ASTM C158-02(2017)
(Test Method)Standard Test Methods for Strength of Glass by Flexure (Determination of Modulus of Rupture)
Standard Test Methods for Strength of Glass by Flexure (Determination of Modulus of Rupture)
SIGNIFICANCE AND USE
4.1 For the purpose of this test, glasses and glass-ceramics are considered brittle (perfectly elastic) and to have the property that fracture normally occurs at the surface of the test specimen from the principal tensile stress. The modulus of rupture is considered a valid measure of the tensile strength subject to the considerations discussed below.
4.2 It is recognized that the modulus of rupture for a group of test specimens is influenced by variables associated with the test procedure. These include the rate of stressing, test environment, and the area of the specimen subjected to stress. Such factors are specified in the test procedure or required to be stated in the report.
4.3 It is also recognized that the variables having the greatest effect on the modulus of rupture value for a group of test specimens are the condition of the surfaces and glass quality near the surfaces in regard to the number and severity of stress-concentrating discontinuities or flaws, and the degree of prestress existing in the specimens. Each of these can represent an inherent part of the strength characteristic being determined or can be a random interfering factor in the measurement.
4.4 Test Method A is designed to include the condition of the surface of the specimen as a factor in the measured strength. It is, therefore, desirable to subject a fixed and significant area of the surface to the maximum tensile stress. Since the number and severity of surface flaws in glass are primarily determined by manufacturing and handling processes, this test method is limited to products from which specimens of suitable size can be obtained with minimal dependence of measured strength upon specimen preparation techniques. This test method is therefore designated as a test for modulus of rupture of flat glass.
4.5 Test Method B describes a general procedure for test, applicable to specimens of rectangular or elliptical cross section. This test method is based on the assumption that ...
SCOPE
1.1 These test methods cover the determination of the modulus of rupture in bending of glass and glass-ceramics.
1.2 These test methods are applicable to annealed and prestressed glasses and glass-ceramics available in varied forms. Alternative test methods are described; the test method used shall be determined by the purpose of the test and geometric characteristics of specimens representative of the material.
1.2.1 Test Method A is a test for modulus of rupture of flat glass.
1.2.2 Test Method B is a comparative test for modulus of rupture of glass and glass-ceramics.
1.3 The test methods appear in the following order:
Sections
Test Method A
6 to 9
Test Method B
10 to 15
1.4 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. Specific hazard statements are given in Section 10 and A1.5, A2.3.3, A2.4.3 and A2.5.3.
1.5 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.
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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: C158 − 02 (Reapproved 2017)
Standard Test Methods for
Strength of Glass by Flexure (Determination of Modulus of
Rupture)
This standard is issued under the fixed designation C158; 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 2. Referenced Documents
2.1 ASTM Standards:
1.1 These test methods cover the determination of the
C148Test Methods for Polariscopic Examination of Glass
modulus of rupture in bending of glass and glass-ceramics.
Containers
1.2 These test methods are applicable to annealed and
E4Practices for Force Verification of Testing Machines
prestressed glasses and glass-ceramics available in varied
SI10-02 IEEE/ASTM SI 10American National Standard for
forms.Alternative test methods are described; the test method
UseoftheInternationalSystemofUnits(SI):TheModern
used shall be determined by the purpose of the test and
Metric System
geometric characteristics of specimens representative of the
3. Terminology
material.
1.2.1 Test Method A is a test for modulus of rupture of flat
3.1 Definitions:
glass. 3.1.1 glass-ceramics—solid materials, predominantly crys-
talline in nature, formed by the controlled crystallization of
1.2.2 Test Method B is a comparative test for modulus of
glasses.
rupture of glass and glass-ceramics.
3.1.2 modulus of rupture in bending—the value of maxi-
1.3 The test methods appear in the following order:
mum tensile or compressive stress (whichever causes failure)
Sections
in the extreme fiber of a beam loaded to failure in bending
Test Method A 6 to 9
Test Method B 10 to 15 computed from the flexure formula:
1.4 This standard does not purport to address all of the
Mc
S 5 (1)
b
safety concerns, if any, associated with its use. It is the
I
responsibility of the user of this standard to establish appro-
where:
priate safety, health, and environmental practices and deter-
M = maximum bending moment, computed from the maxi-
mine the applicability of regulatory limitations prior to use.
mum load and the original moment arm,
Specific hazard statements are given in Section 10 and A1.5,
c = initialdistancefromtheneutralaxistotheextremefiber
A2.3.3, A2.4.3 and A2.5.3.
where failure occurs, and
1.5 This international standard was developed in accor-
I = initial moment of inertia of the cross section about the
dance with internationally recognized principles on standard-
neutral axis.
ization established in the Decision on Principles for the
3.1.3 prestressed—material in which a significant and con-
Development of International Standards, Guides and Recom-
trolled degree of compressive stress has been deliberately
mendations issued by the World Trade Organization Technical
produced in the surfaces.
