ASTM C1211-98a
(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
SCOPE
1.1 This test method covers determination of the flexural strength of advanced ceramics at elevated temperatures. Four-point- 1/4 point and three-point loadings with prescribed spans are the standard. Rectangular specimens of prescribed cross-section are used with specified features in prescribed specimen-fixture combinations.
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 problems, 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.
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Designation: C 1211 – 98a
Standard Test Method for
Flexural Strength of Advanced Ceramics at Elevated
Temperatures
This standard is issued under the fixed designation C 1211; 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.
1. Scope * 2.2 Military Standard:
MIL-STD 1942(A) Flexural Strength of High Performance
1.1 This test method covers determination of the flexural
Ceramics at Ambient Temperature
strength of advanced ceramics at elevated temperatures.
Four-point- ⁄4 point and three-point loadings with prescribed
3. Terminology
spans are the standard. Rectangular specimens of prescribed
3.1 Definitions:
cross-section are used with specified features in prescribed
3.1.1 flexural strength—a measure of the ultimate strength
specimen-fixture combinations.
of a specified beam in bending.
1.2 The values stated in SI units are to be regarded as the
3.1.2 four-point-1/4 point flexure—a configuration of flex-
standard. The values given in parentheses are for information
ural strength testing in which a specimen is symmetrically
only.
loaded at two locations that are situated at one-quarter of the
1.3 This standard does not purport to address all of the
overall span, away from the outer two support bearings (see
safety concerns, if any, associated with its use. It is the
Fig. 1).
responsibility of the user of this standard to establish appro-
3.1.3 inert flexural strength, n—a measure of the strength of
priate safety and health practices and determine the applica-
a specified beam specimen in bending as determined in an
bility of regulatory limitations prior to use.
appropriate inert condition whereby no slow crack growth
2. Referenced Documents occurs.
3.1.4 slow crack growth (SCG), n—Subcritical crack
2.1 ASTM Standards:
growth (extension) which may result from, but is not restricted
C 1161 Test Method for Flexural Strength of Advanced
to, such mechanisms as environmentally-assisted stress corro-
Ceramics at Ambient Temperature
sion or diffusive crack growth.
C 1322 Practice for Fractography and Characterization of
3.1.5 three-point flexure—a configuration of flexural
Fracture Origins in Advanced Ceramics
strength testing in which a specimen is loaded at a position
C 1341 Test Method for Flexural Properties of Continuous
midway between two support bearings (see Fig. 1).
Fiber Reinforced Advanced Ceramic Composites
C 1368 Test Method for Determination of Slow Crack
4. Significance and Use
Growth Parameters of Advanced Ceramics by Constant
3 4.1 This test method may be used for material development,
Stress-Rate Flexural Testing at Ambient Temperature
4 quality control, characterization, and design data generation
E 4 Practices for Force Verification of Testing Machines
purposes. This test method is intended to be used with ceramics
E 220 Method for Calibration of Thermocouples by Com-
5 whose flexural strength is ; 50 MPa (; 7 ksi) or greater.
parison Techniques
4.2 The flexure stress is computed based on simple beam
E 230 Temperature Electromotive Force (EMF) Tables for
5 theory, with assumptions that the material is isotropic and
Standardized Thermocouples
homogeneous, the moduli of elasticity in tension and compres-
sion are identical, and the material is linearly elastic. The
1 1
This test method is under the jurisdiction of ASTM Committee C-28 on average grain size should be no greater than ⁄50 of the beam
Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 on
thickness. The homogeneity and isotropy assumptions in the
Properties and Performance.
Current edition approved June 10, 1998. Published December 1998. Originally
published as C 1211-92. Last previous edition C 1211-98.
Elevated temperatures typically denote, but are not restricted to 200 to 1600°C.
3 6
Annual Book of ASTM Standards, Vol 15.01. Available from Standardization Documents Order Desk, Bldg. 4 Section D, 700
Annual Book of ASTM Standards, Vol 03.01. Robbins Ave., Philadelphia, PA 19111-5094. This document is a 1990 update of the
Annual Book of ASTM Standards, Vol 14.03. original MIL-STD 1942(MR), dated November 1983.
*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.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
C 1211 – 98a
TABLE 1 Fixture Spans
Configuration Support Span Loading Span,
(L), mm mm
A20 10
B40 20
C80 40
specimen during a strength test, thereby causing the elastic
formulation that is used to compute the strength to be in error.
