Plastics - Determination of dynamic mechanical properties - Part 1: General principles (ISO 6721-1:2019)

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 document specifies
the definitions and describes the general principles including all aspects that are common to the
individual test methods described in the subsequent parts.
Different deformation modes can 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.

Kunststoffe - Bestimmung dynamisch-mechanischer Eigenschaften - Teil 1: Allgemeine Grundlagen (ISO 6721-1:2019)

Die verschiedenen Teile von ISO 6721 legen Verfahren zur Bestimmung der dynamisch-mechanischen Eigenschaften von steifen Kunststoffen im Bereich des linear-viskoelastischen Verhaltens fest. Dieses Dokument spezifiziert die Definitionen und beschreibt die allgemeinen Prinzipien, einschließlich aller Gesichtspunkte, die die einzelnen, in den folgenden Teilen beschriebenen Prüfverfahren gemeinsam haben.
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 des Probe¬körpers 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 6721-1:2019)

Les différentes parties de l'ISO 6721 spécifient des méthodes pour la détermination des propriétés mécaniques dynamiques de plastiques rigides dans le domaine de comportement viscoélastique linéaire. Le présent document spécifie les définitions et décrit les principes généraux incluant tous les aspects communs à toutes les méthodes individuelles décrites dans les parties suivantes.
Les différents modes de déformation peuvent produire des résultats qui ne sont pas directement comparables. Par exemple, la vibration en traction conduit à une contrainte uniforme dans toute l'épaisseur de l'éprouvette, alors que les mesurages en flexion sont influencés préférentiellement par les propriétés des couches superficielles de l'éprouvette.
Les valeurs découlant des données de l'essai de flexion seront comparables à celles découlant des données de l'essai de traction seulement aux niveaux de déformation pour lesquels la relation contrainte-déformation est linéaire, et pour des éprouvettes de structure homogène.

Polimerni materiali - Ugotavljanje dinamičnih mehanskih lastnosti - 1. del: Splošna načela (ISO 6721-1:2019)

Različni deli standarda ISO 6721 določajo metode za določanje dinamičnih mehanskih lastnosti togih polimerov v območju linearnega viskoelastičnega vedenja. Ta dokument določa
opredelitve in opisuje splošna načela, vključno z vsemi vidiki, ki so skupni posameznim preskusnim metodam, opisanim v naslednjih delih.
Različni načini deformacije lahko dajo rezultate, ki niso neposredno primerljivi. Natezne vibracije na primer povzročijo napetost, ki je enakomerna po celotni debelini vzorca, medtem ko na upogibne meritve prednostno vplivajo lastnosti površinskih predelov preskušanca.
Vrednosti, pridobljene z upogibnim preskusom, bodo z vrednostmi, pridobljenimi z nateznim preskusom, primerljive le pri stopnji natezanja, pri čemer je razmerje med napetostjo in deformacijo linearno, in za preskušance, ki imajo homogeno strukturo.

General Information

Status
Published
Public Enquiry End Date
30-Apr-2018
Publication Date
17-Jun-2019
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
07-Jun-2019
Due Date
12-Aug-2019
Completion Date
18-Jun-2019

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SLOVENSKI STANDARD
SIST EN ISO 6721-1:2019
01-september-2019
Nadomešča:
SIST EN ISO 6721-1:2012

Polimerni materiali - Ugotavljanje dinamičnih mehanskih lastnosti - 1. del: Splošna

načela (ISO 6721-1:2019)

Plastics - Determination of dynamic mechanical properties - Part 1: General principles

(ISO 6721-1:2019)

Kunststoffe - Bestimmung dynamisch-mechanischer Eigenschaften - Teil 1: Allgemeine

Grundlagen (ISO 6721-1:2019)

