EFFECT OF CROSSLINK DENSITY AND N660 CARBON BLACK ON TEARING
BEHAVIORS OF NATURAL RUBBER VULCANIZATES
A Thesis
Presented to
The Graduate Faulty of The University of Akron
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
Tingling Rao
December, 2012
EFFECT OF CROSSLINK DENSITY AND N660 CARBON BLACK ON TEARING
BEHAVIORS OF NATURAL RUBBER VULCANIZATES
Tingling Rao
Thesis
Approved Accepted
Advisor Dean of the College Dr. Gary R. Hamed Dr. Stephen Z. D. Cheng
Co-Advisor or Faculty Reader Dean of the Graduate School Dr. Darrell H. Reneker Dr. George R. Newkome
Department Chair or School Director Date Dr. Ali Dhinojwala
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ABSTRACT
All tires contain black-filled natural rubber compounds in their belts, the edges of which experience high stress concentration. Black filled natural rubber vulcanizates have tearing resistance unsurpassed by any other elastomer. Previous studies have examined the effect of filler and cut size on tearing resistance and cracking behavior at a single crosslink density. Studies have now been extended to include NR vulcanizates with various crosslink densities.
Conventional sulfur-cured, gum natural rubber vulcanizates were prepared with various crosslink densities. Tensile and tearing strength are quite sensitive to changes in crosslink density. For lightly and moderately crosslinked vulcanizates, the tear strength of edge-cut specimens shows two populations as a function of cut size. The drop-off in strength at the critical cut size is attributed to the lack of bulk crystallization. When crosslink density is increased enough the two populations disappear. Also, the cracking behavior changes as crosslink density in varied. When crosslinked lightly, gum NR vulcanizates exhibit simple lateral cracking with relatively smooth fracture surfaces.
When crosslink density increases, gum NR vulcaniztes show increasingly complicated cracking behavior. The complexity of the fracture surfaces is incrased. Over a limited range of cut size, moderately crosslink vulcanizates exhibit multiple cracks prior to rupture.
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In other experiments, low concentrations of a coarse carbon black (N660) were added to the specific gum vulcanizate that showed crack deviation. Instead of promoting cracking deviation, carbon black (N660) of low concentration suppressed anisotropy.
Multiple cracks only occur when the carbon black loading reaches a critical level.
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TABLE OF CONTENTS
Page
LIST OF TABLES ...... vii
LIST OF FIGURES ...... ix
CHAPTER
I. INTRODUCTION ...... 1
II. HISTORICAL REVIEW ...... 3
2.1 Natural rubber ...... 3
2.2 Fracture mechanics ...... 4
2.2.1 Stress and energy approaches ...... 4
2.2.2 Fracture energy ...... 7
2.3 Effect of strain-induced crystallization, carbon black and vulcanization ...... 7
2.3.1 Strain-induced crystallization ...... 9
2.3.2 Effect of carbon Black ...... 12
2.3.3 Effect of vulcanization ...... 16
2.4 Crack deviation ...... 21
III. EXPERIMENTAL ...... 28
3.1 Materials ...... 28
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3.2 Compounding ...... 28
3.3 Specimen preparation ...... 33
3.4 Tensile Testing ...... 33
3.5 Swelling testing ...... 34
3.6 Cracking pattern photographs ...... 36 IV. EFFECT OF CROSSLINK DENSITY ON PROPERTIES OF GUM NR VULCANIZATES ...... 37 4.1 Crosslink density of gum vulcanizates ...... 37
4.2 Normal tensile testing ...... 42
4.3 Precut tensile testing ...... 45
4.4 Comparison of properties of gun vulcanizates ...... 90 V. THE EFFECT OF LOW CONCENTRATIONS (0-20 PHR) OF CARBON BLACK N660 ON THE REINFORCEMENT OF NR ...... 95 5.1 Swelling and curing testing ...... 95
5.2 Normal tensile testing ...... 97
5.3 Precut tensile testing ...... 102
5.4 Comparison between gum and black-filled NR vulcanizates ...... 141
VI. CONCLUSION ...... 147
REFERENCES ...... 149
APPENDIX ...... 155
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LIST OF TABLES
Table Page
3.1 Compound formulations for varying crosslink density ...... 29
3.2 Compound formulations for vary carbon black loading ...... 30
3.3 Internal mixing procedure (UA0.6x-0 – UA2.0x-0) ...... 32
3.4 Internal mixing procedure (UA1.7x-6—UA1.7x-20) ...... 32
3.5 Mixing procedure on the two-roll mill ...... 33
4.1 Crosslink density of gum NR vulcanizates ...... 37
4.2 APA cure characteristics (T = 140 °C , 3 ° arc) ...... 39
4.3 Normal (uncut specimens) tensile properties ...... 42
4.4 Critical cut size from tensile testing of pre-cut specimens ...... 94
5.1 Values of vvrr0 / obtained from swelling measurement ...... 95
5.2 APA cure characteristics (T = 140 °C , 3 ° arc) ...... 97
5.3 Normal (uncut specimens) tensile properties ...... 99
5.4 Crack pattern distribution ...... 103
APPENDIX ...... 155
A. 1 Tensile properties of UA0.6x-0 ...... 155
A. 2 Tensile properties of UA0.8x-0 ...... 157
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A. 3 Tensile properties of UA1.0x-0 ...... 159
A. 4 Tensile properties of UA1.2x-0 ...... 160
A. 5 Tensile properties of UA1.4x-0 ...... 162
A. 6 Tensile properties of UA1.6x-0 ...... 164
A. 7 Tensile properties of UA1.8x-0 ...... 165
A. 8 Tensile properties of UA1.9x-0 ...... 167
A. 9 Tensile properties of UA2.0x-0 ...... 169
A. 10 Tensile properties of UA1.7x-0 ...... 171
A. 11 Tensile properties of UA1.7x-6 ...... 173
A. 12 Tensile properties of UA1.7x-10 ...... 175
A. 13 Tensile properties of UA1.7x-15 ...... 177
A. 14 Tensile properties of UA1.7x-18 ...... 179
A. 15 Tensile properties of UA1.7x-20 ...... 181
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LIST OF FIGURES
Figure Page
2.1 Schematic diagram of stress concentration at the tip of an elliptical edge crack ...... 5
2.2 Test pieces for fracture energy measurement: (A). trousers tear test piece; (B) tensile trip with an edge cut; (C) simple shear test specimen; (D). splitting tear test specimen ...... 8
2.3 Tearing energy (in ergs/cm2) as a function of temperature and rate of tearing (cm/sec) for gum SBR ...... 10
2.4 Diagram of spherical filler particles arranged on a cubic lattice ...... 15
2.5 Stress-strain curves for compositions S1 (gum SBR), S2 (black-filled SBR), N1 (gum natural rubber) and N2 (black-filled natural rubber) ...... 17 2.6. Degree of crystallinity (%) as a function of carbon black and extension ratio ...... 19 2.7 Effect of carbon black on crack growth of various rubbers. ○, Gum; ●, 50 phr N330; +, 50 phr N990 ...... 20 2.8 Effect of crosslink density on mechanical properties of vulcanizates ...... 23 2.9 Crystallinity as a function of distance from crack tip in unfilled and 40 phr carbon black-filled rubber ...... 25
2.10 (a) Griffith crack meeting an interface; (b) Perpendicular crack moving along the interface ...... 26
4.1 Crosslink density of gum NR vulcanizates versus normalized amount of sulfur ...... 38 4.2 Cure curves of UA0.6x-0 – UA2.0x-0 (T=140oC) ...... 40
4.3. Maximum torque of UA0.6x-0 – UA2.0x-0 ...... 41
4.4. 100% modulus of UA0.6x-0 – UA2.0x-0 ...... 43 ix
4.5. Stress-strain curve of UA0.6x-0 – UA2.0x-0 ...... 44
4.6. Tensile strength of precut specimens (UA0.6x-0) ...... 45 4.7. Cracking pattern of UA0.6x-0 #35 (c = 1.40 mm, Strength = 1.08 MPa, Strain = 2.81) ...... 46
4.8. Cracking pattern of fracture surfaces of UA0.6x-0 #35 ...... 47 4.9. Cracking pattern of UA0.6x-0 #37 (c = 1.51 mm, Strength = 2.36 MPa, Strain = 5.17) ...... 48 4.10. Cracking pattern of fracture surfaces of UA0.6x-0 #37 ...... 49
4.11. Tensile strength of precut specimens (UA0.8x-0)...... 50 4.12. Cracking pattern of UA0.8x-0 #36 (c = 1.55 mm, Strength = 2.94 MPa, Strain = 4.75) ...... 51
4.13. Cracking pattern of fracture surfaces of UA0.8x-0 #36 ...... 52 4.14. Cracking pattern of UA0.8x-0 #37 (c = 1.85 mm, Strength = 0.90 MPa, Strain = 1.74) ...... 53
4.15. Cracking pattern of fracture surfaces of UA0.8x-0 #37 ...... 54
4.16. Tensile stress of precut specimens (UA1.0x-0) ...... 55 4.17. Cracking pattern of UA1.0x-0 #30 (c = 1.17 mm, Strength = 5.79 MPa, Strain = 4.97) ...... 56
4.18. Cracking pattern of fracture surfaces of UA1.0x-0 #30 ...... 57 4.19. Cracking pattern of UA1.0x-0 #32 (c = 1.24 mm, Strength = 2.05 MPa, Strain = 3.38) ...... 58
4.20. Cracking pattern of fracture surfaces of UA1.0x-0 #32 ...... 59
4.21. Tensile stress of precut specimens (UA1.2x-0) ...... 60 4.22. Cracking pattern of UA1.2x-0 #38 (c = 1.35 mm, Strength = 1.81 MPa, Strain = 2.68) ...... 61 4.23. Cracking pattern of fracture surfaces of UA1.2x-0 #38 ...... 62 4.24. Cracking pattern of UA1.2x-0 #42 (c = 1.60 mm, Strength = 4.79 MPa, Strain = 4.73) ...... 63
4.25. Cracking pattern of fracture surfaces of UA1.2x-0 #42 ...... 64
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4.26. Tensile stress of precut specimens (UA1.4x-0) ...... 65 4.27. Cracking pattern of UA1.4x-0 #28 (c = 0.60 mm, Strength = 2.03 MPa, Strain = 2.48) ...... 66
4.28. Cracking pattern of fracture surfaces of UA1.4x-0 #28 ...... 67 4.29. Cracking pattern of UA1.4x-0 #33 (c = 0.80 mm, Strength = 6.00 MPa, Strain = 4.25) ...... 68
4.30. Cracking pattern of fracture surfaces of UA1.4x-0 #33 ...... 69
4.31. Tensile stress of precut specimens (UA1.6x-0) ...... 70 4.32. Cracking pattern of UA1.6x-0 #5 (c = 0.20 mm, Strength = 12.9 MPa, Strain = 4.87) ...... 71
4.33. Cracking pattern of fracture surfaces of UA1.6x-0 #5 ...... 72 4.34. Cracking pattern of UA1.6x-0 #32 (c = 0.94 mm, Strength = 2.34 MPa, Strain = 2.57) ...... 73
4.35 Cracking pattern of fracture surfaces of UA1.6x-0 #32 ...... 74
4.36 Tensile stress of precut specimens (UA1.8x-0) ...... 75 4.37. Cracking pattern of UA1.8x-0 #15 (c = 0.25 mm, Strength = 4.94 MPa, Strain = 3.55) ...... 76
4.38. Cracking pattern of fracture surfaces of UA1.8x-0 #15 ...... 77 4.39. Cracking pattern of UA1.8x-0 #50 (c = 1.72 mm, Strength = 1.38 MPa, Strain = 1.24) ...... 78
4.40. Cracking pattern of fracture surfaces of UA1.8x-0 #50 ...... 79
4.41. Tensile stress of precut specimens (UA1.9x-0) ...... 80 4.42. Cracking pattern of UA1.9x-0 #11 (c = 0.23 mm, Strength = 15.6 MPa, Strain = 4.86) ...... 81
4.43. Cracking pattern of fracture surfaces of UA1.9x-0 #11 ...... 82 4.44. Cracking pattern of UA1.9x-0 #48 (c = 0.23 mm, Strength = 2.51 MPa, Strain = 2.17) ...... 83 4.45. Cracking pattern of fracture surfaces of UA1.9x-0 #48 ...... 84
4.46. Tensile stress of precut specimens (UA2.0x-0) ...... 85
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4.47. Cracking pattern of UA2.0x-0 #3 (c = 0.20 mm, Strength = 15.2 MPa, Strain = 4.55) ...... 86
4.48. Cracking pattern of fracture surfaces of UA2.0x-0 #3 ...... 87 4.49. Cracking pattern of UA2.0x-0 #39 (c = 1.35 mm, Strength = 1.22 MPa, Strain = 0.61) ...... 88
4.50. Cracking pattern of fracture surfaces of UA2.0x-0 #39 ...... 89
4.51. Comparison of UA0.6x-0, UA0.8x-0 and UA1.0x-0 ...... 91
4.52. Comparison of UA1.0x-0, UA1.2x-0, UA1.4x-0 and UA1.6x-0 ...... 92
4.53. Comparison of UA1.0x-0, UA1.8x-0, UA1.9x-0 and UA2.0x-0 ...... 93
5.1. Effect of volume fraction of carbon black on swelling ...... 96
5.2. Cure curves of UA1.7x-0-UA1.7x-20. (T=140oC) ...... 98
5.3. Stress-strain curves for normal tensile test ...... 100
5.4 Comparison between 100% modulus and Ec obtained from Guth-Gold calculation ...... 101
5.5 Tensile strength and distribution of cracking patterns of precut specimens (UA1.7x-0) ...... 104
5.6 Crack pattern of UA1.7x-0 #10 (c = 0.26 mm, Strength = 12.16 MPa, Strain = 4.79) ...... 105
5.7 Cracking pattern of UA1.7x-0 #20 (c = 0.31 mm, Strength = 11.0 MPa, Strain = 4.68) ...... 106
5.8 Cracking pattern of fracture surface of UA1.7x-0 #20 ...... 107 5.9 Cracking pattern of UA1.7x-0 #29 (c = 0.42 mm, Strength = 1.95 MPa, Strain = 2.12) ...... 108
5.10 Cracking pattern of fracture surface of UA1.7x-0 #29 ...... 109 5.11 Cracking pattern of UA1.7x-0 #40 (c = 0.57 mm, Strength = 9.35 MPa, Strain = 4.81) ...... 110
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5.12 Cracking pattern of UA1.7x-0 #54 (c = 1.02 mm, Strength = 1.00 MPa, Strain = 0.98) ...... 111
5.13 Cracking pattern of fracture surface of UA1.7x-0 #54 ...... 112 5.14 Tensile strength and distribution of cracking patterns of precut specimens (UA1.7x-6) ...... 113
5.15 Cracking pattern of UA1.7x-6 #5 (c = 0.26 mm, Strength = 10.63 MPa, Strain = 4.05) ...... 114
5.16 Cracking pattern of fracture surface of UA1.7x-6 #5 ...... 115 5.17 Cracking pattern of UA1.7x-6 #31 (c = 0.67 mm, Strength = 1.49 MPa, Strain = 1.37) ...... 116
5.18 Cracking pattern of fracture surface of UA1.7x-6 #31 ...... 117 5.19 Tensile strength and distribution of cracking patterns of precut specimens (UA1.7x-10) ...... 118
5.20 Cracking pattern of UA1.7x-10 #14(c = 0.30 mm, Strength =9.23 MPa, Strain = 3.66) ...... 119
5.21 Cracking pattern of UA1.7x-10 #40(c = 0.62 mm, Strength =2.04 MPa, Strain = 1.60) ...... 120
5.22 Cracking pattern of fracture surface of UA1.7x-10 #40 ...... 121 5.23 Cracking pattern of UA1.7x-10 #61 (c = 1.16 mm, Strength = 1.16 MPa, Strain = 0.76) ...... 122
5.24 Cracking pattern of fracture surface of UA1.7x-10 #61 ...... 123 5.25 Tensile strength and distribution of cracking patterns of precut specimens (UA1.7x-15) ...... 125
5.26 Cracking pattern of UA1.7x-15 #14 (c = 0.37 mm, Strength = 2.02 MPa, Strain = 1.46) ...... 126
5.27 Cracking pattern of fracture surface of UA1.7x-15 #14 ...... 127 5.28 Crack pattern of UA1.7x-15 #16 (c = 0.38 mm, Strength = 8.21 MPa, Strain = 4.46) ...... 128
5.29 Cracking pattern of UA1.7x-15 #30 (c = 0.55 mm, Strength = 1.91 MPa, Strain = 1.34) ...... 129 xiii
5.30 Cracking pattern of fracture surface of UA1.7x-15 #30 ...... 130 5.31 Tensile strength and distribution of cracking patterns of precut specimens (UA1.7x-18) ...... 131
5.32 Cracking pattern of UA1.7x-18 # 13 (c = 0.32 mm, Strength = 7.97 MPa, Strain = 3.18) ...... 132
5.33 Crack pattern of UA1.7x-18 #16 (c = 0.35 mm, Strength = 9.01 MPa, Strain = 4.36) ...... 133
5.34 Cracking pattern of UA1.7x-18 # 17 (c = 0.38 mm, Strength = 4.11 MPa, Strain = 2.12) ...... 134
5.35 Cracking pattern of fracture surface of UA1.7x-18 # 17 ...... 135 5.36 Cracking pattern of UA1.7x-18 #50 (c = 1.05 mm, Strength = 1.62 MPa, Strain = 0.96) ...... 136
5.37 Cracking pattern of fracture surface of UA1.7x-18 #50 ...... 137 5.38 Tensile strength and distribution of cracking patterns of precut specimens (UA1.7x-20) ...... 138
5.39 Crack pattern of UA1.7x-20 #19 (c = 0.34 mm, Strength = 12.3 MPa, Strain = 3.57) ...... 139 5.40 Comparison between UA1.7x-6 and UA1.7x-0 ...... 142
5.41 Comparison between UA1.7x-10 and UA1.7x-0 ...... 143
5.42 Comparison between UA1.7x-15 and UA1.7x-0 ...... 144
5.43 Comparison between UA1.7x-18 and UA1.7x-0 ...... 145
5.44 Comparison between UA1.7x-20 and UA1.7x-0 ...... 146
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CHAPTER I
INTRODUCTION
Black-filled natural rubber vulcanizates is an irreplaceable part in all kinds of tires for the unsurpassed tear strength. The properties are greatly affected by curing system, carbon black addition, and temperature and so on. Some research about the effect of crosslink density on natural rubber specimens containing razor edge cuts were has been carried out [1,2]. Strengths of different vulcanizates depend on cut size. Lightly crosslinked rubber specimens exhibit an abrupt drop in strength at critical cut size while densely crosslinked rubber vulcanizates don’t. Meanwhile, both lightly and densely cured specimens develop simple crack while moderated crosslinked specimens exhibit crack deviations. In the present work, crosslink density is increased from the light to the moderate. It’s aimed to detect sensitivity of precut tear strength as well as cracking behavior as a function of crosslink density.
Addition of carbon black is an important way to reinforce rubber. The extent of reinforcement largely depends on carbon black loading as well as type. For a typically reinforced rubber specimen, secondary, longitudinal cracks develop near cut tip prior to catastrophic failure. This behavior can result in a high resistance to rupture. On the contrary, carbon black with low concentration will reduce tear strength and produce single lateral crack [3,4]. In this study, a specific moderated crosslinked composition which 1
develops multiple cracks within a narrow cut size range is extracted. The importance of effect of low concentration of carbon black N660 is studied is the focus. And the behavior of fracture surfaces is closely observed.
2
CHAPTER II
HISTORICAL BACKGROUND
2.1 Natural Rubber
With various useful properties, natural rubber is widely used in a large area for applications such as tires, mechanical goods (gaskets, seals, and belts), latex goods, and footwear and so on.
