oSIST prEN 843-2:2026

Advanced technical ceramics - Mechanical properties of monolithic ceramics at room temperature - Part 2: Determination of Young's modulus, shear modulus and Poisson's ratio

This part of EN 843 specifies methods for determining the elastic moduli, specifically Young’s modulus, shear modulus and Poisson’s ratio, of advanced monolithic technical ceramics at room temperature. This European Standard prescribes four 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 flexure.
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, shear modulus and Poisson’s ratio from the time-of-flight of an ultrasonic pulse.
D   The determination of Young’s modulus from the fundamental natural frequency of a struck bar (impulse excitation method).
All the test methods assume the use of homogeneous test pieces of linear elastic materials.
NOTE 1   Not all ceramic materials are equally and linearly elastic in tension and compression, such as some porous materials and some piezoelectric materials.
With the exception of Method C, the test assumes that the test piece has isotropic elastic properties. Method C may be used to determine the degree of anisotropy by testing in different orientations.
NOTE 2   An ultrasonic method for dealing with anisotropic materials (ceramic matrix composites) can be found in
ENV 14186 (see Bibliography). An alternative to Method D for isotropic materials using disc test pieces is given in
Annex A.
NOTE 3   At high porosity levels all of the methods except Method C can become inappropriate. The methods are only suitable for a maximum grain size (see EN 623-3), excluding deliberately added whiskers, of less than 10 % of the minimum dimension of the test piece.
NOTE 4   The different methods given in this European Standard can produce slightly different results on the same material owing to differences between quasi-isothermal quasi-static an

Hochleistungskeramik - Mechanische Eigenschaften monolithischer Keramik bei Raumtemperatur - Teil 2: Bestimmung des Elastizitätsmoduls, Schubmoduls und der Poissonzahl

Céramiques techniques avancées - Propriétés mécaniques des céramiques monolithiques à température ambiante - Partie 2: Détermination du module de Young, du module de cisaillement et du coefficient de Poisson

Sodobna tehnična keramika - Monolitna keramika - Mehanske lastnosti pri sobni temperaturi - 2. del: Ugotavljanje elastičnega modula (Youngov modul), strižnega modula in Poissonovega števila

Ta del standarda EN 843 določa metode za določanje elastičnih modulov, natančneje Youngovega modula, strižnega modula in Poissonovega razmerja, naprednih monolitnih tehničnih keramik pri sobni temperaturi. Ta evropski standard predpisuje štiri alternativne metode za določanje nekaterih ali vseh teh treh parametrov:
A Določanje Youngovega modula z uporabo statičnega upogiba tankega nosilca v tritočkovnem ali štiritočkovnem upogibu.
B Določanje Youngovega modula z uporabo prisilne vzdolžne resonance, ali Youngovega modula, strižnega modula in Poissonovega razmerja z uporabo prisilne upogibne in torzijske resonance tankega nosilca.
C Določanje Youngovega modula, strižnega modula in Poissonovega razmerja iz časa prehoda ultrazvočnega impulza.
D Določanje Youngovega modula iz osnovne naravne frekvence udarjenega droga (metoda vzbujanja impulza).
Vse preskusne metode predvidevajo uporabo homogenih preskusnih kosov linearno elastičnih materialov.
OPOMBA 1 Niso vsi keramični materiali enako in linearno elastični pri natezanju in tlačenju, kot so nekateri porozni materiali in nekateri piezoelektrični materiali.
Z izjemo metode C, preskus predvideva, da ima preskusni kos izotropne elastične lastnosti. Metoda C se lahko uporabi za določanje stopnje anizotropije z izvajanjem preskusov v različnih orientacijah.
OPOMBA 2 Ultrazvočna metoda za obravnavo anizotropnih materialov (kompoziti s keramično matrico) je navedena v ENV 14186 (glej Bibliografijo). Alternativa metodi D za izotropne materiale z uporabo diskastih preskusnih kosov je navedena v Prilogi A.
OPOMBA 3 Pri visokih ravneh poroznosti lahko vse metode, razen metode C, postanejo neprimerne. Metode so primerne le za največjo velikost zrn (glej EN 623-3), brez namerno dodanih vlaken (whiskers), manjšo od 10 % najmanjše dimenzije preskusnega kosa.
OPOMBA 4 Različne metode, navedene v tem evropskem standardu, lahko dajo nekoliko različne rezultate na istem materialu zaradi razlik med kvazi-izotermičnimi kvazi-statičnimi anali.

