ISO 18437-6:2017

Mechanical vibration and shock — Characterization of the dynamic mechanical properties of visco-elastic materials — Part 6: Time-temperature superposition

ISO 18437-6:2017 specifies a standard method for the acquisition and analysis of data obtained using the test methods found in ISO 18437‑1 to ISO 18437‑5, ISO 6721‑4 to ISO 6721‑7 and ISO 6721‑12. ISO 18437-6:2017 is applicable to visco-elastic materials that are thermorheologically simple and that have been tested at equilibrium state for every temperature.

Vibrations et chocs mécaniques — Caractérisation des propriétés mécaniques dynamiques des matériaux visco-élastiques — Partie 6: Superposition du temps et de la température

General Information

• Status: Published
• Publication Date: 29-Nov-2017
• ICS: 17.160 - Vibrations, shock and vibration measurements
• Technical Committee: ISO/TC 108 - Mechanical vibration, shock and condition monitoring
• Drafting Committee: ISO/TC 108/WG 28 - Vibration materials
• Current Stage: 9093 - International Standard confirmed
• Completion Date: 07-Mar-2023

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 18437-6
First edition
2017-11
Mechanical vibration and shock —
Characterization of the dynamic
mechanical properties of visco-elastic
materials —
Part 6:
Time-temperature superposition
Vibrations et chocs mécaniques — Caractérisation des propriétés
mécaniques dynamiques des matériaux visco-élastiques —
Partie 6: Superposition du temps et de la température
Reference number
ISO 18437-6:2017(E)
©
ISO 2017

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ISO 18437-6:2017(E)

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© ISO 2017, Published in Switzerland
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ISO 18437-6:2017(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Prediction of complete range of visco-elastic properties and description of data .3
4.1 Time-temperature superposition (TTS) principle . 3
4.2 Data acquisition . 3
4.2.1 New data . 3
4.2.2 Existing data . 4
4.2.3 Data scatter and determination of thermorheological simplicity . 4
4.3 Shifting . 5
4.3.1 Vertical shifting . 5
4.3.2 Horizontal shifting. 5
4.3.3 Dynamic visco-elastic functions master curves . 6
5 Verification . 6
6 Main sources of uncertainty . 6
6.1 General . 6
6.2 Narrow width of overlapping between the segments (isotherms) . 6
6.3 Presence of big experimental error (more than 10 %) in the segments . 7
6.4 Low density of experimental datum points in the segment . 7
6.5 Inappropriately arranged input data — presence of “end effects” in the segments. 7
6.6 Selection of reference temperature . 7
7 Results and processing. 7
7.1 Data presentation . 7
7.2 Test report . 8
Annex A (informative) Closed form shifting (CFS) methodology . 9
Annex B (informative) Example of storage modulus master curve construction .13
Annex C (informative) Computer-interpretable listings .23
Bibliography .24
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ISO 18437-6:2017(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
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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
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URL: www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 108, Mechanical vibration, shock and
condition monitoring.
A list of all parts in the ISO 18437 series can be found on the ISO website.
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ISO 18437-6:2017(E)