All over the world, more than 2000 species of tropical trees, shrubs or vines can produce latex from which natural rubber is obtained. Among them, latex from Hevea brasiliensis is the most important that can yeild up to 94% rubber particles [5]. And every year, through breeding and selection, modern Hevea are capapble of yielding over 2500 kg rubber per hectare [6]. After tapping, rubber latex needs to be processed, dried and then graded. Grading is by visual examination and is based on the presence o absence of extraneous foreign matter (dirt), bubbles, uniformity and intensity of color, mold and rust spots, and so on [7]. SMR CV is one of the natural rubber grades and is viscosity-stabilized. Three grades are available in the Mooney range of 44-55, 55-65 and
65-75 units.
Freshly prepared natural rubber has a low content of gel. On storage, the rubber hardens or stiffens spontaneously and free radical reactions also take place, which will result an increase of gel content. Gel in rubber can be easily broken down during 3
mastication. Molecular distribution is wide for rubber hydrocarbon in freshly prepared rubber. A random blend of the common clonal rubber would have a weight-average molecular weight of 1−× 1.5 106 and a number average of 3−× 5 105 [7].
It has been shown by Golub et.al [8] that NR has a chemical structure of almost 100% pure cis-1,4-polyisoprene units. Due to the high stereoregularity, natural rubber can crystallize upon stretching or under low temperature. For unstrained natural rubber, the maximum rate of crystallization is around 26oC. Gent et.al [9] has demonstrated the importance of stereo regularity on crystallization by add non-cis units to polyisoprene.
They found that crystallization ability is greatly reduced even when cis content is 98%.
2.2 Fracture Mechanics
Fracture is a process that new free surfaces are created in a solid, which is often initiated from flaws acting as stress concentration. No vulcanizates is completely homogenous. All of them inevitably contain flaws which may result from imperfect cutting, included impurities, in homogeneity of vulcanizates and so on.
2.2.1 Stress and Energy Approaches
Stress at the tip of flaws will be magnified many times than global stress which is applied to such test pieces. And when the local stress reaches a critical value, a flaw will propagate and eventually generate new fracture surfaces. To quantify the critical stress
criteria, Inglis [10] proposed an expression connecting local stress (σ t ) at flaw tip with global stress (σ ) for an elastic solid:
1/2 σσt =[1 + 2(lr / ) ] (1)
4
Here, l is the length of elliptical edge crack and r is the tip radius (Figure 2.1). If
lr , equation (1) can be written as:
σ
σ t r
l σ t
σ
Figure 2.1 Schematic diagram of stress concentration at the tip of an elliptical edge crack
5
1/2 σσt = 2 (/lr ) (2)
It indicates that stress at the flaw tip increases rapidly as edge length and sharpness of the of length l and radius r crack increase. On the contrary, if some processes occurring to reduce sharpness of crack tip, e.g. cracking splitting, local stress will decrease and fracture can be inhibited.
However, the criterion proposed by Inglis is difficult to apply due to the difficulty to accurately measure or predict stress distribution with a solid. Then, Griffith suggested an energy balance criteria [11] to circumvent the problem. In Griffith’s model, a crack of a strained brittle solid will propagate when the released elastic strain energy is larger than energy needed to create new surface area. When an initial cut grows a distance of ∆c , it generates an area of ∆A and the strained energy released is −∆U . Then the Griffith relationship can be expressed as:
−∂(U /) ∂ c >γ (/) ∂ Ac ∂ (3)
Here γ is surface free energy density. Based on the assumption of solid, the above relationship cannot be directly applied to viscoelastic materials because energy dissipation was not involved.
To modify Griffith’s crack growth criteria, Rivlin and Thomas [12] came up with the notion of tearing energy. It takes into account of both energy dissipation and true surface energy. The equation has been stated as:
−∂(U /) ∂ cl = Gt (4)
G is tearing energy which is an energy characteristic of the material; t is thickness of test
6
piece and the suffix l indicates that the differentiation is carried out under conditions of constant displacement. Equation (4) is similar to equation (3), however, G is no longer interpreted as merely a surface free energy.
2.2.2 Fracture Energy
In order to cause a crack to grow, sufficient energy must be supplied to the crack front to meet the requirements of fracture [13]. Energy conservation requires that energy expended during fracture should be met by energy supplied, which can be written as:
Energy Supplied = Energy Expended
∆Wsp +∆ W = GA() ∆ +∆ We (5)
Where ∆Ws is the net stored strain energy released from crack propagation; ∆Wp is the potential energy change of loading device after crack growth; G is the tearing energy which contains both true surface energy as well as energy dissipation; ∆A is the surface
area created by fracture and ∆We is the increased stored strain energy resulted from crack growth. To detect characteristics of tearing energy, Rivlin [12] and Thomas [14, 15] measured tearing energy of test pieces with different shapes (trouser, edge cut, pure shear and split) but of the same material. It’s depicted in Figure 2.2. Those experimental results show that fracture energy G, as the energy characteristic of a material, is independent of the test geometries. Rivlin and Thomas [12] also showed that when an edge cut is introduced to a thin strip shown in Figure 2.2 (D), equation (5) can be expressed as:
∆=∆Ws GA() (6)
If linear elasticity is assumed,
7
2 ∆=Wsb U()() c ∆= V kc tW () ∆ V (7)
where Uc() is the critical stored strain energy density at break, Wb is the strain energy
c
(A) (B)
(C) (D)
Figure 2.2 Test pieces for fracture energy measurement: (A). trousers tear test piece; (B)
tensile trip with an edge cut; (C) pure shear test specimen; (D). splitting tear test specimen
8
density at the moment of rupture, c is the cut depth and k has been found to have the approximate value of πλ −1/2 . Then tearing energy for a crack to propagate across the test piece can be further expressed as:
−1/2 G=22 kcWbb = πλ cW (8)
Although tearing energy is independent of test shapes, it greatly depends on tearing rate and temperature. Normally, it increases as tearing rate increases while as temperature decreases. Figure 2.3 shows fracture energy of SBR at various testing rate and temperature [16]. When temperature increases to sufficiently high and tearing rate is low enough, tearing energy will reach a limiting value G0 which is called threshold tearing
(fracture) energy. The threshold tearing of facture energy (G0) of an elastomer is the minimum amount needed to cause fracture [17]. Lake and Thomas [18] developed a theory which attributes the need for threshold fracture energy to stressing entire length of the chain between crosslink points at the tip in order to break a single C-C bond. Many other experimental results [12, 16-21] show that threshold fracture energy falls in the range of 20 –100 J/m2
2.3 Effect of Strain-induced Crystallization, Carbon Black and Vulcanization
2.3.1 Strain-induced Crystallization
Natural rubber is able to crystallize either upon cooling or stretching. Reduction of temperature generates crystallization not only through promoting formation of nucleus
9
but also by limiting chain mobility. The maximum rate of crystallization for unstrained
NR occurs at -25oC and maximum degree of crystallinity is around 25-30 % [3].
Figure 2.3 Tearing energy (in ergs/cm2) as a function of temperature and rate of tearing r
(cm/sec) for gum SBR [16].
10
When a rubber is subjected to large deformation, the tendency to crystallize can be largely enhanced. When stretched, chains between network junctions will arrange themselves to a more regular manner. The configurational entropies of these chains are consequently decreased which contributes to occurrence of crystallization even at much higher temperature [22]. Flory [23] also developed a theory of oriented crystallization in elongated polymers with network structures, e.g. rubber vulcanizates. It predicted that reciprocal of the absolute temperature for incipient crystallization decreases linearly with simple function of the elongation and average number of chain segments between cross linkage. It also implicitly assumed that growth of crystallites is in the direction along chain axis. On the contrary, Holl et al. [24] and Conradt et al. [25] suggested that development of crystallites is in the form of lamellar, which indicates that direction of crystallites growth is perpendicular to stretching. Recently, Tosaka and coworkers [26] detected strain-induced crystallization of NR with different network-chain density using synchrotron X-ray diffraction measurement. It’s found that surrounding molecular chains facilitated crystallites growth initiated from stretched molecular chains. Shimomura et al.
[3] showed that crystallization rate grew rapidly as stretching deformation increases. And crystallization occurred in the strain region between 300-400%. Magill [27] also showed that strain-induced crystallization of NR initiated when extension ratio λ is above 3.
And as λ increases up to 5, NR crystallites were highly oriented. Some research on strain-induced crystallization also pointed out that there’s a transition from spherulites morphology to fibrils paralleling to chain axis, which happened when stain exceeds 300%
11
[28]. And existence of the fibrous backbones serving to nucleate the lamellae was essential of an extended chain character and the lamellae chain-folded [29]. From the relationship between tensile strength of crosslink density, Flory [30] indicated that when crosslink density was high, crystallization for NR was suppressed. Recently, In Tosaka et al.’s [26] work, they pointed out that onset strain of crystallization was almost independent of network-chain density.
2.3.2 Effect of Carbon black
Reinforcement of rubbers in order to increase the stiffness and resistance to fracture is very important. Many factors can contribute to increasing stiffness [31, 32]. In the model of Guth and Gold [33], they attributed modulus increase to hydrodynamic effect.
Based on Smallwood – Guth relationship [34], they suggested that when black-filled rubber was stretched, elastic energy would increase due to perturbation of stress and strain. For spherical particles the equation can be expressed as:
2 EE=++0 (1 2.5φφ 14.1 ) (9)
where E is the Young’s Modulus of filled rubber; E0 is the Young’s Modulus of gum rubber and φ is the volume fraction embedded in rubber matrix. When non-spherical particles were taken into account, equation (9) was modified into [35]:
22 EE=++0 (1 0.67 fφφ 1.62 f ) (10) where f is the shape factor, which describes the ration of the length to the width of aggregates.
12
There are many factors which can influence rubber reinforcement, such as particle size, particle structure, chemical surface which affects interaction between surface of filler and rubber and so on. Among them, the most important parameter is primary particle size [36]. Addition of filler with particle size more than one micron has nothing to do with enhanced strength but only increases modulus. A simple model was come up with by Hamed and Hatfield [37] for better understanding of reinforcement. The model assumed that a volume fraction, φ , of a spherical filler of radius, r , is dispersed in a rubbery matrix. Each particle is surrounded by a layer of rubber of thickness,t , which is referred as “restricted” rubber. It is depicted in Figure 2.4. And volume fraction of the restricted rubber, v , within thickness t was calculated as follows:
φ[(1+−tr / )3 1] v = (11) 1− x If the filler has a large particle size, only a very small fraction of the rubber is influenced.
However, with the same volume fraction, more chains can be restricted if particle size decreases. Sufficiently small hard domains give good reinforcement, even when matrix/domain bonding is poor. It has been confirmed by Hamed’s group with graphitized or fluorinated carbon black [38-40].
When a randomly crosslinked rubber is deformed, stress distribution within networks chains is different because the topology is not uniform. Those stretched network strands then try to redistribute the stress in order to reduce local stress concentration. However, if an overloaded chain breaks irreversibly and transmits the load to neighboring chains, this chain can never carry load again. So reduction of stress concentration but still maintaining
13
chains loading ability is important for strengthen rubber network. Dannenberg [41] proposed a “molecular slippage” mechanism based on physical adsorption. In this theory, segments of rubber absorbed physically on carbon black dissipated energy though moving on the surface. Through the process, less energy is available to create fracture surface and strength is enhanced. Hamed and Park [42] investigated mechanical properties of black-filed vulcanizates of styrene-butadiene rubber (SBR) and natural rubber (NR).
When filled with carbon black, SBR vulcanizates exhibit greatly increased strength which is dramatically different from that of gum SBR amorphous vulcanizates, shown in Figure
2.5. When a newly broken network chain attached to the carbon black surface, it would regain loadi-carrying ability, which attributes to enhanced “non-catastrophic” energy dissipation [43].
Greensmith [44, 45] promoted that fillers might influence tear behavior in three ways: influencing the basic tear process, affection crystallization and contributing a strengthening structure. Donovan et al. [46-48] showed that compared to gum natural rubber vulcanizates, black filled natural rubber vulcanizates perform stain-induced crystallization at lower strain. They also showed that extent of crystallinity of black-filled rubber is higher than gum vulcanizates and will increase as increase of black loading
(Figure 2.6). Moreover, they compared crystallization and crystallinity area near a cut tip between gum and black-filled NR, and suggested that carbon black with high concentrati-
14
-on facilitated formation of crystallization. Hamed [49] shows that addition of carbon black filler (N115 and N660) doesn’t always increase strength of natural rubber test
r t
s
Figure 2.4 Diagram of spherical filler particles arranged on a cubic lattice [37] pieces. Nonetheless, strength of natural rubber vulcanizates is quite weaker than gum when carbon black concentration was low. It’s attributed to ability of carbon black to
15
reduce strain-crystallization when content is low. The effect of carbon black on threshold
fracture energy T0 is shown by Lake and Lindley [50] in Figure 2.7. For
noncrystallizing rubber (SBR, NBR), a reinforcing black (N330) increasee T0 by a factor of two. A similar effect is found on BR and a even larger effect on IIR. However,
NR and IR do not show much increase of threshold fracture energy.
2.3.3 Effect of Vulcanization
Vulcanization chemically crosslinks rubber strains. Either type or degree of vulcanization can greatly affect mechanical properties of rubber vulcanizates. Two kinds of vulcanizations are often used. One is accelerated sulfur which can form polysulfidic crosslinkers and the other is peroxide which gives out single carbon-carbon bond.
Comparing those two types of crosslink, accelerated sulfur cure system can exhibit higher tensile and tear strength. It is due to the ability of polysulfidic linkages to break and reform, thereby reducing the stress concentration by highly stressed chains and thus resulting in a more uniformly loaded network [13]. On the contrary, carbon-carbon bond is rigid and doesn’t show reversibility. So extent of stress relaxation will be lower than that of polysulfidic vulcanizates. Recently, Ikeda et al. [51] studied strain-induced crystallization behavior of natural rubber cross-linked by peroxide or sulfur through time resolved wide-angle X-ray diffraction measurement. They showed that stretching ratio at the onset of strain-induced crystallization decreases with an increase of network chain density for peroxide cross-linked NR, while it remains constant for sulfur cross-linked
NR. For sulfur cures for diene elastomers, there are two common types which are called
16
conventional and efficient systems. Samsuri and Thomas [52] found that conventional sulfur-cured vulcanizates have higher tear strength when crosslink density is high while
Figure 2.5 Stress-strain curves for compositions S1 (gum SBR), S2 (black-filled SBR),
N1 (gum natural rubber) and N2 (black-filled natural rubber) [42]
17
the opposite is true when crosslink density is low. Hamed [53] also made an explanation for the phenomenon. At high crosslink density, mobile/reversible polysulfidic crosslinks can tolerate high tear strength while non-mobile monosulfidic linkages will result in
“embrittlement”. However, permanent monosulfidic linkages are advantageous when crosslink density approaches gel point.
Crosslink density is often determined through swelling test. When an elastomer above its gel point is immersed in solvent, swelling of network chains will continue until the restrictive forces in the extended molecular strands balance the forces tending to swell the net work. For unfilled rubber vulcanizates, crosslink density can be determined with
Flory- Rehner equation [54]:
2 1 ln(1−vvrr ) ++χ1 v r ρc = − [] 1/3 v 2V v − r r 2 (12) where ρc is crosslink density; V is solvent molar volume; vr is volume fraction of
polymer in swollen gel; and χ1 is polymer solvent interaction parameter.
Effect of crosslink density can be various on tear strength, tensile strength, modulus, hysteresis and so on. Gee and Flory [55,56] have explored the dependence of tensile stre-ngth of natural rubber vulcanizates on degree of cross-linking. And they demonstrated that there is a maximum for tensile strength as crosslink density increases.
The effect of crosslink density on some mechanical properties is shown in Figure 2.8 [57].
As crosslink density increase, material becomes more elastic, so hysteresis continuously goes down while modulus and hardness increase monotonically. Tensile and tear strength first passes through a maximum as crosslink density increases and then decrease steadily 18
to a low degree when crosslink density becomes high. Hamed [58] explained relationship between strength and crosslink density. For an uncrosslinked elastomer, when deformed,
Figure 2.6. Degree of crystallinity (%) as a function of the carbon black loading and
extension ratio [48]
19
polymer chains may slide past one another and disentangle. When a few crosslink is
added, molecules become more branched which can help prevent disentangle. Then
Figure 2.7 Effect of carbon black on crack growth of various rubbers. ○, Gum; ●, 50 phr
N330; +, 50 phr N990 [50]
20
crosslinking is further increased above gel point, strength becomes even higher because fracture can not happen without breaking chemical bonds. However, if the crosslink density is too high, rubber network will gradually lose the ability to dissipate input energy through molecular motion and become brittle. Then, the strength goes down.
Hamed and Rattanasom [1] studied effect of crosslink density on cut growth in gum natural rubber vulcanizates. Conventional sulfur-cured gum natural rubber vulcanizates of various densities were prepared. Lightly crosslinked specimens exhibited an abrupt drop in strength at critical cut size, which became smaller as crosslink density increased due to reducing strain-induced crystallization ability. Lightly and densely crosslinked networks exhibited lateral fracture while a moderately crosslinked composition exhibited crack deviation prior to rupture.
Hamed and Rattanasom [2] also studied effect of crosslink density on cut growth in black-filled natural rubber vulcanizates. It was found that at low crosslink density, the uncut tensile strength of gum and filled vulcanizates is similar. However, when crosslink density is high, gum vulcanizates becomes brittle while the corresponding filled rubber remains strong. The author proposed that filled natural rubber vulcanizates with high crosslink density still have ability of strain-induced crystallization, of which the corresponding gum vulcanizates are lack.
2.4 Crack deviation
Figure 2.2 (B) shows a strip of a vulcanizate with an edge cut perpendicular to the sample length. According to Griffith’s fracture criteria [59], for a solid-like rubber, the crack tip
21
remains rather sharp and the crack will propagate perpendicular to the loading direction.
However, for elastomers capable of energy dissipation, the crack tip may extensively blunt and deviate. Many researchers have studied phenomenon of cracking splitting and tried to figure out factors causing secondary cracks which greatly reduce stress concentration at cut tip thereby enhancing strength. Greensmith [60] found that gum natural rubber vulcanizates as well as various black-filled rubber vulcanizates show knotty tearing in certain range of temperature and tearing rate. Samsuri [61] also found that knotty tearing happens in both sulfur and peroxide cured natural vulcanizates. Busse
[62] studied fibrous structure in black-filled rubber formed in stretching and stated that
“knotty” tear appears between such fibrous structures. Gent and Henry [63] suggested that the major effect dominating reinforcement of filler is to induce tear deviation through increasing effective tear diameter. To demonstrate it, they bonded metal guides parallel to the rubber to restricted lateral deviation. And very little enhancement of strength was observed. Besides anisotropy developed by orientation of carbon black at crack tip, strain-induced crystallization also plays an important role. Coldberg et al. [64] and
Samsuri [61] showed that strain-induced crystallization at crack tip of black filled rubber contributes a lot to crack blunting. Lee and Donovan [48] have detected development of crystallization of natural rubber by the addition of black with X-ray diffraction technique.
Figure 2.9 shows that crystallinity at cut tip in greatly enhanced by addition of carbon black.
22
Cook and Gordon [65] tried to predict crack deviation in the view of energy. The proposed that crack deviation would occur if the adhesive energy is less than one fifth of
Figure 2.8 Effect of crosslink density on mechanical properties of vulcanizates [57].
the cohesive energy. Kendall [66] further studied anisotropy at cut tip which can cause crack deviation and proposed a theoretical condition. In the model (Figure 2.10), crack deviation will happen when a Griffith edge cut meet a weak interface which is
23
perpendicular to the edge cut. The condition for crack deviation is:
2 GGad<− co / 4πυ (1 ) (13)
where Gad is the fracture energy of the interface; Gco is the fracture energy of the bulk and υ is the poison ratio. Gent [67] further carried out finite element calculation and revealed that when the fracture strength for a crack growing in the direction of the applied tension is less than about 40% of that for forward growth, a crack will inevitably turn sideways. Rivlin and Thomas [68] also proposed that when extension ratio is larger than 1, tearing energy required for longitudinal crack growth is only one sixth of that for lateral propagation.