General Information

• Status: Not Published
• Public Enquiry End Date: 30-Jul-2026
• ICS: 81.060.30 - Advanced ceramics
• Technical Committee: I13 - Imaginarni 13
• Current Stage: 4020 - Public enquire (PE) (Adopted Project)
• Start Date: 02-Jun-2026
• Due Date: 20-Oct-2026
• Mandate: M/BC/CEN/90/4 - Request concerning the realisation of a standardization programme in the field of advanced technical ceramics
• Ref Project: prEN 843-2 - Advanced technical ceramics - Mechanical properties of monolithic ceramics at room temperature - Part 2: Determination of Young's modulus, shear modulus and Poisson's ratio

Relations

• Revises: SIST EN 843-2:2007 - Advanced technical ceramics - Mechanical properties of monolithic ceramics at room temperature - Part 2: Determination of Young's modulus, shear modulus and Poisson's ratio
• Effective Date: 18-Jun-2025

Overview

oSIST prEN 843-2:2026: Advanced Technical Ceramics - Mechanical Properties of Monolithic Ceramics at Room Temperature - Part 2 specifies standardized methods for determining key elastic properties-Young’s modulus, shear modulus, and Poisson’s ratio-in advanced monolithic technical ceramics under room temperature conditions. This draft European Standard, prepared by CEN/TC 184, will supersede EN 843-2:2006. It prescribes four alternative methods for accurately characterizing the elastic moduli of ceramics, providing a flexible approach that addresses a variety of material types and technical requirements.

Testing for Young’s modulus, shear modulus, and Poisson’s ratio is essential for understanding the performance and structural reliability of technical ceramics in demanding applications. The document ensures consistency and comparability of measurement results across different laboratories and industries by standardizing test procedures, instrumentation, and reporting.

Key Topics

• Measurement Techniques:
  • Static Flexure (Method A): Young’s modulus determination through three- or four-point bending of thin beams.
  • Resonance Method (Method B): Determination of Young’s modulus, shear modulus, and Poisson’s ratio via forced resonance in flexural, longitudinal, or torsional vibration.
  • Ultrasonic Time-of-Flight (Method C): Uses ultrasonic pulses to simultaneously determine all three elastic moduli.
  • Impulse Excitation (Method D): Young’s modulus calculation from the fundamental natural frequency of a struck thin beam.
• Specimen Requirements: Testing assumes use of homogeneous, isotropic, linear elastic ceramic test pieces, with exceptions and guidance for anisotropic or porous ceramics.
• Measurement Uncertainty and Reproducibility: The standard highlights key factors impacting accuracy-specimen alignment, apparatus calibration, repeatability, and appropriate test selection especially for materials with specific characteristics (porosity, grain size).
• Applicability Limits: Methods are suitable when the grain size is less than 10% of the minimum test piece dimension. Some methods may be unsuitable for high-porosity or strongly anisotropic ceramics.
• Procedural Harmonization: Enhanced consistency in definitions, formulae (including recent updates), apparatus requirements, and recommendations for reliable data collection and reporting.

Applications

oSIST prEN 843-2:2026 is directly applicable to sectors utilizing advanced technical ceramics, such as:

• Aerospace and Defense: For designing lightweight, high-strength components with predictable elastic behavior.
• Electronics and Semiconductors: Ensuring mechanical stability of substrates and insulators made from advanced ceramics.
• Medical Technology: Material qualification for bioceramics used in implants and prosthetics.
• Automotive and Industrial Engineering: Supporting quality control and R&D for ceramic parts exposed to high mechanical and thermal stresses.
• Academic and Industrial Research: Providing reliable, standardized methods for comparing the mechanical properties of various ceramic materials.

Accurately determining the elastic moduli is critical for design, simulation, quality assurance, and performance prediction in environments with significant mechanical demands.

