Modelling the catalyst fragmentation pattern in relation to molecular properties and particle overheating in olefin polymerization

A two-dimensional single particle finite element model was used to examine the effects of particle fragmental pattern on the average molecular weights, polymerization rate and particle overheating in heterogeneous Ziegler-Natta olefin polymerization. A two-site catalyst kinetic mechanism was employed together with a dynamic two-dimensional molecular species in diffusion-reaction equation. The initial catalyst active sites distribution was assumed to be uniform, while the monomer diffusion coefficient was considered to be different inside the fragments and cracks. In other words, the cracks were distinguished from fragments with higher monomer diffusion coefficient. To model the particle temperature a lumped heat transfer model was used. The fragmentation pattern was considered to remain unchanged during the polymerization. A Galerkin finite element method was used to solve the resulting two-dimensional (2-D) moving boundary value, diffusion-reaction problem. A two-dimensional polymeric flow model (PFM) was implemented on the finite element meshes. The simulation results showed that the fragmentation pattern had effects on the molecular properties, reaction rate and the particle temperature at early stages of polymerization

Simulating Mechanical Behavior of a Tread Rubber Compound by a Hyperelastic/Hysteresis Model

This research work is devoted to experimental and theoretical evaluations of a hybrid constitutive model which was designed to simulate the mechanical behavior of a tread rubber compound. The model is a combination of Yeoh hyperelastic model with a strain-rate hysteresis model developed by Bergstrom and Boyce. The parameters of the Yeoh model were calibrated from experimental data of the ASTM D-412 stress-strain test. Three rubber strip specimens with 11 cm length and 1, 2 and 3 cm widths were selected and simulated under tension using ABAQUS/Standard code. Comparison of the results with those obtained by experiments on the samples revealed that ignoring the viscoelasticity led to a signifcant error in prediction of the force-elongation behavior. Consequently, the simulations were repeated by using a hybrid model and the results showed that there were very good agreement between the experimental and simulated results. The model is also capable of calculating the dissipated energy which can be used for the prediction of temperature rise in rubber articles with dynamic loading

Steady State Analysis and Prediction of Rolling Resistance for a Moving Radial Tire Using Hyper-Viscoelastic Model

A 185/65R15 steel belted radial tire was analyzed for the prediction of its rolling resistance using finite element method. The Abaqus code was used for this purpose. A two-dimensional axisymmetric model was first designed to form the tire layout in the mold. After analyzing for rim mounting, an internal pressure was applied to the tire. Having rotated the tire cross-section about rolling axis, a three-dimensional model was then created and used for the analyses under static vertical load and steady state rolling conditions. Owing to the use of arbitrary Lagrangian/Eulerian framework, a constant linear velocity was assumed and the analysis was performed for a range of angular velocity of the tire. An in-house developed user subroutine was employed and linked to the Abaqus for the accurate determination of the free rolling rotational speed (angular velocity) of the tire based on zero force/torque. Two sets of analyses were performed. In the first set, it was assumed that the mechanical behaviors of the rubbery parts could be described by the well-known Ogden hyperelastic model. In the second set, hyper-viscoelastic behaviors were assumed in which the Ogden model was combined with the Prony series to take the material history and time effect into consideration. The difference between the calculated longitudinal forces in rolling state using the mentioned models was attributed to the rolling resistance of the tire. In order to check the accuracy of the proposed method, the predicted rolling resistance force was compared with that of experimentally obtained data which confirmed the applicability and robustness of the model. The contact pressure distributions have been presented and discussed in relation to different types of material model

The Molecular Structure of SBR and Filler Type Effects on Thermal Diffusivity of SBR/BR Compounds Used in Tire Tread

This research work is devoted to the study of the thermal diffusivity of SBR/BR compounds used as the tread of radial tires. Three series of rubber compounds were prepared, in which two solution SBR grades (with and without extra oil) as well as an emulsion SBR were selected. Five compounds with different CB/silica ratios were designed for each of the three series. Moreover, three compounds without fillers were prepared as reference samples. Thermal diffusivities of the compounds were determined by a novel technique to solve an inverse heat transfer problem. Abaqus and Isight codes were used to carry out the finite element solution and optimization. It is shown that, in all the compounds the thermal diffusivities were reduced with increasing the temperature. In addition, the macro- and micro- structures of SBR as well as the CB/silica ratios greatly affected the variations in thermal diffusivities with temperature. The thermal diffusivity and its variabilities were studied and discussed by different structural and functional parameters such as intermolecular distance, molecular vibrational energy, difference between the thermal diffusivities of the polymer and filler, and the chemical bonds between the polymer and silica

Study on the Effectiveness of Some Multicomponent Material Models with Hyper-viscoelasticity and Stress Softening for SBR/Carbon Black Compounds under two Loading Modes