Hamed, Kim and Gent [69] studied cut growth in natural rubber, cis-polybutadiene and a 50/50 blend vulcanization during continuous and repeated extension. It was found that the tensile strength of BR decreases steadily with increasing cut depth, while NR and
NR/BR blend shows an abrupt decrease in tensile strength at critical cut size, which can be attributed to strain-induced crystallization of NR. At the same time, secondary cracks has developed in NR and NR/BR and grown a considerable distance. Such “knotty” crack was also found in NR under repeated extension. This behavior has been attributed to and anisotropic fibrous structure developed near cut tip which has high resistance to high lateral crack growth.
Further, Hamd and Zhao [64] reported on the development of longitudinal cracking in a black-filled NR vulcanizates held at 200% elongation and subjected to aging in a forced-air oven at 72oC. Cracks first form in the edge due to oxidation and grows laterally
24
for a short distance then turns longitudinal. They also calculated the fracture energy, GL , for longitudinal cracking. It assumes that the fracture process consumes the energy released within a strand:
Figure 2.9 Crystallinity as a function of distance from crack tip in unfilled and 40 phr
carbon black-filled rubber [48].
25
GL = Uw (14) where U is the stored strain energy density within the volume of material which will become a strand; w is the strand width. Oxidation plays an important role in enhancing the anisotropy of strength and causes more weakening in the longitudinal direction.
Figure 2. 10 (a) Griffith crack meeting an interface; (b) Perpendicular crack moving along
the interface [66].
26
Hamed and Huang [71] studied tensile and tear resistance of anisotropic double
networks of black-filled natural rubber vulcanizates. A residual extension ratio,αr , is left
in the rubber sheet. When αr is low, tearing strength is high and edge-cut strip
specimens exhibit crack deviation. However, when αr is high, specimens exhibit low tearing resistance and simple lateral crack. This result is consistent with previous ones that longitudinal cracking is accompanied high tear strength. It also indicates that strength anisotropy developed at crack tip is important to resist facile propagation perpendicular to loading.
Hamed and Al-Sheneper [3] studied the effect of carbon black N115, which is a very fine carbon black, on tensile and tear resistance of natural rubber vulcanizates.
Counter-intuitively, NR specimens with 6-12 phr of N115 significantly brings down tensile strength with edge cut and all of them exhibit simple fracture. When carbon black loading is increased to 18 phr, onset of reinforcement occurs associated with longitudinal cracking. Then further increasing carbon black concentration, strength will be greatly enhanced and more pronounced secondary cracking occurs.
Since N115 is a very fine carbon black and difficult to disperse, a much coarser and easily dispersed black N660 is used. Hamed and Cho [4] investigated effect of N660 on tear strength and cut grow of natural rubber. And precut specimens containing 3-12 phr of
N660 are much weaker than gum vulcanizate. More N660 was needed to induce reinforcement.
27
CHAPTER III
EXPERIMENTAL
3.1 Materials
The materials are: SMR CV60 natural rubber (Akrochem), N660 carbon black
(Cabot Corporation), stearic acid (Harwick Chemical Company), zinc oxide (Akrochem),
N-(1, 3-dimethyl butyl)-N’-phenyl-p-phenylene diamine ， 6PPD (Flexsys America),
2,2,4-trimethyl-1-2-hydroquinoline, Antioxidant DQ (Akrochem), Microcrystalline wax,
AkrowaxTM Micro23 (Akrochem), N-(Cyclohexylthio) phthalimide, Santogard PVI
(Flexsys America), Sulfur (Harwick Chemical Company), and TBBS (Flexsys America).
The average primary particle diameter of carbon black N660 is 55 nm; the specific surface area by nitrogen adsorption is 35 m2/g and the DBP absorption value is 91 cc/100 g.
3.2 Compounding
The formulations for studying effect of crosslink density are shown in Table 3.1.
Rubber compounds contain sulfur/TBBS ranging from 1.05/0.45 phr (UA0.6x-0) to
3.50/1.50 phr (UA2.0x-0). The number between “UA” and “x” is the normalized cure additive base on sulfur/TBBS of 1.75/0.75, which is assumed as 1.0. e. g. in UA0.6x-0,
0.6 = 1.05 (sulfur) / 1.75 (sulfur) = 0.45 (TBBS) / 0.75 (TBBS). The suffix “0” of design-1ations indicates they are gum vulcanizates. 28
Table 3.1. Compounds formulations for varying crosslink density Compo UA UA UA UA UA UA UA UA UA -und 0.6x-0 0.8x-0 1.0x-0 1.2x-0 1.4x-0 1.6x-0 1.8x-0 1.9x-0 2.0x-0 SMR 100 100 100 100 100 100 100 100 100 CV 60 Stearic 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 acid
Zinc 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 oxide
Antioz
o-nant 1.5 3.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
6PPD a
Antioxi
-dant 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
DQb
PVI 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
wax 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
S 1.05 1.40 1.75 2.10 2.45 2.80 3.15 3.325 3.50
TBBS c 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.425 1.50 a: N-(1,3-dimethylbutyl)-N’-phenyl-p-phenylenediamine b: Polymerized 2,2,4-trimethyl-1-1-dihydroquinoline c: N-tert-Butyl-2-Benzothiazolesulfenamide
29
Table 3.2. Compound formulation for vary carbon black loading
UA UA UA UA UA UA Compound 1.7x-0 1.7x-6 1.7x-10 1.7x-15 1.7x-18 1.7x-20
SMR CV 60 100 100 100 100 100 100
CB (N660 0 6 10 15 18 20
Stearic acid 1.8 1.8 1.8 1.8 1.8 1.8
Zinc oxide 3.5 3.5 3.5 3.5 3.5 3.5
Antiozonant 1.5 3.5 1.5 1.5 1.5 1.5 6PPD a
Antioxidant 1.0 1.0 1.0 1.0 1.0 1.0 DQ b
PVI 0.1 0.1 0.1 0.1 0.1 0.1
Akrowax 1.0 1.0 1.0 1.0 1.0 1.0
S 2.98 2.98 2.98 2.98 2.98 2.98
TBBS c 1.28 1.28 1.28 1.28 1.28 1.28
v 0 0.0291 0.0476 0.0698 0.0828 0.0909
veff,1 0 0.0306 0.0516 0.0786 0.0960 0.107
veff,2 0 0.0768 0.126 0.184 0.218 0.240 a: N-(1,3-dimethylbutyl)-N’-phenyl-p-phenylenediamine b: Polymerized 2,2,4-trimethyl-1-1-dihydroquinoline c: N-tert-Butyl-2-Benzothiazolesulfenamide 30
The formulations for studying the effect of carbon black on compound UA1.7x-0 is shown in Table 3.2. Carbon black content varied from 0-20 phr. The suffix of designations g/cc and 0.9 g/cc, actual volume fractions v of carbon black were determined from the following equatiaon:
vV=CB/( V CB + V R ) (1)
where VCB is the carbon black volume and VR is the rubber volume. The DBP absorption value of N660 is 91cc/100g, which indicates the occluded rubber. Two
different effective volume fractions of black veff ,1 and veff ,2 were determined from the following equation
veff,1 = VVV CB/ [ CB +− R ( AW DBP ⋅ CB )] (2)
veff,2 =+⋅[ V CB ( AW DBP CB )] / [ VV CB + R ] (3)
where VDBP is the DBP absorption value of N660 and WCB is the weight of carbon black. Occluded rubber decreases the volume of rubber matrix, and hence increases the effective volume fraction of filler. Compared to equation (1), Equation (2) assumes that occluded rubber is all consumed by the carbon black without increasing its volume. In equation (3), occluded rubber performs as additional rigid volume of carbon black. None of them is hidden by carbon black voids.
Natural rubber masterbatches were first prepared in a 250 ml internal mixer (rotor speed: 100 rpm) with a fill factor of 0.7. The procedure of gum compounds is shown in
Table 3.3. And the procedure of black-filled compoundsk is shown in Table 3.4. The next step was curative addition on a two-roll mill (Farrel, 15cm diameter and 30 cm roll
31
length). Roll speeds were 19 rpm for the slow roll and 24 rpm for the fast roll. Sulfur and
TBBS were added on a two-roll mill. The milling procedure is shown in Table 3.5.
Compounds were milled for 1 minutes and then sulfur and TBBS were slowly added to
Table 3.3. Internal mixing procedure (UA0.6x-0 – UA2.0x-0).
Step Time (min) Component Added
1 0 Natural Rubber
2 1.5 ZnO, Stearic acid, PVI, 6PPD, TMQ
3 3 Carbon Black, Wax
4 5 Dump and weigh
Table 3.4. Internal mixing procedure (UA1.7x-6—UA1.7x-20).
Step Time (min) Component Added
1 0 Natural Rubber
2 1 1/2 carbon black
ZnO, Stearic acid, PVI, DQ, 6PPD 3 1.5 and other 1/2 carbon black
4 3 Wax
5 5 Dump and weigh the bank with alternating cuts. After milling 3 minutes（at a 0.8 mm nip）, 10 end –roll passes were made at a 1.2 mm nip before sheeting off. 32
Table 3.5. Mixing procedure on the two-roll mill.
Time (min) Procedure
0 Mix the two masterbatches together with the nip at 1.9 mm
Form rolling bank at 0.6 mm nip
1 Add curing agents (S and TBBS) at 0.6 mm nip
4 10 end roll passes at 1.2 mm nip
Sheet off at a nip setting of about 1.2 mm.
Dump
3.3 Specimen preparation
The stocks were kept at room temperature for at least 16 hours before vulcanization.
Vulcanization kinetics were determined from rheometer curves using using an Alpha
Advanced Polymer Analyzer (APA) 2000 and an Alpha Moving Die Rheometer (MDR)
2000 at 140℃ and 3o arc for 60 min. Rectangular unvulcanizated milled sheets (about 18 g and 20 cc ) were placed in the center of a window mold (160 x 160 x 0.5 mm，13 cc).
Mylar was then placed on each side. Sheets were cured at 140℃ to tc(100) in a Dake hydraulic press and then quenched in water.
3.4 Tensile testing
ASTM D412 Type C was used to cut dumbbells in the milling direction from cured sheets. The width of the narrow section was about 6.35 mm. Thickness was measured using a thickness gouge three times for each specimen and the average was about 0.6 mm.
33
Tensile strength was measured with an Instron 5567 tensile tester at 25°C. Crosshead speed was 50 mm/min with an initial clamp separation of 65 mm (nominal strain rate is
0.77 min-1). And strain was measured in the narrow section of a specimen by a mechanical “clip-on” type extensometer with an initial separation of 25 mm. Test pieces can be divided into two groups: one is normal tensile test (uncut) specimens and the other on is with edge cut. Edge-cuts were introduced in the middle edge point using a razor blade that had been dipped into a soap solution in order to reduce friction. Cut size was measured using a traveling microscope. The engineering tensile stress was calculated as:
σ = Lg/ tw (4)
Where σ is the engineering tensile stress; L is the tensile loading; g is the acceleration due to gravity; t is undeformed thickness and w is entire width of specimen.
3.5 Swelling testing
Samples weighing about 0.4 g (Winitial ) were cut from cured sheets and immersed in
40 ml of toluene in the dark for one week at room temperature. A swollen sample was blotted with a paper towel and quickly transferred into a bottle which has already been weighed to determine the swollen weight (Wgel). Swollen samples were dried to constant weight in vacuum oven at room temperature. Then the dried weights of samples were measured (Wdry). For gum rubber vulcanizates, Flory-Rehner equation is used in quantitative determination of crosslink density.
34
2 1 ln(1−vvrr ) ++χ1 v r ρc = − [] 1/3 v 2V v − r r 2 (5) where ρc is crosslink density; V is solvent molar volume; vr is volume fraction of
polymer in swollen gel and χ1 is polymer solvent interaction parameter. For black-filled rubber vulcanizates, the volume fraction of rubber in the swollen gel, vr, is given by the following equation:
vVVVr= R/( RS + ) (6) where
VWR=(/) dryρ dry − V filler
VWWS=( gel − dry )/ρ toluene
VWwfiller= initial ⋅(/) CBρ CB
VWR0 = (/) dryρ dry = + vVVVr000 R/( RS )
ρdry is the initial density of an unswollen (dry) black filled rubber
ρtoluene is the density of toluene (0.862 g/cc)
ρCB is the density of carbon black (1.8 g/cc)
Wdry is the dry weight of a rubber test piece
Wgel is the swollen weight of a rubber test piece
Winitial is the initial weight of a rubber test piece
wCB is the weight fraction of carbon black in a formulation.
Vfiller is the volume of filler in a test piece
VR is the initial rubber volume in a filled rubber test piece
VS is the solvent volume taken up during swelling
35
VR0 is the initial rubber volume for the gum rubber
vr is the volume fraction of rubber in the swollen gel-phase of a filled rubber
vr0 is the volume fraction of rubber in a swollen gum gel
3.6 Cracking pattern photographs
Low magnification crack pattern photographs were taken with Nikon D1X digital camera. High magnification crack pattern photographs were taken with Scanning Electron
Microscopy (SEM) JEOL JSM7401F. Two short lines in each micrograph indicate the location of the tip of the initial razor cut. The designation Ci means crack “i”, Ii is the site of initiation of crack Ci, and Ai is the site of arrest of crack Ci. The effective fracture
energy Geff, b was determined by the equation below:
− G= 2πλ 1/2 Wc eff, b b b vb (7)
Where λb is the extension ratio ()λεbb= +1 ; Wb is the input strain energy density at
break and cvb is the virtual, effective crack length at break.
36
CHAPTER IV
EFFECT OF CROSSLINK DENSITY ON PROPERTIS OF GUM NR
VULCANIZATES
4.1 Crosslink Density of Gum NR Vulcanizates.
Crosslink densities of gum rubber vulcanizates calculated from Flory-Rehner equation are shown in Table 4.1. UA 0.6x-0, UA 0.8x-0, UA 1.2x-0, UA 1.4x-0, UA 1.6
Table 4.1 Crosslink density of gum NR vulcanizates
Vulcanizates Crosslink density (mole/m3)
UA0.6x-0 32.1±1.6
UA0.8x-0 43.9±2.6
UA1.0x-0 54.6±0.6
UA1.2x-0 67.4±0.9
UA1.4x-0 75.7±3.0
UA1.6x-0 90.5±1.5
UA1.8x-0 98.4±2.1
UA1.9x-0 109.1±2.2
UA2.0x-0 109.3±4.5 x-0, UA1.8x-0, UA1.9x-0 and UA2.0x-0 contain curing agents 0.6, 0.8, 1.2, 1.4, 1.5, 1.6,
1.8, 1.9 and 2.0 times that of UA1.0x-0, respectively. Figure 4.1 shows crosslink density
37
versus the normalized amount of curing agents. Each point is the average of three samples.
Crosslink density increases linearly with the amount of curatives.
120
) 100 3
80
60
40
Crosslink density (mole/m 20
0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Nornalized amount of curing agent
Figure 4.1 Crosslink density values of gum NR vulcanizates versus normalized amount of
sulfur used in each compound
38
Cure characteristics for each compound at 140 oC are shown in Table 4.2. Cure
Table 4.2 APA cure characteristics (T = 140 °C , 3 ° arc).
a b Compound tc (100 ) ts2 Minimum torque Maximum torque
(min) (min) (dN.m) (dN.m)
UA0.6x-0 60 24 0.35 4.3
UA0.8 x-0 56 22 0.33 5.4
UA1.0x-0 48 18 0.30 6.4
UA1.2x-0 43 16 0.30 7.4
UA1.4x-0 44 15 0.33 8.2
UA1.6x-0 42 16 0.25 9.4
UA1.8x-0 42 14 0.25 10.4
UA1.9x-0 42 14 0.23 10.4
UA2.0x-0 42 13 0.30 10.6 a tc (100 ) : time first to reach maximum torque. b ts2 : scorch time (time for torque to rise 2 dN.m above minimum value)
39
curves are shown in Figures 4.2. Maximum torque increases as crosslink density increases
(Figure 4.3) while minimum torque fluctuates around 0.3 dN.m. t100 (time first to reach 12 UA1.9x-0 UA2.0x-0 UA1.8x-0 10 UA1.6x-0
UA1.4x-0 8
UA1.2x-0 6
UA1.0x-0
Touque (dNm) Touque 4 UA0.8x-0
2 UA0.6x-0
0 0 10 20 30 40 50 60 t (min)
Figure 4.2 Cure curves of UA0.6x-0 – UA2.0x-0 (T=140oC). maximum torque) decreases sharply from UA0.6x-0 to UA1.2x-0, and then keeps almost constant from UA1.2x-0 to UA2.0x-0. ts2 (scorch time, time for torque to rise 2 dN.m
40
above minimum value) suddenly drops from UA0.6x-0 to UA1.2x-0 and then decreases slightly from UA1.2x-0 to UA2.0x-0.
12
11
10
9
8
7
6 Maximum torque (dN.m) Maximum
5
4 30 40 50 60 70 80 90 100 110 120 Crosslink density (mole/m3)
Figure 4.3 Maximum torque of UA0.6x-0 – UA2.0x-0. The value of maximum torque is
increasing as crosslink density increases.
41
4.2 Normal Tensile Testing
Results of normal (no pre-cut) tensile tests (σ100, σb0, εb0) are shown in Table 4.3.
Table 4.3. Normal (uncut specimens) tensile properties.
Property
Ultimate Compound 100% Modulus Tensile Strength Elongation (MPa) (MPa) (%)
UA0.6x-0 0.56±0.03 10.5±2.3 726±32
UA0.8x-0 0.67±0.03 19.7±1.7 751±21
UA1.0x-0 0.96±0.08 23.5±2.2 687±5
UA1.2x-0 0.92±0.02 22.7±0.8 641±13
UA1.4x-0 1.05±0.06 22.9±1.1 615±14
UA1.6x-0 1.13±0.02 23.3±0.7 583±6
UA1.8x-0 1.26±0.02 22.5±2.3 557±21
UA1.9x-0 1.31±0.05 21.8±1.2 533±7
UA2.0x-0 1.38±0.09 17.2±3.1 484±7
The results are the average of three specimens. 100% modulus increase linearly with crosslink density (Figure 4.4) while tensile strength passes through a maximum as crossl-
42
-ink density is increased. Accordingly, breaking strain decreases with increased crosslink density because shorter chains reach their finite extensibility faster. Stress-strain curves of
1.4
1.2
1.0
0.8 100% Modulus (MPa) 100%
0.6
30 40 50 60 70 80 90 100 110 120 Crosslink density (mole/m3)
Figure 4.4. 100% modulus of UA0.6x-0 – UA2.0x-0. The value of 100% modulus is
increasing as crosslink density increases.
43
uncut specimens (normal tensile testing) are plotted in Figure 4.5. Each curve ischosen as the one with the ultimate values closest to the average of three uncut specimens. Also, vulcanizates become more transparent with increasing crosslinking.
30 UA1.4x-0 UA1.2x-0 25
20 UA1.6x-0
UA1.8x-0 15
UA1.9x-0 stress (MPa) 10 UA2.0x-0 UA1.0x-0
5 UA0.8x-0 UA0.6x-0 0 0 1 2 3 4 5 6 7 8 9 strain
Figure 4.5. Stress-strain curve of UA0.6x-0 – UA2.0x-0.
44
4.3 Precut Tensile Testing
The tensile strength (σb) of pre-cut UA0.6x-0 specimens (Table A1) is given in
Figure 4.6 (log-log) for various cut depths c. The horizontal dotted line is σb0 = 10.5 MPa,
Figure 4.6. Tensile strength of precut specimens (UA0.6x-0). Horizontal dotted line is σb0
(the normal (no cut) tensile strength)
45
the normal tensile strength. For pre-cut specimens there is a stronger, upper population
(UP) when c<= cw 1.40 mm and only a weaker, lower population (LP) when
c>= cs 1.51 mm . Very few specimens lay in the area between the two limits. In Figure 4.4,
in the region of c<= cw 1.40 mm , specimens undergo bulk strain-crystallization prior to
Figure 4.7. Cracking pattern of UA0.6x-0 #35 (c = 1.40 mm, Strength = 1.08 MPa, Strain
= 2.81)
46
fracture. When c exceeds cs , strain-crystallization is thought to be confined to the cut tip region.
