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.

scholarly journals CHARACTERIZATION OF THE MULLINS EFFECT OF CARBON-BLACK FILLED RUBBERS

2011 ◽  
Vol 84 (3) ◽  
pp. 402-414 ◽  
Author(s):  
Yannick Merckel ◽  
Julie Diani ◽  
Mathias Brieu ◽  
Pierre Gilormini ◽  
Julien Caillard
Keyword(s):  
Carbon Black ◽  
Crosslink Density ◽  
Volume Fraction ◽  
Damage Parameter ◽  
Hencky Strain ◽  
Filler Volume Fraction ◽  
Filled Rubbers ◽  
Styrene Butadiene ◽  
Linear Expression

Abstract Several carbon-black filled styrene-butadiene rubbers showed different sensibilities to the Mullins softening when submitted to cyclic uniaxial tension. In order to quantify this softening, a damage parameter was introduced. It is defined by using a classic damage approach and can be estimated by using either the strain amplification factor method or the tangent modulus at zero stress. The proposed parameter is used to study the effects of crosslink density and filler amount on the Mullins softening. The latter is shown to remain unaffected by a change of crosslink density and to increase with an increase of filler amount. The damage parameter exhibits mere linear dependences on the maximum Hencky strain applied and on the filler volume fraction. A simple linear expression is given finally to predict the Mullins softening of filled rubbers. The parameter also provides an objective analysis for the Mullins softening that supports comments on a better understanding of this effect.

The Steady State Rheological Behavior of Semisolid AlSi6Mg2 Alloy

2011 ◽  
Vol 339 ◽  
pp. 257-260 ◽  
Author(s):  
Hong Chao Luo ◽  
Shi Pu Chen ◽  
Qin Nie ◽  
En Sheng Xu ◽  
Li Ping Ju
Keyword(s):  
Steady State ◽  
Shear Rate ◽  
Rheological Behavior ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Solid Particles ◽  
Experimental Results ◽  
Present System ◽  
Flow Conditions ◽  
Good Agreement

In the present work, basing on the rheological model of Chen and Fan (CF) [1] of semisolid metal slurries (SSMS), the rheological behavior at steady state of AlSi6Mg2 alloy is investigated. Experimental results on steady state viscosity of the present system in the literature are used to determine the parameters of the CF model by fitting. It has been shown that the steady state viscosity and the average agglomerate size increase with increasing the solid volume fraction and decreasing the shear rate. The theoretical prediction of the CF model is in good agreement with the experimental results in the literatures quantitatively. The importance of the effective solid volume fraction is shown by explaining the strong coupling between the viscosity and the microstructure. Specifically, the external flow conditions such as shear rate influences the viscosity by changing the agglomeration degree of the solid particles, that is, the effective solid volume fraction and then changing the viscosity.

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.

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.

Mixing of Carbon Black with Rubber I. Measurement of Dispersion Rate by Changes in Mixing Torque

1984 ◽  
Vol 57 (1) ◽  
pp. 118-133 ◽  
Author(s):  
George R. Cotten
Keyword(s):  
Carbon Black ◽  
Volume Fraction ◽  
Small Samples ◽  
Butadiene Rubber ◽  
Mixing Process ◽  
Carbon Blacks ◽  
Bound Rubber ◽  
Power Peak ◽  
Dispersive Mixing ◽  
Carbon Black Dispersion

Abstract Analysis of the torque data obtained for a large range of carbon blacks in an oil-extended butadiene rubber (CB-441) shows that the rate of decrease of torque (after the second power peak) follows first order kinetics. The rate of decrease represents the rate of reduction in effective filled volume fraction through dispersion of carbon black agglomerates, and thus, a reduction in the volume of rubber occluded between individual aggregates within the agglomerates. The assumption that the rate of torque reduction is proportional to the rate of carbon black dispersion was tested by examining the responses to various factors influencing the mixing process. In general, the conclusions reached from the analysis of torque data were in agreement with the common industrial experience and predictions based on the mathematical analysis of dispersive mixing. Tadmor's analysis of dispersive mixing predicts that the rate of agglomerate rupture depends on the number of particle-particle contacts and thus is related to the size of individual aggregates, but is independent of agglomerate size. Thus, it is in agreement with the present findings that the rate of dispersive mixing increases with decreasing surface area and increasing structure of aggregates. Increasing polymer-filler interaction gives rise to a faster rate of dispersive mixing, possibly by increasing the effective radii of aggregates through bound rubber formation. Increasing the batch temperature increases the rate of dispersive mixing due to reduced cohesion between the aggregates and a more favorable balance between cohesive and shearing forces. Increasing carbon black loading increases the rate of dispersive mixing by increasing the viscosity and, thus, shearing forces generated during the mixing process. The technique developed in this work may provide a better means for measuring dispersibility of carbon blacks, since other available methods suffer certain disadvantages. For instance, the resistivity measurements are not only dependent on carbon black dispersion, but also on the chemical nature of its surface, while microscopic methods depend on the examination of very small samples that may not be representative of the whole batch.