5.2 Surface preparation of the test specimens can introduce
machining flaws that may have a pronounced effect on flexural
strength. Machining damage imposed during specimen prepa-
ration can be either a random interfering factor or an inherent
part of the strength characteristic to be measured. Surface
preparation can also lead to residual stresses. Universal or
standardized test methods of surface preparation do not exist. It
should be understood that final machining steps may or may
NOTE 1—Configuration:
not negate machining damage introduced during the early
A: L = 20 mm
coarse or intermediate machining.
B: L = 40 mm
5.3 Slow crack growth can lead to a rate dependency of
C: L = 80 mm
1 flexural strength. The testing rate specified in this standard may
FIG. 1 Four-Point- ⁄4 Point and Three-Point Fixture Configurations
or may not produce the inert flexural strength whereby negli-
gible slow crack growth occurs. See Method C 1368.
test method rule out the use of it for continuous fiber-reinforced
composites for which Test Method C 1341 is more appropriate.
6. Apparatus
4.3 The flexural strength of a group of test specimens is
6.1 Loading—Specimens may be force in any suitable
influenced by several parameters associated with the test
testing machine provided that uniform rates of direct loading
procedure. Such factors include the testing rate, test environ-
can be maintained. The force measuring system shall be free of
ment, specimen size, specimen preparation, and test fixtures.
initial lag at the loading rates used and shall be equipped with
Specimen and fixture sizes were chosen to provide a balance
a means for retaining readout of the maximum force as well as
between the practical configurations and resulting errors as
a force-time or force-deflection record. The accuracy of the
discussed in MIL-STD 1942(A), Test Method C 1161, and
7 testing machine shall be in accordance with Practices E 4.
Refs (1–3). Specific fixture and specimen configurations were
6.2 Four-Point Flexure Four-Point- ⁄4 Point Fixtures (Fig.
designated in order to permit the ready comparison of data
1), having support spans as given in Table 1.
without the need for Weibull size scaling.
6.3 Three-Point Flexure Three-Point Fixtures (Fig. 1), hav-
4.4 The flexural strength of a ceramic material is dependent
ing a support span as given in Table 1.
on both its inherent resistance to fracture and the size and
6.4 Bearings, three- and four-point flexure.
severity of flaws that are present. Fractographic analysis of
6.4.1 Cylindrical bearings shall be used for support of the
fracture surfaces, although beyond the scope of this test
test specimen and for load application. The cylinders may be
method, is highly recommended for all purposes, especially for
made of a ceramic with an elastic modulus between 200 and
design data. See Practice C 1322.
400 GPa (30 to 60 3 10 psi) and a flexural strength no less
4.5 Flexure strength at elevated temperature may be
than 275 MPa (’40 ksi). The loading cylinders must remain
strongly dependent on testing rate, a consequence of creep,
elastic (and have no plastic deformation) over the load and
stress corrosion, or slow crack growth. This test method
temperature ranges used, and they must not react chemically
measures the flexural strength at high loading rates in order to
with or contaminate the test specimen. The test fixture shall
minimize these effects.
also be made of a ceramic that is resistant to permanent
deformation.
5. Interferences
6.4.2 The bearing cylinder diameter shall be approximately
5.1 Time-dependent phenomena, such as stress corrosion
1.5 times the beam depth of the test specimen size used (see
and slow crack growth, can interfere with determination of the
Table 2).
flexural strength at room and elevated temperatures. Creep
phenomena also become significant at elevated temperatures.
Creep deformation can cause stress relaxation in a flexure
The accuracy requirement is different from that specified in Test Method
C 1161 and is a concession to difficulties incurred in conducting elevated tempera-
The boldface numbers in parentheses refer to the list of references at the end of ture testing. The accuracy required by Practices E 4 is 1 %; Test Method C 1161
the text. calls for 0.5 %.
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C 1211 – 98a
TABLE 2 Nominal Bearing Diameters
that the outer-support bearings roll outward and the inner-
loading bearings roll inward.
Configuration Diameter, mm
6.5 Semiarticulating Four-Point Fixture—Specimens pre-
A 2.0 to 2.5
pared in accordance with the parallelism requirements of 7.1
B 4.5
may be tested in a semiarticulating fixture as illustrated in Fig.
