Glass in building - Determination of the bending strength of glass - Part 1: Fundamentals of testing glass (ISO/DIS 1288-1:2014)

Verre dans la construction - Détermination de la résistance du verre à la flexion - Partie 1: Principes fondamentaux des essais sur le verre

Glas im Bauwesen - Bestimmung der Biegefestigkeit von Glas - Teil 1: Grundlagen der Glasprüfungen (ISO/DIS 1288-1:2014)

Diese Internationale Norm legt die Bestimmung der Biegefestigkeit von monolithischem Glas im Bauwesen fest. Zur Prüfung von Mehrscheiben Isolierglas oder Verbundglas ist diese Norm nicht anwendbar.
Diese Norm beschreibt:
-   Überlegungen, die bei der Prüfung von Glas zu berücksichtigen sind;
-   Erläuterungen der Gründe für die Erarbeitung verschiedener Prüfverfahren;
-   Grenzen der Prüfverfahren
und gibt Hinweise zu Sicherheitsvorschriften für das mit der Prüfeinrichtung arbeitende Personal.
ISO 1288 2, ISO 1288 3, ISO 1288 4 und  ISO 1288 5 legen die Prüfverfahren im Einzelnen fest.
Die in dieser Norm beschriebenen Prüfverfahren sollen dazu dienen, eine Vielzahl von Biegefestigkeitswerten zu liefern, die als Grundlage für eine statistische Abschätzung der Glasfestigkeit benutzt werden können.

Verre dans la construction - Détermination de la résistance du verre à la flexion - Partie 1: Principes fondamentaux des essais sur le verre (ISO/DIS 1288-1:2014)

Steklo v gradbeništvu - Ugotavljanje upogibne trdnosti stekla - 1. del: Uvodno preskušanje stekla (ISO/DIS 1288-1:2014)

General Information

Status
Not Published
Public Enquiry End Date
29-Apr-2014
Current Stage
98 - Abandoned project (Adopted Project)
Start Date
29-Aug-2016
Due Date
03-Sep-2016
Completion Date
29-Aug-2016

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SLOVENSKI STANDARD
oSIST prEN ISO 1288-1:2014
01-april-2014
Steklo v stavbah - Ugotavljanje upogibne trdnosti stekla - 1. del: Uvodno
preskušanje stekla (ISO/DIS 1288-1:2014)
Glass in building - Determination of the bending strength of glass - Part 1: Fundamentals
of testing glass (ISO/DIS 1288-1:2014)
Glas im Bauwesen - Bestimmung der Biegefestigkeit von Glas - Teil 1: Grundlagen der
Glasprüfungen (ISO/DIS 1288-1:2014)
Verre dans la construction - Détermination de la résistance du verre à la flexion - Partie
1: Principes fondamentaux des essais sur le verre (ISO/DIS 1288-1:2014)
Ta slovenski standard je istoveten z: prEN ISO 1288-1 rev
ICS:
81.040.20 Steklo v gradbeništvu Glass in building
oSIST prEN ISO 1288-1:2014 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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oSIST prEN ISO 1288-1:2014

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oSIST prEN ISO 1288-1:2014
DRAFT INTERNATIONAL STANDARD
ISO/DIS 1288-1
ISO/TC 160/SC 2 Secretariat: ANSI
Voting begins on: Voting terminates on:
2014-01-09 2014-06-09
Glass in building — Determination of the bending strength
of glass —
Part 1:
Fundamentals of testing glass
Verre dans la construction — Détermination de la résistance du verre à la flexion —
Partie 1: Principes fondamentaux des essais sur le verre
ICS: 81.040.20
ISO/CEN PARALLEL PROCESSING
This draft has been developed within the International Organization for
Standardization (ISO), and processed under the ISO lead mode of collaboration
as defined in the Vienna Agreement.
This draft is hereby submitted to the ISO member bodies and to the CEN member
bodies for a parallel five month enquiry.
Should this draft be accepted, a final draft, established on the basis of comments
received, will be submitted to a parallel two-month approval vote in ISO and
THIS DOCUMENT IS A DRAFT CIRCULATED
formal vote in CEN.
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
To expedite distribution, this document is circulated as received from the
IN ADDITION TO THEIR EVALUATION AS
committee secretariat. ISO Central Secretariat work of editing and text
BEING ACCEPTABLE FOR INDUSTRIAL,
composition will be undertaken at publication stage.
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
STANDARDS MAY ON OCCASION HAVE TO
BE CONSIDERED IN THE LIGHT OF THEIR
POTENTIAL TO BECOME STANDARDS TO
WHICH REFERENCE MAY BE MADE IN
Reference number
NATIONAL REGULATIONS.
ISO/DIS 1288-1:2013(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
©
PROVIDE SUPPORTING DOCUMENTATION. ISO 2013

