ISO 18437-4:2008
(Main)Mechanical vibration and shock — Characterization of the dynamic mechanical properties of visco-elastic materials — Part 4: Dynamic stiffness method
Mechanical vibration and shock — Characterization of the dynamic mechanical properties of visco-elastic materials — Part 4: Dynamic stiffness method
ISO 18437-4:2008 specifies a direct method for measuring the complex dynamic moduli of elasticity (the Young, shear and bulk moduli, and their respective loss factors corresponding to the tensile, shear and all compressive strains) for polymeric (rubbery and viscous polymers, as well as rigid plastics) materials over a wide frequency and temperature range. Measurements are performed by the dynamic stiffness method, which uses electric signals from sensors attached to a test piece. These signals are proportional to the dynamic forces acting on the test piece and the strains in the test piece due to the effect of these forces. The measurement frequency range is determined by the size of test piece, the accuracy required on the dynamic modulus measurements, the relationship between the stiffness of the oscillation generator and the stiffness of the test piece, and by the resonance characteristics of the test fixture used. The method presented in ISO 18437-4:2008 allows measurement under any static pre-load allowed for the test piece (including the test piece having the non-linear characteristics under different static loads), but under small dynamic (acoustic) strains, i.e. in limits where the linear properties of the test piece are not distorted. Depending on the pre-load conditions, the relation between the moduli is unique.
Vibrations et chocs mécaniques — Caractérisation des propriétés mécaniques dynamiques des matériaux visco-élastiques — Partie 4: Méthode de la raideur dynamique
General Information
Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 18437-4
First edition
2008-06-01
Mechanical vibration and shock —
Characterization of the dynamic
mechanical properties of visco-elastic
materials —
Part 4:
Dynamic stiffness method
Vibrations et chocs mécaniques — Caractérisation des propriétés
mécaniques dynamiques des matériaux visco-élastiques —
Partie 4: Méthode de la raideur dynamique
Reference number
ISO 18437-4:2008(E)
©
ISO 2008
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ISO 18437-4:2008(E)
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ISO 18437-4:2008(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope .1
2 Normative references .1
3 Terms and definitions .2
4 Principle.4
5 Equipment .5
5.1 Hardware.5
5.2 Set-up.5
6 Recommended set-up for applying the different types of strain to the test piece and
calculation of quotients, α .9
E,G,K
6.1 Choosing test piece size.9
6.2 Rigid plastics.9
6.3 Rubbery materials.10
6.4 Viscous materials .11
6.5 Bulk modulus of all materials.13
7 Test pieces .13
7.1 Choosing the shape and size of the test piece.13
7.2 Instructions for manufacturing and preparing test pieces .14
8 Conditioning.16
8.1 Storage.16
8.2 Temperature .16
8.3 Mechanical conditioning.16
8.4 Humidity conditioning.16
8.5 Measurement conditioning .16
9 Main error sources.17
10 Measurement results and processing .17
10.1 Frequency-temperature superposition.17
10.2 Data presentation.18
10.3 Test report .19
Bibliography .20
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ISO 18437-4:2008(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.
The main task of technical committees is to prepare International Standards. 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 document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 18437-4 was prepared by Technical Committee ISO/TC 108, Mechanical vibration, shock and condition
monitoring.
ISO 18437 consists of the following parts, under the general title Mechanical vibration and shock —
Characterization of the dynamic mechanical properties of visco-elastic materials:
⎯ Part 2: Resonance method
⎯ Part 3: Cantilever shear beam method
⎯ Part 4: Dynamic stiffness method
The following parts are under preparation:
⎯ Part 1: Principles and guidelines
⎯ Part 5: Poisson's ratio based on finite element analysis
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ISO 18437-4:2008(E)
Introduction
Visco-elastic materials are used extensively to reduce vibration magnitudes, of the order of hertz to kilohertz,
in structural systems through dissipation of energy (damping) or isolation of components, and in acoustical
applications that require modification of the reflection, transmission, or absorption of energy. The design,
modelling and characterization of such systems often require specific dynamic mechanical properties (the
Young, shear, and bulk moduli and their corresponding loss factors) in order to function in an optimum
manner. Energy dissipation is due to interactions on the molecular scale and can be measured in terms of the
lag between stress and strain in the material. The visco-elastic properties (modulus and loss factor) of most
materials depend on frequency, temperature, and strain amplitude. The choice of a specific material for a
given application determines the system performance. The goal of this part of ISO 18437 is to provide details,
in principle, of the operation of the direct dynamic stiffness method, the measurement equipment used in
performing the measurements, and the analysis of the resultant data. A further aim is to assist users of this
method and to provide uniformity in the use of this method. This part of ISO 18437 applies to the linear
behaviour observed at small strain amplitudes, although the static stiffness may be non-linear.