Figure 4.8. Cracking pattern of fracture surfaces of UA0.6x-0 #35
SEM micrographs of two test pieces #35 and #37, which are shown in Figure 4.7-4.10,
47
were taken to examine cracking behavior from both side view and fracture surface. Dark lines mark the end of the cut tip. Specimen #37 has the elongation of 517% at break while specimen #35, which is located at the lower population, only has 281% elongation.
From the side view, it’s observed that a single crack initiated from cut tip and grew later-
Figure 4.9. Cracking pattern of UA0.6x-0 #37 (c = 1.51 mm, Strength = 2.36 MPa, Strain
= 5.17)
48
-rally across the sample for #35 (Figure 4.7). Specimen # 37 developed a tiny surface crack before running laterally ahead(Figure 4.9). Fracture surfaces of both test pieces are
Figure 4.10. Cracking pattern of fracture surfaces of UA0.6x-0 #37 also smooth (Figures 4.8 and 4.10).
49
Figure 4.11 shows tensile strength (σb) of pre-cut UA0.8x-0 specimens (Table A2) for various cut depths c. The horizontal dotted line is σb0 = 19.7 MPa, which is the normal
σb0 = 19.7 MPa
10
(495%) m=-0.58
(MPa) b
σ UA0.8x-0 # 36
m=-1.03 (220%) 1 # 37
cs=1.85 mm
cw=1.55 mm
0.1 1 c (mm)
Figure 4.11. Tensile strength of precut specimens (UA0.8x-0). Horizontal dotted line is
σb0 (the normal (no cut) tensile strength)
50
tensile strength. There is a stronger, upper population (UP) when c<= cs 1.55 mm and
only a weaker, lower population (LP) when c>= cw 1.85 mm . In Figure 4.11, high strength is attributied to formation of bulk strain-crystallization prior to fracture in the
Figure 4.12. Cracking pattern of UA0.8x-0 #36 (c = 1.55 mm, Strength = 2.94 MPa,
Strain = 4.75)
51
region of c<= cs 1.55 mm . When c exceeds cs , tensile stress substantially drops down.
SEM micrographs of two test pieces #36 and #37 are shown in Figures 4.12 - 4.15 to
Figure 4.13. Cracking pattern of fracture surfaces of UA0.8x-0 #36 examine cracking patterns form both side face as well as fracture surfaces. From the
52
side view, a tiny surface crack is found at the cut tip in test piece #36 (Figure 4.12).
Additionally, in Figure 4.13, small roughness was found in front of the cut tip.
Figure 4.14. Cracking pattern of UA0.8x-0 #37 (c = 1.85 mm, Strength = 0.90 MPa,
Strain = 1.74)
53
Macroscopically, test piece #37 (Figure 4.14) developed single lateral crack without any crack deviation. And the fracture surface in Figure 4.15 is relatively smooth.
Figure 4.15. Cracking pattern of fracture surfaces of UA0.8x-0 #37
54
The tensile strength (σb) of pre-cut UA1.0x-0 specimens (Table A3) as a function of cut size is given in Figure 4.16 (log-log). The horizontal dotted line is σb0 = 23.5 MPa, the
σb0 = 23.5 MPa
10 # 30 m=-0.52
(480%) # 32 (MPa)
b UA1.0x-0 σ m=-1.48
1 (250%)
cs=1.17 mm cw=1.24 mm
0.1 1 c (mm)
Figure 4.16. Tensile stress of precut specimens (UA1.0x-0). Horizontal dotted line is σb0
(the normal (no cut) tensile stress)
55
normal tensile strength. There is a stronger, upper population (UP) when
c<= cs 1.17 mm and only a weaker, lower population (LP) when c>= cw 1.24 mm .
Comparing with compositions UA0.6x-0 and UA0.8x-0, both critical cut sizes of
UA1.0x-0 shift to the left.
Figure 4.17. Cracking pattern of UA1.0x-0 #30 (c = 1.17 mm, Strength = 5.79 MPa,
Strain = 4.97)
56
Test pieces #30 is located at the upper population and has an elongation of 497%.
Cracking pattern of specimen #30 is shown in Figure 4.17 and Figure 4.18. From the
Figure 4.18. Cracking pattern of fracture surfaces of UA1.0x-0 #30 side view, specimen #30 failed by simple lateral cracking, with no crack deviation.
57
However, in the fracture surfaces (Figure 4.18), longitudinal roughness was found along the direction of cracking propagation. Specimen # 32 is located at the lower population.
And the elongation at break is only 338%. It shows a simple lateral cracking pattern
Figure 4.19. Cracking pattern of UA1.0x-0 #32 (c = 1.24 mm, Strength = 2.05 MPa,
Strain = 3.38)
58
(Figure 4.19). There is also longitudinal cracking pattern on fracture surfaces, of which the roughness is smaller than that of specimen #30 (Figure 4.20).
Figure 4.20. Cracking pattern of fracture surfaces of UA1.0x-0 #32
59
Figure 4.21 shows the tensile strength (σb) of pre-cut UA1.2x-0 specimens (Table A4) for various cut depths c. The horizontal dotted line is σb0 = 22.7 MPa, the normal tensile
σb0 = 22.7 MPa
10 (460%) m=-0.43
# 42
(MPa) m=-1.09 b
σ UA1.2x-0
(258%) # 38 1
cs= cw=0.98 mm 1.60 mm
0.1 1 c (mm)
Figure 4.21. Tensile stress of precut specimens (UA1.2x-0). Horizontal dotted line is σb0
(the normal (no cut) tensile stress
60
strength. There is a stronger, upper population (UP) when c<= cw 0.98 mm and only a
weaker, lower population (LP) when c>= cs 1.60 mm . Between the two limits
( ∆=c 0.62) exists mixture of the two seperated populations. There are 9 test pieces
Figure 4.22. Cracking pattern of UA1.2x-0 #38 (c = 1.35 mm, Strength = 1.81 MPa,
Strain = 2.68)
61
located in the region of cws≤≤ cc. 3 of them are in the upper population while 6 are in the lower population.
Figure 4.23. Cracking pattern of fracture surfaces of UA1.2x-0 #38
SEM micrographs of two test pieces #38 and #42 from both side view and fracture
62
surfaces are shown in Figures 4.22-4.25. Test piece #38 is located in the lower population and has the elongation of only 268%. In Figure 4.22, it developed single lateral crack without any crack deviation. However, the fracture surfaces (Figure 4.23) propagated
Figure 4.24. Cracking pattern of UA1.2x-0 #42 (c = 1.60 mm, Strength = 4.79 MPa,
Strain = 4.73)
63
roughly along the crack direction. Specimen # 37 is in the upper population and has 473% elongation at break. At the cut tip of specimen # 37, the crack path deviates slightly
(Figure 4.24). In Figure 4.25, the fracture surfaces show serrated cracking patterns.
Figure 4.25. Cracking pattern of fracture surfaces of UA1.2x-0 #42
64
Figure 4.26 (log-log) shows the tensile strength (σb) of pre-cut UA1.4x-0 specimens
(Table A5) for various cut depths c. The normal tensile strength is σb0 = 22.9 MPa, which
σb0 = 22.9 MPa
10 # 33
(415%)
# 28
(MPa) m=-0.71 b σ (240%)
UA1.4x-0 1 m=-0.69
cw=0.44 mm cw= 0.80 mm
0.1 1 c (mm)
Figure 4.26. Tensile stress of precut specimens (UA1.4x-0). Horizontal dotted line is σb0
(the normal (no cut) tensile stress)
65
is shown as the horizontal dotted line in Figure 4.26. There is a stronger, upper population
(UP) when c<= cw 0.44 mm and only a weaker, lower population (LP) when
c>= cs 0.80 mm . And in the region of cws≤≤ cc( ∆=c 0.36), specimens occurred in both upper and lower populations. There are 13 specimens located in this region, 6 of which are in the upper population while 7 are in the lower population.
Figure 4.27. Cracking pattern of UA1.4x-0 #28 (c = 0.60 mm, Strength = 2.03 MPa,
Strain = 2.48)
66
Figure 4.27 and Figure 4.28 show SEM micrographs of specimen # 28 from side view and fracture surfaces respectively. Specimen # 28 is located in the lower population
Figure 4.28. Cracking pattern of fracture surfaces of UA1.4x-0 #28 and has the elongation of 250%. It has been shown by X-ray measurement that crystallites
67
initiate at about 250% strain for natural rubber [72]. It indicates that strain-induced crystallization is limited at the cut tip for specimens at lower population, which results in lower strength. In Figure 4.27, a tiny surface crack developed diagonally at the cut tip.
Crack propagated laterally to catastrophic rupture. In Figure 4.28, fracture surfaces are
Figure 4.29. Cracking pattern of UA1.4x-0 #33 (c = 0.80 mm, Strength = 6.00 MPa,
Strain = 4.25)
68
macroscopically smooth with small longitudinal roughness. Specimen # 33 is located in the upper population and has a 425% elongation. Tiny deviation as well as surface crack
Figure 4.30. Cracking pattern of fracture surfaces of UA1.4x-0 #33 is observed in Figure 4.29. Accordingly, in Figure 4.30, longitudinal stripe pattern is observed in fracture surfaces. The roughness is much more than that of specimen #28.
69
The tensile strength (σb) of pre-cut UA1.6x-0 specimens (Table A6) is given in Figure
4.31 (log-log) for various cut depths c. The normal tensile strength is σb0 = 23.3
σb0 = 23.3 MPa # 5 m=-0.22
10 (380%)
m=-1.07
# 32 (MPa) b σ (215%)
UA1.6x-0 1 m=-0.55
cw=0.36 mm cw= 0.44 mm
0.1 1 c (mm)
Figure 4.31. Tensile stress of precut specimens (UA1.6x-0). Horizontal dotted line is σb0
(the normal (no cut) tensile stress
70
MPa, which is shown as the horizontal dotted line. There are also two populations, one is
stronger and the other is weaker. In the region of c<= cw 0.36 mm , there is only upper population. Strength decreases slightly as cut size increases. However, when c exceeds
cs = 0.44 mm , there is an abrupt drop of strength to the lower populaiton. Unlike previous compounds having clearly separated two populations, there are specimens continuously located as the junction for two populations for UA1.6x-0.
Figure 4.32. Cracking pattern of UA1.6x-0 #5 (c = 0.20 mm, Strength = 12.9 MPa, Strain
= 4.87)
71
SEM micrographs of specimen # 5 and # 32 were taken to examine cracking behaviors from both side view and fracture surfaces. They are shown in Figures 4.32 –
Figure 4.33. Cracking pattern of fracture surfaces of UA1.6x-0 #5
4. 35, respectively. Specimen # 5 is located at the upper population and show a 487%
72
elongation at break. According to stress-strain response in Figure 4.5, stain-induced crystallization has already occurred in the bulk. Figure 4.32 shows simple lateral crack without any deviation of specimen #5. On the fracture surfaces, longitudinal cracking patterns are observed propagating along crack growth direction from cut tip, shown in
Figure 4.33. Specimen # 32 only has a elongation 257%. Microscopic pictures shows
Figure 4.34. Cracking pattern of UA1.6x-0 #32 (c = 0.94 mm, Strength = 2.34 MPa,
Strain = 2.57)
73
crack deviation as well as surface secondary crack in Figure 4.34. This a surface crack occurs on only one side of the specimen, which grew diagonally about 0.42 mm before
Figure 4.35. Cracking pattern of fracture surfaces of UA1.6x-0 #32 arrested. Accordingly, Figure 4.35 further confirms that the surface crack went deep into
74
the specimen but not catastrophically through entire width. Fracture surfaces of specimen
# 32 were roughly developed and show complicated serrated cracking pattern.
σb0 = 22.5 MPa
10 # 15 UA1.8x-0
(MPa) # 50 b σ
1
0.1 1 c (mm)
Figure 4.36. Tensile stress of precut specimens (UA1.8x-0). Horizontal dotted line is σb0
(the normal (no cut) tensile stress
75
Figure 4.36 shows the tensile strength (σb) of pre-cut UA1.8x-0 specimens (Table A8)
(log-log) as a function of cut depths c. The horizontal dotted line is σb0 = 22.5 MPa, which is the normal (uncut) tensile strength. Tear strength as a function of cut size is rather different from previous vulcanizates discussed above. No critical cut size is observed and strength does not decrease continuously as cut size increases. For specimens with cut size smaller than 0.4 mm, tear strength is widely dispersed, from 2 MPa to stronger than
Figure 4.37. Cracking pattern of UA1.8x-0 #15 (c = 0.25 mm, Strength = 4.94 MPa,
Strain = 3.55)
76
10 MPa. Correspondingly, with similar cut sizes, elongation at break can vary from 200% to 500%. When cut size exceeds 0.4 mm, tear strength decreases continuously as cut depth increases.
Figure 4.38. Cracking pattern of fracture surfaces of UA1.8x-0 #15
Specimen #15 has the elongation at break of 355% which is located in the upturn
77
region of stress-strain response in Figure 4.5. Figure 4.37 shows SEM micrograph from the side face. The catastrophic path deviates from the initial cut direction but there’s no secondary crack developed. In Figure 4.38, fracture surfaces are rather smooth except a few longitudinal cracking initiated from the cut tip. Elongation at break of specimen # 50 is only 124%. Under such a small strain, strain-induced crystallization is greatly restricted. Figure 4.39 shows cracking pattern of specimen # 50 from the side face. It
Figure 4.39. Cracking pattern of UA1.8x-0 #50 (c = 1.72 mm, Strength = 1.38 MPa,
Strain = 1.24)
78
slightly serrated back and forth about 0.38 mm before catastrophic rupture. No secondary cracking is observed. In the fracture surfaces (Figure 4. 40), steps separates
Figure 4.40. Cracking pattern of fracture surfaces of UA1.8x-0 #50 smooth torn region and characteristic strands spread across tear tip. Kausch [73] has
79
attributed the phenomenon to cavitations which take place ahead of the tip, creating strands of rubber between the cavities. It’s also reported that, for natural rubber
σb0 = 21.8 MPa
10 # 11 UA1.9x-0
(MPa) b σ
1
# 50
0.1 1 c (mm)
Figure 4.41. Tensile stress of precut specimens (UA1.9x-0). Horizontal dotted line is σb0
(the normal (no cut) tensile stress
80
vulcanizates, which are much more resistant to tearing than the wholly amorphous elastomers, the step spacing was ranging from 10 to 100 µm [74].
Figure 4.41 shows tensile strength of UA1.9x-0 as a function of cut size. The horizontal dotted line is σb0 = 21.8 MPa, the normal tensile strength. No critical cut size is observed. When cut size is small ( c< 0.25 mm ), tear strength is widely dispersed, e.g. when c≈ 0.2 mm , strength can either go up to 15 MPa or fall below 2 MPa. As cut depth increases beyond 0.25 mm, strength decreases continuously.
Figure 4.42. Cracking pattern of UA1.9x-0 #11 (c = 0.23 mm, Strength = 15.6 MPa,
Strain = 4.86)
81
Specimen # 11 is the strongest one in the population which has a 486% elongation at break. SEM micrographs from side face and fracture surfaces are shown in Figure 4.42
Figure 4.43. Cracking pattern of fracture surfaces of UA1.9x-0 #11 and Figure 4.43, respectively. In Figure 4.42, crack initiated from the cut tip first grew
82
laterally ( ≈ 0.33mm ) and then deviated. Serrated cracking pattern with surface cracks was found along the length of deviation ( ≈ 0.3mm ). Finally, catastrophic rupture occurred. In
Figure 4.44, longitudinal stripes initiated from cut tip were observed along torn direction.
Specimen # 48 has an elongation of only 217%. Cracking deviation started from the cut
Figure 4.44. Cracking pattern of UA1.9x-0 #48 (c = 0.23 mm, Strength = 2.51 MPa,
Strain = 2.17)
83
tip and grew serrated about 0.6 mm before rupture. Fracture surfaces in Figure 4.45 show an enhanced roughness. Macroscopically, cracking patterns on the torn surfaces are
Figure 4.45. Cracking pattern of fracture surfaces of UA1.9x-0 #48 complex and featureless. However, at higher magnification, steps similar to that in
84
UA1.8x-0 were observed.
The tensile strength (σb) of pre-cut UA 2.0x- 0 specimens (Table A10) is given in
σb0 = 17.2 MPa
10 # 3 UA2.0x-0
(MPa) b σ
# 39
1
0.1 1 c (mm)
Figure 4.46. Tensile stress of precut specimens (UA2.0x-0). Horizontal dotted line is σb0
(the normal (no cut) tensile stress.
85
Figure 4.46 (log-log) for various cut depths c. The horizontal dotted line is σb0 = 17.2
MPa, the normal tensile strength. Strength decreases continuously as cut size increases except several specimens with small cut size exhibiting unusual high strength. Specimen
Figure 4.47. Cracking pattern of UA2.0x-0 #3 (c = 0.20 mm, Strength = 15.2 MPa, Strain
= 4.55)
86
# 3 has the elongation at break up to 455%, which gives bulk strain-induced crystallization and high tensile strength. Secondary cracking was observed in Figure 4.47.
Figure 4.48 Cracking pattern of fracture surfaces of UA2.0x-0 #3
This secondary crack initiated immediately from the cut tip and grew diagonally about
87
0.55 mm then arrested. Catastrophic rupture occurred from the original plane. On the torn surfaces (Figure 4.48), longitudinal cracking was initiated form the cut tip and formed comb-like pattern. Elongation at break of specimen # 39 is only 61%. SEM micrograph of side face is shown in Figure 4.49. Crack propagated laterally ( ≈ 0.2mm ) and deviated
Figure 4.49. Cracking pattern of UA2.0x-0 #39 (c = 1.35 mm, Strength = 1.22 MPa,
Strain = 0.61)
88
( ≈ 0.6mm ) before lateral rupture. Fracture surfaces were roughly developed. With higher magnification, regular steps were found.
Figure 4.50. Cracking pattern of fracture surfaces of UA2.0x-0 #39
89
4.4 Comparison of the Properties of Gum Vulcanizates
Comparison of tear strength as a function of cut size for different gum vulcanizates
is shown through Figures 4.51-4.53. Critical cut sizes of both upper population ( cs ) and
lower population ( cw ) are illustrated in Table 4.4. In Figure 4.51, precut tensile strength of UA0.6x-0, UA0.8x-0 and UA1.0x-0 are plotted and compared. As crosslink density increases, strength of upper population of the three compounds slightly increases. Critical
cut sizes cs and cw first increase from UA0.6x-0 to UA0.8x-0 and then decrease from
UA0.8x-0 to UA1.0x-0. Among them, composition UA0.8x-0 has the largest critical cut sizes but UA1.0x-0 has the highest strength of upper population. Precut tensile strength of
UA1.2x-0, UA1.4x-0 and UA1.6x-0 is compared with UA1.0x-0 in Figure 4.52. Strength of the upper populations of the four compounds is comparable. Different from UA1.0x-0, both compounds UA1.2x-0 and UA1.4x-0 have the area where upper and lower
populations share same cut size range. And ∆c ( =ccsw − ) is 0.62 mm for UA1.2x-0 while 0.36 mm for UA1.4x-0 (Table 4.4). The occurrence of overlapping area indicates that instability of the formation of strain-induced crystallization is increasing as crosslink density increases. From UA1.4x-0 to UA1.6x-0, the special cut size range decreases and critical cut sizes dramatically shift to the left. It suggests that crystallization ability is greatly reduced as chain mobility becomes more limited. Precut tensile strength of even higher crosslinked compounds UA1.8x-0, UA1.9x-0 and UA2.0x-0 are compared with
UA1.0x-0 in Figure 4.53. When cut size is small ( c< 0.3 mm ), tear strength decreases as crosslink density increases. When c>1.2 mm , tear strength of the four compounds is
90
comparable. And in between tear strength of UA1.0x-0 is 3-4 times stronger than the other three.