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oSIST prEN ISO 1288-1:2014
ISO/DIS 1288-1:2013(E)

Copyright notice
This ISO document is a Draft International Standard and is copyright-protected by ISO. Except as
permitted under the applicable laws of the user’s country, neither this ISO draft nor any extract
from it may be reproduced, stored in a retrieval system or transmitted in any form or by any means,
electronic, photocopying, recording or otherwise, without prior written permission being secured.
Requests for permission to reproduce should be addressed to either ISO at the address below or ISO’s
member body in the country of the requester.
ISO copyright office
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Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
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Reproduction may be subject to royalty payments or a licensing agreement.
Violators may be prosecuted.
ii © ISO 2013 – All rights reserved

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oSIST prEN ISO 1288-1:2014
FDIS 1288-1
Contents
Foreword
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Symbols (and abbreviated terms) . 2
5 Factors to be taken into account when testing glass . 3
5.1 Glass as a material . 3
5.2 Bending stress and bending strength . 5
5.3 Types of glass . 6
5.4 Orientation of the specimens . 7
5.5 Number of specimens in a sample . 7
6 Explanations of the test methods . 7
6.1 Coaxial double ring test for large test surface areas . 7
6.2 Test with specimen supported at two points (four point bending) . 11
6.3 Coaxial double ring test for small test surface areas . 13
7 Range of application of the test methods . 14
7.1 General limitations . 14
7.2 Limitations to ISO 1288-2 . 15
7.3 Limitations to ISO 1288-3 . 15
7.4 Limitations to ISO 1288-4 . 15
7.5 Limitations to ISO 1288-5 . 15
8 Calibration of the testing machines . 15
9 Recommendations for safe use of test equipment . 15
Bibliography . 17

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oSIST prEN ISO 1288-1:2014
FDIS 1288-1
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO
member bodies). The work of preparing International Standards is normally carried out through ISO technical
committees. Each member body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, governmental and non-governmental, in
liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this part of ISO 1288 may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 1288-1 was prepared by Technical Committee ISO/TC 160, Glass in building,
Subcommittee SC 2, Use considerations
ISO 1288 consists of the following parts, under the general title Glass in building — Determination of the bending
strength of glass:
 Part 1: Fundamentals of testing glass
 Part 2: Coaxial double ring test on flat specimens with large test surface areas
 Part 3: Test with specimen supported at two points (four point bending)
 Part 4: Testing of channel shaped glass
 Part 5: Coaxial double ring test on flat specimens with small test surface areas
This Standard has been based on EN 1288-1 Glass in building - Determination of the bending strength of glass" -
Part 1: Fundamentals of testing glass prepared by Technical Committee CEN/TC 129 "Glass in building"/WG8
"Mechanical Strength".

