EFFECT OF TENSILE RATE AND CARBON BLACK ON THE FRACTURE OF
NATURAL RUBBER AND STYRENE-BUTADIENE RUBBER
A Thesis
Presented to
The Graduate Faculty of The University of Akron
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
Qinwei Wang
May, 2013
EFFECT OF TENSILE RATE AND CARBON BLACK ON THE FRACTURE OF
NATURAL RUBBER AND STYRENE-BUTADIENE RUBBER
Qinwei Wang
Thesis
Approved:
Accepted:
_______________________________
Advisor
Dr. Gary R. Hamed
_______________________________
Dean of the College
Dr. Stephen Z. D. Cheng
_______________________________
Faculty Reader
Dr. Li Jia
_______________________________
Dean of the Graduate School
Dr. George R. Newkome
_______________________________
Department Chair
Dr. Coleen Pugh
_______________________________
Date
ii
ABSTRACT
Tensile strengths and ultimate elongations of both crystallizing NR and amorphous
SBR increase with increasing tensile rate and increasing carbon black N115 loading,
although the dependence of N115 loading is at least ten-fold stronger.
Previous research has shown that edge-cut specimens of gum NR show an abrupt
drop in tensile strength, when tested at 50 mm/min at a critical cut size, because of lack
of time to crystallize in bulk. In this thesis, the behavior of critical cut size with respect to
tensile rate is completed. Critical cut size increases monotonously, but not linearly, with
increasing tensile rate. Changes in precut tensile strength of NR at various tensile rates
are measured and compared with those of SBR. Previous research has shown a critical
loading of N115 black tested at 50 mm/min, before which precut NR will only be
weakened. In this thesis, precut tensile results of NR with various N115 black contents
were measured and compared to those of SBR. Only NR shows an critical black loading
to reinforce precut specimens and this concentration doesn’t change with tensile rate.
Reinforcement of precut NR is due to the formation of a rubber/ black network. But,
reduce tensile rate can decrease the N115 content for reinforcing NR with all possible cut
sizes. This is noted as a second turning point of black concentration.
iii
DEDICATION
To my beloved parents
Who support me all the time
And to whom I owe everything I have today
To my cherished love
Who accompanies me in distance
And to whom I have a word of promise
iv
ACKNOWLEDGEMENTS
After the accomplishment of my master thesis, I would like to express my sincere
gratitude to my advisor Dr. Gary R. Hamed for his guidance, patience, encouragement
and supports during my research. I also express my sincere gratitude to Dr. Li Jia for his
trust and invitation to his research group for a part of my research.
I appreciate Mr. Robert H. Seiple and Mr. Bojie Wang for their guidance in the
operation of relevant instruments. I appreciate my roommate Weizheng Fan for his
assistance in photographing my samples.
I also thank my group members: Tamon Itahashi, Guangzhuo Rong, Adeyemi
Adepetun, Tianxiang Xue, Jiali Jiang, Yu Sun, Minghang Yang, Yanxiao Li, Xin Tan,
Zhenpeng Li, Chao Wang, Nishant Kumar, Joseph Scavuzzo, Kai Li, for their friendliness,
helps and suggestions.
Lastly and most importantly, my deepest gratitude goes to my entire family for their
unselfish and everlasting love. I wish to thank my parents, Xia Wang and Jianbin Zhang,
they have continuously supported me both morally and economically after my arrival of
United States without which I would not have a chance to insist to the end. I wish to
thank my aunt Qi Wang, uncle Xugang Mei who serve as my health instructor and help
me out when I was ill. I wish to thank my grandfather Haishou Wang for his stay in
health and save me a lot of time worrying about him.
v
TABLE OF CONTENTS
Page
LIST OF TABLES ............................................................................................................. ix
LIST OF FIGURES ............................................................................................................ x
CHAPTER
I. INTRODUCTION ........................................................................................................... 1
1.1 Gum Natural Rubber ................................................................................................ 1
1.2 Styrene Butadiene Rubber (SBR) ............................................................................ 2
1.3 System and Role of Vulcanization ........................................................................... 3
1.4 Fracture of Rubber ................................................................................................... 8
1.4.1 Mechanism of Rubber Fracture ........................................................................ 9
1.4.2 Effect of Chemistry and Fatigue..................................................................... 10
1.4.3 Effect of Crystallization ..................................................................................11
1.4.4 Effect of Energy Dissipation .......................................................................... 12
1.4.5 Effect of Crack Blunting and Crack Deviation .............................................. 13
1.4.6 Effect of Temperature and Strain Rate ........................................................... 14
1.5 Pre-introduced Edge Cut ........................................................................................ 15
1.5.1 Effect of Edge Cut .......................................................................................... 16
1.5.2 Previous Research on Gum Rubber with Precut ............................................ 17
1.6 Fillers...................................................................................................................... 18
1.6.1 Filler and Carbon Black.................................................................................. 19
vi
1.6.2 Effect of Carbon Black on Mechanical Properties ......................................... 21
1.6.3 Fracture of Carbon Black Filled Natural Rubber ........................................... 22
II. EXPERIMENTAL........................................................................................................ 25
2.1 Materials ................................................................................................................. 25
2.2 Formulations .......................................................................................................... 26
2.3 Mixing .................................................................................................................... 26
2.4 Milling .................................................................................................................... 27
2.5 Vulcanization Characterization .............................................................................. 27
2.6 Molding .................................................................................................................. 27
2.7 Swelling Test .......................................................................................................... 28
2.8 Bound Rubber ........................................................................................................ 29
2.9 Tensile Strength ..................................................................................................... 30
2.10 Crack Pattern Photographs ................................................................................... 30
III. RESULTS AND DISCUSSION.................................................................................. 31
3.1 Characterization of Vulcanization.......................................................................... 31
3.2 Swelling Test and Crosslink Density ..................................................................... 32
3.3 Bound Rubber Test ................................................................................................ 36
3.4 Normal Tensile Results (c = 0) of SBR and NR at Various Tensile Rates ............ 38
3.4.1 Tensile Tests of SBR and NR at 50 mm/min .................................................. 39
3.4.2 Rate Dependence of Tensile Strength of gum SBR and NR .......................... 46
3.4.3 Rate Dependence of Tensile Results of Black-Filled NR and SBR ............... 51
3.5 Precut Tensile Results of SBR and NR at 50 mm/min .......................................... 58
3.5.1 Precut Tensile Results of Gum Rubbers at 50 mm/min.................................. 58
3.5.2 Precut Tensile Results of Black-Filled SBR at 50 mm/min ........................... 62
vii
3.5.3 Reduced Strength of Slightly Carbon Black Filled NR at 50 mm/min .......... 68
3.5.4 Critical Carbon Black Loading for Partial Reinforcement at 50 mm/min ..... 70
3.5.5 Critical Carbon Black Loading for Completed Reinforcement at 50 mm/min
......................................................................................................................... 76
3.6 Precut Tensile Results of SBR at Various Tensile Rates ....................................... 81
3.6.1 Rate Dependence of Precut Tensile Results of Unfilled SBR ........................ 81
3.6.2 Rate Dependence of Precut Tensile Results of Black Filled SBR .................. 83
3.7 Precut Tensile Results of NR at Various Tensile Rates ......................................... 91
3.7.1 Completed Tensile Rate- Critical Cut Size Profile of Gum NR ..................... 91
3.7.2 Effect of Tensile Rate on the Carbon Black Loading for Reinforcement of NR
......................................................................................................................... 96
3.8 Slopes of Fitted Line of Strength-Cut Size Plot ................................................... 105
IV. CONCLUSIONS ....................................................................................................... 109
REFERENCES ................................................................................................................ 111
APPENDIX ......................................................................................................................116
viii
LIST OF TABLES
Table
Page
2.1 Parts of carbon black and volume fraction…………………………………………..28
3.1 Cure characteristics of gum and black filled SBR and NR………………….……….32
3.2 Swelling tests of unfilled and black-filled SBR and NR ............................................ 36
3.3 Bound rubber test of carbon black N115 filled NR .................................................... 38
3.4 Tensile results of uncut SBR and NR at 50 mm/min .................................................. 39
3.5 Tensile results of uncut B0S and B0N at various tensile rates.................................... 47
3.6 Tensile strength of SBR with various amount of N115 at various tensile rates .......... 52
3.7 Tensile strength of NR with various amounts of N115 at various tensile rates .......... 53
3.8 Strength loss of precut SBR at c = 0.2 mm ................................................................. 66
3.9 Characteristic values of tensile results of B0N, B5N and B14N at 50 mm/min......... 68
3.10 Collection of SL values of all NR compounds at 50 mm/min .................................. 79
3.11 Strength loss of precut B0S at various tensile rates. ................................................. 83
3.12 Strength loss of B0S, B8S and B20S at various tensile rates ................................... 85
3.13 Characteristic values of tensile results of B0N at various tensile rates .................... 97
3.14 Characteristic values of precut tensile results of black-filled NR............................. 97
3.15 Slopes in strength-cut plot of gum SBR/ NR .......................................................... 106
3.16 Slopes in strength-cut plot of black-filled SBR ...................................................... 106
3.17 Slopes in strength-cut plot of black-filled NR ........................................................ 107
ix
LIST OF FIGURES
Figure
Page
1.1 Chemical structure of natural rubber (cis-1,4-polyisoprene) ........................................ 1
1.2 Chemical structure of SBR ........................................................................................... 2
1.3 Network in rubber cured by sulfur ................................................................................ 3
1.4 Free radical mechanism of sulfur vulcanization ........................................................... 4
1.5 TBBS activation mechanism in curing process ............................................................ 5
1.6 Mechanism for peroxide vulcanization......................................................................... 6
1.7 Crosslink structures ....................................................................................................... 7
1.8 Simple tensile testpiece with edge cut of length c ........................................................ 9
1.9 Fraction of crystallinity, Φc, as a function of time for Hevea as a function of time at
different extension ratios. Λ: () 2.0; () 3.0; () 4.0; () 5.0; () 6.0 ...................... 12
1.10 Failure envelop of an amorphous gum SBR ............................................................. 15
1.11 Effect of edge cut on fracture of gum NR (SMR CV60) .......................................... 16
1.12 Effect of temperature on tensile strength of gum NR (SMR CV60) ........................ 18
1.13 Morphology of carbon black ..................................................................................... 19
1.14 Particle spacing cubic lattice model .......................................................................... 20
1.15 Stress-strain for gum and black filled SBR, NR (S1, 2 and N1, 2) .......................... 22
1.16 Payne Effect: strain on dynamic storage modulus G’ ............................................... 23
1.17 Effect of precut on the strength of gum NR (N1) and black-filled NR (N2) ............ 23
1.18 Tensile strength of precut specimens with 0, 3, 6, 12 phr of N115 ........................... 24
3.1 Vulcanization characterization of NR………………………………………………..33
x
3.2 Vulcanization characterization of SBR ....................................................................... 34
3.3 Maximum torque versus true volume fraction of carbon black N115, v .................... 35
3.4 Crosslink density ρc of NR and SBR versus true volume fraction of N115, v............ 37
3.5 Strength and elongation of NR versus N115 concentration, C, at 50 mm/min........... 40
3.6 Strength and elongation of SBR versus N115 concentration, C, at 50 mm/min......... 41
3.7 Comparison of stress-strain curve of B0S and B0N at 50 mm/min............................ 42
3.8 Comparison of stress-strain curve of NR with N115-black at 50 mm/min ................ 43
3.9 Comparison of stress-strain curve of SBR with N115-black at 50 mm/min .............. 44
3.10 Rate dependence of tensile results of B0N and B0S................................................. 48
3.11 Rate dependence of stress-strain curve of B0N ........................................................ 49
3.12 Rate dependence of stress-strain curve of B0S ......................................................... 50
3.13 Normal tensile strength versus tensile rate for N115 filled NR ................................ 54
3.14 Normal tensile strength of NR versus N115 loading at various tensile rates ........... 55
3.15 Normal tensile strength versus tensile rate for N115 filled NR ................................ 56
3.16 Normal tensile strength of NR versus N115 loading at various tensile rates ........... 57
3.17 Tensile strength of B0N with precut c at 50 mm/min ............................................... 60
3.18 Strength of B0S with precut c at 50 mm/min ........................................................... 61
3.19 Stress-strain curve of B0N at 50 mm/min, with precut specimens labeled .............. 63
3.20 Comparison of stress-strain curve of precut B0N in SP and WP at 50 mm/min ...... 64
3.21 Comparison of strength of gum SBR and NR with precut c at 50 mm/min ............. 65
3.22 Tensile strength of SBR filled with various amount of carbon black with precut c at
50 mm/min ........................................................................................................................ 67
3.23 Tensile strength of precut B0N, B5N and B14N at 50 mm/min ............................... 71
3.24 Tensile results of B15N with precut c at 50 mm/min ............................................... 73
3.25 Comparison of precut tensile results of B0N, B14N and B15N at 50 mm/min........ 74
xi
3.26 Crack pattern of specimen of B15N at 50 mm/min (c = 1.09 mm, 8.11 MPa) ......... 75
3.27 Crack pattern of specimen of B15N at 50 mm/min (c = 1.40 mm, 7.44 MPa)......... 75
3.28 Comparison of precut tensile results of B0N, B18N and B19N at 50 mm/min........ 77
3.29 Crack pattern of B19N specimen at 50 mm/min (c = 1.09 mm, 12.52 MPa) ........... 78
3.30 Comparison of precut tensile results of N115 filled NR with crack deviation at 50
mm/min ............................................................................................................................. 80
3.31 Rate dependence of precut tensile strength of B0S .................................................. 82
3.32 Rate dependence of precut strength of B8S .............................................................. 86
3.33 Rate dependence of precut strength of B20S ............................................................ 87
3.34 Comparison of precut tensile strength of B0S, B8S, B20S at various rates ............. 88
3.35 Comparison of precut strength of B0S (r=250, 50) and B8S (r=25, 0.1) ................. 89
3.36 SL versus tensile rate to decide slope A .................................................................... 90
3.37 Comparison of precut tensile strength of B0N at 250, 50 and 25 mm/min .............. 93
3.38 Comparison of precut tensile strength of B0N at 500, 250, 10, 0.05 mm/min ......... 94
3.39 Completed tensile rate- cs/ cw profile ........................................................................ 95
3.40 Precut strength of B0N, B5N, B14N and B15N at 250 mm/min.............................. 98
3.41 Precut tensile strength of B0N, B5N, B14N, B15N at 0.1 mm/min ......................... 99
3.42 Precut tensile strengths of B0N, B18N, B19N and B20N at 250 mm/min............. 100
3.43 Comparison of precut tensile strength of B0N and B18N at 0.1 mm/min.............. 101
3.44 Effect of tensile rates on critical N115 loadings CT1 and CT2 ................................. 102
3.45 Comparison of precut strengths of B25N at 250, 50, 10, 0.1 mm/min ................... 104
xii
CHAPTER I
INTRODUCTION
1.1 Gum Natural Rubber
Natural rubber is widely used both in households and in industry. Although
synthetic rubbers, such as styrene butadiene rubber (SBR) and synthetic polyisoprene
(IR), can replace natural rubber in some situations, the combination of good properties
such as high green strength (the strength before cross-linking), good mechanical strength
under severe deformations, high tensile strength, high resilience and good low
temperature performance make natural rubber irreplaceable for many applications. 1
But, natural rubber has shortcomings. Its resistance to ozone and oxygen is
relatively poor. 2 Ozone can react with double bond in natural rubber and thus degrade it.
Antioxidants and antiozonants are necessary additives for natural rubber.2
The chemical structure of natural rubber is believed to be nearly 100% cis-1,
4-polyisoprene (Figure 1.1) 3 with weight average molecular weight ranging from 106 to
107 g/mol and number average molecular weight ranging from 105 to 106 g/mol. 4
H2 C
CH2
C
n
C
H
H3 C
Figure 1.1 Chemical structure of natural rubber (cis-1,4-polyisoprene)
1
1.2 Styrene Butadiene Rubber (SBR)
Styrene butadiene rubber (SBR) is a synthetic rubber and there are two major ways
to co-polymerize styrene and butadiene. The first one is emulsion copolymerization
(E-SBR) via a free radical mechanism. 5 Two examples of this kind of SBR are high
temperature SBR (1000 series) and low temperature SBR (1500 series). 6 The second one
is copolymerization in solution (S-SBR) which occurs by an anionic mechanism.5 The
microstructure of SBR is a combination of cis, trans and vinyl butadiene with styrene, as
shown in Figure 1.2.
C
C C
C
t rans
w
C
C
C C
x
C C
C
C
vinyl
ci s
y
C C
z
n
styrene
Figure 1.2 Chemical structure of SBR
Increasing styrene content increases glass transition temperature and modulus, but
reduce elasticity. A common styrene content is 23.5% by weight. Increasing vinyl content
group increases glass transition temperature, but resistance to abrasion is decreased.
Increased cis-butadiene content increases elasticity and reduce tensile strength. Increased
trans-butadiene content increases structural symmetry and improves modulus. 7
SBR has better wear resistance than NR (especially at high temperature) and lower
elasticity. 8 Also, SBR has better oxidant resistance than NR.8 The curing rate of SBR is
slower than NR due to SBR’s lower content of carbon-carbon double bond and bulky
styrene substituent.8
2
A very important difference between natural rubber and SBR is in the ability to
crystallize. 9 Natural rubber can undergo crystallization upon straining, while SBR
remains amorphous. This behavior is discussed extensively later.
1.3 System and Role of Vulcanization
Natural rubber and SBR before vulcanization is entangled and viscous liquid with
high molecular weight. It is weak and unable to maintain its shape due to molecular
slippage under deformation. Once vulcanized, rubber becomes an elastic solid with a
three dimensional network, as shown in Figure 1.3. 10 Various curing agents are used to
vulcanize rubber. Sulfur is the most common and extensively used curing agent for diene
rubbers,10 such as natural rubber, styrene-butadiene rubber. Peroxide curing agents are
also popular.
Figure 1.3 Network in rubber cured by sulfur
Free radical mechanism was proposed for sulfur vulcanization, as illustrated in
Figure 1.4.10- 12 Additives in vulcanization step includes activators (zinc oxide and fatty
3
acid) and accelerators.10 Sulfur alone without accelerator is rarely used because it’s
inefficient: as many as 40-55 sulfur atoms are involved in per crosslink; vulcanizes aging
properties are poor; curing time is long and crosslinks are unstable.12
C
C C C C
S S
S
S
S
S
C
C C C C
n
S
+
S xH
n
S S
S S
C
C C C C
S
S
+
n
C
C C C C
Sx n
C
C C C C
Sx n
S
S
S S
C
C C C C
Sx n
C C C C
C
C C C C
+
+ S8-x
m
C
C
C C C C
Sx n
+
C C C C
m
C
C
C C C C
Sx n
C
C C C C
x
m
+
C C C C
m
C
C
C C C C
x
Figure 1.4 Free radical mechanism of sulfur vulcanization
There are three common types of accelerator that are widely applied.10 The first one
is thiazole type and sulenamides type.10 Increase the size of substituent R will delay the
onset of curing, i.e., increase the scorch time. Therefore, more processing operation are
allowed before crosslinking reaction. A famous example is 2-mercaptobenzothiazole
(MBT). The second one is dithiocarbamate type.10 Its cure rate is extremely fast with very
short scorch time. It can be applied to the polymer needn’t much processing. Example is
tetra methyl thiuramdisulfide (TMTD). The last common type of accelerator is amine
type (e.g. diphenylguanidine).10 It’s cure rate and scorch time are moderate.
4
Scorch time doesn’t very sensitive to accelerator concentration or the ratio of sulfur
and accelerator, but the accelerator concentration does have important effect on
vulcanizate which will be discussed later.