Plastiques - Détermination des propriétés mécaniques dynamiques - Partie 1: Principes

généraux (ISO 6721-1:2019)
Ta slovenski standard je istoveten z: EN ISO 6721-1:2019
ICS:
83.080.01 Polimerni materiali na Plastics in general
splošno
SIST EN ISO 6721-1:2019 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 6721-1:2019
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SIST EN ISO 6721-1:2019
EN ISO 6721-1
EUROPEAN STANDARD
NORME EUROPÉENNE
May 2019
EUROPÄISCHE NORM
ICS 83.080.01 Supersedes EN ISO 6721-1:2011
English Version
Plastics - Determination of dynamic mechanical properties
- Part 1: General principles (ISO 6721-1:2019)

Plastiques - Détermination des propriétés mécaniques Kunststoffe - Bestimmung dynamisch-mechanischer

dynamiques - Partie 1: Principes généraux (ISO 6721- Eigenschaften - Teil 1: Allgemeine Grundlagen (ISO

1:2019) 6721-1:2019)
This European Standard was approved by CEN on 8 June 2018.

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 CEN-CENELEC 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 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, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,

Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,

Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 6721-1:2019 E

worldwide for CEN national Members.
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SIST EN ISO 6721-1:2019
EN ISO 6721-1:2019 (E)
Contents Page

European foreword ....................................................................................................................................................... 3

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SIST EN ISO 6721-1:2019
EN ISO 6721-1:2019 (E)
European foreword

This document (EN ISO 6721-1:2019) has been prepared by Technical Committee ISO/TC 61 "Plastics"

in collaboration with Technical Committee CEN/TC 249 “Plastics” the secretariat of which is held by

NBN.

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 November 2019, and conflicting national standards

shall be withdrawn at the latest by November 2019.

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

This document supersedes EN ISO 6721-1:2011.

According to the CEN-CENELEC Internal Regulations, the national standards organizations of the

following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,

Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,

France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,

Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,

Turkey and the United Kingdom.
Endorsement notice

The text of ISO 6721-1:2019 has been approved by CEN as EN ISO 6721-1:2019 without any

modification.
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SIST EN ISO 6721-1:2019
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SIST EN ISO 6721-1:2019
INTERNATIONAL ISO
STANDARD 6721-1
Fourth edition
2019-04
Plastics — Determination of dynamic
mechanical properties —
Part 1:
General principles
Plastiques — Détermination des propriétés mécaniques
dynamiques —
Partie 1: Principes généraux
Reference number
ISO 6721-1:2019(E)
ISO 2019
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2019

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 2

4 Principle ........................................................................................................................................................................................................................ 9

5 Test apparatus ......................................................................................................................................................................................................12

5.1 Type ...............................................................................................................................................................................................................12

5.2 Mechanical, electronic and recording systems .........................................................................................................12

5.3 Temperature-controlled enclosure ....................................................................................................................................12

5.4 Gas supply ................................................................................................................................................................................................12

5.5 Temperature-measurement device ....................................................................................................................................12

5.6 Devices for measuring test specimen dimensions ................................................................................................12

6 Test specimens.....................................................................................................................................................................................................12

6.1 General ........................................................................................................................................................................................................12

6.2 Shape and dimensions ...................................................................................................................................................................13

6.3 Preparation .............................................................................................................................................................................................13

7 Number of test specimens .......................................................................................................................................................................13

8 Conditioning ...........................................................................................................................................................................................................13

9 Procedure..................................................................................................................................................................................................................13

9.1 Test atmosphere .................................................................................................................................................................................13

9.2 Measurement of specimen cross-section ......................................................................................................................13

9.3 Mounting the test specimens ...................................................................................................................................................13

9.4 Varying the temperature .............................................................................................................................................................13

9.5 Varying the frequency ....................................................................................................................................................................14

9.6 Varying the dynamic-strain amplitude............................................................................................................................14

10 Expression of results .....................................................................................................................................................................................14

11 Precision ....................................................................................................................................................................................................................15

12 Test report ................................................................................................................................................................................................................15

Annex A (informative) Resonance curves .....................................................................................................................................................16

Annex B (informative) Deviations from linear behaviour ..........................................................................................................22

Bibliography .............................................................................................................................................................................................................................23

© ISO 2019 – All rights reserved iii
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(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.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso

.org/iso/foreword .html.

