SIST-TS CEN/TS 820-5:2005

Advanced technical ceramics - Methods of testing monolithic ceramics. Thermomechanical properties - Part 5: Determination of elastic moduli at elevated temperatures

This part of ENV 820 describes methods for determining the elastic moduli, specifically Young's modulus, shear modulus and Poisson's ratio, of advanced monolithic technical ceramics at temperatures above room temperature. The Technical Specification prescribes three alternative methods for determining some or all of these three parameters:
A   The determination of Young's modulus by static flexure of a thin beam in three- or four-point bending.
B   The determination of Young's modulus by forced longitudinal resonance, or Young's modulus, shear modulus and Poisson's ratio by forced flexural and torsional resonance, of a thin beam.
C   The determination of Young's modulus from the fundamental natural frequency of a struck bar (impulse excitation method).
This Technical Specification extends the above-defined room-temperature methods described in ENV 843-2 to elevated temperatures. All the test methods assume the use of homogeneous test pieces of linear elastic materials. The test assumes that the test piece has isotropic elastic properties. At high porosity levels all of the methods can become inappropriate. The maximum grain size (see EN 623-3), excluding deliberately added whiskers, should be less than 10% of the minimum dimension of the test piece.

Hochleistungskeramik - Monolithische Keramik - Thermomechanische Eigenschaften - Teil 5: Bestimmung der elastischen Moduln bei erhöhten Temperaturen

Céramiques techniques avancées - Méthodes d'essai des céramiques monolithiques - Propriétés thermomécaniques - Partie 5: Détermination des modules élastiques a températures élevées

La présente partie de EN 820 décrit des méthodes de détermination des modules élastiques, en particulier du module de Young, du module de cisaillement et du coefficient de Poisson des céramiques techniques avancées a des températures supérieures a la température ambiante Cette Spécification Technique décrit trois méthodes possibles permettant de déterminer un ou plusieurs de ces trois parametres.
A   - Détermination du Module de Young par flexion statique d'une poutre mince en trois ou quatre points.
B   - Détermination du Module de Young par résonance longitudinale forcée ou détermination du module de Young, du module de cisaillement et du coefficient de Poisson par résonance forcée en flexion et en torsion d'une poutre mince.
C   - Détermination du module de Young a partir de la fréquence naturelle fondamentale d'une barre que l'on frappe( méthode d'excitation par impulsion);
La présente Spécification Technique étend les méthodes a température ambiante définies ci-dessus  et décrites dans ENV 843-2 aux températures élevées. Toutes les méthodes d'essai supposent l'utilisation d'éprouvettes homogenes faites en matériaux élastiques linéaires. L'essai est fait en considérant que l'éprouvette a des propriétés élastiques isotropes. Toutes ces méthodes peuvent se révéler inappropriées pour des niveaux de porosité élevés. Il convient que la granulométrie maximale (voir EN 623-3),qui ne tient pas compte de l'ajout de « whiskers », représente moins de 10% de la plus petite dimension de l'éprouvette.

Sodobna tehnična keramika – Metode za preskušanje monolitske keramike – Termomehanske lastnosti – 5. del: Ugotavljanje elastičnih modulov pri povišanih temperaturah

General Information

• Status: Withdrawn
• Publication Date: 31-Dec-2004
• Withdrawal Date: 14-Jul-2009
• ICS: 81.060.30 - Advanced ceramics
• Technical Committee: I13 - Imaginarni 13
• Current Stage: 9900 - Withdrawal (Adopted Project)
• Start Date: 15-Jul-2009
• Due Date: 07-Aug-2009
• Completion Date: 15-Jul-2009
• Mandate: M/076 - Mandate to CEN/CENELEC for standardization in the field of advanced ceramics
• Ref Project: CEN/TS 820-5:2004 - Advanced technical ceramics - Methods of testing monolithic ceramics. Thermomechanical properties - Part 5: Determination of elastic moduli at elevated temperatures

Relations

• Replaced By: SIST EN 820-5:2009 - Advanced technical ceramics - Thermomechanical properties of monolithic ceramics - Part 5: Determination of elastic moduli at elevated temperatures
• Effective Date: 01-Sep-2009

Standards Content (Sample)

