SIST EN ISO 6721-1:2012
(Main)Plastics - Determination of dynamic mechanical properties - Part 1: General principles (ISO 6721-1:2011)
Plastics - Determination of dynamic mechanical properties - Part 1: General principles (ISO 6721-1:2011)
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.
Kunststoffe - Bestimmung dynamisch-mechanischer Eigenschaften - Teil 1: Allgemeine Grundlagen (ISO 6721-1:2011)
Die verschiedenen Teile von ISO 6721 legen 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 des Probekörpers
beeinflusst sind.
Eigenschaftswerte aus Biegeprüfungen sind nur mit solchen aus Zugprüfungen vergleichbar in Spannungsbereichen,
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 6721-1:2011)
Les diff�rentes parties de l'ISO 6721 sp�cifient des m�thodes pour la d�termination des propri�t�s m�caniques dynamiques de plastiques rigides dans le domaine de comportement visco�lastique lin�aire. L'ISO 6721-1:2011 �tablit des principes g�n�raux incluant les d�finitions et tous les aspects communs � toutes les m�thodes individuelles, d�crites dans les parties subs�quentes.
Les diff�rents modes de d�formation peuvent produire des r�sultats qui ne sont pas directement comparables. Par exemple, la vibration en traction conduit � une contrainte uniforme dans toute l'�paisseur de l'�prouvette, alors que les mesurages en flexion sont influenc�s pr�f�rentiellement par les propri�t�s des couches superficielles de l'�prouvette.
Les valeurs d�coulant des donn�es de l'essai de flexion seront comparables � celles d�coulant des donn�es de l'essai de traction seulement aux niveaux de d�formation pour lesquels la relation contrainte-d�formation est lin�aire, et pour des �prouvettes de structure homog�ne.
Polimerni materiali - Ugotavljanje dinamičnih mehanskih lastnosti - 1. del: Splošna načela (ISO 6721-1:2011)
Različni deli ISO 6721 določajo metode za ugotavljanje dinamičnih mehanskih lastnosti togih polimernih materialov v okviru linearnega viskoelastičnega obnašanja. Ta del ISO 6721 je uvodni del, ki vključuje definicije in vse vidike, ki so skupni posameznim preskusnim metodam, opisanim v naslednjih delih. Različni načini deformacije lahko privedejo do rezultatov, ki niso neposredno primerljivi. Natezna vibracija ima na primer za posledico napetost, ki je enakomerna po vsej debelini vzorca, na upogibne meritve pa vplivajo lastnosti površinskih predelov vzorca. Vrednosti, dobljene iz podatkov upogibnega preskusa, so primerljive z vrednostmi, dobljenimi iz podatkov nateznega preskusa, le pri ravneh deformacije, pri katerih je razmerje med napetostjo in deformacijo linearno, in pri vzorcih s homogeno strukturo.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 6721-1:2012
01-januar-2012
1DGRPHãþD
SIST EN ISO 6721-1:2003
SIST EN ISO 6721-1:2003/kprA1:2010
3ROLPHUQLPDWHULDOL8JRWDYOMDQMHGLQDPLþQLKPHKDQVNLKODVWQRVWLGHO 6SORãQD
QDþHOD ,62
Plastics - Determination of dynamic mechanical properties - Part 1: General principles
(ISO 6721-1:2011)
Kunststoffe - Bestimmung dynamisch-mechanischer Eigenschaften - Teil 1: Allgemeine
Grundlagen (ISO 6721-1:2011)
Plastiques - Détermination des propriétés mécaniques dynamiques - Partie 1: Principes
généraux (ISO 6721-1:2011)
Ta slovenski standard je istoveten z: EN ISO 6721-1:2011
ICS:
83.080.01 Polimerni materiali na Plastics in general
splošno
SIST EN ISO 6721-1:2012 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
SIST EN ISO 6721-1:2012
---------------------- Page: 2 ----------------------
SIST EN ISO 6721-1:2012
EUROPEAN STANDARD
EN ISO 6721-1
NORME EUROPÉENNE
EUROPÄISCHE NORM
May 2011
ICS 83.080.01 Supersedes EN ISO 6721-1:2002
English Version
Plastics - Determination of dynamic mechanical properties - Part
1: General principles (ISO 6721-1:2011)
Plastiques - Détermination des propriétés mécaniques Kunststoffe - Bestimmung dynamisch-mechanischer
dynamiques - Partie 1: Principes généraux (ISO 6721- Eigenschaften - Teil 1: Allgemeine Grundlagen (ISO 6721-
1:2011) 1:2011)
This European Standard was approved by CEN on 14 May 2011.