Barriers to Trade (TBT) Committee.
3.1.4 standard laboratory atmosphere—an atmosphere hav-
ingatemperatureof23 62°Candarelativehumidityof40 6
10%.
These test methods are under the jurisdiction of ASTM Committee C14 on
Glass and Glass Products and are the direct responsibility of Subcommittee C14.04
on Physical and Mechanical Properties. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Nov. 1, 2017. Published November 2017. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1940. Last previous edition approved in 2012 as C158–02(2012). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/C0158-02R17. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C158 − 02 (2017)
3.2 Definitions of Terms Specific to This Standard: comparative measurement of strength on groups of specimens
3.2.1 abraded—describes a test specimen that has at least a is of significance for many purposes, such as determining the
portionoftheareaofmaximumsurfacetensilestresssubjected effect of environment or stress duration, or the effectiveness of
to an operationally defined procedure for mechanical abrasion. varied prestressing techniques or strengths characteristic of
The severity and uniformity of abrasion should be sufficient to glass-ceramics of differing composition or heat treatment. In
ensureoriginoffailuresubstantiallyintheregionofmaximum this test method the surfaces of the specimens are not assumed
stress. to be characteristic of a product or material, but are considered
to be determined by the procedures used to prepare the
3.2.2 annealed glass—describes a specimen that shall not
specimens. Though the stated procedure permits a wide varia-
have a temper or degree of residual stress resulting from prior
tion in both specimen size and test geometry, it is necessary to
thermal treatment in excess of the following limits when
use identical test conditions and equivalent procedures for
measured polarimetrically (see Annex A1):
specimen preparation to obtain comparable strength values.
3.2.2.1 Specimens of rectangular section shall not have a
The use of a controlled abrasion of the specimen as a final
tensile stress at the midplane of more than 1.38-MPa (200-psi)
normalizing procedure is recommended for such comparative
nor more than 2.76-MPa (400-psi) compression at the surface.
tests.
3.2.2.2 Specimensinrodformmaybeexaminedbyviewing
through a diameter at least four diameters from an end. The 4.6 A comparative abraded strength, determined as sug-
apparent central axial tension shall not exceed 0.92 MPa gestedinTestMethodB,isnottobeconsideredasaminimum
(133psi). Surface compression, if measured on sections cut valuecharacteristicofthematerialtestednorasdirectlyrelated
from the rods, shall not exceed 2.76 MPa (400 psi) when to a maximum attainable strength value through test of
viewed axially. specimens with identical flaws. The operationally defined
abrasion procedure undoubtedly produces flaws of differing
4. Significance and Use
severity when applied to varied materials, and the measured
comparative strengths describe the relative ability to withstand
4.1 For the purpose of this test, glasses and glass-ceramics
externally induced stress as affected by the specific abrasion
are considered brittle (perfectly elastic) and to have the
procedure.
property that fracture normally occurs at the surface of the test
specimen from the principal tensile stress. The modulus of
5. Apparatus
rupture is considered a valid measure of the tensile strength
subject to the considerations discussed below.
5.1 Testing Machine—The loading mechanism shall be
sufficiently adjustable to give the required uniform rate of
4.2 It is recognized that the modulus of rupture for a group
increase of stress. The load-measuring system shall be essen-
oftestspecimensisinfluencedbyvariablesassociatedwiththe
tially free of inertial lag at the loading rates used and shall be
test procedure. These include the rate of stressing, test
equipped with means for retaining indication of the maximum
environment, and the area of the specimen subjected to stress.
load applied to the specimen. The accuracy of the testing
Suchfactorsarespecifiedinthetestprocedureorrequiredtobe
machine shall conform to the requirements of Practice E4.
stated in the report.
5.2 Bearing Edges—Cylindrical bearing edges of approxi-
4.3 It is also recognized that the variables having the
mately3-mm( ⁄8-in.)radiusshallbeusedforthesupportofthe
greatest effect on the modulus of rupture value for a group of
test specimen and the application of the load. The bearing
test specimens are the condition of the surfaces and glass
edges shall be of steel and sufficiently hardened to prevent
quality near the surfaces in regard to the number and severity
excessive deformation under load. Two-point loading tests
of stress-concentrating discontinuities or flaws, and the degree
shall be performed with the loading member pivoted about a
of prestress existing in the specimens. Each of these can
central transverse axis to ensure equal distribution of load
represent an inherent part of the strength characteristic being
betweenthetwobearingedges.Forthetestingofspecimensof
determined or can be a random interfering factor in the
rectangular section, both loading bearing edges and one sup-
measurement.