SLOVENSKI STANDARD
SIST-TS CEN/TS 820-5:2005
01-januar-2005
6RGREQDWHKQLþQDNHUDPLND±0HWRGH]DSUHVNXãDQMHPRQROLWVNHNHUDPLNH±
7HUPRPHKDQVNHODVWQRVWL±GHO8JRWDYOMDQMHHODVWLþQLKPRGXORYSULSRYLãDQLK
WHPSHUDWXUDK
Advanced technical ceramics - Methods of testing monolithic ceramics.
Thermomechanical properties - Part 5: Determination of elastic moduli at elevated
temperatures
Hochleistungskeramik - Monolithische Keramik - Thermomechanische Eigenschaften -
Teil 5: Bestimmung der elastischen Moduln bei erhöhten Temperaturen
Céramiques techniques avancées - Méthodes d'essai des céramiques monolithiques -
Propriétés thermomécaniques - Partie 5: Détermination des modules élastiques a
températures élevées
Ta slovenski standard je istoveten z: CEN/TS 820-5:2004
ICS:
81.060.30 Sodobna keramika Advanced ceramics
SIST-TS CEN/TS 820-5:2005 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST-TS CEN/TS 820-5:2005

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SIST-TS CEN/TS 820-5:2005
TECHNICAL SPECIFICATION
CEN/TS 820-5
SPÉCIFICATION TECHNIQUE
TECHNISCHE SPEZIFIKATION
February 2004
ICS 81.060.30
English version
Advanced technical ceramics - Methods of testing monolithic
ceramics. Thermomechanical properties - Part 5: Determination
of elastic moduli at elevated temperatures
Céramiques techniques avancées - Céramiques Hochleistungskeramik - Monolithische Keramik -
monolithiques - Propriétés thermomécaniques - Partie 5: Thermomechanische Eigenschaften - Teil 5: Bestimmung
Détermination du module élastique à température élevée der elastischen Moduln bei erhöhten Temperaturen
This Technical Specification (CEN/TS) was approved by CEN on 19 October 2003 for provisional application.
The period of validity of this CEN/TS is limited initially to three years. After two years the members of CEN will be requested to submit their
comments, particularly on the question whether the CEN/TS can be converted into a European Standard.
CEN members are required to announce the existence of this CEN/TS in the same way as for an EN and to make the CEN/TS available
promptly at national level in an appropriate form. It is permissible to keep conflicting national standards in force (in parallel to the CEN/TS)
until the final decision about the possible conversion of the CEN/TS into an EN is reached.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2004 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TS 820-5:2004: E
worldwide for CEN national Members.

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SIST-TS CEN/TS 820-5:2005
CEN/TS 820-5:2004 (E)
Page
Contents
Foreword .3
1 Scope.4
2 Normative references.4
3 Terms and definitions.5
4 Method A: Static bending method.5
4.1 Principle .5
4.2 Apparatus.5
4.3 Test pieces.7
4.4 Procedure.7
4.5 Calculation of results.8
4.6 Accuracy and interferences.9
5 Method B: Resonance method .10
5.1 Principle .10
5.2 Apparatus.10
5.3 Test pieces.12
5.4 Procedure.12
5.5 Calculation of results.13
5.6 Accuracy and interferences.15
6 Method C: Impulse excitation method .15
6.1 Principle .15
6.2 Apparatus.15
6.3 Test pieces.16
6.4 Procedure.16
6.5 Calculation .17
6.6 Accuracy and interferences.18
7 Test report.18
Bibliography .24
2

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Foreword
This document (CEN/TS 820-5:2004) has been prepared by Technical Committee CEN/TC 184
“Advanced technical ceramics”, the secretariat of which is held by BSI.
This document has been prepared under a mandate given to CEN by the European Commission and
the European Free Trade Association.
EN 820 Advanced technical ceramics — Methods of testing monolithic ceramics —
Thermomechanical properties comprises five parts:
Part 1: Determination of flexural strength at elevated temperatures
Part 2: Determination of self-loaded deformation
Part 3: Determination of resistance to thermal shock by water quenching
Part 4: Determination of flexural creep deformation at elevated temperatures
Part 5: Determination of elastic moduli at elevated temperatures
Part 4 is a European Prestandard (ENV) and Part 5 is a Technical Specification (CEN TS).
This document includes a bibliography.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to announce this Technical Specification: Austria, Belgium, Cyprus,
Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland,
Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
3

