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Thermomechanical Characterization of Carbon Black Reinforced Rubbers During Rapid Adiabatic Straining


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The thermo-mechanical properties of carbon black reinforced natural and styrene butadiene rubbers are investigated under rapid adiabatic conditions. Eleven carbon black grades with varying surface area and structure properties at 40 parts per hundred (phr) loading are studied and the unreinforced equivalents are included for reference. The results show a strong correlation of the modulus, mechanical hysteresis, temperature rise and calculated crystallinity of the rubbers measured in tensile extension with strain amplification factors. This highlights the influence of matrix overstraining on microstructural deformations of the rubber upon extension. The strain amplification factors are calculated via the Guth-Gold equation directly from carbon black type and loading, allowing a correlation of the fundamental morphological properties of carbon black with thermal and mechanical properties of rubbers upon extension. Analysis of the thermal measurements of the rubber compounds upon extension and retraction and contrasting between crystallizing and non-crystallizing rubbers reveals that a substantial irreversible heat generation is present upon extension of the rubber compounds. These irreversible effects most likely originate from microstructural damage mechanisms which have been proposed to account for the Mullins Effect in particle reinforced rubbers.
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Thermomechanical Characterization
of Carbon Black Reinforced Rubbers
During Rapid Adiabatic Straining
William Amoako Kyei-Manu
*, Lewis B. Tunnicliffe
, Jan Plagge
, Charles R. Herd
Keizo Akutagawa
, Nicola M. Pugno
and James J. C. Buseld
School of Engineering and Materials Science, Queen Mary University of London, London, United Kingdom,
Birla Carbon,
Marietta, GA, United States,
School of Mathematics and Natural Sciences, Bergische Universität Wuppert al, Wuppertal,
Laboratory of Bio-Inspired, Bionic, Nano, Meta Materials & Mechanics, Department of Civil, Environmental and
Mechanical Engineering, Università di Trento, Trento, Italy
The thermo-mechanical properties of carbon black reinforced natural and styrene
butadiene rubbers are investigated under rapid adiabatic conditions. Eleven carbon
black grades with varying surface area and structure properties at 40 parts per
hundred (phr) loading are studied and the unreinforced equivalents are included for
reference. The results show a strong correlation of the modulus, mechanical
hysteresis, temperature rise and calculated crystallinity of the rubbers measured in
tensile extension with strain amplication factors. This highlights the inuence of matrix
overstraining on microstructural deformations of the rubber upon extension. The strain
amplication factors are calculated via the Guth-Gold equation directly from carbon black
type and loading, allowing a correlation of the fundamental morphological properties of
carbon black with thermal and mechanical properties of rubbers upon extension. Analysis
of the thermal measurements of the rubber compounds upon extension and retraction and
contrasting between crystallizing and non-crystallizing rubbers reveals that a substantial
irreversible heat generation is present upon extension of the rubber compounds. These
irreversible effects most likely originate from microstructural damage mechanisms which
have been proposed to account for the Mullins Effect in particle reinforced rubbers.
Keywords: carbon black, strain amplication, thermomechanical characterization, strain induced crytallization,
elastomer, Mullins effect, thermography, hysteresis
Particle reinforced rubbers are an important class of materials. Despite their ubiquity, there is still a
lack of understanding of the mechanisms controlling their behaviors at both small and large strains.
In this article we focus on effects at large strains (strains >50%). Figure 1 illustrates the complex
strain and strain history dependence of a typical particle reinforced rubber. The cyclic stress
softening and strain history dependence are often referred to as the Mullins effect (Mullins, 1948). In
addition, hysteresis and set effects are also present. Despite intensive investigation, the
microstructural origins of this large strain behavior and the Mullins Effect are still not entirely
clear. Theories to account for the pronounced stiffening (stress upturn) observed at very large strains
include approaching the nite extensibility of the rubber network and also the self-reinforcement for
rubber materials able to undergo strain induced crystallization. Strain history and hysteresis effects
are commonly ascribed to several prosed microstructural damage mechanisms (Diani et al., 2009)
Edited by:
Dong Xiang,
Southwest Petroleum University,
Reviewed by:
Sanjay Mavinkere Rangappa,
King Mongkuts University of
Technology North Bangkok, Thailand
Xiaodong Qi,
Southwest Jiaotong University, China
William Amoako Kyei-Manu
Specialty section:
This article was submitted to
Polymeric and Composite Materials,
a section of the journal
Frontiers in Materials
Received: 17 July 2021
Accepted: 23 September 2021
Published: 15 October 2021
Kyei-Manu WA, Tunnicliffe LB,
Plagge J, Herd CR, Akutagawa K,
Pugno NM and Buseld JJC (2021)
Thermomechanical Characterization of
Carbon Black Reinforced Rubbers
During Rapid Adiabatic Straining.
Front. Mater. 8:743146.
doi: 10.3389/fmats.2021.743146
Frontiers in Materials | October 2021 | Volume 8 | Article 7431461
published: 15 October 2021
doi: 10.3389/fmats.2021.743146
which include: chain breakage at the interface between the rubber
and reinforcing particulates, slippage of rubber macromolecules
at the particle interface leading to a stress redistribution to
neighbouring molecules, rupture of occulated clusters of
reinforcing particulates, progressive chain disentanglements,
covalent bond scission and crosslink rupture (Clough et al.,
2016) and yielding and rebirth of glass-like immobilized
bridges between adjacent particles (Merabia et al., 2008)A
common feature of all these proposed damage mechanisms is
that they are associated with dissipation of strain energy in the
form of heat.
When particulate reinforced rubbers are deformed in uniaxial
tension, the heat evolved (Gough, 1805;Joule, 1859) can be
attributed, to various degrees, to the intrinsic entropic
elasticity (Meyer and Ferri, 1935;Anthony et al., 1942) and
viscoelasticity (Payne and Whittaker, 1972) of the rubber
matrix and to the hysteretic breakdown of the particulate
network within the rubber (Grosch et al., 1967). Where
rubbers are amenable to strain induced crystallization (SIC),
the heat of fusion of the crystallites at high global strains may
also contribute substantially to the observed evolution of heat
from the specimen. These effects are strain and strain rate
dependent (Tosaka, 2007;Brüning et al., 2015).
More recent numerical (Behnke et al., 2016;Dhawan and
Chawla 2019) and experimental (Samaca Martinez et al., 2013;
Samaca Martinez et al., 2014;Spratte et al., 2017)
thermomechanical studies have expanded on these concepts.
Akutagawa et al. (2015) concluded that temperature changes
during stretching and retraction of rubber can be reduced to two
processes: reversible and irreversible processes. Entropy elasticity
and SIC are reversible processes whereas the hysteretic
breakdown of the particulate network (particle-particle and
particle-polymer breakdown) are irreversible. Le et al. (2020)
conducted thermo-mechanical experiments on rubber and
developed a quantitative model for the temperature variation
caused by isentropic, entropic and viscous dissipation effects
under steady state uniaxial tensile cyclic loading. Le Cam et al.
(2015) used a calorimetric approach to characterize several
important effects such as entropic elasticity, reinforcement by
particulates, strain-induced crystallization and Mullins effect of
lled and unlled natural rubber (NR) and styrene butadiene
rubber (SBR). Similarly, Le Saux et al. (2013) used a calorimetric
approach to detect the onset strains for SIC and correlated this
with data from X-ray measurements in literature.
