Archimedes.ing.Unibs.it Andrea Bibliografia Gomma Fatica Int-Jou-Fatigue-27 Kim

A study on the material properties and fatigue life of natural

rubber with different carbon blacks

J.-H. Kima, H.-Y. Jeongb,*

aKorea Railroad Research Institute, 360-1, Woulam-Dong, Uiwang-City, Kyounggi-Do 437-050, South KoreabDepartment of Mechanical Engineering, Sogang University, 1 Shinsoo-Dong, Mapo-Gu, Seoul 121-742, South Korea

Received 14 November 2003; received in revised form 6 April 2004; accepted 9 July 2004

Abstract

Natural rubber compounds filled with N330, N650 or N990 were experimentally investigated in order to examine the effects of carbon

black on the fatigue life, the hysteresis, the fracture surface morphology and the critical J-value. The fatigue life was obtained by conducting

a displacement-controlled fatigue test on an hourglass-shaped specimen, and the hysteresis was calculated from the loading and unloading

curves obtained during the fatigue test. The fracture surface obtained after the fracture test was examined by a microscope, and its roughness

was calculated for the surface profile obtained by using a stylus-type roughness tester. In addition, the critical J-value was obtained by

conducting a tensile test for pre-cracked dumbbell specimens. Based on the test data, it was noticed that the fatigue life, the hysteresis, the

small-scale roughness and the critical J-value were ranked in the following order for the NR compound filled with N330, N990 or N650. It

was also noticed that the logarithmic value of the fatigue life was linearly proportional to the square root of the product of the critical J-value

and the hysteresis.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Carbon black; Natural rubber; Fatigue life; Critical J-value; Hysteresis; Fracture surface morphology; Roughness

1. Introduction

Carbon black is used as a reinforcement to increase the

structural and thermal properties of NR (natural rubber).

When a rubber component filled with carbon black is under

loading, the rubber matrix around carbon black is strained

more than the rest. If a large or repeated force is applied,

carbon black is separated from the matrix nucleating

microcracks. There are other sources of microcracks in

rubber including contaminants or voids in the matrix,

imperfectly dispersed compounding ingredients, mold

lubricants and surface flaws [1,2]. Upon further loading,

the microcracks coalesce resulting in a noticeable crack that

may lead to failure [3]. On the torn surface of stronger

elastomers vertical steps are more frequent and larger, and

each step is associated with a carbon black particle [4].

0142-1123/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijfatigue.2004.07.002

* Corresponding author. Fax: C82 2 712 0799.

E-mail address: [email protected] (H.-Y. Jeong).

Therefore, it is important to figure out the characteristics

and effects of carbon black in order to understand the

material behavior of NR.

For this purpose, many researchers have studied the

characteristics and effects of carbon black using diverse

methods. Greensmith [5] investigated the effect of carbon

black on the tearing behavior of NR and SBR (styrene

butadiene rubber, then called GR-S), and he discovered

that the reinforcement of carbon black was effective only

in a limited range of temperature and rate of crack

propagation. Hess and Ford [6] reviewed microscopy of

filled rubbers, and they showed evidence that a micro-

crack nucleated from a carbon black, and a crack followed

a path through reagglomeration areas. Lake and Lindley

[1] investigated the effects of deformation, testing

environment, protective agents and fillers on the fatigue

life and the crack growth rate, and they noticed that the

crack growth rate decreased by addition of carbon black

especially small carbon black particles such as HAF (high

abrasion furnace), and the fatigue life of NR decreased

International Journal of Fatigue 27 (2005) 263–272

www.elsevier.com/locate/ijfatigue

Table 1

Characteristics of NR compounds filled with N330, N650 and N990

N330 N650 N990

CB particle

diameter (nm)