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SIST-TS CEN/TS 820-5:2005
CEN/TS 820-5:2004 (E)
1 Scope
This part of EN 820 describes methods for determining the elastic moduli, specifically Young's modulus,
shear modulus and Poisson's ratio, of advanced monolithic technical ceramics at temperatures above
room temperature. The Technical Specification prescribes three alternative methods for determining
some or all of these three parameters:
A - the determination of Young's modulus by static flexure of a thin beam in three- or four-point
bending.
B - the determination of Young's modulus by forced longitudinal resonance, or Young's modulus,
shear modulus and Poisson's ratio by forced flexural and torsional resonance, of a thin beam.
C - the determination of Young's modulus from the fundamental natural frequency of a struck bar
(impulse excitation method).
This Technical Specification extends the above-defined room-temperature methods described in
ENV 843-2 to elevated temperatures. All the test methods assume the use of homogeneous test pieces
of linear elastic materials. The test assumes that the test piece has isotropic elastic properties. At high
porosity levels all of the methods can become inappropriate. The maximum grain size (see EN 623-3),
excluding deliberately added whiskers, should be less than 10 % of the minimum dimension of the test
piece.
NOTE 1 Method C in ENV 843-2 based on ultrasonic time of flight measurement has not been incorporated
into this Technical Specification. Although the method is feasible to apply, it is specialised, and outside the
capabilities of most laboratories. There are also severe restrictions on test piece geometries and methods of
achieving pulse transmission. For these reasons this method has not been included in CEN/TS 820-5.
NOTE 2 The upper temperature limit for this test depends on the properties of the test pieces, and can be
limited by softening within the timescale of the test. In addition, for method A there can be limits defined by the
choice of test jig construction materials.
NOTE 3 Methods B and C may not be appropriate for materials with significant levels of porosity (i.e. >15%)
which cause damping and an inability to detect resonances or natural frequencies, respectively.
NOTE 4 This method does not provide for the effects of thermal expansion, i.e. the measurements are based
on room temperature dimensions. Depending upon the use to which the data are put, it can be necessary to
make a further correction by multiplying each dimensional factor in the relevant equations by a factor (1 + a
T)
where a

 



 
 
T from room temperature.
2 Normative references
This Technical Specification incorporates by dated or undated reference, provisions from other
publications. These normative references are cited at the appropriate places in the text, and the
publications are listed hereafter. For dated references, subsequent amendments to or revisions of any
of these publications apply to this Technical Specification only when incorporated in it by amendment
or revision. For undated references the latest edition of the publication referred to applies (including
amendments).
EN 820-1, Advanced technical ceramics — Method of testing monolithic ceramics — Thermo-
mechanical properties — Part 1: Determination of flexural strength at elevated temperatures
EN 843-1:1995, Advanced technical ceramics — Monolithic ceramics — Mechanical properties at
room temperature — Part 1: Determination of flexural strength
EN 60584-2, Thermocouples — Part 2: Tolerances (IEC 60584-2:1982 + A1:1989)
4

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EN ISO 7500-1, Metallic materials — Verification of static uniaxial testing machines —
Part 1: Tension/compression testing machines — Verification and calibration of th eforce-measuring
system (ISO 7500-1:1999)
EN ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories
(ISO/IEC 17025:1999)
ISO/R 463, Dial gauges reading in 0,01 mm, 0,001 in and 0,0001 in
ISO 3611, Micrometer callipers for external measurement
ISO 6906, Vernier callipers reading to 0,02 mm
3 Terms and definitions
For the purposes of this Technical Specification, the following terms and definitions apply.
3.1
Young's modulus
stress required in a material to produce unit strain in uniaxial extension or compression
3.2
shear modulus
shear stress required in a material to produce unit angular distortion
3.3
Poisson's ratio
negative value of the ratio of lateral strain to longitudinal strain in an elastic body stressed longitudinally
3.4
static elastic moduli
elastic moduli determined in an isothermal condition by stressing statically or quasistatically
3.5
dynamic elastic moduli
elastic moduli determined non-quasistatically, i.e. under adiabatic conditions, such as in the resonant,
ultrasonic pulse or impulse excitation methods
4 Method A: Static bending method
4.1 Principle
Using three- or four-point bending of a thin beam test piece, the elastic distortion is measured, from which
Young's modulus may be calculated according to thin beam equations.
4.2 Apparatus
Test jig, in accordance with that described in EN 820-1 for flexural strength testing at elevated
4.2.1
temperatures in terms of its function, i.e. the support and loading rollers shall be free to roll, and to
articulate to ensure axial and even loading as described in EN 843-1. The test jig shall be made of
materials which do not interact with the test piece and which remain essentially elastic at the
maximum test temperature. A typical arrangement is shown in Figure 1.
NOTE 1 Articulation is not essential for carefully machined flat and parallel-faced test pieces.
5

