SIST EN ISO 6721-1:2003

Plastics - Determination of dynamic mechanical properties - Part 1: General principles (ISO 6721-1:2001)

Revision instead of amendment in order to follow ISO + UAP instead of EN/ENQ+FV-VA/ISO (CC/000817)

Kunststoffe - Bestimmung dynamisch-mechanischer Eigenschaften - Teil 1: Allgemeine Grundlagen (ISO 6721-1:2001)

Diese Internationale Norm legt Verfahren zur Bestimmung der dynamisch-mechanischen Eigenschaften von steifen Kunststoffen im Bereich des linear-viskoelastischen Verhaltens fest. Dieser Teil von ISO 6721 ist ein Einführungsteil, der die Definitionen und alle Gesichtspunkte enthält, die für die einzelnen, in den folgenden Teilen beschriebenen Prüfverfahren gültig sind.
Unterschiedliche Deformationsarten können Ergebnisse hervorrufen, die nicht direkt vergleichbar sind. Zum Beispiel ergeben Zugschwingungen Spannungen, die über die gesamte Dicke des Probekörpers gleichförmig sind, während Biege-Messungen bevorzugt durch die Eigenschaften von Oberflächen-Gebieten beeinflusst sind.
Eigenschaftswerte aus Biegeprüfungen sind nur mit solchen aus Zugprüfungen vergleichbar in Spannungs-bereichen, in denen die Spannungs-Dehnungs-Beziehung linear ist, und für Probekörper mit homogener Struktur.

Plastiques - Détermination des propriétés mécaniques dynamiques - Partie 1: Principes généraux (ISO 6721-1:2001)

Polimerni materiali - Določanje dinamičnih mehanskih lastnosti - 1. del: Splošna načela (ISO 6721-1:2001)

General Information

• Status: Withdrawn
• Publication Date: 30-Apr-2003
• Withdrawal Date: 16-Nov-2011
• ICS: 83.080.01 - Plastics in general
• Technical Committee: IPMA - Polimer materials and products
• Current Stage: 9900 - Withdrawal (Adopted Project)
• Start Date: 16-Nov-2011
• Due Date: 09-Dec-2011
• Completion Date: 17-Nov-2011
• Ref Project: EN ISO 6721-1:2002 - Plastics - Determination of dynamic mechanical properties - Part 1: General principles (ISO 6721-1:2001)

Relations

• Replaced By: SIST EN ISO 6721-1:2012 - Plastics - Determination of dynamic mechanical properties - Part 1: General principles (ISO 6721-1:2011)
• Effective Date: 01-Jan-2012
• Replaces: SIST EN ISO 6721-1:1999 - Plastics - Determination of dynamic mechanical properties - Part 1: General principles (ISO 6721-1:1994, including Technical Corrigendum 1:1995)
• Effective Date: 24-Dec-2008

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN ISO 6721-1:2003
01-maj-2003
1DGRPHãþD
SIST EN ISO 6721-1:1999
SIST EN ISO 6721-1:1999
3ROLPHUQLPDWHULDOL'RORþDQMHGLQDPLþQLKPHKDQVNLKODVWQRVWLGHO6SORãQD
QDþHOD,62
Plastics - Determination of dynamic mechanical properties - Part 1: General principles
(ISO 6721-1:2001)
Kunststoffe - Bestimmung dynamisch-mechanischer Eigenschaften - Teil 1: Allgemeine
Grundlagen (ISO 6721-1:2001)
Plastiques - Détermination des propriétés mécaniques dynamiques - Partie 1: Principes
généraux (ISO 6721-1:2001)
Ta slovenski standard je istoveten z: EN ISO 6721-1:2002
ICS:
83.080.01 Polimerni materiali na Plastics in general
splošno
SIST EN ISO 6721-1:2003 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