30 61 285

Specific weight 1.1245 1.1485 1.2270

CB phr 46 54 90

Volume fraction (%) 16.8 18.4 28.0

Total phr 171.26 183.00 219.26

Curing time (s) 420 420 420

Curing temperature (8C) 173 173 173

Hardness 62 62 62

J.-H. Kim, H.-Y. Jeong / International Journal of Fatigue 27 (2005) 263–272264

less than that of SBR as temperature increased. Goldberg

et al. [7] investigated the effect of carbon black loading on

stretching, tearing and failure of NR and SBR, and they

noted that knotty tearing was more frequently observed in

NR than in SBR, and the tearing energy increased as the

loading increased from 0 to 35 phr. Chung et al. [8]

measured the tearing energies of SBR, HNBR (hydrogen-

ated nitrile rubber) and NR with different loading of

carbon black, and they noticed that the tearing energy

became maximized around the loading of 40 phr in SBR

and NR, but the effect of carbon black on the tearing

energy was not considerable in NR because of crystal-

lization occurring in front of a crack. Wang [9]

thoroughly reviewed the effect of carbon black on

dynamic properties of filled vulcanizates such as the

elastic modulus, the viscous modulus and the loss tangent,

and he noted that the loss tangent was dependent on the

temperature, the strain amplitude and the loading of

carbon black. Legorju-jago and Bathias [10] investigated

the effects of the load ratio, the temperature, the thickness

and the stress state on the fatigue life and the crack

growth rate of NR, CR (polychloroprene rubber) and

SBR, and they noticed that for the high load ratio or

thickness, the fatigue life of NR increased because of

crystallization.

However, no research was conducted on the change of

the material property and the failure behavior of filled NR

due to different types of carbon black. Thus, in this paper

the material properties (the critical J-value and the

hysteretic loss), the fatigue life and the fracture mor-

phology of NR compounds filled with three types of

carbon black, N330, N650 and N990, were experimentally

obtained. The fatigue life was measured for an hourglass-

type specimen under a displacement control with three

different amplitudes. The fracture morphology was

examined not only by photos but also by fracture surface

roughness. In addition, the roughness was classified into a

large-scale roughness and a small-scale roughness. By

reviewing the experimental data, several interesting points

could be noted. First, the material properties, the fatigue

life and the fracture morphology became different due to

variant types of carbon black. Secondly, the trend of the

large-scale roughness was opposite to that of the small-

scale roughness, and the critical J-value increased as the

small-scale roughness increased. Thirdly, the logarithmic

value of the fatigue life for each of the displacement

amplitude was linearly proportional to the square root of

the product of the critical J-value and the hysteretic loss.

Thus, the logarithmic value of the fatigue life could be

represented as a function of the displacement amplitude,

the critical J-value and the hysteretic loss. This implies

that the fatigue life of a rubber component can be

predicted from the displacement amplitude and the

material properties such as the critical J-value and the

hysteretic loss.

2. Experimental results

2.1. NR filled with three types of carbon black

In this research, NR compounds filled with three kinds of

carbon black, N330, N650 and N990, were investigated.

Table 1 shows the characteristics of the NR compounds

along with carbon black. Carbon black can be classified into

the small, medium and large size according to ASTM

D1765 [11], and a representative carbon black for each size

was selected. When a rubber component is under develop-

ment in industry, the static stiffness of a rubber component

is usually specified. Since there is a relationship between

Young’s modulus and the hardness of rubber, the hardness

can be determined from the required static stiffness [12,13].

For this study, the amount of carbon black in each

compound was determined in a way that the hardness of

the rubber compound remained the same at 62. In addition,

the hardness was measured using durometer type A on a

compression specimen of diameter of 28.8 mm and height

of 12.5 mm [14,15].

2.2. Fatigue life

The hourglass-shaped specimen designed by Takeychi

et al. [16] was used to measure the fatigue life of the filled

NR compounds, and it is shown in Fig. 1. It has an elliptical

cross section, and the seam line is located on the surface of

the minor axis. Since the stress on the surface of the major

axis is higher than that on the surface of the minor axis, a

crack usually starts at the major axis, and the seam line

hardly affects the fatigue life of the specimen. The fatigue

test was conducted at room temperature, 23 8C, and it was

displacement-controlled using MTS810. The displacement

was prescribed as a sinusoidal pulse at the frequency of 1 Hz

with the maximum displacement of 16, 19 or 22 mm and the

minimum displacement of 0 mm. Thus, the maximum

displacement was equal to the double displacement

amplitude, and the load ratio, which is defined to be the

ratio of the minimum load (or displacement) to the

maximum load (or displacement), was equal to 0. During

the test, the specimen was air-cooled to keep the

temperature around 23 8C. The fatigue life was defined to

Fig. 1. Hourglass-shaped fatigue test specimen (all dimensions in mm).

J.-H. Kim, H.-Y. Jeong / International Journal of Fatigue 27 (2005) 263–272 265

be the cycle at which the load became half the load

measured at 10,000 cycles.