SIC signicantly enhances a number of mechanical properties
of rubber compounds including crack growth resistance and tear
resistance and tensile failure properties. These improvements in
compound properties are traced back to a retardation of
catastrophic and/or incremental crack growth due to
crystallization of a portion of the highly strained rubber ahead
of a crack tip (Brüning et al., 2013). NR exhibits SIC because close
to 100% of its poly-isoprene chains have cis-conguration
(Huneau, 2011;Gent, 2012). This stereo-regular structure of
NR enables the polymer chains to crystallize either at low
temperatures and/or at high strains, leading to a pronounced
self-reinforcement. Despite this intrinsic reinforcement
mechanism, unlled NR compounds are unable to provide
sufcient mechanical reinforcement, notably abrasion
resistance, to be of practical use in many engineering
applications and is therefore further reinforced by
incorporating ne particulates such as carbon black (CB).
Both SIC and the inclusion of CB play critical roles in the
reinforcement of rubber products.
Various researchers have investigated the effect of CB on SIC
in NR. Lee and Donovan (1987) showed that the inclusion of CB
facilitates SIC and increases the size of the crystallized zone at
the stressed crack tip. Trabelsi et al. (2003) demonstrated that in
NR reinforced with 50 parts per hundred rubber (phr) CB, the
onset strain for SIC was 100%, versus 300% for unreinforced
NR. This reduction in global onset strains for SIC was attributed
to matrix strain amplication due to the presence of rigid CB
within the rubber. This process was rst proposed by Mullins
and Tobin (1966) to explain the stiffening effect that reinforcing
particles such as CB had on rubbers. The presence of rigid
particles within the rubber causes local overstraining of the
rubber matrix when compared with the applied macroscopic
strain level. Trabelsi et al. (2003) observed two different regions
of strain amplication: a lower strain region where SIC has not
occurred and in which the strain amplication factor is
independent of applied global strains and a region where SIC
has occurred and strain amplication is weakly dependent on
applied global strain. The reduction in onset strain of SIC due to
the inclusion of reinforcing particulates was also observed by
Chenal et al. (2007) who found that the extent of SIC and onset
strain required for SIC also depends on the cyclic strain history
of the reinforced rubber. Raultetal.(2006)studied SIC and
reinforcement in CB reinforced rubbers in relation to strain
amplication factors. From their analysis of the strain
amplication factors, they observed that in rubbers that do
not undergo SIC, reinforcement in lled rubbers has two causes:
overstraining/strain amplication of the chains due to a purely
geometrical effect and particles acting as new effective crosslinks
within the rubber. The latter point of view is shared by Plagge
FIGURE 1 | Complex stress-strain behavior observed in 50 parts per
hundred (phr) N550 carbon black reinforced natural rubber under cyclic tensile
extension. Tests were done at a rate of 500 mm/min at room temperature.
Frontiers in Materials | October 2021 | Volume 8 | Article 7431462
Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
and Lang (2021) who related the large-strain stiffening to the
physicochemical compatibility of carbon black and rubber.
When the samples crystallize, the crystallites act as giant
cross-links causing the stress to increase drastically with
macroscopic extension. Raultetal.(2006)also observed that
the addition of small amounts (20 phr) of CB strongly decreases
the onset strains required for SIC. They hypothesize that this is
due to the CB particles acting as crystal nucleation sites. This
point of view is supported by a recent work by Sotta and Albouy
(2020), where the SIC-related hysteresis of NR is traced back to
nucleation-limited crystallization during stretching.
Many of these aforementioned studies have utilized X-ray
scattering techniques to directly study SIC. Recently, two research
groups, M. Klüppel and co-workers (Plagge and Klüppel, 2018)
and J. B. Le Cam and co-workers (Le Cam et al., 2020), have lead
efforts to measure SIC from the increase in temperature upon
extension of rubber. While such thermographic techniques do
not necessarily provide details on the structure of the crystallites
formed, it might potentially provide a much more accessible way
to determine the degree of crystallization in stretched rubber. For
the case of particle reinforced rubbers, thermal characterization
during extension also captures the heat generated from non-SIC
related mechanisms (particle network breakdown, polymer-
particle de-cohesion etc.).
Furthermore, although there have been numerous previous
studies on the effect of CB on mechanical and thermal properties
of rubber, there has been limited effort to correlate these effects
with the fundamental size and morphological properties of
carbon black. This is an important step to make, since these
CB properties are already extensively utilized by rubber
compound designers to engineer various properties of their
compounds to meet end user requirements. Further
quantitative understanding of their effects on SIC and other
thermomechanical properties of rubbers offer potential for
enhancement of rubber product performance.
This study evaluates the evolution of mechanical and thermal
properties of NR and SBR compounds reinforced with different
types of CB subjected to rapid adiabatic cyclic stretching and
retraction. The mechanical results are analyzed in the context of
the well-established strain amplication model. The temperature
changes during stretching and retraction are similarly analyzed
and extraction of information on the crystallization process is
attempted. By contrasting NR compounds which are amenable to
SIC to those which are notStyrene Butadiene Rubber (SBR),
various contributions to the observed stress and temperature
changes upon extension and retraction are qualitatively
Compounds of SMR CV60 NR reinforced with eleven different
CB grades at 40 parts per hundred rubber (phr) loading were
prepared. An unreinforced NR counterpart was also included in
the tests. The range of CBs used in this study was selected to cover
a broad range of surface area and structure space as shown in
Figure 2. The insert in Figure 2 shows a schematic representation
of an aggregate of CB and representative images from TEM for
N772, N330, N326 and N134 CBs using the same scale bar of
100 nm. The aggregate is comprised of a fused assembly of para-
crystalline primary particles. The size of the primary particles is
the key parameter determining the surface area of the CB while
the number and spatial arrangement of the primary particles
FIGURE 2 | Colloidal plot of carbon blacks studied in this article. A measure of the structure (COAN) is plotted against a measure of the surface area (STSA). Insert:
Schematic of the primary particle-aggregate hierarchical structure of carbon black and representative TEM images of N772, N326, N330 and N134.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
denes the structure level of CB. The surface area of carbon black
is typically determined using nitrogen gas adsorption methods
such as the nitrogen surface area (NSA) and statistical thickness
surface area (STSA) methods (ASTM International, 2019) The
structure level of CB is determined by measuring the amount of
oil that is absorbed by a specic amount of carbon black-Oil
absorption number (OAN) and compressed oil absorption
number (COAN) methods (ASTM International, 2019;ASTM
International, 2019).
Unreinforced emulsion SBR 1502 and SBR reinforced with
N220 and N772 CBs at 40 phr were also prepared. These
compounds were included to contrast with the NR
compounds as SBR, unlike NR, does not undergo SIC. Table 1
shows the compositions of the various compounds used in this
study. Table 2 gives the compound properties such as densities
measured using a pycnometer and specic heat capacities
measured using a differential scanning calorimeter.