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oSIST prEN ISO 1288-1:2014
FDIS prEN/ISO 1288-1

Glass in building — Determination of the bending strength of
glass — Part 1: Fundamentals of testing glass
1 Scope
This International Standard specifies the determination of the bending strength of monolithic glass for use in
buildings. The testing of insulating units or laminated glass is excluded from this standard.
This standard describes:
- considerations to be taken into account when testing glass,
- explanations of the reasons for designing different test methods,
- limitations of the test methods,
and gives pointers to safety requirements for the personnel operating the test equipment.
ISO 1288-2, ISO 1288-3, ISO 1288-4 and ISO 1288-5 specify test methods in detail.
The test methods specified in this standard are intended to provide large numbers of bending strength values that can
be used as the basis for statistical evaluation of glass strength.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO 1288. For dated references, subsequent amendments to, or revisions of, any of these publications
do not apply. However, parties to agreements based on this part of ISO 1288 are encouraged to investigate the
possibility of applying the most recent editions of the normative documents indicated below. For undated
references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain
registers of currently valid International Standards.
ISO 1288-2, Glass in building — Determination of the bending strength of glass — Part 2 : Coaxial double ring test
on flat specimens with large test surface areas
ISO 1288-3, Glass in building — Determination of the bending strength of glass — Part 3 : Test with specimen
supported at two points (four point bending)
ISO 1288-4, Glass in building — Determination of the bending strength of glass — Part 4 : Testing of channel
shaped glass
ISO 1288-5, Glass in building — Determination of the bending strength of glass — Part 5 : Coaxial double ring test
on flat specimens with small test surface areas
ISO16293-1: Glass in building – Basic soda lime silicate glass products – Part 1: Definitions and general physical
and mechanical properties
DIS 16293-2: Glass in building – Basic soda lime silicate glass products – Part 2: Float glass