port bearing edge also shall be provided laterally to compen-
4.4 Test Method A is designed to include the condition of
sate for irregularities of the test specimen. Fig. 1 shows a
the surface of the specimen as a factor in the measured
suitable arrangement using pinned bearing edges. In test of
strength. It is, therefore, desirable to subject a fixed and
specimens of a circular or elliptical section, the fixed cylindri-
significant area of the surface to the maximum tensile stress.
cal support edges may have a curvature of approximately
Since the number and severity of surface flaws in glass are
76mm (3 in.) in the plane of the bearing edge to stabilize the
primarily determined by manufacturing and handling
alignment of the specimens. Such support edges are shown in
processes, this test method is limited to products from which
Fig. 2.
specimens of suitable size can be obtained with minimal
dependence of measured strength upon specimen preparation
TEST METHOD A—TEST FOR MODULUS OF
techniques. This test method is therefore designated as a test
RUPTURE OF FLAT GLASS
for modulus of rupture of flat glass.
6. Test Specimens
4.5 Test Method B describes a general procedure for test,
applicable to specimens of rectangular or elliptical cross 6.1 Preparation of Specimens—Test specimens shall be cut
section. This test method is based on the assumption that a from the sheet stock with a diamond or a cutting wheel. Both
C158 − 02 (2017)
FIG. 1 Pinned Bearing Edges
FIG. 2 Fixed Cylindrical Support Edges
longitudinalcutsshallbeonthesameoriginalsurfaceandnone remainder of the specimens shall be examined and those
of the original edge of the sheet shall be used as a longitudinal exceeding the stated limit shall be rejected.
side of the specimen. End cuts may be on either surface. The
6.5 Float Glass—The surface of float glass in contact with
direction of cutting of half of the total number of specimens
tin has been found to be lower in strength (1) as compared to
shall be perpendicular to the direction of cutting of the
the “air” surface. For comparative tests, therefore, surface
remainder. Specimens that must be cut from sheet stock prior
orientation should be kept constant.
to the use of a prestressing treatment shall have the corners of
the longitudinal edges rounded to minimize damage to the
7. Procedure
edges in the prestressing process. All operations shall be
performed with the direction of grind or polish parallel to the
7.1 Space the supporting edges of the test fixture 200 mm
longitudinal axis. The radius of the corner shall not exceed
(8.00 in.) apart and centrally position the loading edges with a
1.6mm ( ⁄16 in.). separation of 100 mm (4.00 in.). Break specimens having cut
edges with the cutter marks on the face under compression.
6.2 Size of Specimens—The specimens shall be approxi-
Carefully place each specimen in the test fixture to minimize
mately 250 mm (10 in.) in length and 38.1 6 3.2 mm (1 ⁄2 6
possible damage and to ensure alignment of specimen in the
⁄8 in.) in width. The variation in width or thickness shall not
fixture. The permissible maximum fiber stress due to initial
exceed 5% from one end to the other.
load on the specimen shall not exceed 25% of the mean
6.3 Number of Specimens—At least 30 specimens shall be
modulus of rupture. Load the specimen at a constant rate to
used for one test and shall preferably be taken from several
failure. For annealed glass the rate of loading shall correspond
sheets, or regions of a single sheet.
to a rate of increase of maximum stress of 1.1 6 0.2 MPa/s
6.4 Examination of Specimens—Any specimen may be re- (10000 6 2000 psi/min). Test prestressed glasses with the
jected prior to test for observable defects considered likely to increase of maximum stress per minute between 80 and 120%
affect the modulus of rupture. To be considered representative of the modulus of rupture.The first six specimens of the group
of annealed glass the specimens must meet the requirement of may be tested at a loading rate based on an estimate of the
3.2.2. At least 30% of the specimens shall be examined for modulus of rupture and the average value for these specimens
residual stress. If any of these fail to meet the requirement, the used to correct this estimate. If range of width and thickness
C158 − 02 (2017)
variation in the specimens is less than 5%, the mean values 9.1.4 Test environment if other than standard laboratory
may be used to represent all specimens for the purpose of atmosphere,
calculation of rate of loading. 9.1.5 Rate of increase of maximum stress,
9.1.6 Value of modulus of rupture for each specimen and
7.2 Determine the thickness and width of each specimen to
designation of point of failure as edge or face, and
61%. To avoid damage from gaging in the critical area, take
9.1.7 Average value of the modulus of rupture for the group
measurements prior to testing near each end with a separation
and the standard deviation estimate of the mean. Separate
equal to the support span, and average the values. Measure-
values may be determined for edge and face origins.
ments following test shall be in the uniformly stressed region
of the specimen.
NOTE1—SeeAnnexA3forconversionfrominch-poundunitsandother
non-SI units to SI units.
7.3 Determine the location of point of failure and note it as
edgeorfaceorigin.Plasticorothertapeoflowelasticmodulus
TEST METHOD B—COMPARATIVE TEST FOR
may be used on the compressive surface to contain the
MODULUS OF RUPTURE OF GLASS AND GLASS-
fragmentation and allow observation of point of failure for
CERAMICS
highly prestressed specimens. Report all values, although
segregation of edge break values is permitted.