Introduction
Visco-elastic materials are used extensively to reduce vibration amplitudes in structural systems
through dissipation of energy (damping) or isolation of components and in acoustical applications that
require a modification of the reflection, transmission or absorption of energy. The design, modelling
and characterization of such systems often require specific dynamic mechanical properties in order
to function in an optimum manner. For most visco-elastic materials, these properties depend on
frequency, temperature and amplitude of applied excitation. The aim of this document is to provide
details on the best way of data acquisition for subsequent processing and to provide a standard method
for analysis using the time-temperature superposition principle. This document applies to the linear
behaviour observed at small strain (stress) amplitudes and to thermorheologically simple materials.
This document presents a method for checking the validity of a thermorheological simplicity of a
material and for identifying and eliminating questionable data. It provides minimal criteria for data
acquisition to be applied in mathematical methodologies, which allow multiple data sets of dynamic
visco-elastic properties measured at different temperatures to be cast into a single master curve
according to the time-temperature superposition (TTS) principle. When sufficient data are obtained or
[16][17]
available, a standard method, which uses a closed form shifting algorithm , is defined.
TTS is the most widely-used method for accelerated prediction of long-term visco-elastic behaviour of
[13]
materials . In the frequency domain, TTS can be used for predicting the behaviour of materials at
frequencies that are experimentally not assessable.
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INTERNATIONAL STANDARD ISO 18437-6:2017(E)
Mechanical vibration and shock — Characterization
of the dynamic mechanical properties of visco-elastic
materials —
Part 6:
Time-temperature superposition
1 Scope
This document specifies a standard method for the acquisition and analysis of data obtained using the
test methods found in ISO 18437-1 to ISO 18437-5, ISO 6721-4 to ISO 6721-7 and ISO 6721-12.
It is applicable to visco-elastic materials that are thermorheologically simple and that have been tested
at equilibrium state for every temperature.
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 18437-1, Mechanical vibration and shock — Characterization of the dynamic mechanical properties of
visco-elastic materials — Part 1: Principles and guidelines
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 18437-1 and the following 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/
3.1
dynamic visco-elastic function
fundamental visco-elastic property, i.e. storage moduli and loss moduli, measured in tension, shear and
compression and loss factor as functions of frequency and temperature
3.2
storage modulus
M′
real part of the complex modulus
Note 1 to entry: It is a measure of the energy stored and regained during a loading cycle.
Note 2 to entry: Storage moduli in tension, shear and compression are denoted as E′, G′ and K′, respectively.
Note 3 to entry: It is expressed in pascals (Pa).
[SOURCE: ISO 472:2013, 2.998, modified — Notes to entry have been added.]
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3.3
loss modulus
M′′
imaginary part of the complex modulus
Note 1 to entry: It is a measure of the energy lost (dissipated) during a loading cycle.
Note 2 to entry: Loss moduli in tension, shear and compression are denoted as E′′, G′′ and K′′, respectively.
Note 3 to entry: It is expressed in pascals (Pa).
[SOURCE: ISO 472:2013, 2.559, modified — Notes to entry have been added.]
3.4
loss factor
tan δ
ratio of the loss modulus (3.3) to the storage modulus (3.2) measured in tension, shear, compression or
longitudinal compression
Note 1 to entry: It is given by the quotient tan δ = M′′/M′
.
[SOURCE: ISO 472:2013, 2.557, modified — the definition has been revised.]
3.5
time-temperature superposition
TTS
principle by which, for visco-elastic materials, time 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 logarithmic time axis
Note 1 to entry: In case of dynamic measurements, the term “frequency-temperature superposition” would be
more accurate, but is less commonly used. The term “method of reduced variables” is also used to refer to this
principle.
[SOURCE: ISO 18437-2:2005, 3.3, modified — “frequency axis” has been replaced by “logarithmic time
axis” and Note 1 to entry has been added.]
3.6
thermorheologically simple material
material for which time-temperature superposition (3.5) is applicable
Note 1 to entry: A material which fails to superimpose, due to multiple transitions or crystallinity is, for example,
thermorheologically complex.
Note 2 to entry: In thermorheologically complex systems, all relaxation times at a certain temperature may
not be simply related to the relaxation times at a different temperature by a constant ratio. Thus, a multiphase
system is thermorheologically complex if the individual shift factors (3.7) depend on time as well as temperature.
3.7
shift factor
lg a
T
measure of the amount of shift along the logarithmic (base 10) axis of frequency for one set of constant-
temperature data to superimpose upon another set of data
Note 1 to entry: The expression “shift factor” commonly refers to horizontal shift factor.