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oSIST prEN ISO 1288-1:2014
FDIS 1288-1
NOTE 1: ISO TC160 SC1 WG1 is commencing work on standards for ‘polished wired glass’, ‘wired patterned glass’ and
‘patterned glass
NOTE 2: ISO TC160 SC1 WG2 is commencing work on standards for ‘thermally tempered soda lime silicate safety glass’, ‘heat
strengthened soda lime silicate glass’ and ‘chemically strengthened glass’.
3 Terms and definitions
For the purposes of this part of ISO 1288, the following terms and definitions apply.
3.1
flat glass
any glass product conforming to ISO 162934or any transformed glass made from these products without
deliberately inducing profile or curvature.
3.2
bending stress
the tensile bending stress induced in the surface of a specimen.
NOTE: For testing purposes, the bending stress should be uniform over a specified part of the surface.
3.3
effective bending stress
a weighted average of the tensile bending stresses, calculated by applying a factor to take into account
non-uniformity of the stress field.
3.4
bending strength
the bending stress or effective bending stress which leads to breakage of the specimen.
3.5
equivalent bending strength
the apparent bending strength of patterned glass, for which the irregularities in the thickness do not allow precise
calculation of the bending stress.
3.6
profile bending strength
the quotient of the maximum bending moment and the section modulus of a channel shaped glass.
3.7
stress intensity factor
a measure of the stress at a crack tip.
3.8
prestressed glass
any glass product that has a surface prestress, i.e. thermally tempered soda lime silicate safety glass, heat
strengthened soda lime silicate glass and chemically strengthened glass.
4 Symbols (and abbreviated terms)
F Applied load N
h Specimen thickness m
L Length of side of square test sample m
k Constant for calculation of bending stress in ISO 1288-3 m
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oSIST prEN ISO 1288-1:2014
FDIS 1288-1
K ,K Constants for calculation of bending stress in ISO 1288-5
1 2
M Maximum bending moment Nm
bB
p Gas pressure applied within loading ring in ISO 1288-2 Pa
P Profile bending strength (of channel shaped glass) = M /Z Pa
bB bB
r Radius of loading ring m
1
r Radius of supporting ring m
2
r Radius of circular specimen m
3
r Average specimen radius (for evaluation) m
3m
y Central deflection of specimen m
0
3
Z Section modulus ( of channel shaped glass ) m
µ Poisson number of specimen
NOTE : for soda lime silicate glass (see ISO 16293-1EN 572-1) a value of 0,23 is used.
σ Bending stress Pa
b
σ Effective bending stress Pa
beff
σ Bending strength Pa
bB
σ Equivalent bending strength Pa
beqB
Radial stress Pa
σ
rad
Tangential stress Pa
σ
T
Stress in a direction along the length of the specimen Pa
σ
L
5 Factors to be taken into account when testing glass
5.1 Glass as a material
5.1.1 General
Glass is a homogeneous isotropic material having almost perfect linear-elastic behaviour over its tensile strength
range.
Glass has a very high compressive strength and theoretically a very high tensile strength, but the surface of the
glass has many irregularities which act as weaknesses when glass is subjected to tensile stress. These
irregularities are caused by attack from moisture and by contact with hard materials (e.g. grit) and are continually
modified by moisture which is always present in the air.
Tensile strengths of around 10 000 MPa can be predicted from the molecular structure, but bulk glass normally fails
at stresses considerably below 100 MPa.
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oSIST prEN ISO 1288-1:2014
FDIS 1288-1
The presence of the irregularities and their modification by moisture contributes to the properties of glass which
need consideration when performing tests of strength.
Because of the very high compressive strength, glass always fails under tensile stress. Since glass in buildings is
very rarely used in direct tension, the most important property for load resistance is the tensile bending strength.
All the tests described in this standard are intended to evaluate the tensile bending strength of glass.
The bending strength is influenced by the following factors:
a) surface condition (see 5.1.2);
b) rate and duration of loading (see 5.1.3);