10. Hazards
10.1 Care should be exercised in all handling of specimens
8. Calculation
to avoid the introduction of random and severe flaws.
8.1 Calculate the modulus of rupture, initial maximum fiber
10.2 Abrasionofspecimensofrectangularsectionshouldbe
stress, and rate of increase of stress as follows:
performed so that corn
...
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: C158 − 02 (Reapproved 2017)
Standard Test Methods for
Strength of Glass by Flexure (Determination of Modulus of
Rupture)
This standard is issued under the fixed designation C158; 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 2. Referenced Documents
2.1 ASTM Standards:
1.1 These test methods cover the determination of the
C148 Test Methods for Polariscopic Examination of Glass
modulus of rupture in bending of glass and glass-ceramics.
Containers
1.2 These test methods are applicable to annealed and
E4 Practices for Force Verification of Testing Machines
prestressed glasses and glass-ceramics available in varied
SI10-02 IEEE/ASTM SI 10 American National Standard for
forms. Alternative test methods are described; the test method
Use of the International System of Units (SI): The Modern
used shall be determined by the purpose of the test and
Metric System
geometric characteristics of specimens representative of the
3. Terminology
material.
1.2.1 Test Method A is a test for modulus of rupture of flat
3.1 Definitions:
glass. 3.1.1 glass-ceramics—solid materials, predominantly crys-
talline in nature, formed by the controlled crystallization of
1.2.2 Test Method B is a comparative test for modulus of
glasses.
rupture of glass and glass-ceramics.
3.1.2 modulus of rupture in bending—the value of maxi-
1.3 The test methods appear in the following order:
mum tensile or compressive stress (whichever causes failure)
Sections
in the extreme fiber of a beam loaded to failure in bending
Test Method A 6 to 9
Test Method B 10 to 15 computed from the flexure formula:
1.4 This standard does not purport to address all of the
M c
S 5 (1)
b
safety concerns, if any, associated with its use. It is the
I
responsibility of the user of this standard to establish appro-
where:
priate safety, health, and environmental practices and deter-
M = maximum bending moment, computed from the maxi-
mine the applicability of regulatory limitations prior to use.
mum load and the original moment arm,
Specific hazard statements are given in Section 10 and A1.5,
c = initial distance from the neutral axis to the extreme fiber
A2.3.3, A2.4.3 and A2.5.3.
where failure occurs, and
1.5 This international standard was developed in accor-
I = initial moment of inertia of the cross section about the
dance with internationally recognized principles on standard-
neutral axis.
ization established in the Decision on Principles for the
3.1.3 prestressed—material in which a significant and con-
Development of International Standards, Guides and Recom-
trolled degree of compressive stress has been deliberately
mendations issued by the World Trade Organization Technical
produced in the surfaces.
Barriers to Trade (TBT) Committee.
3.1.4 standard laboratory atmosphere—an atmosphere hav-
ing a temperature of 23 6 2°C and a relative humidity of 40 6
10 %.
These test methods are under the jurisdiction of ASTM Committee C14 on
Glass and Glass Products and are the direct responsibility of Subcommittee C14.04
on Physical and Mechanical Properties. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Nov. 1, 2017. Published November 2017. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1940. Last previous edition approved in 2012 as C158 – 02 (2012). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/C0158-02R17. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C158 − 02 (2017)
3.2 Definitions of Terms Specific to This Standard: comparative measurement of strength on groups of specimens
3.2.1 abraded—describes a test specimen that has at least a is of significance for many purposes, such as determining the
portion of the area of maximum surface tensile stress subjected effect of environment or stress duration, or the effectiveness of
to an operationally defined procedure for mechanical abrasion. varied prestressing techniques or strengths characteristic of
The severity and uniformity of abrasion should be sufficient to glass-ceramics of differing composition or heat treatment. In
ensure origin of failure substantially in the region of maximum this test method the surfaces of the specimens are not assumed
stress. to be characteristic of a product or material, but are considered
to be determined by the procedures used to prepare the
3.2.2 annealed glass—describes a specimen that shall not
specimens. Though the stated procedure permits a wide varia-
have a temper or degree of residual stress resulting from prior
tion in both specimen size and test geometry, it is necessary to
thermal treatment in excess of the following limits when
use identical test conditions and equivalent procedures for
measured polarimetrically (see Annex A1):
specimen preparation to obtain comparable strength values.
3.2.2.1 Specimens of rectangular section shall not have a
The use of a controlled abrasion of the specimen as a final
tensile stress at the midplane of more than 1.38-MPa (200-psi)
normalizing procedure is recommended for such comparative
nor more than 2.76-MPa (400-psi) compression at the surface.
tests.