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CEN/TS 820-5:2004 (E)
The outer span of the test jig shall be 40 mm or greater.
NOTE 2 If the displacement is to be measured by method 1 (see 4.2.5), a span of up to 100 mm, or a span to
thickness ratio in excess of 20, is recommended to obtain large displacements and to ensure that the compliance
of the machine is a small correction if displacement is recorded as a machine cross-head movement.
The test jig may be either for three-point or four-point flexure. The latter method is required if
displacement is determined by differential transducer.
4.2.2 Mechanical testing machine, capable of applying a force to the test jig at a constant
displacement rate. The test machine shall be equipped for recording the load applied to the test jig at
any point in time. The accuracy of the test machine shall be in accordance with EN ISO 7500-1,
Grade 1 (1% of indicated load), and shall be capable of recording to a sensitivity of better than 0,1%
of the maximum load employed.
4.2.3 Thermal enclosure and control system, surrounding the test piece, capable of achieving the
o o
maximum desired temperature and maintaining it to ± 2 C for test temperatures up to 1000 C, and ±
o
4 C at higher temperatures.
NOTE The system can operate with an air or inert atmosphere, or with a vacuum inside the thermal
enclosure. Especially with regard to use in vacuum, efforts should be made to ensure that the force applied at the
test piece is correctly recorded by the load cell outside the enclosure, taking account of friction or elastic
resistances in seals or bellows systems.
4.2.4 Thermocouple, conforming to EN 60584-2 for measuring the test piece temperature. The
thermocouple shall be in close proximity to but shall not touch the test piece.
4.2.5 Displacement measuring device, for recording the displacement of the loaded test piece by
one of two methods:
Method 1. Recording the apparent displacements of the test machine as the test piece is loaded in
the test jig, and again with the test piece replaced by a ceramic bar at least 15 mm thick
with flat and parallel faces to within 0,05 mm. The difference between these
displacements is equivalent to the displacement of the test piece in the test jig. The
displacement recording device (chart recorder, digital indicator, etc.) shall be calibrated
by comparing machine cross-head displacement with the movement indicated on a dial
gauge contacting the cross-head. The dial gauge shall be in accordance with ISO/R 463,
or other certified device accurate to 0,01 mm.
The parts of the load train subjected to elevated temperatures shall be made of
materials which remain elastic at the maximum test temperature.
Method 2. Recording the displacement of the test piece directly using a transducer extensometer
contacting at least two defined points on the surface of the test piece between the
support loading rollers in three-point or four-point bending. The defined points shall
preferably be:
for four-point bending: the centre of the span and one or both loading rollers (see, for
example, Figure 1, right);
for three-point bending: the centre of the span and one or both support rollers (see, for
example, Figure 1, left).
NOTE The equations given in 4.5 assume these preferred positions. Other displacement
detection positions require alternative formulations.
The transducer shall be capable of detecting movements with an accuracy of 0,001 mm,
shall have output linear to 1 % over the expected displacement range in making this test
and its sensitivity shall be calibrated to an accuracy of 0,1 %.
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CEN/TS 820-5:2004 (E)
The extensometer parts subjected to elevated temperatures shall remain elastic to the
maximum test temperature, and their tips shall not interact with the test piece (see also
EN 820-1).
4.2.6 Micrometer, in accordance with ISO 3611, capable of recording to 0,01 mm.
4.2.7 Dial gauge, in accordance with ISO/R 463 or other suitable calibrated displacement
measuring device, capable of recording to 0,01 mm.
4.3 Test pieces
Test pieces shall be rectangular section bars selected and prepared by agreement between parties. They
may be directly prepared close to final dimensions or machined from larger blocks. This test measures
Young's modulus parallel to the length of the test piece. If the test material is likely to be elastically
anisotropic, care shall be taken in selection of the test piece orientation and in the interpretation of the test
results.
The length of the test pieces shall be at least 10 mm longer than the test-jig span. The width of the test
piece shall be in the range 4 mm to 10 mm. For method 1, the thickness of the test piece shall be in the
range 0,8 mm to 1,5 mm. For method 2, the test piece may be up to 3 mm thick, but preferably should be
in the range 1 mm to 2 mm thick. The test pieces shall be machined to final dimensions. They shall be flat
and parallel-faced to better than ± 0,5 % of thickness on the faces to be placed on the loading rollers of
the test jig. They shall similarly be machined flat and parallel-faced to better than ± 0,5 % of width on the
