Review of Non-Newtonian Mathematical Models for Rheological Characteristics of Viscoelastic Composites

This study presents an overview of viscoelastic characteristics of biocomposites derived of natural-fibre-reinforced thermoplastic polymers and predictive models have been presented in order to understand their rheological behavior. Various constitutive equations are reviewed for a better understanding of their applicability to polymer melt in determining the viscosity. The models to be investigated are the Giesekus-Leonov model, the Upper Convected Maxwell (UCM) model, the White-Metzner model, K-BKZ model, the Oldroyd-B model, and the Phan-Thien-Tanner models. The aforementioned models are the most powerful for predicting the rheological behavior of hybrid and green viscoelastic materials in the presence of high shear rate and in all dimensions. The Phan-Thien Tanner model, the Oldroyd-B model, and the Giesekus model can be used in various modes to fit the relaxation modulus accurately and to predict the shear thinning as well as shear thickening characteristics. The Phan-Thien Tanner, K-BKZ, Upper convected Maxwell, Oldroyd-B, and Giesekus models predicted the steady shear viscosity and the transient first normal stress coefficient better than the White-Metzner model for green-fibre-reinforced thermoplastic composites.

A new shear rheological model for a soft interlayer with varying water content

The rheological behavior of a soft interlayer is critical to understanding slope stability, which is closely related to the water content of the soft interlayer. This study used the soft interlayer of the Permian Maokou Formation in Southwest China as an example to perform ring shear creep tests with different water content amounts. The effect of water content on the creep properties of the soft interlayer was analyzed, and a new shear rheological model was established. This research produced several findings. First, the ring shear creep deformation of the soft interlayer samples varied with the water content and the maximum instantaneous shear strain increment occurred near the saturated water content. As the water content increased, the cumulative creep increment of the samples increased. Second, the water content significantly affected the long-term strength of the soft interlayer, which decreased with the increase of water content, exhibiting a negative linear correlation. Third, a constitutive equation for the new rheological model was derived, and through fitting of the ring shear creep test data, the validity and applicability of the constitutive equation were proven. This study has developed an important foundation for studying the long-term deformation characteristics of a soft interlayer with varying water content.

Simulation of rheological behavior of asphalt mixture with lattice model

A three-dimensional(3D) lattice model for predicting the rheological behavior of asphalt mixtures was presented.In this model asphalt mixtures were described as a two-phase composite material consisting of asphalt sand and coarse aggregates distributed randomly.Asphalt sand was regarded as a viscoelastic material and aggregates as an elastic material.The rheological response of asphalt mixture subjected to different constant stresses was simulated.The calibrated overall creep strain shows a good approximation to experimental results.

A RHEOLOGICAL MODEL FOR POLYMER MELTS WITH INTERNAL STRUCTURE IN FLOW FIELDS

Conceptually, an imagined conformation ellipsoid is supposed to represent the shape of a polymer chain for polymer melts in flow fields and to be equivalent to the volume element in a mathematical sense in continuum mechanics. A power law dependence of shear modulus of polymer melts on detC, referred to as envelope volume, is proposed. Based on those assumptions and the non-linear relation of shear modulus, a phenomenological viscoelastic model is derived. The model is tested in simple shear flow, simple elongational flow, oscillatory shear flow, and relaxation process after flow suddenly stopped. The results show that the model works well to predict the change of internal structure and viscoelastic performance of polymer melts in flow fields.

A Nonlinear Rheological Model of Soft Clay and Its Application in Settlement of Sunk Ship

A one-dimensional consolidation-creep model test on the creep deformation of soft muddy clay in the littoral area of Tianjin is performed. A nonlinear rheologic model is established and the model coefficients are determined, in consideration of the characteristics of soft muddy clay. Furthermore, a settlement equation is deduced from the theologic model and verified by the field settlement measurements of Beitang Reservoir dam in Tianjin littoral area. Finally, the settlement e- quation is applied in calculating the settlement of ＂FAIRWAY-＂ suction dredger, which sunk in the external channel of Tianjin Port, induced by the soft clay consolidation of seabed. These results provide useful information for the decision of salvage plan.