Because all processing procedure must be accomplished before scorch time, the
first type of accelerator, i.e., thiazole type accelerator, is the most welcomed. Usually,
thiazole accelerators perform at the presence of zinc salt, zinc oxide, or fatty acid. Their
mechanism and functions are shown in Figure 1.5.
The rate of vulcanization is accelerated by addition of zinc-oxide because it
activates the breakage of Ac-S bond.
N
SH
Ac-H
Ac-H
S8
Ac-Ac
S8-x + Ac-Sx-Ac
S
fatty acid such as ZnO
activates Ac-S bond
Ac-H +
C
C C C C
n
Sx
C
C C C C
C C C C
m
C
m
C
C C C C
+
n
Sx
Ac
C
C C C C
n
Ac-H
Figure 1.5 TBBS activation mechanism in curing process
Besides sulfur, peroxide type curing agents are also developed and examined. It’s
mechanism is shown in Figure 1.6. 13,14
Dialkyl peroxides give efficient crosslinking. Di-t-butyl peroxide yield good cured
rubbers but di-t-butyl peroxide is too volatile which limits its use.
5
O O
heat
O
C
C C C C
n
C
C C C C
n
OR
C
C C C C
OR
C
C C C C
OR
n
ORC
C C C C
C C C C
ORC
n
C
C C C C
C
C C C C
C C C C
ORC
n
Figure 1.6 Mechanism for peroxide vulcanization
Acidic compounding ingredients such as stearic acids can cause decomposition of
peroxides can reduce the cross-linking efficiency.
Many properties of rubbers cured by sulfur are poorer than that cured by sulfur, but
rubbers cured by peroxides have better thermal resistance, excellent aging properties and
set resistance.13
Vulcanization transforms an rubber from a visco-elastic liquid with high molecular
weight into an elastic solid. Generally speaking, elastic and recovery stiffness increase as
crosslink density increases while hysteresis and friction decrease with increased
cross-linking. Some properties show a maximum value with the increasing crosslink
density, such as tear strength, fatigue life, and tensile strength, because these properties
depend on hysteresis as well as on the number of network chains. The number of network
chains increases monotonously with increased cross-linking, but hysteresis, also known
as energy dissipation decreases with increased cross-linking.10
Increase in sulfur and accelerators concentration yields higher crosslink density.
Hamed discussed the dependence of strength on crosslink density and accordingly offer
6
higher modulus, stiffness. 15 With increasing crosslink density, the fracture changes from
viscous flow without breaking chemical bonds to elastic fracture of chemical bonds
above the gel point, and finally to brittle fracture at high crosslink levels. Crosslink levels
must be high enough to prevent failure by viscous flow, but low enough to avoid brittle
failure.
The type of crosslinks has effects on properties.15,16 With increasing ratio of sulfur
concentration to accelerator concentration, polysulfide crosslink are increased and more
sulfur will be attached to rubber to form sulfur ring structure, as shown in Figure 1.7.15
Figure 1.7 Crosslink structures
Elastomers with monosulfidic cross-links have better heat stability than elastomers
with polysulfidic cross-links, because C-S bonds have better stability than S-S bonds. On
the other hand, elastomers with polysulfidic cross-links have better tensile strength and
fatigue resistance than elastomers with monosulfic cross-links. This is due to the ability
of S-S bonds to break reversibly.16
7
1.4 Fracture of Rubber
All solids are heterogeneous and contain flaws. When a solid is exposed to global
stress, the local stress at flaws is magnified. 17 When the local stress at a critical flaw is
sufficiently high, fracture occurs. Thus, the measured tensile strength is smaller than that
predicted theoretically for a perfect solid. 18
Inglis12 derived an equation relating local stress at crack tip, σt, to global stress σ:

σ t = σ 1 + 2

l

r
(1.1)
where l is the depth of an edge flaw; r is the radius of the flaw tip.
When the flaw size is much larger than the radius of the flaw tip, Equation 1.1 can
be approximated by: 19
σt =
2σ l
(1.2)
r
Sharper and longer flaws increase stress concentration. So introduced sharp precut
will give lower strength.
Griffith 20,21 proposed another way to analyze fracture. A crack won’t grow in a
stressed material unless the decrease in elastically stored energy overwhelms the increase
in surface energy to form a new crack surface. This theory can be expressed
mathematically:
−
∆A
∆W
>γs
∆c
∆c
8
(1.3)
where ∆W is the decrease of stored energy caused by crack growth, ∆c; ∆A is surface area
created by crack growth; γs is the surface energy. The Griffith equation is valid for an
ideal elastic solid that fractures without any bulk energy dissipation.
1.4.1 Mechanism of Rubber Fracture
For a rubber sheet of thickness t, Thomas and Rivlin 22 proposed that: at fixed
deformation l,
 ∂W 
−
 = Gt
 ∂c  l
(1.4)
where G is fracture energy, which includes surface energy and bulk energy dissipation
during crack growth.
Generally, uniaxial tensile testpieces are used (Figure 1.8). An edge-cut of depth c
is introduced and a specimen is pulled at constant rate until fracture. The shadowed
triangular region in Figure 1.8 is not deformed during stretching; and the remaining parts
of the specimen contain elastically stored energy, W.
Figure 1.8 Simple tensile testpiece with edge cut of length c
9
Thus, Equation 1.4 yields:
G = 2kWc
(1.5)
where k is weakly dependant on strain. It can be taken as a constant value in many cases.
W is equal to σb2/2E, where σb is the ultimate stress and E is the Young’s modulus for a
linearly elastic material. Thus, for simple fracture involving the lateral growth of a single
crack, Equation 1.5 becomes: 23
σb =
GE
kc
(1.6)
1.4.2 Effect of Chemistry and Fatigue
Chain rupture may be mainly due to mechanical loading, but in addition, rubber
networks are altered by the environment. Oxygen and ozone are two degradants.
Oxidation results in chain scission and chain cross-linking, while chain scission
dominates for ozone attack.2,24 If a test is rapidly carried out, time is insufficient for
chemical attack of rubber and fracture is purely mechanical. But, fatigue fracture involves
long-time cycling thus chemical attack may occur prior to and during fracture.
A description of oxidative attack follows: 25 First, allylic or tertiary hydrogen
abstraction initiates oxidation. This creates a macro-radical, which then rapidly reacts
with oxygen to form a peroxy radical. Second, this peroxy radical abstracts an active
hydrogen to give a hydroperoxide and a new macro-radical, which can add more oxygen.
This chain reaction may affect many polymer chains before the propagating radical
becomes dormant. The peroxide then goes 10 eptanes 10 cleavage and yields a
macro-oxy radical and a hydroxyl radical. These give two different successive reactions:
10
one is cross-linking by coupling of macro-radicals or addition of macro-radicals to
another unsaturated bond; one is chain scission which produces a dead chain. If the
former process dominates, the rubber becomes stiffer, if the latter dominates, the rubber
becomes softer.
Next, the mechano-chemistry of rubber under fatigue is considered.25 Oxygen
affects both the force necessary to break a network chain and the micro-structure at a
crack tip. A smaller stress is needed to break a chain undergoing oxidation. Oxidation is
accelerated when a rubber is deformed.25 It is likely that during oxidation, a stress
network will suffer a higher ratio of chain scission to chain cross-linking compared to
that of an unstressed network.
1.4.3 Effect of Crystallization
Natural rubber can crystallize when stretched due to its high stereo regularity but
SBR remains amorphous.9 Thermal crystallization of natural rubber occurs slowly at
room temperature and is inhibited at elevated temperature. Thermal crystallization
reaches a maximum rate at -24°C. 26 This causes hardening of uncured rubber during
storage.
Strain-induced crystallization imparts high tensile strength and tearing resistance to
natural rubber. Synthetic cis-1, 4-polyisoprene contains a very small amount of non-cis
units. These irregularities in microstructure hinders crystallization upon straining. Gent 27
demonstrated that, at high strain rate, synthetic cis-1, 4-polyisoprene has lower tensile
strength than NR due to a reduced rate of strain-induced crystallization within synthetic
cis-1, 4-polyisoprene.
11
Shimomura 28 demonstrated that the degree and rate of crystallization increase with
increased extension ratio (λ) (Figure 1.9). Gehman and Field 29 found that the
crystallization upon straining of gum natural rubber starts at about 250% elongation.
With increasing strain, crystalline morphology transitions from spherulitic to fibrillar. 30,31
Figure 1.9 Fraction of crystallinity, Φc, as a function of time for Hevea as a function of
time at different extension ratios. Λ: () 2.0; () 3.0; () 4.0; () 5.0; () 6.0
1.4.4 Effect of Energy Dissipation
Ideally, if stress concentration upon straining in a network were totally absent, all
chains that bear load would have the same stress. In this limit, stress would be very high.
But, unfortunately, this ideal situation is never true, because, at least in part, of inevitable
flaws. Increasing the uniformity of loading among polymer chains in a network is
desirable.25
12
If highly stressed polymer chains can reduce the load they carry without breaking
irreversibly, uniformity in chain load is ameliorated and macroscopic strength is
enhanced.
This mechanism can be involved to explain why sulfur cured rubbers are stronger
than peroxide cured ones.25 Polysulfidic linkages between polymer chains are able to
reversibly break and reform when they are overloaded. This results in a more uniformly
loaded network. This process is non-catastrophic energy dissipation. On the other hand,
peroxide linkages are unable to reform after rupture. Energy dissipation results from
nonreversible and catastrophic chain rupture.
1.4.5 Effect of Crack Blunting and Crack Deviation
Microscopic effects of crystallization and energy dissipation have been discussed.
These factors manifest macroscopically. A crack tip for a weak rubber remains sharp
during deformation and perpendicular to the direction of external stress. But strong
rubbers, especially those reinforced with fine fillers, behave differently due to their
capability of energy dissipation.25 When deformed, a crack tip blunts and develops two or
more secondary cracks. These grow in two opposite directions. Secondary cracks reduce
stress concentration. Therefore, a new crack must initiate before fracture occurs, which
enhances strength.
Chain alignment at crack tip also occurs in strong rubbers.25 This leads to the
anisotropy at a crack tip. If chain alignment is sufficient, a fibrous structure develops, and
cracks propagate between laminae which causes crack deviation. Non-catastrophic
energy dissipation at a crack tip allows such a process. If chain rupture before enough
anisotropy develops, a crack simply grows forward.
13
Kendall proposed a crack deflection mechanism. 32 He proved that a small, initially
introduced crack perpendicular to loading direction will deviate along the loading
direction if the following condition is met:
G // <
G⊥
4π 1 − ν 2
(
)
(1.7)
where ν is Poisson’s ratio, G// is the fracture energy for splitting along the stress direction,
G⊥ is the fracture energy for tearing across the stress direction.
1.4.6 Effect of Temperature and Strain Rate
Smith 33 investigated tensile strength and ultimate strain as a function of
temperature and strain rate. For an amorphous elastomer, such as SBR, these properties at
different temperatures could be shifted to form a master curve at a reference temperature.
The shift factor was defined by the ratio of internal viscosity at various temperatures to
the viscosity at a certain reference temperature (WLF equation). 34
When tensile rate is low, polymer chains in a rubber network have enough time to
relax, bulk energy dissipation will be hindered and tensile strength is thus relatively low
(This only holds for amorphous rubber.). Lake and Lindley 35 found a minimum fracture
energy for cured rubber tested at sufficiently high temperature and sufficiently low rate.
The threshold mechanic tearing energy below which catastrophic fracture didn’t occur
was about 50 J/m2, which is larger than the dissociation energy of chemical bonds per
area at the fracture surface. Lake and Thomas 36 proposed a theory to account for this
finding. To break a single bond in a network chain, the entire chain must be extended to
the break point. As a result, fracture energy and average molecular weight between
cross-links was is related by:36
14
G ∝ Mc
(1.8)
where Mc is the average molecular weight between cross-links.
Smith36 also plotted breaking stress versus the ultimate strain at different
temperatures and strain rates. The parabolic shaped curve is called a failure envelope.
Figure 1.10
37
shows the failure envelope of an amorphous, cured SBR. The
anticlockwise direction along the parabolic curve corresponds to increasing strain rate or
decreasing temperature. The failure envelope is independent of time and temperature.
Figure 1.10 Failure envelop of an amorphous gum SBR
1.5 Pre-introduced Edge Cut
An easy way to investigate the effect of flaws on strength is to introduce a precut into
specimens before testing.
15
1.5.1 Effect of Edge Cut
. Hamed 38 studied how edge-cuts of different depth affect the fracture of ethylene
propylene diene terpolymer, EPDM, with various cross-link densities. Equation 1.6 is
applicable for lightly cross-linked specimens when crack pattern is simple.
Natural rubber doesn’t follow Equation 1.6 due to strain crystallization. An abrupt
drop in strength at a critical cut size, ccr, for gum natural rubber was observed by Thomas
and Whittle38 (Figure 1.11). This sudden drop was attributed to the failure of bulk
crystallization when cut size, c, is large. When c is small, bulk crystallization occurs
before catastrophic crack growth take place. But when cut size reaches a critical point,
upturn occurs prior to the bulk crystallization.
Figure 1.11 Effect of edge cut on fracture of gum NR (SMR CV60)
16
Hamed and Park 39 compared the strengths of gum natural rubber with SBR filled
with carbon black. These two materials have the similar normal tensile strengths about 30
MPa. When c was small, NR crystallized in bulk and the gum natural rubber was stronger
than the black filled SBR. However, when c was sufficiently large so that bulk
crystallization of NR was absent, the gum NR was weaker than the black-filled SBR.
1.5.2 Previous Research on Gum Rubber with Precut
Hamed and Rattanasom 40 studied the effect of crosslink density on the fracture of
sulfur-cured gum natural rubber. An abrupt drop in strength was observed in lightly cured
natural rubber in strength at a critical cut size ccr. At the critical cut size, specimens’
crack patterns after fracture were photographed by scanning electron microscopy, SEM,
and only a simple smooth crack was found. The value of ccr deceased quickly with
increased crosslink density, ρc, indicating a hindrance of crystallization at higher ρc.
Sufficiently cross-linked natural rubber did not show a critical cut size. These specimens
exhibited simple lateral fracture from the tip of the precut. Crack surfaces were rough. A
cured natural rubber specimen with intermediate crosslink density showed slight crack
deviation prior to rupture. This indicates a slightly crystalline region, which deviates a
crack and strengthens a rubber.
Thomas and Whittle 41 examined the effect of temperature on the tensile strength of
cured natural rubber cross-linked with DCP (dicumyl peroxide). There was an abrupt
drop in tensile strength at a critical temperature, Tc, as shown in Figure 1.12. This was
attributed to the lack of strain crystallization at high temperatures, although there was
some indirect evidence showing that the slight local stain crystallization at the cut tip
might exist. The critical temperature depends on the type and density of cross-linking.
17
Polysulfidic crosslinks (cured by sulfur) give high Tc and carbon-carbon cross-links
(cured by dicumyl peroxide) give low Tc. The slippage of polysulfidic cross-links at high
stress enables better chain orientation and promotes strain-crystallization and reversibility
of polysulfidic linkage facilitates non-catastrophic energy dissipation. High cross-linking
restricts chain movement and decreases strain-crystallization.
Bell, Stinson and Thomas 42 studied the effect of temperature on the tearing of
cured gum natural rubber. In the temperature ranging from 20 to 80°C, the strength
decreased abruptly at a critical cut size. The ccr decreased with increasing temperature. At
a critical temperature at 80°C, there was no critical cut size, or the ccr reduced to zero.
Figure 1.12 Effect of temperature on tensile strength of gum NR (SMR CV60)
1.6 Fillers
Fillers are widely used for almost all commercial rubber products because they can
reinforce rubbers by increasing their modulus, strength, etc.
18
1.6.1 Filler and Carbon Black
The most widely used filler is carbon black.2
Two common types of carbon black are furnace black and thermal black 43. Furnace
blacks can be obtained by combustion of oil or natural gas with insufficient oxygen.
Thermal blacks are obtained by using natural gas in heated chambers without air. The
morphological structure of one carbon black is shown in Figure 1.13. 44,45 The smallest
single particles are called primary particles or nodules, consisting overlapping graphitic
layers. The primary particles group together to form aggregates whose structure is largely
maintained during rubber processing, e.g., mixing, milling, molding. Further combination
of aggregates gives agglomerates. These are decomposed during processing.
Figure 1.13 Morphology of carbon black
Primary particle size and specific area of carbon black are two important factors
influencing the reinforcement of rubber. 46 These two factors are inter-related: smaller
19
primary particle’s have larger specific surface area. Specific surface areas are measured
by BET nitrogen adsorption 47 or CTAB adsorption. 48 Particle sizes of carbon black
range from 20 to 300 nm. 49 Increased specific area enhances interaction between rubber
and carbon black. Hamed 50 showed the crucial importance of particle size in carbon
black reinforcement with a particle spacing cubic lattice model (Figure 1.14). It assumes
spherical filler with radius r is dispersed on a square lattice at volume fraction, x. For
each particle, there is assumed to be a layer with thickness t around each particle. Here
the movement of chains is restricted by rubber-filler interactions. The particle spacing s
and volume fraction x of this additional layer were calculated for different particle sizes
at the same concentration. When particles are fine, s is similar to the distance between
cross-links. Fracture is hindered because of the reduced mobility of network chains. On
the contrary, with a sufficient increase in particle size, particle spacing is sufficient that
the rubber motions are little influenced by the filler.
Figure 1.14 Particle spacing cubic lattice model
20
Another important parameter of carbon black is its structure.44 Effective reinforcing
volume of aggregates depends on structure. Occluded rubber is defined as the part of a
the rubber occupies the internal void space of aggregates.45 Occluded rubber is shielded
from deformation and increases the effective volume fraction of carbon black.
1.6.2 Effect of Carbon Black on Mechanical Properties
The addition of carbon black increases the modulus of rubber due to the strain
amplification. 51 Also, the interaction of carbon black with rubber reduces the volume of
deformable phase, Vd, when compared to unfilled rubber. The Vd is further reduced by
occluded rubber in the void space of carbon black aggregates. The decrease of Vd
increases the local strain and strain rate.
Carbon black dramatically enhances the tensile strength of amorphous rubbers, but
its effect on strain-crystallizing NR is limited.39 As shown in Figure 1.15, the stress-strain
curve of gum NR (without carbon black) is similar to that of SBR up to its breaking point.
Carbon black does not increase the tensile strength of strain-crystallizing natural rubber,
but the ultimate elongation is nearly reduced by 50%. On the contrary, the addition of
carbon black sharply increases the tensile strength of amorphous SBR while maintaining
elongation at break.
At very low tensile strain (Figure 1.16)45, carbon black-filled rubber shows a
constant dynamic storage modulus G’ which decreases with increasing strain and reaches
a plateau. This phenomenon is called the Payne effect. 52 This effect is explained by the
breakage and recovery of a filler network.
21
Figure 1.15 Stress-strain for gum and black filled SBR, NR (S1, 2 and N1, 2)
1.6.3 Fracture of Carbon Black Filled Natural Rubber
Hamed and Park39 investigated the tensile strengths of gum and carbon black-filled
NR, as shown in Figure 1.17. Gum and black-filled NR have similar normal tensile
strength (tensile strength of NR without precut), but their tensile strength with a precut is
quite different. At small c, the tensile strength of black-filled NR is two times larger than
that of the gum NR. At these cut sizes, both rubbers undergo bulk crystallization. When c
is larger, the tensile strength of black-filled NR is nearly 10 times that of the gum NR.