SIST EN ISO 6721-1:2003

---------------------- Page: 2 ----------------------

SIST EN ISO 6721-1:2003
EUROPEAN STANDARD
EN ISO 6721-1
NORME EUROPÉENNE
EUROPÄISCHE NORM
September 2002
ICS 83.080.01 Supersedes EN ISO 6721-1:1996
English version
Plastics - Determination of dynamic mechanical properties - Part
1: General principles (ISO 6721-1:2001)
Plastiques - Détermination des propriétés mécaniques Kunststoffe - Bestimmung dynamisch-mechanischer
dynamiques - Partie 1: Principes généraux (ISO 6721- Eigenschaften - Teil 1: Allgemeine Grundlagen (ISO 6721-
1:2001) 1:2001)
This European Standard was approved by CEN on 19 August 2002.
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. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Management Centre or to any CEN member.
This European Standard exists 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 Management Centre has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece,
Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway, Portugal, 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
© 2002 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 6721-1:2002 E
worldwide for CEN national Members.

---------------------- Page: 3 ----------------------

SIST EN ISO 6721-1:2003
EN ISO 6721-1:2002 (E)
Foreword
The text of ISO 6721-1:2001 has been prepared by Technical Committee ISO/TC 61 "Plastics"
of the International Organization for Standardization (ISO) and has been taken over as
EN ISO 6721-1:2002 by Technical Committee CEN/TC 249 "Plastics", the secretariat of which is
held by IBN.
This European Standard shall be given the status of a national standard, either by publication of
an identical text or by endorsement, at the latest by March 2003, and conflicting national
standards shall be withdrawn at the latest by March 2003.
This document supersedes EN ISO 6721-1:1996.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to implement this European Standard: Austria, Belgium, Czech
Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg,
Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of the International Standard ISO 6721-1:2001 has been approved by CEN as a
European Standard without any modifications.
NOTE Normative references to International Standards are listed in annex ZA (normative).
2

---------------------- Page: 4 ----------------------

SIST EN ISO 6721-1:2003
EN ISO 6721-1:2002 (E)
Annex ZA
(normative)
Normative references to international publications
with their relevant European publications
This European Standard 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 European Standard only when incorporated in it by
amendment or revision. For undated references the latest edition of the publication referred to
applies (including amendments).
NOTE Where an International Publication has been modified by common modifications, indicated by (mod.),
the relevant EN/HD applies.
Publication Year Title EN/HD Year
ISO 291 1997 Plastics - Standard atmospheres for EN ISO 291 1997
conditioning and testing
ISO 294-1 1996 Plastics - Injection moulding of test EN ISO 294-1 1998
specimens of thermoplastic materials -
Part 1: General principles, and moulding
of multipurpose and bar test specimens
ISO 294-2 1996 Plastics - Injection moulding of test EN ISO 294-2 1998
specimens of thermoplastic materials -
Part 2: Small tensile bars
ISO 294-3 1996 Plastics - Injection moulding of test EN ISO 294-3 1998
specimens of thermoplastic materials -
Part 3: Small plates
ISO 294-4 1996 Plastics - Injection moulding of test EN ISO 294-4 1998
specimens of thermoplastic materials -
Part 4: Determination of moulding
shrinkage
ISO 295 1991 Plastics - Compression moulding of test EN ISO 295 1998
specimens of thermosetting materials
ISO 2818 1994 Plastics - Preparation of test specimens EN ISO 2818 1996
by machining
ISO 6721-2 1994 Plastics - Determination of dynamic EN ISO 6721-2 1996
mechanical properties - Part 2: Torsion-
pendulum method
ISO 6721-3 1994 Plastics - Determination of dynamic EN ISO 6721-3 1996
mechanical properties - Part 3: Flexural
vibration - Resonance-curve method
3

---------------------- Page: 5 ----------------------

SIST EN ISO 6721-1:2003

---------------------- Page: 6 ----------------------

SIST EN ISO 6721-1:2003
INTERNATIONAL ISO
STANDARD 6721-1
Second edition
2001-05-15
Plastics — Determination of dynamic
mechanical properties —
Part 1:
General principles
Plastiques — Détermination des propriétés mécaniques dynamiques —
Partie 1: Principes généraux
Reference number
ISO 6721-1:2001(E)
© ISO 2001

