ISO 4664:1998

INTERNATIONAL ISO
STANDARD 4664
Third edition
1998-05-01
Rubber — Guide to the determination
of dynamic properties
Caoutchouc — Lignes directrices pour la détermination des propriétés
dynamiques
A
Reference number
ISO 4664:1998(E)

---------------------- Page: 1 ----------------------
ISO 4664:1998(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.
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.
International Standard ISO 4664 was prepared by Technical Committee
Rubber and rubber products, Subcommittee SC 2, Physical
ISO/TC 45,
and degradation tests.
This third edition cancels and replaces the second edition (ISO 4664:1987)
as well as ISO 2856:1981, of which it constitutes a technical revision.
©  ISO 1998
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 the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet central@iso.ch
X.400 c=ch; a=400net; p=iso; o=isocs; s=central
Printed in Switzerland
ii

---------------------- Page: 2 ----------------------
©
INTERNATIONAL STANDARD  ISO ISO 4664:1998(E)
Rubber — Guide to the determination of dynamic
properties
WARNING – Persons using this International Standard should be familiar with normal laboratory practice.
This standard does not purport to address all of the safety problems, if any, associated with its use. It is the
responsibility of the user to establish appropriate safety and health practices and to ensure compliance
with any national regulatory conditions.
1 Scope
This International Standard provides guidance on the determination of dynamic properties of vulcanized and
thermoplastic rubbers. It includes both free- and forced-vibration methods for use with both materials and products.
It does not cover rebound resilience nor cyclic tests in which the main objective is to fatigue the rubber.
2 Normative references
The following standards contain provisions which, through reference in this text, constitute provisions of this
International Standard. At the time of publication, the editions indicated were valid. All standards are subject to
revision, and parties to agreements based on this International Standard are encouraged to investigate the
possibility of applying the most recent editions of the standards indicated below. Members of IEC and ISO maintain
registers of currently valid International Standards.
ISO 471:1995, Rubber – Temperatures, humidities and times for conditioning and testing.
Rubber, vulcanized or thermoplastic – Determination of compression set at ambient, elevated or low
ISO 815:1991,
temperatures.
ISO 3383:1985, Rubber – General directions for achieving elevated or subnormal temperatures for test purposes.
ISO 4648:1991, Rubber, vulcanized or thermoplastic – Determination of dimensions of test pieces and products for
test purposes.
Rubber – Determination of dynamic behaviour of vulcanizates at low frequencies – Torsion
ISO 4663:1986,
pendulum method.
ISO 5893:1993, Rubber and plastics test equipment – Tensile, flexural and compression types (constant rate of
traverse) – Description.
ISO 7743:1989, Rubber, vulcanized or thermoplastic – Determination of compression stress-strain properties.
3 Definitions
For the purposes of this International Standard, the following definitions apply (for the symbols used, see clause 4):
3.1 Terms applying to any periodic deformation
3.1.1 mechanical-hysteresis loop
The closed curve representing successive stress-strain states of the material during a cyclic deformation.
NOTE – Loops may be centred on the origin of the coordinate system or, more frequently, displaced to various levels of
strain or stress; in the latter case, the shape of the loop becomes asymmetrical, but this fact is frequently disregarded.
1

---------------------- Page: 3 ----------------------
©
ISO
ISO 4664:1998(E)
3
3.1.2 energy loss (J/m )
The energy per unit volume which is lost in each deformation cycle. It is the hysteresis loop area, calculated with
reference to coordinate scales.
3
3.1.3 power loss (W/m )
The power per unit volume which is transformed into heat through hysteresis. It is the product of energy loss and
frequency.
3.1.4 mean stress (Pa)
The average value of the stress during a single complete hysteresis loop (see figure 1).
3.1.5 mean strain (dimensionless)
The average value of the strain during a single complete hysteresis loop (see figure 1).
NOTE – Open initial loops are shown as well as equilibrium mean strain and mean stress as time-averages of
instantaneous strain and stress.
Figure 1 – Heavily distorted hysteresis loop obtained under forced pulsating sinusoidal strain
2