The highly improved tensile strength of black-filled NR at large c has been
contributed to the enhanced strain-crystallization in the presence of carbon black.
Gehman and Field found that crystallization is initiated at elongation of 250% for gum
NR and at about 100% for black-filled NR (calculated by X-Ray Diffraction, XRD). 53
22
Lee and Donovan 54 studied strain-crystallization at the cut tips with XRD and found that
the lower limit of strain required to develop crystallization at cut tip is lower for
black-filled NR than for gum NR.
Figure 1.16 Payne Effect: strain on dynamic storage modulus G’
Figure 1.17 Effect of precut on the strength of gum NR (N1) and black-filled NR (N2)
23
Hamed and Al-Sheneper 55 investigated the effect of a very fine carbon black (N115)
on the tensile strength in NR, as shown in Figure 1.18.
Remarkably, the low concentrations of carbon black decreased tensile strength: NR
specimens filled with less than 12 phr of N115 were weaker than the gum and ccr
decreased with increased black concentration. At about 18 phr of black, the strength of
filled specimens increased. Thus, there is a minimum concentration of N115 required to
enhance the tensile strength of precut NR. The lowest concentration increases as black
filler becomes coarser. 56
Figure 1.18 Tensile strength of precut specimens with 0, 3, 6, 12 phr of N115
24
CHAPTER II
EXPERIMENTAL
2.1 Materials
1) Nature rubber: SMR CV60 (Akrochem Corporation, received in February 2010).
2) SBR: Plioflex 1502 (Akrochem Corporation, received in April 2012)
3) N115 carbon black: (Cabot Corporation. Average primary particle size if 27nm. DBP
absorption value is 112 cm3/100g black, received in June 2007)
4) Stearic acid: softening agents (Harwick Chemical Company, received in June 2007).
5) Zinc oxide: reinforcing agents and pigments (Akrochem, received in June 2007)
6) Sulfur: crosslinking agent (Harwick Chemical Company, received in June 2007).
7) TBBS: N-tert-butyl-1,2-benzothiazolesulfnamide, accelerator (Flexsys America,
received in June 2007).
8) PD-2: N- (1,3- dimethyl butyl)-N’- phenyl- p- phenylene diamine, antiozonant
(Akrochem, received in June 2007).
9) Microcrystalline wax: antiozonant (Akrochem received in June 2007).
10) DQ: 2, 2, 4-trimethyl-1-2-hydroquinoline, antioxidant (Akrochem, received in June
2007)
11) Santogard PVI: N-(cyclohexylthio) phthalimide, antiscorching agent (Flexsys
America, received in June 2007).
25
2.2 Formulations
The nomenclature of natural rubber and SBR compounds follows:
B-n-R
where R indicates the type of rubber (N: natural rubber; S: SBR); B-n means carbon
black content. For example, B5N means natural rubber with 5 phr of carbon black. Each
compound contains the same composition: 100 phr rubber, 1.8 phr stearic acid, 3.5 phr
zinc oxide, 1.5 phr antiozonant PD-2, 1 phr antioxidant DQ, 1 phr microcrystalline wax,
0,1 phr santogard PVI, 1.75 phr sulfur and 0.75 phr accelerator TBBS, where phr means
parts of additive per hundred weight of rubber. Densities of carbon black and natural
rubber are 1.8 g/cm3 and 0.9 g/cm3 respectively. Carbon blacks’ true volume fraction, v,
and effective volume fraction, veff, are calculated as Equation 2.1 and 2.2, and results are
listed in Table 2.1.
v=V
veff = V
VB
R +VB
VB
B +VR −DBP×WB
(2.1)
(2.2)
where VB is the volume of carbon black, VR is the volume of rubber, WB is the weight of
carbon black, DBP is the indication of occluded rubber which decreases the volume of
rubber and increases the effective volume fraction of carbon black. DBP is 113 cm3/100g
black for N115.
2.3 Mixing
Rubber masterbatches were initially prepared in a 250 mL Banbury internal mixer
with a fill factor of 0.7. After the internal mixer was cleaned with pure natural rubber
three times and the machine was allowed to cool down to 90oC, natural rubber or SBR
26
was added into the mixer in the first 1.5 minutes. Then zinc oxide, stearic acid, PVI, DQ
and PD-2 were fed into the mixer and mixed with rubber for the next 1.5 minutes. Then,
wax was added and mixing for 2 minutes. Finally the masterbatch was dumped and
weighed.
2.4 Milling
A masterbatch after mixing was separated into four groups. In the first two minutes,
two parts of the masterbatch were mixed at one time, then two new bigger masterbatches
were mixed again. This process was done at a nip of 1.9 mm. In the next minute, the nip
was adjusted to 0.6 mm and a rolling bank was formed. Then, sulfur and TBBS were fed
to the rolling bank and thoroughly mixed with natural rubber and other additives for three
minutes. The nip was set to 1.2 mm and the rubber was given ten end-roll passes. Finally,
the nip was adjusted to 1.9 mm and the rubber sheeted off. The whole process
temperature was about 50oC. Milling direction was masked with a marker pen.
Stocks were stored at room temperature at least 24 hours before vulcanization.
2.5 Vulcanization Characterization
Characterization of vulcanization was accomplished using an Alpha Moving Die
Rheometer (MDR) 2000. Curing temperature was 140oC for natural rubber and 160oC for
SBR. The cure time tc (100) was the time to reach maximum torque, while tc (90) was the
time to reach 90 % of highest torque.
2.6 Molding
Milled sheets (about 15.5 g) were put in the center of a window mold (160 × 160 ×
0.5 mm). Both sides covered with Mylar films (for natural rubber) or with Kevlar films
(for SBR because SBR was cured at higher temperature) and two aluminum plates.
27
Curing took place in a Dake hydraulic press. Press load was 30 tons. After cure, the
pressure was relieved and sheets were cooled by quenching with flowing tap water.
Cured sheets were dried on paper. The average thickness of the cured sheets ranged from
0.55 to 0.65 mm.
Table 2.1 Parts of carbon black and volume fraction
Formulation
N115 Loading (phr)
v
veff
B0S
0
-
-
B8S
8
0.038
0.042
B20S
20
0.091
0.112
B0N
0
-
-
B5N
5
0.024
0.026
B14N
14
0.065
0.075
B15N
15
0.070
0.081
B18N
18
0.083
0.099
B19N
19
0.087
0.105
B20N
20
0.091
0.112
B25N
25
0.111
0.144
2.7 Swelling Test
About 0.4g cured natural rubber were immersed in toluene and about 0.4 g cured
SBR were immersed in heptanes in small bottles and put in the dark for 1 week at room
temperature. The swollen rubbers were dried with paper and weighed again and noted as
Wgel. Then these rubbers were put into a vacuum oven and dried at room temperature for
28
24 h until the weight was constant at dried weight Wdry. Crosslink densities are calculated
by the following equations:
VR =
VS =
Wdry
ρ dry
W gel − Wdry
vR =
ρ solvent
VR
V R + VS
(2.3)
(2.4)
(2.5)
where vR is the volume fraction of rubber in swollen gel; VR is the volume of rubber
matrix; VS is the volume of solvent; ρdry is the density of dried rubber which is calculated
by dividing the total weight of rubber all additives by total volume; ρsolvent is the density
of solvent (toluene: 0.862 g/ml; heptanes: 0.69 g/ml).
The Flory-Rehner equation32,33 was used to calculate crosslink density, ρc.
ρc = −
1 ln (1 − ν r ) + ν r + χν r2
1
2ν s
v
ν r3 − r
2
(2.4)
where ρc is the crosslink density, νs is the molar volume of the solvent, νr is the volume
fraction of rubber in the swollen gel, χ is the interaction parameter of the solvent and
rubber. The interaction parameter, χ, of the solvent and rubber is calculated by: χ = 0.43 +
0.05 vr for natural rubber in toluene and χ = 0.47 + 0.39 vr for SBR in heptanes. 57
2.8 Bound Rubber
About 0.4 g of uncured rubber is weighed (Winitial) and immersed in toluene for one
week at room temperature and solvent is changed twice. After one weak, solvent is
removed and gel is weighed (Wgel).
29
The bound rubber content is calculated by Equation 2.5: 58
2.9 Tensile Strength
Bound rubber % =
phr of �iller
×Winitial
100+phr of �iller
100
×Winitial
100+phr of �iller
Wgel −
(2.5)
ASTM D412 Type C dumbbells were cut from cured sheets in the milling direction.
The width of the narrow section was 6.35 mm and the thickness ranges from 0.55 to 0.65
mm.
In tensile strength measurements, crosshead speed varies from 5 to 250 mm/min,
with an initial clamp separation of 65 mm. Strain in the narrow section of a specimen was
measured by a mechanical “clip-on” type extensometer. The initial separation of the
extensometer was 25 mm.
Edge-cuts were introduced with a razor blade that had been wetted in a soap solution
to reduce friction with the rubber. Cut depth was measured using a traveling optical
microscopy. Cut depth was measured at least three times on each side and the difference
between the average of each side was less than 0.08 mm (Otherwise a sample was
discarded). The difference of cut depth on each side was minimized by cutting vertically.
Calculation of stress was based on the original specimen width, 6.35 mm, regardless of
the cut depth.
2.10 Crack Pattern Photographs
High magnification photographs of crack patterns were taken with a scanning
electron microscopy (SEM) JEOL JSM7401F. Two parts of a fractured specimen were
placed together on an aluminum mount using carbon tape and coated with silver. An
arrow in an SEM picture indicates the tip of an initial razor cut.
30
CHAPTER III
RESULTS AND DISCUSSION
3.1 Characterization of Vulcanization
The cure characteristics of the natural rubber and SBR are listed in Table 3.1.
Rheometer curves are shown in Figure 3.1 (NR) and Figure 3.2 (SBR)
Curing of the SBR was carried out at 160°C while that of the natural rubber was
done at 140°C. SBR was cured at higher temperature than natural rubber because it
contains less unsaturated bonds.
Vulcanization time doesn’t rely on the loading of carbon black. Curing time (tc(100))
of SBR is nearly 30 min and curing time of NR is around 50 min.
Torques of B0N, B5N, B0S, B8S and B20S are stable after tc(100), but torques of
B14N, B15N, B18N, B20N and B25N decreases after tc(100). Time for this decrease (td)
reduces with increasing black concentration: td(25phr)=50min, td(20-15phr)=60min,
td(14phr)=75min. Perhaps, rubber/ black network breaks at high temperature when time is
enough.
Maximum torque, Tmax, increases monotonously and linearly with increasing true
volume fraction of carbon black N115, v, as plotted in Figure 3.3. As v increases,
interaction between rubber and carbon black is more intense, thus torque increases.
31
Table 3.1 Cure characteristics of gum and black filled SBR and NR
tc (90)a
tc(100)a
ts2a
Tmin b
Tmax b
B0S
13.00
32.02
5.81
0.72
6.26
B8S
15.20
35.18
5.77
0.86
8.82
B20S
14.33
34.30
6.05
1.02
11.03
B0N
37.59
52.79
24.42
0.48
6.38
B5N
34.10
50.91
22.49
0.65
6.75
B14N
30.08
50.65
19.00
0.44
8.35
B15N
31.90
52.04
20.25
1.02
9.02
B18N
29.19
51.18
17.43
0.84
9.38
B19N
32.37
52.36
17.82
0.79
9.82
B20N
27.30
47.97
14.88
0.68
10.02
B25N
29.07
49.02
17.51
1.24
11.36
a. Unit of time is min
b. Tmin is minimum torque and Tmax is maximum torque, unit is dNm.
3.2 Swelling Test and Crosslink Density
Swelling tests were done as described in Chapter 2.7 and crosslink densities of all
formulations are calculated by Equation 2.3 to 2.4. Results are listed in Table 3.2 and
plotted in Figure 3.4. Crosslink density of both SBR and NR increases with increasing
loading of carbon black because of strong rubber/ black interaction. Crosslink density of
SBR is smaller than that of NR. Slope of NR in Figure 3.4 is 5 times larger than that of
SBR which indicates that NR/ black interaction increases faster with increasing black
loading than SBR/ black interaction does.
32
12
11
B25N
10
B20N
B18N
B15N
B14N
9
8
7
B5N
B0N
Torque6
(dNm)
5
4
3
2
1
0
0
20
40
60
time (min)
Figure 3.1 Vulcanization characterization of NR
33
80
100
15
14
13
12
11
B20S
10
9
B8S
torque
(dNm) 8
7
T0S
6
5
4
3
2
1
0
0
10
20
30
40
50
60
time (min)
Figure 3.2 Vulcanization characterization of SBR
34
70
80
90
12
11
SBR: Tmax=51.7v+6.47
10
Tmax 9
(dNm)
8
7
NR: Tmax=35.3v+6.04
6
0.00
0.04
0.08
0.12
0.16
v
Figure 3.3 Maximum torque versus true volume fraction of carbon black N115, v
35
Table 3.2 Swelling tests of unfilled and black-filled SBR and NR
Compounds
Wdry (g)
Wgel (g)
ρc (*10-5 mol/cm3)
B0S
0.32
1.88
0.366
B8S
0.35
1.92
0.429
B25S
0.37
1.83
0.549
B0N
0.35
1.95
0.413
B5N
0.37
1.98
0.455
B14N
0.46
2.28
0.546
B15N
0.35
1.72
0.558
B18N
0.41
1.99
0.575
B19N
0.44
2.12
0.585
B20N
0.39
1.87
0.592
B25N
0.43
2.03
0.615
3.3 Bound Rubber Test
The addition of fine carbon black to gum rubber yields a filler/rubber network when
the loading of carbon black is high enough. Black’s aggregates are bound together by the
adsorption of rubber chains. At this critical loading, swelling ratio of cured rubber
decreases and modulus increases because of the rubber/ black interaction. Bound rubber
tests were done as described in Chapter 2.8 and results are shown in Table 3.3.
36
0.65
0.60
NR: ρc=1.49v+0.42
0.55
ρc 0.50
0.45
SBR: ρc=0.31v+0.36
0.40
0.35
0.0
0.1
0.2
0.3
0.4
0.5
0.6
v
Figure 3.4 Crosslink density ρc of NR and SBR versus true volume fraction of N115, v
37
The critical loading of N115 for the formation of black/ rubber network is 15 phr. No
gel can be observed after immersing NR in toluene with carbon black loading less than or
equal to 14 phr. After the critical loading, the bound rubber of NR doesn’t change a lot
with increasing loading of black. SBR starts to have interaction with carbon black N115
and form bound rubber at a relatively low black loading (8 phr) , but this interaction is
weaker than NR (55.8 ± 4.8% vs. 62.4 ± 2.3%). This explains why the crosslink density
of NR depends more on black loading than that of SBR does.
Table 3.3 Bound rubber test of carbon black N115 filled NR
Compounds
Bound Rubber (%)
B8S
57.3
B25S
54.2
B5N
No coherent gel
B14N
No coherent gel
B15N
61%
B18N
64%
B19N
62%
B20N
62%
B25N
63%
3.4 Normal Tensile Results (c = 0) of SBR and NR at Various Tensile Rates
Normal tensile test means to stretch a rubber band without a precut. All flaws are
microscopic intrinsic flaw. Normal tensile strength is the highest strength that a rubber
with fixed compounds can expect.
38
3.4.1 Tensile Tests of SBR and NR at 50 mm/min
Tensile results of normal specimens (without precut) (tensile strength, σb0, and
elongation at break, εb0) for gum SBR, gum NR and black N115-filled NR tested at 50
mm/min are listed in Table 3.4. The results for all compounds are the average of at least
three specimens. Tensile strengths and ultimate elongations versus carbon black N115
concentration, C, are plotted in Figure 3.5 (NR) and Figure 3.6 (SBR), respectively.
Table 3.4 Tensile results of uncut SBR and NR at 50 mm/min
Rubber
SBR
NR
N115 Loading
σb0 (MPa)
εb0
0
3.63
5.46
8
11.2
6.52
20
18.5
7.48
0
23.7
7.70
5
24.1
6.93
14
24.5
6.58
15
25.2
6.41
25
26.1
6.32
Gum SBR has lower extensibility and 8-times lower tensile strength than gum NR.
Tensile strength of NR increases very slightly with increasing loading of carbon black
N115 while ultimate elongation decreases rapidly. But both tensile strength and ultimate
elongation of SBR increase with increasing carbon black N115 concentration.
Stress-strain curves of gum SBR (B0S) and gum NR (B0N) at 50 mm/min are
compared in Figure 3.7. Stress-strain curves of NR and SBR with various loading of
carbon black are compared in Figure 3.8 and Figure 3.9 .
39
26.5
8.0
26.0
7.5
25.5
σb0 25.0
(MPa)
σ=0.09C+23.6
24.5
7.0
ε
ε=-0.06C+7.4
6.5
24.0
23.5
6.0
0
5
10
15
20
25
N115 loading, C (phr)
Figure 3.5 Strength and elongation of NR versus N115 concentration, C, at 50 mm/min
40
8
20
18
σ=0.72C+4.30
16
7
14
12
σb0
(MPa)10
ε=0.1C+5.56
ε
6
8
6
4
2
5
0
5
10
15
20
N115 loading, C (phr)
Figure 3.6 Strength and elongation of SBR versus N115 concentration, C, at 50 mm/min
41
25
20
rate=50 mm/min
Crystallization period
B0N
σ
15
(MPa)
10
Amorphous period
5
B0S
0
0
2
4
6
8
ε
Figure 3.7 Comparison of stress-strain curve of B0S and B0N at 50 mm/min
42
NR
rate=50 mm/min
30
25
B25N
20
B15N
σ
(MPa) 15
B14N
B5N
10
B0N
5
0
0
1
2
3
4
5
6
7
ε
Figure 3.8 Comparison of stress-strain curve of NR with N115-black at 50 mm/min
43
8
20
SBR
18 rate=50 mm/min
B20S
16
14
12
σ 10
(MPa)
8
B8S
6
4
B0S
2
0
0
1
2
3
4
5
6
7
8
σ
Figure 3.9 Comparison of stress-strain curve of SBR with N115-black at 50 mm/min
44
The stress strain curve of the NR (Figure 3.7) at 50 mm/min can be divided into two
separate stages. In the first stage (ε < 4.5), stress increases slowly with increasing strain
and rubber is soft. In the second stage, stress increases quite rapidly and rubber is stiffer.
There is an inflection point between the two stages. No separated stages can be observed
in stress-strain curve of SBR. In first stage, the stress-strain curve of natural rubber and
SBR are similar and NR and SBR have the same 100% modulus. This indicates similar
crosslinking. The upturn in Figure 3.7 is due to the crystallization when the strain is large
enough. Crystallization upon straining gives high strength to natural rubber. The
crystallized domain must first be destroyed before fracture can occur. Crystallization
inhibits mechanical chain rupture. Amorphous gum rubbers such as SBR have lower
fracture energy than NR. Tearing in amorphous rubbers often propagates smoothly, with
the crack perpendicular to the direction of loading, showing no indication of hindrance to
growth.
When NR is filled with carbon black, tensile strength increases and the slope in the
first stage increases with increasing carbon black loading according to Figure 3.8.
Besides, elongation at which upturn takes place decreases with increasing carbon black
concentration. Thus, 100% modulus is increased by carbon black. When carbon black
concentration reaches 25 phr, the separation of two stages almost disappears. Perhaps,
addition of carbon black hinders crystallization and increases stiffness and consequently,
the difference in two stages is reduced.
When carbon black concentration increases, more polymer chain can be absorbed by
carbon black and thus, the rubber/ black interaction is stronger. As a result, the rubber is
stiffer. So strength increases with increasing carbon black concentration. And, increase of
45
normal tensile strength does not depend on the formation of rubber/ network because
strength of NR shows an increase before 15 phr where bound rubber starts to form.