3.2.2.2 Specimens in rod form may be examined by viewing
through a diameter at least four diameters from an end. The 4.6 A comparative abraded strength, determined as sug-
apparent central axial tension shall not exceed 0.92 MPa gested in Test Method B, is not to be considered as a minimum
(133 psi). Surface compression, if measured on sections cut value characteristic of the material tested nor as directly related
from the rods, shall not exceed 2.76 MPa (400 psi) when to a maximum attainable strength value through test of
viewed axially. specimens with identical flaws. The operationally defined
abrasion procedure undoubtedly produces flaws of differing
4. Significance and Use
severity when applied to varied materials, and the measured
comparative strengths describe the relative ability to withstand
4.1 For the purpose of this test, glasses and glass-ceramics
externally induced stress as affected by the specific abrasion
are considered brittle (perfectly elastic) and to have the
procedure.
property that fracture normally occurs at the surface of the test
specimen from the principal tensile stress. The modulus of
5. Apparatus
rupture is considered a valid measure of the tensile strength
subject to the considerations discussed below.
5.1 Testing Machine—The loading mechanism shall be
sufficiently adjustable to give the required uniform rate of
4.2 It is recognized that the modulus of rupture for a group
increase of stress. The load-measuring system shall be essen-
of test specimens is influenced by variables associated with the
tially free of inertial lag at the loading rates used and shall be
test procedure. These include the rate of stressing, test
equipped with means for retaining indication of the maximum
environment, and the area of the specimen subjected to stress.
load applied to the specimen. The accuracy of the testing
Such factors are specified in the test procedure or required to be
machine shall conform to the requirements of Practice E4.
stated in the report.
5.2 Bearing Edges—Cylindrical bearing edges of approxi-
4.3 It is also recognized that the variables having the
mately 3-mm ( ⁄8-in.) radius shall be used for the support of the
greatest effect on the modulus of rupture value for a group of
test specimen and the application of the load. The bearing
test specimens are the condition of the surfaces and glass
edges shall be of steel and sufficiently hardened to prevent
quality near the surfaces in regard to the number and severity
excessive deformation under load. Two-point loading tests
of stress-concentrating discontinuities or flaws, and the degree
shall be performed with the loading member pivoted about a
of prestress existing in the specimens. Each of these can
central transverse axis to ensure equal distribution of load
represent an inherent part of the strength characteristic being
between the two bearing edges. For the testing of specimens of
determined or can be a random interfering factor in the
rectangular section, both loading bearing edges and one sup-
measurement.
port bearing edge also shall be provided laterally to compen-
4.4 Test Method A is designed to include the condition of
sate for irregularities of the test specimen. Fig. 1 shows a
the surface of the specimen as a factor in the measured
suitable arrangement using pinned bearing edges. In test of
strength. It is, therefore, desirable to subject a fixed and
specimens of a circular or elliptical section, the fixed cylindri-
significant area of the surface to the maximum tensile stress.
cal support edges may have a curvature of approximately
Since the number and severity of surface flaws in glass are
76 mm (3 in.) in the plane of the bearing edge to stabilize the
primarily determined by manufacturing and handling
alignment of the specimens. Such support edges are shown in
processes, this test method is limited to products from which
Fig. 2.
specimens of suitable size can be obtained with minimal
dependence of measured strength upon specimen preparation
TEST METHOD A—TEST FOR MODULUS OF
techniques. This test method is therefore designated as a test
RUPTURE OF FLAT GLASS
for modulus of rupture of flat glass.
6. Test Specimens
4.5 Test Method B describes a general procedure for test,
applicable to specimens of rectangular or elliptical cross 6.1 Preparation of Specimens—Test specimens shall be cut
section. This test method is based on the assumption that a from the sheet stock with a diamond or a cutting wheel. Both
C158 − 02 (2017)
FIG. 1 Pinned Bearing Edges
FIG. 2 Fixed Cylindrical Support Edges
longitudinal cuts shall be on the same original surface and none remainder of the specimens shall be examined and those
of the original edge of the sheet shall be used as a longitudinal exceeding the stated limit shall be rejected.
side of the specimen. End cuts may be on either surface. The
6.5 Float Glass—The surface of float glass in contact with
direction of cutting of half of the total number of specimens
tin has been found to be lower in strength (1) as compared to
shall be perpendicular to the direction of cutting of the
the “air” surface. For comparative tests, therefore, surface
remainder. Specimens that must be cut from sheet stock prior
orientation should be kept constant.
to the use of a prestressing treatment shall have the corners of
the longitudinal edges rounded to minimize damage to the
7. Procedure
edges in the prestressing process. All operations shall be
performed with the direction of grind or polish parallel to the
7.1 Space the supporting edges of the test fixture 200 mm
longitudinal axis. The radius of the corner shall not exceed (8.00 in.) apart and centrally position the loading edges with a
1.6 mm ( ⁄16 in.).
separation of 100 mm (4.00 in.). Break specimens having cut
edges with the cutter marks on the face under compression.