[SOURCE: ISO 18437-2:2005, 3.4, modified — Note 1 to entry has been added.]
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3.8
vertical shift factor
lg b
T
measure of the amount of shift along the logarithmic (base 10) axis of modulus to account the effect of a
change from reference temperature to the temperature of interest
3.9
master curve
curve constructed by time-temperature superposition (3.5), which is identical to the behaviour of
material that would be found (measured) at broad frequency range at the reference temperature if the
experiment can be performed
4 Prediction of complete range of visco-elastic properties and description of data
4.1 Time-temperature superposition (TTS) principle
TTS is the most widely-used method for the accelerated prediction of complete visco-elastic behaviour
[13]
of materials . TTS is applied as follows: a series of dynamic mechanical experiments is carried
out at different constant temperatures over a given short frame of frequencies, commonly called the
experimental window. Thus, a set of isothermal segments of dynamic visco-elastic function is obtained.
The isotherms are first shifted vertically, to account for temperature and density change and then
horizontally along the logarithmic frequency scale towards a reference segment measured at reference
temperature, T . The curve constructed by TTS is called a master curve. TTS asserts that the resulting
R
master curve is identical to the behaviour of a material if it was measured with a broad frequency range
at the reference temperature. The result of applying TTS to isotherms measured within experimentally
reasonable frequency frames is a measure of material behaviour over a broad frequency range.
[17]
NOTE 1 Loss factor, as the ratio between loss and storage data, does not require vertical shifting .
[13]
There are several criteria for the applicability of TTS .
a) The shapes of the isotherms at different temperatures shall match over a substantial range of
frequencies.
b) The same values of shift factor, a , shall superimpose all dynamic visco-elastic functions.
T
c) The temperature dependence of a shall be a smooth function of temperature with no gross
T
fluctuations or irregularities.
NOTE 2 The temperature dependence of the shift function, a , is commonly modelled with time-temperature
T
[14] [13]
superposition models, such as Arrhenius or Williams-Landel-Ferry (WLF) relationships. More information
on the WLF model is given in ISO 18437-4 and ISO 4664-1.
4.2 Data acquisition
4.2.1 New data
The acquisition of new data shall be sufficiently detailed with enough temperatures and frequencies
so as to provide sufficient overlap of the frequency data points when shifted from one temperature to
another. An example of good quality data are dynamic mechanical analyser (DMA) data taken every
5 °C using frequencies of: 0,1; 0,2; 0,3; 0,5; 1; 2; 3; 5; 10; 20; and 30 Hz and/or the dynamic data which
has one decade of overlapping between neighbouring isotherms along the logarithmic frequency axis.
Theoretically, TTS is not limited to any frequency range of experimental window. However, the
frequency range shall be selected in line with other existing standards and capabilities of a measuring
instrument.
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The temperature range shall be defined according to capabilities of an experimental setup, taking into
account that the maximum temperature shall be limited to the temperature at which the sample still
sustains its geometry, i.e. does not change geometry due to its own weight.
4.2.2 Existing data
If the existing data meet the criteria in 4.2.1, then they may be processed in the same way as new data.
If the data are isochronal or do not have sufficient overlapping, then the corresponding experiments
shall be carried out in accordance with the requirements given in this document.
[15]
If this is not possible, then an alternative method that is not part of this document can suffice but
shall not be construed to be part of this document.
4.2.3 Data scatter and determination of thermorheological simplicity
If the material is thermorheologically simple, a is a smooth function of temperature with no gross
T
fluctuations or irregularities and there is only one transition in the complete spectrum of frequencies
and temperatures, then a plot of the loss factor versus storage modulus (called a wicket plot) will be a
[15]
simple smooth curve, usually of an inverted “U” shape .
NOTE If there is more than one temperature transition in a polymer but all have the same shift function, a
T
, then all the temperature and frequency data will still reduce to a single wicket plot curve but that curve will not
be a simple single inverted “U”.
The wicket plot shall be used as a quantitative indication of the scatter of experimental data. The
width of the band of data, as well as the departure of individual points from the centre of the band, is
indicative of scatter. Individual points that are sufficiently displaced from the smooth wicket plot band
shall be removed or the data shall be repeated to determine its validity. Nothing is revealed about the
accuracy of the temperature and frequency data or about any systematic error.
Figure 1 is an example of a wicket plot.
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ISO 18437-6:2017(E)