---------------------- Page: 7 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not be
edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this file,
parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters
were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event
that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2001
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, elec-
tronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO's mem-
ber body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail [e-mail]
Web www.iso.ch
Printed in Switzerland
©
ii ISO 2001 – All rights reserved

---------------------- Page: 8 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
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 6721 may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 6721-1 was prepared by Technical Committee ISO/TC 61, Plastics, Subcommittee SC 2,
Mechanical properties.
This second edition cancels and replaces the first edition (ISO 6721-1:1994), of which it constitutes a minor revision
(two further references have been added to the bibliography).
ISO 6721 consists of the following parts, under the general title Plastics — Determination of dynamic mechanical
properties:
— Part 1: General principles
— Part 2: Torsion-pendulum method
— Part 3: Flexural vibration — Resonance-curve method
— Part 4: Tensile vibration — Non-resonance method
— Part 5: Flexural vibration — Non-resonance method
— Part 6: Shear vibration — Non-resonance method
— Part 7: Torsional vibration — Non-resonance method
— Part 8: Longitudinal and shear vibration — Wave-propagation method
— Part 9: Tensile vibration — Sonic-pulse propagation method
— Part 10: Complex shear viscosity using a parallel-plate oscillatory rheometer
Additional parts are planned.
Annexes A and B of this part of ISO 6721 are for information only.
©
ISO 2001 – All rights reserved iii

---------------------- Page: 9 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
Introduction
The methods specified in the first nine parts of ISO 6721 can be used for determining storage and loss moduli of
plastics over a range of temperatures or frequencies by varying the temperature of the specimen or the frequency of
oscillation. Plots of the storage or loss moduli, or both, are indicative of viscoelastic characteristics of the specimen.
Regions of rapid changes in viscoelastic properties at particular temperatures or frequencies are normally referred to
as transition regions. Furthermore, from the temperature and frequency dependencies of the loss moduli, the
damping of sound and vibration of polymer or metal-polymer systems can be estimated.
Apparent discrepancies may arise in results obtained under different experimental conditions. Without changing the
observed data, reporting in full (as described in the various parts of ISO 6721) the conditions under which the data
were obtained will enable apparent differences observed in different studies to be reconciled.
The definitions of complex moduli apply exactly only to sinusoidal oscillations with constant amplitude and constant
frequency during each measurement. On the other hand, measurements of small phase angles between stress and
strain involve some difficulties under these conditions. Because these difficulties are not involved in some methods
based on freely decaying vibrations and/or varying frequency near resonance, these methods are used frequently
(see ISO 6721-2 and ISO 6721-3). In these cases, some of the equations that define the viscoelastic properties are
only approximately valid.
©
iv ISO 2001 – All rights reserved

---------------------- Page: 10 ----------------------

SIST EN ISO 6721-1:2003
INTERNATIONAL STANDARD ISO 6721-1:2001(E)
Plastics — Determination of dynamic mechanical properties —
Part 1:
General principles
1 Scope
The various parts of ISO 6721 specify methods for the determination of the dynamic mechanical properties of rigid
plastics within the region of linear viscoelastic behaviour. This part of ISO 6721 is an introductory section which
includes the definitions and all aspects that are common to the individual test methods described in the subsequent
parts.
Different deformation modes may produce results that are not directly comparable. For example, tensile vibration
results in a stress which is uniform across the whole thickness of the specimen, whereas flexural measurements are
influenced preferentially by the properties of the surface regions of the specimen.
Values derived from flexural-test data will be comparable to those derived from tensile-test data only at strain levels
where the stress-strain relationship is linear and for specimens which have a homogeneous structure.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO 6721. 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 6721 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 291:1997, Plastics — Standard atmospheres for conditioning and testing.
ISO 293:1986, Plastics — Compression moulding test specimens of thermoplastic materials.
ISO 294 (all parts), Plastics — Injection moulding of test specimens of thermoplastic materials.
ISO 295:1991, Plastics — Compression moulding of test specimens of thermosetting materials.
Plastics — Methods of producting test plates.
ISO 1268 (all parts),
ISO 2818:1994, Plastics — Preparation of test specimens by machining.
ISO 4593:1993, Plastics — Film and sheeting — Determination of thickness by mechanical scanning.
ISO 6721-2:1994, Plastics — Determination of dynamic mechanical properties — Part 2: Torsion-pendulum method.
ISO 6721-3:1994, Plastics — Determination of dynamic mechanical properties — Part 3: Flexural vibration —
Resonance-curve method.
©
ISO 2001 – All rights reserved 1