scholarly journals Study on Microstructure Effect of Carbon Black Particles in Filled Rubber Composites

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Li Hong Huang ◽  
Xiaoxiang Yang ◽  
Jianhong Gao
Keyword(s):  
Particle Size ◽  
Carbon Black ◽  
Polymer Nanocomposites ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Uniaxial Tensile ◽  
Particle Volume ◽  
Carbon Particles ◽  
The Difference ◽  
Microstructure Effect

The cross sections of blended natural/styrene-butadiene (NSBR) composites filled with different volume fractions of carbon particles were observed using a Quanta 250 scanning electron microscope. In addition, the sizes and distributions of the carbon particles were analyzed using Nano Measurer. A two-dimensional representative volume element model (RVE) for a rubber composite reinforced with circular carbon particles was established, and the uniaxial tensile behaviors of polymer nanocomposites with different particle size distribution patterns were simulated using the ABAQUS software. The results showed the following. (1) For the random models, if the difference of particle size was larger and particle distance was closer, stress distribution would be denser as well as the stress concentration would become greater. However, if the difference of particle size was small, for the case of same particle volume fraction, the particle size has little influence on the macromechanical properties whether the average size is large or small. (2) The correlation between the volume fraction and distribution of the carbon particles revealed that when the volume fraction of carbon black particles was larger than 12%, clusters between carbon particles in the polymer nanocomposites could not be avoided and the modulus of the composites increased with an increase in the cluster number.

Structure and Strength of Silica-PDMS Nanocomposites

2011 ◽  
Vol 1312 ◽  
Author(s):  
Adrian Camenzind ◽  
Thomas Schweizer ◽  
Michael Sztucki ◽  
Sotiris E. Pratsinis
Keyword(s):  
Primary Particle ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Tensile Tests ◽  
Thin Sections ◽  
Filler Volume Fraction ◽  
X Ray Scattering ◽  
Bonded Particles ◽  
Bound Rubber ◽  
Particle Aggregate

ABSTRACTCommercially available SiO2 nanoparticles (Aerosil, Degussa) with varying primary particle diameter, specific surface area (SSA), degree of aggregation and structure (fractal dimension) were compounded into PDMS-based nanocomposites. Thin sections of cured nanocomposites were analyzed with TEM and small and ultra-small angle X-ray scattering (U/SAXS) with respect to nanocomposite structure such as: filler primary particle, aggregate (chemically or sinter-bonded particles) and agglomerate (physically-bonded particles). Tensile tests (Young’s modulus) were used to determine the nanocomposite strength which increased with increasing filler volume fraction (up to 12 vol%) consistent with “bound rubber” theory.

A Steady State Model for the Rheological Behavior of Semisolid Al-6.5wt%Si Alloy

2011 ◽  
Vol 228-229 ◽  
pp. 858-863
Author(s):  
Li Ping Ju ◽  
Hong Chao Luo ◽  
Wei Wang ◽  
Dan Xu
Keyword(s):  
Steady State ◽  
Shear Rate ◽  
Rheological Behavior ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Solid Particles ◽  
State Behavior ◽  
Packing Parameter ◽  
Steady State Model ◽  
Good Agreement

In the present work, The Chen and Fan (CF) model [1] of semisolid metal slurries (SSMS) is improved by modifying the expression of the packing parameter, of the solid particles and then the modified CF (MCF) model is obtained. Subsequently, the MCF model is applied to the Al-6.5wt%Si alloy to investigate its rheological behavior at steady state. The factors which affect the steady state behavior have been studied. It has been shown that the steady state viscosity and the average agglomerate size increase with increasing the solid volume fraction and decreasing the shear rate. The prediction of the model is in good agreement with the experimental results in the literatures qualitatively. The importance of the effective solid volume fraction is shown by explaining the strong coupling between the viscosity and the microstructure. The external flow conditions such as shear rate etc change the agglomeration degree, that is, the effective solid volume fraction and then the viscosity

scholarly journals Heat Treatment Evaluation for the Camshafts Production of ADI Low Alloyed with Vanadium