Three fatigue tests were conducted at three different

double displacement amplitudes for each type of carbon

black. Table 2 shows the average and the standard deviation

of the fatigue life of the NR compounds. As expected, the

fatigue life reduced as the amplitude increased. Regardless

of the amplitude, the NR filled with N650 resulted in the

shortest fatigue life, but the NR filled with N330 resulted in

the longest fatigue life. However, there were comparatively

small deviations among tests showing the repeatability of

the test. Previous research showed that the fatigue life of NR

is dependent on testing environment [1], the load ratio [10]

and additives [17]. In addition, this study showed that the

fatigue life is also dependent on the type of carbon black.

2.3. Measurement of the hysteresis

Rubber has a characteristic of viscoelasticity resulting in

an energy loss during a cyclic loading. The energy loss is

called the hysteresis (or hysteretic loss), and it eventually is

converted to heat causing temperature increase [18]. Since

the temperature increase gradually degrades rubber, it

is important to understand the mechanism and effects of

Table 2

Fatigue life test data (cycle)

N330 N650 N990

Double amplitude

of 16 mm

Ave. 625,800 213,940 457,310

Std. 7860 34,150 6720

Double amplitude

of 19 mm

Ave. 480,650 98,930 323,860

Std. 10,530 7200 5550

Double amplitude

of 22 mm

Ave. 382,210 41,110 214,340

Std. 6140 1040 14,000

the hysteretic loss. The specimen shown in Fig. 1 was also

used to measure the amount of hysteresis, and the conditions

were the same as that for the fatigue test. It is well known

that the material properties of NR change during the first set

of loadings due to so-called Mullins effect [19]. Thus, the

hysteresis was measured after several thousands of loadings.

For example, when the double displacement amplitude was

22 mm, the specimen was loaded up to 10,000, 15,000, and

20,000 cycles, and the force vs. displacement curve was

measured for the next 100 cycles. Then, the hysteresis was

obtained from the average of the energy loss occurring for

the 100 cycles. The number of cycles for the first

measurement, 10,000 cycles, was chosen at about a quarter

of the minimum fatigue life which occurred for the rubber

compound with N650 at the fatigue test with the amplitude

of 22 mm. When the amplitude was 16 or 19 mm, the cycles

for which the hysteresis was measured were higher than

those for the amplitude of 22 mm.

Three sets of tests were conducted for each test

condition, and the averages and the standard deviations of

the hysteresis for three rubber compounds are shown in

Table 3. As expected, the hysteresis increased as the

amplitude increased. Note that the hysteresis was ranked in

the following order for the rubber compound filled with

N330, N990 or N650, and there were negligible deviations

showing the repeatability of the test.

Carbon black particles are firmly fused together in

rubber, and the smallest discrete entity existing in rubber is

always the aggregate [20]. By virtue of their irregular

morphology, the aggregates are bulky, and occupy an

effective volume considerably larger than that of carbon

black itself. The bulkiness of the aggregate is the property

commonly called structure. It is adequate to describe carbon

black morphology by two parameters—one related to the

structure and the other to the mean particle size.

The most commonly used techniques for measuring

carbon black structure have been based on internal void

volume using absorptive measurements or volumetric

measurements under pressure [20]. Dibutylphthalate

(DBP) is continuously added using a constant rate buret to

dry carbon black in an internal mixer fitted with a device

measuring the torque on the mixer blades. When the

interstices between carbon black particles are filled with

DBP, an appreciable torque level is developed, and the

absorptometer and buret will shut off automatically. The

volume of DBP per unit mass of carbon black is the DBP

Table 3

Hysteresis test data (N mm)

N330 N650 N990

Double amplitude

of 16 mm

Ave. 355.3 44.5 205.3

Std. 7.8 1.6 3.3

Double amplitude

of 19 mm

Ave. 465.5 47.4 276.3

Std. 0.9 0.4 0.8

Double amplitude

of 22 mm

Ave. 487.1 49.3 359.3

Std. 5.4 1.3 3.3

Table 4

DBPA number and CTAB surface area of N330, N650 and N990

N330 N650 N990

DBPAa (cm3/100 g) 100 129 35

CTABa (m2/g) 84 38 9

a Carbon black science and expanded. Marcel Dekker; 1993. p. 113.

Fig. 2. Dumbbell specimen used to measure the critical J-value (all

dimensions in mm).


absorption (DBPA) number. The test method for DBPA

number determination is described in ASTM2414-00 [21].