c) area of surface stressed in tension (see 5.1.4);
d) ambient medium, through stress corrosion cracking as well as healing of surface damage in the glass (see
5.1.5 and [1] in Bibliography));
e) age, i.e. time elapsing since the last mechanical surface treatment or modification to simulate damage (see
5.1.6);
f) temperature (see 5.1.7).
The influence exerted by factors b) to f) on bending strength has been taken into account in this standard.
5.1.2 Effect of surface condition
For the purpose of bending strength tests according to this standard, glass behaves as an almost ideally linear-
elastic material that fails in a brittle manner. This brittleness means that contact with any hard object can lead to
surface damage in the form of ultra-fine, partly submicroscopic cracks and chips. Surface damage of this kind,
which is practically unavoidable during normal handling of glass, exerts a notch action which is a major factor in
reducing mechanical strength, whereas the chemical composition of the glass has only a minor and in some cases
entirely negligible, significance.
Hence it follows that the bending strength determined by the methods referred to in this standard is related largely
to the surface condition of the specimen to be tested.
This surface condition is characterized by the following main features.
a) The surface condition imparted by a particular method of treatment, which produces a specific damage
spectrum and thus results in a strength which is specific to the finished surface condition;
b) Residual stress, e.g. in the form of thermal or chemical prestress intentionally imparted, as well as unintended
residual stresses.
5.1.3 Effect of rate of loading
For the interpretation of the bending strength values determined as described in this standard, the rate of loading is
of special importance.
Cracks propagate in glass over a wide range of values of tensile stress (see [2] in Bibliography)). There is a lower
limit to the stress intensity factor below which cracks do not propagate ( see [1] in Bibliography)). There is then
some subcritical crack propagation at higher levels of stress intensity factor, which is influenced by humidity,
temperature and chemical agents. Above a critical stress intensity factor crack propagation is very rapid and leads
to (almost) instantaneous failure. The consequence of the subcritical crack propagation is, for example, that the
rate of load increase and/or the duration of static loading influences the bending strength.
For prestressed glass, this time dependence does not manifest itself until the tensile stress induced in the surface
exceeds the compressive stress permanently present there (see [3] in Bibliography)).
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oSIST prEN ISO 1288-1:2014
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5.1.4 Effect of test surface area
The decrease in bending strength of glass with increasing size of the test area exposed to high stress is also of
importance (see [4] in Bibliography)). This area effect is accounted for by the statistical distribution of surface
defects varying in effectiveness; the larger the test area, the greater is the probability of its containing a large
surface defect. Consequently, the influence of the area effect increases with decreasing incidence of defects in the
surface, so that this influence is more pronounced in the case of undamaged, e.g. fire-finished glass surfaces (see
[5] in Bibliography).
Differences are likely between the mean values of the bending strength as measured in accordance with EN ISO
2
1288-2 (maximally stressed area: 240 000 mm ), or by using devices R105, R60, R45 and R30 in accordance with
2 2 2 2
EN ISO 1288-5 (maximally stressed areas: 3850 mm , 1260 mm , 254 mm and 113 mm ), due to the size of the
stressed area. Depending on surface damage, the results obtained from testing smaller surface areas may be
significantly higher than those obtained from testing larger surface areas, as shown in table 1.
Table 1 — Approximate effects of test surface area on the mean measured bending strength
Test Method Device Relative bending strength
ISO 1288-2 -- 100 %
ISO 1288-5 R105 120 % to 180 %
ISO 1288-5 R65 125 % to 210 %
ISO 1288-5 R45 140 % to 270 %
ISO 1288-5 R30 145 % to 300 %