---------------------- Page: 4 ----------------------
©
ISO
ISO 4664:1998(E)
3.1.6 mean modulus (Pa)
The ratio of the mean stress to the mean strain.
3.1.7 stress amplitude (Pa)
The ratio of the maximum applied force, measured from the mean force, to the cross-sectional area of the
unstressed test piece (zero to peak on one side only).
3.1.8 root-mean-square stress (Pa)
The square root of the mean value of the square of the stress averaged over one deformation cycle.
2
NOTE – For a symmetrical sinusoidal stress, the root-mean-square stress equals the stress amplitude divided by .
3.1.9 strain amplitude (dimensionless)
The ratio of the maximum deformation, measured from the mean deformation, to the free length (thickness) of an
unstrained test piece (zero to peak on one side only) in the direction of loading.
3.1.10 root-mean-square strain (dimensionless)
The square root of the mean value of the square of the strain averaged over one cycle of deformation.
NOTE – For a symmetrical sinusoidal strain, the root-mean-square strain equals the strain amplitude divided by 2 .
3.2 Terms applying to sinusoidal motion
NOTE 1 A sinusoidal response to a sinusoidal motion implies hysteresis loops which are or can be considered to be
elliptical. The term "incremental" may be used to designate dynamic response to sinusoidal deformation about various
levels of mean stress or mean strain (for example, incremental spring constant, incremental elastic shear modulus).
NOTE 2 For large sinusoidal deformations, the hysteresis loop will deviate from an ellipse since the stress-strain
relationship of rubber is non-linear and the response is no longer sinusoidal.
3.2.1 spring constant, k (N/m)
The component of applied force which is in phase with the deformation, divided by the deformation.
3.2.2 elastic shear modulus (storage shear modulus), G' (Pa)
The component of applied shear stress which is in phase with the shear strain, divided by the strain.
E' (Pa)
3.2.3 elastic normal modulus (storage normal modulus; elastic Young's modulus),
The component of applied normal stress which is in phase with the normal strain, divided by the strain.
c
3.2.4 damping constant, (N.s/m)
The component of applied force which is in quadrature with the deformation, divided by the velocity of the
deformation.
3.2.5 loss shear modulus, G" (Pa)
The component of applied shear stress which is in quadrature with the shear strain, divided by the strain.
3.2.6 loss normal modulus (loss Young's modulus), E" (Pa)
The component of applied normal stress which is in quadrature with the normal strain, divided by the strain.
3

---------------------- Page: 5 ----------------------
©
ISO
ISO 4664:1998(E)
G*
3.2.7 complex shear modulus, (Pa)
The ratio of the shear stress to the shear strain, where each is a vector which may be represented by a complex
number.
G* G' jG"
= +
3.2.8 complex normal modulus (complex Young's modulus), E* (Pa)
The ratio of the normal stress to the normal strain, where each is a vector which may be represented by a complex
number.
E* = E' + jE"
3.2.9 absolute (value of) complex shear modulus
The magnitude of the complex shear modulus.
22
′ ′′
G*=GG*= +G     (Pa)
3.2.10 loss factor tanδ (dimensionless)
The ratio of the loss modulus to the elastic modulus. For shear stresses tanδ = G"/G' and for normal stresses
tanδ = E"/E'.
3.2.11 loss angle (rad)
The phase angle between the stress and the strain, the tangent of which is the loss factor.
3.3 Other terms applying to periodic motion
Λ
3.3.1 logarithmic decrement, (dimensionless)
The natural (Naperian) logarithm of the ratio between successive amplitudes of the same sign of a damped
oscillation.
3.3.2 damping ratio, u (dimensionless)
The ratio of the actual to the critical damping, where critical damping is that required for the borderline condition
between oscillatory and non-oscillatory behaviour. The damping ratio is a function of the logarithmic decrement:
L
L
 