Interferometric microscope (IFM) dispersion index values are
given in Table 2. IFM dispersion characterizes the level of
incorporation of the CB into the rubber compounds on the
macroscale and is a quantication of undispersed carbon black
at a length scale greater than 5 µm diameter. Values of DI greater
than 90 indicate an excellent dispersion. IFM DI measurements
were performed according to ASTM D2663-14 (2019) method D.
Table 2 also presents the surface area (NSA, STSA) and
structure (OAN, COAN) properties of the CBs in the
compounds. Compounds were prepared by Birla Carbon
(Marietta, GA, United States) using a 1.6 L capacity Banbury
mixer and vulcanized sheets measuring 11 mm ×11 mm ×
2 mm were prepared by compression molding at 150°C for
NR samples and 160°C for SBR samples to a time of T
where T
(time taken at 150°C/160°C for the specimen to reach
90% of maximum torque) was measured using an Alpha
Technologies moving die rheometer (MDR). The mixing
procedure is included in the supplemental information.
Experimental Method
Dumbbells for uniaxial extension and retraction experiments
were cut from vulcanized sheets using a hydraulic die press.
The dumbbells had approximate gauge length, width and
thickness of 45, 6 and 2 mm respectively. To investigate
thermal responses under adiabatic conditions, the samples
were deformed using an Instron 8801 hydraulic mechanical
testing machine equipped with a 1 kN load cell. The tests were
run in a position-control mode with the lower grip moving to the
targeted position(s). The specimens were extended to target
uniaxial strains of 150, 250 and 350% at speeds of 20,000 mm/
min giving a strain rate of about 7.40 s
and a stretching time of
0.5 s for the maximum strain of 350%. For contrast, Candau et al.
(2012) determined the time needed for NR to crystallize once
samples are elongated above the critical elongation for SIC as
0.02 s during cyclic tensile tests at high strain rates from 8 s
280 s
. After straining, the samples were held at the maximum
TABLE 1 | Composition of tested compounds.
Component Loading/parts per hundred (phr)
Natural rubber Styrene butadiene rubber
NR SMR CV (60) 100 NA
SBR 1502 NA 100
Carbon black 40 40
Zinc oxide 5 3
Stearic acid 3 1
Sulphur 2 1.75
N-Tertiarybutyl-2-benzothiazole sulfenamide.
TABLE 2 | Colloidal
and compound properties and calculated strain amplication of tested compounds.
Natural rubber compounds
Carbon black
Carbon black properties Compound properties Strain amplication
Heat capacity,
N234 116 110 126 104 1.119 1.314 92 3.102
N134 140 130 125 104 1.120 1.406 91 3.100
N339 91 88 121 99 1.108 1.301 98 2.998
N220 110 103 113 99 1.104 1.348 97 2.991
N115 131 116 112 93 1.111 1.350 94 2.865
N330 76 76 102 89 1.111 1.374 97 2.794
N550 38 38 121 83 1.113 1.303 99 2.678
N660 35 34 93 75 1.106 1.308 95 2.515
N326 77 77 73 73 1.115 1.370 92 2.485
N772 32 31 69 62 1.114 1.351 78 2.290
N990 11 10 34 34 1.114 1.296 96 1.853
Unlled NA NA NA NA 0.976 1.564 NA 1.000
Styrene Butadiene Rubber Compounds
N220 110 103 113 99 1.119 1.292 98 2.991
N772 32 31 69 62 1.122 1.314 93 2.290
Unlled NA NA NA NA 0.976 1.635 NA 1.000
NSA is nitrogen surface area, STSA is statistical thickness surface area, OAN is oil absorption number and COAN is compressed oil absorption number.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
strain for 2 min to regain thermal equilibrium before being
rapidly retracted to zero strain at the same strain rate. This
process was repeated 10 times for each specimen with three
specimens being measured for each compound.
The specimen temperature was measured using a FLIR A35
(focal length 9 mm) infrared camera. The camera has a thermal
sensitivity/noise equivalent temperature difference (NETD) of
<0.05°C at +30°C/50 mK and an IR resolution of 320 ×250 pixels.
The camera was turned on 2 h prior to the measurements to
ensure the internal temperature of the camera was stabilized. The
acquisition frequency was set to the maximum rate of 60 Hz. The
mean average temperature of a rectangle covering a pixel area of
about 225 pixels was used to track and measure the temperature
in the center of the specimen during straining and retraction
using the FLIR Research IR software. The emissivity was set to
0.95 which is a reasonable approximation for CB reinforced
rubber (Browne and Wickliffe, 1979;Luukkonen et al., 2009).
The ambient room temperature was measured by placing a black
body in the view of the camera and this was veried with a
standard thermocouple.
The mechanical and temperature data were recorded on the
1st, 5th and 10th loading and unloading cycles to investigate the
effect of Mullins softening on mechanical properties and
temperature evolution. However, due to the high permanent
set of the lled samples, particularly at high strains, the
samples at 350% were re-gripped prior to the 5th and 10th cycles.
Strain Amplication
The results obtained from the thermomechanical experiments are
quantitatively discussed using strain amplication factors, X.Itis
therefore necessary to discuss how these are calculated for the
purpose of this paper. Mullins and Tobin (1966) proposed the
general concept that when rigid particles are introduced into a
rubber matrix they cause greater average deformation on the local
scale, εlocal versus the globally applied strain level, εglobal.
εlocal Xεglobal
Xis therefore a strain amplication factor that quanties the
degree to which the applied global strain is amplied on average
at the local scale level. Models with varying levels of
sophistication can be used for calculating the strain
amplication factor (Huber and Vilgis 1999;Klüppel 2003;
Allegra et al., 2008;Domurath et al., 2012), with each having
distinct advantages and limitations.
In this paper, we use the simple and widely used Guth-Gold
equation which predicts the strain amplication in the compound
from the effective volume fraction of particulates in the
X1+2.5φeff +14.1φ2
The Guth-Gold equation was developed for spherical particles at
low to moderate volume fractions (Mullins and Tobin 1966). The
Guth-Gold equation does not account for any substantial
networking of particulates within the rubber-which commonly
occurs at small to moderate strains-nor any breakdown of the
particle-particle network or de-cohesion of the particle-rubber
interface. This assumes therefore that Xis independent of applied
strain level.
The effective volume fraction of CB in each compound, φeff ,is
dened as the volume fraction of the carbon black in the rubber
plus the volume fraction of rubber occluded from global strain by
the CB aggregate structure. In practice it is calculated using the
actual volume fraction of CB, φand the compressed oil
absorption number (COAN) which is a measure of the
structure of carbon black aggregates. This approach is based
on the method initially developed by Medalia (1972) and later
modied by Wang et al. (1993). They considered the end point of
absorption titration of CB with a specic volume of oil and de-
convoluted the intra-aggregate and inter-aggregate oil volumes in
the oil/CB cake at the end of the test. The permeated equivalent
sphere volume and inter-aggregate oil volume are calculated by
assuming that the equivalent spheres pack randomly at a volume
fraction of 0.63. The effective volume fraction in a rubber
compound, φeff is then given by the following equation where
Vpis the permeated volume of equivalent spheres, Vfis the
volume of ller, Vvis the volume between the permeated
equivalent spheres, and ρCB is the density of the CB.