Increase of strength of SBR is more obvious than that of NR: slope of σ-C plot of
SBR is 8-times larger than that of NR (0.72 vs. 0.09, Figure 3.5, Figure 3.6). When N115
loading is 20 phr, strength of SBR increases 4 times but increases of strength of NR with
20 phr of N115 is negligible (1.1 times). Decrease in chain relaxation and crystallization
ability in NR cancels out the effect of rubber/ black interaction.
3.4.2 Rate Dependence of Tensile Strength of gum SBR and NR
Tensile rates for SBR and NR were changed from 0.1 mm/min to 250 mm/min.
Tensile results (σb0 and εb0) of normal specimens (c = 0) of unfilled SBR and NR are
listed in Table 3.5 and plotted in Figure 3.10. Stress-strain curves of B0N and B0S at
various rates are compared in Figure 3.11 and Figure 3.12, respectively.
According to Figure 3.10, ultimate elongations and tensile strengths of gum SBR and
gum NR increase with increasing tensile rate. Changes in ultimate elongations of gum
SBR is more obvious than that of gum NR. Stress-strain curves of both gum NR and gum
SBR (Figure 3.11, Figure 3.12) are not very distinguishable.
Monotonous increase of both tensile rate and ultimate elongation is because of the
extensive chain relaxation at sufficient low tensile rate: when specimen is pulled at low
tensile rate, polymer chains have more time to relax and beads have more chances to
move around, and thus polymer chains will carry on less load. Consequently, polymer is
softened and weakened at lower tensile rate.
But effect of tensile rate on tensile strength of NR is less significant than that of SBR:
when tensile rate decreases from 250 mm/min to 0.1 mm/min, strength of NR reduces 55%
46
(27.5 MPa to 12.3 MPa) but strength of SBR reduces 72% (5.0 MPa to 1.4 MPa). NR can
undergo strain-induced crystallization and extensive chain relation at low tensile rate
favors crystallization: lower tensile rate allows polymer chain to move more freely, which
enables polymer chains rearrange to form nuclei and further to crystallize. So, the effect
of crystallization partially offset the effect of chain-softening and the slope of fitted lines
of gum NR (0.1 for strength-rate and 0.03 for elongation-rate) is smaller than those of
gum SBR (0.16 for strength-rate and 0.14 for elongation-rate).
Table 3.5 Tensile results of uncut B0S and B0N at various tensile rates
Rubber
Rate (mm/min)
σb0 (MPa)
εb0
250
27.5
7.72
50
23.7
7.71
25
21.2
7.36
10
18.2
7.37
1
16.4
6.98
0.1
12.3
6.33
250
5.0
6.11
50
3.6
5.46
25
3.0
4.98
10
2.9
4.98
1
2.0
3.34
0.1
1.4
2.04
B0N
B0S
47
+ 0.1R
9
1
.
1
=
B0N: σ
10
B0N:
σb0
(MPa)
8
03R
.
0
+
4
ε = 0.8
σ
B0S:
6
.16R
0
+
9
= 0.2
1
:ε
S
B0
.49
0
=
ε
R
4
1
.
+0
4
2
0.1
0.1
1
10
100
rate, R (mm/min)
Figure 3.10 Rate dependence of tensile results of B0N and B0S
48
30
B0N
r=250 mm/min
r=50 mm/min
r=25 mm/min
r=10 mm/min
r=1 mm/min
r=0.1 mm/min
25
20
σ 15
(MPa)
10
5
0
0
1
2
3
4
ε
5
6
Figure 3.11 Rate dependence of stress-strain curve of B0N
49
7
8
7
B0S
r=250 mm/min
r=50 mm/min
r=25 mm/min
r=10 mm/min
r=1 mm/min
r=0.1 mm/min
6
5
4
σ
(MPa)
3
2
1
0
0
1
2
3
4
5
ε
Figure 3.12 Rate dependence of stress-strain curve of B0S
50
6
7
3.4.3 Rate Dependence of Tensile Results of Black-Filled NR and SBR
Tensile results of carbon black N115-filled rubber at various tensile rates are listed in
Table 3.6 (SBR) Table 3.7 (NR). Data of NR is plotted in Figure 3.13 (strength vs. rate)
and Figure 3.14 (strength vs. rate/ N115 loading). Data of SBR is plotted in Figure 3.15
(strength vs. rate) and Figure 3.16 (strength vs. N115 loading).
Tensile strength of both NR and SBR monotonously increases with increasing tensile
rate and increasing loading of carbon black when the other variant remains. But the rate
dependence is less significant than the carbon black’s loading-dependence. Range of
slope D (rate-dependence of NR) is 0.06-0.1 while range of slope C (N115
loading-dependence of NR) is 9.8-11.2; there is a sharp hundred-folds difference between
them. The contrast for SBR is a little smaller: range of slope B (rate-dependence of SBR)
is 0.06-0.16 while range of slope A (N115 loading-dependence of SBR) is 0.65-0.96;
there is only ten-folds difference. Chain relaxation is less decisive for the determination
of strength of rubber because the major part of strength comes from other issues such as
crosslinking, chain entanglement, crystallization and rubber/ filler interaction. Rate
dependence for NR is even weaker because the effect of bulk crystallization of NR upon
strain conflicts the effect of chain relaxation and chain softening. SBR doesn’t crystallize
when stretched, so the difference of rate-dependence and N115 concentration-dependence
is smaller.
51
Table 3.6 Tensile strength of SBR with various amount of N115 at various tensile rates
Rate
B0S
B8S
B20S
Slope Aa
0.1b
1.4d
5.3
14.2
0.65
1
2.0
-
-
-
10
2.9
-
-
-
25
3
8.6
19.3
0.82
50
3.6
12.4
21.5
0.88
250
5.0
14.3
24.4
0.96
Slope Bc
0.16
0.12
0.06
a. Slope A is the slope of fitted line of black loading-strength of SBR plot at each rates
b. Tensile rates are in unit of mm/min
c. Slope B is the slope of fitted line of the rate- strength of SBR plot at each black loading
d. Normal tensile strength of a certain compound tested at certain tensile rate.
52
Table 3.7 Tensile strength of NR with various amounts of N115 at various tensile rates
Rate
B0N
B5N
B14N
B15N
B25N
Slope Ca
0.1b
12.3d
13.4
13.8
14.2
14.5
10.6
1
16.4
16.2
17.1
17.6
18.5
9.8
10
18.2
18.5
18.8
19.2
20.3
10.6
25
21.2
21.5
22.1
22.4
23.6
10.2
50
23.7
24.1
24.5
25.2
26.1
9.8
250
27.4
27.8
27.5
28.2
29.2
11.2
Slope Dc
0.102
0.092
0.081
0.076
0.063
a. Slope C is the slope of fitted line of the black loading- strength of NR plot at each rates
b. Tensile rates are in unit of mm/min
c. Slope D is the slope of fitted line of the rate- strength of NR plot at each black loading
d. Normal tensile strength of a certain compound tested at certain tensile rate.
53
30
B0N
B5N
B14N
B15N
B25N
25
20
σb0
(MPa)
15
0.1
1
10
100
rate (mm/min)
Figure 3.13 Normal tensile strength versus tensile rate for N115 filled NR
54
32
30
R=250
28
26
R=50
24
R=25
σb0
(MPa)20
22
R=10
18
16
R=1
14
R=0.1
12
10
0
5
10
15
20
25
N115 loading (phr)
Figure 3.14 Normal tensile strength of NR versus N115 loading at various tensile rates
55
B20S
10
σb0
(MPa)
B8S
B0S
1
0.01
0.1
1
10
100
rate (mm/min)
Figure 3.15 Normal tensile strength versus tensile rate for N115 filled NR
56
25
20
R=250
15
R=50
σb0
(MPa)10
R=25
R=0.1
5
0
0
5
10
15
20
N115 loading (phr)
Figure 3.16 Normal tensile strength of NR versus N115 loading at various tensile rates
57
Slope B and slope D (rate-dependence) drops as the loading of carbon black
increases (Table 3.7). From B0N to B25N, slope D (NR) decreases about 40%; from B0S
to B20S, slope B (SBR) decreases about 60%. This indicates that increasing amount of
carbon black make the tensile strength less dependent on tensile rate because the rubber/
filler interaction reduces the chain flexibility and consequently, changes in chain
relaxation is less prominent when tensile rate changes if rubber is sufficiently filled by
carbon black.
Slope A (N115 concentration-dependence of SBR) decreases with decreasing tensile
rate. Effect of rubber/ black interaction is partially offset by the effect of chain-relaxation
at low tensile rate. But changes in slope C (N115 concentration-dependence of NR) with
tensile rate doesn’t follow a simple rule. Rubber/ black interaction, chain relaxation and
chain crystallization affect each other and make this trend hard to predict.
3.5 Precut Tensile Results of SBR and NR at 50 mm/min
When SBR and NR, gum or black-filled, are introduced a precut and tested at 50
mm/min, results show a significant difference.
3.5.1 Precut Tensile Results of Gum Rubbers at 50 mm/min
A precut on one edge was introduced to some specimens with a razor blade. Tensile
strength σbc of specimen with a precut c was measured. Results of precut gum NR and
SBR tested at 50 mm/min are plotted in Figure 3.17 and Figure 3.18 separately.
For natural rubber, when the cut size c is extremely small, as small as only 0.12 mm,
the tensile strength drops significantly from 23.6 MPa to 16.5 MPa (30%). The tensile
strength is exceedingly sensitive to cut size. Then, until c ≈ 0.42 mm, strength doesn’t
drop much, only from 16.5 MPa to 12.4 MPa (2.5%). At larger c, strength decreases
58
faster with increasing c. From c = 0.42 mm to c = 1.61 mm, tensile strength drops from
12.4 MPa to 4.9 MPa (60%). The drop of tensile strength of specimens with 1.61 mm < c
< 1.71 mm is sudden and discontinuous: 60% of the tensile strength (from 4.88 MPa to
1.97 MPa) is lost in this 0.10 mm while the total strength loss from 0.12 mm to 1.61 mm
is only 70%. For simplification, specimens before this sudden drop are labeled as the
strong population, SP, and those after sudden drop are labeled as the weak population,
WP. In some cases, there are overlap area in SP and WP, i.e., both SP and WP may be
observed in a certain cut size region. This area is unstable. Cut size of strong population,
cs, is defined as largest cut size before unstable region; this sample is noted as SS. Cut
size of weak population, cw, is defined as the smallest cut size after the unstable region;
this sample is noted as WS. Between the SP and the WP is a region with no specimens.
Specimens of SBR at cut size of c give one straight and descending line. No separate
strong population and weak population can be observed. When c is as small as 0.25mm,
strength drops from 3.65 MPa to 1.02 MPa (72%). This drop is larger than NR (30%).
The stress-strain curve is shown in Figure 3.19. Each black solid square represents a
precut specimen. All precut specimens, regardless of cut size, have εbc > 5.19 (εs) or εbc <
2.42 (εw) and σbc > 4.61 MPa (σs) or σbc > 1.99 MPa (σw). SS and WS doesn’t necessarily
has εs, σs, εw, σw but these four values should be at somewhere near SS and WS. This gives
an exclusion zone: Δε = 2.77 or Δσ= 2.62 MPa, where gum NR at 50 mm/min never fails.
If the uncut condition is such that the natural flaw can be regarded as a micro circle
with l and r nearly the same, σt can be approximated by 2σ (Eq. 1.2). But for precut
specimens, l is far larger than r and therefore, σt(precut) >> 2σ = σt(uncut). So a very
small precut can cause a large decrease in tensile strength.
59
σb0 = 23.6 MPa, εb0 = 757%
B0N
rate = 50 mm/min
10
strong population
(SP)
SS
σbc
(MPa)
WS
weak population
(WP)
cs=1.61, 526%, 4.89MPa
1
cw=1.71, 282%, 1.97 MPa
0.1
1
c (mm)
Figure 3.17 Tensile strength of B0N with precut c at 50 mm/min
60
5
4
σb0 = 3.65 MPa εb0 = 552
B0S
rate = 50 mm/min
3
2
σbc
(MPa)
1
1
c (mm)
Figure 3.18 Strength of B0S with precut c at 50 mm/min
61
When c is small in NR, the time for bulk crystallization upon straining is sufficiently
long, so that the effect of c on σbc is not much when compared to the changes in cut size
in first stage. Although bulk crystallization still plays a role, its extent is somewhat
limited by larger c and may be incomplete before catastrophic fracture. Another factor is
that the area available for crystallization is decreased due to a precut. Secondly, when the
decrease in σbc becomes discontinuous, this indicates that the rubber lacks the time
required to undergo bulk crystallization upon straining. Figure 3.20 compares the
stress-strain curve of precut gum NR specimen in SP and WP. WP specimen does not
show an upturn stage in stress-strain curve (Figure 3.7, Chapter 3.4.1) while SP specimen
does. This plot indicates bulk crystallization in WP is hindered.
On the whole range of c, the SBR is several times weaker than the natural rubber
(Figure 3.21). Perhaps, crystallization at cut tip makes gum NR in WP still stronger than
gum SBR.
3.5.2 Precut Tensile Results of Black-Filled SBR at 50 mm/min
Precut tensile results of carbon black N115-filled SBR tested at 50 mm/min are
shown and compared with unfilled SBR in Figure 3.22 and normal tensile strengths are
labeled.
Tensile strength of all these three compound decreases continuously with increasing
cut size. Strength of B20S at c = 2.5 mm is about 1.7 MPa (according to linear fit),
almost 2 times than that of B8S and B0S. High concentration of carbon black N115
improves the performance of SBR, especially when SBR contains a large flaw.
62
B0N
rate = 50 mm/min
25
20
15
σ
(MPa)
10
Exclusion zone
∆ε=1.81, ∆σ=2.62MPa
5
0
0
1
2
3
4
5
6
7
8
ε
Figure 3.19 Stress-strain curve of B0N at 50 mm/min, with precut specimens labeled
63
B0N
rate = 50 mm/min
10
8
c=0.67 mm, SP
σ
(MPa)
6
4
2
c=2.02 mm, WP
0
0
1
2
3
4
5
6
7
ε
Figure 3.20 Comparison of stress-strain curve of precut B0N in SP and WP at 50 mm/min
64
B0N, Strong population
10
σbc
(MPa)
B0N, Weak population
1
B0S
0.1
1
c (mm)
Figure 3.21 Comparison of strength of gum SBR and NR with precut c at 50 mm/min
65
When cut size c is small as 0.2 mm, the percents of strength loss, SL, compared to
uncut specimen is defined in Eq.3.1. Difference in normal tensile strength is excluded in
SL by definition and only the change in tensile strength is considered. SL of B0S, B8S
and B20S are listed in Table 3.8.
SL =
σb0 −σbc (c=0.2)
(3.1)
σb0
The effect of small edge cut on tensile strength can be expressed by strength loss at a
small cut. Strength loss describes how significantly a precut will decrease tensile strength
and thus the larger the value is, the more sensitive to precut the rubber is.
Table 3.8 Strength loss of precut SBR at c = 0.2 mm
Strength Loss at c = 0.2 mm
B0S
72%
B8S
64%
B20S
51%
According to Table 3.8, SL decreases with increasing concentration of carbon black,
i.e., carbon black reduces sensitivity of SBR to precut. Because additional carbon black
introduces interaction with rubber which is only thermodynamically determined and
doesn’t depend on the edge cut. Therefore, Sensitivity of tensile strength on precut is
reduced by the carbon black.
66
rate = 50mm/min
10
B20S
σb0=18.3 MPa
σbc
(MPa)
1
B8S
σb0=11.2MPa
B0S
σb0=3.63MPa
0.1
1
c (mm)
Figure 3.22 Tensile strength of SBR filled with various amount of carbon black with
precut c at 50 mm/min
67
3.5.3 Reduced Strength of Slightly Carbon Black Filled NR at 50 mm/min
Contrast to the clear increase in tensile strength of precut SBR after addition of
carbon black, slight addition of carbon black to precut NR not only doesn’t reinforce the
rubber, but also reduces the tensile strength as well as cs, cw. (Figure 3.23).
Characteristic values are compared in Table 3.9.
Table 3.9 Characteristic values of tensile results of B0N, B5N and B14N at 50 mm/min
cs
cw
εs
εw
σs
σw
Δε
Δσ
SL
B0N
1.61
1.71
4.89
3.09
4.61
1.99
1.80
2.62
33%
B5N
1.04
1.10
4.13
2.66
4.05
2.16
1.47
1.89
42%
B14N
0.85
1.05
3.52
2.69
4.03
2.22
0.83
1.81
56%
According to Table 3.9, critical cut size decreases with increasing carbon black
loading when N115 loading is below 14 phr. Difference between strong population and
weak population diminishes (Δε and Δσ for B15N are only 0.83 and 1.81 MPa,
respectively). Strength loss is calculated by Eq. 3.1. SL increases as the carbon black
loading increases (less than 14 phr). This indicates that slightly filled rubber is more
sensitive to precut when the concentration of carbon black increases, which is contrast to
SBR. Slight loading of carbon black can only weaken the NR instead of reinforcing it.
Addition of little amount of carbon black interferes strain-induced crystallization
negatively. Crystallization requires enough chain orientation to give stable nuclei; crystal
growth requires long range chain mobility. Carbon black addition decreases the
proportion of deformable phase. The actual deformation and speed of deformation of the
rubber phase in filled rubber is higher than that in the gum. But, adsorption of chains on a
black surface decreases its mobility. The net rate of crystallization upon strain
68
crystallization depends on the relative strength of these effects which depends on the
black content. Gent 59 has shown that thermal-crystallization of NR is inhibited by carbon
black. X-ray analyses29,54 have shown that strain-crystallization of black-filled NR
initiates at lower strain than the gum.
Tensile results will be discussed in three regions: 0.10 mm ≤ c ≤ 0.85 mm (cs of
B14N); 0.85 mm ≤ c ≤ 1.71 mm (cw of B0N) and c > 1.71 mm.
When 0.10 mm ≤ c ≤ 0.85 mm (cs of B14N), c is smaller than the critical cut sizes of
B0N, B5N and B14N. Tensile strength decreases as black concentration increases. B14N
has only about 75% of the strength of the B0N. All specimens go bulk crystallization
before the rupture occurs. Rate and extent of crystallization decreases as the carbon black
concentration increases (less than 14 phr), thus the strength decreases with increasing
carbon black concentration.
When 0.85 mm < c ≤ 1.71 mm (cw of B0N), each compound has a very narrow cut
size region where the tensile strength drops significantly. Tensile strength of B0N, B5N
and B14N drops about two folds when cut size increases from 0.85 mm to 1.71 mm. All
critical cut sizes (cw and cs) of all three compounds locate in this region. But cw and cs
shift to lower size as the carbon black loading increases. This indicates that the
crystallization is inhibited when a little amount of carbon black is added: B14N can
crystallize upon strain only when c < 0.85 mm while B0N can crystallize until c > 1.61
mm. Nevertheless, although εs and σs decreases when N115 loading increases due to the
limited crystallization, εw and σw increases with increasing N115. In weak population,
bulk crystallization is almost absent. Consequently, inhibited crystallization doesn’t affect
the tensile results in this region. When carbon black concentration increases, rubber/
69
black interaction also increases and thus, σw of B14N is larger than that of B0N.
Difference between strong and weak population is narrowed.
When c > 1.71 mm, all specimens are in weak population. Data of three compounds
in this region almost overlaps.