side faces. For method 1 they shall not be chamfered. For method 2 they may be chamfered as specified
in EN 843-1.
At least three test pieces shall be prepared.
4.4 Procedure
Measure the width and thickness of the test pieces at several places and record the average values.
Insert a test piece in the test-jig and centralise it in accordance with the requirements of EN 843-1. Select
a maximum force to be applied to the test piece which will avoid fracture.
NOTE 1 The upper level of force can be estimated by employing the strength calculation in EN 843-1:1995,
clause 8, and inserting a stress level of no more than 0,5 s, where s is the mean fracture stress expected at the
f f
test temperature.
Heat the thermal enclosure to the required test temperature and allow the temperature to stabilize such
°
that the thermocouple recording test piece temperature varies by no more than 2 C in a 15 minute period
up to 1000 °C, and by no more than 4 °C at higher temperatures.
Apply a steadily increasing force to the test jig at a constant test machine cross-head displacement rate in
the range 0,001 mm/min to 0,5 mm/min. Record the load and displacement (either cross-head
displacement, or transducer displacement output) continuously. When the maximum selected force is
achieved, reverse the direction of the machine and reduce the load to zero. Repeat the cycle at least
twice more to the same peak load, or until repeatable results are obtained. Repeat the test on each test
piece. If the machine displacement is to be employed (method 1) or if the transducer method is employed
using a support roller as one of the defined points (method 2), replace the test piece with the thick
parallel-sided steel (for use to 300 °C) or ceramic bar and repeat the loading cycles to the same peak
load, recording load and displacement.
NOTE 2 The use of both loading and unloading cycles is required in order to take into account machine
hysteresis in method 1, transducer hysteresis in method 2.
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4.5 Calculation of results
4.5.1 From cross-head displacement (Method 1)
Inspect the recordings of load and displacement for the test piece and the thick steel or ceramic bar for
uniformity and linearity. Select a region of the recordings from a minimum load of not less than 10 % of
peak load or 0,2 N, whichever is the greater, to a maximum load of not more than 90 % of the peak load
applied. The same load range shall be selected for each loading cycle on the test piece and the thick bar.
NOTE 1 The region of the recordings selected should avoid strong non-linearities at low load which may
include irreproducible effects of machine movement and test piece alignment, and also the effects of cross-head
reversal near peak load.
NOTE 2 If the force - displacement traces show evidence of a reduction of stiffness at upper load levels, this
can be taken as evidence of plastic softening. At this temperature and any higher test temperature, the results of
the test should be deemed invalid.
Calculate or measure the displacement recorded over the selected load range for each loading and
unloading cycle for the test piece and for the thick bar. Calculate the average displacement in each
direction. If the displacement of the first cycle is more than 2 % different from that of the second or
subsequent cycle, ignore the first cycle when computing the average.
NOTE 3 The first cycle can show a different response to subsequent cycles as the test piece beds down into
the test jig and the machine movement stabilizes.
Calculate Young's modulus according to the following formulae:
For displacement of loading points in three-point bending:
3
()-P P l
2 1
E = (1)
3
4bh()-d d
c s
For displacement of loading points in four-point bending:
2
()-P P d(d + d)
2 3
2 1 1 1 2
E = (2)
3
bh()-d d
c s
where:
E = Young's modulus expressed as Newtons per square metre;
P = Lower load level selected from recordings, expressed in Newtons;
1
P = upper load level selected from recordings, expressed in Newtons;
2
l = test jig outer span, expressed in metres;
d = test jig inner roller to outer roller spacing in four-point bending, expressed in metres;
1
d = one half of the test jig inner span in four-point bending, expressed in metres;
2
b = test piece width, expressed in metres;
h = test piece thickness, expressed in metres;
d = displacement recorded for the test piece in the jig over load interval P to P , expressed in
c 1 2
metres;
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CEN/TS 820-5:2004 (E)
d = displacement recorded for the thick bar in the jig over load interval P to P , expressed in
s 1 2
metres.
NOTE 4 For the case of quarter-point bending, d = d , and equation 2 reduces to:
1 2
3
()-P P l
2 1
E = (2A)
3
8bh()-d d
c s
Calculate the average Young's modulus figures for the loading and unloading curves. If these values
differ by more than 2 %, repeat the tests. If they differ by less than 2 %, take the overall average as the
determined value from the test.
4.5.2 From transducer displacement measurements (Method 2)
Use the procedure defined in 4.5.1 to obtain displacements for a defined load range. If one of the defined