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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2011 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 6721-1:2011: E
worldwide for CEN national Members.
---------------------- Page: 3 ----------------------
SIST EN ISO 6721-1:2012
EN ISO 6721-1:2011 (E)
Contents Page
Foreword .3
2
---------------------- Page: 4 ----------------------
SIST EN ISO 6721-1:2012
EN ISO 6721-1:2011 (E)
Foreword
This document (EN ISO 6721-1:2011) 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 2011, and conflicting national standards shall be withdrawn
at the latest by November 2011.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 6721-1:2002.
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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of ISO 6721-1:2011 has been approved by CEN as a EN ISO 6721-1:2011 without any modification.
3
---------------------- Page: 5 ----------------------
SIST EN ISO 6721-1:2012
---------------------- Page: 6 ----------------------
SIST EN ISO 6721-1:2012
INTERNATIONAL ISO
STANDARD 6721-1
Third edition
2011-05-15
Plastics — Determination of dynamic
mechanical properties —
Part 1:
General principles
Plastiques — Détermination des propriétés mécaniques dynamiques —
Partie 1: Principes généraux
Reference number
ISO 6721-1:2011(E)
©
ISO 2011
---------------------- Page: 7 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2011
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member 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 copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2011 – All rights reserved
---------------------- Page: 8 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
Contents Page
Foreword .iv
Introduction.vi
1 Scope.1
2 Normative references.1
3 Terms and definitions .2
4 Principle .8
5 Test apparatus .10
5.1 Type .10
5.2 Mechanical, electronic and recording systems .10
5.3 Temperature-controlled enclosure .10
5.4 Gas supply .11
5.5 Temperature-measurement device.11
5.6 Devices for measuring test specimen dimensions.11
6 Test specimens.11
6.1 General .11
6.2 Shape and dimensions .11
6.3 Preparation.11
7 Number of test specimens .11
8 Conditioning .12
9 Procedure.12
9.1 Test atmosphere.12
9.2 Measurement of specimen cross-section.12
9.3 Mounting the test specimens.12
9.4 Varying the temperature .12
9.5 Varying the frequency.13
9.6 Varying the dynamic-strain amplitude .13
10 Expression of results.13
11 Precision .13
12 Test report.14
Annex A (informative) Resonance curves.15
Annex B (informative) Deviations from linear behaviour.19
Bibliography.20
© ISO 2011 – All rights reserved iii
---------------------- Page: 9 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(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 2.
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.
ISO 6721-1 was prepared by Technical Committee ISO/TC 61, Plastics, Subcommittee SC 2, Mechanical
properties.
This third edition cancels and replaces the second edition (ISO 6721-1:2001), of which it constitutes a minor
revision involving the following changes:
⎯ a new subclause (9.6), covering the case when the dynamic-strain amplitude is varied, has been added to
the procedure clause;
⎯ the expression of results clause (Clause 10) and the test report clause (Clause 12) have been modified
accordingly [Clause 10 by the addition of a new paragraph (the third) and Clause 12 by the addition of a
new item, item n)].
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
iv © ISO 2011 – All rights reserved
---------------------- Page: 10 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
⎯ Part 11: Glass transition temperature
⎯ Part 12: Compressive vibration — Non-resonance method
© ISO 2011 – All rights reserved v
---------------------- Page: 11 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(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.
