Low Strain Dynamic Properties of Filled Rubbers

1971 ◽  
Vol 44 (2) ◽  
pp. 440-478 ◽  
Author(s):  
A. R. Payne ◽  
R. E. Whittaker
Keyword(s):  
Carbon Black ◽  
Dynamic Properties ◽  
Fatigue Behavior ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Solid Particles ◽  
Spherical Particles ◽  
Filled Rubber ◽  
Secondary Network ◽  
Filled Rubbers

Abstract Carbon black does not exist as single spherical particles but forms itself into a rodlike primary structure. These rodlike structures then form into an aggregated secondary network. This secondary network is believed to be held together by Van der Waals-London attraction forces. The decrease in shear modulus of filled rubber vulcanizates with strain is due almost certainly to these secondary forces. Special mixing techniques such as attrition of the carbon black, increased time of mixing, or the addition of chemical promoters which aim at dispersing the carbon black within the mix better are shown to decrease the value of G′0−G′∞. The absence of any modulus change with strain for unfilled vulcanizates and secondly the little change observed in values of G′0−G′∞ with increasing vulcanization of the rubber when containing the same amount of carbon black confirms that the decrease in modulus with strain amplitude is in no way associated with the gum phase of the filled vulcanizate. The similarity in behavior of carbon black filled rubbers with clay/water and clay/rubber systems indicates that the decrease in modulus with amplitude is due to the breakdown of the three dimensional filler aggregates. A number of rheological studies on clay systems has confirmed that clay particles form into rigid three dimensional structures when dispersed in a medium. Evidence for the aggregated filler structure to be held together by Van der Waals-London attraction forces comes from the reasonable agreement between the experimental values for the forces required to breakdown the carbon black aggregates in paraffin oil and the forces calculated from Van den Tempel's model for flocculated solid particles in a liquid. The successful application of a domain model to the hysteretical behavior exhibited by carbon black filled vulcanizates at low strains indicates that the carbon black structure breaks down under stress but reforms to the original state when the stress is removed. This conclusion is also supported by the similarity in behavior between filled rubbers and a dendritic crystal structure of PBNA in rubber. Under the optical microscope the PBNA is seen to break down and reform under a stress-strain cycle. The breakdown and reformation of this secondary aggregated carbon black structure increases the hysteresis in filled rubber vulcanizates. Other sources of hysteresis include viscoelasticity of the polymer, crystallization, stress-softening, and changes in network structure (e.g., breakage of weak crosslinks). These mechanisms have been discussed in depth in previous publications. Recent work has shown, however, that the strength of a rubber is dependent on the combined effect of the different hysteretical mechanisms. The breakdown and reformation of the carbon black structure at low strains in filler reinforced rubbers therefore not only affects the heat build up, transmissibility, and fatigue behavior but also influences the failure properties of the filled vulcanizate.

Non-Spheric Colloidal Suspensions in Three-Dimensional Space

1997 ◽  
Vol 08 (04) ◽  
pp. 985-997 ◽  
Author(s):  
Dewei Qi
Keyword(s):  
Reynolds Number ◽  
Dimensional Space ◽  
Low Reynolds Number ◽  
Paper Industry ◽  
Three Dimensional ◽  
Colloidal Suspensions ◽  
Solid Particles ◽  
Spherical Particles ◽  
Dynamic Simulations ◽  
Low Reynolds

The translation and rotation of non-spherical particles, such as ellipsoidal, cylindric or disk-like pigment particles, in a Couette flow system similar to a blade coating system in the paper industry6 have been successfully simulated by using the lattice-Boltzmann method combined with Newtonian dynamic simulations. Hydrodynamic forces and torques are obtained by the use of boundary conditions which match the moving surface of solid particles. Then Euler equations have been integrated to include three-dimensional rotations of the suspensions by using four quaternion parameters as generalized coordinates. The three-dimensional rotations have been clearly observed. Consequently, the motion of the particles suspended in fluids of both low-Reynolds-number and finite-Reynolds-number, up to several hundreds, has been studied. It appears that the 3D translation and rotation of the non-spherical particles are more clearly observed in a high-Reynolds-number fluid than in a low-Reynolds-number fluid.