6.2 Size of Specimens—The specimens shall be approxi-
Carefully place each specimen in the test fixture to minimize
mately 250 mm (10 in.) in length and 38.1 6 3.2 mm (1 ⁄2 6
possible damage and to ensure alignment of specimen in the
⁄8 in.) in width. The variation in width or thickness shall not
fixture. The permissible maximum fiber stress due to initial
exceed 5 % from one end to the other.
load on the specimen shall not exceed 25 % of the mean
6.3 Number of Specimens—At least 30 specimens shall be
modulus of rupture. Load the specimen at a constant rate to
used for one test and shall preferably be taken from several
failure. For annealed glass the rate of loading shall correspond
sheets, or regions of a single sheet.
to a rate of increase of maximum stress of 1.1 6 0.2 MPa/s
6.4 Examination of Specimens—Any specimen may be re- (10 000 6 2000 psi/min). Test prestressed glasses with the
jected prior to test for observable defects considered likely to increase of maximum stress per minute between 80 and 120 %
affect the modulus of rupture. To be considered representative of the modulus of rupture. The first six specimens of the group
of annealed glass the specimens must meet the requirement of may be tested at a loading rate based on an estimate of the
3.2.2. At least 30 % of the specimens shall be examined for modulus of rupture and the average value for these specimens
residual stress. If any of these fail to meet the requirement, the used to correct this estimate. If range of width and thickness
C158 − 02 (2017)
variation in the specimens is less than 5 %, the mean values 9.1.4 Test environment if other than standard laboratory
may be used to represent all specimens for the purpose of atmosphere,
calculation of rate of loading. 9.1.5 Rate of increase of maximum stress,
9.1.6 Value of modulus of rupture for each specimen and
7.2 Determine the thickness and width of each specimen to
designation of point of failure as edge or face, and
61 %. To avoid damage from gaging in the critical area, take
9.1.7 Average value of the modulus of rupture for the group
measurements prior to testing near each end with a separation
and the standard deviation estimate of the mean. Separate
equal to the support span, and average the values. Measure-
values may be determined for edge and face origins.
ments following test shall be in the uniformly stressed region
of the specimen.
NOTE 1—See Annex A3 for conversion from inch-pound units and other
non-SI units to SI units.
7.3 Determine the location of point of failure and note it as
edge or face origin. Plastic or other tape of low elastic modulus
TEST METHOD B—COMPARATIVE TEST FOR
may be used on the compressive surface to contain the
MODULUS OF RUPTURE OF GLASS AND GLASS-
fragmentation and allow observation of point of failure for
CERAMICS
highly prestressed specimens. Report all values, although
segregation of edge break values is permitted.
10. Hazards
10.1 Care should be exercised in all handling of specimens
8. Calculation
to avoid the introduction of random and severe flaws.
8.1 Calculate the modulus of rupture, initial maximum fiber
10.2 Abrasion of specimens of rectangular section should be
stress, and rate
...
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: C158 − 02 (Reapproved 2012) C158 − 02 (Reapproved 2017)
Standard Test Methods for
Strength of Glass by Flexure (Determination of Modulus of
Rupture)
This standard is issued under the fixed designation C158; 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 These test methods cover the determination of the modulus of rupture in bending of glass and glass-ceramics.
1.2 These test methods are applicable to annealed and prestressed glasses and glass-ceramics available in varied forms.
Alternative test methods are described; the test method used shall be determined by the purpose of the test and geometric
characteristics of specimens representative of the material.
1.2.1 Test Method A is a test for modulus of rupture of flat glass.
1.2.2 Test Method B is a comparative test for modulus of rupture of glass and glass-ceramics.
1.3 The test methods appear in the following order:
Sections
Test Method A 6 to 9
Test Method B 10 to 15
Sections
Test Method A 6 to 9
Test Method B 10 to 15
1.4 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 safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use. Specific hazard statements are given in Section 10 and A1.5, A2.3.3, A2.4.3
and A2.5.3.
1.5 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:
C148 Test Methods for Polariscopic Examination of Glass Containers
E4 Practices for Force Verification of Testing Machines
SI10-02 IEEE/ASTM SI 10 American National Standard for Use of the International System of Units (SI): The Modern Metric
System
3. Terminology
3.1 Definitions:
3.1.1 glass-ceramics—solid materials, predominantly crystalline in nature, formed by the controlled crystallization of glasses.
3.1.2 modulus of rupture in bending—the value of maximum tensile or compressive stress (whichever causes failure) in the
extreme fiber of a beam loaded to failure in bending computed from the flexure formula:
These test methods are under the jurisdiction of ASTM Committee C14 on Glass and Glass Products and are the direct responsibility of Subcommittee C14.04 on Physical
and Mechanical Properties.