2p
u = = sin arctan  .(1)
2
 
2p
L
 
1+
 
 
2p
u Λ π Λ
NOTE –  = 2 for small values of .
K
3.3.3 dynamic spring rate,
0
K = F /x
0 0 0
C
3.3.4 damping coefficient,
C = 1/ωK sinδ
0
where ω = 2πf
4

---------------------- Page: 6 ----------------------
©
ISO
ISO 4664:1998(E)
3.3.5 transmissibility, V
T
2
1+()tan d
V=
T 2
2
 
 
w
2
1− +()tan d
 w
 
0
 
where ω is the natural angular frequency of the measured undamped vibrator:

0
11
K Kg
1
ϖ==  and  K = K cosδ
0 0
m preload
4 Symbols
A test piece cross-sectional area
a(θ) Williams, Landel, Ferry (WLF) shift factor
a angle of twist
b test piece width
c heat capacity
p
γ
strain
γ
maximum strain amplitude
o
δ
loss angle
E Young’s modulus
E
effective Young’s modulus
c
E' elastic modulus
E" loss normal modulus
E* Complex normal modulus (complex Young’s modulus)
F force
f frequency
G
shear modulus
G'
in phase or storage shear modulus
G" out-of-phase or loss shear modulus
G* complex shear modulus
G* magnitude of complex shear modulus
h test piece thickness
θ absolute temperature (in kelvins)
θ low-frequency glass transition temperature
G
θ reference temperature
0
k numerical factor
k shape factor in torsion
1
l test piece length
λ
extension ratio
Λ
logarithmic decrement
M'
in-phase or storage modulus
M" out-of-phase or loss modulus
M* complex modulus
M* magnitude of complex modulus
m mass
p rubber density
Q torque
s shape factor
S'
in-phase component of stiffness
S" out-of-phase component of stiffness
t time
tanδ tangent of the loss angle
5

---------------------- Page: 7 ----------------------
©
ISO
ISO 4664:1998(E)
τ
stress
τ
maximum stress amplitude
o
τ'
in-phase stress
τ" out-of-phase stress
u damping ratio
ω
angular frequency
x displacement
5 Basic principles
5.1 Types of dynamic test
There are two basic classes of dynamic test, i.e. free vibration in which the test piece is set into oscillation and the
amplitude allowed to decay due to damping in the system and forced vibration in which the oscillation is maintained
by external means. Forced-vibration test machines may operate at resonance or away from resonance. Wave
propagation (e.g. ultrasonics) is a special form of forced vibration and rebound resilience is a simple form of
dynamic test in which one half cycle of deformation is applied.
5.2 Dynamic motion
Rubbers are viscoelastic materials and hence their response to dynamic stressing is a combination of an elastic
response and a viscous response, and energy is lost in each cycle.
For sinusoidal strain, the motion is described by
γγ= sinωt  (see figure 2) .(2)
0
Figure 2 – Sinusoidal stress-strain time cycles
6

---------------------- Page: 8 ----------------------
©
ISO
ISO 4664:1998(E)
τ
The stress ( ) will not be in phase with the strain and can be considered to precede it by the phase angle so that
()
ττ=+sinωt δ
...(3)
0
τ'
Considering the stress as a vector having two components, one in phase with the displacement ( ) and one 90° out
τ" M*
of phase ( ) and defining the corresponding in-phase and out-of-phase moduli, the complex (resultant) modulus
is given by the following equation:
M* M' jM"
= + .(4)
Also
t' t
0
MM'==cos codd=*s
g g
00
t''t
0
MM''==sin sidd=*n
gg
00
The absolute value, or magnitude, of the complex modulus is given by the following equation:
22
MM*=+'M'' .(5)
M''
The loss tangent, tan d =
M'
For a freely vibrating rubber and mass system, the equation of motion is given by the following equation:
2
dx Sd'' x
m ++Sx'=0 .(6)
2
dt ω dt
The solution of this equation gives
2
 