MODIFIED GUTH–GOLD EQUATION FOR CARBON BLACK–FILLED RUBBERS

2013 ◽  
Vol 86 (2) ◽  
pp. 218-232 ◽  
Author(s):  
Y. Fukahori ◽  
A. A. Hon ◽  
V. Jha ◽  
J. J. C. Busfield
Keyword(s):  
Carbon Black ◽  
Volume Fraction ◽  
Solid Particles ◽  
Carbon Particles ◽  
Filler Volume Fraction ◽  
Rigid Filler ◽  
Bound Rubber ◽  
Small Volume Fraction ◽  
Filled Rubbers ◽  
Good Agreement

ABSTRACT The modulus increase in rubbers filled with solid particles is investigated in detail here using an approach known widely as the Guth–Gold equation. The Guth–Gold equation for the modulus increase at small strains was reexamined using six different species of carbon black (Printex, super abrasion furnace, intermediate SAF, high abrasion furnace, fine thermal, and medium thermal carbon blacks) together with model experiments using steel rods and carbon nanotubes. The Guth–Gold equation is only applicable to such systems where the mutual interaction between particles is very weak and thus they behave independently of each other. In real carbon black–filled rubbers, however, carbon particles or aggregates are connected to each other to form network structures, which can even conduct electricity when the filler volume fraction exceeds the percolation threshold. In the real systems, the modulus increase due to the rigid filler deviates from the Guth–Gold equation even at a small volume fraction of the filler of 0.05–0.1, the deviation being significantly greater at higher volume fractions. The authors propose a modified Guth–Gold equation for carbon black–filled rubbers by adding a third power of the volume fraction of the blacks to the equation, which shows a good agreement with the experimental modulus increase (G/G0) for six species of carbon black–filled rubbers, where G and G0 are the modulus of the filled and unfilled rubbers, respectively; ϕeff is the effective volume fraction; and S is the Brunauer, Emmett, Teller surface area of the blacks. The modified Guth–Gold equation indicates that the specific surface volume ()3 closely relates to the bound rubber surrounding the carbon particles, and therefore this governs the reinforcing structures and the level of the reinforcement in carbon black–filled rubbers.

COMPARISON OF STRESS–SOFTENINGS IN CARBON-BLACK FILLED NATURAL RUBBER AND STYRENE–BUTADIENE RUBBER

2013 ◽  
Vol 86 (4) ◽  
pp. 572-578 ◽  
Author(s):  
Julie Diani ◽  
Yannick Merckel ◽  
Mathias Brieu ◽  
Julien Caillard
Keyword(s):  
Carbon Black ◽  
Natural Rubber ◽  
Cyclic Softening ◽  
Styrene Butadiene Rubber ◽  
Amplitude Dependence ◽  
Butadiene Rubber ◽  
Fatigue Lifetime ◽  
Filled Rubber ◽  
Filled Rubbers ◽  
Styrene Butadiene

ABSTRACT The authors compared the mechanical behavior and, more precisely, the Mullins and the cyclic (post-Mullins) softenings of two filled rubbers. A crystallizing natural rubber and a noncrystallizing styrene–butadiene rubber of similar compositions resulting in similar cross-link densities and filled with 40 phr of N347 carbon-black fillers were tested in cyclic uniaxial tension at room temperature and at 85 °C. Crystallization in filled rubbers is known to increase stress at high stretch, stretch at break, cycle hysteresis, and fatigue lifetime and to reduce crack propagation. In this study, it is shown that crystallization also seems to enhance the Mullins softening (softening at the first cycle) and to favor the apparent cyclic softening. Results reveal that natural rubber shows an amplitude dependence on the cyclic softening, whereas the styrene–butadiene rubber does not. Finally, results demonstrate that studying filled rubber softening cannot help predict lifetime.