Current edition approved Oct. 1, 2012Nov. 1, 2017. Published October 2012November 2017. Originally approved in 1940. Last previous edition approved in 20022012
as C158 – 02 (2012).(2007). DOI: 10.1520/C0158-02R12.10.1520/C0158-02R17.
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
C158 − 02 (2017)
M c
S 5 (1)
b
I
where:
M = maximum bending moment, computed from the maximum load and the original moment arm,
c = initial distance from the neutral axis to the extreme fiber where failure occurs, and
I = initial moment of inertia of the cross section about the neutral axis.
3.1.3 prestressed—material in which a significant and controlled degree of compressive stress has been deliberately produced
in the surfaces.
3.1.4 standard laboratory atmosphere—an atmosphere having a temperature of 23 6 2°C and a relative humidity of 40 6 10 %.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 abraded—describes a test specimen that has at least a portion of the area of maximum surface tensile stress subjected to
an operationally defined procedure for mechanical abrasion. The severity and uniformity of abrasion should be sufficient to ensure
origin of failure substantially in the region of maximum stress.
3.2.2 annealed glass—describes a specimen that shall not have a temper or degree of residual stress resulting from prior thermal
treatment in excess of the following limits when measured polarimetrically (see Annex A1):
3.2.2.1 Specimens of rectangular section shall not have a tensile stress at the midplane of more than 1.38-MPa (200-psi) nor
more than 2.76-MPa (400-psi) compression at the surface.
3.2.2.2 Specimens in rod form may be examined by viewing through a diameter at least four diameters from an end. The
apparent central axial tension shall not exceed 0.92 MPa (133 psi). (133 psi). Surface compression, if measured on sections cut
from the rods, shall not exceed 2.76 MPa (400 psi) when viewed axially.
4. Significance and Use
4.1 For the purpose of this test, glasses and glass-ceramics are considered brittle (perfectly elastic) and to have the property that
fracture normally occurs at the surface of the test specimen from the principal tensile stress. The modulus of rupture is considered
a valid measure of the tensile strength subject to the considerations discussed below.
4.2 It is recognized that the modulus of rupture for a group of test specimens is influenced by variables associated with the test
procedure. These include the rate of stressing, test environment, and the area of the specimen subjected to stress. Such factors are
specified in the test procedure or required to be stated in the report.
4.3 It is also recognized that the variables having the greatest effect on the modulus of rupture value for a group of test
specimens are the condition of the surfaces and glass quality near the surfaces in regard to the number and severity of
stress-concentrating discontinuities or flaws, and the degree of prestress existing in the specimens. Each of these can represent an
inherent part of the strength characteristic being determined or can be a random interfering factor in the measurement.
4.4 Test Method A is designed to include the condition of the surface of the specimen as a factor in the measured strength. It
is, therefore, desirable to subject a fixed and significant area of the surface to the maximum tensile stress. Since the number and
severity of surface flaws in glass are primarily determined by manufacturing and handling processes, this test method is limited
to products from which specimens of suitable size can be obtained with minimal dependence of measured strength upon specimen
preparation techniques. This test method is therefore designated as a test for modulus of rupture of flat glass.
4.5 Test Method B describes a general procedure for test, applicable to specimens of rectangular or elliptical cross section. This
test method is based on the assumption that a comparative measurement of strength on groups of specimens is of significance for
many purposes, such as determining the effect of environment or stress duration, or the effectiveness of varied prestressing
techniques or strengths characteristic of glass-ceramics of differing composition or heat treatment. In this test method the surfaces
of the specimens are not assumed to be characteristic of a product or material, but are considered to be determined by the
procedures used to prepare the specimens. Though the stated procedure permits a wide variation in both specimen size and test
geometry, it is necessary to use identical test conditions and equivalent procedures for specimen preparation to obtain comparable
strength values. The use of a controlled abrasion of the specimen as a final normalizing procedure is recommended for such
comparative tests.
4.6 A comparative abraded strength, determined as suggested in Test Method B, is not to be considered as a minimum value
characteristic of the material tested nor as directly related to a maximum attainable strength value through test of specimens with
identical flaws. The operationally defined abrasion procedure undoubtedly produces flaws of differing severity when applied to
varied materials, and the measured comparative strengths describe the relative ability to withstand externally induced stress as
affected by the specific abrasion procedure.
C158 − 02 (2017)
FIG. 1 Pinned Bearing Edges
5. Apparatus
5.1 Testing Machine—The loading mechanism shall be sufficiently adjustable to give the required uniform rate of increase of
stress. The load-measuring system shall be essentially free of inertial lag at the loading rates used and shall be equipped with means
for retaining indication of the maximum load applied to the specimen. The accuracy of the testing machine shall conform to the
requirements of Practice E4.