The traditional particle size count of electron micro-

graphs is difficult and inherently imprecise. Thus, the

specific surface area is determined instead. The absorption

of cetyltrimethyl ammonium bromide (CTAB) by carbon

black in an aqueous solution is a method for surface area

determination. This method covers the measurement of the

specific surface area of carbon black exclusive of area

contained in micropores too small to admit CTAB

molecules, and it is described in ASTM 3765-99 [22].

The amount of hysteresis depends on both the structure

and the surface area per unit volume of carbon black

aggregate [23]. In Table 4, the DBPA number and the

CTAB surface area are shown for the three types of carbon

black. If the structure of carbon black aggregate develops

well, the carbon black aggregate is more likely to be cut off

by a blade in the mixing process, and new surface is more

likely to be created. This causes stronger cohesion and

smaller friction between rubber and carbon black, sub-

sequently resulting in less hysteresis. When the specific

surface area of carbon black is high, there occurs more

friction between rubber and carbon black, subsequently

resulting in more hysteresis. Therefore, the hysteresis

increases as the DBPA number decreases or the CTAB

surface area increases. Data in Table 4 indicate that the

structure of N650 was well developed, and the surface area

of the carbon black was comparatively small. Therefore, the

hysteresis of the NR filled with N650 turned out to be the

smallest. The opposite situation happened to N330, and

the hysteresis of the NR filled with N330 turned out to be

the largest.

Hysteresis of an elastomer can be approximately

obtained from the loss tangent multiplied by input energy

[24]. In addition, the loss tangent is a function of the strain

amplitude, temperature as well as the type of carbon black.

As an example, the loss tangent of filled SBR has a critical

temperature around 0 8C below which it decreases but over

which it increases as the CTAB surface area increases [9].

Therefore, the ranking of hysteresis of the three filled NR

compounds could change at different temperatures, and the

hysteresis obtained from this study should be accepted with

caution.
Table 5
Critical J-value of NR compounds filled with N330, N650 or N990 (N/mm)

N330 N650 N990

Ave. 1.416 0.379 1.167

Std. 0.012 0.019 0.030

2.4. Measurement of the critical J-value

Since the fatigue life depends on the growth of a crack,

which is related to the critical J-value, it is important to

investigate the effect of carbon black on the critical J-value.

Thus, the critical J-value of the NR compounds was

measured. Based on the method of Begley and Landes

[25], the critical J-value was measured using the dumbbell

specimen shown in Fig. 2 [26]. For each type of the NR

compound, a set of five specimens were pre-cracked, the

crack length ranging from 1 to 3 mm, every 0.5 mm apart.

The specimen was stretched under the standard speed of

500 mm/min using UTM (Universal Test Machine).

The J-value can be calculated from the following

equation:

J ZK1

B

vU

va

� �D

(1)

Here, B is the thickness of the specimen, U is the strain

energy, a is the crack length, and D is the displacement. The

J-value is the amount of decrease of the strain energy per

unit area of new crack surface with the displacement fixed.

While the specimen was being loaded, it was video-

recorded by a digital motion camera. The moment when

the geometry around the crack became asymmetric with

respect to the crack line was regarded as the moment of the

crack growth [7], and the J-value at the moment was

assumed to be the critical J-value. Thus, the critical J-value

is the same physical quantity as the tearing energy [27].

The critical J-value remained almost the same regardless

of the pre-crack length, and the test showed a good

repeatability. Thus, only the average and the standard

deviation of the critical J-values for the NR compounds

obtained for three sets of five specimens are shown in

Table 5. Note that the critical J-value is ranked in the

following order for the compound filled with N330, N990 or

N650, which is in the same order for the fatigue life and the

hysteretic loss. The critical J-value of the NR filled

with N330 is smaller by a factor of about 3 than that of

gum NR and filled NR measured by Chung et al. [8].

This difference stemmed from different definitions on

Fig. 3. Large-scale fracture surface.


the moment of the crack growth. The process of crack

growth can be described by two steps [8]. First, the crack

starts at one or two spots on the inside surface of the tip, then

it propagates across the thickness of the specimen to form a

full initial crack before it propagates along the width of the

specimen. In this study, the moment of the crack growth was

defined to be the time when the crack surface lost its

symmetry, but Chung et al. defined the moment to be the

time when a full crack through the thickness started to grow.