φeff φ1+e
φeff φ0.0181COAN +1
φphr CB
phr CB
ρCB +phr NR
}phr CB}and }phr NR}are the ller loadings of carbon black
and natural rubber respectively in the compound. ρCB and ρNR
are the densities of carbon black and natural rubber which are
taken as 1.81 g
cm3and 0.92 g
cm3respectively based on Birla Carbon
Tunnicliffe (2021a) recently demonstrated that the Guth-Gold
strain amplication factor can be used to scale fatigue crack
growth resistance of CB reinforced NR and showed good
correlations between calculated strain amplication factors and
the state of strain immediately ahead of crack tips in NR Liu et al.,
2015.Trabelsi et al. (2003) also showed that experimentally
measured strain amplication factors were in good agreement
with the Guth-Gold equation. The calculated strain amplication
factors of the tested specimen are listed in Table 2.
Calculating the Extent of Crystallinity from
Thermal Measurements
The methods for calculating crystallinity directly from
temperature measurements are described in detail in Plagge
and Klüppel (2018) and Le Cam et al. (2020). Le Cams
method is a four step approach that is based on quantitative
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
calorimetry and temperature measurements. To date it
currently has not been applied to reinforced rubber
materials and will be the objective of subsequent studies.
Plagge and Klüppels method depends on an energy balance
process where the mechanical energy input δW, is balanced
with the internal energy, dU, and heat exchange with the
environment, δQ. The internal energy is split into a kinetic
part which measures microscopic excitations such as vibration,
translation and rotation in terms of the heat capacity, Cp,
density, ρ, and change in sample temperature and energy gain
from crystallization which is labelled as Uc. It is assumed here
that all the energy gained is due to crystallization and ignores
non-reversible energy dissipation mechanisms in lled rubber
such as particle-particle and particle-polymer breakdown. The
calculated crystallinity is therefore very likely over estimated
by this calculation.
The resulting equation is similar to the rst law of
thermodynamics (written per volume) as follows:
UcEnergy for Crystallization
The greatest uncertainty in using this approach is how to
determine the amount of heat, δQexchanged with the
environment through convection and radiation. It requires
using an algorithm to optimize functions that smoothly vary
with time. Rapid extension and retraction rates minimize heat
exchange with the environment as discussed in Heat Exchange
Characterization Section, and this allows us to assume adiabatic
conditions and ignore this contribution. The total energy and
index of crystallization is therefore simply calculated without
UcEnergy for Crystallization
KApparent Crystallinity Percentage
where Kwhich is the percentage of the rubber that is crystalline is
calculated from the enthalpy of fusion of the pure polymer, ΔH,
which is estimated to be about 61 J cm
for NR. For the lled
compounds, Kis normalized by taking into account the ller
volume fraction, φfiller.
Heat Exchange Characterization
A fundamental solution to the heat diffusion equation (Plagge
and Klüppel, 2018) is:
T(x, t)1
where xis the thickness of the specimen, κis the thermal
diffusivity and tis time elapsed. From the exponent, the
timescale of heat diffusion therefore scales as
For rubber, κ1.5 x107m2
sand for our samples,
xsample thickness
21×103m and hence τ1.7s.
This implies that an inhomogeneous temperature eld within
the rubber strip (size 2 mm) will equilibrate in approximately
2 s. Due to the rapid extension and retraction, the timescale of the
experiments are of the order of milliseconds; well within the
timescale of heat diffusion. The temperature measurements are
therefore more likely the real localized temperature of the samples
instead of an averaged one due to diffusion.
To characterize the adiabatic nature of the current experimental
set up, a specimen similar to those used in the main experiments of
this work was heated in an oven for about 3 h at 60°Ctoensurea
homogenous temperature distribution. The specimen was then
quickly gripped in the testing machine and the natural return to
room temperature was recorded as a function of time. A heat
exchange equation (based on a best tlinewithanR
value of 0.97,
see Supplemental Data sheet) which considers the experimental
set up and environment was obtained from this graph as
T17.02 eΔt
where Tis the temperature variation and tis the time elapsed.
The maximum time for extension/retraction in our experiments
is about 0.5 s, which produces a 0.08°C temperature variation to
the environment. This drop is very close to the smallest
temperature resolution of <0.05°C at +30°C/50 mK of the
infrared camera.
Mechanical Properties
Stress-Strain and Mooney-Rivlin Curves
Figures 3ACshows the stress-strain curves for the 1st, 5th and
10th cycles of CB reinforced and unreinforced NR specimens
when extended to 350% strain and retracted following a 2 min
hold. There is a clear distinction between the initial extension
curves depending on the CB types. The CBs with higher strain
amplication factors, which is the result of higher structure level
of the CB, have a higher incremental modulus response versus
CBs with lower strain amplication factors and hence a lower
structure. This is illustrated in Figure 3D where the measured
stress at 300% strain is plotted versus the compound strain
amplication factor. Strong linear correlations between the
stress value at 300% and strain amplication factors are
observed for each cycle level (R
values are indicated in the
Figure). Upon retraction of the specimens however, there is
minimal distinction between the stress-strain curves of the
different compounds. This is an interesting observation which
requires additional investigation, including a further analysis of
the polymer and CB-related stress relaxation occurring during the
2 min hold period. Subsequent papers, would attempt to
decompose the contribution of the stress relaxation resulting
from strain induced crystallization and post-stretch relaxation
based on a model proposed by Tosaka et al. (2006).
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
It has been shown by different authors (Mullins and Tobin
1966;Mark and Erman 2007) that the Mooney-Rivlin relation
can be used to describe the stress-strain behavior of rubber at
nite extensions. Typically stress-strain data plotted according to
the Mooney-Rivlin model show a large and abrupt increase in
modulus at high elongations which corresponds to a signicant
stiffening of the rubber. The molecular origin for this upturn is
widely debated. Most attribute it to the limit of the nite
extensibility of the network chain (Treloar 1975). Others have
attributed it to crystallization upon stretching since experiments
in NR showed the upturns diminish with increase in temperature
and swelling (Su and Mark, 1977). The reduced stress is
calculated and plotted as a function of the inverse of extension
ratio in Figure 4 for cycles 1, 5 and 10.
Reduced Stress σ
where σis the engineering stress and λis the extension ratio. C1
and C2are constants where C2is the straight line portion of the
graph and C1+C2is the intercept on the vertical axis (Mooney
1940;Rivlin 1948;Treloar 1975)
The qualitative shapes of the stress-strain extension curves and
Mooney-Rivlin curves differ between different cycles. Cycles 5
and 10 have a more distinct sigmoid shape with an upward
inection of the curve at strains greater than about 150% for the
extension curves. The Mooney-Rivlin curves also show an upturn
in stress on cycles 5 and 10 at higher strain values. This stress
upturn is due to the progressive crystallization of the NR which
stiffens the specimen and/or from the rubber macromolecules
approaching nite extensibility. On the 1st cycle of the stress
strain curve, however, this upturn is not as distinct. The upturn in
stress on the 1st cycle is almost gradual and starts at lower strains
compared to cycles 5 and 10 for the Mooney-Rivlin curves as well.