Metals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1036
Author(s):  
Eduardo Colin García ◽  
Alejandro Cruz Ramírez ◽  
Guillermo Reyes Castellanos ◽  
José Federico Chávez Alcalá ◽  
Jaime Téllez Ramírez ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Heat Treatment ◽  
Tensile Strength ◽  
Ductile Iron ◽  
Volume Fraction ◽  
Energy Impact ◽  
Treatment Conditions ◽  
Mold Casting ◽  
Grade 3 ◽  
Good Agreement

Ductile iron camshafts low alloyed with 0.2 and 0.3 wt % vanadium were produced by one of the largest manufacturers of the ductile iron camshafts in México “ARBOMEX S.A de C.V” by a phenolic urethane no-bake sand mold casting method. During functioning, camshafts are subject to bending and torsional stresses, and the lobe surfaces are highly loaded. Thus, high toughness and wear resistance are essential for this component. In this work, two austempering ductile iron heat treatments were evaluated to increase the mechanical properties of tensile strength, hardness, and toughness of the ductile iron camshaft low alloyed with vanadium. The austempering process was held at 265 and 305 °C and austempering times of 30, 60, 90, and 120 min. The volume fraction of high-carbon austenite was determined for the heat treatment conditions by XRD measurements. The ausferritic matrix was determined in 90 min for both austempering temperatures, having a good agreement with the microstructural and hardness evolution as the austempering time increased. The mechanical properties of tensile strength, hardness, and toughness were evaluated from samples obtained from the camshaft and the standard Keel block. The highest mechanical properties were obtained for the austempering heat treatment of 265 °C for 90 min for the ADI containing 0.3 wt % V. The tensile and yield strength were 1200 and 1051 MPa, respectively, while the hardness and the energy impact values were of 47 HRC and 26 J; these values are in the range expected for an ADI grade 3.

scholarly journals Modelling the Molecular Permeation through Mixed-Matrix Membranes Incorporating Tubular Fillers

Membranes ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 58
Author(s):  
Ali Zamani ◽  
F. Handan Tezel ◽  
Jules Thibault
Keyword(s):  
Aspect Ratio ◽  
Relative Permeability ◽  
Polymer Matrix ◽  
Volume Fraction ◽  
Mixed Matrix Membranes ◽  
Analytical Prediction ◽  
Mixed Matrix ◽  
Permeability Ratio ◽  
Filler Volume Fraction ◽  
Matrix Membranes

Membrane-based processes are considered a promising separation method for many chemical and environmental applications such as pervaporation and gas separation. Numerous polymeric membranes have been used for these processes due to their good transport properties, ease of fabrication, and relatively low fabrication cost per unit membrane area. However, these types of membranes are suffering from the trade-off between permeability and selectivity. Mixed-matrix membranes, comprising a filler phase embedded into a polymer matrix, have emerged in an attempt to partly overcome some of the limitations of conventional polymer and inorganic membranes. Among them, membranes incorporating tubular fillers are new nanomaterials having the potential to transcend Robeson’s upper bound. Aligning nanotubes in the host polymer matrix in the permeation direction could lead to a significant improvement in membrane permeability. However, although much effort has been devoted to experimentally evaluating nanotube mixed-matrix membranes, their modelling is mostly based on early theories for mass transport in composite membranes. In this study, the effective permeability of mixed-matrix membranes with tubular fillers was estimated from the steady-state concentration profile within the membrane, calculated by solving the Fick diffusion equation numerically. Using this approach, the effects of various structural parameters, including the tubular filler volume fraction, orientation, length-to-diameter aspect ratio, and permeability ratio were assessed. Enhanced relative permeability was obtained with vertically aligned nanotubes. The relative permeability increased with the filler-polymer permeability ratio, filler volume fraction, and the length-to-diameter aspect ratio. For water-butanol separation, mixed-matrix membranes using polydimethylsiloxane with nanotubes did not lead to performance enhancement in terms of permeability and selectivity. The results were then compared with analytical prediction models such as the Maxwell, Hamilton-Crosser and Kang-Jones-Nair (KJN) models. Overall, this work presents a useful tool for understanding and designing mixed-matrix membranes with tubular fillers.

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