Thus, the crack growth defined in this study happened

earlier, and the critical J-values measured turned out to be

smaller.

2.5. Measurement of the fracture surface morphology

In general, fracture surface morphologies give infor-

mation about failure process and mechanisms [3]. As shown

in Fig. 3, the (large-scale) fracture surface morphologies of

the three types of the NR compounds look quite rough.

Thus, the stereo optical microscope that had a poor depth of

focus could not be used for the analysis of the fracture

surfaces. Instead, LG DSP color camera, a microscope for

the inspection of semiconductor, which had a good depth of

focus, was used and its magnification was from !100 to !1000. The large-scale and the small-scale fracture surface

morphologies of the NR compounds are shown in Figs. 3

and 4, respectively. Figs. 3 and 4 show that the NR

compound filled with N330 or N990 has many small humps,

but the NR compound filled with N650 has a small number

of large humps. In other words, the NR compound filled

Fig. 4. Small-scale fr

with N330 or N990 has a smoother surface in the large-scale

but a rougher surface in the small-scale than the NR

compound filled with N650.

To quantify the roughness of the fracture surfaces, the

profile of the fracture surfaces was obtained by using a

stylus type roughness tester, and the root-mean-square

(RMS) roughness was employed. Moreover, the RMS

roughness was calculated in two different scales. The

profile along the major axis of 14 mm long was obtained,

and the RMS roughness was calculated for the profile. This

roughness was named the large-scale roughness in this

paper. The profile of four 1 mm long segments along the

major axis was obtained, and the average of the roughness

of the four segments was assumed to be the RMS roughness

for the profile. This roughness was named the small-scale

roughness. The large and small-scale RMS roughness data

are shown in Tables 6 and 7, respectively. It is striking to

notice that the order of magnitude of roughness is opposite

to each other; the order of large-scale roughness is N650ON990ON330, but the order of small-scale roughness is

N330ON990ON650.

Fukahori and Andrews [28] found out that the hyteresis

of highly deformable polymers decreased as the fracture

surface roughness increased. As shown in Fig. 5, the

hysteresis of the NR compounds studied in this paper

decreased as the large-scale roughness increased. However,

as shown in Fig. 6, the hysteresis increased as the small-

scale roughness increased. Therefore, when the roughness

of a NR compound is examined, the scale should be taken

into account, otherwise the conclusion would be opposite.

acture surface.

Table 6

Large-scale RMS roughness data (mm)

N330 N650 N990

Ave. 0.311 0.771 0.425

Std. 0.012 0.027 0.066

Table 7

Small-scale RMS roughness data (mm)

N330 N650 N990

Ave. 0.095 0.028 0.045

Std. 0.040 0.008 0.017

Fig. 6. Hysteresis as a function of the small-scale roughness.


Note also that the test data are located near the regression

line in Fig. 5, but they are located off the regression line in

Fig. 6. The poor linearity of the test data shown in Fig. 6

stemmed from the fact that the small-scale roughness was

obtained for four short profiles, and it in itself had a high

variance relative to the average value (refer to Table 7). In

other words, the small-scale roughness is quantitatively less

reliable than the large-scale roughness. However, the trend

of the small-scale roughness is correct in that the small-scale

roughness increases as the critical J-value increases (refer to

Fig. 8). As Gent and Pulford [4] noted, vertical steps are

more frequent, higher and less spaced on the torn surfaces of

tougher elastomers, and the spacing is in the order of 10 mm.

Therefore, the small-scale roughness should be higher for

tougher elastomers.

Table 8

Carbon black dispersion data

N330 (%) N650 (%) N990 (%)

1 99.90 98.10 98.40

2 99.70 96.90 97.80

3 99.70 97.20 97.70

Avg. 99.77 97.40 97.40

2.6. Analysis of the carbon black distribution

The fracture surface was sliced to a thin sheet using a

glass knife in liquid nitrogen. Three locations on the thin

sheet were randomly selected to examine the carbon black

distribution using an optical microscope. Each location was

a square of 1 mm!1 mm, and it was divided into 10,000

cells. The dispersion of carbon black agglomerates was

Fig. 5. Hysteresis as a function of the large-scale roughness.

examined, and Table 8 shows the percentage of cells in

which carbon black agglomerates were observed, proving

that they were well distributed in all three NR compounds.