UA1.0x-0 10 UA0.8x-0
(MPa) b
σ UA0.6x-0
1
0.1 1 c (mm)
Figure 4.51 Comparison of UA0.6x-0, UA0.8x-0 and UA1.0x-0.
Crosslink density changing also introduces differences in cracking behaviors for
91
different compounds. When rubber was lightly vulcanized, crack initiated from cut tip propagated laterally to rupture, no secondary cracking was observed. Fracture surfaces
UA1.0x-0 UA1.2x-0
10
UA1.4x-0
(MPa) b σ
UA1.6x-0
1
0.1 1 c (mm)
Figure 4.52 Comparison of UA1.0x-0, UA1.2x-0, UA1.4x-0 and UA1.6x-0. also smoothly developed. As crosslink density increased, cracking deviation occurred
92
associated with surface crack near the cut tip. Fracture surfaces were no longer smooth, instead, longitudinal roughness were created along torn direction neat the cut tip. When
UA1.0x-0
10
UA1.9x-0
UA1.8x-0 (MPa) b σ
1 UA2.0x-0
0.1 1 c (mm)
Figure 4.53 Comparison of UA1.0x-0, UA1.8x-0, UA1.9x-0 and UA2.0x-0. crosslink density further increased, crack initiated from cut tip deviated and grew serrated
93
before rupture. If anisotropy was high enough, secondary crack would develop. For such moderated crosslinked compositions (UA1.8x-0, UA1.9x-0 and UA2.0x-0), fracture patterns in the torn surfaces can be dramatically different for specimens with high or low strengths. Longitudinal stripes were often observed from specimens exhibiting high sten-
Table 4.4 Critical cut size from tensile testing of pre-cut specimens
Compound cs (mm) cw (mm) ∆=ccsw − c (mm)
UA0.6x-0 1.51 1.40 0.11
UA0.8x-0 1.55 1.85 -0.30
UA1.0x-0 1.17 1.24 -0.07
UA1.2x-0 1.60 0.98 0.62
UA1.4x-0 0.80 0.44 0.36
UA1.6x-0 0.44 0.36 0.08
UA1.8x-0
UA1.9x-0
UA2.0x-0 gth. And for specimens exhibit lower tear strength, regular structured steps were often observed under higher magnification. .
94
CHAPTER V
THE EFFECT OF LOW CONCENTRATIONS (0-20) OF N660 IN THE
REINFORCEMENT OF NATRUAL RUBBER
5.1 Swelling and Curing Testing
Reinforcing fillers restrict swelling of vulcanizates in solvents. The volume fraction
of rubber in the swollen gel-phase of a filled rubber ( vr ) is different from that in swollen
Table 5.1 values of vvrr0 / obtained from swelling measurement.
Compound v vvrr0 /
UA1.7x-0 0 1
UA1.7x-6 0.0291 0.906
UA1.7x-10 0.0476 0.899
UA1.7x-15 0.0698 0.878
UA1.7x-18 0.0826 0.867
UA1.7x-20 0.0909 0.794
v : The volume fraction of carbon black
vr0 : The volume fraction of rubber in a swollen gum gel
vr : The volume fraction of rubber in the swollen gel- phase of a filled rubber
gum rubber ( vr0 ). The ratio vvrr0 / decreases as filler loading increases as shown in Table
95
5.1. Figure 5.1 shows that effect of carbon black (N660) loading on swelling is nonlinear.
Cure characteristics for each compound at 140 oC are shown in Table 5.2 . Cure
1.05
1.00
0.95
r 0.90 /v
r0 v
0.85
0.80
0.75 0.00 0.02 0.04 0.06 0.08 0.10
v Figure 5.1 Effect of volume fraction of carbon black on swelling curves are shown in Figure 5.2. Maximum torque increases as carbon black loading
96
increases. Minimum torque fluctuates around 0.3 dNm. Moreover, tc (100) (time first to reach maximum torque) decrease slightly as black content increases. Scorch time (time for torque to rise 2 dN.m above minimum value) is longest for the gum vulcanizates.
5.2 Normal Tensile Testing
Table 5.2 APA cure characteristics (T = 140 °C , 3 ° arc).
a b Compound tc (100 ) ts2 Minimum torque Maximum torque
(min) (min) (dN.m) (dN.m)
UA1.7x-0 42 16. 0.25 9.1
UA1.7x-6 37 11 0.31 10.8
UA1.7x-10 36 12 0.33 11.5
UA1.7x-15 35 11 0.34 12.2
UA1.7x-18 35 11 0.34 12.4
UA1.7x-20 34 8 0.26 13.8 a tc (100 ) : time first to reach maximum torque. b ts2 : scorch time (time for torque to rise 2 dN.m above minimum value)
97
Results of normal (no pre-cut) tensile tests (σ100, σb0, εb0) are shown in Table 5.3.
The results are the average of three specimens. Small amount of carbon black N660 has
16 UA1.7x-20 UA1.7x-18 14 UA1.7x-15
12
10 UA1.7x-6
8
UA1.7x-0
6 UA1.7x-10 Torque (dNm)
4
2
0 0 10 20 30 40 50 60 t (min)
Figure 5.2 Cure curves of UA1.7x-0-UA1.7x-20. (T=140oC) limited effect on normal tensile strain εb0 and normal tensile stress σb0. However, 100%
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modulus σ100 gradually increases as black content increases. Stress-strain curves are shown in Figure 5.3. Each curve is chosen as the one that has the ultimate value closest to
Table 5.3 Normal (uncut specimens) tensile properties.
Property
Ultimate Compound 100% Modulus Tensile Strength Elongation (MPa) (MPa) (%)
UA1.7x-0 1.10±0.01 23.9±2.5 502.8±10.8
UA1.7x-6 1.38±0.04 23.2±1.4 531.5±11.9
UA1.7x-10 1.43±0.05 24.3±1.7 497.6±14.9
UA1.7x-15 1.45±0.03 24.6+0.5 531.8+24.1
UA1.7x-18 1.56±0.09 24.2±1.1 498.4±15.7
UA1.7x-20 2.06±0.06 23.5±0.9 477.8±10.3
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the average. In the gum rubber (UA1.7x-0), stress slowly increases up to about 350% strain and then concave up. With increasing loading of carbon black, modulus increases.
Figure 5.3 Stress-strain curves for normal tensile test.
And the upturn also occurs earlier, which suggests that bulk crystallization in filled
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natural rubber occurs at lower strain than the gum. An attempt was made to fit 100% modulus to both Guth-Gold equation (Eq. 2.9) and modified Guth-Gold equation (Eq. 2.
2.2
2.0 modified Guth-Gold Expt. 1.8
1.6
1.4 Guth-Gold 100% modulus (MPa) 100% 1.2
1.0 0.00 0.05 0.10 0.15 0.20
v
Figure 5.4 Comparison between 100% modulus and Ec obtained from Guth-Gold relation. 10). Figure 5.4 shows that a better fit is obtained for modified Guth-Gold equation.
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5.3 Precut Tensile Testing
The tensile strength (σb) of edge-cut UA1.7x-0 specimens (Table A11) is given in
Figure 5.5 (log-log) for various cut depths c. The horizontal dotted line is σb0 = 23.9 MPa,
the normal tensile strength. There is a stronger, upper population when c<= cw 0.27 mm
and only a weaker, lower population when c>= cs 0.57 mm . In the region between
( cws≤≤ cc), upper and lower populations co-exist. The overlap width is
∆=c csw − c =0.30 mm .
In this system, specimens are divided into 5 categories according to different cracking patterns from their side face:
simple crack: simple catastrophic rupture;
surface crack: surface crack developed near cut tip;
serrated crack: crack deviates with more than one surface cracks along the serrated curvature ;
longitudinal crack: crack initiated from cut tip deviates and grows along the stretching direction before rupture;
multiple crack: secondary crack is observed.
Cracking pattern distribution of 55 specimens is shown in Figure 5.5. There are 2 test pieces (3.63%) with simple crack, 31 (56.4%) with surface crack, 12 (20.2%) with serrated crack, 6 (10.9%) with longitudinal crack and 5 (9.09%) with multiple cracks
（Table 5.4）. Among the five categories, multiple and longitudinal crack only occurred in the upper population while simple lateral crack only existed in the lower population. To
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Table 5.4. Crack pattern distribution.
UA1.7x-0 UA1.7x-6 UA1.7x-1 UA1.7x-1 UA1.7x-1 UA1.7x-2 0 5 8 0 Total 55 45 62 70 64 55 precut specimens Simple 2 0 0 0 0 0 crack Simple 3.63 0 0 0 0 0 crack % Surface 31 38 55 38 36 0 crack Surface 56.4 84.4 88.7 54.3 56.3 0 crack % Serrated 12 7 6 22 16 0 crack Serrated 20.2 15.6 9.68 31.4 25.0 0 crack % Longitudi- 6 0 1 0 1 0 nal crack Longitudi- 10.9 0 1.62 0 1.5 0 nal crack % Multiple 5 0 0 10 11 55 crack Multiple 9.09 0 0 14.3 17.2 100 crack %
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examine cracking behaviors, SEM micrographs of 5 test pieces #10 (multiple cracks), #
20 (serrated crack), # 29 (surface crack), # 40 (longitudinal crack, photograph) and # 54
σb0 = 23.9 MPa m=-0.22
(460%)
10 # 14 longitudinal crack
# 10 multiple # 20 serrated crack crack
(315%) UA1.7x-0
(MPa) b σ
# 29 surface crack m=-0.65 1 # 54 simple crack cw=0.27 mm cw= 0.57 mm
0.1 1 c (mm)
Figure 5.5 Tensile strength and distribution of cracking patterns of precut specimens
(UA1.7x-0). Horizontal dotted line is σb0 (the normal (no cut) tensile strength)
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(simple crack) were taken from the side face. Additionally, fracture surfaces were also studied for a better understanding. The results are shown in Figures 5.6-5.13. Test piece
# 10 (Figure 5.6) is located in the stronger population. Crack initiated from the cut tip deviated diagonally ( ≈ 0.21mm ), then turned laterally ( ≈ 0.10mm ) and arrested.
Figure 5.6 Crack pattern of UA1.7x-0 #10 (c = 0.26 mm, Strength = 12.16 MPa, Strain =
4.79)
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Catastrophic crack C2 initiated from the midway of the diagonal crack and propagated to
rupture. The virtual, effective crack length is cvb = 0.44 mm. This is 0.18 mm longer
Figure 5.7 Cracking pattern of UA1.7x-0 #20 (c = 0.31 mm, Strength = 11.0 MPa,
Strain = 4.68)
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2 than the initial cut size (c = 0.26 mm). The effective tearing energy Geff, b = 33.5 kJ/m
and tensile strength σ b =12.2 MPa (Table A11).
Figure 5.8 Cracking pattern of fracture surface of UA1.7x-0 #20.
Test piece # 20 (Figure 5.7) shows serrated cracking. There is a forward crack
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growth ( ≈ 0.20mm ) before deviating diagonally ( ≈ 0.50mm ).Then surface cracks occurred after fracture turning laterally again. Catastrophic rupture propagated in front of
Figure 5.9 Cracking pattern of UA1.7x-0 #29 (c = 0.42 mm, Strength = 1.95 MPa, Strain
= 2.12)
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the saw tooth cracking patter. Additionally, micrograph of fracture surfaces is shown in
Figure 5.8. Regularly formed steps were found. The area is according to the diagonal
Figure 5.10 Cracking pattern of fracture surface of UA1.7x-0 #29 region in Figure 5.7. The effective tearing energy of specimen #20 is 23.1 kJ/m2 and tensile strength is 11.0 MPa (Table A11).
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Teat piece # 29 (Figure 5.9) exhibited surface crack at the cut tip, which grew diagonally about 0.09 mm. In Figure 5.10, it’s found that the surface crack occurred only on one side and extended into the bulk ( ≈ 0.10mm ). Fracture surfaces are relatively smooth except several stripes along torn direction. The effective tearing energy 10.5
2 kJ/m and tensile strength σ b =1.95 MPa (Table A11).
Figure 5.11 Cracking pattern of UA1.7x-0 #40 (c = 0.57 mm, Strength = 9.35 MPa, Strain
= 4.81)
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Picture of test piece # 40 (Figure 5.11) was taken with Nikon D1X digital camera.
Crack first grew forward from the cut tip and then deviated and propagated longitudinally along the stretching direction about 1.3 cm. Catastrophic rupture occurred in two places: one is about 0.5 cm above the initial edge cut, the other immediately follows the longitudinal crack and propagated laterally to rupture. The apparent tearing energy is 42.6 kJ/m2 and tensile strength is 9.35 MPa (Table A11).
Figure 5.12 Cracking pattern of UA1.7x-0 #54 (c = 1.02 mm, Strength = 1.00 MPa, Strain
= 0.98)
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Test piece # 54 (Figure 5.12) exhibit a single lateral crack, which propagated all the way across the sample. However, facture surfaces were roughly developed, which is
Figure 5.13 Cracking pattern of fracture surface of UA1.7x-0 #54
shown in Figure 5.13. The effective tearing energy Geff, b and σ b of test piece #54 are
6.60 kJ/m2 and 1.00 MPa (Table A11).
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The tensile strength (σb) of pre-cut UA1.7x-6 specimens (Table A12) is given in
Figure 5.14 (log-log) for various cut depths c. The horizontal dotted line is σb0 = 23.2
σb0 = 23.2 MPa
# 5 surface crack 10 m=-0.03 m=-1.03 UA1.7x-6
(MPa) b σ
m=-0.46 1 # 31 serrated crack
0.1 1 c (mm)
Figure 5.14 Tensile strength and distribution of cracking patterns of precut specimens
(UA1.7x-6). Horizontal dotted line is σb0 (the normal (no cut) tensile strength)
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MPa for normal tensile strength. There are no clearly separated upper or lower populations. When c< 0.25 mm , specimens exhibited high tear strength while when
c> 0.40 mm , tear strength was 3-4 times lower than the gum In the region between, tear strength decreased dramatically with increasing cut size. Cracking pattern distribution of
UA1.7x-6 is also shown in Figure 5.14. Total 45 test pieces gave out only 2 types of cracking patterns: surface crack and serrated crack. There are 38 (84.4%) in the first type
Figure 5.15 Cracking pattern of UA1.7x-6 #5 (c = 0.26 mm, Strength = 10.63 MPa, Strain
= 4.05)
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and 12 (15.6%) in the second type（Table 5.4）. Specimens developing serrated crack all exhibited low tear strength. SEM micrographs of two test pieces #5 and #31 from both side face and fracture surfaces are shown in Figures 5.15 – 5.18.
Figure 5.16 Cracking pattern of fracture surface of UA1.7x-6 #5.
Test piece # 5 (Figure 5.15) exhibited higher tear strength. It developed diagonal
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surface crack ( ≈ 0.15mm ) very near cut tip. No secondary cracking was observed. In
Figure 5.16, the fracture surfaces shows roughness near cut tip. The effective tearing
2 energy Geff, b and tensile strength σ b are 14.5 kJ/m and 10.6 MPa for specimen # 5.
Figure 5.17 Cracking pattern of UA1.7x-6 #31 (c = 0.67 mm, Strength = 1.49 MPa, Strain
= 1.37)
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Test piece # 31 (Figure 5.17) developed a saw tooth crack pattern macroscopically.
With high magnification, surface cracks initiated from the serrated curvature and grew
Figure 5.18 Cracking pattern of fracture surface of UA1.7x-6 #31 diagonally. Magnification of the fracture surfaces (Figure 5.18) show leaf-shaped steps.
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The effective tearing energy Geff, b and tensile strength σ b for specimen # 31 are 5.44 kJ/m2 and 1.49 MPa, respectively (Table A12).
σb0 = 24.3 MPa
10 # 14 longitudinal crack
UA1.7x-10
(MPa) b σ
1 # 40 surface crack
# 61 serrated crack
0.1 c (mm) 1
Figure 5.19 Tensile strength and distribution of cracking patterns of precut specimens
(UA1.7x-10). Horizontal dotted line is σb0 (the normal (no cut) tensile strength)
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The tensile strengths of pre-cut UA1.7x-10 specimens (Table A13) as a function of cut depths are given in Figure 5.19 (log-log). The horizontal dotted line is σb0 = 24.3 MPa, the normal tensile strength. A critical cut size is not apparent. However, when cut size is small ( < 0.3mm ), the distribution of strength with similar cut sizes is large. As cut size increases, specimens become weaker and strength decrease continuously with cut size.
Cracking pattern distribution of UA1.7x-10 is also shown in Figure 5.19. Total 62 test pieces give out 3 types of cracking patterns: surface crack, serrated crack and longitudinal
Figure 5.20 Cracking pattern of UA1.7x-10 #14(c = 0.30 mm, Strength =9.23 MPa, Strain
= 3.66)
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crack. There are 56 (88.7%) specimens with surface crack, 12 (9.68%) with serrated crack and only 1 (1.62%) with longitudinal crack.（Table 5.4）. Photograph of test piece # 14
(longitudinal crack) is shown in Figure 5.20. SEM micrographs of test pieces #40 (surface crack) and #61 (serrated crack) are shown in Figures 5.21-5.24.
Figure 5.21 Cracking pattern of UA1.7x-10 #40(c = 0.62 mm, Strength =2.04 MPa, Strain
= 1.60)
120
Test piece # 14 (Figure 5.21) has a crack that grew a short distance from cut tip and then turned into the stretch direction. After propagating about 1.8 cm, it eventually turned
Figure 5.22 Cracking pattern of fracture surface of UA1.7x-10 #40. laterally and ran to rupture. No secondary crack was observed. The apparent tearing
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energy is 15.3 kJ/m2 and tensile strength is 9.23 MPa (Table A13).
Test piece # 40 (Figure 5.21) has a diagonal surface crack developed from the cut tip.
Figure 5.23 Cracking pattern of UA1.7x-10 #61 (c = 1.16 mm, Strength = 1.16 MPa,
Strain = 0.76)
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Catastrophic rupture initiated coplanar with the cut tip an run straightly ahead.
Figure 5.22 shows fracture surfaces of specimen # 40 with small roughness. The apparent tearing energy 15.3 kJ/m2 and tensile strength 9.23 MPa (Table A13).
Test piece # 40 (Figure 5.22) developed a diagonal surface crack at the cut tip. The
Figure 5.24 Cracking pattern of fracture surface of UA1.7x-10 #61. contour of catastrophic rupture grew serrated. Under higher magnification, surface cracks
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along the torn direction were observed. Additionally, micrograph of fracture surfaces is shown in Figure 5.23. Roughness was greatly enhanced compared with specimen # 40.
It’s also found that steps separating smooth torn region developed along rupture direction.
2 The effective tearing energy Geff, b and tensile strength σ b are 10.7 kJ/m and 2.04 MPa
(Table A13).
The tensile strengths of pre-cut UA1.7x-15 specimens (Table A14) are given in
Figure 5.24 (log-log) for various cut depths c. The horizontal dotted line indicates the normal tensile strength, which is σb0 = 24.6 MPa. Two populations occurred in this compound. For the weaker, lower population, specimens existed in the whole range of cut size. And the strength decreased continuously with increasing cut size. However, the stronger, upper population only occurred within a limited cut size range
( 0.38mm≤≤ c 0.92 mm ). Cracking pattern distribution of UA1.7x-15 is demonstrated with different symbols in Figure 5.25. Total 70 test pieces were divided into 3 types of cracking patterns: surface crack, serrated crack and multiple crack. There are 38 (54.3%) specimens with surface crack, 32 (31.4%) with serrated crack and 10 (14.3%) with multiple crack（Table 5.4）. Specimens developing multiple cracks are all located in the upper population. Micrographs of 3 test pieces #14 (surface crack), #16 (multiple crack) and #30 (serrated crack) are shown in Figures 5.26 – 5.30 to examine cracking behaviors on side face as well as fracture surfaces.