Mechanism of the Modulus Increase of Carbon-Black-Filled Rubber at Small Extension

2011 ◽  
Vol 284-286 ◽  
pp. 1969-1973
Author(s):  
Xiao Ling Hu ◽  
Yong Ouyang ◽  
Xiong Zhou ◽  
Wen Bo Luo
Keyword(s):  
Carbon Black ◽  
Tensile Stress ◽  
Volume Fraction ◽  
Tensile Modulus ◽  
Homogenization Method ◽  
Stress Strain ◽  
Filled Rubber ◽  
Strain Relationship ◽  
Filled Rubbers ◽  
Relationship Of

The tensile stress-strain relationship of rubbers is fairly linear and can be used for obtaining tensile modulusE. In this work we analyzed the tensile stress-strain relationship of filled rubber experimentally and employed the extended 2D homogenization method to compute the modulus of the carbon black (CB) filled rubbers with various CB volume fractions ranging from 5% to 25%. The results reveal that the modulus of CB-filled rubbers increased with the increase in CB volume fraction and in CB aggregation.

Distribution of Carbon Black in SBR

1978 ◽  
Vol 51 (2) ◽  
pp. 278-284 ◽  
Author(s):  
Ryo Oono
Keyword(s):  
Carbon Black ◽  
Physical Properties ◽  
Abrupt Change ◽  
Interparticle Distance ◽  
Average Diameter ◽  
Spherical Particles ◽  
Maximum Diameter ◽  
Electron Micrograph ◽  
Fraunhofer Diffraction ◽  
Filled Rubber

Abstract The interparticle distance between black aggregates in rubber was estimated by Fraunhofer diffraction with the mask of an electron micrograph of filled rubber. Up to 40 phr, the distribution of interpartiele distance has a sharp peak centered at 8000 A˚ with 20 phr and at 7000 A˚ with 40 phr. Above 60 phr, the interparticle distance distributes broadly in the vicinity of 4000 A˚. The size of black aggregates at 20 phr extends from 300 A˚ (one particle) to 3000 A˚, and the average diameter is 1200 A˚. Above 40 phr, black trends to aggregate more than at 20 phr, and the average diameter is about 1500–1600 A˚, the maximum diameter being 5000 A˚. In one black aggregate, there are about 40 spherical particles. The relation between the size and interparticle distance shows that isolated black aggregates are distributed in rubber under 40 phr and that at 40 phr they begin to connect partly with each other. Above 60 phr, a network of chains of black develops everywhere. The contact of black aggregates at 40 phr level corresponds to the abrupt change of physical properties of filled rubber.

Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates

1990 ◽  
Vol 63 (5) ◽  
pp. 792-805 ◽  
Author(s):  
O. H. Yeoh
Keyword(s):  
Carbon Black ◽  
Shear Modulus ◽  
Elastic Properties ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Stress Strain ◽  
Filled Rubber ◽  
Filled Rubbers

Abstract A novel strain-energy function which is a simple cubic equation in the invariant (I1−3) is proposed for the characterization of the elastic properties of carbon-black-filled rubber vulcanizates. Conceptually, the proposed function is a material model with a shear modulus which varies with deformation. This contrasts with the neo-Hookean and Mooney-Rivlin models which have a constant shear modulus. The variation of shear modulus with deformation is commonly observed with filled rubbers. Initially, the modulus falls with increasing deformation, leading to a flattening of the shear stress/strain curve. At large deformations, the modulus rises again due to finite extensibility of the network, accentuated by the strain amplication effect of the filler. This characteristic behavior of filled rubbers may be described approximately by the proposed strain-energy function by requiring the coefficient C20 to be negative, while the coefficients C10 and C30 are positive. The use of the proposed strain-energy function has been shown to permit the prediction of stress/strain behavior in different deformation modes from data obtained in one simple deformation mode. This circumvents the need for a rather difficult experiment in general biaxial extension. The simple form of the proposed function also simplifies the regression analysis. This strain-energy function is consistent with the general Rivlin strain-energy function and is easily obtained from the popular third-order deformation approximation. Thus, it is already available in many existing finite-element analysis programs.