This document was prepared by Technical Committee ISO/TC 61, Plastics, Subcommittee SC 5, Physical-

chemical properties.

This fourth edition cancels and replaces the third edition (ISO 6721-1:2011), which has been technically

revised. The main changes compared to the previous edition are as follows:
— the document has been revised editorially;

— normative references have been changed to undated and added as references into Tables 4 and 5.

A list of all parts in the ISO 6721 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/members .html.
iv © ISO 2019 – All rights reserved
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(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.

© ISO 2019 – All rights reserved v
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SIST EN ISO 6721-1:2019
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SIST EN ISO 6721-1:2019
INTERNATIONAL STANDARD ISO 6721-1:2019(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 document specifies

the definitions and describes the general principles including all aspects that are common to the

individual test methods described in the subsequent parts.

Different deformation modes can 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 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.

ISO 291, Plastics — Standard atmospheres for conditioning and testing

ISO 4593, Plastics — Film and sheeting — Determination of thickness by mechanical scanning

ISO 6721-2, Plastics — Determination of dynamic mechanical properties — Part 2: Torsion-pendulum method

ISO 6721-3, Plastics — Determination of dynamic mechanical properties — Part 3: Flexural vibration —

Resonance-curve method

ISO 6721-4, Plastics — Determination of dynamic mechanical properties — Part 4: Tensile vibration —

Non-resonance method

ISO 6721-5, Plastics — Determination of dynamic mechanical properties — Part 5: Flexural vibration —

Non-resonance method

ISO 6721-6, Plastics — Determination of dynamic mechanical properties — Part 6: Shear vibration — Non-

resonance method

ISO 6721-7, Plastics — Determination of dynamic mechanical properties — Part 7: Torsional vibration —

Non-resonance method

ISO 6721-8, Plastics — Determination of dynamic mechanical properties — Part 8: Longitudinal and shear

vibration — Wave-propagation method

ISO 6721-9, Plastics — Determination of dynamic mechanical properties — Part 9: Tensile vibration —

Sonic-pulse propagation method
© ISO 2019 – All rights reserved 1
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(E)

ISO 6721-10, Plastics — Determination of dynamic mechanical properties — Part 10: Complex shear

viscosity using a parallel-plate oscillatory rheometer

ISO 6721-12, Plastics — Determination of dynamic mechanical properties — Part 12: Compressive

vibration — Non-resonance method
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/

NOTE Some of the terms defined here are also defined in ISO 472. The definitions given here are not strictly

identical with, but more detailed than those in ISO 472.
3.1
complex modulus

ratio of dynamic stress, given by σ(t) = σ exp(i2πft) and dynamic strain, given by ε(t) = ε exp[i(2πft – δ)],

A A

of a viscoelastic material that is subjected to a sinusoidal vibration, where σ and ε are the amplitudes of

A A

the stress and strain cycles, f is the frequency, δ is the phase angle between stress and strain and t is time

Note 1 to entry: It is expressed in Pascals (Pa).
Note 2 to entry: The phase angle (3.5), δ, is shown in Figure 1.

Note 3 to entry: Depending on the mode of deformation, the complex modulus might be one of several types: E ,

∗ ∗ ∗
G , K or L (see Table 3).
M* = M’ + i M”
where i=−()11=− and M’ and M” are as defined in 3.2 and 3.3 respectively.

For the relationships between the different types of complex modulus, see Table 1.

∗ ∗ ∗ ∗ ∗

Note 4 to entry: For isotropic viscoelastic materials, only two of the elastic parameters G , E , K , L and µ are

∗ ∗
independent (µ is the complex Poisson's ratio, given by µ = µ′ + iµ″).

