ASTM C1211-18(2023)
(Test Method)Standard Test Method for Flexural Strength of Advanced Ceramics at Elevated Temperatures
Standard Test Method for Flexural Strength of Advanced Ceramics at Elevated Temperatures
SIGNIFICANCE AND USE
4.1 This test method may be used for material development, quality control, characterization, and design data generation purposes. This test method is intended to be used with ceramics whose flexural strength is ∼50 MPa (∼7 ksi) or greater.
4.2 The flexure stress is computed based on simple beam theory, with assumptions that the material is isotropic and homogeneous, the moduli of elasticity in tension and compression are identical, and the material is linearly elastic. The average grain size should be no greater than 1/50 of the beam thickness. The homogeneity and isotropy assumptions in the test method rule out the use of it for continuous fiber-reinforced composites for which Test Method C1341 is more appropriate.
4.3 The flexural strength of a group of test specimens is influenced by several parameters associated with the test procedure. Such factors include the testing rate, test environment, specimen size, specimen preparation, and test fixtures. Specimen and fixture sizes were chosen to provide a balance between the practical configurations and resulting errors as discussed in Test Method C1161, and Refs (1-3).4 Specific fixture and specimen configurations were designated in order to permit the ready comparison of data without the need for Weibull size scaling.
4.4 The flexural strength of a ceramic material is dependent on both its inherent resistance to fracture and the size and severity of flaws. Variations in these cause a natural scatter in test results for a sample of test specimens. Fractographic analysis of fracture surfaces, although beyond the scope of this test method, is highly recommended for all purposes, especially if the data will be used for design as discussed in Ref (4) and Practices C1322 and C1239.
4.5 This method determines the flexural strength at elevated temperature and ambient environmental conditions at a nominal, moderately fast testing rate. The flexural strength under these conditions may or may not necessarily be the...
SCOPE
1.1 This test method covers determination of the flexural strength of advanced ceramics at elevated temperatures.2 Four-point-1/4-point and three-point loadings with prescribed spans are the standard as shown in Fig. 1. Rectangular specimens of prescribed cross-section are used with specified features in prescribed specimen-fixture combinations. Test specimens may be 3 by 4 by 45 to 50 mm in size that are tested on 40-mm outer span four-point or three-point fixtures. Alternatively, test specimens and fixture spans half or twice these sizes may be used. The test method permits testing of machined or as-fired test specimens. Several options for machining preparation are included: application matched machining, customary procedures, or a specified standard procedure. This test method describes the apparatus, specimen requirements, test procedure, calculations, and reporting requirements. The test method is applicable to monolithic or particulate- or whisker-reinforced ceramics. It may also be used for glasses. It is not applicable to continuous fiber-reinforced ceramic composites.
1.2 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only.
1.3 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.
1.4 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.
General Information
Relations
Standards Content (Sample)
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: C1211 − 18 (Reapproved 2023)
Standard Test Method for
Flexural Strength of Advanced Ceramics at Elevated
Temperatures
This standard is issued under the fixed designation C1211; 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 2. Referenced Documents
1.1 This test method covers determination of the flexural 2.1 ASTM Standards:
strength of advanced ceramics at elevated temperatures. C1161 Test Method for Flexural Strength of Advanced
Four-point- ⁄4-point and three-point loadings with prescribed Ceramics at Ambient Temperature
spans are the standard as shown in Fig. 1. Rectangular C1239 Practice for Reporting Uniaxial Strength Data and
specimens of prescribed cross-section are used with specified Estimating Weibull Distribution Parameters for Advanced
features in prescribed specimen-fixture combinations. Test Ceramics
specimens may be 3 by 4 by 45 to 50 mm in size that are tested C1322 Practice for Fractography and Characterization of
on 40-mm outer span four-point or three-point fixtures. Fracture Origins in Advanced Ceramics
Alternatively, test specimens and fixture spans half or twice C1341 Test Method for Flexural Properties of Continuous
these sizes may be used. The test method permits testing of Fiber-Reinforced Advanced Ceramic Composites
machined or as-fired test specimens. Several options for C1368 Test Method for Determination of Slow Crack
machining preparation are included: application matched Growth Parameters of Advanced Ceramics by Constant
machining, customary procedures, or a specified standard Stress Rate Strength Testing at Ambient Temperature
procedure. This test method describes the apparatus, specimen C1465 Test Method for Determination of Slow Crack
requirements, test procedure, calculations, and reporting re- Growth Parameters of Advanced Ceramics by Constant
quirements. The test method is applicable to monolithic or Stress-Rate Flexural Testing at Elevated Temperatures
particulate- or whisker-reinforced ceramics. It may also be E4 Practices for Force Calibration and Verification of Test-
used for glasses. It is not applicable to continuous fiber- ing Machines
reinforced ceramic composites. E220 Test Method for Calibration of Thermocouples By
Comparison Techniques
1.2 The values stated in SI units are to be regarded as the
E230 Specification for Temperature-Electromotive Force
standard. The values given in parentheses are for information
(emf) Tables for Standardized Thermocouples
only.