These differences are likely due to the differences in
microstructural damage history between the 1st and
subsequent cycles. As discussed in the introduction, such
damagecould be the result of CB aggregate-aggregate
network breakdown, polymer-particle de-cohesion and sliding,
and disentanglement of the rubber network (Toki et al., 2013).
Mechanical Hysteresis
The hysteresis losses in rubber are an important factor
inuencing the rubbers fracture properties. Hysteresis losses
dissipate energy input into the rubber thereby increasing the
threshold required for fracture. The mechanical hysteresis is
calculated as the difference between the area under the loading
and unloading curves and plotted as functions of the strain
FIGURE 3 | Stress-strain plots of carbon black reinforced and unreinforced natural rubber extended to 350% strain and retracted after a 2 min hold on cycles 1, 5
and 10. Tensile stress at 300% strain as a function of strain amplication factor for cycles 1, 5 and 10.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
amplication factor in Figure 5. Similar to the tensile stress at
300%, the mechanical hysteresis strongly scales with the strain
amplication factor. This observation indicates that selection of
CB structure level is important in determining the moduli and
mechanical hysteresis of the rubber compound at nite strains.
Note that this contrasts with the effect of CB on hysteresis at small
to medium strains (the strain range under consideration when
examining the Payne Effect), where the surface area of the carbon
black generally dictates the levels of hysteresis (Fröhlich et al.,
2005,Tunnicliffe (2021b).
Temperature Measurements
Figure 6 is the temperature, stress and strain as a function of time
for the 1st cycle of the N234 CB reinforced NR strained to 350%,
held for about 2 min and retracted. The signicantly slower rate
of cooling during the 2 min hold in comparison to the timescale
of heating and cooling during extension and retraction highlights
that the thermal measurements are conducted under adiabatic
conditions. The stress drops signicantly in the rst few seconds
of the 2 min hold, another interesting observation, which a
further analysis of the polymer and CB-related stress
relaxation during the 2 min hold period will help explain.
The rise and drop in temperature of the specimens extended to
350% and then retracted are plotted in Figure 7 for the rst cycle.
Analogous to the mechanical data, there is a clear distinction
between the temperature rises upon extension depending on CB
type, but minimal differences between the samples upon
retraction. Processes such as breakdown of the CB network
and strain-induced crystallization dissipate energy during
extension causing the observed temperature rise.
Temperature Rise Temperaturefinal Temperatureinitial
Temperature Drop Temperaturefinal Temperatureafter2minhold
function of the calculated strain amplication factor for strains of
350% (black), 250% (yellow) and 150% (red) for cycles 1, 5 and 10 in
Figure 8. The data above Temperature Change 0°C show a rise in
temperature and those below 0°Creect a drop in temperature.
From the graph there is a strong correlation of the rise in
temperature with strain amplication factormirroring the
observation for the corresponding mechanical data. As strain
amplication increases, the rise in temperature increases, as does
the measured stress at a given strain level. There seems to be no
apparent correlation with drop in temperature upon retraction.
Again this is an area for further investigation. During repeated
cycling of the materials, the maximum achieved temperature change
upon extension is reducedmost notably between the 1st and 5th
cycles. Conversely, the magnitude of temperature change upon
retraction appears to be broadly unaffected by cycle number.
FIGURE 4 | Mooney-Rivlin plots of carbon black reinforced and unreinforced natural rubber extended to 350% strain on cycles 1, 5 and 10.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
Figure 9 plots the peak stress upon extension and the
corresponding temperature rise upon extension for all strains
and cycles for all NR compounds. All the points collapse on a
master curve with reasonable correlation (R
independent of the cycle number, strain level or CB type,
suggesting the CB structure controls the maximum stress and
corresponding temperature rise.
Strain Induced Crystallization Estimations
Using the approach detailed in Calculating the Extent of
Crystallinity from Thermal Measurements Section, the apparent
crystallinity percentage was estimated for NR specimens after the
1st, 5th and 10th cycles. Figures 10A,B show the graphs of the
calculated apparent crystallinity percentage upon extension and
retraction respectively to and from 350% strain on the 1st cycle.
Mirroring the stress-strain and temperature change graphs
discussed in Mechanical Properties Section and Temperature
Measurements Section, there is a clear distinction between the
calculated apparent crystallinity percentages formed upon
extension dependent on the type of CB, but the extent of
percentage crystallinity change upon retraction is largely
indistinguishable between compounds. Figures 11ACplots
the peak apparent crystallinity for each compound at 150, 250
and 350% extension, for the 1st, 5th and 10th cycles, as a function
of strain amplication factor. The calculated crystallinity extent
correlates well with the strain amplication factors, with a higher
strain amplication factor leading generally to a higher
crystallinity value, as would be anticipated from a simple
consideration of matrix overstraining. The calculated
crystallinity extents are observed to decrease successively on
FIGURE 5 | Mechanical hysteresis on cycles 1, 5 and 10 as a function of strain amplication factor of natural rubber samples extended to 350% strain.
FIGURE 6 | Temperature prole, stress and strain as a function of test
time for N234 reinforced natural rubber rapidly extended to 350% strain, held
for 2 min and rapidly retracted.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
each cycle. For contrast, in situ Wide Angle X-ray synchrotron
(WAXS) experiments conducted on 45 phr N234 reinforced NR
extended at a strain rate of 0.25 min
(0.0042 s
) produced
similar decreasing crystallinity values upon successive cycles with
maximum crystallinities of about 28, 22 and 21% on the rst,
second and third cycles at a peak strain of 250% (Chenal et al.,
Figure 11D shows the onset strain percent for crystallite
formation for each compound also plotted as a function of the
strain amplication factor. Higher strain amplication generally
FIGURE 7 | Temperature rise and temperature drop of carbon black reinforced and unre inforced natural rubber extended to 350% strain and retracted after a 2 min
hold for 1st cycle.
FIGURE 8 | Temperature change as a function of strain amplication factor of carbon black reinforced and unreinforc ed natural rubber extended on cycles 1, 5 and
10. Positive values are the temperature rise upon extension and negative values are the corresponding temperature drop upon retraction.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
leads to an earlier onset of the crystallinity. The onset strain
percent for crystallinity also shows a slight increase (shift to
higher strains) after the rst cycle-similar to that reported by
Chenal et al. (2007) who observed an increase in onset strain
percent until a stable value is reached typically after three to ve
It appears from Figure 10 that not all crystals formed upon
extension are melted during retraction. The maximum
percentage change in crystallinity upon retraction is always
signicantly lower than the maximum percentage change in
crystallinity during extension. These ndings are problematic
for the following reasons: 1) even when accounting for the fact
that crystallinity is known to persist for a while during retraction
(Treloar 1975), the values in Figures 10A,B imply that the
majority of crystallites persist in the fully relaxed state
following full retraction. 2) while the crystallization extent
upon extension appears to strongly depend on the type of CB,
this dependence is lost in the retraction data, despite the fact that
the nal levels of crystallinity achieved upon maximum extension
should persist or even increase during the 2 min hold period as
the material progresses towards an equilibrium level of
crystallinity (Tosaka, 2007).