vi © ISO 2011 – All rights reserved
---------------------- Page: 12 ----------------------
SIST EN ISO 6721-1:2012
INTERNATIONAL STANDARD ISO 6721-1:2011(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 referenced documents are indispensable for the application 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 293, Plastics — Compression moulding of test specimens of thermoplastic materials
ISO 294 (all parts), Plastics — Injection moulding of test specimens of thermoplastic materials
ISO 295, Plastics — Compression moulding of test specimens of thermosetting materials
ISO 1268 (all parts), Fibre-reinforced plastics — Methods of producting test plates
ISO 2818, Plastics — Preparation of test specimens by machining
ISO 4593, Plastics — Film and sheeting — Determination of thickness by mechanical scanning
ISO 6721-2:2008, 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 2011 – All rights reserved 1
---------------------- Page: 13 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
[7]
NOTE Some of the terms defined here are also defined in ISO 472 . The definitions given here are not strictly
identical with, but are equivalent to, those in ISO 472.
3.1
complex modulus
∗
M
ratio of dynamic stress, given by σσtf=πexp i2t , and dynamic strain, given by
() ( )
A
⎡⎤
εεtf=πexp i 2t−δ , of a viscoelastic material that is subjected to a sinusoidal vibration, where σ and
() ( )
A
A
⎣⎦
ε are the amplitudes of the stress and strain cycles, f is the frequency, δ is the phase angle between stress
A
and strain (see 3.5 and Figure 1) and t is time
NOTE 1 It is expressed in pascals (Pa).
∗ ∗ ∗ ∗
NOTE 2 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′ + iM″ (see 3.2 and 3.3) (1)
where
1/ 2
i1=−() = −1
For the relationships between the different types of complex modulus, see Table 1.
∗ ∗ ∗ ∗ ∗
NOTE 3 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 4 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 5 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 6 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 7 The relationships given in Table 1 are valid for the complex moduli as well as their magnitudes (see 3.4).
NOTE 8 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 9 For linear-viscoelastic behaviour, the complex compliance C is the reciprocal of the complex modulus M , i.e.
∗ ∗ −1
M = (C ) (2)
Thus
′′′
CC− i
′′′
MM+=i (3)
22
CC′′′
() +( )
2 © ISO 2011 – All rights reserved
---------------------- Page: 14 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
a) b)
The phase shift δ /2π f between the stress σ and strain ε in a The relationship between the storage modulus
viscoelastic material subjected to sinusoidal oscillation (σ and ε are M′, the loss modulus M″, the phase angle δ and
A A
∗
the respective amplitudes, f is the frequency). the magnitude M of the complex modulus M .
Figure 1 — Phase angle and complex modulus
Table 1 — Relationships between moduli for uniformly isotropic materials
a
G and µ E and µ K and µ G and E G and K E and K G and L
Poisson's ratio, µ E E 1
GK/
3 −
b
1 − 2µ =
G 1/+GK3 3K LG/ −1
Shear modulus,
E E
31K −2µ
()
G =
21 + µ 3/− E3K
()
21 + µ
()
Tensile modulus, 2G(1 +µ )
3G
31GG−4 /3L
31K −2µ ()
()
E =
1/+GK3
1/−GL
Bulk modulus,
E G 4G
21G()+ µ
L −
c
K =
3
31()−2µ 33()GE/ −1
31()−2µ
Unaxial-strain or 4G
21G − µ E 1 − µ 31K − µ GG4/E −1 K1/+EK3
() () ()() ()
K +
longitudinal-wave
3
12− µ 11+−µµ2 1 + µ 3/GE −1 1/− E9K
()( )
modulus, L =
a
See Note 6 to definition 3.1.
b
See Note 4 to definition 3.1.
c
See Note 5 to definition 3.1.
© ISO 2011 – All rights reserved 3
---------------------- Page: 15 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
3.2
storage modulus
′
M
∗
real part of the complex modulus M [see Figure 1b)]
NOTE 1 The storage modulus is expressed in pascals (Pa).
NOTE 2 It is proportional to the maximum energy stored during a loading cycle and represents the stiffness of a
viscoelastic material.
NOTE 3 The different types of storage modulus, corresponding to different modes of deformation, are: E′ tensile
t
′ ′ ′
storage modulus, E flexural storage modulus, G shear storage modulus, G torsional storage modulus, K′ bulk
f s to
storage modulus, L′ uniaxial-strain storage modulus and L′ longitudinal-wave storage modulus.
c w
3.3
loss modulus
″
M
imaginary part of the complex modulus [see Figure 1b)]
NOTE 1 The loss modulus is expressed in pascals (Pa).