3.5.4 Critical Carbon Black Loading for Partial Reinforcement at 50 mm/min
NR with low concentration of carbon black (less than 14 phr) shows a decrease in cs,
cw and tensile strength as carbon black concentration increases. But addition of high
content of carbon black starts to reinforce NR. Tensile results of B15N are given in
Figure 3.24 and compared with those of B0N, B14N in Figure 3.25. Bold solid line
represents for the results of gum NR (B0N) (only linear fit is shown). Solid triangles
represent for precut specimens with simple lateral crack when they are pulled apart;
hollow triangles represent for precut specimens with multiple cracks or with strong
deviation from initial cut when they are pulled apart.
The precut tensile tests of B15N also give two separated populations. In the cut
region of 1.04 mm ≤ c ≤ 2.26 mm, strength of B15N is intrinsically unstable: some
specimens are two-fold stronger than the others. This separation is based on the different
crack patterns instead of the lack in bulk crystallization as in the separation of strong and
weak population. Crack patterns of some representative specimens are shown Figure 3.26
and Figure 3.27. Figure 3.26 shows a specimen with crack deviation at point A. Figure
3.27 shows a specimen with multiple crack which starts at point A and stop at point B and
crack deviation at point C, D.
70
rate=50 mm/min
10
σbc
(MPa)
B14N
1
B5N
gum (only line)
0.1
1
c (mm)
Figure 3.23 Tensile strength of precut B0N, B5N and B14N at 50 mm/min
71
10
The smallest cut size where multiple crack or crack deviation appears is noted as cm,s;
the largest cut size after which multiple crack or crack deviation disappear is noted as cm,l.
For B15N at 50 mm/min, multiple crack or crack deviation cannot be observed below c =
1.04 mm and after c = 2.26 mm. Thus, cm,s = 1.04 mm and cm,l = 2.26 mm for B15N at 50
mm/min
Crystallization is enhanced with the help of high loading of carbon black.39
Fiber-like strain-crystallites cause sufficient anisotropy in strength to block lateral crack
growth and allow propagation between fibrils.25 Approved crystallization and rubber/
black network are necessary for crack deviation, i.e., heavily loaded SBR doesn’t show
multiple cracks. Specimens of B15N with multiple cracks have only about the same
strength as the gum NR at comparable cut size.
Slow and stable multiple cracks help to blunt the cut tip, and reduce stress
concentration. The stable pre-cracks allow more time for the formation crystalline
domain and provide additional resistance to fracture.
15 phr of N115 black is the lowest concentration where multiple cracks form and
reinforcement begins. This amount of black is also the concentration for incipient bound
rubber formation. A continuous filler/rubber network combined with crystallized domain
is necessary for reinforcement.
15 phr of N115 black is also the lowest concentration where the separated strong and
weak population disappears. But reinforcement at 15 phr is still incomplete: specimens
before cm,s and after cm,l still show single lateral crack and have low tensile strength.
72
B15N
rate=50 mm/min
10
σbc
(MPa)
simple crack
multiple crack
1
cm,l=2.26mm
cm,s=1.04mm
1
c (mm)
Figure 3.24 Tensile results of B15N with precut c at 50 mm/min
73
rate=50 mm/min
10
σbc
(MPa)
B15N
B15N
B14N
1
gum (only line)
0.1
1
10
c (mm)
Figure 3.25 Comparison of precut tensile results of B0N, B14N and B15N at 50 mm/min
74
Figure 3.26 Crack pattern of specimen of B15N at 50 mm/min (c = 1.09 mm, 8.11 MPa)
Figure 3.27 Crack pattern of specimen of B15N at 50 mm/min (c = 1.40 mm, 7.44 MPa)
75
3.5.5 Critical Carbon Black Loading for Completed Reinforcement at 50 mm/min
Precut tensile results of NR with higher content of carbon black (B18N and B19N)
are plotted and compared with that of B0S in Figure 3.28. Solid line represents for the
linear fit of the results of B0N. Hollow squares or triangles represent for specimens with
multiple cracks or crack deviation. Solid triangles represent for specimens with simple
lateral crack.
Simple lateral crack pattern is still observable in results of B18N: cm,s = 0.36 mm, cm,l
= 3.15 mm. But all specimens of B19N show strong crack deviation or multiple cracks.
19 phr of N115 black is the lowest concentration where the simple lateral crack pattern
disappears and all specimens show a deviated crack pattern. Reinforcement of precut NR
filled with 19 phr of N115 black starts to be completed: all specimens are reinforced
regardless of the cut size.
First turning point of concentration of black, CT,1, is defined as the concentration of
N115 where multiple crack starts to occur. Second turning point of concentration of black,
CT,2, is defined as the concentration of N115 where the reinforcement is completed. In the
case of NR at 50 mm/min, CT,1 = 15 phr and CT,2 = 19 phr.
When N115 black concentration is larger than CT,2 = 19 phr (25 phr), changes in
tensile results at given tensile rate are not obvious (Figure 3.30). Tensile strength show
some increases in the specimens with multiple cracks from B15N to B19N, but
strength-cut profile of B19N and B25N at whole range of cut size is almost overlapped.
Reinforcement performance is stabilized after CT,2.
76
rate=50 mm/min
B19N
B18N
10
σbc
(MPa)
B18N
1
gum (only line)
0.1
1
10
c (mm)
Figure 3.28 Comparison of precut tensile results of B0N, B18N and B19N at 50 mm/min
77
When black loading is increased to CT2, crack pattern becomes more complicated.
Figure 3.29 shows one representative specimen (B19N at 50 mm/min, c = 1.09 mm)
Figure 3.29 Crack pattern of B19N specimen at 50 mm/min (c = 1.09 mm, 12.52 MPa)
When the specimen with initial cut tip (shown by the arrow) was stretched, the initial
crack first grew quickly to point A. At point A the crack separated into two direction. One
of them stopped in point B as secondary crack and dispersed a lot of energy. The other
one formed another secondary crack at point C. Then, the crack grew a little back to cut
edge at C (at about 45o angle). After the short returning crack, the crack deviated and
propagated rapidly to point D, where the crack formed into the last secondary crack and
propagated until the specimen was pulled apart.
78
Strength Loss, SL, of N115 black-filled rubber is calculated by Eq.3.1 and listed in
Table 3.10. Part of the data is taken from Table 3.9. NR with more than 14 phr of N115
black don’t show cs and cw. All the information about strong and weak population has
already been collected in Table 3.9.
Table 3.10 Collection of SL values of all NR compounds at 50 mm/min
Compounds
SL (single crack)
SL (multiple crack)
B0N
33%
N/A
B5N
42%
N/A
B14N
56%
N/A
B15N
64%
N/Aa
B18N
62%
26.3%b
B19N
N/A
10%
B25N
N/A
6%
a. cm,s = 1.04 mm is too far from 0.20 mm as definition, so calculation is not carried out.
b. cm,s = 0.36 mm. SL is calculated by the strength at this cut size.
Sensitivity (described by SL) of strength of specimens with single crack to precut
first increase with increasing N115 black loading, then stabilizes at 64% at CT,1 where the
rubber/ black network starts to form. Sensitivity of strength of multiple crack to precut
(only when N115 loading larger than 15 phr) decreases rapidly to only 10% at CT,2. At
high loading of N115 black, NR vulcanizates can tolerate a relatively large precut (about
0.4-0.5 mm) without a huge decrease in strength.
79
rate=50 mm/min
B19N
B25N
B18N
10
σbc
(MPa)
B15N
1
gum (only line)
0.1
1
10
c (mm)
Figure 3.30 Comparison of precut tensile results of N115 filled NR with crack deviation
at 50 mm/min
80
3.6 Precut Tensile Results of SBR at Various Tensile Rates
Tensile rates are changed widely from 0.1 mm/min to 250 mm/min for both gum and
black-filled SBR. Previous precut tensile tests are repeated.
3.6.1 Rate Dependence of Precut Tensile Results of Unfilled SBR
Results of tensile tests of precut unfilled SBR specimens testes are three tensile rates:
250 mm/min, 50 mm/min and 25 mm/min, are shown in Figure 3.31. Results of precut
unfilled SBR at 50 mm/min has been described in Chapter 3.5.1 (Figure 3.18). Tensile
strengths of unfilled SBR at 250 mm/min and 25 mm/min follow the same rule of the one
at 50 mm/min: Strength decrease monotonously and continuously with increasing cut size
without a turning point in slope or a sudden drop. At each comparable cut size, tensile
strength decreases with decreasing tensile rate, e.g., at c = 1 mm. tensile strength at 25
mm/min is only 65% of the one at 250 mm/min. This trend of reduced strength at lower
tensile rate is quite similar to the tensile results of uncut SBR (Chapter 3.4.2, Figure 3.10)
Although tensile strength increases with increasing tensile rate, specimens tested at
higher tensile rate have a larger strength loss, SL. SLs of B0S at each tensile rate
calculated by Eq.3.1 and listed in Table 3.11. SL of B0S at 250 mm/min is 10% larger
than that at 25 mm/min. Unfilled SBR is more sensitive to precut at higher tensile rate.
But this sensitivity to flaw is compensated by less sufficiency in chain relaxation and
higher absolute tensile strength.
81
B0S
rate=250mm/min
1
σbc
(MPa) rate=50mm/min
rate=25mm/min
0.1
1
c (mm)
Figure 3.31 Rate dependence of precut tensile strength of B0S
82
Table 3.11 Strength loss of precut B0S at various tensile rates.
Tensile Rate (mm/min)
Strength Loss, SL (%) (at c = 0.2 mm)
250
78%
50
72%
25
68%
3.6.2 Rate Dependence of Precut Tensile Results of Black Filled SBR
Effect of carbon black N115 on the rate dependence of precut tensile strength of SBR
is investigated. 8 phr and 20 phr of N115 black is added. Results are shown Figure 3.32
(B8S) and Figure 3.33 (B20S).
Figure 3.34 compares the tensile results of precut B0S, B8S and B20S (only linear
fits are shown; solid lines represent for B20S at four rates, dash line represent for B8S at
four rates and dot line represent for B0S at three rates). Results of B0S at 250 and 50
mm/min and B8S at 25 and 0.1 mm/min in Figure 3.34 is zoomed in Figure 3.35.
Both B8S and B20S show a decrease in tensile strength with decreasing tensile rate
and increasing cut size. B20S is stronger than B8S at any tensile rates although the
difference between B20S at 0.1 mm/min and B8S at 250 mm/min is small, especially
when c < 0.50 mm. B8S at 250 mm/min and 50 mm/min is stronger than B0S at any cut
size. But, when c > 0.58 mm, strength of B0S at 250 mm/min (σB0S, 250) is larger than σB8S,
0.1.
When c > 1.52 mm, σB0S, 50 > σB8S, 0.1. When c > 2.04 mm, σB0S, 250 > σB8S, 25. Interaction
between rubber and N115 black at only 8 phr is not strong enough, so the effect of
insufficiency in chain relaxation at high tensile rate may overwhelm the rubber/ black
interaction in B8S, especially at low tensile rate and large cut size.
83
Strength loss, SL, of B0S, B8S and B20S at each tensile rate is calculated by Eq.3.1
and compared in Table 3.12. Previous results have shown that at r = 50 mm/min, SL
decreases with increasing carbon black loading (Chapter 3.5.2); at zero loading of carbon
black (B0S, gum SBR), SL decreases with decreasing tensile rate (Chapter 3.6.1). Table
3.12 demonstrates that SL of all SBR compounds (B0S, B8S, B20S) show a decrease
with decreasing tensile rate. It also shows that at any given tensile rates (from 0.1
mm/min to 250 mm/min), SL decreases with increasing loading of carbon black.
Increasing carbon black loading and decreasing tensile rate can reduce the sensitivity of
SBR to a flaw.
Carbon black N115 loading and related strength loss give a monotonous and
continuous decreasing line without a turning point at each given tensile rate. The absolute
value of this slope is noted as Slope B. At each tensile rate, slope B shows an average
value of 0.8, which doesn’t rely on the tensile rate.
Tensile rate and related strength loss at each carbon black concentration give a
monotonous increasing line but there is a turning point for all three compounds (Figure
3.36). Turning point occurs at 25 mm/min regardless of carbon black loading. Before 25
mm/min, slope doesn’t change a lot with increasing tensile rate, i.e., SL can be regarded
constant and sensitivity to flaw is stabilized by low rate. After 25 mm/min. slope
increases to give Slope A. Slope A is about 0.057 and doesn’t change with black loading.
84
Table 3.12 Strength loss of B0S, B8S and B20S at various tensile rates
r = 250a
r = 50
r = 25
r = 0.1
Slope Ab
0 phr
78%d
72%
68%
62%e
0.058f
8 phr
68%
64%
61%
57%
0.056f
20 phr
57%
51%
48%
46%
0.058f
Slope Bc
0.80
0.81
0.79
0.80
a. Tensile rate. Unit is mm/min
b. Slope A is the slope of fitted line of tensile rate- strength loss relation plot (log-log
scale) at each N115 loading
c. Slope B is the slope of fitted line of N115 loading- strength loss relation plot at each
given tensile rate
d. Strength Loss, SL at given tensile rate and given carbon black loading
e. Initially, B0S hasn’t been run at 0.1 mm/min. In order to finish this table, a new batch
of B0S was made. Some uncontrollable error or deviation may be introduced to this 62%
data because it’s from a new sample batch. But the trend seems fine compared to other
results.
f. Definition of slope A is shown in Figure 3.36
85
10
B8S
r=250 mm/min
r=50 mm/min
r=25 mm/min
r=0.1 mm/min
σbc
(MPa)
1
0.1
1
c (mm)
Figure 3.32 Rate dependence of precut strength of B8S
86
B20S
rate=250mm/min
10
rate=50mm/min
rate=25mm/min
σbc
(MPa)
rate=0.1mm/min
1
0.1
1
c (mm)
Figure 3.33 Rate dependence of precut strength of B20S
87
B20S
B8S
B0S
10
σbc
(MPa)
1
0.1
1
c (mm)
Figure 3.34 Comparison of precut tensile strength of B0S, B8S, B20S at various rates
88
B8S, r=25
B8S, r=0.1
σbc 1
(MPa)
B0S, r=250
B0S, r=50
2.04
0.58
1.52
1
c (mm)
Figure 3.35 Comparison of precut strength of B0S (r=250, 50) and B8S (r=25, 0.1)
89
85
80
75
70
slo
pe
A
B0S
65
SL 60
(%)
B8S
55
50
B20S
45
0.01
0.1
1
10
rate (mm/min)
Figure 3.36 SL versus tensile rate to decide slope A
90
100
Slope A (rate-dependence) is much smaller than slope B (N115-loading dependence).
This indicates that precut tensile strength of SBR is more sensitive to carbon black
instead of to tensile rate. This behavior is similar to that of uncut SBR (chapter 3.4.3,
Table 3.6).
3.7 Precut Tensile Results of NR at Various Tensile Rates
Tensile rates are changed quite widely from 0.05 mm/min to 500 mm/min for gum
NR to examine how critical cut sizes will vary with tensile rate. Tensile rates for
black-filled NR are changed to examine how the black-loading affect the rate-dependence
of precut tensile results.
3.7.1 Completed Tensile Rate- Critical Cut Size Profile of Gum NR
Precut gum NR tested at 50 mm/min shows a separation of strong and weak
population at cs = 1.61 mm, cw = 1.71 mm, with a 33% strength loss (SL) (Figure 3.17
and Table 3.8).
Tensile rate was then firstly changed to 250 mm/min and 50 mm/min respectively.
Precut tensile results are plotted against cut size in log-log scale in Figure 3.37. In the
whole range of c, tensile strengths overlap in both strong and weak population. At small
cut (c < 0.4 mm), strength drop slowly and smoothly with increasing cut size. Strengths
at c = 0.2 mm at 3 tensile rates are nearly the same while normal strength increases at
higher tensile rate, so SL decreases at when tensile rate is reduced. Critical cut sizes, cs
and cw slightly increases when tensile rate decreases: cs increases from 1.58 mm (r = 250
mm/min) to 1.65 mm (r = 25 mm/min) and cw increases from 1.69 mm (r = 250 mm/min)
to 1.76 mm (r = 25 mm/min).
91
Tensile rate was changed to higher rates and lower rates. Only two cut size regions
are investigated: the first one is 0.15 mm < c < 0.45 mm (for the determination of SL); the
second one is 1.60 mm < c < 2.50 mm (for the determination of cs and cw). Results are
plotted in Figure 3.38. When c < 0.45 mm, tensile strength shown a decrease with
decreasing tensile rate: σbc (c = 0.2 mm) decreases from 16.4 MPa (r = 500 mm/min) to
9.95 MPa (r = 0.05 mm/min). In the region of 1.60 mm < c < 2.50 mm, data from 500
mm/min to 25 mm/min is not distinguishable.
But when tensile rate is further reduced, tensile strength in strong population
decreases: σs = 4.63 MPa at 500 mm/min but only 2.94 MPa at 0.05 mm/min. Data in
weak population overlap at all tensile rates. Critical cut sizes (cs and cw) clearly shift to
higher cut sizes when tensile rate decreases: cs is 1.57 mm at r = 500 mm/min but 2.13
mm at r = 0.05 mm/min; cw is 1.70 mm at r = 500 mm/min but 2.18 mm at r = 0.05
mm/min. There is a 36% and 28% increase in cs and cw.
Characteristic values in tensile results are given in Table 3.13. Completed tensile
rate- cs/ cw relation is given in Figure 3.39.
When tensile rate reduces from 500 mm/min to 0.05 mm/min, cs and cw first change
slowly (r ≥ 25 mm/min), then they increase at a relatively high speed until r = 0.5
mm/min, finally the increasing trend is slowed down. If the tensile result at extremely
slow tensile rate, e.g., 0.001 mm/min, is defined as equilibrium tensile results (cs, eq and cw,
eq),
then the extrapolation of the last period (0.05 mm/min ≤ r ≤ 0.5 mm/min) to the line
of r = 0.001 gives cw, eq = 2.27 mm and cs, eq = 2.25 mm. This is the equilibrium critical
cut size which can be obtained only when NR is stretched as a sufficiently slow rate that
crystallization is maximized.
92
B0N
r=250mm/min
10
r=50mm/min
σbc
(MPa)
r=25mm/min
r=50mm/min
r=250mm/min
1
r=25mm/min
0.1
1
c(mm)
Figure 3.37 Comparison of precut tensile strength of B0N at 250, 50 and 25 mm/min
93
B0N
r=500mm/min
10
r=250mm/min
σbc
(MPa)
r=10 mm/min
r=0.05mm/min
1
0.1
1
c (mm)
Figure 3.38 Comparison of precut tensile strength of B0N at 500, 250, 10, 0.05 mm/min
94
2.5
B0N
cw,eq=2.27mm
∆ceq=0.02mm
cs, cw
(mm) c
=2.25mm
s,eq
2.0
cw
cs
1.5
1E-3
0.01
0.1
1
10
rate (mm/min)
Figure 3.39 Completed tensile rate- cs/ cw profile
95
100
1000
Absolute values of σs, εs and with respect to tensile rate generally decrease with
decreasing tensile rate, but changes in σw, εw is totally random. Because in strong
population, tensile strength is mainly controlled by bulk crystallization. Δσ and Δε is
decreasing when tensile rate is reduced: they show a 67% and 53% decrease respectively.
Reducing tensile rate can diminish the difference between strong and weak population
SL is calculated in Table 3.13. SL decreases when tensile rate decrease from 500
mm/min to 0.05 mm/min. Decrease in SL is due to the enhanced crystallinity: crystalline
domain increases the strength and make material less sensitive to precut (similar to the
behavior of precut SBR, Table 3.11, Table 3.12).