Test piece # 14 (Figure 5.26) developed a surface crack immediately from the cut tip and grew 0.25 mm longitudinally. Eventually, crack initiated from cut tip catastrophically
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propagated to rupture. In Figure 5.27, fracture surfaces show enhanced featureless complexity. The effective tearing energy for specimen # 14 are 5.05 KJ/m2 and 2.02 MPa,
σb0 = 24.6 MPa
# 16 multiple crack UA1.7x-15 10 m=-0.38
(MPa) b
σ m=-0.59
# 14 surface crack 1 # 30 serrated crack
0.1 c (mm) 1
Figure 5.25 Tensile strength and distribution of cracking patterns of precut specimens
(UA1.7x-15). Horizontal dotted line is σb0 (the normal (no cut) tensile strength)
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respectively (Table A4).
Test piece # 16 (Figure 5.27) has similar cut size with test piece # 14. However, the
Figure 5.26 Cracking pattern of UA1.7x-15 #14 (c = 0.37 mm, Strength = 2.02 MPa,
Strain = 1.46)
126
fracture behavior is dramatically different. Crack initiated from the cut tip grew slightly forward (c0 = 0.15 mm) and then split. Crack C1 then grew 0.90 mm longitudinally and
Figure 5.27 Cracking pattern of fracture surface of UA1.7x-15 #14 got arrested. Finally, catastrophic rupture occurred at a distance about 0.25 mm away
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from the initial cut tip. A surface crack is observed in front of cut tip, which grew 0.15
2 mm longitudinally and then arrested. For test piece # 16, Geff, b and σb of are 29.8 kJ/m and 8.21 MPa (Table A14).
Figure 5.28 Crack pattern of UA1.7x-15 #16 (c = 0.38 mm, Strength = 8.21 MPa, Strain =
4.46).
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Test piece # 30 (Figure 5.29) shows serrated cracking pattern, which is very similar with specimen # 61 of UA1.7x-10 (Figure 5.23). Crack serrated back and forth before
Figure 5.29 Cracking pattern of UA1.7x-15 #30 (c = 0.55 mm, Strength = 1.91 MPa,
Strain = 1.34)
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catastrophically running straight ahead. High magnification show surface cracks along the serrated curvature. Roughness of fracture surfaces was examined in Figure 5.30. Layer
Figure 5.30 Cracking pattern of fracture surface of UA1.7x-15 #30 by layer steps existed with enhanced roughness of the step edges.
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The tensile strengths of pre-cut UA1.7x-18 specimens (Table A15) as a function of cut size are shown in Figure 5.31 (log - log). The horizontal dotted line is the normal
σb0 = 24.2 MPa # 16 multiple crack UA1.7x-18
10 # 13 longitudinal m=-0.65 crack
(MPa) b σ
m=-0.68 # 17 surface crack
1 # 50 serrated crack
0.1 1 c (mm)
Figure 5.31 Tensile strength and distribution of cracking patterns of precut specimens
(UA1.7x-18). Horizontal dotted line is σb0 (the normal (no cut) tensile strength) tensile strength (σb0 = 24.2 MPa). In the whole cut size range, there is a weaker, lower
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population Strength deceases continuously as cut size increases. And a stronger, upper population (UP) only occurs when 0.29mm≤≤ c 1.13 mm . This cut size range is larger than that in UA1.7x-15. Cracking pattern distribution of UA1.7x-18 is shown in Figure
5.31. Total 64 test pieces exhibited 4 types of cracking patterns: surface crack, serrated crack, longitudinal crack and multiple crack. There are 36 (56.3%) with surface crack, 16
(25.0%) with serrated crack, only 1 (1.5%) with longitudinal crack and 10 (17.2%) with
Figure 5.32 Cracking pattern of UA1.7x-18 # 13 (c = 0.32 mm, Strength = 7.97 MPa,
Strain = 3.18)
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multiple crack.（Table 5.4）. The upper population is occupied by specimens with multiple cracks and longitudinal crack. Photograph of specimen # 13 (longitudinal crack) is shown in Figure 5.32. SEM micrographs of specimens #16 (multiple crack), #17 (surface crack) and #50 (serrated crack) are shown in Figures 5.33 – 5.37.
Figure 5.33 Crack pattern of UA1.7x-18 #16 (c = 0.35 mm, Strength = 9.01 MPa, Strain =
4.36).
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Test piece # 13 (Figure 5.32) is located in the upper population. Crack first grew forward and then deviated to the stretch direction. After propagating about 0.5 cm longitudinally, it turned laterally to rupture. The apparent tearing energy is 12.1 kJ/m2 and tensile strength is 7.97 MPa (Table A15).
Figure 5.34 Cracking pattern of UA1.7x-18 # 17 (c = 0.38 mm, Strength = 4.11 MPa,
Strain = 2.12)
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Test piece # 16 (Figure 5.33) is also in stronger group. There was a forward crack growth ( ≈ 0.05mm ) before secondary crack splitting. Crack C1 then grew 0.61 mm and arrested. Catastrophic crack initiated nearly coplanar with the cut tip, deviated and ran
Figure 5.35 Cracking pattern of fracture surface of UA1.7x-18 # 17.
2 straight across the sample. Geff, b and σb are 24.7 KJ/m and 9.01 MPa, respectively (Table
A15). 135
Test piece # 17 (Figure 5.34) developed a surface crack 0.15 mm away from the cut tip. It grew diagonally ( ≈ 0.09mm ) with the tendency to circle back. In the fracture
Figure 5.36 Cracking pattern of UA1.7x-18 #50 (c = 1.05 mm, Strength = 1.62 MPa,
Strain = 0.96)
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surfaces (Figure 5.35), longitudinal patterns propagated serrated along the torn surfaces.
2 The effective tearing energy Geff, b and σb are 7.13 KJ/m and 4.11 MPa, respectively
(Table A15).
Figure 5.37 Cracking pattern of fracture surface of UA1.7x-18 #50
Test piece # 50 (Figure 5.36) falls in the weaker group. A surface crack occurred
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immediately at the cut tip. Crack from the cut tip deviated and the fracture curvature serrated back and forth before straight rupture. Accordingly, in the fracture surfaces
(Figure 5.37), vertical steps separating smooth torn regions dominated the characteristic
2 features. The effective tearing energy Geff, b and σ b are 7.91 kJ/m and 1.05 MPa (Table
A15).
σb0 = 23.5 MPa
# 19 multiple crack 10 m=-0.17
m=-0.92
(MPa) b σ UA1.7x-20
1
0.1 1 c (mm)
Figure 5.38 Tensile strength and distribution of cracking patterns of precut specimens
(UA1.7x-20). Horizontal dotted line is σb0 (the normal (no cut) tensile strength)
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Figure 5.38 shows the tear strength as a function of cut size of pre-cut UA1.7x-20 specimens (Table A16). The horizontal dotted line is σb0 = 23.5 MPa, the normal tensile strength. When cut size is small ( < 0.35mm ), tear strength is high and almost independent of cut size. When cut size further increases, tear strength decreases continuously. All of the 55 precut test pieces develop multiple cracks (Table 5.4). In Figure 5.39, test piece #
19 shows a secondary crack C1 occurred immediately from the cut tip and grew 0.64 mm longitudinally and arrested. Crack coplanar with initial cut then propagated a small distance ( ≈ 0.10mm ) and deviated to the stretch direction. The effective tearing energy
2 Geff, b and σb of test piece # 19 are 14.8 KJ/m and 12.3 MPa, respectively (Table A16)
Figure 5.39 Crack pattern of UA1.7x-20 #19 (c = 0.34 mm, Strength = 12.3 MPa, Strain =
3.57).
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5.4 Comparison between Gum and Black-filled NR Vulcanizates.
Now, stress at break of N660 filled NR vulcanizates is plotted individually and compared to gum vulcanizates. Figure 5.40 shows the comparison between UA1.7x-6 and
UA1.7x-0. Both compounds exhibit comparable strength for lower populations. However, for UA1.7x-6, strength dramatically decreases when cut size exceeds 0.25 mm, while the critical cut size of upper population for UA1.7x-0 is 0.57 mm. In Figure 5.41, compositon
UA1.7x-10 doesn’t show two separating populations. Compared with UA1.7x-0, strengths of UA1.7x-10 specimens with small cut sizes further drop down. And the strength of large cut size specimens remains comparable with that of UA1.7x-0. For compounds UA1.7x-15 and UA1.7x-0 (Figure 5.42), both of them have two populations but with different styles. For UA1.7x-15, when cut size is very small or very large, there is only lower population, while upper and lower populations coexist in between. Strength of the lower population of UA1.7x-15 is slightly higher than UA1.7x-0 and the opposite is true. The behavior is similar for UA1.7x-18 (Figure 5.43). However, strength of upper population of UA1.7x-18 is comparable with that of UA1.7x-0. And strength of the lower population of UA1.7x-18 is further enhanced. Tensile strength of specimens of
UA1.7x-20 and UA1.7x-0 is shown in Figure 5.44. With 20 phr N660 black, no separating populations are observed. When cut is small, strength is comparable for both compounds. As cut size increases, UA1.7x-0 is significantly weaker than UA1.7x-20.
Gent and De [75] proposed that crosslink density plays an important role for occurrence of knotty tear. When crosslink density is unusually high or unusually low,
140
knotty tear is suppressed. Hamed and Rattanasam [1] studied the cut growth in tensile specimens of NR vulcanizates. They found that for lightly and densely crosslinked compounds, crack growth is simply perpendicular to the loading direction and side surfaces are smooth. However, moderated crosslinked compositions exhibit crack deviation prior to rupture. In the present study, cracking behavior of a moderated crosslinked composition UA1.7x-0 was studied. According to their characteristic cracking feathers, test pieces were separated into five categories. And within a very narrow range of cut size ( 0.25mm≤≤ c 0.32 mm ), precursor longitudinal crack growth occurred. Carbon black is also an important factor for anisotropy. It’s well known that NR filled with typical ( ≈ 50 phr) levels of carbon black develops stable, slowly-growing longitudinal cracks before catastrophic rupture. Hamed group [3,4] also studied effect of carbon black
(N115 and N660) on cracking behavior of NR vulcanizates, The degree of crosslinking was selected to be one where the gum vulcanizate does not exhibit longitudinal cracking for any cut size. Most interesting, when carbon black concentration is low, filled specimens are weaker than gum and fracture occurs by simple forward growth of original cut tip. So the question comes to what behavior will be when gum vulcanizate that exhibits multiple-cracking get filled. When carbon black (N660) loading was increased to
6 phr, degree of complexity of cracking was greatly reduced. No secondary cracking was observed. Critical cut size also shifted to left. As black concentration further increased to
10 phr, strength of vulcanizate was further reduced. Only one specimen developed longitudinal deviation without secondary cracking. At 15 phr, within a range of cut size,
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crack split prior to catastrophic rupture. And at 18 phr of carbon black, strength of filled specimens become even stronger. And more specimens
UA1.7x-0 10
(MPa) b σ
UA1.7x-6
1
0.1 1 c (mm)
Figure 5.40 Comparison between UA1.7x-6 and UA1.7x-0. within a wider cut size range exhibit crack splitting. At 20 phr of black, all specimens
142
developed multiple cracks. Strength is further enhanced and unset of reinforcement occurs
UA1.7x-0
10
(MPa) b σ
UA1.7x-10 1
0.1 1 c (mm)
Figure 5.41 Comparison between UA1.7x-10 and UA1.7x-0.
Two transitions can be observed from the phenomenon. One is the strength transition.
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As carbon black concentration increases, strength first decreases and then increases.
Small amount of carbon black facilitate the process of nucleation but suppress crystallite
UA1.7x-0
10 UA1.7x-15
(MPa) b σ
1
0.1 c (mm) 1
Figure 5.42 Comparison between UA1.7x-15 and UA1.7x-0. growth. The other one is cracking transition. Degree of complexity of cracking pattern
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decreases when black concentration is low. It suggests reduced anisotropy. Then multiple cracks occur only when black loading further increases and reaches a critical level. And
UA1.7x-18 10
(MPa) b σ
UA1.7x-0 1
0.1 1 c (mm)
Figure 5.43 Comparison between UA1.7x-18 and UA1.7x-0. cracking splitting is necessary for reinforcement. Additionally, specimens which develop
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serrated cracking in the side face all have characteristic step patterns in their fracture surfaces.
UA1.7x-20 10
(MPa) b σ
UA1.7x-0
1
0.1 1 c (mm)
Figure 5.44 Comparison between UA1.7x-20 and UA1.7x-0.
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CHAPTER VI
CONCLUSION 1. As crosslink density increases, tearing strength first increases, pass a maximum and then decreases.
2. Two populations of tear strength as a function of cut size are present from composition UA0.6x-0 to UA1.6x-0. Critical cut sizes first shift to the right and then to the left as crosslink density increases.
3. Critical cut size disappears from composition UA1.8x-0. After that, crosslinked rubber becomes brittle and tear strength dramatically decreases with increasing crosslink density.
4. For lightly crosslinked NR vulcanizates, strain-induced crystallization ability increases with increasing crosslink concentration. When crosslink becomes denser, crystallization ability become limited. Instability occurs that with the same cut size, specimens can fall in either upper or lower population. The length of instable area will decrease and eventually disappear when crosslink density become even higher.
5. Varying crosslink density results in different cracking behaviors. The crack path for lightly crosslink NR is almost perpendicular to the loading direction and secondary cracking is not found at the tip region. As crosslink density increases, surface crack neat the cut tip occurs. Following that, serrated or longitudinal crack can be observed with higher crosslink density. If the anisotropy exceeds critical value, secondary crack occurs within a limited crosslink density and cut size.
6. Crosslink density also plays an important role in the cracking behavior on fracture surfaces. For lightly crosslinking vulcanizates, fracture surfaces are relatively smooth. Then longitudinal stripes develop along torn direction and roughness is increasing with increasing crosslink. Vertical steps separating smooth featureless torn regions occur when gum vulcanizates have even higher crosslink densities.
7. For moderately crosslinked gum NR vulcanizates (UA1.6x-0 – UA2.0x-0), cracking patterns on fracture surfaces are different for specimens exhibiting higher tensile strength (small cut size) or lower tensile strength (larger cut size). In the former case, longitudinal stripes occur frequently. And for the latter,
147
vertical steps are often observed.
8. Composition UA1.7x-0 exhibits complex cracking behaviors, of which multiple cracks are observed within a limited cut size.
9. Low concentration of the coarse N660 black not only gives lower (pre-cut) strength than the gum, but also depresses complexity of cracking behavior. Cracking splitting occurs again when black loading exceeds 15 phr.
10. A critical amount (20 phr) of carbon black N660 is required for the unset of reinforcement of UA1.7x-0. Cracking splitting is necessary for reinforcement.
11. Vertical steps exit in both gum and black filled composition of UA1.7x-0. It’s related to serrated cracking observed from the side face.