Related Standards

The following standards are closely related to, or referenced by, oSIST prEN 843-2:2026:

• EN 843-1: Advanced technical ceramics - Mechanical properties of monolithic ceramics at room temperature - Part 1: Determination of flexural strength.
• EN 623-4: Monolithic ceramics - General and textural properties - Part 4: Determination of surface roughness.
• EN ISO 13383-1: Fine ceramics - Microstructural characterization - Determination of grain size and distribution.
• EN ISO 18754: Fine ceramics - Determination of density and apparent porosity.
• EN ISO 7500-1: Calibration and verification of static uniaxial testing machines.
• EN ISO 463, EN ISO 3611, EN ISO 13385-1: Standards for dimensional measuring equipment essential for accurate specimen preparation and measurement.
• ENV 14186, EN ISO 18610, EN 15335: Addressing advanced ultrasonic and resonant methods for anisotropic ceramic matrix composites.

These standards together build a robust framework for the mechanical characterization and quality assurance of advanced technical ceramics, supporting innovation and reliability in high-performance applications.

Standards Content (Sample)

SLOVENSKI STANDARD
01-julij-2026
Sodobna tehnična keramika - Monolitna keramika - Mehanske lastnosti pri sobni
temperaturi - 2. del: Ugotavljanje elastičnega modula (Youngov modul), strižnega
modula in Poissonovega števila
Advanced technical ceramics - Mechanical properties of monolithic ceramics at room
temperature - Part 2: Determination of Young's modulus, shear modulus and Poisson's
ratio
Hochleistungskeramik - Mechanische Eigenschaften monolithischer Keramik bei
Raumtemperatur - Teil 2: Bestimmung des Elastizitätsmoduls, Schubmoduls und der
Poissonzahl
Céramiques techniques avancées - Propriétés mécaniques des céramiques
monolithiques à température ambiante - Partie 2: Détermination du module de Young, du
module de cisaillement et du coefficient de Poisson
Ta slovenski standard je istoveten z: prEN 843-2
ICS:
81.060.30 Sodobna keramika Advanced ceramics
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

DRAFT
EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
May 2026
ICS 81.060.30 Will supersede EN 843-2:2006
English Version
Advanced technical ceramics - Mechanical properties of
monolithic ceramics at room temperature - Part 2:
Determination of Young's modulus, shear modulus and
Poisson's ratio
Céramiques techniques avancées - Propriétés Hochleistungskeramik - Mechanische Eigenschaften
mécaniques des céramiques monolithiques à monolithischer Keramik bei Raumtemperatur - Teil 2:
température ambiante - Partie 2: Détermination du Bestimmung des Elastizitätsmoduls, Schubmoduls und
module de Young, du module de cisaillement et du der Poissonzahl
coefficient de Poisson
This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee
CEN/TC 184.
If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations
which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.

This draft European Standard was established by CEN in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC
Management Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
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.

Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without
notice and shall not be referred to as a European Standard.

EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATIO N

EUROPÄISCHES KOMITEE FÜR NORMUN G

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2026 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 843-2:2026 E
worldwide for CEN national Members.