3.7.2 Effect of Tensile Rate on the Carbon Black Loading for Reinforcement of NR
When NR is filled by carbon black N115, the critical N115 loading where the
separation of strong and weak population disappeared can be observed at each tensile rate.
Detailed characteristic values are collected in Table 3.14. All designators follow the ones
in Chapter 3.5.3 and Chapter 3.5.4. SL at CT,1 (SL(CT,1)) is calculated with strengths of
specimens with single lateral crack patterns.
Representative data of precut tensile results of N115 black-filled NR tested at various
tensile results are plotted in Figure 3.40 (B0~B15N, at 250 mm/min), Figure 3.41 (B0N,
B18~B20N, at 250 mm/min), Figure 3.42 (B0~B15N, at 0.1 mm/min) and Figure 3.43
(B0N, B18N, at 0.1 mm/min), in which solid plots are specimens with single crack
pattern; hollow and star plots are specimens with multiple cracks pattern. Turning points
in N115 concentration (CT,1 and CT,2) are plotted against tensile rates in Figure 3.44.
96
Table 3.13 Characteristic values of tensile results of B0N at various tensile rates
rate
cs
cw
εs
εw
σs
σw
Δε
Δσ
SL
500
1.57
1.70
5.22
2.24
4.63
1.62
2.98
3.01
N/A
250
1.58
1.69
5.12
2.24
4.84
1.85
2.88
2.99
46%
50
1.61
1.71
5.19
2.42
4.61
1.99
2.77
2.62
33%
44
1.62
1.73
4.68
1.96
4.01
1.43
2.72
2.58
N/A
38
1.63
1.73
4.41
1.75
4.05
1.59
2.66
2.46
N/A
29
1.63
1.75
4.11
1.54
4.11
1.64
2.57
2.47
N/A
25
1.65
1.76
4.06
1.62
4.13
1.69
2.44
2.44
29%
10
1.73
1.84
3.80
1.62
4.02
1.62
2.18
2.40
29%
5
1.81
1.92
3.87
1.75
3.84
1.45
2.12
2.39
N/A
1
2.00
2.06
3.85
1.73
3.86
1.65
2.12
2.21
23%
0.5
2.05
2.11
3.62
2.01
3.88
1.84
1.61
2.04
N/A
0.1
2.11
2.16
3.38
1.69
3.41
1.74
1.69
1.67
18%
0.05
2.13
2.18
3.07
1.67
2.94
1.94
1.40
1.00
N/A
Table 3.14 Characteristic values of precut tensile results of black-filled NR
rate
CT1
cs(CT1-1)
cw(CT1-1)
cm,s(CT1)
cm,l(CT1)
SL(CT1)
CT2
SL(CT2)
SL(C=25)
0.1
15
1.42
1.52
0.54
3.17
48%
18
14%
8%
10
15
1.12
1.29
0.98
2.41
54%
19
13%
14%
50
15
0.85
1.05
1.04
2.26
64%
19
10%
6%
250
15
0.71
0.78
1.09
2.13
66%
20
14%
6%
97
rate = 250 mm/min
B15N
(multiple crack)
10
σbc
(MPa)
gum NR
(only line)
B15N
(single crack)
B5N
1
B14N
0.1
1
c (mm)
Figure 3.40 Precut strength of B0N, B5N, B14N and B15N at 250 mm/min
98
rate = 0.1 mm/min
gum NR
(only line)
B15N
(Multiple crack)
10
σbc
(MPa)
B15N
(Single crack)
B14N
1
B5N
0.1
1
c (mm)
Figure 3.41 Precut tensile strength of B0N, B5N, B14N, B15N at 0.1 mm/min
99
rate = 250 mm/min
star: B20N
10
σbc
(MPa)
1
square: B18N
gum NR
(only line)
round: B19N
0.1
0.1
1
c (mm)
Figure 3.42 Precut tensile strengths of B0N, B18N, B19N and B20N at 250 mm/min
100
rate = 0.1 mm/min
B18N
10
σbc
(MPa)
gum NR
(only line)
1
0.1
1
c (mm)
Figure 3.43 Comparison of precut tensile strength of B0N and B18N at 0.1 mm/min
101
22
NR
21
20
19
CT2
18
CT1, CT2
(phr) 17
16
CT1
15
14
13
0.01
0.1
1
10
100
rate (mm/min)
Figure 3.44 Effect of tensile rates on critical N115 loadings CT1 and CT2
102
Precut strength after CT,2 slightly reduce with tensile rate as an effect of chain
relaxation as bulk crystallization is enough. But relation of SL after CT,2 with tensile rates
is unclear. Perhaps, SL is also partially controlled by crystallization.
Changes in critical cut sizes, cs, cw, cm, s, cm, l, and strength loss at CT,1 (SL(CT,1)) is
controlled by tensile rate, more precisely, by crystallization. At CT,1-1, crystallization is
strongly limited but chain relaxation at lower tensile rate helps NR to crystallize to a
reduced degree, so cs and cw show an increase at lower tensile rate. At CT,1, rubber/ black
network is formed and crystallization is favored. Difference between cm, s and cm, l shows
how well the combination of network and crystallization can give multiple cracks. Since
crystallization is favored at lower rate, difference between cm, s and cm, l should increase at
lower tensile rates.
First turning point in N115 concentration, CT,1, doesn’t change with tensile rates
because CT,1 is determined by the lower limit of concentration where rubber/ black
network forms and the formation of network is thermodynamically controlled and doesn’t
rely on the tensile rate. But the second turning point in N115 concentration, CT,2,
increases with increasing tensile rate. After CT,1, rubber/ black network is formed and CT,2
is decided by the interaction between network and crystallization. If crystallization in
network is strong, filled NR has more chance to have multiple crack and reinforce rubber.
Therefore, CT,2 is reduced at lower tensile rate.
When NR is sufficiently loaded by N115 (B25N), precut tensile results are measured
and plotted at various tensile rates (Figure 3.45). After CT,2, tensile strength decreases
with tensile rate, which is determined by the effect of chain relaxation.
103
rate=250mm/min
B25N
rate=50mm/min
10
rate=10mm/min
σbc
(MPa)
rate=0.1mm/min
1
0.1
1
10
c (mm)
Figure 3.45 Comparison of precut strengths of B25N at 250, 50, 10, 0.1 mm/min
104
3.8 Slopes of Fitted Line of Strength-Cut Size Plot
According to Equation 1.6, precut tensile strength should be related to cut size by a
slope of -0.5 in a log-log plot (Equation 3.2).
1
lgσbc = 2 lg
EG
k
1
− 2 lgc
(3.2)
But deviation from this theoretical value always exists in this plot. Some
representative slopes in strength-cut log-log plots are selected and collected from Table
3.15 to Table 3.17. Only NR has the different slopes in one plot: slope1 is the slope at
very small cut size and strength drop slowly with cut size (if this period exists); slope2 is
the slope after the largest cut size in slope1 and before cs; slope3 is the slope in weak
population. If multiple cracks are observed together with single crack, slope4 is the slope
of strength-cut plot of specimens with multiple cracks. If only multiple cracks can be
observed at all cut sizes, slope1 is the slope at small cut sizes and strength drop slowly
with cut size and slope2 is the slope of rest specimens.
B0N at high tensile rate, B5N, B14N at low rate, B15N/ B18N with multiple cracks,
B8S and B20S at all tensile rate have slopes close to -0.5. But, majority of the slopes
listed below show a large deviation from -0.5. For both gum SBR and gum NR, slope
increase with decreasing tensile rate (for gum NR, changes in slope1 and slope3 are
almost random). For when SBR and NR are filled by black, this tendency is reversed:
increase in tensile rate generally increase slope (for NR, only slope2 and slope4 follow
this rule; changes in slope1 and slope3 are random). Generally, slope of SBR increases
with carbon black concentration with the only exception of B8S at 250 mm/min. Changes
of slope of NR with carbon black concentration is unclear.
105
Table 3.15 Slopes in strength-cut plot of gum SBR/ NR
Specimen
B0S
Rate
Slope1
Slope2
Slope3
250
-0.23
N/A
N/A
50
-0.20
N/A
N/A
25
-0.28
N/A
N/A
250
-0.25
-0.52
-0.55
50
-0.26
-0.50
-0.56
25
-0.19
-0.88
-1.50
10
N/A
-0.90
-4.07
0.1
-0.28
-0.99
-2.93
0.05
-0.07
-1.47
-7.40
B0N
Table 3.16 Slopes in strength-cut plot of black-filled SBR
Specimen
Rate
Slope
250
-0.69
50
-0.61
25
-0.43
0.1
-0.34
250
-0.52
50
-0.61
25
-0.47
0.1
-0.48
B8S
B20S
106
Table 3.17 Slopes in strength-cut plot of black-filled NR
Specimen
B5N
B14N
B15N
B18N
B19N
B25N
Rate
Slope1
Slope2
Slope3
Slope4
250
N/A
-0.61
-0.54
N/A
50
N/A
-0.63
-0.17
N/A
0.1
N/A
-0.48
-0.51
N/A
250
N/A
-0.86
-0.76
N/A
50
N/A
-0.67
-1.05
N/A
0.1
N/A
-0.57
-1.38
N/A
250
N/A
-1.14
N/A
-0.90
50
N/A
-0.71
N/A
-0.51
0.1
N/A
-0.65
N/A
-0.28
250
N/A
-0.76
N/A
-0.63
50
N/A
-0.58
N/A
-0.54
0.1
-0.17
-0.94
N/A
N/A
250
-0.26
-1.90
N/A
N/A
50
-0.37
-1.29
N/A
N/A
10
-0.38
-1.27
N/A
N/A
250
-0.20
-1.15
N/A
N/A
50
-0.18
-1.06
N/A
N/A
0.1
-0.16
-1.02
N/A
N/A
107
When Equation 1.6 is transformed into Equation 3.2 to give the slope of -0.5,
modulus, E, and fracture energy, G, are considered as irrelevant to cut size, c, i.e., E and
G should not be a function of c. Although modulus is mainly determined by the material
and filler itself, fracture energy is affected by a lot of other factors, and some of these
factors are related to cut size. Conflict between chain relaxation and crystallization is one
of the factors. When tensile rate is reduced, crystallization of NR is favored and the
crystalline domain can increase the fracture energy, G. But when cut size is large (even c
< cs), ability of crystallization is reduced and consequently, effect of softening by chain
relaxation may offset some effect of crystallization and decreases G. Rubber/ Black
interaction is another problem. This interaction itself is not affected by cut size, but it can
affect the relaxation which can be cut-dependent. When polymer chain is partially
absorbed by black, polymer chain requires more time to relax at any tensile rate when
compared to unfilled rubber. Large cut size reduces the time for rubber to be pulled apart
and thus limits the relaxation. Fracture energy is then higher than expected, especially at
low tensile rates. Rubber/ black interaction also interferes crystallization for NR. Before
CT,1, crystallization is limited by carbon black and large cut size limits the crystallization
and reduces fracture energy furthermore. After CT,1, crystallization is improved but
reinforcement requires the formation of deviated crack pattern which is aroused by
coexistence of the crystallization and rubber/ black network. Thus, effect of large precut
on tensile strength is greater than the pure reduced crystallization ability. Therefore, G
becomes an implicit function of c. Many factors coexist under experimental condition
and conflict or strength each other. It is hard to derive analytical formulae of G versus c at
each tensile rate and each black-loading. So it is hard to predict the slope in this plot.
108
CHAPTER IV
CONCLUSIONS
1. Tensile strength and ultimate elongation of SBR increase with increasing carbon black
N115 loading. Tensile strength of NR increases with carbon black concentration, but
ultimate elongation decreases
2. Tensile strength and ultimate elongation of SBR and NR increase with tensile rate.
3. Strength of uncut SBR and NR is more sensitive to carbon black loading than to tensile
rate. Carbon black decreases sensitivity of rubber’s strength to tensile rate. Increase of
tensile rate increases sensitivity of rubber’s strength to carbon black loading.
4. Precut tensile strength of gum NR shows separated strong and weak populations due to
lack of crystallization, when cut size is larger than cs, cw.
5. Precut tensile strength of gum SBR decreases continuously with cut size.
6. Precut tensile strength of SBR increase monotonously with carbon black loading and
sensitivity to precut is reduced by carbon black.
7. Precut tensile strength of unfilled or filled SBR increases monotonously with tensile
rate, but strength loss of SBR also increases.
8. Precut tensile strength and strength loss of NR reduces with decreasing tensile rate.
9. Critical cut sizes for gum NR, cs and cw, shift to higher cut size with increasing tensile
rate to give equilibrium cut size cs, eq = 2.25 mm, cw, eq = 2.27 mm at extremely low tensile
rate. Difference between two populations diminishes with decreasing tensile rate.
109
10. The difference in strong and weak population decreases with increasing black
loading.
11. A critical carbon black concentration for reinforcement of precut NR (CT,1) exist.
Below CT,1, tensile strength and cs, cw decrease and strength loss increases with increasing
black loading.
12. At CT,1, rubber/ black network forms and crack deviation occurs, which helps to
reinforce precut NR. Separation of strong and weak population disappears.
13. A critical carbon black concentration for completed reinforcement of precut NR (CT,2)
exist to strengthen NR at all cut sizes. Strength loss at low cut size is very small after CT,2
14. CT,1 is 15 phr for NR at all tensile rates. CT,2 is 20 phr for NR at 250 mm/min and
decreases to 18 phr for NR at 0.1 mm/min.
15. After CT,2, precut strength is stabilized under given tensile rate, but still decreases
with decreasing tensile rate.
110
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115
APPENDIX
TABLES OF TENSILE RESULTS
Table A.1 Tensile results of B0N at 500 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Thickness (mm)
0.598
0.611
0.632
0.581
0.573
0.586
0.564
0.611
0.607
0.662
0.614
0.633
0.582
0.599
0.601
0.573
0.600
0.605
0.612
0.627
0.619
c (mm)
0.18
0.25
0.46
0.78
1.13
1.28
1.32
1.41
1.44
1.51
1.57
1.62
1.68
1.70
1.74
1.82
1.91
2.05
2.13
2.26
2.31
116
σbc (MPa)
16.42
15.91
12.33
11.01
8.08
7.31
7.09
6.79
5.19
4.77
4.63
1.34
3.92
1.62
1.42
1.56
1.41
1.38
1.26
1.14
1.20
εbc
7.78
7.72
7.65
6.91
6.23
5.75
5.58
6.04
5.52
5.42
5.31
5.23
4.74
1.84
2.25
1.94
2.02
1.42
1.11
2.05
1.89
Table A.2 Tensile results of B0N at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Thickness (mm)
0.652
0.611
0.555
0.602
0.597
0.623
0.611
0.603
0.643
0.600
0.612
0.650
0.572
0.617
0.580
0.564
0.614
0.626
0.605
0.598
0.603
0.625
0.612
0.599
0.644
0.600
0.644
0.607
0.577
0.632
0.590
0.633
0.598
0.622
c (mm)
0.00
0.00
0.00
0.18
0.28
0.36
0.47
0.53
0.68
0.73
0.91
1.05
1.08
1.14
1.23
1.29
1.49
1.58
1.63
1.66
1.69
1.77
1.90
1.96
2.01
2.09
2.10
2.23
2.29
2.31
2.33
2.41
2.56
2.71
117
σbc (MPa)
26.75
27.02
28.57
15.09
14.12
12.75
12.00
9.91
11.70
10.15
9.84
8.42
9.50
7.41
6.42
6.41
4.84
6.47
1.29
4.41
1.25
1.29
1.26
1.23