148
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154
APPENDIX
EFFECT OF CROSSLINK DENSITY AND N660 CARBON BLACK ON TEARING
BEHAVIORS OF NATURAL RUBBER VULCANIZATES
Table A1 Tensile properties of UA0.6x-0 specimen c Thickness σb εb Wb Gapp,b # (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 10.5 726 - - 1 0.11 0.603 11.5 719 18.8 4.54 2 0.13 0.583 12.5 751 20.9 5.85 3 0.16 0.68 9.99 669 16.0 5.79 4 0.18 0.597 7.46 661 13.1 5.37 5 0.20 0.651 8.96 705 15.6 6.91 6 0.20 0.61 8.70 666 14.5 6.58 7 0.22 0.569 8.02 694 13.8 6.77 8 0.24 0.637 6.83 608 11.3 6.40 9 0.27 0.503 7.88 616 12.4 7.86 10 0.30 0.653 7.75 693 13.6 9.10 11 0.33 0.643 6.53 621 11.2 8.65 12 0.34 0.628 7.10 600 11.6 9.36 13 0.34 0.622 6.39 648 11.4 8.89 14 0.35 0.519 6.61 615 11.3 9.29 15 0.36 0.643 6.53 621 11.2 9.43 16 0.38 0.598 6.03 654 11.5 9.99 17 0.40 0.606 7.05 677 12.5 11.3 18 0.40 0.623 6.03 607 10.4 9.83 19 0.44 0.595 7.22 616 12.0 12.3 20 0.47 0.501 6.49 643 11.8 12.7 21 0.50 0.581 5.41 633 10.4 12.0 22 0.50 0.657 4.97 577 8.90 10.7 23 0.53 0.639 4.83 585 8.82 11.2 24 0.58 0.545 5.20 619 9.92 13.4
155
25 0.58 0.602 5.40 644 10.6 14.1 26 0.60 0.579 5.21 631 10.2 14.2 27 0.70 0.649 4.72 552 8.51 14.6 28 0.75 0.673 4.13 563 7.84 14.3 29 0.78 0.64 4.60 584 8.84 16.5 30 0.90 0.629 2.99 542 6.41 14.3 31 0.90 0.553 4.30 522 7.73 17.5 32 0.98 0.602 3.81 551 7.87 18.9 33 1.11 0.576 3.20 530 6.59 18.3 34 1.28 0.665 2.99 540 6.42 20.3 35 1.40 0.63 1.08 281 1.92 8.65 36 1.50 0.598 3.28 521 6.62 25.0 37 1.51 0.563 2.36 517 5.54 21.1 38 1.85 0.627 1.05 290 1.92 11.2 39 1.88 0.608 1.41 367 3.17 17.3 40 1.92 0.609 1.62 429 3.81 19.9 41 2.50 0.542 0.82 196 1.06 9.67 42 2.60 0.643 0.73 192 1.00 9.55 43 2.98 0.521 0.64 140 0.61 7.36
156
Table A2 Tensile properties of UA0.8x-0 specimen# c Thickness σb εb Wb Gapp,b (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 19.7 751 - - 1 0.18 0.539 13.8 677 21.4 8.68 2 0.21 0.613 9.30 613 14.6 7.21 3 0.21 0.611 10.4 621 15.8 7.76 4 0.22 0.649 8.51 615 14.1 7.28 5 0.23 0.642 8.97 634 14.6 7.78 6 0.25 0.661 8.58 632 14.1 8.18 7 0.26 0.579 10.0 615 15.7 9.59 8 0.28 0.557 8.41 618 13.7 8.99 9 0.28 0.589 8.15 601 13.4 8.90 10 0.29 0.673 7.44 604 12.3 8.44 11 0.30 0.678 8.51 598 13.6 9.69 12 0.35 0.664 - - 13 0.38 0.629 7.73 593 12.6 11.4 14 0.38 0.622 7.56 576 12.2 11.2 15 0.38 0.576 7.80 562 12.2 11.3 16 0.41 0.569 7.43 598 12.3 11.9 17 0.42 0.607 7.26 597 11.9 11.8 18 0.43 0.655 7.04 585 11.8 12.1 19 0.44 0.659 7.37 580 12.1 12.8 20 0.44 0.593 7.52 597 12.4 12.9 21 0.45 0.631 6.77 606 12.1 12.8 22 0.50 0.565 6.32 550 10.6 13.0 23 0.53 0.655 5.93 545 10.2 13.3 24 0.62 0.676 5.42 542 9.65 14.8 25 0.62 0.693 6.49 613 11.5 16.7 26 0.67 0.673 5.17 576 9.82 15.8 27 0.72 0.675 4.72 544 8.71 15.5 28 0.72 0.689 4.80 543 8.80 15.7 29 0.73 0.541 4.86 546 9.02 16.2 30 0.81 0.615 5.67 559 10.1 20.0 31 0.98 0.561 3.64 521 7.43 18.3 32 1.00 0.577 4.67 556 8.92 21.8 33 1.20 0.621 3.21 505 6.80 20.8 34 1.31 0.635 3.13 489 6.55 22.2 35 1.32 0.579 4.32 528 8.30 27.4 36 1.55 0.600 2.94 475 6.29 25.5
157
37 1.85 0.533 0.90 174 1.03 7.23 38 2.12 0.669 1.21 265 2.02 14.0 39 2.22 0.61 0.90 199 1.14 9.10 40 2.70 0.652 0.66 142 0.66 7.20
158
Table A3 Tensile properties of UA1.0x-0 specimen# c Thickness σb εb Wb Gapp,b (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 23.5 687 - - 1 0.15 0.609 14.9 621 21.7 7.61 2 0.16 0.653 15.7 628 22.5 8.38 3 0.17 0.649 14.1 626 20.2 8.00 4 0.18 0.668 16.4 628 24.3 10.1 5 0.19 0.692 11.5 602 18.2 8.20 6 0.20 0.625 13.0 593 19.2 9.16 7 0.22 0.590 13.9 579 20.0 10.6 8 0.26 0.657 11.6 608 17.4 10.6 9 0.28 0.600 13.7 587 20.2 13.5 10 0.28 0.608 12.0 580 16.8 11.3 11 0.30 0.724 10.8 598 15.9 11.3 12 0.30 0.704 13.4 612 19.3 13.6 13 0.32 0.637 9.85 572 14.9 11.5 14 0.36 0.638 10.9 581 17.1 14.8 15 0.36 0.555 10.3 576 15.6 13.5 16 0.41 0.643 9.83 549 15.3 15.4 17 0.43 0.690 10.3 578 15.7 16.2 18 0.47 0.669 8.03 552 13.2 15.2 19 0.48 0.598 8.41 551 13.3 15.7 20 0.52 0.615 8.21 563 13.4 17.0 21 0.54 0.701 8.87 556 14.2 18.8 22 0.54 0.683 8.84 558 13.8 18.2 23 0.70 0.621 7.19 527 11.7 20.5 24 0.75 0.647 7.13 535 12.0 22.4 25 0.76 0.592 6.50 524 11.0 21.0 26 0.78 0.573 6.29 520 11.5 22.6 27 0.85 0.548 6.60 523 11.3 24.1 28 0.89 0.581 5.18 500 10.3 23.5 29 1.08 0.655 5.66 497 9.71 26.9 30 1.17 0.573 5.79 497 10.1 30.3 31 1.23 0.667 1.43 236 2.01 8.47 32 1.24 0.541 2.05 338. 4.08 15.1 33 1.54 0.554 1.12 181 1.25 7.22 34 1.66 0.645 1.36 215 1.80 10.5 35 1.80 0.607 0.91 130 0.74 5.51 36 1.84 0.658 0.91 144 0.83 6.13
159
Table A4 Tensile properties of UA1.2x-0 specimen# c Thickness σb εb Wb Gapp,b (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 22.7 641 - - 1 0.07 0.631 14.7 616 15.0 14.8 2 0.16 0.601 13.6 495 14.8 6.10 3 0.21 0.653 10.9 553 16.2 8.36 4 0.25 0.631 11.6 544 16.7 10.3 5 0.26 0.726 10.2 573 16.1 10.1 6 0.26 0.650 10.2 530 15.2 9.89 7 0.26 0.609 12.6 581 18.7 11.7 8 0.28 0.663 9.70 539 14.5 10.0 9 0.28 0.637 11.8 526 16.1 11.3 10 0.30 0.679 11.0 566 16.8 12.2 11 0.32 0.708 11.2 552 15.9 12.5 12 0.32 0.661 9.61 561 15.2 11.8 13 0.33 0.566 12.2 575 12.2 9.73 14 0.35 0.688 9.95 518 14.7 13.0 15 0.37 0.685 10.3 539 15.3 14.0 16 0.40 0.649 7.97 516 12.8 12.9 17 0.40 0.613 9.63 543 15.0 14.8 18 0.49 0.615 8.10 535 13.2 16.1 19 0.49 0.693 9.09 558 15.0 18.0 20 0.54 0.556 12.5 560 17.7 23.3 21 0.58 0.631 9.35 531 14.4 20.8 22 0.60 0.591 8.35 524 13.2 19.9 23 0.62 0.569 7.58 515 12.4 19.4 24 0.64 0.707 5.41 482 9.96 16.6 25 0.65 0.673 6.08 490 10.7 17.9 26 ------27 0.67 0.595 7.23 456 8.68 15.4 28 0.70 0.673 7.85 503 12.4 22.2 29 0.71 0.651 5.76 497 10.4 18.9 30 0.73 0.659 3.38 407 6.86 13.9694 31 0.73 0.596 3.89 438 7.58 14.9 32 0.85 0.627 6.39 456 10.2 23.0 33 0.90 0.650 6.19 492 11 25.5 34 0.98 0.620 1.67 219 2.13 7.33 35 ------36 1.04 0.627 5.38 456 9.53 26.4
160
37 1.28 0.558 1.32 171 1.38 6.74 38 1.35 0.615 1.81 268 2.80 12.3 39 1.36 0.644 1.38 176 1.47 7.55 40 1.51 0.623 1.13 142 1.01 6.15 41 1.57 0.516 1.21 158 1.24 7.60 42 1.60 0.725 4.79 473 9.22 38.7 43 1.68 0.527 1.07 133 0.92 6.36 44 2.00 0.576 1.00 121 0.79 6.67 45 2.22 0.538 0.88 102 0.57 5.58 46 3.24 0.646 0.72 70.8 0.34 5.29
161
Table A5 Tensile properties of UA1.4x-0 specimen# c Thickness σb εb Wb Gapp,b (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 22.9 615 - - 1 0.13 0.674 15.7 567 22.4 7.08 2 0.16 0.585 13.3 5252 18.5 7.44 3 0.17 0.727 12.1 530 17.4 7.40 4 0.18 0.639 15.1 538 21.1 9.45 5 0.20 0.587 13.0 519 18.2 9.18 6 0.23 0.570 10.6 494 15.3 9.07 7 0.24 0.665 10.5 522 15.7 9.49 8 0.24 0.631 9.31 509 14.5 8.86 9 0.24 0.693 11.3 511 16.1 9.81 10 0.24 0.701 10.0 520 15.4 9.32 11 0.25 0.617 11.7 494 16.4 10.5 12 0.25 0.602 10.4 521 15.3 9.64 13 0.27 0.599 11.0 513 16.1 11.0 14 0.30 0.699 10.5 528 15.8 11.8 15 0.31 0.654 10.4 521 15.6 12.1 16 0.32 0.729 10.4 504 15.4 12.6 17 0.34 0.661 10.4 526 15.8 13.4 18 0.36 0.614 10.8 505 15.8 14.5 19 0.38 0.599 6.95 475 11.6 11.5 20 0.40 0.698 5.86 436 9.86 10.7 21 0.43 0.737 5.19 428 9.35 10.9 22 0.44 0.677 2.00 238 2.69 4.04 23 0.46 0.651 1.90 229 2.44 3.88 24 0.47 0.765 7.70 478 12.5 15.3 25 0.48 0.632 6.14 455 10.6 13.6 26 0.50 0.681 9.16 509 14.2 18.0 27 0.55 0.661 5.90 449 10.3 15.1 28 0.6 0.730 2.03 248 2.79 5.63 29 0.65 0.629 1.76 201 2.10 4.94 30 0.75 0.717 5.65 453 9.94 19.9 31 0.77 0.679 1.56 188 1.76 5.01 32 0.80 0.628 1.47 179 1.58 4.75 33 0.80 0.628 6.00 425 10.1 22.1
162
34 0.81 0.601 1.24 127 1.00 3.37 35 0.88 0.609 1.34 160 1.3 4.45 36 1.35 0.695 0.95 92.2 0.57 3.48 37 1.57 0.639 1.02 106 0.67 4.60 38 2.80 0.645 1.48 183 1.63 17.0
163
Table A6 Tensile properties of UA1.6x-0 specimen# c Thickness σb εb Wb Gapp,b (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 23.3 583 - - 1 0.10 0.665 13.1 506 18.0 4.59 2 0.11 0.612 13.4 521 18.9 5.24 3 0.16 0.627 13.2 515 18.6 7.54 4 0.19 0.603 10.9 479 15.4 7.64 5 0.20 0.601 12.9 487 17.4 9.02 6 0.21 0.595 10.0 495 15.0 8.11 7 0.21 0.607 10.9 462 14.9 8.29 8 0.24 0.684 12.0 498 17.0 10.5 9 0.26 0.668 11.4 498 16.2 10.8 10 0.26 0.663 8.84 471 13.3 9.08 11 0.26 0.579 10.6 478 15.1 10.2 12 0.27 0.575 9.23 478 13.8 9.74 13 0.27 0.573 9.01 471 13.4 9.51 14 0.30 0.640 9.20 472 13.8 10.8 15 0.33 0.616 7.97 441 12.0 10.6 16 0.35 0.676 10.3 487 14.9 13.5 17 0.35 0.639 9.69 473 13.9 12.7 18 0.36 0.659 5.21 393 8.61 8.77 19 0.37 0.647 9.80 474 14.3 13.8 20 0.39 0.651 2.97 292 4.46 5.52 21 0.41 0.605 2.83 281 4.15 5.47 22 0.44 0.552 4.05 345 6.53 8.55 23 0.45 0.616 1.99 210 2.43 3.90 24 0.47 0.540 1.61 160 1.61 2.94 25 0.47 0.697 1.77 191 1.98 3.42 26 0.50 0.610 1.87 202 2.19 3.96 27 0.51 0.631 1.80 190 2.01 3.78 28 0.57 0.647 1.51 162 1.48 3.27 29 0.57 0.655 2.24 243 3.00 5.80 30 0.76 0.707 1.29 140 1.10 3.38 31 0.89 0.537 2.58 269 3.67 10.6 32 0.94 0.737 2.34 257 3.21 10.0 33 1.23 0.641 2.33 248 3.13 12.9 34 1.28 0.541 1.28 108 0.87 4.85 35 2.25 0.691 0.90 84.4 0.47 4.89
164
Table A7: Tensile properties of UA1.8x-0 specimen# c Thickness σb εb Wb Gapp,b (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 22.5 557 - - 1 0.15 0.586 11.6 472 16.2 6.38 2 0.18 0.540 4.61 337 7.09 3.83 3 0.18 0.550 7.25 404 11.2 5.64 4 0.19 0.634 2.67 234 3.33 2.17 5 0.20 0.667 5.29 361 8.19 4.79 6 0.21 0.654 2.21 210 2.56 1.91 7 0.22 0.621 8.08 369 8.85 5.64 8 0.22 0.651 4.10 322 6.18 4.15 9 0.22 0.662 10.2 455 14.5 8.51 10 0.23 0.625 4.18 331 6.41 4.46 11 0.23 0.603 3.62 300 5.34 3.85 12 0.23 0.660 12.4 486 17.2 10.2 13 0.24 0.616 4.63 350 7.16 5.09 14 0.25 0.615 11.6 471 16.2 10.6 15 0.25 0.639 4.94 355 7.72 5.68 16 0.25 0.628 2.69 236 3.39 2.90 17 0.26 0.634 2.33 216 2.76 2.53 18 0.28 0.625 3.25 281 4.58 4.13 19 0.28 0.613 4.94 346 7.52 6.26 20 0.29 0.703 2.25 213 2.66 2.74 21 0.30 0.609 6.91 388 9.34 7.96 22 0.31 0.593 1.66 146 1.46 1.81 23 0.36 0.699 6.53 406 10.4 10.4 24 0.36 0.636 1.89 184 1.95 2.61 25 0.39 0.673 2.04 196 2.29 3.26 26 0.40 0.605 2.07 191 2.25 3.31 27 0.44 0.617 2.21 202 2.49 3.96 28 0.47 0.585 1.31 107 0.87 1.78 29 0.47 0.636 1.66 145 1.46 2.75 30 0.5 0.615 1.50 133 1.21 2.48 31 0.52 0.610 1.84 175 1.88 3.70 32 0.53 0.657 5.38 375 8.51 13.0 33 0.70 0.665 2.43 219 2.89 7.11 34 0.72 0.649 1.39 115 0.98 3.02 35 0.75 0.647 1.35 121 0.98 3.10 36 0.76 0.610 1.80 162 1.74 5.12 37 0.86 0.563 1.26 100 0.78 2.97 165
38 0.90 0.653 0.98 71.0 0.43 1.85 39 0.91 0.691 1.11 86.0 0.59 2.47 40 0.94 0.644 1.33 113 1.33 5.37 41 0.97 0.657 1.97 182 2.08 7.54 42 1.08 0.581 0.99 73.7 0.45 2.31 43 1.08 0.590 1.52 142 1.31 5.71 44 1.10 0.550 0.97 69.8 0.42 2.22 45 1.14 0.632 1.58 141 1.36 6.26 46 1.24 0.631 1.14 93.2 0.65 3.64 47 1.25 0.589 1.19 88.3 0.66 3.77 48 1.27 0.660 2.41 228 2.97 13.0 49 1.29 0.600 1.49 133 1.19 6.30 50 1.72 0.635 1.38 124 1.06 7.64 51 2.03 0.653 1.09 92.4 0.61 5.60 52 2.20 0.606 0.88 70.3 0.38 4.02
166
Table A8: Tensile properties of UA1.9x-0 specimen# c Thickness σb εb Wb Gapp,b (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 21.8 533 - - 1 0.10 0.572 4.70 326 6.96 2.11 2 0.13 0.588 4.53 328 6.74 2.66 3 0.15 0.641 2.72 231 3.35 1.73 4 0.17 0.546 8.48 418 12.7 5.96 5 0.17 0.589 5.22 345 7.80 3.95 6 0.17 0.627 4.21 306 6.04 3.20 7 0.18 0.663 4.06 308 5.82 3.26 8 0.18 0.579 3.41 261 4.45 2.65 9 0.19 0.588 5.47 361 8.46 4.70 10 0.19 0.653 4.90 328 7.28 4.19 11 0.20 0.649 15.6 486 20.9 10.8 12 0.21 0.611 3.17 246 4.00 2.83 13 0.21 0.617 2.89 238 3.61 2.59 14 0.21 0.683 2.20 195 2.52 1.93 15 0.23 0.613 2.51 217 2.96 2.40 16 0.26 0.598 2.38 205 2.71 2.53 17 0.27 0.575 2.38 203 2.71 2.63 18 0.29 0.618 3.01 239 3.70 3.66 19 0.31 0.536 1.83 158 1.73 2.09 20 0.32 0.565 2.01 170 1.97 2.41 21 0.34 0.653 1.58 139 1.30 1.79 22 0.35 0.620 1.80 155 1.64 2.25 23 0.35 0.686 2.33 206 2.71 3.40 24 0.36 0.674 2.09 182 2.19 2.95 25 0.43 0.675 1.54 135 1.24 2.18 26 0.45 0.592 1.51 123 1.12 2.11 27 0.46 0.623 1.86 158 1.74 3.13 28 0.48 0.550 1.31 95.4 0.79 1.70 29 0.48 0.675 1.64 145 1.41 2.71 30 0.51 0.684 1.32 103 0.84 1.89 31 0.52 0.614 1.34 109 1.30 1.79 32 0.56 0.631 1.41 113 0.96 2.31 33 0.58 0.608 1.20 88.2 0.66 1.75 34 0.60 0.674 1.35 109 0.90 2.34 35 0.61 0.639 1.37 107 0.90 2.39 36 0.62 0.637 1.96 175 1.99 4.67 37 0.65 0.598 1.86 169 1.91 4.75 167
38 0.68 0.667 1.14 81.8 0.59 1.86 39 0.76 0.543 1.06 70.8 0.48 1.75 40 0.82 0.590 1.17 81.4 0.60 2.29 41 0.82 0.643 1.51 126 1.17 4.00 42 0.83 0.611 1.19 78.3 0.58 2.26 43 0.85 0.666 1.10 78.2 0.54 2.16 44 1.10 0.537 1.06 75.5 0.51 2.66 45 1.12 0.603 1.55 131 1.23 5.68 46 1.15 0.597 1.27 99.0 0.78 3.99 47 1.16 0.625 1.57 135 1.26 5.99 48 1.30 0.671 1.06 69.5 0.48 3.01 49 1.69 0.559 1.19 95.5 0.71 5.39 50 1.80 0.583 1.37 111 0.98 7.62 51 3.40 0.610 0.70 45.4 0.21 3.72
168
Table A9: Tensile properties of UA2.0x-0 specimen# c Thickness σb εb Wb Gapp,b (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 17.2 484 - - 1 0.18 0.705 2.02 159 1.87 1.31 2 0.20 0.615 3.13 229 4.02 2.78 3 0.20 0.623 15.2 455 20.4 10.8 4 0.21 0.599 1.83 148 1.61 1.34 5 0.21 0.721 1.69 130 1.32 1.14 6 0.23 0.688 1.59 125 1.21 1.16 7 0.24 0.619 2.53 192 2.71 2.39 8 0.25 0.653 2.09 163 1.96 1.89 9 0.26 0.656 1.58 131 1.21 1.30 10 0.27 0.701 1.72 141 1.47 1.60 11 0.28 0.627 1.57 114 1.21 1.45 12 0.30 0.678 1.56 125 1.23 1.54 13 0.30 0.636 4.67 308 6.52 6.08 14 0.31 0.644 1.72 131 1.37 1.75 15 0.34 0.723 1.61 127 1.21 1.71 16 0.35 0.675 1.47 121 1.07 0.67 17 0.36 0.639 1.77 136 1.43 2.10 18 0.37 0.691 1.22 93.4 0.71 1.18 19 0.39 0.691 1.24 90.0 0.69 1.22 20 0.40 0.697 1.44 113 0.98 1.68 21 0.41 0.616 1.46 113 1.12 1.97 22 0.45 0.684 1.38 103 0.88 1.74 23 0.50 0.711 1.22 87.9 0.66 1.51 24 0.52 0.655 1.33 103 0.86 1.97 25 0.60 0.634 1.16 81.5 0.58 1.62 26 0.65 0.587 0.99 65.7 0.43 1.36 27 0.66 0.737 1.66 141 0.38 3.65 28 0.67 0.62 1.07 70.2 0.48 1.54 29 0.72 0.645 1.63 133 1.28 3.79 30 0.72 0.772 1.00 70.0 0.44 1.52 31 0.76 0.604 1.05 58.1 0.39 1.48 32 0.80 0.644 1.24 73.8 0.60 2.28 33 0.82 0.753 0.96 66.6 0.43 1.71 34 0.88 0.594 1.38 106 0.93 3.57 35 0.91 0.677 0.96 49.5 0.32 1.49 36 0.95 0.707 0.93 55.8 0.33 1.57 37 1.04 0.605 0.77 42.2 0.20 1.09 169