Then, the number of cells in which an agglomerate of

carbon black larger than 50 mm2 existed was counted, and

the diameters of those large agglomerates were also

measured. In Fig. 7, the number of cells is shown as a

function of the diameter of the agglomerates. In the rubber

compound filled with N330, an agglomerate with diameter

of 9 or 10 mm was observed in one or two cells. In the

rubber compound filled with N990, an agglomerate with

diameter of 9 or 10 mm was observed in seven or three cells,

Fig. 7. Diameter and frequency of carbon black agglomerates.

Fig. 8. Critical J-value as a function of the small-scale roughness.


and an agglomerate with diameter of 12 mm at highest was

observed. However, in the rubber compound filled with

N650, an agglomerate with diameter of 9 mm was observed

in ten cells, and even an agglomerate with diameter of about

15 mm was observed. This observation on the distribution is

compatible with the DBPA numbers shown in Table 4. In

the case of the NR compound filled with N650, for example,

the DBPA number is high. This means that the carbon black

is well developed, and the agglomerate of the carbon black

is big.

Knotty tearing is an important aspect of the reinforcing

mechanism of carbon black, and it results in a rough torn

surface and a high critical J-value [5]. For the NR

compounds studied in this paper, the critical J-value was

also high when the small-scale roughness was high, as

shown in Fig. 8. The rubber compound filled with N330 had

a rough surface in the small-scale, and its critical J-value

turned out to be high. This means that the carbon black,

N330, formed small agglomerates, which acted as a local

stress raiser. The small agglomerates deflected the direction

of a crack growth causing the knotty tearing [29]. However,

the rubber compound filled with N650 had a clean surface in

the small-scale, and its critical J-value turned out to be low.

This means that the carbon black, N650, formed large

agglomerates, which were easily separated from the rubber

matrix. Thus, a crack propagated rapidly creating a cleaner

surface in the small-scale.

Fig. 9. Logarithmic value of the fatigue life as a function of

[(JC/EL)(hysteresis/EV)]1/2.

3. Function of the fatigue life

NR has good mechanical characteristics of large elastic

deformation and damping. In addition, it can be readily

manufactured at a comparatively low cost. Because of

these characteristics, rubber is widely used in numerous

products such as automobiles, locomotives and commod-

ities [30]. However, a rubber component is susceptible to

fatigue failure, and its durability is one of the major

concerns. Thus, when a rubber component is under

development using various compositions, the fatigue life

of the component is to be measured from a fatigue test,

which usually takes a long period of time. If the fatigue

life of a rubber component can be predicted from material

properties which can be obtained from simple exper-

iments, it can save time and efforts to select a composition

which results in the best durability.

By reviewing the experimental data obtained from this

study, it was easily noticed that the fatigue life increased

as the critical J-value or the hysteresis increased. After

trying many different functional forms, it was finally

noticed that the logarithmic value of the fatigue life was

linearly proportional to the square root of the product of

the critical J-value and the hysteresis. In Fig. 9, the

logarithmic value of the fatigue life is shown with respect

to the square root of the product of the critical J-value and

the hysteresis. For the case of N650 for which the value

of the square root was low, the fatigue life was also low.

In contrast, for the case of N330 for which the value of

the square root was high, the fatigue life was also high.

As mentioned previously, the fatigue life increased as the

displacement amplitude decreased. The regression lines

for the test data are also shown in Fig. 9, and it is

noteworthy that they fit the test data well for all three

displacement amplitudes. Thus, the regression lines can be

expressed as the following Eq. (2)

logðNfÞ Z AJC

EL

� �Hysteresis

EV

� �� 12

CB (2)

Here, Nf is the number of cycles at failure, JC is the

critical J-value, and A and B are proportionality constants

which are different for a different displacement amplitude.

Since the fatigue life is given in cycles, i.e. it is

dimensionless, the right-hand side of Eq. (2) should be

made dimensionless by dividing the critical J-value and

the hysteresis by some representative values, E, L and V,

Fig. 10. Coefficient A as a function of the double displacement amplitude

(R2Z0.9777).Fig. 12. Comparison of the fatigue life equation with test data for the double

displacement amplitude of 16 mm (R2Z0.9621).


of the rubber specimen. E is the representative Young’s

modulus of the rubber compounds, and it is given as a

function of IRHD (International Rubber Hardness Degree)

as long as the hardness of the rubber is between 30 and 85

IRHD [12,13]. In addition, hardness measured by

durometer type A is compatible with that in IRHD [12].