L
2
Sm'=+w1
 
2
4p
2
mw L
S''=
p
L
tan d = .(7)
2
 
L
p 1+
 
2
 4p 
Λ
where is the log decrement.
5.3 Use of dynamic-test data
The reasons for measuring dynamic properties can be given, in general terms, as follows:
a) material characterization
b) design data
c) product performance
Dynamic measurements made as a function of temperature are used to determine the glass transition temperature.
7

---------------------- Page: 9 ----------------------
©
ISO
ISO 4664:1998(E)
Because of the complex viscoelastic behaviour of elastomers, results of dynamic measurements are highly
sensitive to test conditions such as frequency, amplitude of applied force or deformation, test piece geometry and
mode of deformation. Hence, such parameters need to be specified and controlled if results are to be comparable.
An important practical consequence is that the conditions under which data is produced should be suitable for the
intended purpose of the data. In turn, this may mean that, depending on the intended purpose, a different type of
test machine may be suitable. In particular, small dynamic analyser machines which are especially suitable for
material characterization may not be capable of operating at the frequencies, amplitudes and modes of deformation
required for generating design data or for measuring product performance.
6 Mode of deformation
Dynamic tests are most frequently carried out in shear and compression, but tension and bending are also used.
For free-vibration tests, torsion is normally used.
The preferred form of impressed strain is sinusoidal, and the strain should be impressed on the test piece with a
harmonic distortion which is as low as possible, and in no case greater than 10 %.
The preferred mode for the generation of design data is simple shear with constant impressed strain. This has the
merits that a substantial proportion of manufactured articles are used in this type of strain and the stress-strain
behaviour is more nearly linear than in compression or tension, especially for rubbers containing little filler. Forced
oscillations rather than free vibration or resonance are preferred because this ensures control of the strain
amplitude.
For material characterization, and particularly comparison of materials and quality control, the mode of deformation
may be less important than experimental convenience.
For products, the mode of deformation will normally simulate service use.
7 Test pieces
7.1 Test piece preparation
Test pieces may be moulded or cut from moulded sheet. Moulding is preferred for shear and compression test
pieces. Plates for shear and compression test pieces may be bonded during moulding or bonded afterwards with a
thin layer of suitable adhesive.
7.2 Test piece dimensions
7.2.1 General
Test piece shape and dimensions will vary depending on the mode of deformation and the type and capacity of
machine used.
For test pieces bonded to metal plates during moulding, the thickness of the metals should be measured before
moulding and the thickness of the rubber deduced by measurement of the overall thickness of the moulding.
7.2.2 Shear
Double shear test pieces are preferred with either round or square rubber elements. It is essential that the diameter
(or side in the case of square elements) is at least four times the thickness to ensure that the deformation is
essentially simple shear, i.e. bending is negligible. The thickness should be no greater than 12 mm to avoid
difficulties in obtaining uniform vulcanization.
The thickness and area of each test piece should be measured to ± 1 %.
8

---------------------- Page: 10 ----------------------
©
ISO
ISO 4664:1998(E)
7.2.3 Compression
Cylindrical test pieces are preferred with a height/diameter ratio of approximately 1,5. This ratio minimizes
uncertainties due to shape factor correction for unlubricated test pieces. However, the test pieces specified in
ISO 815 are convenient and widely used.
The thickness and area of each test piece should be measured to ± 1 %.
7.2.4 Tension
Rectangular test pieces are preferred of thickness between 1 mm and 3 mm and length between the grips five
times the width.
The thickness, width and gauge length should be measured to ± 1 %.
7.2.5 Bending
Rectangular test pieces are preferred of thickness between 1 mm and 3 mm. For three- or four-point loading, the
span should ideally be 16 mm, but this may have to be reduced to obtain an adequate measurable force. In this
case, the maximum practicable value should be used, and it should be accepted that the deformation will have a
significant shear component.
Measure the span, width and thickness to ± 1 %.
7.2.6 Torsion
Rectangular test pie
...