Key
X lg Young’s modulus, in Pa
Y loss factor
Figure 1 — Example of a Wicket plot of computer-generated data for a high loss material with a
maximum 10 % error in modulus and maximum 10 % error in loss factor
4.3 Shifting
4.3.1 Vertical shifting
Storage and loss data shall be firstly adjusted vertically and then shifted horizontally.
Frequently for solid visco-elastic materials the vertical shifting is small and may be ignored when
[14]
forming master curves by TTS . However, for some visco-elastic materials and/or certain testing
conditions, e.g. broad temperature range, the vertical adjustment of dynamic visco-elastic functions
can be significant. The lack of implementation of vertical shifting can lead to substantial errors in the
prediction of properties over a wide frequency range. Therefore, vertical shifting shall proceed any
horizontal shifting.
4.3.2 Horizontal shifting
[16][17]
The closed form shifting (CFS) algorithm for calculation of horizontal shift factors shall be used
whenever sufficient data are available to use this method. The method is based on the assumption that
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ISO 18437-6:2017(E)

two neighbouring segments can be superimposed when the overlapping area between them is equal
to zero.
The details of the method are beyond the scope of this document but are presented in Annex A and
Annex B.
1)
This methodology shall be used when implementing this document. As an example, a Microsoft® Excel
macro with CFS methodology is included in Annex C.
4.3.3 Dynamic visco-elastic functions master curves
Criterion b) of the applicability of TTS (see 4.1) implies that the horizontal shift factors shall be
defined from one function only. Since the storage modulus is usually measured more accurately and
has less scatter than the loss modulus or loss factor, it shall be chosen for TTS. Horizontal shift factors
determined from 4.3.2 shall be applied for shifting of other dynamic visco-elastic functions such as
loss modulus and loss factor (see ISO 18437-2 and ISO 18437-3). It shall be taken into account that loss
modulus, in the same way as storage modulus, requires vertical shifting.
A master curve of the storage modulus based on data measured at different temperatures is obtained
′
by plotting bM versus a ω using base 10 logarithmic scale for both axes.
T T
NOTE When the storage modulus is essentially flat, the loss modulus or loss factor can provide more
accurate shifting. Corresponding formulae are available in Reference [17] but are not part of this document.
5 Verification
A check of the data consistency shall be done by plotting loss factor versus the logarithmic magnitude
of the storage modulus without regard to temperature or frequency to verify that it is a single smooth
band of data. For more details, see 4.3, ISO 18437-4 and ISO 10112.
The segments of dynamic visco-elastic functions to be shifted shall fulfil the TTS criteria in 4.1. If for
any reason the criteria are violated, the TTS in its simple form as described in 4.1 shall be rejected; no
[13]
master curve shall be drawn without subjecting the data to a more complicated analysis .
6 Main sources of uncertainty
6.1 General
Uncertainties of the shifting procedure (not the experimental technique) mostly follow from the
anomalies in measured segments due to the weaknesses of the experiment itself, such as the improper
sample preparation or sample treatment, bad clamping of the sample, improper implementation of the
experiment or improper pre-processing of the data.
The main sources of uncertainties are described in 6.2 to 6.6.
6.2 Narrow width of overlapping between the segments (isotherms)
When the experiment yields segments with narrow overlapping, the shifting may result in the master
curve and/or shift factors with a low precision. In this case, it is recommended to reestablish the
experimental procedure that will yield segments with satisfactory overlapping (see 4.2.1).
1) Excel is the trademark of a product supplied by Microsoft®. This information is given for the convenience of
users of this document and does not constitute an endorsement by ISO of the product named. Equivalent products
may be used if they can be shown to lead to the same results.
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6.3 Presence of big experimental error (more than 10 %) in the segments
Since the master curve is usually composed of several curves, the cumulative error will be a sum of