Contents Page
European foreword . 4
1 Scope . 5
2 Normative references . 5
3 Terms and definitions . 6
4 Method A: Static flexure method . 7
4.1 Principle . 7
4.2 Apparatus . 7
4.3 Preparation of test pieces . 8
4.4 Procedure . 8
4.5 Calculations . 10
4.5.1 From crosshead displacement (Method A.1) . 10
4.5.2 From transducer displacement measurements (Method A.2) . 11
4.5.3 From strain gauges (Method A.3) . 12
4.6 Measurement uncertainty . 12
5 Method B: Resonance method . 12
5.1 Principle . 12
5.2 Apparatus . 13
5.3 Preparation of test pieces . 14
5.3.1 General. 14
5.3.2 Flexural resonance . 14
5.3.3 Torsional resonance . 15
5.3.4 Longitudinal resonance . 15
5.3.5 Number of test pieces . 15
5.4 Procedure . 15
5.4.1 General. 15
5.4.2 Measurement of the size and the mass . 15
5.4.3 Flexural resonance . 17
5.4.4 Torsional resonance . 17
5.4.5 Longitudinal resonance . 17
5.5 Calculations . 17
5.6 Measurement uncertainty . 19
6 Method C: Ultrasonic method . 20
6.1 Principle . 20
6.2 Apparatus . 20
6.3 Preparation of test pieces . 21
6.4 Procedure . 21
6.5 Calculations . 22
6.6 Measurement uncertainty . 23
7 Method D: Impulse excitation method . 23
7.1 Principle . 23
7.2 Apparatus . 23
7.3 Preparation test pieces . 23
7.3.1 General. 23
7.3.2 Flexural resonance . 24
7.3.3 Torsional resonance . 24
7.3.4 Longitudinal resonance . 24
7.3.5 Number of test pieces . 24
7.4 Procedure . 24
7.4.1 General . 24
7.4.2 Measurement of the size and the mass . 24
7.4.3 Measurement of resonant frequency . 24
7.5 Calculations . 27
7.6 Measurement uncertainty . 27
8 Report . 27
8.1 General . 27
8.2 Method A . 27
8.3 Method B . 28
8.4 Method C . 28
8.5 Method D . 29
Annex A (informative) Impact excitation method applied to disc test pieces . 30
A.1 General . 30
A.2 Principle . 30
A.3 Apparatus . 31
A.4 Test pieces . 31
A.5 Procedure . 31
A.6 Calculations . 31
A.7 Interferences . 32
A.8 Measurement uncertainty . 32
A.9 Test report . 33
Annex B (informative) Young’s modulus correction for edge treatments of rectangular cross
section test piece . 36
B.1 General . 36
B.2 Principle . 36
B.3 Procedure . 36
Annex C (informative) Round-robin validation of test methods . 38
C.1 Objectives . 38
C.2 Materials . 38
C.3 Test facilities . 38
C.4 Results . 38
C.5 Conclusions . 39
Bibliography . 40