C 9.0
2 and in Fig. A2.1(a). All four bearings shall be free to roll. The
two inner bearings shall be parallel to each other to within
TABLE 3 Specimen Sizes
0.015 mm over their length. The two outer bearings shall be
parallel to each other to within 0.015 mm over their length. The
Configuration Width (b), Depth (d), Length (L ),
T
inner bearings shall be supported independently of the outer
mm mm mm, min
bearings. All four bearings shall rest uniformly and evenly
A 2.0 1.5 25
across the specimen surfaces. The fixture shall be designed to
B 4.0 3.0 45
C 8.0 6.0 90
apply equal load to all four bearings.
6.6 Fully Articulating Four-Point Fixture—Specimens that
are as-fired, heat treated, or oxidized often have slight twists or
unevenness. Specimens that do not meet the parallelism
6.4.3 The bearing cylinders shall be positioned carefully
such that the spans are accurate to within 60.10 mm. The load requirements of 7.1 shall be tested in a fully articulating fixture
as illustrated in Fig. 3 and in Fig. A2.1(b). Well-machined
application bearing for the three-point configurations shall be
positioned midway between the support bearings within 60.10 specimens may also be tested in fully-articulating fixtures. All
mm. The load application (inner) bearings for the four-point four bearings shall be free to roll. One bearing need not
configurations shall be centered with respect to the support articulate. The other three bearings shall articulate to match the
(outer) bearings within 60.10 mm. specimen’s surface. All four bearings shall rest uniformly and
evenly across the specimen surfaces. The fixture shall apply
6.4.4 The bearing cylinders shall be free to rotate in order to
relieve frictional constraints (with the exception of the middle- equal load to all four bearings.
load bearing in three-point flexure, which need not rotate). This
6.7 Semiarticulated Three-Point Fixture—Specimens pre-
can be accomplished as shown in Fig. 2 and Fig. 3. Annex A2
pared in accordance with the parallelism requirements of 7.1
illustrates the action required of the bearing cylinders. Note may be tested in a semiarticulating fixture as illustrated in Fig.
A2.2(a). The middle bearing shall be fixed and not free to roll.
The two outer bearings shall be parallel to each other to within
0.015 mm over their length. The two outer bearings shall
articulate together to match the specimen surface, or the middle
bearing shall articulate to match the specimen surface. All three
bearings shall rest uniformly and evenly across the specimen
surface. The fixture shall be designed to apply equal load to the
two outer bearings.
6.8 Fully Articulated Three-Point Flexure—Specimens that
do not meet the parallelism requirements of 7.1 shall be tested
in a fully-articulating fixture as illustrated in Figs. A2.2(b) or
A2.2(c). Well-machined specimens may also be tested in
fully-articulating fixtures. The two support (outer) bearings
shall be free to roll outwards. The middle bearing shall not roll.
Any two of the bearings shall be capable of articulating to
match the specimen surface. All three bearings shall rest
In general, fixed-pin fixtures have frictional constraints that can cause a
systematic error on the order of 5 to 15 % in flexure strength (see Refs (1, 2, 4 to
7)). Since this error is systematic (constant for all specimens in a sample), it will
lead to a bias in estimates of the mean strength and will shift a Weibull curve a fixed
amount of stress. The scatter, however, will remain constant.
Rolling-pin fixtures are required by this test method. It is recognized that they
may not be feasible in some instances, in which case fixed-pin fixtures may be used,
but this must be stated explicitly in the report, and justification must be given as
NOTE 1—Configuration:
noted in 10.1.16.
A: L = 20 mm
Some fixtures have loading cylinders that fit into square slots with a slight
B: L = 40 mm
clearance. Of course, the clearance must be such that the possible spans are within
C: L = 80 mm
the prescribed limits of this test method. Unfortunately, for any given test, it is
FIG. 2 Schematics of Semiarticulated Four-Point Fixtures
usually not possible to ascertain whether a roller rests against an inner or outer
Suitable for Flat and Parallel Specimens; Load is Applied
shoulder, and thus it is possible that some rollers may be free to roll and others not.
Through a Rounded and Well-Centered Tip that Permits the
This can lead to the superimposition of a random error on the results. Such fixtures
Loading Member to Tilt as Necessary to Ensure Uniform Loading should therefore be used with caution.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
C 1211 – 98a
NOTE 1—Configuration:
A: L = 20 mm
B: L = 40 mm
C: L = 80 mm
FIG. 3 Schematics of Fully Articulating Four-Point Fixtures Suitable for Twisted or Uneven Specimen
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