Since glass for use in buildings is often in large sizes, the test methods specified in ISO 1288-2 and ISO 1288-3
give values which are more appropriate as the basis for designing flat glass for use in buildings. The test method
specified in ISO 1288-5 can be useful as a method of evaluating the comparative bending strength of flat glass.
5.1.5 Effect of ambient medium
The surrounding medium in which the glass is tested has an influence on the strength of the glass, particularly if
the moisture level is very low. When glass is used in buildings, the relative humidity typically ranges from 30 % to
100 %. Within this range, the effect on the bending strength, as tested according to this standard, is not great.
However, tests on glass for use in buildings shall be undertaken in test conditions with relative humidity levels in
the range of 40 % to 70 %, in order to eliminate this effect when comparing bending strength results.
5.1.6 Effect of aging
If the glass surface is modified (by abrasion, etching, edge working etc.) before the testing, it is necessary to allow
the fresh damage to heal before the test is undertaken. The continual surface modification by moisture affects the
damage in a way that can reduce any weakening effect (see [1] of Bibliography). In practice, glass is highly
unlikely to be stressed directly after it has been treated, so it shall be conditioned for at least 24 h before testing.
5.1.7 Effect of temperature
The bending strength of glass is affected by changes in temperature. Within the normal range of temperatures
experienced by glass in buildings, this effect is not very significant, but, to avoid possible complications in the
comparison of bending strength values, testing shall be undertaken in a restricted range of temperatures.
5.2 Bending stress and bending strength
5.2.1 General
The test methods described in ISO 1288-2, ISO 1288-3, ISO 1288-4 and ISO 1288-5 are designed to induce a
uniform bending stress over an area (the test area) of the specimen. However, the tests are statically
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oSIST prEN ISO 1288-1:2014
FDIS 1288-1
indeterminate, that is, the stresses induced by the applied loads depend on the nature of the material tested as well
as the load distribution.
5.2.2 Effective stress
Where the stress varies significantly over the test area, as is the case in ISO 1288-3 (see 6.2.2), it can be
represented by a weighted average stress, called the effective bending stress, σ . The weighting is obtained by
beff
statistically evaluating the probability of fracture at any point in the stressed area.
5.2.3 Equivalent bending strength
Variations in homogeneity or thickness of the specimen affect the stress distribution. Hence, the bending strength,
σ , is never entirely an accurate value and, in some instances, it is better termed the equivalent bending strength,
bB
σ .
beqB
For some of the glass types tested (for example float glass), such variations are very small and the bending
strength determined by the tests is sufficiently close to the actual bending strength for the difference to be
unimportant.
In the case of patterned glass, however, only the equivalent bending strength can be determined.
5.2.4 Profile bending strength
When channel shaped glass is tested according to EN ISO 1288-4, most of the specimens fail from fractures
originating at the corner of the profile, where the web and flange meet, and not at the extreme of the flange or
surface of the web. This is due to secondary stresses generated by the spreading of the flanges when the channel
section is bent. In this test the bending strength is better expressed as the profile bending strength, P .
bB
5.3 Types of glass
5.3.1 General
The tests specified in ISO 1288-2, ISO 1288-3 and ISO 1288-5 are for testing flat glass. This includes float glass,
drawn sheet glass, patterned glass, patterned wired glass, polished wired glass and prestressed glass, provided
there has been no deliberately induced curvature or profile (other than the patterned surface of patterned glass).
5.3.2 Patterned glass
The coaxial double ring test for large test surface areas (EN ISO 1288-2) can be used to determine the equivalent
bending strength of patterned glass, provided the maximum and minimum thicknesses do not deviate by more than
30 % or 2 mm, whichever is the lower, from the average thickness. This is because of difficulties in sealing the
pressure ring to a patterned surface.
There is no limitation on the depth of pattern if the four point bending test (ISO 1288-3) is used.
5.3.3 Laminated glass
The testing of the bending strength of laminated glass (see ISO 12543-1) is excluded from this standard.
In a bending test, additional shear deformation arises in the elastic or plastic interlayers (sliding of the hard glass
plies on the interlayer). This effect means that measuring the bending strength of laminated glass is likely to give a
strength value less than the actual bending strength of a monolithic glass of the same thickness. This shear
deformation is particularly sensitive to the effects of temperature and loading rate.
Laminated glass is manufactured from monolithic glass products that can be tested individually by the test methods
described in ISO 1288-2, ISO 1288-3 and ISO 1288-5.
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oSIST prEN ISO 1288-1:2014
FDIS 1288-1
The process of manufacture is unlikely to cause significant changes in the bending strength of the component
glasses, so it is unnecessary to test laminated glass, which can be assumed to have bending strengths appropriate
to their individual components.
The load resistance of laminated glass depends on the interactions between the component parts of the composite
structure, which is beyond the scope of this standard.
5.4 Orientation of the specimens
Many glass products lack symmetry in their production. This may be immediately obvious, such as a patterned
glass, which is likely to have one surface much more deeply patterned than the other and possibly in which the
pattern is directional, or it may be less obvious, such as the side on which the wheel cut was made (see figure 1 in
ISO 1288-3).
Where such asymmetry is present, it may be necessary to test the glass in several different orientations in order to
determine the bending strength. Samples of glass to be tested shall have all the specimens nominally identical.
5.5 Number of specimens in a sample
The bending strength of glass displays a large variation between nominally identical specimens. Very little
information can be obtained by testing only a few specimens, since there is considerable uncertainty about whether
the results are representative.
In statistical terms, this uncertainty can be expressed as confidence limits, values between which there is a given
probability that the target being sought will lie.
Where the target being sought is in the central part of the bending strength distribution (for instance the mean
value), then the confidence limits can be fairly narrow even with just a few specimens.
An accurate determination of the tensile stress which leads to a low crack probability can require large numbers of
specimens when, for example, a characteristic stress, or a permissible stress, or a design value of bending strength
is to be determined.
6 Explanations of the test methods
6.1 Coaxial double ring test for large test surface areas
NOTE: This test is specified in ISO 1288-2.
6.1.1 Elimination of edge effects
The special feature of the coaxial double ring bending test in accordance with ISO 1288-2 lies in the fact that only a
circular shaped limited area of the surface of the specimen - not, however, its edges - is subjected to maximum
stressing. In contrast to other bending tests (for example see ISO 1288-3), in which the edge of the specimen is
subjected to the maximum stress, the procedure in accordance with SO 1288-2 is suitable for exclusively
subjecting surfaces (or different surface conditions) to bending stress. The effect of the specimen edge condition is
for the most part suppressed.
6.1.2 Analysis of the stress development
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oSIST prEN ISO 1288-1:2014
FDIS 1288-1
When the deflections are relatively small, the central surface area is subjected to uniform tensile stressing (see
figure 1a)), where the radial and tangential stresses are of equal size.
F
h
+
σ
T
σ
ra d
-
a)
+
σ
ra d
σ
T
b)
-
a) in the small deflection range
b) in the large deflection range
Figure 1 — Schematic dependence of radial and tangential stresses upon the radius of the specimen, when
loaded by a double ring device
If the deflections become larger, i.e. if they exc
...

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