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INTERNATIONAL STANDARD ISO 18437-4:2008(E)
Mechanical vibration and shock — Characterization of the
dynamic mechanical properties of visco-elastic materials —
Part 4:
Dynamic stiffness method
1 Scope
This part of ISO 18437 specifies a direct method for measuring the complex dynamic moduli of elasticity (the
Young, shear and bulk moduli, and their respective loss factors corresponding to the tensile, shear and all
compressive strains) for polymeric (rubbery and viscous polymers, as well as rigid plastics) materials over a
wide frequency and temperature range. Measurements are performed by the dynamic stiffness method, which
uses electric signals from sensors attached to a test piece. These signals are proportional to the dynamic
forces acting on the test piece and the strains in the test piece due to the effect of these forces.
The measurement frequency range is determined by the size of test piece, the accuracy required on the
dynamic modulus measurements, the relationship between the stiffness of the oscillation generator and the
stiffness of the test piece, and by the resonance characteristics of the test fixture used.
The method presented in this part of ISO 18437 allows measurement under any static pre-load allowed for the
test piece (including the test piece having the non-linear characteristics under different static loads), but under
small dynamic (acoustic) strains, i.e., in limits where the linear properties of the test piece are not distorted.
Depending on the pre-load conditions, the relation between the moduli is unique.
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 472, Plastics — Vocabulary
ISO 483, Plastics — Small enclosures for conditioning and testing using aqueous solutions to maintain the
humidity at a constant value
ISO 2041, Mechanical vibration, shock and condition monitoring — Vocabulary
ISO 4664-1, Rubber, vulcanized or thermoplastic — Determination of dynamic properties — Part 1: General
guidance
ISO 6721-1, Plastics —Determination of dynamic mechanical properties — Part 1: General principles
ISO 6721-4, Plastics — Determination of dynamic mechanical properties — Part 4: Tensile vibration — Non-
resonance method
ISO 6721-6, Plastics — Determination of dynamic mechanical properties — Part 6: Shear vibration — Non-
resonance method
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ISO 18437-4:2008(E)
ISO 10112, Damping materials — Graphical presentation of the complex modulus
ISO 10846-1, Acoustics and vibration — Laboratory measurement of vibro-acoustic transfer properties of
resilient elements — Part 1: Principles and guidelines
ISO 23529, Rubber — General procedures for preparing and conditioning test pieces for physical test
methods
NOTE ISO 10846-1 is concerned with the global measurement of dynamic input and transfer stiffness and
mechanical resistance of resilient fixtures. This part of ISO 18437 is concerned with the characterization of the dynamic
Young modulus, shear modulus, bulk modulus, and corresponding loss factors of the visco-elastic materials that are used
in the fixtures.
3 Terms and definitions
For the purposes of this part of ISO 18437, the terms and definitions given in ISO 472, ISO 483, ISO 2041,
ISO 4664-1, ISO 6721-1, ISO 6721-4, ISO 6721-6, ISO 10112, ISO 10846-1, ISO 23529, and the following
apply.
3.1
dynamic mechanical properties
〈visco-elastic materials〉 fundamental elastic properties, i.e., elastic modulus, shear modulus, bulk modulus
and loss factor
3.2
damped structure
structure containing elements made from damping materials
3.3
Young modulus
modulus of elasticity
E
ratio of the normal stress to linear strain
[9]
NOTE 1 Adapted from ISO 80000-4-18.1:2006 .
NOTE 2 The Young modulus is expressed in pascals.
NOTE 3 The complex Young modulus, E*, for a visco-elastic material is represented by E* = E′ + iE″, where E′ is the
real (elastic) component of the Young modulus and E″ is the imaginary (loss modulus) component of the Young modulus.
The real component represents elastically stored mechanical energy, while the imaginary component is a measure of
mechanical energy loss.
3.4
shear modulus
modulus of rigidity
Coulomb modulus
G
ratio of the shear stress to the shear strain
[9]
NOTE 1 Adapted from ISO 80000-4-18.2:2006 .
NOTE 2 The shear modulus is expressed in pascals.
