2016)
5. Significance and Use
5.1 Coefficients of linear thermal expansion are required for design purposes and are used, for example, to determine
dimensional behavior of structures subject to temperature changes, or thermal stresses that can occur and cause failure of a solid
artifact composed of different materials when it is subjected to a temperature excursion.
5.2 This test method is a reliable method of determining the linear thermal expansion of solid materials.
5.3 For accurate determinations of thermal expansion, it is absolutely necessary that the dilatometer be calibrated by using a
reference material that has a known and reproducible thermal expansion. The appendix contains information relating to reference
materials in current general use.
5.4 The measurement of thermal expansion involves two parameters: change of length and change of temperature, both of them
equally important. Neglecting proper and accurate temperature measurement will inevitably result in increased uncertainties in the
final data.
5.5 The test method can be used for research, development, specification acceptance, quality control (QC) and quality assurance
(QA).
6. Interferences
6.1 Materials Considerations:
6.1.1 The materials of construction may have substantial impact on the performance of the dilatometer. It is imperative that
regardless of the materials used, steps be taken to ascertain that the expansion behavior is stabilized, so that repeated thermal
cycling (within the operating range of the device) causes no measurable change.
6.2 General Considerations:
6.2.1 Inelastic creep of a specimen at elevated temperatures can often be prevented by making its cross section sufficiently large.
6.2.2 Avoid moisture in the dilatometer, especially when used at cryogenic temperatures.
6.2.3 Means to separate the bath from the specimen are required when the dilatometer is immersed in a liquid bath.
6.2.4 Support or hold the specimen in a position so that it is stable during the test without unduly restricting its free movement.
6.2.5 The specimen holder and push-rod shall be made from the same material. The user must not practice uncontrolled
substitutions (such as when replacing broken parts), as serious increase of the uncertainties in the measured expansion may result.
6.2.6 A general verification of a dilatometer is a test run using a specimen cut from the same material as the pu
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