ASTM E228-22 2022

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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.

Designation:E228-22

Standard Test Method for

Linear Thermal Expansion of Solid Materials With a Push-

Rod Dilatometer¹

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(e)indicates an editorial change since the last revision or reapproval.

This standard has been approved for use by agencies of the U.SDepartment 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℃.

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℃.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·℃)for a 1000℃ range,and under special circum-

stances 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.

IThis test method is under the jurisdiction of ASTM Committee E37 on Thermal

Measurements and is the direct responsibility of Subcommittee E37.05 on Thermo-

physical Properties.

Current edition approved Dec.1,2022.Published January 2023.Originally

approved in 1963.Last previous edition approved in 2017 as E228-17.DOI:

10.1520/E0228-22.

1.4 Units—The values stated in SI units are to be regarded

as standard.No other units of measurement are included in this

standard.

1.5 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 appro-

priate safety,health,and environmental practices and deter-

mine the applicability of regulatory limitations prior to use.

1.6 This international standard was developed in accor-

dance with internationally recognizedprinciples on standard-

ization established in the Decision on Principles for the

Development ofInternational Standards,Guides andRecom-

mendations issued by the World Trade Organization Technical

Barriers to Trade(TBT)Committee.

2.Referenced Documents

2.1 ASTM Standards:²

D696 Test Method for Coefficient of Linear Thermal Expan-

sion of Plastics Between-30℃ and 30℃ with a Vitreous

Silica Dilatometer

E220 Test Method for Calibration of Thermocouples By

Comparison Techniques

E230/E230M Specification for Temperature-Electromotive

Force (emf)Tables for Standardized Thermocouples

E289 Test Method for Linear Thermal Expansion ofRigid

Solids with Interferometry

E473 Terminology Relating to Thermal Analysis and Rhe-

ology

E644 Test Methods for Testing Industrial Resistance Ther-

mometers

E831Test 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:

²For referenced ASTM standards,visit the ASTM website,www.astm.org,or

contact ASTM Customer Service at service@astm.org.For Annual Book ofASTM

Standards volume information,refer to the standard's Document Summary page on

the ASTM website.

coefficient of linear thermal expansion,thermodilatometry,and

thermomechanical analysis.

3.2 Definitions of Terms Specific to This Standard:

3.2.1 dilatometer; n—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 character-

ized 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 expan-

sion 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,

△

L/Lo, n—the change in

length relative to the initial length of the specimen accompa-

nying a change in temperature,between temperatures To and

T₁,expressed as:

(1)

3.2.2.1 Discussion—It is a dimensionless quantity,but for

practical reasons the units most often used are μm/m.

3.2.3 mean (average)coefficient of linear thermal

expansion, αmn—the ratio between the expansion and the

temperature difference that is causing it.It is referred to as the

average coefficient of thermal expansion for the temperature

range between To and T₁.

(2)

3.2.3.1 Discussion—Most commonly,it is expressed in

μm/(m℃),and it is determined for a sequence of temperature

ranges,starting with 20℃ by convention,being presented as a

function of temperature.In case the reference temperature

differs from 20℃,the specific temperature used for reference

has to be indicated in the report.

3.2.4 thermal expansivity(instantaneous coeficient of ther-

mal expansion),α,n—identical to the above,except that the

derivative 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:

(3)

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 Symbols:

=mean or average coefficient of linear thermal

expansion over a temperature range,μm/(m·℃)

=expansivity or instantaneous coefficient of linear

thermal expansion at temperature T,μm/(m·℃)

=original length of specimen at temperature T₀,mm

=length of specimen at temperature T₁,mm

=length of specimen at temperature T₂,mm

=length of specimen at a particular temperature Ti,

=change in length of specimen between any two

temperatures T₁and T₂,T₀and T₁,etc.,μm

=expansion

=temperature at which initial length is L₀,℃

=two temperatures at which measurements are

made,℃

=temperature at which length is L;,℃

=temperature difference between any two tempera-

tures T₂and T₁,T₁and T₀,etc.,℃

=measured expansion of the reference material

=true or certified expansion of the reference mate-

rial

=assumed or known expansion of the parts of the

dilatometer

=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.

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

L₀

L₁

L₂

△L

(4L/L₀)

T₀

T,T₂

△T

αT

αm

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 push rod

and specimen holder.The resultant mean coefficient of linear

thermal expansion should be smaller than±0.3 μm/(m·℃)for

a properly constructed system(after applying the system's

correction).

6.2.7 Conditioning of specimens is often necessary before

reproducible expansion data can be obtained.For example,

heat treatments are frequently necessary to eliminate certain

effects(stress caused by machining,moisture,etc.)that may

introduce irreversible length changes that are not associated

with thermal expansion.

7.Apparatus

7.1 Push-Rod Dilatometer System,consisting of the follow-

ing:

7.1.1 Specimen Holder—A structure of thermally stable

material constructed in a fashion such that when a specimen of

the same material is placed into it for a test,the qualifications

given in 6.2.7 are satisfied.In any push rod dilatometer,both

the sample holder and the push-rod(s)shall be made of the

same material,having been proven to exhibit thermal expan-

sion characteristics within±1%of each other.Illustrations of

typical tube and rod-type configurations are given in Fig.1.It

is often practiced to configure specimen holders that are not

shaped as a tube,but serve the same structural purpose.This is

an acceptable practice,as long as the shape is mechanically

Vitreous

Silica

Outer Tube

Spacer

Specimen

Closed Tube Open Tube

FIG.1 Common Forms Specimen Holders

FIG.2 Suggested Shapes of Specimen's and Push-Rod Ends

stable and is not prone to reversible configurational changes

(such as twisting,etc.)upon heating and cooling.

NoTE 2—The tube and the push-rod beyond the specimen,while

parallel to each other,are expected to have identical thermal gradients

along them,thereby identical thermal expansion.This is a critical factor,

as differences in net expansion between the tube and the push-rod will

appear very much like expansion produced by the specimen.To a limited

extent,calibration(see Section 9)can be used to account for these

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

dilatometers.To minimize this effect,the tube and the push-rod shall be in

close proximity of each other and heated slowly enough to prevent

substantial thermal gradients that occur radially.

7.1.2 Test Chamber; composed of:

7.1.2.1 Furnace,Cryostat,or Bath, used for heating or

cooling the specimen uniformly at a controlled rate over the

temperature range of interest,and able to maintain the tem-

perature uniform along the sample during its heating,cooling,

or just equilibrating.

NoTE 3—Extreme care must be exercised in using furnaces for high

temperatures,to prevent interaction with the dilatometer's parts or with

the specimen.In many instances,it is necessary to protect the specimen

and the dilatometer from oxidation and in some cases this may be

accomplished with the use of a muffle tube.If it is necessary,the furnace,

in such cases,shall contain provisions to provide inert atmosphere or

vacuum environment,as well as provisions to protect against air back-

streaming on cooling.

Vitreous

Silica

Push Rod

optional

Specimen

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1ThisinternationalstandardwasdevelopedinaccordancewithinternationallyrecognizedprinciplesonstandardizationestablishedintheDecisiononPrinciplesfortheDevelopmentofInternationalStandards,GuidesandRecommendationsissuedbytheWorldTradeOrganizationTechnicalBarrierstoTrade(TBT)Committee.Designation:E228-22S...

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