NOTE 3 The complex shear modulus, G*, for a visco-elastic material is represented by G* = G′ + iG″, where G′ is the
real (elastic) component of the shear modulus and G″ is the imaginary (loss modulus) component of the shear modulus.
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ISO 18437-4:2008(E)
3.5
bulk modulus
modulus of compression
K
the negative ratio of pressure to volume strain
[9]
NOTE 1 Adapted from ISO 80000-4-18.3:2006 .
NOTE 2 The bulk modulus is expressed in pascals.
NOTE 3 The complex bulk modulus is represented by K* = K′ + iK″, where K′ is the real (elastic) component of the bulk
modulus and K″ is the imaginary (loss modulus) component of the bulk modulus.
3.6
loss factor
ratio of the imaginary component to the real component of a complex modulus
NOTE When a material shows a phase difference, δ, between dynamic stress and strain in harmonic deformations,
the loss factor is equal to tanδ.
3.7
magnitude of complex modulus
absolute value of the complex modulus
NOTE The magnitude of the complex moduli are defined as:
2 2
a) magnitude of the Young modulus: = √[(E′) + (E″) ];
E
2 2
b) magnitude of shear modulus: = √[(G′) + (G″) ];
G
2 2
c) magnitude of bulk modulus: = √[(K′) + (K″) ].
K
These magnitudes are expressed in pascals.
3.8
frequency-temperature superposition
principle by which, for visco-elastic materials, frequency and temperature are equivalent to the extent that data
at one temperature can be superimposed upon data taken at different temperature merely by shifting the data
curves along the frequency axis
3.9
shift factor
measure of the amount of shift along the logarithmic axis of frequency for one set of data at one temperature
to superimpose upon another set of data at another temperature
3.10
glass transition temperature
T
g
〈visco-elastic materials〉 temperature at which a material changes state reversibly from glassy to rubbery
NOTE 1 The glass transition temperature is expressed in degrees Celsius.
NOTE 2 The glass transition temperature is typically determined from the inflection point of a specific heat vs.
temperature plot and represents an intrinsic material property.
NOTE 3 T is not the peak in the dynamic mechanical loss factor. That peak occurs at a temperature higher than T
g g
and varies with the measurement frequency, hence it is not an intrinsic material property.
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ISO 18437-4:2008(E)
3.11
linearity
〈visco-elastic materials〉 property of dynamic behaviour of a resilient material if it satisfies the principle of
superposition
NOTE 1 The principle of superposition can be stated as follows: if an input x (t) produces an output y (t) and in a
1 1
separate test an input x (t) produces an output y (t), superposition holds if the input α x (t) + β x (t) produces the output
2 2 1 2
α y (t) + β y (t), where α and β are arbitrary constants. This must hold for all values of α, β and x (t), x (t).
1 2 1 2
NOTE 2 In practice, the above test for linearity is impractical and a limited check of linearity is done by measuring the
dynamic modulus for a range of input levels. For a specific preload, if the dynamic modulus is nominally invariant, the
system measurement can be considered linear. In effect, this procedure checks for a proportional relationship between the
response and the excitation.
4 Principle
The dynamic stiffness method is a technique for determining the frequency characteristics of the complex
dynamic modulus of elasticity of resilient materials using small test pieces mounted in an appropriate test
fixture.
Before performing the measurement, test pieces of the material are manufactured and placed in a test fixture
where they are subjected to a strain with the help of a displacement actuator. The force transducer electric
output is proportional to the force acting on the test piece; the displacement actuator electric input signal is
proportional to the strain in the test piece. The test piece shall have dimensions such that its impedance is
completely elastic in character over the total frequency range of interest. Hence the inertial component of this
impedance shall be negligible in comparison with the elastic component. To meet this requirement, the test
piece sizes shall be such that the first eigenfrequency should be three to five times larger than the upper
frequency limit of measurement.
In the dynamic stiffness method, when using special fixtures, it is possible to apply the three different types of
strain: the Young (tensile or compressive), shear, and bulk to the test piece and thus measure the three
corresponding moduli of elasticity and their corresponding loss factors (when the displacement actuator
generates deformation only along the test piece axis). The user can choose a test piece shape and fixture for
applying an appropriate type of strain in each specific case.