Although the data reported in Figure 10A, and Figures
11ACare in reasonable agreement with literature for direct
measurements of SIC from X-ray scattering techniques, the
inconsistency of the retraction data sets with known
phenomenological behavior of SIC implies that additional
thermal effects both upon extension and retraction are likely
inuencing the crystallinity values obtained here. For lled rubber
samples, it is challenging to use thermography alone to accurately
measure the extent of crystallinity due to the irreversible heat
generating mechanisms such as particle-particle and particle-
polymer breakdown during extension which are difcult to de-
convolute from reversible SIC effects.
Styrene Butadiene Rubber Samples
SBR is a non-crystallizing rubber and provides a useful contrast to
the NR materials. Figures 12A,B show the stress-strain curves
and Mooney-Rivlin plots for the SBR compounds strained to
350% for cycles 1, 5 and 10. Similar to the NR stress-strain data,
the reinforced SBR compounds show a sigmoid-like curve with
distinct stress upturns at high strains, which is especially
noticeable for cycles 5 and 10, despite the absence of SIC for
SBR. This highlights the pronounced reinforcement effects of CB
in non-crystallizing rubbers. Also note that the modulus/stress
builds for the SBR compounds scale as expected according to
strain amplication factors (with N220 being greater than N772).
The unreinforced SBR does not exhibit any stress upturn. It is
also worth noting that the unreinforced SBR specimens failed
during the 2 min hold period after initial extension and hence,
there is no retraction data for this compound. In comparison, the
unreinforced NR displays a moderate stress upturn (Figure 2),
and did not fail during the 2 min hold period, again highlighting
the intrinsic reinforcing effects of SIC in NR.
The Mooney-Rivlin plots also display similar trends to those
observed in the NR compounds. On the 1st cycle, the upturn in
reduced stress is observed at relatively low strain levels (100%).
However, the stress upturn shifts to higher strains (200%) after
FIGURE 9 | Master-line relating peak stress upon extension and
corresponding temperature rise at all tested strain percent and cycles.
FIGURE 10 | Apparent crystallinity percent of carbon black reinforced and unreinforced natural rubber extended and retracted at 350% strain during cycle 1.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
cycles 5 and 10. The unreinforced SBR shows no stress upturn
even at higher strains unlike the unreinforced NR specimen at
350% strain. Since the stress-strain and Mooney-Rivlin plots of
reinforced styrene butadiene rubber specimens show similar
behavior to the particulate reinforced NR specimens, it is
difcult to conclusively attribute the upturn in stress and
reduced stress observed in the NR specimens solely to the
onset of SIC. Effects of particle-particle and particle-polymer
interactions are clearly inuencing the stiffening of the materials
examined here.
Figures 12C,D show the temperature rise and drop for the
SBR compounds. Again the observed temperature rise mirrors
the evolution of stress during extension. The maximum observed
temperature rise is 13°C for the SBR compounds, which cannot
be attributed to SIC but rather to entropic elasticity and particle-
particle and particle-polymer mechanisms. When comparing
analogous SBR and NR materials head to head as shown in
Figures 13AC, the NR specimens consistently show a higher
change in temperature versus the SBR specimens. The
temperature rise of N220 reinforced NR extended to 350%
strain on the 1st cycle is 16°C while the temperature rise of
the N220 reinforced SBR is 13°C. The drops in temperature
when retracted from 350% strain on the 1st cycle is 6°C and 4°C
for the N220 reinforced NR and SBR respectively. While the
temperature drops of the SBR specimens are lower compared to
the NR specimens, it is worth highlighting the temperature drops
of the SBR specimens which are entirely due to entropic elasticity
are still relatively large. The difference in temperature evolution
between the NR and SBR specimens may be due to the additional
contribution from SIC in the NR compounds, but it is not
possible to quantitatively attribute this difference in the
temperature between the two analogous compounds directly to
SIC due to inherent differences in polymer molecular
architectures, viscoelasticity and crosslink densities.
Nevertheless, these results demonstrate that entropic elasticity
and particle-particle and particle-polymer mechanisms can
contribute substantially to thermal evolution in strained
rubbers and would need to be appropriately incorporated into
quantitative evaluations of SIC from thermal measurements in
reinforced NR compounds.
The tensile extension moduli of both the NR and SBR compounds
scale linearly with strain amplication factors. This is due to
FIGURE 11 | Apparent crystallinity percent and onset of crystallinity as a function of strain amplication factor of carbon black reinforced and unreinforced natural
rubber extended on cycles 1, 5 and 10.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
matrix overstrain effects; with the CBs with higher aggregate
structure enhancing the local strain levels. The mechanical
retraction data following the 2 min hold collapse onto each
other-independent of the type of CB. This requires further
investigation but it may be due to particle-particle and
particle-polymer breakdown effects during extension and the
2 min hold which are absent upon retraction. Further analysis
to de-convolute the contributions to the stress relaxation during
the 2 min hold will provide more insight into this.
Mechanical hysteresis scales with strain amplication factors
as well, which is most likely a reection of these experiments
being strain controlled, therefore a stiffer compound naturally
gives higher hysteresis at xed strain.
The thermal data for the NR compounds mirrors the
mechanical data with the temperature rise upon extension
scaling linearly with the strain amplication factor. Similar to
the mechanical data, this is due to matrix overstrain effects where
the carbon black aggregates with higher structure CBs enhance
microstructural heat dissipation process such as the particle-
particle and particle-polymer breakdown and SIC for the NR
compounds during extension. The peak stress upon extension
scales linearly with the corresponding temperature rise
independent of cycle number, strain level and CB type. Upon
retraction, the temperature drops show similar values,
independent of the CB type.
The temperature data of the non-crystallizing SBR suggests
that signicant temperature generation upon extension must be
related to reversible heat generation from entropic elasticity as
well as particle-particle and particle-polymer irreversible heat
generation. Substantial temperature drops upon retraction for the
SBR compounds is related primarily to entropy elasticity and the
values of the temperature drop is also very similar between the
unreinforced and reinforced SBR compounds.
The calculation of the SIC extent of the NR compounds using
the Plagge-Klüppel method shows some consistency with
literature data for direct measurement of SIC from X-ray
scattering but also produces some crucial differences. The lack
of agreement between calculated crystallinity extents upon
extension and then retraction, implies that additional,
irreversible thermal effects arising from the inclusion of
reinforcing particles are as important or maybe even dominate
over the SIC contribution to heat evolution upon extension at
these high strain rates. Further studies at varied strain rates could
help to characterize the rate dependent nature of this dissipation
FIGURE 12 | Stress-strain, Mooney-Rivlin and temperature change plots of reinforced and unreinforced styrene butadiene rubber extended to 350% strain.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
in non-strain crystallizing rubbers. For particle reinforced
rubbers, it will be necessary to quantitatively account for all
these different effects in the future analysis of thermal data sets.
Direct measurement of the SIC by X-ray scattering is planned to
help de-convolute these thermal effects.
The thermomechanical properties of CB reinforced and
unreinforced rubber compounds at large strains were
characterized under adiabatic conditions. Two major
conclusions can be drawn from the experiments:
1) Matrix overstrain effects play a signicant role on
microstructure mechanisms such as entropy elasticity,
particle-particle and particle-polymer breakdown and
SIC during extension. The modulus and temperature rise
of the compounds during extension correlated well with
calculated strain amplication factors for the various
compounds. The calculated strain amplication factors
were derived from the morphological properties of CB
and based on our results show that the CB aggregate
structure inuences these microstructural mechanisms at
large strain deformations.