---------------------- Page: 11 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
3 Terms and definitions
For the purposes of this part of ISO 6721, the following terms and definitions apply.
NOTE Most of the terms defined here are also defined in ISO 472:1999, Plastics — Vocabulary. The definitions given here are
not strictly identical with, but are equivalent to, those in ISO 472:1999.
3.1
complex modulus
�
M
the ratio of dynamic stress, given by  (t)= exp (i2ft), and dynamic strain, given by
A
" (t)=" exp [i (2ft−)], of a viscoelastic material that is subjected to a sinusoidal vibration, where and"
A A A
are the amplitudes of the stress and strain cycles,fis the frequency, is the phase angle between stress and strain
(see 3.5 and Figure 1) andt is time
It is expressed in Pascals (Pa).
� � � �
Depending on the mode of deformation, the complex modulus may be one of several types:E ,G ,K orL (see
Table 3).
� 0 00
M =M + iM (see 3.2 and 3.3) (1)
where
p
1=2
i =(−1) = −1
For the relationships between the different types of complex modulus, see Table 1.
� � � � � �
NOTE 1 For isotropic viscoelastic materials, only two of the elastic parametersG ,E ,K ,L and are independent ( is
� 0 00
the complex Poisson’s ratio, given by = + ).
NOTE 2 The most critical term containing Poisson’s ratio is the “volume term” 1− 2, which has values between 0 and 0,4 for
 between 0,5 and 0,3. The relationships in Table 1 containing the “volume term” 1− 2 can only be used if this term is known
with sufficient accuracy.
It canbeseenfromTable1thatthe volumetricterm 1− 2 canonlybeestimated with anyconfidencefromaknowledgeofthe
bulk modulusKLor the uniaxial-strain modulus and eitherE orG. This is becauseK andL measurements involve
deformations when the volumetric strain component is relatively large.
K
NOTE 3 Up to now, no measurement of the dynamic mechanical bulk modulus , and only a small number of results relating to
relaxation experiments measuringK (t), have been described in the literature.
NOTE 4 The uniaxial-strain modulusL is based upon a load with a high hydrostatic-stress component. Therefore values ofL
compensate for the lack ofK values, and the “volume term” 1− 2 can be estimated with sufficient accuracy based upon the
modulus pairs (GL, ) and (E,L). The pair (GL, ) is preferred, becauseG is based upon loads without a hydrostatic component.
NOTE 5 The relationships given in Table 1 are valid for the complex moduli as well as their magnitudes (see 3.4).
NOTE 6 Most of the relationships for calculating the moduli given in the other parts of this International Standard are, to some
extent, approximate. They do not take into account e.g. “end effects” caused by clamping the specimens, and they include other
simplifications. Using the relationships given in Table 1 therefore often requires additional corrections to be made. These are given
in the literature (see e.g. references [1] and [2] in the Bibliography).
� �
NOTE 7 For linear-viscoelastic behaviour, the complex complianceC is the reciprocal of the complex modulusM , i.e.
−1
� �
M =(C ) (2)
©
2 ISO 2001 – All rights reserved