When performing the measurement using the specific conditions detailed above, the general expression for
determination of the complex elastic modulus, E*,G*,K*( f ), has the form
E*,G*,K*( f ) = α [F( f )/s( f )]. (1)
E,G,K
where
α is the ratio of the measured modulus of the tested material to stiffness of the test piece under the
E,G,K
appropriate strain (longitudinal, shear or bulk);
NOTE Methods of calculating α are shown in Clause 6.
E,G,K
F( f )/s( f ) is the complex ratio of the output force and the test piece displacement.
Hence, the real part of the modulus, E′, G′, K′( f ), is given by Equation (2):
E′,G′,K′( f ) = α Re[F( f )/s( f)] (2)
E,G,K
The imaginary part of the modulus, E″,G″,K″( f ), is given by Equation (3):
E″,G″,K″( f ) = α Im[F( f )/s( f)] (3)
E,G,K
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ISO 18437-4:2008(E)
The magnitude of the modulus, E,,GK f , is given by Equation (4):
()
E,,GK f = α F f /s f (4)
() ( )( )
EG,,K
The loss factors, η ( f ), are given by Equation (5):
E,G,K
η ( f ) = Im[F( f )/s( f )]/Re[F( f )/s( f)] (5)
E,G,K
5 Equipment
5.1 Hardware
The following items are used for carrying out the measurements:
5.1.1 2-Channel fast Fourier transform (FFT) analyser, which provides a measurement of complex value
frequency response function.
5.1.2 Input and output transducer, and preamplifiers as required.
5.1.3 Computer.
5.1.4 Test device and test piece, including force transducer and displacement actuator.
A temperature sensor (such as a thermocouple or thermostat) shall be placed in the test device when
temperature dependence of moduli and loss factors is to be measured. The device for controlling the
temperature of the test piece may be mounted inside the test device. The thermostat shall measure the actual
temperature of the test piece over the range −60 °C up to +70 °C, at minimum increments of 5 °C.
5.2 Set-up
A typical measurement set-up and test device for measuring the visco-elastic characteristics, such as the
dynamic moduli of elasticity and loss factors, of a polymeric material are shown in Figure 1 and Figure 2
respectively (Reference [1]). Depending on the test device and the material, the frequency range can be up to
10 kHz.
If the application of the visco-elastic material is for structure-borne noise or vibration suppression, it should be
tested up to 500 Hz (see ISO 10846-1).
The test set-up comprises the following components:
• rigid restrictive construction;
• means of fixing or attaching test pieces to the test set-up;
• two electromechanical units, a displacement actuator and a force transducer — the former converts the
electrical signal from the power amplifier into a surface displacement that is in contact with the test piece
and deforms it, while the latter converts the force acting on the test piece into an electric signal (see
Figure 2);
• annular washers for adjustment of the gap between the force transducer and the displacement actuator
when carrying out test piece measurements under any permissible static pre-load;
• external fixture to generate a known static compression in the test piece when attached to the
electromechanical units.
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ISO 18437-4:2008(E)
In the following, the numbers in parentheses refer to the labels in Figure 2. The test piece (3) rigidity shall be
far less than the rigidity of the displacement actuator (1), force transducer (2), annular washer (4) and the rigid
restrictive construction (6).
The test piece (3) is placed between operational surfaces of displacement actuator and force transducer.
When measuring the characteristics of the test piece under a pre-load, if required for testing, the distance
between the support surfaces of the cylindrical shells shall be adjusted by the annular washer (4). These
washers are parallel to the test piece surfaces. When the objective is measurement under zero static
displacement, the height of the annular washer shall be 3 % to 5 % less than that of the test piece. This
arrangement produces zero static pre-load.
Key
1 test device 6 power amplifier A channel A — displacement from displacement
actuator input
2 force transducer 7 dual channel spectrum FFT
b
B channel B — force from force transducer output
analyser
3 test piece
C channel C — excitation signal from the FFT
8 PC
4 displacement actuator
analyser
a
9 voltage divider
5 amplifier
a
The amplifier shall have the functions of amplification and attenuation of the signal. If the signal from the output of the
power amplifier is too large for the amplifier, a voltage divider shall be added before the amplifier. The voltage divider shall
not distort the signal’s phase by more than 0,05°.
b
Channel A is the displacement from displacement actuator input, channel B is the force from force transducer output
and channel C is the excitation signal from the FFT analyser.