European foreword
This document (prEN 843-2:2026) has been prepared by Technical Committee CEN/TC 184 “Advanced
technical ceramics”, the secretariat of which is held by DIN.
This document is currently submitted to the CEN Enquiry.
This document will supersede EN 843-2:2006.
This document includes the following main significant technical changes with respect to EN 843-2:2006:
a) update of the normative references;
b) revised Formula (8) and Formula (9) for the calculation of the dynamic shear modulus of a
rectangular prism, tested by the resonance method (Method B) or by the impulse excitation method
(Method D);
c) addition of a Formula (10) for the calculation of the dynamic shear modulus of a cylindrical rod in
torsional resonance (5.5.2);
d) addition of a new Annex B addressing the Young’s modulus correction for edge treatments of
rectangular cross section test piece;
e) harmonization of the requirements of Method B and Method D;
f) editorial revision.
A list of all parts in the EN 843 series, published under the general title Advanced technical ceramics —
Mechanical properties of monolithic ceramics at room temperature, can be found on the CEN website.
1 Scope
This document specifies test methods for determining the elastic moduli, specifically Young’s modulus,
shear modulus and Poisson’s ratio, of advanced monolithic technical ceramics at room temperature. This
document specifies four alternative methods for determining some or all of these three parameters:
a) Method A - the determination of Young’s modulus by static flexure of a thin beam in three- or four-
point flexure;
b) Method 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) Method C - the determination of Young’s modulus, shear modulus and Poisson’s ratio from the time-
of-flight of an ultrasonic pulse;
d) Method D - the determination of Young’s modulus from the fundamental natural frequency of a
struck thin beam (impulse excitation method).
All the test methods assume the use of homogeneous test pieces of linear elastic materials.
NOTE 1 Not all ceramic materials are equally and linearly elastic in tension and compression, such as some
porous materials and some piezoelectric materials.
With the exception of Method C, the test methods assume that the test piece has isotropic elastic
properties. Method C can be used to determine the degree of anisotropy by testing in different
orientations.
NOTE 2 An ultrasonic method and a resonant method for dealing with anisotropic materials (ceramic matrix
composites) can be found respectively in EN ISO 18610 [1] and EN 15335 [2]. An alternative to Method D for
isotropic materials using disc test pieces is given in Annex A.
NOTE 3 It is possible that at high porosity levels all of the methods except Method C become inappropriate. The
methods are only suitable for a maximum grain size measured in accordance with EN ISO 13383-1, excluding
deliberately added whiskers, of less than 10 % of the minimum dimension of the test piece.
NOTE 4 The different methods given in this document can produce slightly different results on the same material
owing to differences between quasi-isothermal quasi-static and quasi-adiabatic dynamic conditions. In addition, the
calculation routines for different methods have different origins and different potential uncertainties which have
not been rigorously evaluated in preparing this document. Some information is given in Annex C (see also [8]).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
EN 623-4, Advanced technical ceramics - Monolithic ceramics - General and textural properties - Part 4:
Determination of surface roughness
EN 843-1, Advanced technical ceramics - Mechanical properties of monolithic ceramics at room
temperature - Part 1: Determination of flexural strength
EN ISO 463, Geometrical Product Specifications (GPS) - Dimensional measuring equipment - Design and
metrological characteristics of mechanical dial gauges (ISO 463)
EN ISO 3611, Geometrical product specifications (GPS) - Dimensional measuring equipment - Design and
metrological characteristics of micrometers for external measurements (ISO 3611)
EN ISO 7500-1, Metallic materials - Calibration and verification of static uniaxial testing machines - Part 1:
Tension/compression testing machines - Calibration and verification of the force-measuring system (ISO
7500-1)
EN ISO 13383-1, Fine ceramics (advanced ceramics, advanced technical ceramics) - Microstructural
characterization - Part 1: Determination of grain size and size distribution (ISO 13383-1)
EN ISO 13385-1, Geometrical product specifications (GPS) - Dimensional measuring equipment - Part 1:
Design and metrological characteristics of callipers (ISO 13385-1)
EN ISO 18754, Fine ceramics (advanced ceramics, advanced technical ceramics) - Determination of density
and apparent porosity (ISO 18754)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in EN 843-1 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https://www.iso.org/obp/
— IEC Electropedia: available at https://www.electropedia.org/
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 a quasi-isothermal condition by stressing statically or quasi-statically
3.5
dynamic elastic moduli
elastic moduli determined non-quasi-statically, i.e. under quasi-adiabatic conditions, such as in the