points for the transducer contact in three-point bending is the support roller, calculate the displacement
recorded for the thick bar. Subtract the mean value of the thick bar displacement from the mean
specimen displacement over the same load range for both loading and unloading.
NOTE 1 If the force - displacement traces show evidence of a reduction of stiffness at upper load levels, this
can be taken as evidence of plastic softening. At this temperature and any higher test temperature, the results of
the test should be deemed invalid.
For three-point bending using defined points at the span centre and one or both support rollers, calculate
Young's modulus using equation 1.
For four-point bending using defined points at the span centre and one or both loading rollers, calculate
Young's modulus from the formula:
2
3()-P P d d
2 1 1 2
E = (3)
3
bh d
t
where:
d = transducer displacement recorded between the test piece centre and the inner loading point in
t
four-point bending over the selected load range, expressed in metres.
NOTE 2 For the case of quarter-point bending, d1 = d2, and equation 3 reduces to:
3
3()-P P l
2 1
E = (3A)
3
bh d
64
t
Calculate the average Young's modulus figures for the loading and unloading parts of the cycles. If these
values differ by more than 2 %, repeat the tests. If they differ by less than 2 %, take the overall average
as the determined value from the test.
4.6 Accuracy and interferences
A simple analysis based on the flexure equation can be used to show that the principal sources of error
are in measuring the force range (P – P ), the thickness of the test piece b, and the deflection d or (d -
2 1 t c
d ). In contrast, measurement of temperature, test span and test piece width play only a minor role. The
s
following analysis is based on the conditions specified for this method, but the overall error is dependent
on the choice of equipment, the accuracy of calibration, and the repeatability of mechanical contact
between the system and the test piece. Assuming that the accuracy of recording the force is limited to
± 1 % by the calibration accuracy of the load cell in the test machine, the noise in the output, and any
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reading error if a chart recorder is used, the error in (P – P ) is likely to be of the order ± 2 %. The error in
2 1
measuring the thickness of the test piece using a micrometer as specified above is probably ± 0,01 mm,
allowing also for test piece roughness, flatness and parallelism, or typically ± 1 % of the recommended
thickness. The error in measuring the deflection depends not only on the linearity and accuracy of
calibration of the crosshead movement or displacement transducer, but also on the repeatability of
contact of the test piece with the measuring system and the minimization of friction effects. Assuming that
the test is made to a maximum force equivalent to approximately half the fracture force of a test piece
which fails at a strain of 0,1 %, it can be shown that the test piece deflection in three point bending, d, is
given by:
2
-5
l
d£7·10 ( ) (4)
h
For a test span l of 40 mm and a typical value for the recommended thickness for the crosshead
displacement method of 1 mm, d = 0,11 mm. The calibration accuracy for the displacement measurement
shall therefore be 1% or better for the error in displacement to play a negligible role in the overall errors.
This should be achieved if the conditions on calibration of deflection given in 4.2.5 are upheld. The
repeatability aspects are not readily quantifiable, but may be minimized by ensuring repeatability of
recorded displacements in load cycling, and similarity of values in loading and unloading. The overall
error of measurement is thus likely to be typically ± 5 % when the force, thickness and displacement
contributions are appropriately summed. The error can in principle be reduced by (1) lengthening the test
piece span, (2) improving the force calibration over the range used for the test and the recording of force,
(3) employing a higher quality displacement transducer or cross-head movement measuring device.
Interferences that can arise in undertaking this test include (1) irreversible deformation of the test piece
and/or load train during load cycling, (2) undetected movements of the test piece within the loading and
displacement recording system, (3) oxidation of non-oxide ceramic materials during the course of the test.
In each case the effects tend to increase with increasing test temperature. The influence of these
interferences can be minimised by taking appropriate actions in the design of the test facility, specifically
in the materials used for the parts to be subject to elevated temperatures, the design of the loading jig for
the test piece, and the test atmosphere. Inelastic deformation within the test piece may be detected either
by permanent offsets over a loading cycle, or by a softening with increasing force. Results obtained under
such conditions should be noted in the report, and may have little value.
5 Method B: Resonance method
5.1 Principle
A beam test piece is excited mech
...