Note 5 to entry: The most critical term containing Poisson's ratio µ is the “volume term” 1 − 2µ, which has values

between 0 and 0,4 for µ between 0,5 and 0,3. The relationships in Table 1 containing the “volume term” 1 − 2µ can

only be used if this term is known with sufficient accuracy.

It can be seen from Table 1 that the “volume term” 1 − 2µ can only be estimated with any confidence from a

knowledge of the bulk modulus K or the uniaxial-strain modulus L and either E or G. This is because K and L

measurements involve deformations when the volumetric strain component is relatively large.

Note 6 to entry: Up to now, no measurement of the dynamic mechanical bulk modulus K, and only a small number

of results relating to relaxation experiments measuring K(t), have been described in the literature.

Note 7 to entry: The uniaxial-strain modulus L is based upon a load with a high hydrostatic-stress component.

Therefore, values of L compensate for the lack of K values, and the “volume term” 1 − 2µ can be estimated with

sufficient accuracy based upon the modulus pairs (G, L) and (E, L). The pair (G, L) is preferred, because G is based

upon loads without a hydrostatic component.

Note 8 to entry: The relationships given in Table 1 are valid for the complex moduli as well as their magnitudes (3.4).

2 © ISO 2019 – All rights reserved
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(E)

Note 9 to entry: 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, for example “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 [7] and [8]

in the Bibliography).

Note 10 to entry: For linear-viscoelastic behaviour, the complex compliance C is the reciprocal of the complex

modulus M , i.e.
−1
M* = (C*)
Thus
CC''−i '
MM''+=i '
CC''+ '
() ()

a) Phase shift δ/2πf between the stress σ and strain ε b) Relationship between the storage

in a viscoelastic material subjected to sinusoidal oscil- modulus M′, the loss modulus M″, the

lation (σ and ε are the respective amplitudes, f is the phase angle δ and the magnitude [M]

A A
frequency) of the complex modulus M*
Figure 1 — Phase angle and complex modulus
© ISO 2019 – All rights reserved 3
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(E)
Table 1 — Relationships between moduli for uniformly isotropic materials
G and µ E and µ K and µ G and E G and K E and K G and L
Poisson's ratio,
E GK/ E 1
µ 1 − 2µ = 3−
G 13+GK/ 3K LG/ −1
Shear modulus,
E 31K −2μ E
G =
33−EK/
21()+μ
21()+μ
Tensile 2G(1 + μ ) 3K(1 − 2μ)
31GG()−43/ L
modulus, E =
13+GK/
1−GL/
Bulk modulus,
E 4G
21G +μ
K =
33GE/ −1
31−2μ () 3
31−2μ
Unaxial-strain
E 1−μ GG41/E − 4G KE13+ / K
21G −μ () 31K −μ () ()
() ()
K +
or longitudi-
11+μμ−2 31GE/ − 19−EK/
()()
12− μ 1+μ
nal-wave
modulus, L =
See 3.1, Note 7 to entry
See 3.1, Note 5 to entry.
See 3.1, Note 6 to entry.
3.2
storage modulus
real part of the complex modulus M
Note 1 to entry: The storage modulus is expressed in pascals (Pa).
Note 2 to entry: The storage modulus M' is shown in Figure 1 b).

Note 3 to entry: It is proportional to the maximum energy stored during a loading cycle and represents the

stiffness of a viscoelastic material.

Note 4 to entry: The different types of storage modulus, corresponding to different modes of deformation, are:

' ' ' '

E tensile storage modulus, E flexural storage modulus, G shear storage modulus, G torsional storage

t f s to
' '

modulus, K′ bulk storage modulus, L uniaxial-strain storage modulus and L longitudinal-wave storage

c w
modulus.
3.3
loss modulus
imaginary part of the complex modulus
Note 1 to entry: The loss modulus is expressed in pascals (Pa).
Note 2 to entry: The loss modulus M” is shown in Figure 1 b).