resonant, ultrasonic pulse or impulse excitation methods
4 Method A: Static flexure method
4.1 Principle
Using three- or four-point flexure of a thin beam test piece, the elastic distortion is measured, from which
Young’s modulus may be calculated according to thin-beam formulae.
4.2 Apparatus
4.2.1 Test jig, capable of three-point or four-point flexure.
The test jig shall be in accordance with that described in EN 843-1 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.
NOTE Articulation is not essential for carefully machined flat and parallel-faced test pieces.
The outer span of the test jig shall be 40 mm or greater.
If the availability of test material allows, a span of at least 100 mm 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 crosshead movement.
The test jig shall be for four-point flexure, if displacement is determined by strain gauges or differential
transducer.
4.2.2 Test 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 ≤ 0,1 % of the maximum load employed. The calibration shall
have been checked within the previous year.
4.2.3 Displacement or strain measuring device.
4.2.3.1 General
The device shall be installed to measure the displacement or strain of the loaded test piece by one of three
methods, in accordance with 4.2.3.2, 4.2.3.3 or 4.2.3.4.
4.2.3.2 Method A.1
A facility is designed to measure the apparent displacements of the test machine with the test piece
(Figure 1 a), and with the test piece replaced by a steel or ceramic bar at least 15 mm thick. The difference
between these displacements is equivalent to the displacement of the test piece in the test jig. The
displacement recording device shall be calibrated by comparing machine crosshead displacement with
the movement indicated on a dial gauge or other displacement measuring device (see 4.2.5) contacting
the crosshead.
4.2.3.3 Method A.2
A facility is designed to measure the displacement of the test piece directly using transducers contacting
two defined points on the surface of the test piece between the support loading rollers in three-point or
four-point bending (Figure 1 b). The defined points shall be the centre of the span and one or both loading
rollers in four-point bending, or the centre of the span and one or both support rollers in three-point
bending. The transducer shall be capable of detecting movements with an accuracy of 0,001 mm, shall
have output linear to 0,1 % and shall be calibrated to an accuracy of 0,1 %.
4.2.3.4 Method A.3
A facility is designed to record the strain on the surface of the test piece by using a strain gauge placed on
the surface of the test piece between the central loading rollers in four-point bending (Figure 1 c). The
strain gauge and its associated bridge circuit shall have an accuracy of better than 0,1 % and shall be
−5
capable of resolving a strain of less than 10 .
It is recommended that the strain gauge should only be applied by experienced personnel in order to
ensure it performs accurately. It is also recommended that two or more gauges are fitted and their
outputs recorded simultaneously in order to provide a check on reproducibility.
4.2.4 Micrometer, in accordance with EN ISO 3611, but capable of recording to 0,002 mm, or other
device of equivalent accuracy, for measuring the dimensions of the test piece.
4.2.5 Dial gauge, in accordance with EN ISO 463 or other calibrated displacement measuring device,
capable of recording to 0,01 mm.
4.3 Preparation of 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 maximum grain size measured in accordance with EN ISO 13383-1, excluding
deliberately added whiskers, shall be less than 10 % of the minimum dimension of the test piece.
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 A.1 (4.2.3.2), the thickness of the test piece shall
be in the range 0,8 mm to 1,5 mm. For Method A.2 (4.2.3.3) and Method A.3 (4.2.3.4), the test piece may
be up to 3 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 A.1 they shall not be chamfered.
For Method A.2 and Method A.3 they can 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 centralize 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.
The upper level of force can be estimated by employing the strength calculation as specified in EN 843-1
and inserting a stress level of no more than 0,5 σ , where σ is the mean fracture stress.
f f
Apply a steadily increasing force to the test jig at a constant test machine crosshead displacement rate in
the range 0,001 mm/min to 0,5 mm/min. Record the load and displacement (either crosshead
displacement (Method A.1, 4.2.3.2), transducer displacement (Method A.2, 4.2.3.3), or strain gauge output
(Method A.3, 4.2.3.4)) 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 A.1) or if the transducer method is employed using a support roller as one of the
defined points (Method A.2), replace the test piece with the thick parallel-sided steel or ceramic bar and
repeat the loading cycles to the same peak load, recording load and displacement.
The use of both loading and unloading cycles is required in order to take into account machine hysteresis
in Method A.1, transducer hysteresis in Method A.2 and to test strain gauge adhesion in Method A.3.
a) Method A.1, using machine displacement