1.16
1.86
1.28
1.15
1.76
1.17
1.21
1.15
1.29
1.11
εbc
7.62
7.98
7.55
6.88
6.63
6.64
6.34
6.04
6.12
6.77
5.99
6.28
5.91
5.86
5.55
5.75
5.12
5.60
2.94
4.68
1.97
2.05
2.04
1.94
1.65
2.14
1.83
1.71
2.24
1.86
1.95
1.85
2.19
1.53
Table A.3 Tensile results of B0N at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
Thickness (mm)
0.583
0.591
0.632
0.612
0.589
0.633
0.585
0.598
0.578
0.633
0.608
0.612
0.615
0.588
0.609
0.611
0.624
0.653
0.597
0.600
0.578
0.632
0.617
0.578
0.566
0.628
0.578
0.608
0.612
0.613
0.579
0.600
0.578
0.579
0.579
0.614
0.612
c (mm)
0.00
0.00
0.00
0.12
0.25
0.33
0.42
0.53
0.67
0.72
0.91
0.99
1.03
1.17
1.19
1.23
1.25
1.39
1.47
1.51
1.53
1.58
1.61
1.71
1.80
1.89
1.91
1.96
2.00
2.02
2.14
2.23
2.25
2.33
2.44
2.57
2.63
118
σbc (MPa)
23.38
23.58
24.13
16.45
15.19
11.74
12.41
9.67
9.65
10.66
8.44
9.23
8.04
7.03
7.89
7.09
7.00
6.06
6.19
7.04
5.24
4.62
4.89
1.97
1.01
1.26
0.94
2.00
1.14
1.81
1.66
1.48
1.94
1.12
1.49
1.04
0.94
εbc
7.81
7.65
7.62
6.88
6.63
6.12
6.34
6.49
5.87
6.63
5.99
6.04
5.91
5.69
6.28
6.08
5.86
5.15
5.55
5.88
5.25
5.19
5.27
2.42
1.54
1.94
1.73
1.23
1.65
1.20
1.59
1.34
1.25
1.85
1.83
1.66
1.39
Table A.4 Tensile results of B0N at 44 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Thickness (mm)
0.582
0.567
0.573
0.583
0.560
0.562
0.555
0.590
0.567
0.585
0.554
0.593
0.618
0.596
0.600
0.633
0.613
0.595
0.600
0.584
c (mm)
1.13
1.25
1.31
1.44
1.52
1.57
1.62
1.73
1.79
1.85
1.96
2.08
2.16
2.18
2.20
2.43
2.50
2.51
2.51
2.94
119
σbc (MPa)
5.98
5.10
4.85
4.54
4.71
4.47
4.02
0.91
1.10
1.43
1.16
1.28
1.20
1.06
1.10
0.94
1.33
1.37
0.97
0.92
εbc
7.00
6.56
5.81
5.34
4.69
6.49
4.91
1.50
1.22
1.96
1.78
1.85
1.96
1.92
1.63
1.44
1.43
2.54
1.40
1.50
Table A.5 Tensile results of B0N at 38 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Thickness (mm)
0.624
0.641
0.655
0.598
0.628
0.606
0.557
0.595
0.557
0.606
0.607
0.623
0.635
0.600
0.639
0.656
0.689
0.583
c (mm)
1.28
1.36
1.41
1.46
1.52
1.57
1.63
1.69
1.71
1.71
1.73
1.85
1.90
1.96
2.09
2.12
2.23
2.31
120
σbc (MPa)
6.27
5.74
4.61
3.92
3.49
4.06
4.98
0.82
3.46
3.05
0.97
1.09
1.01
1.59
1.37
0.90
1.09
1.03
εbc
5.55
5.18
4.81
5.00
4.92
4.41
6.92
1.47
4.44
3.70
1.75
2.12
1.72
1.59
1.50
1.72
1.95
2.03
Table A.6 Tensile results of B0N at 29 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Thickness (mm)
0.594
0.573
0.584
0.576
0.589
0.607
0.578
0.576
0.570
0.584
0.553
0.557
0.580
0.596
0.606
0.600
0.594
0.604
0.604
0.570
c (mm)
0.98
1.03
1.06
1.12
1.16
1.22
1.25
1.37
1.46
1.58
1.63
1.75
1.86
1.94
1.99
2.04
2.12
2.28
2.36
2.51
121
σbc (MPa)
6.12
4.97
5.63
5.54
4.85
3.93
4.29
5.11
4.11
4.12
4.16
1.44
0.94
0.90
1.65
1.05
1.11
0.83
1.03
0.92
εbc
6.70
5.28
2.79
2.71
3.39
2.17
2.18
6.42
3.93
4.95
3.35
1.94
1.28
1.49
2.76
1.02
1.77
1.48
1.80
1.52
Table A.7 Tensile results of B0N at 25 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Thickness (mm)
0.557
0.642
0.633
0.582
0.618
0.656
0.577
0.627
0.590
0.537
0.581
0.508
0.650
0.610
0.564
0.557
0.577
0.592
0.571
0.605
0.567
0.585
0.547
0.568
0.583
0.586
0.564
0.580
0.639
0.645
0.635
0.604
0.595
0.620
c (mm)
0.00
0.00
0.00
0.22
0.35
0.43
0.53
0.69
0.71
0.86
0.92
1.08
1.14
1.21
1.35
1.38
1.40
1.49
1.50
1.65
1.68
1.71
1.76
1.80
1.88
1.96
2.07
2.14
2.23
2.29
2.36
2.50
2.66
2.85
122
σbc (MPa)
21.34
21.16
21.05
14.81
12.98
13.20
11.47
9.10
5.91
7.83
9.17
6.54
7.78
6.04
5.76
4.91
5.99
4.13
5.28
4.58
1.70
5.49
1.13
1.47
1.45
0.98
1.47
1.15
0.86
1.36
1.06
0.96
0.93
1.22
εbc
7.31
7.43
7.35
6.50
6.34
6.26
6.32
5.86
5.38
6.07
6.11
5.55
5.94
5.53
5.78
5.34
5.02
5.27
5.19
4.06
2.23
5.24
1.62
1.74
1.33
1.41
1.50
1.72
1.40
1.37
1.68
1.74
1.36
1.37
Table A.8 Tensile results of B0N at 10 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Thickness (mm)
0.612
0.593
0.607
0.593
0.621
0.612
0.591
0.628
0.574
0.606
0.604
0.608
0.584
0.596
0.608
0.600
0.586
0.576
0.568
0.578
0.558
0.600
0.640
0.642
c (mm)
0.00
0.00
0.00
0.22
0.36
0.42
1.18
1.22
1.35
1.41
1.50
1.54
1.62
1.68
1.73
1.79
1.81
1.84
1.96
2.07
2.26
2.44
2.58
2.71
123
σbc (MPa)
18.60
18.14
17.80
12.67
11.32
10.33
5.02
4.08
4.37
4.01
4.13
4.30
4.29
4.02
4.28
1.28
1.09
1.56
1.62
1.57
1.55
1.66
1.44
1.06
εbc
7.35
7.32
7.44
6.43
5.32
6.12
4.70
6.19
5.43
4.54
3.79
3.70
4.78
1.50
1.62
1.06
1.63
1.20
0.99
1.34
1.56
1.40
1.31
1.20
Table A.9 Tensile results of B0N at 5 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Thickness (mm)
0.555
0.632
0.618
0.620
0.661
0.650
0.644
0.637
0.583
0.575
0.588
0.590
0.571
0.564
0.599
0.612
0.620
0.621
c (mm)
1.33
1.41
1.48
1.50
1.55
1.62
1.69
1.75
1.81
1.87
1.90
1.92
1.99
2.07
2.14
2.28
2.41
2.52
124
σbc (MPa)
4.42
4.13
4.25
3.91
4.04
4.42
3.85
3.99
3.92
1.02
5.45
1.46
1.32
1.24
1.34
1.27
1.15
1.05
εbc
5.42
5.34
4.35
5.17
4.71
4.24
4.94
3.94
3.87
2.41
5.42
1.48
1.52
1.34
1.75
1.19
1.62
1.65
Table A.10 Tensile results of B0N at 1 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Thickness (mm)
0.652
0.633
0.599
0.642
0.631
0.647
0.642
0.602
0.614
0.605
0.613
0.620
0.611
0.584
0.577
0.592
0.571
0.598
0.582
0.622
0.620
0.631
c (mm)
0.00
0.00
0.22
0.28
0.37
1.51
1.66
1.70
1.72
1.77
1.83
1.91
1.96
2.00
2.06
2.09
2.11
2.17
2.25
2.33
2.41
2.59
125
σbc (MPa)
16.47
16.33
13.60
11.53
9.90
4.31
3.91
4.05
4.14
3.99
4.01
4.04
3.97
3.87
1.65
1.34
1.39
1.42
1.38
1.39
1.24
1.14
εbc
7.02
6.94
5.67
6.32
5.54
4.47
4.92
4.15
4.19
4.32
3.94
4.02
3.85
4.04
1.52
1.65
1.12
1.73
1.46
1.42
1.72
1.56
Table A.11 Tensile results of B0N at 0.5 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Thickness (mm)
0.633
0.627
0.572
0.572
0.580
0.566
0.600
0.594
0.588
0.583
0.595
0.601
0.609
0.605
0.603
0.616
c (mm)
1.69
1.76
1.82
1.87
1.93
1.97
2.01
2.05
2.11
2.15
2.19
2.23
2.28
2.33
2.39
2.42
126
σbc (MPa)
3.94
4.04
4.46
3.95
3.88
4.01
4.00
3.88
1.45
1.85
1.72
1.55
1.42
1.22
1.13
1.10
εbc
4.42
4.13
4.04
3.78
3.94
3.62
3.95
3.67
1.94
2.01
1.42
1.91
1.53
1.42
1.33
1.45
Table A.12 Tensile results of B0N at 0.1 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Thickness (mm)
0.604
0.572
0.588
0.631
0.620
0.608
0.609
0.616
0.613
0.607
0.622
0.614
0.630
0.625
0.619
0.588
0.582
0.589
0.600
0.594
c (mm)
0.00
0.00
0.19
0.21
0.33
1.81
1.86
1.93
1.98
2.01
2.04
2.07
2.11
2.16
2.19
2.23
2.27
2.29
2.34
2.40
127
σbc (MPa)
13.20
11.42
10.11
9.52
8.53
3.95
3.88
3.84
3.70
3.74
3.52
3.60
3.41
1.58
1.74
1.62
1.46
1.64
1.32
1.22
εbc
6.49
6.16
4.53
4.41
3.97
3.42
3.72
3.89
3.70
4.04
3.52
3.41
3.38
1.41
1.69
1.34
1.55
1.50
1.41
1.52
Table A.13 Tensile results of B0N at 0.05 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Thickness (mm)
0.582
0.533
0.617
0.600
0.597
0.563
0.570
0.568
0.577
0.571
0.603
0.602
0.621
0.615
0.619
0.620
0.622
c (mm)
0.21
0.47
0.52
0.21
0.47
0.52
1.74
1.88
1.94
2.01
2.05
2.09
2.13
2.13
2.16
2.18
2.23
128
σbc (MPa)
9.93
9.12
9.44
9.93
9.12
9.44
3.56
3.68
3.50
3.37
3.27
3.14
3.07
1.67
3.62
1.51
1.52
εbc
5.32
5.18
5.12
3.42
3.85
3.56
3.31
3.14
2.94
3.12
2.04
3.04
1.94
1.50
1.24
1.22
1.42
Table A.14 Tensile results of B0S at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Thickness (mm)
0.592
0.633
0.640
0.632
0.605
0.581
0.563
0.579
0.613
0.604
0.563
0.624
0.562
0.600
0.643
0.556
0.577
0.614
0.550
0.632
0.597
c (mm)
0.00
0.00
0.00
0.43
0.46
0.61
0.64
0.75
0.76
0.80
0.89
1.15
1.19
1.37
1.45
1.55
1.63
1.90
2.20
2.21
2.64
129
σbc (MPa)
4.41
4.47
6.13
1.10
1.08
1.04
1.02
0.98
0.95
0.97
0.94
0.91
0.87
0.82
0.80
0.85
0.71
0.73
0.81
0.78
0.78
εbc
5.98
6.52
5.85
1.57
1.43
1.32
1.44
1.31
1.21
1.06
1.22
1.20
1.13
1.01
1.06
0.95
0.90
0.90
0.60
0.58
0.78
Table A.15 Tensile results of B0S at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Thickness (mm)
0.552
0.583
0.577
0.592
0.565
0.587
0.590
0.601
0.607
0.612
0.593
0.650
0.647
0.634
0.648
0.629
0.633
0.636
0.600
0.611
0.617
c (mm)
0.00
0.00
0.00
0.25
0.38
0.45
0.59
0.62
0.69
0.76
0.98
1.11
1.5
1.57
1.61
1.72
1.73
1.85
2.25
2.3
2.41
130
σbc (MPa)
3.86
3.56
3.47
1.02
0.91
0.99
0.93
0.90
0.82
0.80
0.81
0.80
0.79
0.79
0.75
0.75
0.76
0.71
0.70
0.71
0.65
εbc
5.41
5.53
5.43
1.63
1.51
1.57
1.43
1.46
1.44
1.35
1.30
1.23
1.08
0.99
0.88
0.82
0.75
0.64
0.70
0.60
0.73
Table A.16 Tensile results of B0S at 25 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Thickness (mm)
0.633
0.580
0.574
0.591
0.566
0.600
0.639
0.641
0.570
0.601
0.627
0.651
0.622
0.624
0.618
0.623
0.589
0.592
0.565
0.574
0.547
0.558
0.612
c (mm)
0.00
0.00
0.00
0.22
0.42
0.52
0.57
0.62
0.67
0.72
0.87
1.02
1.17
1.45
1.47
1.56
1.59
1.63
1.89
1.93
1.94
2.28
2.51
131
σbc (MPa)
3.01
3.15
2.89
0.97
0.88
0.85
0.80
0.77
0.71
0.70
0.72
0.72
0.70
0.64
0.61
0.61
0.63
0.63
0.54
0.55
0.54
0.53
0.57
εbc
5.14
5.17
4.63
1.42
1.34
1.32
1.22
1.11
1.13
1.09
1.03
1.08
0.94
0.85
0.82
0.77
0.69
0.72
0.70
0.68
0.62
0.65
0.64
Table A.17 Tensile results of uncut B0S at 10, 1, 0.1 mm/min
Tensile Rate
(mm/min)
10
1
0.1
Specimen #
1
2
3
1
2
3
1
2
3
Thickness
(mm)
0.672
0.665
0.669
0.672
0.643
0.650
0.621
0.613
0.617
132
σbc (MPa)
εbc
2.80
2.79
3.10
2.03
2.13
1.91
1.13
1.73
1.47
4.87
4.75
5.32
3.74
3.42
2.85
1.63
2.15
2.33
Table A.18 Tensile results of B5N at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Thickness (mm)
0.583
0.609
0.616
0.580
0.593
0.616
0.573
0.605
0.589
0.594
0.583
0.566
0.604
0.602
0.590
0.577
0.590
0.600
0.596
0.601
0.599
0.633
0.582
0.557
0.614
0.602
0.630
c (mm)
0.00
0.00
0.17
0.29
0.32
0.37
0.49
0.60
0.61
0.76
0.80
0.84
0.88
0.91
0.96
1.02
1.07
1.09
1.12
1.23
1.46
1.70
1.83
2.13
2.15
2.31
2.48
133
σbc (MPa)
28.41
27.19
15.16
12.49
8.81
9.70
8.47
7.81
7.69
5.80
5.46
6.35
4.68
6.47
5.02
5.24
1.56
1.62
1.78
1.34
1.34
1.45
1.00
1.00
1.12
1.12
1.12
εbc
7.68
7.92
6.85
6.41
5.95
6.13
5.79
5.82
5.53
5.03
4.42
4.45
4.85
5.40
5.09
5.10
2.37
4.91
2.63
2.21
1.93
2.25
1.23
1.29
1.42
1.34
1.59
Table A.19 Tensile results of B5N at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Thickness (mm)
0.578
0.608
0.611
0.579
0.600
0.626
0.576
0.603
0.583
0.572
0.572
0.544
0.611
0.603
0.587
0.578
0.587
0.599
0.590
0.592
0.593
0.571
0.638
0.664
0.519
0.630
0.616
0.564
0.633
c (mm)
0.00
0.00
0.18
0.21
0.25
0.31
0.38
0.42
0.55
0.68
0.69
0.75
0.76
0.85
0.90
1.04
1.10
1.21
1.26
1.28
1.34
1.39
1.45
1.49
1.64
1.94
2.41
2.58
3.01
134
σbc (MPa)
22.61
26.20
13.19
12.60
13.89
10.86
9.66
8.44
7.37
7.84
7.73
7.62
5.71
5.82
4.19
4.05
1.67
1.10
1.52
1.67
1.76
1.41
1.89
2.16
1.62
1.62
1.76
1.22
1.22
εbc
6.89
6.97
5.23
4.90
4.83
4.90
4.54
4.68
4.42
4.70
4.47
4.46
4.33
4.06
3.65
3.67
4.01
4.46
4.11
3.89
1.74
1.81
3.75
2.01
1.68
1.47
1.72
0.94
0.98
Table A.20 Tensile results of B5N at 10 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Thickness (mm)
0.582
0.609
0.615
0.580
0.595
0.618
0.574
0.604
0.588
0.590
0.581
0.562
0.605
0.602
0.590
0.577
0.590
0.600
0.595
0.599
0.598
0.587
0.619
0.605
0.570
0.595
c (mm)
0.00
0.00
0.23
0.27
0.32
0.40
0.52
0.64
0.71
0.74
0.97
0.99
1.08
1.10
1.21
1.26
1.31
1.33
1.34
1.37
1.47
1.56
1.92
2.04
2.54
2.97
135
σbc (MPa)
18.13
18.18
14.07
12.08
12.44
13.66
9.64
9.51
8.29
8.44
7.68
6.95
5.56
6.22
4.53
1.75
4.33
1.42
1.50
1.71
1.95
1.63
1.46
1.59
1.10
1.10
εbc
6.93
7.01
6.27
6.03
6.32
6.05
5.85
5.84
5.74
5.50
5.08
5.76
5.46
5.55
3.65
5.42
3.83
3.34
3.57
2.85
2.90
6.27
6.03
6.32
6.05
5.85
Table A.21 Tensile results of B5N at 0.1 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Thickness (mm)
0.608
0.594
0.595
0.585
0.580
0.609
0.606
0.623
0.579
0.595
0.604
0.606
0.614
0.613
0.604
0.600
0.589
0.596
0.580
0.586
0.573
0.608
0.574
0.595
0.582
0.580
0.634
c (mm)
0.00
0.00
0.42
0.49
0.57
0.73
0.81
0.88
1.17
1.22
1.43
1.46
1.59
1.61
1.77
1.89
1.92
2.08
2.16
2.16
2.24
2.29
2.39
2.47
2.65
2.91
3.46
136
σbc (MPa)
11.11
13.52
7.20
6.37
6.00
5.38
5.24
5.46
4.14
4.40
4.37
4.29
4.21
3.85
3.93
1.89
1.33
1.43
1.97
1.43
1.60
1.53
1.50
1.40
1.60
1.20
1.20
εbc
6.73
6.81
5.75
5.38
5.31
5.38
4.99
5.14
4.86
5.21
4.88
4.64
4.63
4.50
4.22
3.71
3.73
4.07
4.53
4.00
4.17
4.27
1.91
1.99
2.21
1.85
1.62
Table A.22 Tensile results of B14N at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Thickness (mm)
0.620
0.587
0.584
0.588
0.573
0.605
0.623
0.632
0.574
0.598
0.615
0.629
0.618
0.618
0.611
0.611
0.589
0.594
c (mm)
0.00
0.00
0.25
0.35
0.43
0.53
0.58
0.62
0.71
0.78
0.86
0.91
1.15
1.36
1.55
1.62
1.88
2.03
137
σbc (MPa)
27.51
27.40
11.58
8.27
7.17
6.53
5.89
5.01
4.58
2.21
1.65
1.88
1.32
1.43
1.32
1.32
0.99
0.88
εbc
6.92
6.74
5.89
5.19
4.99
4.70
4.16
3.04
2.80
2.57
2.04
2.29
1.57
1.73
1.55
1.61
1.12
1.06
Table A.23 Tensile results of B14N at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Thickness (mm)
0.596
0.598
0.597
0.583
0.591
0.621
0.598
0.615
0.577
0.574
0.587
0.572
0.617
0.610
0.596
0.593
0.587
0.596
c (mm)
0.00
0.00
0.26
0.38
0.48
0.52
0.61
0.69
0.72
0.77
0.85
0.91
0.96
1.05
1.33
1.57
1.68
1.87
138
σbc (MPa)
23.63
25.37
9.87
8.48
7.35
6.10
5.90
4.58
4.03
4.15
2.22
1.90
2.05
1.90
1.90
1.42
0.95
0.88
εbc
6.38
6.78
4.21
3.71
3.57
3.36
2.97
2.17
2.00
1.84
1.46
1.63
1.13
1.24
1.11
1.15
0.80
0.76
Table A.24 Tensile results of B14N at 10 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Thickness (mm)
0.619
0.576
0.581
0.611
0.593
0.604
0.624
0.629
0.592
0.604
0.625
0.633
0.626
0.625
0.619
0.606
0.586
0.591
0.583
c (mm)
0.00
0.00
0.26
0.42
0.54
0.69
0.89
1.02
1.12
1.17
1.23
1.29
1.37
1.46
1.58
1.79
2.10
2.21
2.62
139
σbc (MPa)
18.22
19.38
8.03
7.45
6.59
6.64
5.29
5.12
4.13
2.34
4.29
2.34
1.91
2.00
1.91
1.91
1.65
1.40
1.12
εbc
5.92
5.61
4.36
3.84
3.69
3.48
3.08
2.25
2.07
1.90
1.51
1.69
1.16
1.28
1.31
1.36
0.95
0.89
1.99