5.2 Bearing Edges—Cylindrical bearing edges of approximately 3-mm ( ⁄8-in.) radius shall be used for the support of the test
specimen and the application of the load. The bearing edges shall be of steel and sufficiently hardened to prevent excessive
deformation under load. Two-point loading tests shall be performed with the loading member pivoted about a central transverse
axis to ensure equal distribution of load between the two bearing edges. For the testing of specimens of rectangular section, both
loading bearing edges and one support bearing edge also shall be provided laterally to compensate for irregularities of the test
specimen. Fig. 1 shows a suitable arrangement using pinned bearing edges. In test of specimens of a circular or elliptical section,
the fixed cylindrical support edges may have a curvature of approximately 76 mm 76 mm (3 in.) in the plane of the bearing edge
to stabilize the alignment of the specimens. Such support edges are shown in Fig. 2.
TEST METHOD A—TEST FOR MODULUS OF RUPTURE OF FLAT GLASS
6. Test Specimens
6.1 Preparation of Specimens—Test specimens shall be cut from the sheet stock with a diamond or a cutting wheel. Both
longitudinal cuts shall be on the same original surface and none of the original edge of the sheet shall be used as a longitudinal
side of the specimen. End cuts may be on either surface. The direction of cutting of half of the total number of specimens shall
be perpendicular to the direction of cutting of the remainder. Specimens that must be cut from sheet stock prior to the use of a
prestressing treatment shall have the corners of the longitudinal edges rounded to minimize damage to the edges in the prestressing
process. All operations shall be performed with the direction of grind or polish parallel to the longitudinal axis. The radius of the
corner shall not exceed 1.6 mm 1.6 mm ( ⁄16 in.).
1 1
6.2 Size of Specimens—The specimens shall be approximately 250 mm (10 in.) in length and 38.1 6 3.2 mm (1 ⁄2 6 ⁄8 in.) in
width. The variation in width or thickness shall not exceed 5 % from one end to the other.
6.3 Number of Specimens—At least 30 specimens shall be used for one test and shall preferably be taken from several sheets,
or regions of a single sheet.
6.4 Examination of Specimens—Any specimen may be rejected prior to test for observable defects considered likely to affect
the modulus of rupture. To be considered representative of annealed glass the specimens must meet the requirement of 3.2.2. At
least 30 % of the specimens shall be examined for residual stress. If any of these fail to meet the requirement, the remainder of
the specimens shall be examined and those exceeding the stated limit shall be rejected.
6.5 Float Glass—The surface of float glass in contact with tin has been found to be lower in strength (1) as compared to the
“air” surface. For comparative tests, therefore, surface orientation should be kept constant.
7. Procedure
7.1 Space the supporting edges of the test fixture 200 mm (8.00 in.) apart and centrally position the loading edges with a
separation of 100 mm (4.00 in.). Break specimens having cut edges with the cutter marks on the face under compression. Carefully
place each specimen in the test fixture to minimize possible damage and to ensure alignment of specimen in the fixture. The
permissible maximum fiber stress due to initial load on the specimen shall not exceed 25 % of the mean modulus of rupture. Load
C158 − 02 (2017)
FIG. 2 Fixed Cylindrical Support Edges
the specimen at a constant rate to failure. For annealed glass the rate of loading shall correspond to a rate of increase of maximum
stress of 1.1 6 0.2 MPa/s (10 000 6 2000 psi/min). Test prestressed glasses with the increase of maximum stress per minute
between 80 and 120 % of the modulus of rupture. The first six specimens of the group may be tested at a loading rate based on
an estimate of the modulus of rupture and the average value for these specimens used to correct this estimate. If range of width
and thickness variation in the specimens is less than 5 %, the mean values may be used to represent all specimens for the purpose
of calculation of rate of loading.
7.2 Determine the thickness and width of each specimen to 61 %. To avoid damage from gaging in the critical area, take
measurements prior to testing near each end with a separation equal to the support span, and average the values. Measurements
following test shall be in the uniformly stressed region of the specimen.
7.3 Determine the location of point of failure and note it as edge or face origin. Plastic or other tape of low elastic modulus may
be used on the compressive surface to contain the fragmentation and allow observation of point of failure for highly prestressed
specimens. Report all values, although segregation of edge break values is permitted.
8. Calculation
8.1 Calculate the modulus of rupture, initial maximum fiber stress, and rate of increase of stress as follows:
8.1.1 Modulus of rupture:
3 La
S 5 (2)
bd
8.1.2 Maximum stress due to initial load if present:
3 L a
S 5 (3)
0 2
bd
8.1.3 Rate of increase of maximum stress:
3a ΔL
R 5 3 (4)
bd Δt
S
R 5 S 2
t
where:
S = modulus of rupture, MPa (psi),
S = maximum fiber stress due to initial load if present, MPa (psi),
R = rate of increase of maxi
...
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