1.3 This standard does not purport to address all of the
3. Terminology
safety concerns, if any, associated with its use. It is the
3.1 Definitions:
responsibility of the user of this standard to establish appro-
3.1.1 complete gage section, n—the portion of the specimen
priate safety, health, and environmental practices and deter-
between the two outer bearings in four-point flexure and
mine the applicability of regulatory limitations prior to use.
three-point flexure fixtures.
1.4 This international standard was developed in accor-
dance with internationally recognized principles on standard- NOTE 1—In this standard, the complete four-point flexure gage section
is twice the size of the inner gage section. Weibull statistical analyses, in
ization established in the Decision on Principles for the
this instance, only include portions of the specimen volume or surface
Development of International Standards, Guides and Recom-
which experience tensile stresses.
mendations issued by the World Trade Organization Technical
–2
3.1.2 flexural strength, [FL ], n—a measure of the ultimate
Barriers to Trade (TBT) Committee.
strength of a specified beam in bending.
3.1.3 four-point- ⁄4-point flexure, n—a configuration of flex-
This test method is under the jurisdiction of ASTM Committee C28 on
ural strength testing in which a specimen is symmetrically
Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 on
Mechanical Properties and Performance.
Current edition approved Jan. 1, 2023. Published February 2023. Originally
approved in 1992. Last previous edition approved in 2018 as C1211 – 18. DOI: For referenced ASTM standards, visit the ASTM website, www.astm.org, or
10.1520/C1211-18R23. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Elevated temperatures typically denote, but are not restricted to, 200 to Standards volume information, refer to the standard’s Document Summary page on
1600 °C. 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
C1211 − 18 (2023)
surfaces. In addition, the upper or lower pairs are free to pivot
to distribute force evenly to the bearing cylinders on either
side.
NOTE 4—See Annex A1 for schematic illustrations of the required
pivoting movements.
NOTE 5—A three-point fixture has the inner pair of bearing cylinders
replaced by a single bearing cylinder.
3.1.9 slow crack growth (SCG), n—subcritical crack growth
(extension) which may result from, but is not restricted to, such
mechanisms as environmentally assisted stress corrosion or
diffusive crack growth.
3.1.10 three-point flexure, n—a configuration of flexural
strength testing in which a specimen is loaded at a position
midway between two support bearings (see Fig. 1).
4. Significance and Use
4.1 This test method may be used for material development,
quality control, characterization, and design data generation
purposes. This test method is intended to be used with ceramics
NOTE 1—Configuration:
whose flexural strength is ;50 MPa (;7 ksi) or greater.
A: L = 20 mm
B: L = 40 mm
4.2 The flexure stress is computed based on simple beam
C: L = 80 mm
theory, with assumptions that the material is isotropic and
FIG. 1 Four-Point- ⁄4-Point and Three-Point Fixture Configurations
homogeneous, the moduli of elasticity in tension and compres-
sion are identical, and the material is linearly elastic. The
average grain size should be no greater than ⁄50 of the beam
thickness. The homogeneity and isotropy assumptions in the
loaded at two locations that are situated at one-quarter of the
test method rule out the use of it for continuous fiber-reinforced
overall span, away from the outer two support bearings (see
composites for which Test Method C1341 is more appropriate.
Fig. 1).
4.3 The flexural strength of a group of test specimens is
3.1.4 fully articulating fixture, n—a flexure fixture designed
influenced by several parameters associated with the test
to be used either with flat and parallel specimens or with
procedure. Such factors include the testing rate, test
uneven or nonparallel specimens. The fixture allows full
environment, specimen size, specimen preparation, and test
independent articulation, or pivoting, of all rollers about the
fixtures. Specimen and fixture sizes were chosen to provide a
specimen long axis to match the specimen surface. In addition,
balance between the practical configurations and resulting
the upper or lower pairs are free to pivot to distribute force
errors as discussed in Test Method C1161, and Refs (1-3).
evenly to the bearing cylinders on either side.
Specific fixture and specimen configurations were designated
NOTE 2—See Annex A1 for schematic illustrations of the required
in order to permit the ready comparison of data without the
pivoting movements.
need for Weibull size scaling.
NOTE 3—A three-point fixture has the inner pair of bearing cylinders
4.4 The flexural strength of a ceramic material is dependent
replaced by a single bearing cylinder.
–2
on both its inherent resistance to fracture and the size and
3.1.5 inert flexural strength, [FL ], n—a measure of the
severity of flaws. Variations in these cause a natural scatter in
strength of a specified beam specimen in bending as deter-
test results for a sample of test specimens. Fractographic
mined in an appropriate inert condition whereby no slow crack
analysis of fracture surfaces, although beyond the scope of this
growth occurs.
test method, is highly recommended for all purposes, espe-
–2
3.1.6 inherent flexural strength, [FL ], n—the flexural
cially if the data will be used for design as discussed in Ref (4)
strength of a material in the absence of any effect of surface
and Practices C1322 and C1239.
grinding or other surface finishing process, or of extraneous
4.5 This method determines the flexural strength at elevated
damage that may be present. The measured inherent strength is
temperature and ambient environmental conditions at a
in general a function of the flexure test method, test conditions,
nominal, moderately fast testing rate. The flexural strength
and test specimen size.