Figure 1 — Measurement set-up
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ISO 18437-4:2008(E)
Key
1 displacement actuator
2 force transducer
3 test piece and nearby temperature sensor
4 annular washer
5 static pressure-generating fixture
6 rigid restrictive construction
Figure 2 — Schematic diagram of the measurement device
When measuring the unknown values by using the test device shown in Figure 2, the real part of each
modulus, E′,G′,K′( f ), is given by Equation (6):
E′,G′,K′( f ) = α Re[β( f )·H( f)] (6)
E,G,K
where β( f ) is defined in Equation (10) and H( f ). in Equation (11).
The imaginary part of the modulus, E″,G″,K″( f ), is given by Equation (7):
E″,G″,K″( f ) = α Im[β( f )·H( f)] (7)
E,G,K
The magnitude of the modulus, E,,GK f , is given by Equation (8):
()
⎡ ⎤
EG,,K f=⋅αλH f / K (8)
( ) ( )
E,,GK s F
⎣ ⎦
The loss factors, η ( f ), are given by Equation (9):
E,G,K
η ( f ) = Im[β( f )⋅H( f )]/Re[β( f )⋅H( f)] (9)
E,G,K
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ISO 18437-4:2008(E)
The complex function, β( f), describes the characteristics of the displacement actuator and the force
transducer of the test device in the absence of the annular washer and test piece, and is determined using
Equation (10):
cos∆(ϕϕf)− i sin∆( f)
β( f ) = (10)
K ⋅ λ
sF
where
K is the modulus of the transformer quotient, in metres per volt, of the displacement actuator;
s
λ is the modulus of the force transducer sensitivity with respect to the applied force, in volts per
F
newton;
∆ϕ ( f) is the phase angle, in degrees, between the signals at the output of the force transducer and the
input of the displacement actuator if their measurement surface is in rigid mechanical contact.
These quotients are determined during the calibration of the force transducer and the displacement actuator.
The complex function, H( f), when a test piece is placed into the device (see Figure 1), is given by Equation
(11):
H( f ) = U ( f )/U ( f ) (11)
F s
where
U ( f ) is the complex signal, in volts, at the output of the force transducer;
F
U ( f ) is the complex valued input, in volts, of the displacement actuator.
s
Signal, U ( f ), is applied through the amplifier to channel A of the two-channel analyser; input, U ( f ), is applied
F s
to channel B of the two-channel analyser.
When using this type of test device, measurement errors do not exceed 2,5 % to 3,0 % in the frequency range
10 Hz to 10 kHz, if the measuring devices have the metrological characteristics shown in Table 1.
Table 1 — Characteristics of measuring equipment
Specifications for measurement process
Measurement tools and equipment
Frequency and voltage
Accuracy
range
5 Hz to 10 kHz Response ripple 2 %
Dual channel FFT analyser, equipped with signal generator
(random noise, sine wave)
100 µV to 100 V (RMS) Channel phase < 0,02°
Response ripple 1 %
10 Hz to 10 kHz;
Amplifiers
Input/output phase
electric noise level u 5 µV
difference < 0,1°
Non-linear distortions
Power amplifier 10 Hz to 10 kHz
< 10 %
If the phase responses of measurement tools are different from those given in Table 1, such responses should
be taken into account during the signal processing.
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ISO 18437-4:2008(E)
6 Recommended set-up for applying the different types of strain to the test piece
and calculation of quotients, α
E,G,K
6.1 Choosing test piece size
Test piece sizes should be chosen according to the conditions for ensuring:
• the error allowed when measuring the moduli of elasticity and loss factor for polymeric damping material;
• the required upper frequency limit, f = 10 kHz;
max
• the test piece shall not collapse under maximum test pre-load.
6.2 Rigid plastics
6.2.1 The Young modulus of rigid plastics
Cylindrical test pieces are recommended for measuring the Young moduli and the corresponding loss factors
for rigid plastics (see Figure 3).
Under these conditions, the quotient, α , in Equation (1) is given by Equation (12):
E
4h
α = (12)
E
2
πd
where
h is the height of the cylindrical test piece;
d is the diameter of the cylindrical test piece.
Key
1 test piece
2 washers
d diameter
h height
Figure 3 — Test device for the Young modulus measurement
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ISO 18437-4:2008(E)
6.2.2 Shear modulus of rigid plastics
For the shear modulus and the corresponding loss factor measurement, parallelepipeds as shown in Figure 4
are required. The test piece sizes should be chosen so that their total shear stiffnesses are within the dynamic
range of the test device.
The quotient, α , of Equation (1) is given by Equation (13):
G
δ
α = (13)
G
2lb
for a rectangular area of length,
...
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