---------------------- Page: 12 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
Thus
0 00
C − iC
0 00
M + iM = (3)
2 2
0 00
(C ) +(C )
a) b)
The phase shift =2f between the stress  and strain " in a viscoelastic The relationship between the storage modu-
0 00
material subjected to sinusoidal oscillation ( and" are the respective ampli- lus M , the loss modulus M , the phase
A A
tudes,f is the frequency). angle and the magnitudejMj of the com-
�
plex modulusM .
Figure 1 — Phase angle and complex modulus
Table 1 — Relationships between moduli for uniformly isotropic materials
a
Gand Eand K and GEand GKand EKand
GLand
Poisson’s ratio,
G=K 1
E E
3−
b
L=G− 1
G 1 +G=3K 3K
1− 2 =
3K (1− 2)
E E
Shear modulus,G =
2 (1 +) 3−E=3K
2 (1 +)
3G (1− 4G=3L)
3G
Tensile modulus,E = 2G (1 +) 3K (1− 2)
1 +G=3K 1−G=L
2G (1 +)
E G
c
4G
K = L−
Bulk modulus,
3 (1− 2) 3
3 (1− 2) 3 (3G=E− 1)
Unaxial-strain or
E (1−) G (4G=E− 1) K (1 +E=3K)
2G (1−) 3K (1−)
4G
longitudinal-wave
K +
1− 2 1 + 3
(1 +)(1− 2) 3G=E− 1 1−E=9K
modulus,L =
a
See note 4 to definition 3.1.
b
See note 2 to definition 3.1.
c
See note 3 to definition 3.1.
3.2
storage modulus
0
M
�
the real part of the complex modulusM [see Figure 1 b)]
The storage modulus is expressed in pascals (Pa).
©
ISO 2001 – All rights reserved 3

---------------------- Page: 13 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
It is proportional to the maximum energy stored during a loading cycle and represents the stiffness of a viscoelastic
material.
0
The different types of storage modulus, corresponding to different modes of deformation, are: E tensile storage
t
0 0 0 0
modulus,E flexural storage modulus,G shear storage modulus,G torsional storage modulus,K bulk storage
f s to
0 0
modulus,L uniaxial-strain andL longitudinal-wave storage modulus.
c w
3.3
loss modulus
00
M
the imaginary part of the complex modulus [see Figure 1 b)]
The loss modulus is expressed in pascals (Pa).
It is proportional to the energy dissipated (lost) during one loading cycle. As with the storage modulus (see 3.2), the
00
mode of deformation is designated as in Table 3, e.g.E is the tensile loss modulus.
t
3.4
magnitudejMj of the complex modulus
the root mean square value of the storage and the loss moduli as given by the equation
2 2
2
2 0 00
jMj =(M ) +(M ) =( =" ) (4)
A A
where and" are the amplitudes of the stress and the strain cycles, respectively.
A A
The complex modulus is expressed in pascals (Pa).
0 00
The relationship between the storage modulusM , the loss modulusM , the phase angle, and the magnitude
jMj of the complex modulus is shown in Figure 1 b). As with the storage modulus, the mode of deformation is
designated as in Table 3, e.g.jEj is the magnitude of the tensile complex modulus.
t
3.5
phase angle

the phase difference between the dynamic stress and the dynamic strain in a viscoelastic material subjected to a
sinusoidal oscillation (see Figure 1)
The phase angle is expressed in radians (rad).
As with the storage modulus (see 3.2), the mode of deformation is designated as in Table 3, e.g. is the tensile
t
phase angle.
3.6
loss factor (tan)
the ratio between the loss modulus and the storage modulus, given by the equation
00 0
tan =M =M (5)
where is the phase angle (see 3.5) between the stress and the strain
The loss factor is expressed as a dimensionless number.
The loss factor tan is commonly used as a measure of the damping in a viscoelastic system. As with the storage
modulus (see 3.2), the mode of deformation is designated as in Table 3, e.g. tan is the tensile loss factor.
t
©
4 ISO 2001 – All rights reserved