Hypothesis: Determination of the parameters of the material models for rubber compounds is usually carried out under simple modes such as uniaxial tension. These models are typically consisted of hyper-viscoelastic and stress-softening equations. However, due to the complicated behaviors of rubbery materials, the effectiveness and accuracy of such models under combined loads of tension, compression, and shear should be verified.Methods: Three rubber compounds were prepared based on SBR reinforced by three different amounts of carbon blacks and underwent uniaxial cyclic under two loading/unloading rates and volumetric tests. The experimental data were used for the determination of parameters of three complex material models using a nonlinear curve fitting method. These models were selected based on the results of our previous findings. We have verified the uniaxial condition of the chosen test method and sample size using finite element method. The computed parameters were employed to simulate cylindrical rubber samples prepared from the same compounds through the finite element method using Abaqus code under compressive-contact loads. The predicted results were next compared with their experimentally measured data.Findings: The results showed that the effectiveness of a material model in the prediction of stress-strain or stress-time behavior of a rubber compound under a simple load case does not necessarily guarantee that the same level of accuracy is obtained for the other loading modes, especially for highly filled compounds.  It is shown here that to obtain accurate results in such cases, in addition to hyper-viscoelastic and stress softening equations, the material model should include proper terms to consider the effect of the filler-filler interactions into account, especially for highly carbon black-loaded compounds. It is found that the best model is the one in which the viscoelastic behavior of the filler-filler structure is independently included

Optimization of Mechanical, Dynamical and Thermal Properties of a High Performance Tread Compound for Radial Tires

A high performance passenger tire tread compound was optimized for its mechanical, dynamical and thermal properties. A reference compound was based on a blend of SBR and BR, sulfur and other ingredients without accelerator, carbon black and aromatic oil. The effects of CBS/TMTD and TBBS/TMTD as accelerator systems were studied with different quantities and the best accelerator system was chosen. Then, the blends of N330 and N550 carbon blacks were added in different quantities and the properties of these samples were studied to determine the best carbon black blend. Finally, the effect of different quantities of aromatic oil was investigated and the optimized quantity of aromatic oil and the final properties of tire tread compound were defined. The mechanical and dynamical tests were carried out on appropriate samples to determine tensile strength, elongation-at-break, fatigue-to-failure, abrasion resistance, hardness, resilience, dynamical-mechanical properties and temperature rise due to the heat build-up. The results showed that the compound containing 0.8 phr CBS, 0.7 phr TMTD, 40 phr N330,20 phr N550 and 15 phr aromatic oils demonstrated the best properties

Effect of Carbon Black Blends on the Mechanical Properties of a Tread Compound for Passenger Radial Tires

This study is devoted to the study of carbon black blends in passenger tire tread compounds with respect to their mechanical, dynamical and thermal properties. A reference compound based on SBR/BR and 60 phr carbon black as reinforcing filler was initially designed. Ten samples based on this compound were prepared usingfour different types of carbon black. The mechanical, dynamical and thermal tests were carried out on appropriate samples made from these compounds to determine tensile strength, elongation-at-break, abrasion resistance, hardness, resilience, tan δ and heat build-up. The results indicated that the compound containing N550 carbonblack has the lowest abrasion resistance and temperature rise. On the other hand, the compound containing N220 carbon black showed the highest temperature rise, energy dissipation and abrasion resistance due to high structure and iodine adsorption number. To achieve improvement in mechanical and dynamical properties, mixturesof carbon blacks were used and the best results (low rolling resistance, high abrasion resistance and high traction) were obtained. We have shown in our previous research works that the viscoelastic behavior of cured compounds can be accurately described by the experimental data of tensile deformation vs. force of rubber strips and itscorresponding finite element models. Therefore, a new method for calculating the energy dissipation was proposed which was based on the finite element modeling of the tension in an in-house designed rubber sample. The results obtained by employing this technique were in very good agreement with the experimentally measureddynamical data

Computer Simulation and Experimental Study of Deformation in a Radial Tire under Different Static Loads Using Finite Element Method

This research work is devoted to the simulation of a steel-belted radial tire under different static loads. The nonlinear finite element calculations were performed using the MSC.MARC code, installed on a computer system equipped with a parallel processing technology. Hybrid elements in conjunction with two hyperelastic models, namely Marlow and Yeoh, and rebar layer implemented in surface elements were used for the modeling of rubbery and reinforcing parts, respectively. Linear elastic material models were also used for the modeling of the reinforcing elements including steel cord in belts, polyester cord in carcass and nylon cord in cap ply section. Two-dimensional axisymmetric elements were used for the modeling of rim-mounting and inflation and three-dimensional models were developed for the application of the radial, tangential, lateral and torsional loads. Different finite element models were developed, in which both linear and quadratic elements were used in conjunction with different mesh densities in order to find the optimum finite element model. Based on the results of the load deflection (displacement) data, the tire stiffness under radial, tangential, lateral and torsional loads were calculated and compared with their corresponding experimentally measured values. The comparison was verified by the accuracy of the measured radial stiffness. However, due to the neglecting of the stiffness in shear and bending modes in cord-rubber composites, modeled with rebar layer methodology, the difference between computed values and real data are not small enough so that a more robust material models and element formulation are required to be developed

A Theoretical and Experimental Investigation of Mechanical Behavior of Steel-Rubber Long Fiber Composites Using Finite Element Method and Analytical Models

A comprehensive study is launched to compare different simulation techniques for the mechanical behavior of steel cord/rubber composites. A brief literature review is first performed and then various developed computational methods are examined. Uncured pre-shaped steel cord/rubber specimens, collected from a tire factory, were cured with different cord angles. These test samples were tested under tensile and shear modes. In order to check the validity and accuracy of the different computational techniques, the samples were analyzed using both analytical and numerical procedures which were based on the finite element method. The results showed that the accuracy and convergence of the computational methods are highly dependent on the selected numerical approach, the angle between cord and direction of applied load and also the hyperelastic or hyperviscoelastic model used to describe the mechanical behavior of the rubbery part. None of these models could predict nonlinear behavior of the cord/rubber composites in shear mode. Therefore, developing new constitutive models for this purpose is necessary