NOTE 2 It is proportional to the energy dissipated (lost) during one loading cycle. As with the storage modulus
(see 3.2), the mode of deformation is designated as in Table 3, e.g. E′′
is the tensile loss modulus.
t
3.4
magnitude M of the complex modulus
root mean square value of the storage and the loss moduli as given by the equation
22 2
2
MM=+′′M′=σε (4)
() ( )()
AA
where σ and ε are the amplitudes of the stress and the strain cycles, respectively
A A
NOTE 1 The complex modulus is expressed in pascals (Pa).
NOTE 2 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 1b). 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.
t
3.5
phase angle
δ
phase difference between the dynamic stress and the dynamic strain in a viscoelastic material subjected to a
sinusoidal oscillation (see Figure 1)
NOTE 1 The phase angle is expressed in radians (rad).
NOTE 2 As with the storage modulus (see 3.2), the mode of deformation is designated as in Table 3, e.g. δ is the
t
tensile phase angle.
3.6
loss factor
tanδ
ratio between the loss modulus and the storage modulus, given by the equation
tanδ = M ′′/ M ′ (5)
where δ is the phase angle (see 3.5) between the stress and the strain
NOTE 1 The loss factor is expressed as a dimensionless number.
NOTE 2 The loss factor tanδ 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. tanδ is the tensile loss factor.
t
4 © ISO 2011 – All rights reserved
---------------------- Page: 16 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
3.7
stress-strain hysteresis loop
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
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(−β t) × sin2πf 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
β is the decay constant (see 3.9)
© ISO 2011 – All rights reserved 5
---------------------- Page: 17 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
[X is the time-dependent deformation or deformation rate, X is the amplitude of the qth cycle and X and β define the
q 0
envelope 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
β
coefficient that determines the time-dependent decay of damped free vibrations, i.e. the time dependence of
the amplitude X of the deformation or deformation rate [see Figure 3 and Equation (6)]
q
−1
NOTE The decay constant is expressed in reciprocal seconds (s ).
3.10
logarithmic decrement
Λ
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
Λ = ln(X /X ) (7)
q q+1
where X and X are two successive amplitudes of deformation or deformation rate in the same direction
q q+1
NOTE 1 The logarithmic decrement is expressed as a dimensionless number.
NOTE 2 It is used as a measure of the damping in a viscoelastic system.
NOTE 3 Expressed in terms of the decay constant β and the frequency f , the logarithmic decrement is given by the
d
equation
Λ = β /f (8)
d
NOTE 4 The loss factor tanδ is related to the logarithmic decrement by the approximate equation
tanδ ≈ Λ/π (9)
NOTE 5 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).
6 © ISO 2011 – All rights reserved
---------------------- Page: 18 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
3.11
resonance curve
curve representing the frequency dependence of the deformation amplitude D or deformation-rate amplitude
A
R of an inert viscoelastic system subjected to forced vibrations at constant load amplitude L and at
A A
frequencies 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 amplitude R versus frequency f at constant load amplitude; logarithmic frequency scale)
A
3.12
resonance frequencies
f
r i
frequencies of the peak amplitudes in a resonance curve
NOTE 1 The subscript i refers to the order of the resonance vibration.
NOTE 2 Resonance frequencies are expressed in hertz (Hz).
NOTE 3 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
difference between the frequencies f and f of the ith-order resonance peak, where the height R of the
1 2 Ah
resonance curve at f and f is related to the peak height R of the ith mode by
1 2 AMi
−1/2
R = 2 R = 0,707R (10)
Ah AM AM
(see Figure 4)
NOTE 1 The width ∆f is expressed in hertz (Hz).
i
© ISO 2011 – All rights reserved 7
---------------------- Page: 19 ----------------------
SIST EN ISO 6721-1:2012
ISO 6721-1:2011(E)
NOTE 2 It is related to the loss factor tanδ by the equation
tanδ = ∆ 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 the
i
resonance curve is based on the deformation-rate amplitude (see also Annex A).
4 Principle
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 parti
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.