Strain-Dependent Dynamic Properties of Carbon-Black Reinforced Vulcanizates. II. Elastomer Blends

1975 ◽  
Vol 48 (1) ◽  
pp. 89-96 ◽  
Author(s):  
A. K. Sircar ◽  
T. G. Lamond
Keyword(s):  
Carbon Black ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Individual Characteristics ◽  
The Individual ◽  
Dispersing Medium ◽  
Polymeric Medium ◽  
Strain Dependent ◽  
Filler Structure ◽  
Predominant Effect

Abstract The three-dimensional aggregated structure of carbon black in elastomer blends behaves in a similar fashion to that of the individual elastomers. The elastomer seems to act merely as a dispersing medium. The properties of the rubber reflect the structural effects of the filler superimposed upon the elastomer itself. The elastomer molecules no doubt retain their individual characteristics of rotation of bonds which govern the stiffness of the molecule. However, the superimposed carbon-black network exerts the predominant effect, as far as the low-strain dynamic characteristics are concerned. The polymeric medium seems to influence this interaction by determining the magnitude of agglomeration and distribution of black in the phases, but does not have visible influence on the overall characteristics of the carbon-black networks. In this respect blends of two elastomers behave as a single elastomer. The importance of the present work is that the strain-dependent dynamic properties of blends of elastomers are very similar to those of single elastomers. In tires and antivibration applications, the strain imposed is usually less than 10%. More and more blends of elastomers are being used for these applications. The filler structure and its breakdown at these strains have an important contribution to hardness, modulus, and hysteresis of these compounds.

Interaggregate Interaction in Filled Rubber

1990 ◽  
Vol 63 (4) ◽  
pp. 554-566 ◽  
Author(s):  
C. M. Roland ◽  
G. F. Lee
Keyword(s):  
Carbon Black ◽  
Dynamic Properties ◽  
Loss Modulus ◽  
Complete Recovery ◽  
Small Strain ◽  
Dynamic Mechanical Properties ◽  
Constrained Layer Damping ◽  
High Concentration ◽  
Dynamic Mechanical ◽  
Filled Rubber

Abstract Measurements of the dynamic properties of carbon-black-filled rubber can be carried out on most instrumentation at strains within the limits of linear behavior; thus, assessments of acoustic performance can readily be made. The equivalence of small-strain dynamic-mechanical testing and acoustic measurements has been demonstrated herein. Blends of NR with a high concentration of 1,2-BR are attractive candidates for damping applications because of the extended frequency range of the glass to rubber transition. One approach to improving the magnitude of the damping is to incorporate high levels of carbon black into the material. Significant interaggregate interaction, promoted for example by a low degree of carbon-black dispersion, will amplify the energy dissipation. The strain dependence of the dynamic properties implicit in such an approach can result in a damping performance sensitive to deformation. The loss tangent rises significantly after such a deformation, while the loss modulus experiences a barely measurable decline. This sensitivity to deformation will thus impact more on constrained layer damping applications than on simple extensional damping. For the materials tested in the present study, complete recovery of the damage to the carbon-black network (which engenders the changes in dynamic mechanical properties) required more than a day at room temperature.

Filler-Elastomer Interactions. Part VIII. The Role of the Distance between Filler Aggregates in the Dynamic Properties of Filled Vulcanizates

1993 ◽  
Vol 66 (2) ◽  
pp. 178-195 ◽  
Author(s):  
Meng-Jiao Wang ◽  
Siegfried Wolff ◽  
Ewe-Hong Tan
Keyword(s):  
Gas Chromatography ◽  
Carbon Black ◽  
Inverse Gas Chromatography ◽  
Dynamic Properties ◽  
Random Packing ◽  
Attractive Potential ◽  
Carbon Blacks ◽  
Filled Rubber ◽  
Tan Δ

Abstract Based on the concepts of the occlusion of rubber and random packing of spheres whose volume is equivalent to that permeated by individual aggregates, an equation was deduced to estimate the distance between carbon-black aggregates in filled rubber. It was found that when the interaggregate distance reaches a critical point which is approximately identical for all carbon blacks investigated (furnace blacks), the elastic modulus measured at very low strain deviates from the modified Guth-Gold equation. Tan δ and resilience are mainly determined by the distance between aggregates. These phenomena are related to filler networking which is determined by the attractive potential and the distance between individual aggregates. Since the factor Sf, used to characterize the strength of secondary filler networks in hydrocarbon rubbers and measured by means of inverse gas chromatography, is approximately the same for all furnace blacks, the interaggregate distance seems to determine filler networking. A comparison of fillers with different Sf (graphitized vs. nongraphitized carbon blacks, carbon black vs. silica) shows that at the same interaggregate distance, a lower Sf leads to higher tan δ of the filled vulcanizates.

Sign in / Sign up

Export Citation Format

Share Document