38 1.08 0.689 1.26 95.6 0.72 3.49 39 1.35 0.717 0.96 61.1 0.38 2.53 40 1.60 0.686 1.03 74.2 0.48 3.65 41 1.78 0.647 0.81 43.5 0.23 2.14
170
Table A10: Tensile properties of UA1.7x-0 specimen c (mm) Thickness σb (MPa) εb Wb Gapp,b # (mm) (%) (MJ/m3) (KJ/m2) - 0 - 23.9 - 1 0.14 0.589 14.3 492 32.1 11.6 2 0.15 0.658 16.4 508 34.7 13.2 3 0.17 0.543 19.6 464 28.1 12.6 4 0.19 0.673 10.1 455 26.7 13.5 5 0.19 0.701 11.3 448 27.1 13.8 6 0.21 0.631 16.2 475 28.7 15.7 7 0.23 0.679 12.3 470 29.5 17.8 8 0.25 0.574 14.9 500 33.1 21.1 9 0.25 0.617 12.1 471 29.2 19.1 10 0.26 0.598 12.2 479 29.2 19.8 11 0.27 0.635 3.40 312 11.5 9.56 12 0.27 0.681 13.0 435 24.57 17.9 13 0.27 0.659 13.7 460 28.5 20.3 14 0.29 0.662 9.56 3712 18.1 15.1 15 0.29 0.639 8.38 432 23.8 18.7 16 0.30 0.657 13.6 4556 27.0 21.6 17 0.30 0.688 10.5 463 27.8 22.0 18 0.30 0.627 11.5 459 27.4 21.8 19 0.30 0.629 2.54 260 7.77 7.71 20 0.31 0.622 11.0 467 28.4 23.1 21 0.32 0.639 9.82 461 26.9 22.8 22 0.33 0.630 9.09 444 24.8 22.0 23 0.33 0.529 2.72 273 11.2 11.9 24 0.35 0.664 12.28 400 22.4 22.0 25 0.35 0.623 13.3 482 30.1 27.4 26 0.35 0.629 13.3 477 29.7 27.1 27 0.36 0.626 2.96 278 9.14 10.6 28 0.39 0.590 11.4 463 27.8 28.2 29 0.42 0.646 1.95 212 7.10 10.5 30 0.44 0.630 11.3 425 22.8 27.5 31 0.44 0.587 15.2 518 35.6 39.5 32 0.47 0.694 2.55 260 7.98 12.4 33 0.47 0.571 1.61 176 4.63 8.22 34 0.48 0.562 1.97 214 5.31 9.02 35 0.48 0.712 14.7 490 32.0 39.7 36 0.50 0.626 3.26 300 10.6 16.7 37 0.50 0.658 10.5 443 25.3 34.1 171
38 0.53 0.587 1.46 151 3.26 6.83 39 0.56 0.643 1.66 180 4.18 8.78 40 0.57 0.666 9.35 480 28.7 42.6 41 0.61 0.637 1.44 150 3.51 8.51 42 0.61 0.661 2.42 256 7.49 15.2 43 0.62 0.650 2.38 248 7.57 15.8 44 0.62 0.683 3.35 315 11.8 22.5 45 0.63 0.584 1.99 218 6.30 13.9 46 0.63 0.685 1.58 155 4.12 10.2 47 0.72 0.685 1.71 188 4.27 11.3 48 0.75 0.620 3.12 298 10.7 24.9 49 0.85 0.597 1.38 141 3.45 11.8 50 0.87 0.593 1.12 111 1.84 6.94 51 0.91 0.601 1.02 94 1.42 5.84 52 0.94 0.636 2.23 243 7.28 23.2 53 0.96 0.625 1.27 131 2.11 8.39 54 1.02 0.571 1.00 97 1.44 6.59 55 1.09 0.622 1.236 129 3.36 15.2
172
Table A11: Tensile properties of UA1.7x-6 specimen c Thickness σb εb Wb Gapp,b # (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 23.2 - - - 1 0.16 0.651 13.2 502 27.8 11.4 2 0.20 0.654 15.0 457 25.8 13.7 3 0.22 0.678 11.2 436 23.0 13.7 4 0.25 0.690 13.1 450 25.0 16.7 5 0.26 0.630 10.6 405 20.0 14.5 6 0.26 0.676 13.8 458 26.3 18.1 7 0.27 0.673 9.52 411 19.8 14.8 8 0.27 0.644 7.53 370 15.7 12.3 9 0.29 0.627 7.53 367 15.9 13.4 10 0.29 0.670 9.44 398 18.9 15.4 11 0.29 0.644 6.05 352 13.7 11.8 12 0.30 0.676 6.91 363 15.1 13.2 13 0.31 0.687 3.29 241 6.27 6.61 14 0.35 0.665 9.84 454 21.5 20.1 15 0.36 0.571 5.12 309 10.7 11.9 16 0.38 0.713 5.88 372 14.1 15.5 17 0.45 0.635 2.76 206 4.49 7.26 18 0.46 0.657 2.20 1684 4.04 7.13 19 0.48 0.601 2.21 186 4.13 7.37 20 0.50 0.682 2.30 183 4.39 8.20 21 0.51 0.657 2.80 210 4.70 8.54 22 0.52 0.661 2.56 205 4.33 8.09 23 0.53 0.605 2.05 163 3.84 7.89 24 0.53 0.661 2.03 158 3.61 7.48 25 0.54 0.643 2.37 198 5.25 10.3 26 0.57 0.575 1.69 133 3.04 7.12 27 0.57 0.707 2.16 195 4.21 8.79 28 0.57 0.673 1.81 140 2.89 6.68 29 0.63 0.646 1.93 181 3.66 8.65 30 0.64 0.644 2.34 176 4.73 11.4 31 0.67 0.609 1.49 137 1.99 5.44 32 0.69 0.647 2.76 199 4.26 10.7 33 0.71 0.679 1.76 137 3.27 9.47 34 0.76 0.647 2.76 205 4.56 12.5 35 0.85 0.523 1.58 118 2.25 8.15 36 0.86 0.691 1.47 113 1.66 6.13 37 0.87 0.718 2.14 178 4.49 14.7 173
38 0.96 0.599 2.14 181 4.32 15.5 39 1.03 0.575 1.77 142 3.27 13.7 40 1.12 0.649 1.64 125 2.46 11.5 41 1.22 0.604 1.50 134 2.02 10.1 42 1.33 0.653 1.40 119 1.58 8.90 43 1.39 0.671 1.39 106 1.93 11.7 44 2.70 0.713 1.24 110 1.36 15.9 45 2.90 0.659 0.88 66.2 0.748 10.6
174
Table A12: Tensile properties of UA1.7x-10 specimen c Thickness σb εb Wb Gapp,b # (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) 0 - 24.3 - - - 1 0.13 0.654 3.88 237 6.75 3.00 2 0.20 0.592 5.85 308 11.3 7.00 3 0.20 0.573 8.79 351 16.0 9.48 4 0.21 0.643 2.48 167 3.33 2.68 5 0.21 0.684 7.03 328 13.1 8.35 6 0.21 0.634 12.7 409 22.6 13.2 7 0.21 0.669 6.05 308 11.8 7.74 8 0.23 0.631 4.66 266 8.64 6.52 9 0.24 0.679 7.07 334 13.9 10.1 10 0.25 0.645 4.53 251 7.97 6.68 11 0.28 0.639 3.11 212 5.14 5.11 12 0.29 0.599 3.04 202 4.75 4.97 13 0.29 0.632 3.88 239 6.80 6.72 14 0.30 0.671 9.23 366 17.5 15.3 15 0.30 0.675 3.56 222 5.89 6.18 16 0.31 0.621 6.34 310 11.84 11.3 17 0.31 0.653 11.9 402 20.7 18.0 18 0.32 0.598 2.98 195 4.49 5.26 19 0.32 0.581 5.18 281 9.45 9.73 20 0.33 0.621 6.08 310 11.6 11.9 21 0.35 0.640 3.21 207 5.05 6.34 22 0.37 0.659 3.01 208 4.88 6.46 23 0.39 0.682 11.8 401 20.5 22.4 24 0.41 0.596 2.24 161 4.49 7.16 25 0.42 0.705 5.35 291 10.3 13.8 26 0.42 0.695 2.72 187 4.14 6.45 27 0.42 0.571 2.06 159 3.86 6.34 28 0.44 0.619 2.35 164 4.79 8.16 29 0.48 0.676 1.87 137 5.46 10.7 30 0.48 0.593 1.72 117 2.48 5.07 31 0.49 0.641 2.25 165 5.02 9.51 32 0.49 0.640 4.56 264 8.24 13.3 33 0.51 0.646 2.13 146 6.28 12.8 34 0.51 0.595 1.98 142 5.48 11.3 35 0.52 0.591 2.26 164 4.29 8.61 36 0.53 0.651 3.03 201 4.69 8.98 37 0.56 0.611 2.27 156 5.16 11.3 175
38 0.57 0.654 1.97 135 3.46 8.08 39 0.60 0.673 2.11 149 5.00 11.9 40 0.62 0.620 2.04 160 4.44 10.7 41 0.62 0.663 1.58 111 2.59 6.96 42 0.64 0.730 2.33 171 3.33 8.12 43 0.67 0.655 1.68 118 2.47 7.02 44 0.67 0.699 1.99 149 4.34 11.5 45 0.68 0.677 1.93 141 3.87 10.6 46 0.70 0.744 1.45 104 2.12 6.52 47 0.73 0.703 1.77 131 3.71 11.2 48 0.74 0.571 1.21 80.6 2.73 9.44 49 0.74 0.649 2.54 183 3.75 10.4 50 0.76 0.643 1.47 110 2.22 7.30 51 0.78 0.661 2.50 171 3.44 10.2 52 0.81 0.595 1.69 121 2.16 7.39 53 0.88 0.589 1.47 104 1.78 6.90 54 0.95 0.655 1.29 92.0 1.47 6.35 55 1.00 0.661 2.11 145 4.32 17.3 56 1.10 0.665 1.27 85.4 2.98 15.1 57 1.12 0.580 1.43 103 4.17 20.6 58 1.14 0.68 1.52 120 2.82 13.6 59 1.14 0.646 1.32 92.9 1.54 7.95 60 1.16 0.653 1.10 73.1 1.29 7.16 61 1.16 0.659 1.16 75.7 2.26 12.4 62 1.68 0.596 1.35 102 3.30 24.5
176
Table A4: Tensile properties of UA1.7x-15 specimen c Thickness σb εb Wb Gapp,b # (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 24.6 - - - 1 0.11 0.731 4.71 351 11.5 3.75 2 0.12 0.645 7.03 341 13. 1 4.69 3 0.18 0.582 5.50 371 12.4 6.45 4 0.21 0.573 5.14 347 11.6 7.22 5 0.24 0.708 4.43 248 6.92 5.58 6 0.24 0.674 3.77 225 5.50 4.59 7 0.25 0.679 3.60 261 7.02 5.79 8 0.30 0.647 3.08 210 4.68 5.00 9 0.31 0.705 2.67 183 3.71 4.28 10 0.33 0.591 2.84 221 3.26 3.77 11 0.33 0.659 3.87 231 5.86 6.67 12 0.35 0.706 6.09 290 9.63 10.7 13 0.35 0.596 2.88 200 4.17 5.29 14 0.37 0.639 2.02 146 3.42 5.05 15 0.38 0.703 7.57 474 21.2 21.1 16 0.38 0.547 8.21 446 19.2 19.6 17 0.38 0.676 3.53 267 7.27 9.04 18 0.40 0.647 2.71 207 3.99 5.72 19 0.42 0.653 2.99 230 5.03 7.31 20 0.43 0.647 2.93 190 3.89 6.16 21 0.43 0.68 8.70 451 18.9 21.8 22 0.43 0.565 1.79 133 2.20 3.90 23 0.51 0.697 2.33 168 3.01 5.89 24 0.51 0.690 2.07 144 3.07 6.29 25 0.51 0.590 2.45 191 4.24 7.96 26 0.52 0.709 2.87 187 3.80 7.32 27 0.54 0.568 3.07 234 4.99 9.27 28 0.54 0.583 1.87 137 2.14 4.72 29 0.55 0.624 1.89 131 2.56 5.81 30 0.55 0.686 1.91 134 2.93 6.61 31 0.57 0.761 1.98 141 4.31 9.93 32 0.57 0.683 4.33 256 7.03 13.3 33 0.59 0.652 1.88 127 2.39 5.87 34 0.60 0.719 2.47 173 3.14 7.15 35 0.62 0.735 5.80 371 14.5 26.1 36 0.65 0.735 2.06 139 3.49 9.20 37 0.66 0.611 1.82 127 2.83 7.78 177
38 0.67 0.693 2.13 169 3.06 7.86 39 0.69 0.767 6.83 337 13.4 27.7 40 0.70 0.649 1.80 124 2.79 8.23 41 0.72 0.707 4.79 257 7.66 18.3 42 0.72 0.625 2.04 147 3.83 11.0 43 0.73 0.624 1.78 121 1.92 5.94 44 0.73 0.733 1.48 122 1.79 5.49 45 0.75 0.681 6.21 388 14.9 31.7 46 0.8 0.670 1.85 122 1.29 4.35 47 0.81 0.693 2.42 171 3.18 9.83 48 0.82 0.621 6.37 386 13.8 32.3 49 0.85 0.719 1.64 124 2.62 9.33 50 0.87 0.643 1.47 108 0.962 3.66 51 0.87 0.685 1.59 106 1.30 4.96 52 0.87 0.603 2.07 144 3.37 11.8 53 0.90 0.646 1.48 100 1.36 5.44 54 0.91 0.721 4.54 294 9.02 25.9 55 0.92 0.647 5.63 370 13.5 35.9 56 0.92 0.657 1.95 136 1.95 7.34 57 0.95 0.660 1.79 141 2.72 10.4 58 0.96 0.695 1.73 123 2.49 10.0 59 0.98 0.601 1.88 136 2.56 10.2 60 1.00 0.634 2.03 161 3.24 12.6 61 1.00 0.665 1.53 127 1.83 7.64 62 1.07 0.654 1.43 95.7 2.14 10.3 63 1.26 0.673 1.58 112 1.66 9.04 64 1.26 0.697 1.68 116 1.99 10.7 65 1.27 0.713 1.34 85.1 2.13 12.5 66 1.28 0.673 1.66 117 2.17 11.9 67 1.42 0.683 1.24 77.3 1.93 12.9 68 1.43 0.708 1.14 75.8 1.89 12.8 69 1.56 0.674 1.26 78.6 0.962 7.05 70 1.96 0.589 1.20 79.4 2.33 21.4
178
Table A14: Tensile properties of UA1.7x-18 specimen c Thickness σb (MPa) εb Wb Gapp,b # (mm) (mm) (%) (MJ/m3) (KJ/m2) 0 - 24.2 - - - 1 0.18 0.687 6.02 263 8.19 4.86 2 0.22 0.739 3.31 200 4.30 3.43 3 0.22 0.693 6.33 274 8.93 6.39 4 0.26 0.616 5.79 259 7.93 6.83 5 0.27 0.663 4.09 204 4.75 4.62 6 0.29 0.697 3.38 203 4.48 4.68 7 0.29 0.673 3.44 191 4.06 4.33 8 0.29 0.58 10.6 330 13.3 11.6 9 0.30 0.639 4.37 307 9.26 8.64 10 0.3 0.678 4.63 230 5.93 6.14 11 0.31 0.683 5.06 246 7.15 7.48 12 0.32 0.669 5.59 253 7.68 8.21 13 0.32 0.713 7.97 317 12.3 12.1 14 0.33 0.685 5.99 252 7.77 8.57 15 0.34 0.671 3.89 203 4.67 5.73 16 0.35 0.708 9.01 435 18.1 17.3 17 0.38 0.705 4.11 212 5.28 7.13 18 0.38 0.718 11.2 384 17.8 19.4 19 0.40 0.636 4.82 229 6.03 8.35 20 0.42 0.645 3.75 200 4.51 6.86 21 0.43 0.623 4.43 218 5.52 8.36 22 0.45 0.755 3.73 266 7.28 10.7 23 0.45 0.643 3.87 199 4.48 7.33 24 0.48 0.674 2.76 156 2.73 5.15 25 0.52 0.717 3.53 196 4.35 8.26 26 0.53 0.724 6.90 288 9.83 16.6 27 0.55 0.675 3.48 190 3.98 8.07 28 0.55 0.679 3.95 204 4.77 9.45 29 0.58 0.693 3.91 208 4.95 10.3 30 0.58 0.671 4.16 211 4.991 10.3 31 0.61 0.619 3.64 225 5.64 11.9 32 0.62 0.594 2.81 163 3.00 7.19 33 0.64 0.687 3.28 185 3.77 8.99 34 0.65 0.739 3.58 201 4.65 10.9 35 0.65 0.664 2.81 162 2.97 7.47 36 0.66 0.693 2.70 155 2.73 7.09 37 0.66 0.690 3.65 196 4.38 10.6 179
38 0.69 0.663 2.47 144 2.37 6.57 39 0.72 0.687 6.63 274 9.15 21.4 40 0.74 0.727 3.54 200 4.40 11.8 41 0.75 0.690 3.30 180 3.73 10.5 42 0.76 0.584 2.50 148 2.91 8.82 43 0.77 0.695 5.67 251 7.49 19.3 44 0.85 0.687 2.34 142 2.16 7.41 45 0.85 0.691 2.16 127 2.43 8.60 46 0.86 0.684 2.15 133 2.74 9.69 47 0.92 0.673 5.29 255 7.37 22.6 48 0.97 0.669 2.35 135 2.04 8.10 49 0.98 0.644 4.34 215 5.25 18.2 50 1.05 0.651 1.62 95.5 1.68 7.91 51 1.06 0.641 1.88 115 2.15 9.74 52 1.10 0.720 4.66 243 6.58 24.6 53 1.13 0.646 3.67 189 4.10 17.1 54 1.25 0.638 1.56 93.4 1.28 7.25 55 1.30 0.688 1.58 105 1.32 7.51 56 1.35 0.683 1.47 83.1 1.21 7.56 57 1.43 0.656 1.37 87.5 1.12 7.34 58 1.63 0.683 1.35 82.2 1.02 7.77 59 1.80 0.601 1.36 80.2 1.10 9.25 60 1.85 0.605 1.05 60.5 1.28 11.7 61 2.00 0.603 1.29 74.0 0.825 7.85 62 2.03 0.617 0.848 43.8 0.236 2.51 63 2.36 0.700 1.07 62.3 1.30 15.1 64 2.49 0.680 1.61 100 1.41 15.6
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Table A15: Tensile properties of UA1.7x-20 specimen c Thickness σb εb Wb Gapp,b # (mm) (mm) (MPa) (%) (MJ/m3) (KJ/m2) - 0 - 23.5 - 1 0.15 0.653 12.2 353 14.9 6.58 2 0.15 0.657 12.2 359 15.2 6.69 3 0.18 0.629 10.9 324 12.2 6.71 4 0.21 0.675 11.1 335 13.3 8.46 5 0.21 0.667 11.6 345 14.2 8.91 6 0.23 0.687 10.2 329 13.0 9.03 7 0.23 0.693 11.1 338 13.6 9.41 8 0.25 0.689 7.44 275 8.72 7.06 9 0.25 0.647 11.9 304 14.9 11.6 10 0.26 0.651 11.7 346 14.2 11.0 11 0.26 0.655 10.7 329 12.7 9.98 12 0.29 0.699 7.66 280 13.7 12.8 13 0.29 0.666 11.1 337 9.13 7.95 14 0.30 0.616 9.36 318 11.7 10.8 15 0.31 0.665 7.26 270 8.15 8.24 16 0.33 0.649 12.0 360 15.3 14.7 17 0.33 0.682 9.09 309 11.3 11.5 18 0.33 0.637 15.2 386 17.9 16.8 19 0.34 0.631 12.3 356 14.8 14.8 20 0.36 0.693 9.54 314 11.5 12.8 21 0.36 0.709 8.81 305 10.8 12.1 22 0.37 0.601 11.1 340 13.3 14.7 23 0.37 0.673 9.52 315 11.6 13.2 24 0.40 0.689 9.37 317 11.8 14.6 25 0.41 0.679 12.1 353 14.8 17.9 26 0.44 0.667 7.23 269 8.32 11.9 27 0.44 0.625 8.45 298 10.2 14.1 28 0.47 0.627 11.7 407 16.4 21.5 29 0.47 0.633 9.71 322 12.0 17.3 30 0.48 0.635 5.80 234 5.99 9.87 31 0.50 0.725 7.35 284 9.27 14.8 32 0.54 0.59 5.41 229 5.67 10.6 33 0.61 0.667 2.28 117 1.91 4.96 34 0.65 0.681 8.93 317 11.9 23.7 35 0.66 0.605 3.56 168 2.99 7.57 36 0.68 0.608 8.06 284 9.13 19.9 37 0.72 0.68 4.51 202 9.04 23.5 181
38 0.75 0.653 3.62 172 3.18 9.08 39 0.77 0.654 4.61 207 4.58 12.6 40 0.81 0.656 3.46 165 2.86 8.94 41 0.82 0.719 3.10 159 2.76 8.81 42 0.83 0.655 6.60 253 7.12 19.7 43 0.84 0.659 3.77 167 3.04 9.82 44 0.89 0.679 4.16 188 3.86 12.7 45 0.95 0.651 6.48 263 7.71 24.1 46 1.00 0.569 4.45 202 4.38 15.8 47 1.35 0.594 3.40 167 2.90 15.02 48 1.37 0.695 3.93 190 3.89 19.6 49 1.40 0.652 3.16 158 2.60 14.2 50 1.70 0.675 2.54 136 1.91 13.2 51 1.95 0.568 2.00 102 1.32 11.3 52 2.03 0.553 1.77 92.1 1.03 9.52 53 2.08 0.596 1.49 78.5 0.581 5.68 54 2.20 0.717 2.12 117 2.22 20.8
182