2) Observed thermal effects upon extension are inuenced and
maybe even dominated by irreversible particle-particle and
particle-polymer damage effects based on comparison of the
results from non-crystallizing SBR and NR. This makes it
difcult to accurately decompose the reversible contribution of
SIC from the thermal measurements alone. Direct measurements
of SIC by X-Ray scattering are planned as a next step in this work.
From a practical standpoint, the correlation of the mechanical
and thermal effects with morphological properties of CB is
signicant since it can be a useful tool in the design of rubber
compounds for engineering applications.
The original contributions presented in the study are included in
the article/Supplementary Material, further inquiries can be
directed to the corresponding author.
WK-M conducted the experiments, analyzed the results and
contributed to the preparation of the manuscript. LT, JP, CH,
FIGURE 13 | Temperature change as a function of strain amplication factor comparing SBR (lled shapes) and NR (unlled shapes) extended to 350% (black),
250% (red) and 150% (yellow) and retracted after 2 min.
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Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
KA, NP, and JB provided signicant intellectual input and guidance
in conducting the experiments, analyzing and interpreting the results
and contributed to the preparation of the manuscript.
The PhD project for which this research work was conducted is
sponsored by Birla Carbon. NP is supported by the European
Union within the project LIFE19 ENV/IT/000213LIFE GREEN
The authors would like to thank Birla Carbon for funding and
providing the materials studied in this article.
The Supplementary Material for this article can be found online at:
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Conict of Interest: Authors LT and CH were employed by company Birla
Carbon, United States.
The remaining authors declare that the research was conducted in the absence of
any commercial or nancial relationships that could be construed as a potential
conict of interest.
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Frontiers in Materials | October 2021 | Volume 8 | Article 74314616
Kyei-Manu et al. Particulate Reinforced Rubbers Thermomechanical Characterization
... • At a practical level, the degree of mechanical hysteresis (and therefore softening) of a rubber compound at a fixed strain level scales with the virgin modulus of the compound at that strain. All other parameters being equal (such as CB volume fraction, polymer type, and crosslink density), this modulus is determined by the structure of the CB in the formulation [45]. • At a microstructural level, the strong correlation between hysteresis and CB structure provides several hints as to the origin of the Mullins-type hysteresis and softening. ...
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The influence of carbon black (CB) structure and surface area on key rubber properties such as monotonic stress-strain, cyclic stress–strain, and dynamic mechanical behaviors are investigated in this paper. Natural rubber compounds containing eight different CBs were examined at equivalent particulate volume fractions. The CBs varied in their surface area and structure properties according to a wide experimental design space, allowing robust correlations to the experimental data sets to be extracted. Carbon black structure plays a dominant role in defining the monotonic stress–strain properties (e.g., secant moduli) of the compounds. In line with the previous literature, this is primarily due to strain amplification and occluded rubber mechanisms. For cyclic stress–strain properties, which include the Mullins effect and cyclic softening, the observed mechanical hysteresis is strongly correlated with carbon black structure, which implies that hysteretic energy dissipation at medium to large strain values is isolated in the rubber matrix and arises due to matrix overstrain effects. Under small to medium dynamic strain conditions, classical strain dependence of viscoelastic moduli is observed (the Payne effect), the magnitude of which varies dramatically and systematically depending on the colloidal properties of the CB. At low strain amplitudes, both CB structure and surface area are positively correlated to the complex moduli. Beyond ~2% strain amplitude the effect of surface area vanishes, while structure plays an increasing and eventually dominant role in defining the complex modulus. This transition in colloidal correlations reflects the transition in stiffening mechanisms from flexing of rigid percolated particle networks at low strains to strain amplification at medium to high strains. By rescaling the dynamic mechanical data sets to peak dynamic stress and peak strain energy density, the influence of CB colloidal properties on compound hysteresis under strain, stress, and strain energy density control can be estimated. This has considerable significance for materials selection in rubber product development.
... The characterisation of viscoelastic material behavior is the subject of ongoing research, in which Tárrago et al. [16] investigated the properties of elastomeric bearings in radial and axial direction under small amplitudes. Regarding the self-heating behavior, Behnke et al. [17] used uniaxial multi-stage tests for characterisation, whereas Kyei-Manu et al. [18] and Suphadon et al. [19] applied the cyclic stretching process with different predeformations. Mars and Fatemi [20,21] combined axial and radial cyclic loads while identifying material parameters. ...
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The experimental investigation of viscoelastic behavior of cyclically loaded elastomeric components with respect to the time and the frequency domain is critical for industrial applications. Moreover, the validation of this behavior through numerical simulations as part of the concept of virtual prototypes is equally important. Experiments, combined measurements and test setups for samples as well as for rubber-metal components are presented and evaluated with regard to their industrial application. For application in electric vehicles with relevant excitation frequencies substantially higher than by conventional drive trains, high-frequency dynamic stiffness measurements are performed up to 3000 Hz on a newly developed test bench for elastomeric samples and components. The new test bench is compared with the standard dynamic measurement method for characterization of soft polymers. A significant difference between the measured dynamic stiffness values, caused by internal resonance of the bushing, is presented. This effect has a direct impact on the acoustic behavior of the vehicle and goes undetected by conventional measurement methods due to their lower frequency range. Furthermore, for application in vehicles with internal combustion engine, where the mechanical excitation amplitudes are significantly larger than by vehicles with electric engines, a new concept for the identification of viscoelastic material parameters that is suitable for the representation of large periodic deformations under consideration of energy dissipation is described. This dissipated energy causes self-heating of the polymer and leads to the precocious aging and failure of the elastomeric component. The validation of this concept is carried out thermally and mechanically on specimen and component level. Using the approaches developed in this work, the behavior of cyclically loaded elastomeric engine mounts in different applications can be simulated to reduce the time spent and save on the costs necessary for the production of prototypes.
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A new rheological methodology is used to quantify the kinetics and thermal activation of thixotropic recovery (flocculation) of uncrosslinked carbon black–reinforced emulsion SBR following high shears and over a range of annealing temperatures. A wide range of carbon black types are examined to determine the influence of aggregate morphology and surface area on compound flocculation. Several kinetic parameters are correlated with the carbon black aggregate structure and surface area, the results of which imply a transition in mechanisms controlling modulus recovery between shorter and longer recovery time scales. Thermal activation of flocculation is found to scale to the surface area and to the mean aggregate diameter of the carbon blacks following power law relationships. The thermal activation data for a subset of compounds with different carbon blacks prepared at different loadings collapses onto a single master line by rescaling the data to a parameter that is proportional to the theoretical interparticle force calculated for the idealized situation of two spherical particles in proximity. Three different van der Waals force models are evaluated, and in each case, an effective superposition of the thermal activation data is achieved. This indicates that the attractive force between aggregates plays a key role in the flocculation of carbon black in rubber, and this force can be traced back to the aggregate and primary particle sizes, interaggregate distances, and effective volume fractions. The activation energy for the viscosity of the unfilled, uncrosslinked SBR is similar to analogous values calculated for the thermal activation of flocculation. This coupling of energetics may be the result of creep/flow of rubber out of gaps between aggregates resulting from interaggregate attractive forces and any potential diffusive motion of the aggregates. Bound rubber data appear to contain information relating to aggregate packing, which could be exploited in future work to further explore the mechanism of flocculation.