---------------------- Page: 14 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
3.7
stress-strain hysteresis loop
the stress expressed as a function of the strain in a viscoelastic material subject to sinusoidal vibrations
NOTE Provided the viscoelasticity is linear in nature, this curve is an ellipse (see Figure 2).
Figure 2 — Dynamic stress-strain hysteresis loop for a linear-viscoelastic material subject to
sinusoidal tensile vibrations
3.8
damped vibration
the time-dependent deformation or deformation rate X (t) of a viscoelastic system undergoing freely decaying
vibrations (see Figure 3), given by the equation
X (t)=X exp (−t)� sin 2f t (6)
0 d
where
X is the magnitude, at zero time, of the envelope of the cycle amplitudes;
0
f is the frequency of the damped system;
d
 is the decay constant (see 3.9).
©
ISO 2001 – All rights reserved 5

---------------------- Page: 15 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
[XXis the time-dependent deformation or deformation rate, is the amplitude of theqth cycle andX and define the enve-
q 0
lope of the exponential decay of the cycle amplitudes — see equation (6).]
Figure 3 — Damped-vibration curve for a viscoelastic system undergoing freely decaying vibrations
3.9
decay constant

the coefficient that determines the time-dependent decay of damped free vibrations, i.e. the time dependence of the
amplitudeX of the deformation or deformation rate [see Figure 3 and equation (6)]
q
−1
The decay constant is expressed in reciprocal seconds (s ).
3.10
logarithmic decrement

the natural logarithm of the ratio of two successive amplitudes, in the same direction, of damped free oscillations of a
viscoelastic system (see Figure 3), given by the equation
 = In (X =X ) (7)
q q+1
whereX andX are two successive amplitudes of deformation or deformation rate in the same direction
q q+1
The logarithmic decrement is expressed as a dimensionless number.
It is used as a measure of the damping in a viscoelastic system.
Expressed in terms of the decay constantfand the frequency , the logarithmic decrement is given by the equation
d
 ==f (8)
d
The loss factor tan is related to the logarithmic decrement by the approximate equation
tan�= (9)
©
6 ISO 2001 – All rights reserved

---------------------- Page: 16 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
NOTE Damped freely decaying vibrations are especially suitable for analysing the type of damping in the material under test (i.e.
whether the viscoelastic behaviour is linear or non-linear) and the friction between moving and fixed components of the apparatus
(see annex B).
3.11
resonance curve
the curve representing the frequency dependence of the deformation amplitudeD or deformation-rate amplitude
A
R of an inert viscoelastic system subjected to forced vibrations at constant load amplitudeL and at frequencies
A A
close to and including resonance (see Figure 4 and annex A)
Figure 4 — Resonance curve for a viscoelastic system subjected to forced vibrations
(Deformation-rate amplitudeR versus frequencyf at constant load amplitude; logarithmic frequency scale)
A
3.12
resonance frequencies
f
ri
the frequencies of the peak amplitudes in a resonance curve
The subscripti refers to the order of the resonance vibration.
Resonance frequencies are expressed in hertz (Hz).
NOTE Resonance frequencies for viscoelastic materials derived from measurements of displacement amplitude will be slightly
different from those obtained from displacement-rate measurements, the difference being larger the greater the loss in the
material (see annex A). Storage and loss moduli are accurately related by simple expressions to resonance frequencies obtained
from displacement-rate curves. The use of resonance frequencies based on displacement measurements leads to a small error
which is only significant when the specimen exhibits high loss. Under these conditions, resonance tests are not suitable.
3.13
width of a resonance peak

f
i
the difference between the frequencies f and f of the ith-order resonance peak, where the height R of the
1 2 Ah
resonance curve atf andf is related to the peak heightR of theith mode by
1 2 AMi
−1=2
R = 2 R = 0,707R (10)
Ah AM AM
(see Figure 4)
©
ISO 2001 – All rights reserved 7