the errors of the individual segment shiftings. In the case of a high experimental error, the resulting
master curve will contain a higher error than the original segments. Therefore, it is recommended to
reestablish or change the selected experimental procedure that will yield segments with the acceptable,
i.e. smaller, experimental error.
6.4 Low density of experimental datum points in the segment
A small number of datum points in the segment leads to poor approximation of the overlapping between
the segments. It is recommended to reestablish or change the selected experimental procedure that will
yield the number of datum points sufficient to describe all the peculiarities of the individual segment.
6.5 Inappropriately arranged input data — presence of “end effects” in the segments
When the experiment yields segments with certain anomalies at the beginning and/or at the end of
[18] [19]
the segment (segments with “end effects”), say, due to local overheating or inertia effects , it is
necessary to remove these anomalies before applying the shifting procedure. It is a matter of a critical
judgement whether to exclude the complete segment or just a part representing the “end effects”.
6.6 Selection of reference temperature
The most reliable master curve will be achieved when a central segment is selected as a reference
segment. This is explained by the accumulation of error from segment to segment when shifting the data.
7 Results and processing
7.1 Data presentation
7.1.1 Data obtained in this document shall be presented in the form of several graphs and tables, as
described in 7.1.2 to 7.1.6.
7.1.2 A graph of raw segments before shifting in double logarithmic (base 10) scale for moduli and in
semi-logarithmic (lin-log) scale for loss factor.
7.1.3 A graph of a master curve at selected reference temperature in double logarithmic (base 10)
scale for moduli and in semi-logarithmic (lin-log) scale for loss factor.
In order to promote uniformity and ease in interpreting the data at temperatures other than the
reference temperature, it is recommended that the master curves of storage and loss moduli and loss
factor are presented as a nomogram (see ISO 10112).
7.1.4 A table which contains
a) base 10 logarithm of horizontal shift factors for each segment, and
b) base 10 logarithm of vertical shift factors for each segment.
7.1.5 A graph of base 10 logarithm of horizontal shift factors as function of temperature at selected
reference temperature.
7.1.6 A graph of base 10 logarithm of vertical shift factors as function of temperature at selected
reference temperature.
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7.2 Test report
The test report shall include the following information:
a) a reference to this document, i.e. ISO 18437-6;
b) all details necessary for complete identification of the material tested, type, source, manufacturer’s
code number or commercial name from any previous history, when these are known;
c) all details on methods, sample geometry and preparation used for input data measurements;
d) the estimated level of error (uncertainty) in the input data;
e) a table of raw data;
f) details on data treatment, if it was performed, e.g. elimination of bad input data;
g) the reference temperature for master curve generation;
h) the graphs and table described in 7.1;
i) the date of implementing the shifting procedure.
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Annex A
(informative)

Closed form shifting (CFS) methodology
A.1 Vertical shifting
The vertical shift factor, b , is represented by the ratio shown by Formula (A.1):
T
ρT
b = (A.1)
T
ρ T
RR
where
T is the temperature of interest (K);
T is the reference temperature (K);
R
3
ρ is the density of a polymer at the temperature of interest (kg/m );
3
ρ is the density of a polymer at the reference temperature (kg/m ).
R
In the case when the ratio of densities is not known, the vertical shift factor shall be defined as shown
by Formula (A.2):
bT= /T (A.2)
TR
A.2 Horizontal shifting of two segments
The CFS methodology for calculation of horizontal shift factors is based on the assumption that two
neighbouring segments can be superimposed when the overlapping area between them is equal to
[16][17]
zero . The overlapping area is an area between two adjacent segments, which is bounded from the
left and right sides by overlapping parts of the segments and from top and bottom with the
...