under these conditions may or may not necessarily be the inert
3.1.7 inner gage section, n—the portion of the specimen
flexural strength. Flexure strength at elevated temperature may
between the inner two bearings in a four-point flexure fixture.
be strongly dependent on testing rate, a consequence of creep,
3.1.8 semi-articulating fixture, n—a flexure fixture designed
stress corrosion, or slow crack growth. If the purpose of the test
to be used with flat and parallel specimens. The fixture allows
some articulation, or pivoting, to ensure the top pair (or bottom
pair) of bearing cylinders pivot together about an axis parallel
The boldface numbers in parentheses refer to the list of references at the end of
to the specimen long axis, in order to match the specimen the text.
C1211 − 18 (2023)
TABLE 1 Fixture Spans
is to measure the inert flexural strength, then extra precautions
are required and faster testing rates may be necessary. Support Span Loading Span,
Configuration
(L), mm mm
NOTE 6—Many ceramics are susceptible to either environmentally
A 20 10
assisted slow crack growth or thermally activated slow crack growth.
B 40 20
Oxide ceramics, glasses, glass ceramics, and ceramics containing bound-
C 80 40
ary phase glass are particularly susceptible to slow crack growth.
Time-dependent effects that are caused by environmental factors (for
example, water as humidity in air) may be minimized through the use of
inert testing atmosphere such as dry nitrogen gas or vacuum. Alternatively,
testing rates faster than specified in this standard may be used if the goal or may not produce the inert flexural strength whereby negli-
is to measure the inert strength. Thermally activated slow crack growth
gible slow crack growth occurs. See Test Methods C1368 and
may occur at elevated temperature even in inert atmospheres. Testing rates
C1465 and Ref (5) for more information about possible rate
faster than specified in this standard should be used if the goal is to
dependencies of flexural strength and methodologies for quan-
measure the inert flexural strength. On the other hand, many ceramics such
tifying the rate sensitivity
as boron carbide, silicon carbide, aluminum nitride, and many silicon
nitrides have no sensitivity to slow crack growth at room or moderately
elevated temperatures and for such materials, the flexural strength
6. Apparatus
measured under laboratory ambient conditions at the nominal testing rate
6.1 Loading—Specimens may be force in any suitable
is the inert flexural strength.
testing machine provided that uniform rates of direct loading
4.6 The three-point test configuration exposes only a very
can be maintained. The force measuring system shall be free of
small portion of the specimen to the maximum stress.
initial lag at the loading rates used and shall be equipped with
Therefore, three-point flexural strengths are likely to be much
a means for retaining readout of the maximum force as well as
greater than four-point flexural strengths. Three-point flexure
a force-time or force-deflection record. The accuracy of the
has some advantages. It uses simpler test fixtures, it is easier to
testing machine shall be in accordance with Practices E4.
adapt to high temperature, and it is sometimes helpful in
Weibull statistical studies. However, four-point flexure is 6.2 Four-Point Flexure Four-Point- ⁄4-Point Fixtures (Fig.
1), having support spans as given in Table 1.
preferred and recommended for most characterization pur-
poses.
6.3 Three-Point Flexure Three-Point Fixtures (Fig. 1), hav-
ing a support span as given in Table 1.
4.7 The three-point test configuration exposes only a very
small portion of the specimen to the maximum stress.
6.4 Bearings, Three- and four-point flexure.
Therefore, three-point flexural strengths are likely to be much
6.4.1 Cylindrical bearings shall be used for support of the
greater than four-point flexural strengths. Three-point flexure
test specimen and for load application. The cylinders may be
has some advantages. It uses simpler test fixtures, it is easier to
made of a ceramic with an elastic modulus between 200 and
adapt to high temperature, and it is sometimes helpful in
400 GPa (30 to 60 × 10 psi) and a flexural strength no less
Weibull statistical studies. However, four-point flexure is
than 275 MPa (≈40 ksi). The loading cylinders must remain
preferred and recommended for most characterization pur-
elastic (and have no plastic deformation) over the load and
poses.
temperature ranges used, and they must not react chemically
with or contaminate the test specimen. The test fixture shall
5. Interferences
also be made of a ceramic that is resistant to permanent
5.1 Time-dependent phenomena, such as stress corrosion
deformation.
and slow crack growth, can interfere with determination of the
6.4.2 The bearing cylinder diameter shall be approximately
flexural strength at room and elevated temperatures. Creep
1.5 times the beam depth of the test specimen size used (see
phenomena also become significant at elevated temperatures.
Table 2).
Creep deformation can cause stress relaxation in a flexure
6.4.3 The bearing cylinders shall be positioned carefully
specimen during a strength test, thereby causing the elastic
such that the spans are accurate to within 60.10 mm. The load
formulation that is used to compute the strength to be in error.
application bearing for the three-point configurations shall be
5.2 Surface preparation of the test specimens can introduce
positioned midway between the support bearings within
machining damage such as microcracks that may have a
60.10 mm. The load application (inner) bearings for the
...
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