---------------------- Page: 17 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
The width
f is expressed in hertz (Hz).
i
It is related to the loss factor tan by the equation
tan =
f =f (11)
i ri
If the loss factor does not vary markedly over the frequency range defined by
f , equation (11) holds exactly when
i
the resonance curve is based on the deformation-rate amplitude (see also annex A).
4Principle
A specimen of known geometry is subjected to mechanical oscillation, described by two characteristics: the mode of
vibration and the mode of deformation.
Four oscillatory modes, I to IV, are possible, depending on whether the mode of vibration is non-resonant, natural
(resonant) or near-resonant. These modes are described in Table 2.
The particular type of modulus depends upon the mode of deformation (see Table 3).
Table 4 indicates ways in which the various types of modulus are commonly measured. Table 5 gives a summary of
the methods covered by the various parts of this International Standard.
Table 2 — Oscillatory modes
(Terms written in bold type give the designation of the mode; terms in normal type provide additional information.)
a
Mode of oscillation I II III IV
Forced vibration
Damped,freelydecaying
amplitude
Constant frequency Resonance frequency Resonance curve
Frequency Non-resonance Resonance (natural) Sweep, near resonance Approximately resonant
b
Load amplitude Constant Constant
Oneofthe twoconstant,
Excitation pulse
Deformation
the other measured
Measured Measured
amplitude
Inertial mass None Specimen and/or additional masses, depending on frequency range
a
The type of torsion pendulum used shall be indicated by adding the relevant letter, A or B (see ISO 6721-2:1994, Figures 1
and 2).
b
The load must be in phase with the deformation rate.
Table 3 — Type of modulus (mode of deformation)
Designation Type of modulus
E Tensile
t
E Flexural
f
G Shear
s
G Torsion
to
K Bulk compression
L Uniaxial compression (of thin sheets)
c
L Longitudinal bulk wave
w
©
8 ISO 2001 – All rights reserved

---------------------- Page: 18 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
Table 4 — Commonly used test arrangements
Type of modulus
Relevant part of Typical frequency,
Test arrangement and mode of Inertial mass
ISO 6721 Hz
oscillation
G IV Part 2 Inertial member 0,1 to 10
to
III Part 3 Specimen 10 to 1 000
E
t
E IPart5
t
G IPart7
to
−3
None 10 to 100
E IPart4
t
G IPart6
s
Key to figures: 1 — Clamps, pivots or supports; 2 — Specimen; 3 — Inertial member.
©
ISO 2001 – All rights reserved 9

---------------------- Page: 19 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
Table 4 — Commonly used test arrangements (continued)
Type of modulus
Relevant part of Typical frequency,
Test arrangement and mode of Inertial mass
ISO 6721 Hz
oscillation
−3
L I— 10 to 100
c
None
−3
E I— 10to10
f
Specimen and
E II — 3to60
f
arms
Key to figures: 1 — Clamps, pivots or supports; 2 — Specimen; 3 — Inertial member.
Table 5 — Methods covered by the various parts of this International Standard
Type of modulus (see Table 3)
Mode of oscillation
(see Table 2)
E E G G KL L
t f s to c w
I Part 4 Part 5 Part 6 Part 7 Part 8
II
III Part 3
IV Part 2
5 Test apparatus
5.1 Type
The apparatus used is specified in detail in the relevant part of this International Standard (see the Introduction and
clause 4).
5.2 Mechanical, electronic and recording systems
See the relevant part of this International Standard.
5.3 Temperature-controlled enclosure
The test specimen and the clamps or supports shall be enclosed in a temperature-controlled enclosure containing air
or a suitable inert gas.
The enclosure shall be designed so that its temperature can be varied over a range sufficient for the material under
� �
test (e.g.− 100 C to + 300 C). It is recommended that the chamber be equipped with temperature-programming
facilities.
©
10 ISO 2001 – All rights reserved

---------------------- Page: 20 ----------------------

SIST EN ISO 6721-1:2003
ISO 6721-1:2001(E)
�
The temp
...