Since the NR compounds studied in this paper had the

same hardness, 62, the representative Young’s modulus

turned out to be 3.87 MPa. L was selected to be the radius

of the minor axis, i.e. LZ5 mm. In addition, V was

assumed to be the volume of the most deformable part of

the specimen, i.e. between K2.5 and C2.5 mm from the

middle plane of the specimen, and it turned out to be

549.78 mm3. However, note that as long as the same

specimen is used to evaluate the fatigue life, any

representative value can be used. Even if a different

representative value is used, the constant A will be

adjusted accordingly.

Fig. 11. Coefficient B as a function of the double displacement amplitude

(R2Z0.9956).

The constants A and B are shown with respect to the

double displacement amplitude D in Figs. 10 and 11,

respectively. Note that there is a linear relationship of A or B

to the double displacement amplitude. Thus, A and B can be

expressed as a function of D as shown in the following Eqs.

(3) and (4)

A Z a CDb

L(3)

B Z c CDd

L(4)

Plugging Eqs. (3) and (4) into (2), the logarithmic value

of the fatigue life can be expressed as a function of the

critical J-value, the hysteresis, and the double displacement

amplitude as in the following Eq. (5)

logðNfÞ Z a CDb

L

� �JC

EL

� �hysteresis

EV

� �� 12

C a CDd

L

� �

Z 0:623JC

EL

� �hysteresis

EV

� �� 12 d

L

� �

K0:135JC

EL

� �hysteresis

EV

� �� 12

K4:878D

L

� �C7:4 (5)

In order to evaluate the adequacy of the final equation,

the equation is shown graphically along with the test data

for the amplitude of 16 mm (shown in Fig. 12), 19 mm

(shown in Fig. 13) and 22 mm (shown in Fig. 14). Note that

the equation is in good agreement with the test data for all

three amplitudes. In other words, the fatigue life can be

Fig. 13. Comparison of the fatigue life equation with test data for the double



predicted from the displacement amplitude and the material

properties, the critical J-value and the hysteresis, which can

be obtained from simple tests. Therefore, it may be said that

when a rubber component is under development using

various compositions, a composition for which the product

of the critical J-value and the hysteresis is the highest will

result in the best durability.

In this study, the hysteresis was measured from the same

specimen and at the same deformation mode as the fatigue

life was evaluated. If hysteresis had been measured from a

different specimen or at a different deformation mode, the

fatigue life prediction equation (5) would not be in good

agreement with the test data mainly because hysteresis is

dependent on the strain amplitude and the load ratio [9,10].

Therefore, in order to predict the fatigue life based on the

critical J-value and the hysteresis, more reliable prediction

will be obtained if the hysteresis is measured at the same

deformation mode and for the same rubber component for

which the fatigue life is to be predicted.

Fig. 14. Comparison of the fatigue life equation with test data for the double


4. Conclusion

In this paper, NR compounds filled with three types of

carbon black, N330, N650 and N990 were experimentally

investigated in order to evaluate the effects of carbon black

on the fatigue life, the hysteresis, the critical J-value and the

fracture morphology. By reviewing all the test data, the

following conclusions could be reached.

(1)
The fatigue life, the hysteresis and the critical J-value
were ranked in the following order for the NR

compound filled with N330, N990 or N650.

(2)
The small-scale roughness showed a trend opposite to
that of the large-scale roughness. The hysteresis or the

critical J-value increased as the small-scale roughness

increased.

(3)
In the NR compound filled with N650, there existed
large carbon black agglomerates, which separated from

the rubber matrix comparatively easily. Thus, the

fatigue life of the NR compound filled with N650 was

shorter, and its fracture surface was cleaner in the small-

scale than that of the NR compound filled with N330 or

N990.

(4)
The logarithmic value of the fatigue life of the NR
compounds was linearly proportional to the square root

of the product of the critical J-value and the hysteresis.

In addition, the proportionality constants were linearly

proportional to the double displacement amplitude.

Thus, the logarithmic value of the fatigue life could be

expressed as a function of the double displacement

amplitude, the critical J-value and the hysteresis.

Acknowledgements

The specimens were provided by Pyoung Hwa Industrial

Company, and some experiments were conducted at

Hankook Tire R&D Center. All of these supports are highly

appreciated.

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