Table A.25 Tensile results of B14N at 0.1 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Thickness (mm)
0.619
0.592
0.580
0.605
0.598
0.593
0.611
0.613
0.598
0.598
0.614
0.616
0.622
0.618
0.614
0.603
0.588
c (mm)
0.00
0.00
0.51
0.63
0.99
1.09
1.15
1.29
1.35
1.42
1.51
1.67
1.83
2.06
2.15
2.46
2.63
140
σbc (MPa)
13.71
13.90
6.56
5.24
4.15
3.79
3.73
3.60
3.77
3.03
1.49
1.35
1.66
1.43
1.31
1.31
0.95
εbc
5.67
5.23
4.37
3.85
3.70
3.48
3.08
2.25
2.08
1.91
1.51
1.70
1.17
1.29
1.15
1.19
0.83
Table A.26 Tensile results of B15N at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Thickness (mm)
0.597
0.613
0.605
0.578
0.590
0.604
0.580
0.602
0.589
0.592
0.586
0.575
0.605
0.603
0.594
0.587
0.592
0.601
0.599
0.602
0.600
0.599
0.613
0.625
c (mm)
0.00
0.00
0.31
0.40
0.46
0.61
0.62
0.63
0.77
0.80
0.81
0.88
1.02
1.09
1.17
1.18
1.29
1.33
1.42
1.52
1.73
1.85
2.13
2.32
141
σbc (MPa)
27.44
28.66
9.44
8.72
7.34
6.14
6.45
5.16
5.26
4.81
3.94
3.54
3.31
8.62
6.76
2.87
2.48
1.82
7.90
1.61
4.19
1.22
4.91
1.41
εbc
6.41
6.50
4.94
4.82
4.92
4.16
4.32
4.25
3.06
3.77
2.44
2.52
4.53
4.79
4.25
2.76
1.79
2.34
4.54
1.81
3.41
2.18
3.80
1.40
Table A.27 Tensile results of B15N at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Thickness (mm)
0.596
0.627
0.603
0.577
0.596
0.609
0.586
0.608
0.589
0.571
0.587
0.561
0.621
0.606
0.587
0.587
0.588
0.598
0.593
0.604
0.598
0.543
0.634
0.603
c (mm)
0.00
0.00
0.38
0.47
0.52
0.67
0.67
0.68
0.81
0.85
0.86
0.92
1.05
1.09
1.19
1.20
1.31
1.35
1.40
1.63
1.78
2.09
2.26
2.44
142
σbc (MPa)
22.61
27.79
8.89
8.21
6.72
7.01
6.08
6.17
5.16
4.53
3.78
3.23
2.18
8.11
6.37
2.68
1.71
2.20
7.44
4.94
2.00
4.62
4.62
1.09
εbc
6.68
6.14
4.20
4.10
4.18
3.55
3.69
3.63
2.65
3.23
2.14
2.21
3.86
4.07
3.63
2.41
1.61
2.06
3.87
5.62
2.94
4.93
3.26
1.29
Table A.28 Tensile results of B15N at 10 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Thickness (mm)
0.608
0.627
0.599
0.579
0.593
0.600
0.591
0.606
0.592
0.582
0.592
0.577
0.617
0.608
0.595
0.597
0.593
0.602
0.601
0.607
0.599
0.643
0.623
0.577
c (mm)
0.00
0.00
0.23
0.27
0.30
0.47
0.52
0.63
0.77
0.81
0.82
0.89
0.98
1.06
1.11
1.34
1.47
1.52
1.74
1.86
2.05
2.41
2.53
2.66
143
σbc (MPa)
18.80
19.61
8.71
7.57
6.12
5.77
5.04
4.23
3.65
3.14
3.09
2.05
5.82
7.47
5.82
5.32
1.40
1.86
6.83
1.40
4.52
4.82
1.16
1.03
εbc
5.91
5.64
4.70
4.58
4.68
3.90
4.07
4.00
2.78
3.50
2.15
2.23
4.28
4.54
4.00
2.47
1.49
2.04
4.29
1.50
3.14
1.89
3.54
1.08
Table A.29 Tensile results of B15N at 0.1 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Thickness (mm)
0.632
0.641
0.604
0.591
0.603
0.602
0.608
0.616
0.605
0.598
0.607
0.601
0.628
0.622
0.613
0.618
0.609
0.617
0.620
0.621
0.616
0.633
0.631
0.604
c (mm)
0.00
0.00
0.12
0.22
0.36
0.46
0.54
0.64
0.77
0.93
0.97
1.24
1.47
1.64
1.82
2.20
2.43
2.68
2.92
3.08
3.17
3.28
3.46
3.67
144
σbc (MPa)
14.21
14.19
8.18
7.48
6.24
5.77
9.11
9.82
4.76
4.17
3.22
8.92
2.11
7.38
5.58
1.78
0.78
1.28
6.68
0.78
5.82
1.08
1.02
0.98
εbc
5.71
5.56
4.06
3.97
4.04
3.49
3.61
3.56
2.70
3.21
2.25
2.31
3.76
3.94
3.56
2.48
1.79
2.18
3.77
1.79
2.95
2.07
3.23
1.50
Table A.30 Tensile results of B18N at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Thickness (mm)
0.572
0.626
0.624
0.583
0.614
0.648
0.580
0.616
0.587
0.553
0.575
0.523
0.635
0.611
0.580
0.573
0.586
0.600
0.585
c (mm)
0.17
0.27
0.39
0.42
0.46
0.76
0.81
1.20
1.34
1.59
1.72
2.05
2.25
2.58
2.77
2.93
2.97
3.16
3.42
145
σbc (MPa)
11.13
10.17
8.22
21.49
13.66
17.85
13.22
3.97
9.15
9.81
9.21
2.64
9.70
1.97
5.62
5.84
4.08
1.32
1.01
εbc
4.85
6.30
5.62
6.39
5.36
5.80
5.24
3.06
4.50
4.64
4.73
2.33
4.62
3.01
3.76
3.77
3.10
1.38
1.33
Table A.31 Tensile results of B18N at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Thickness (mm)
0.619
0.614
0.604
0.647
0.687
0.629
0.642
0.617
0.656
0.597
0.646
0.565
0.623
0.678
0.627
0.619
0.642
0.658
c (mm)
0.18
0.22
0.27
0.30
0.36
0.44
0.52
0.78
1.03
1.37
1.69
1.82
2.20
2.68
3.06
3.15
3.37
3.45
146
σbc (MPa)
9.73
8.12
7.67
6.84
18.94
17.34
15.48
14.17
10.08
8.63
9.00
2.65
8.54
7.75
5.13
5.32
1.82
1.54
εbc
4.37
5.68
5.07
5.75
4.83
5.22
4.72
2.76
4.06
4.18
4.26
2.10
4.16
2.71
3.39
3.40
2.79
1.25
Table A.32 Tensile results of B18N at 10 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Thickness (mm)
0.596
0.670
0.664
0.615
0.651
0.689
0.611
0.657
0.622
0.575
0.611
0.544
0.679
0.644
0.604
0.596
c (mm)
0.17
0.25
0.33
0.41
0.65
1.05
1.18
1.51
1.81
2.24
2.57
2.90
3.13
3.52
3.75
3.91
147
σbc (MPa)
8.28
7.15
17.23
15.99
13.40
11.80
9.84
8.60
6.81
7.30
7.63
1.37
7.22
5.50
1.13
0.87
εbc
4.33
5.58
5.00
5.66
4.77
5.15
4.67
2.79
4.03
4.15
4.23
2.16
4.14
2.74
3.39
3.40
Table A.33 Tensile results of B18N at 0.1 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Thickness (mm)
0.608
0.692
0.684
0.631
0.669
0.709
0.626
0.677
0.639
0.586
0.628
0.554
0.701
0.661
0.615
0.608
0.628
0.644
c (mm)
0.23
0.54
0.82
1.22
1.67
1.98
2.23
2.66
2.95
3.36
3.78
4.11
4.55
4.92
5.37
5.78
5.91
6.18
148
σbc (MPa)
12.02
10.05
9.69
8.24
6.90
5.63
4.76
4.52
4.23
3.77
3.54
3.31
2.44
1.83
2.60
2.70
1.89
1.42
εbc
4.60
4.68
4.18
4.75
3.99
4.31
3.90
2.28
3.35
3.45
3.52
3.73
3.43
2.24
2.79
2.80
2.30
2.03
Table A.34 Tensile results of B19N at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Thickness (mm)
0.544
0.616
0.610
0.563
0.597
0.635
0.558
0.603
0.569
0.523
0.558
0.493
0.625
0.591
0.551
0.544
0.561
0.576
0.557
0.582
c (mm)
0.18
0.56
0.91
1.35
1.78
1.99
2.36
2.68
2.91
3.24
3.58
3.87
4.16
4.79
5.23
5.57
5.68
5.71
5.85
6.08
149
σbc (MPa)
23.41
21.43
14.54
11.50
7.22
6.13
4.50
3.58
2.55
2.33
1.92
1.73
1.56
1.43
1.24
1.17
1.20
1.32
0.56
0.32
εbc
4.92
5.23
4.37
3.82
4.01
3.66
2.58
3.72
3.12
3.44
2.99
2.78
3.03
3.12
2.59
2.81
2.56
2.30
1.92
1.68
Table A.35 Tensile results of B19N at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Thickness (mm)
0.570
0.643
0.637
0.589
0.624
0.662
0.585
0.630
0.595
0.549
0.584
0.518
0.652
0.618
0.577
0.570
0.587
0.603
c (mm)
0.21
0.72
1.09
1.45
1.83
2.17
2.54
2.96
3.45
3.71
4.11
4.56
4.88
5.29
5.53
5.82
6.11
6.22
150
σbc (MPa)
23.98
17.82
12.52
9.51
6.37
5.08
4.32
3.16
2.82
2.30
1.85
1.64
1.57
1.78
1.61
1.55
1.49
1.38
εbc
6.05
5.23
5.76
4.88
4.67
4.04
3.63
4.22
3.88
3.35
3.42
2.95
3.17
3.20
2.78
2.66
2.31
2.43
Table A.36 Tensile results of B19N at 10 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Thickness (mm)
0.591
0.637
0.632
0.584
0.635
0.681
0.600
0.625
0.617
0.560
0.570
0.565
0.639
0.641
0.595
0.588
0.578
0.572
0.547
c (mm)
0.18
0.42
1.02
1.22
1.62
1.66
2.02
2.49
2.89
3.34
3.41
3.81
4.22
4.72
4.83
5.05
5.31
5.88
6.15
151
σbc (MPa)
17.21
14.33
12.12
10.58
6.27
7.88
3.99
4.26
4.98
3.08
2.71
1.94
1.71
1.96
2.04
1.99
1.37
1.25
1.21
εbc
5.26
4.96
4.48
3.89
4.30
4.01
3.84
3.60
3.74
3.45
3.26
3.26
3.23
2.68
2.69
2.81
2.43
2.17
1.96
Table A.37 Tensile results of B20N at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
Thickness (mm)
0.601
0.633
0.630
0.582
0.640
0.690
0.608
0.623
0.627
0.565
0.563
c (mm)
0.19
0.68
1.23
1.79
2.18
2.67
3.44
3.98
5.11
5.68
6.09
152
σbc (MPa)
24.72
19.88
10.05
8.11
5.67
3.22
2.44
1.68
1.42
1.34
1.05
εbc
5.42
4.81
4.53
3.90
3.31
3.26
3.11
2.92
2.72
2.42
2.24
Table A.38 Tensile results of B25N at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Thickness (mm)
0.588
0.632
0.652
0.603
0.597
0.574
0.556
0.529
0.514
0.585
0.581
0.612
0.552
0.609
0.557
0.674
c (mm)
0.00
0.00
0.22
0.63
0.92
1.43
1.88
2.17
2.58
3.04
3.65
3.92
4.27
4.72
5.54
6.12
153
σbc (MPa)
29.61
28.79
27.42
19.85
11.62
6.33
5.14
4.55
3.72
3.20
2.77
2.13
1.92
1.72
1.59
1.33
εbc
6.44
6.58
5.32
4.97
5.74
4.65
4.13
4.55
3.92
3.45
3.82
3.51
2.70
2.52
1.33
1.78
Table A.39 Tensile results of B25N at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Thickness (mm)
0.616
0.627
0.621
0.581
0.566
0.595
0.629
0.645
0.611
0.595
0.576
0.575
0.559
0.541
0.525
0.616
c (mm)
0.00
0.00
0.18
0.44
1.17
1.65
2.07
2.43
2.96
3.31
3.78
4.05
4.72
5.17
5.83
6.22
154
σbc (MPa)
30.4
21.9
23.77
20.16
10.52
6.18
4.33
3.76
3.10
2.51
2.67
2.34
1.98
1.75
1.92
1.55
εbc
6.38
6.25
5.23
5.31
4.57
4.76
3.99
4.32
3.68
3.32
2.96
2.73
3.04
2.05
2.14
1.37
Table A.40 Tensile results of B25N at 10 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Thickness (mm)
0.604
0.628
0.612
0.569
0.573
0.566
0.637
0.635
0.598
0.586
0.581
0.585
0.568
0.567
0.546
0.604
c (mm)
0.00
0.00
0.22
0.72
1.58
2.18
2.61
2.99
3.53
4.04
4.34
4.97
5.24
5.66
6.04
6.18
155
σbc (MPa)
21.4
19.2
17.30
12.80
6.54
4.37
3.98
3.54
3.04
2.68
1.65
1.35
1.51
1.40
1.19
1.32
εbc
6.11
6.32
5.14
5.02
4.75
4.32
4.51
3.66
3.48
2.12
2.33
2.04
1.78
1.52
1.22
1.10
Table A.41 Tensile results of B25N at 0.1 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Thickness (mm)
0.608
0.629
0.612
0.575
0.572
0.574
0.635
0.635
0.603
0.587
0.580
0.588
0.573
0.568
0.551
0.608
c (mm)
0.00
0.00
0.20
0.53
1.07
1.41
1.92
2.34
2.69
3.31
3.72
4.23
4.68
5.39
5.86
6.08
156
σbc (MPa)
14.40
14.60
13.52
11.07
5.86
4.09
2.89
3.08
3.51
1.95
1.36
1.41
1.52
1.48
1.19
1.23
εbc
6.03
5.94
5.14
4.92
4.51
4.33
3.78
3.56
3.27
2.42
2.11
1.70
1.52
1.22
1.08
0.85
Table A.42 Tensile results of uncut B5N, B14N, B15N, B25N at 1, 25 mm/min
Tensile Rate
N115 Loading
5 phr
14 phr
1 mm/min
15 phr
25 phr
5 phr
14 phr
25 mm/min
15 phr
25 phr
Specimen #
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
157
σbc (MPa)
14.31
18.09
17.42
16.76
17.51
17.71
18.54
17.96
21.41
22.00
22.70
21.52
22.48
22.37
23.71
23.58
εbc
6.72
6.82
6.65
6.54
6.67
6.43
6.13
6.19
6.93
7.19
6.42
6.31
6.34
6.20
6.17
6.12
Table A.43 Tensile results of B8S at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Thickness (mm)
0.612
0.630
0.628
0.580
0.645
0.700
0.616
0.620
0.638
0.570
0.556
0.611
0.626
0.664
0.612
0.606
c (mm)
0.00
0.00
0.22
0.48
0.89
1.08
1.29
1.31
1.46
1.51
1.65
1.87
1.90
2.09
2.37
2.75
158
σbc (MPa)
12.70
12.16
2.05
1.89
1.50
1.43
1.35
1.25
1.31
1.27
1.23
1.12
1.10
1.04
0.93
0.88
εbc
6.69
6.70
2.86
2.82
1.80
1.94
1.61
1.76
1.75
1.41
1.81
1.26
1.59
1.23
1.14
1.08
Table A.44 Tensile results of B8S at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Thickness (mm)
0.638
0.639
0.604
0.630
0.574
0.618
0.618
0.624
0.634
0.588
0.584
0.632
0.648
0.622
0.644
0.616
c (mm)
0.00
0.00
0.42
0.68
0.92
1.17
1.23
1.45
1.55
1.62
1.70
1.86
1.91
2.11
2.20
2.43
159
σbc (MPa)
11.50
10.52
1.63
1.50
1.20
1.03
0.96
0.96
0.96
0.94
0.92
0.86
0.82
0.80
0.83
0.79
εbc
5.88
5.74
2.40
2.30
2.02
1.97
1.10
1.11
1.36
1.09
1.15
1.12
1.02
1.11
1.04
1.08
Table A.45 Tensile results of B8S at 25 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Thickness (mm)
0.564
0.678
0.646
0.616
0.612
0.634
0.626
0.596
0.582
0.638
0.650
0.648
0.644
0.652
0.650
0.664
c (mm)
0.00
0.00
0.38
0.61
0.92
1.16
1.28
1.38
1.41
1.63
1.70
1.82
1.93
2.20
2.44
2.71
160
σbc (MPa)
9.57
7.65
1.44
1.27
1.02
0.97
0.92
0.93
0.92
0.91
0.30
0.81
0.80
0.74
0.71
0.69
εbc
6.85
6.74
3.04
1.93
1.79
1.68
1.61
1.62
1.68
1.65
1.34
1.26
1.30
1.04
0.97
0.75
Table A.46 Tensile results of B8S at 0.1 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Thickness (mm)
0.632
0.661
0.657
0.642
0.644
0.637
0.625
0.653
0.572
0.598
0.557
0.600
0.631
0.622
0.571
c (mm)
0.00
0.00
0.31
0.55
0.78
0.98
1.17
1.35
1.44
1.59
1.74
1.82
2.03
2.25
2.68
161
σbc (MPa)
5.15
5.25
1.24
1.12
1.03
0.94
0.90
0.85
0.87
0.82
0.77
0.72
0.69
0.65
0.60
εbc
5.45
5.15
3.02
2.79
2.57
2.68
1.81
1.76
1.34
1.27
1.15
2.10
1.73
1.19
1.21
Table A.47 Tensile results of B20S at 250 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Thickness (mm)
0.608
0.646
0.626
0.596
0.614
0.578
0.638
0.635
0.575
0.584
0.572
0.601
0.607
0.616
0.576
0.633
0.646
0.561
0.576
c (mm)
0.00
0.00
0.19
0.34
0.57
0.69
0.83
1.00
1.08
1.35
1.46
1.58
1.64
1.71
1.87
2.04
2.15
2.42
2.53
162
σbc (MPa)
24.08
24.72
13.81
11.09
8.20
10.44
4.74
5.21
5.63
4.70
4.78
3.73
4.24
4.18
4.00
4.02
3.83
3.27
3.15
εbc
6.83
6.42
5.13
4.54
5.03
5.02
4.97
4.88
4.01
4.16
3.73
4.22
3.65
3.63
3.71
3.55
3.49
3.73
3.02
Table A.48 Tensile results of B20S at 50 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Thickness (mm)
0.592
0.631
0.607
0.571
0.595
0.549
0.634
0.621
0.567
0.571
0.568
0.593
0.591
0.604
0.569
0.599
0.611
0.672
0.571
c (mm)
0.00
0.00
0.19
0.34
0.47
0.67
0.76
0.82
1.18
1.27
1.39
1.54
1.62
1.74
1.88
1.93
2.11
2.25
2.39
163
σbc (MPa)
22.5
24.5
9.79
8.72
6.57
4.43
6.38
4.44
4.06
2.69
3.46
3.36
3.23
3.03
2.97
2.53
2.67
2.27
2.05
εbc
6.52
6.21
5.22
4.89
4.63
4.85
4.61
4.22
4.59
3.95
3.80
3.52
3.67
3.53
3.63
3.40
3.34
3.22
3.10
Table A.49 Tensile results of B20S at 25 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Thickness (mm)
0.605
0.642
0.621
0.608
0.607
0.580
0.611
0.621
0.586
0.590
0.588
0.600
0.604
0.599
0.597
0.605
0.639
0.612
0.638
0.637
c (mm)
0.00
0.00
0.22
0.29
0.35
0.67
0.89
0.89
1.09
1.18
1.39
1.48
1.52
1.66
1.88
1.92
2.04
2.18
2.25
2.37
164
σbc (MPa)
19.3
19.2
7.17
5.77
4.08
4.29
3.48
4.09
3.40
3.27
2.98
2.88
2.61
2.77
2.48
2.28
2.14
1.70
1.72
1.56
εbc
6.02
5.78
4.63
4.82
4.35
4.56
4.44
4.21
4.37
3.99
3.82
3.65
3.71
3.50
3.24
3.58
2.92
2.64
2.77
2.30
Table A.50 Tensile results of B20S at 0.1 mm/min
Specimen #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Thickness (mm)
0.593
0.633
0.606
0.581
0.596
0.551
0.634
0.620
0.586
0.581
0.592
0.605
0.596
0.609
0.594
0.593
0.613
0.616
c (mm)
0.00
0.00
0.20
0.34
0.48
0.55
0.87
1.06
1.26
1.43
1.59
1.70
1.89
1.91
1.97
2.18
2.25
2.56
165
σbc (MPa)
14.0
14.4
4.60
4.20
3.26
2.60
2.41
2.27
2.20
2.09
1.97
2.02
1.94
1.42
1.36
1.43
1.59
1.32
εbc
5.53
5.72
4.37
4.05
3.92
4.11
3.82
3.52
2.98
3.05
2.86
2.55
2.32
1.87
1.66
1.70
1.52
1.43