b) Method A.2, using a displacement transducer
c) Method A.3, using a strain gauge
Key
1 push-rod or top platen 8 rods detecting deflection
2 metallic half-sphere 9 support frame
3 metallic loading block 10 adjusting screw
4 loading rollers (freely rolling) 11 suspension springs
5 test piece 12 displacement transducer
6 support rollers (freely rolling) 13 load cell
7 support block 14 strain gauge
Figure 1 — Methods of measuring displacement or strain in quasi-statically loaded flexural test
pieces, a) Method A.1 using machine displacement, b) Method A.2 using a displacement
transducer and c) Method A.3 using a strain gauge
4.5 Calculations
4.5.1 From crosshead displacement (Method A.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.
The region of the recordings selected should avoid strong nonlinearities at low load which can include
irreproducible effects of machine movement and test piece alignment and also the effects of crosshead
reversal near peak load.
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 1 It is possible that the first cycle shows 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 Formula (1) or Formula (2).
For displacement of loading points in three-point bending:
F − F l
( )
E= (1)
4 bh d − d
( )
cs
For displacement of loading points in four-point bending:
23 F −+ Fd d d
( ) ( )
2 1 1 1 2
E= (2)
bh d − d
( )
cs
where
E is the Young’s modulus expressed in pascals (Pa);
F is the lower load level selected from recordings, expressed in newtons (N);
F is the upper load level selected from recordings, expressed in newtons (N);
l is the test jig outer span in three-point or four-point bending, expressed in metres (m);
d is the test jig inner roller to outer roller spacing in four-point bending, expressed in metres
(m);
d2 is the one half of the test jig inner span in four-point bending, expressed in metres (m);
b is the test piece width, expressed in metres (m);
h is the test piece thickness, expressed in metres (m);
d is the displacement recorded for the test piece in the jig over the load interval F to F
c 1 2
expressed in metres (m);
d is the displacement recorded for the thick bar in the jig over the load interval F to F
s 1 2
expressed in metres.
NOTE 2 For the case of quarter-point bending, d1 = d2, and Formula (2) reduces to:
F − F l
( )
E=
8 bh d − d
( )
cs
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 A.2)
Use the procedure specified 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.
For three-point bending using defined points at the span centre and under one or both support rollers,
calculate Young’s modulus using Formula (1).
For four-point bending using defined points at the span centre and under one or both loading rollers,
calculate Young’s modulus from Formula (3):
3 F − F dd
( )
2 1 12
E= (3)
bh d
t
where
d is the transducer displacement recorded between the test piece centre and the inner loading
t
point in four-point bending over the selected load range, expressed in metres (m).
NOTE For the case of quarter-point bending, d1 = d2, and Formula (3) reduces to:
3 F − F l
( )
E=
64 bh d
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.
4.5.3 From strain gauges (Method A.3)
Use the procedure defined in 4.5.1 to obtain strain gauge outputs for a defined load range. Calculate the
strain change over the load range for each loading and unloading of the test piece.
Calculate Young’s modulus from Formula (4):
3 F − Fd
( )
2 1 1
E=
bh ε
(4)
where
ε is the strain change over the defined load range, expressed as a fraction without units.
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 Measurement uncertainty
The uncertainty of Young’s modulus determined in accordance with this method derives primarily from
the parallelism of the test piece faces and the accuracy of measurement of thickness in the direction of
flexure. Additional factors are the alignment in the loading jig and the repeatability of measurement of
deflections or strain. For example, using test pieces 1 mm in thickness and with a span of 100 mm, a
mechanically reliable fixture of the piece typically permits a repeatability in load cycling of ± 2 % in
flexural displacement or strain measurement. Overall, an uncertainty of typically less than ± 5 % should
be achievable.
5 Method B: Resonance method
5.1 Principle
A beam test piece is excited mechanically or electromechanically to vibrate at a given frequency, and the
magnitude of the vibration is determined by a detector. The peak response is obtained at the resonant
frequency, either the fundamental or an overtone. The test is performed to excite either longitudinal or
flexural and torsional vibration. Young’s modulus may be determined from longitudinal resonance and
Young’s modulus, shear modulus and Poisson’s ratio may be determined from the flexural and torsional
resonant frequencies, together with the test piece dimensions and mass.
5.2 Apparatus
There are various techniques that may be used to determine the resonant frequency of the test piece. The
test piece may be excited by direct mechanical contact of a vibrator (especially appropriate for
longitudinal vibration) such as a piezoelectric transducer, or it may be suspended by a wire from a
vibrator (appropriate for flexural and torsional vibration), such as a record player cartridge or
loudspeaker cone. Alternatively, it may be driven electromagnetically by attaching thin foils of magnetic
material to one surface, or electrostatically by attaching an electrode to, or painting a conducting film of
metal or graphite on, one surface.
5.2.1 Driving electronics. The driving electronics shall consist of a variable frequency oscillator and a
record player cartridge assembly, loudspeaker cone, or other suitable transducer. It is recommended that
the oscillator is equipped with a digital frequency display. It shall have sufficient power to drive high-
modulus ceramic test pieces through the transducer in the frequency range 100 Hz to 100 kHz, with a flat