Note 3 to entry: It is proportional to the energy dissipated (lost) during one loading cycle. As with the storage

modulus (3.2), the mode of deformation is designated as in Table 3, e.g. E is the tensile loss modulus.

3.4
magnitude of the complex modulus
[M]

root mean square value of the storage and the loss moduli as given by the formula

2 2 2 2
[M] = (M′) + (M′′) = (σ / ε )
A A
4 © ISO 2019 – All rights reserved
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(E)

where σ and ε are the amplitudes of the stress and the strain cycles, respectively

A A
Note 1 to entry: The complex modulus is expressed in pascals (Pa).

Note 2 to entry: The relationship between the storage modulus M′, the loss modulus M″, the phase angle δ, and

the magnitude [M] 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. [E ] is the magnitude of the tensile complex modulus.

3.5
phase angle

phase difference between the dynamic stress and the dynamic strain in a viscoelastic material

subjected to a sinusoidal oscillation
Note 1 to entry: The phase angle is expressed in radians (rad).
Note 2 to entry: The phase angle δ is shown in Figure 1.

Note 3 to entry: As with the storage modulus (3.2), the mode of deformation is designated as in Table 3, e.g. δ is

the tensile phase angle.
3.6
loss factor
tan δ
ratio between the loss modulus and the storage modulus given by the formula
tan δ = M′′ / M′
where δ is the phase angle between the stress and the strain
Note 1 to entry: The loss factor is expressed as a dimensionless number.

Note 2 to entry: The ratio between loss modulus M” and storage modulus M' is shown in Figure 1 b).

Note 3 to entry: The loss factor tan δ is commonly used as a measure of the damping in a viscoelastic system. As with

the storage modulus (3.2), the mode of deformation is designated as in Table 3, e.g. tan δ is the tensile loss factor.

3.7
stress-strain hysteresis loop

stress expressed as a function of the strain in a viscoelastic material subject to sinusoidal vibrations

Note 1 to entry: Provided the viscoelasticity is linear in nature, this curve is an ellipse (see Figure 2).

© ISO 2019 – All rights reserved 5
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(E)

Figure 2 — Dynamic stress-strain hysteresis loop for a linear-viscoelastic material subject to

sinusoidal tensile vibrations
3.8
damped vibration

time-dependent deformation or deformation rate X(t) of a viscoelastic system undergoing freely

decaying vibrations, given by the formula
X(t) = X exp(−βt) × sin2πf t
0 d
where
X is the magnitude, at zero time, of the envelope of the cycle amplitudes;
f is the frequency of the damped system;
β is the decay constant (3.9)

Note 1 to entry: A typical curve of freely decaying damped vibrations is shown in Figure 3.

6 © ISO 2019 – All rights reserved
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SIST EN ISO 6721-1:2019
ISO 6721-1:2019(E)
Key
X is the time-dependent deformation or deformation rate
X is the amplitude of the q cycle

X and β define the envelope of the exponential decay of the cycle amplitudes — see formula in 3.8

Figure 3 — Damped-vibration curve for a viscoelastic system undergoing freely decaying

vibrations
3.9
decay constant

coefficient that determines the time-dependent attenuation of damped free vibrations, i.e. the time

dependence of the amplitude X of the deformation or deformation
Note 1 to entry: The decay constant is expressed in reciprocal seconds (s ).

Note 2 to entry: The decay constant β of freely decaying damped vibrations is shown in Figure 3.

3.10
logarithmic decrement

natural logarithm of the ratio of two successive amplitudes, in the same direction, of damped free

oscillations of a viscoelastic system given by the formula
Λ = ln(X / X )
q q + 1

where X and X are two successive amplitudes of deformation or deformation rate in the same

q q + 1
direct
...

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