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Fatigue crack growth behavior of carbon black–reinforced natural rubber is investigated. Rubber compounds of Shore A = 70 are prepared by varying the formulation loadings of a wide range of carbon black types based on their structure and surface area properties. The resulting fatigue crack growth behavior shows significant variation in β exponent values, depending on the properties of the carbon black. These variations are rationalized by considering the strain amplification of natural rubber by carbon black aggregates in the region of compound directly ahead of the crack tip. An assumption is made that little networking of the carbon black aggregates exists in this region of very high strain and that hydrodynamic calculations that consider occluded rubber can therefore provide realistic values for strain amplification. A reasonable scaling of power law crack growth parameters to calculated strain amplification factors is found, with the exponent, β, decreasing with increasing strain amplification. The implication here is that enhanced strain amplification promotes the formation of strain-induced crystallites in the crack tip region. Performance tradeoffs resulting from the crossover of crack growth data sets dependent on the carbon black type are discussed. Of practical significance is the fact that the strain amplification factors can be calculated directly from knowledge of carbon black type and loading in rubber formulations.
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Many theories on the origin of rubber reinforcement have been presented over the last decades. None of them explains beyond reasonable doubt why the dispersion of carbon black into a polymer matrix induces an immense improvement of ultimate properties. We present a throughout analysis of ethylene-propylene-diene rubber (EPDM), filled with carbon blacks treated at temperatures between 900 °C and 2500 °C. The fillers are investigated extensively using static gas adsorption, transmission-electron microscopy and elemental analysis. Afterwards, correlations between filler surface properties of the filler and properties of the compounds are drawn with a special focus on large-strain softening effects (Mullins’ softening). The latter successively vanishes with temperature treatment of carbon black. Moreover, the softened samples do not recover at temperatures below 100 °C or by swelling. A very simple model involving a stress-limiting process at the polymer-filler interface is derived, which reproduces the experimental results well. Equilibrium hysteresis is found to be originated in physical interaction only. It turns out that the softening-generating effect (“reinforcement”) is best explained by chemical filler-polymer bonds, successively breaking down during stretching, and low-strain modulus and equilibrium hysteresis by physical compatibility.
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The crystallinity of stretched crystallizable rubbers is classically evaluated using x-ray diffraction (XRD). As crystallization is a strongly exothermal phenomenon, quantitative surface calorimetry from infrared thermography offers an interesting alternative to XRD for determining the crystallinity. In this paper, the two measurement techniques have been used for evaluating the strain-induced crystallinity of the same unfilled natural rubber. This study provides the first comparison between the two techniques. The results obtained highlight the very satisfactory agreement between the two measurements, which opens a simple way for evaluating the strain-induced crystallinity from temperature measurements.
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Strain induced crystallization is essential to the physicochemical properties of polymer materials, but is difficult to investigate, as it usually requires X-ray sources in combination with stretching machines. We improve and validate a recently developed method which allows the calculation of the crystallinity index using easily available thermography and stress-strain data. For natural rubber, the method is shown to be reproducible and delivers results quantitatively comparable to spectroscopic methods such as wide angle X-ray scattering. The incorporation of different amounts of carbon black is shown to increase the level of crystallization and to change the shape of the strain-crystallization curves. Additionally, crystallinity during partial retraction is investigated and reveals that crystallization characteristics change at sufficiently high strain.
Rubber materials under cyclic mechanical loading show special properties compared to other materials. This research aims to quantitatively clarify the relationship between cyclic deformation and temperature variation of carbon black filled styrene-butadiene rubber (SBR) under steady state condition after the rubber is accommodated enough both mechanically and thermally. A dumbbell specimen was subjected to uniaxial cyclic tension at various loading conditions. Temperature variation on the gauge zone surface of the specimen was measured by infrared thermography. In addition to the experiment, the temperature variation of the specimen was also predicted theoretically. The prediction is composed of three parts. The first part shows a three-elements model to reproduce the mechanical behavior with considering residual strain and stress softening. The material parameters are determined to match the experimental data at each loading condition. The second part predicts the temperature variation under adiabatic condition by considering three factors: isentropic elastic, entropic elastic and viscous dissipation effects. Third, a correction scheme is proposed to consider the heat transfer between the specimen and the surrounding air or others. As a result, the temperature amplitude and phase difference between temperature and strain are predicted. The predicted results were compared with the experimental data. It is confirmed that the predicted results are in good agreement with ones obtained by the infrared thermography. Furthermore, the phase difference between temperature and strain is about 180∘ at the small deformation area (isentropic elastic effect dominated) while it is almost about 0∘ at large deformation area (entropic elastic effect dominated). In addition to this, there exists a phase transition area between these two areas. It is concluded that the proposed method is a good way to provide quantitative information of the temperature variation of rubber materials subjected to uniaxial cyclic loading under steady state.
A computational study based on molecular dynamics simulation technique has been used to predict the mechanical and thermal behavior of carbon nanotube (CNT) reinforced natural rubber (NR) composites. A single-walled 5,5 armchair type CNT has been used for this purpose. In this study, a comparison has been made between pristine and functionalized CNTs. The functionalization groups used in this study were carboxylic (COOH), ester (COOCH3) and hydroxyl (OH). The studies show the improvement in elastic properties of developed composites in the presence of functionalization group. In addition, the effect of volume fraction and 1-25% addition of functionalization group has been studied. The obtained simulation results show the better load-transfer capacity in developed polymer system and improved elastic modulus. Thermal properties of developed composite systems were studied by non-equilibrium molecular dynamics method (NEMD). The addition of functionalized CNTs shows enhanced mechanical and thermal properties.
Strain-induced crystallization (SIC) in unfilled and carbon black or silica filled Natural Rubber (NR) with and without silane is investigated. The method introduced in this paper is based on measurements of the surface temperature during tensile test, whereby SIC is quantified by dividing the produced heat into different contributions, namely the dissipative heat, entropy-related reversible heat and crystallization enthalpy. It turns out that there is pronounced SIC in unfilled and carbon black filled NR, while silica/silane systems show less SIC. The degree of crystallinity correlates with the tensile strength of the samples. For silica/silane systems at the same strain level self-reinforcement by SIC is less pronounced possibly due to a lower crosslink density or strain amplification factor. Because of its simplicity, the method developed here is a promising option to investigate SIC on a broad experimental scale and provides an alternative access next to well-established methods like WAXS.
Recent investigations of failure of rubbers and plastics have indicated that hysteresial losses in a polymer are an important factor in fracture. This communication reports experimental evidence that the energy density at break of a polymer is amply related to the hysteresis loss in the polymer. A previously unstrained sample is stressed at a constant extension rate to rupture and the mean value of the rupture load is determined from a number of these measurements. A fresh rubber test piece is then extended under the same conditions until just before rupture, and then retracted at the same rate as was used for extending the rubber. The energy at or near break is determined by measuring the area under the load extension curve, and the hysteresis loss determined from the area between the extension and the retraction curves.