response curve (i.e. no resonances of its own). The stability and accuracy of the digital display shall be
checked against a standard frequency, preferably from a transfer standard source.
5.2.2 Detecting electronics. The detecting electronics shall consist of a record player cartridge
assembly or other suitable transducer, a linear amplifier, and a voltmeter, ammeter or oscilloscope. The
detector shall generate a voltage proportional to the amplitude of vibration, the velocity, or the
acceleration of the test piece.
The oscilloscope is recommended for identifying resonant conditions.
5.2.3 Test piece support. The test piece support shall permit the test piece to vibrate in the desired
mode without significant restriction. If the test piece is to be supported from beneath, the supports shall
be made of rubber, cork, or similar material and shall have a minimum contact area with the test piece.
NOTE For the electrostatic method it can be necessary to make the support electrically conducting.
Alternatively, if the test piece is to be suspended from the driving and detecting transducers, fine thread
or metal wires shall be used. The supports shall be placed at or close to the ends of the vibrating test piece
(see 5.4.1). The vibrating mass of the suspension system shall be negligible compared with the mass of
the test piece. For the electromagnetic or electrostatic method, the mass of any magnetic foil or electrode
attached to the test piece shall be negligible compared with the mass of the test piece.
For the electrostatic method, a thin evaporated coating of a suitable metal will usually suffice. For the
electromagnetic method, the magnetic foil should be of nickel or iron, typically less than 0,05 mm thick
and should be attached to the test piece near the centre with a minimum of adhesive.
5.2.4 Laboratory balance, capable of weighing the test piece to the nearest 1 mg.
5.2.5 Micrometer, conforming to EN ISO 3611, but capable of recording to the nearest 0,002 mm or
similar device of equivalent accuracy for measuring the dimensions of the test piece.
5.2.6 Vernier callipers, conforming to EN ISO 13385-1, but capable of recording to the nearest
0,01 mm or similar device of equivalent accuracy for measuring the dimensions of the test piece.
5.2.7 Oven, for drying test pieces at (120 ± 10) °C, or other suitable device.
5.2.8 Desiccator, for storage of dried test pieces.
5.3 Preparation of test pieces
5.3.1 General
The test pieces shall be rectangular prisms in accordance with 5.3.2.1, 5.3.3.1 and 5.3.4.1, or circular cross
section rods in accordance with 5.3.2.2, 5.3.3.2 and 5.3.4.2.
The edges of rectangular section test pieces shall not be chamfered. However, if the chipping of the test
pieces from the edges affects the results, the edges may be chamfered, but the amount of the chamfering
shall be as small as possible. Annex B provides a method to correct the calculation of Young’s modulus
for an edge chamfered test piece or test piece with rounded edges.
If the test material is likely to be elastically anisotropic, care shall be taken in the selection of test piece
orientations and in the interpretation of the test results.
NOTE This test method measures Young’s modulus parallel to the length of the test piece and shear modulus
as an aggregate of different directions.
The maximum grain size measured in accordance with EN ISO 13383-1, excluding deliberately added
whiskers, shall be less than 10 % of the minimum dimension of the test piece.
This test method is not satisfactory for test pieces that have major discontinuities, such as large cracks
(surface or internal) or internal voids.
The surface of the test piece shall be smooth and flat. The surface shall be finished using a fine grind
(400 grit or finer). The machining procedure shall not affect the test results.
For the suspension method, the mass of the test piece is, with advantage, at least 5 g in order to assist
keeping a suspension system straight.
5.3.2 Flexural resonance
5.3.2.1 Rectangular prism
The test piece shall have a ratio L/h > 10 where h is the thickness of the test piece in the direction of
flexural vibration and L is the overall length (Figure 2a). The ratio L/b shall be ≥ 10 where b is the width
of the test piece.
The dimensions of the test piece shall be such as to have a fundamental flexural resonant frequency in
the range 100 Hz to 20 kHz.
For convenience, a flexural test piece as defined in EN 843-1 can be used, provided that the ends of the
bar are machined square and parallel, subject to the allowable frequency range above.
If the moduli of the test material are high (E > 200 GPa), or when the available oscillator power is
marginal, it is recommended that L/h ≫ 10 and that 10 > b/h > 2,5. It is also recommended that b/h
is > 1,1 or < 0,9 to avoid confusion of different vibration modes.
The parallelism of the upper and lower surfaces perpendicular to the direction of flexural vibration shall
be better than h/100, of the sides parallel to the direction of vibration, better than b/100, and of the ends
of the test piece, better than L/200.
5.3.2.2 Circular rod
The test-piece shall be a circular cross-section rod with L/d > 10 where d is the diameter of the test piece.
The diameter of the test piece shall be constant to within d/100, and the ends shall be flat and parallel to
better than L /200.
5.3.3 Torsional resonance
5.3.3.1 Rectangular prism
The test piece shall have a ratio L/h > 20. The ratio b/h shall be greater than 1,5 and may be with
advantage as high as 10 (Figure 2 b)).
The parallelism of the surfaces shall be better than h/100 and b/100, and of the ends of the test piece,
better than L/200
5.3.3.2 Circular rod
The test-piece shall be a circular cross-section rod with L/d > 10 where d is the diameter of the test piece.
The diameter of the test piece shall be constant to within d/100, and the ends shall be flat and parallel to
better than L/200
5.3.4 Longitudinal resonance
5.3.4.1 Rectangular pri
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