Modelling the Rheological Properties of Epoxy Asphalt Concrete

This paper presents an investigation into modelling the rheological properties of epoxy asphalt concrete( EAC) by using the Huet-Sayegh model. Complex modulus tests were conducted on EAC specimens at various temperature and loading frequency conditions. Dynamic modulus and phase angles obtained from the complex modulus tests were used in the construction of the Huet-Sayegh model. The dynamic modulus master curve was developed by the Huet-Sayegh model as well as the Burgers model for comparison purpose. The results showed that EAC exhibits typical rheological behavior whose dynamic modulus decreases with the increase of temperature while increases with the increase of frequency,and phase angles increase with the decrease of frequencies and the increase of temperatures. The Huet-Sayegh model predicts the dynamic modulus master curve of EAC very well and much better than the Burgers model over a wide range of frequencies.

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅲ: A New Multiple Entanglement Model to Predict the Dependence of Linear Viscoelastic Function (η_0, Ψ_(10)~0,η_(ext)~0) on the Ranges of Primary Molecular Weights and th

It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer chain and the sequence distribution of constituent chains in entanglement spacings. A unified quantity for the three combing factors is the average constrained dimensional number of constituent chains in the long entanglement spacings (v). A new relation of v to the primary molecular weight and the number of testing polymers were derived from the multiple entanglement and reptation model, and a new method for determining v was proposed. The dependences of linear viscoelastic functions on the primary molecular weight and its distribution were derived by the statistical method. When Mn=6Me to 18 Me, the values of (v) can range from 3.33 to 3.70. Their values are in a good agreement with the experiment data, and it can slightjy vary with the different species of polymers and the different ranges of molecular weight of polymers

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅰ:A New Multiple Reptation Model to Predict the Nonlinear Visco-elasticity with Nagai Chain Constraints in Entangled Polymer Melts

An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results

A new general rheological model for rheological lubrication

Limitation and deficiency of main thcoogical models at present are descrital and analyzed, and seteralgeneral rheological models are discussed and compared with each other, and basic demands for a general model aresummarized. The constitutive eqUation is proposetl for a new general theobocal model. The general medel feaaressimple structure and wide coverage, and can take the Place of many edsting thcofogical ed. The whel has suc-cessfully been used for Elastohydrodynamic lubrication calculation.

Identification of structure and parameters of rheological constitutive model for rocks using differential evolution algorithm

To determine structure and parameters of a rheological constitutive model for rocks,a new method based on differential evolution(DE) algorithm combined with FLAC3D(a numerical code for geotechnical engineering) was proposed for identification of the global optimum coupled of model structure and its parameters.At first,stochastic coupled mode was initialized,the difference in displacement between the numerical value and in-situ measurements was regarded as fitness value to evaluate quality of the coupled mode.Then the coupled-mode was updated continually using DE rule until the optimal parameters were found.Thus,coupled-mode was identified adaptively during back analysis process.The results of applications to Jinping tunnels in China show that the method is feasible and efficient for identifying the coupled-mode of constitutive structure and its parameters.The method overcomes the limitation of the traditional method and improves significantly precision and speed of displacement back analysis process.

ON THE RHEOLOGICAL MODEL OF STEELS AT ELEVATED TEMPERATURES

Mechanical properties of steels ZG15CrMoV and 35 in the temperature range of 500 to 1400℃ have been experimently researched by means of Gleeble-1500.The experi- mental results is used as input-output responses,a rhelological model with five elements of the mechanical behaviour of steels ZG15CrMoV and 35 at elevated temperatures, i.e[M]=[H_1]-[H_2/[N_2]-[S/N_3],is determined by a system identification method,and the parameters of the model in the temperature range are also identified.

PREDICTION OF THE RHEOLOGICAL PROPERTIES OF STAR—TYPE BRANCHED POLYMER SOLUTIONS BY MEANS OF THE FIXED SPECTRUM MODEL

The Rouse-Zimm model with slippage was improved and the basic parameters of modelwere modified to explain the rheological properties of star-type branched polymersolutions. The theoretical results show good agreement with experimental data.

Modeling the Rheological Characteristics of Flexible High-Yield Pulp-Fibre-Reinforced Bio-Based Nylon 11 Bio-Composite

The aim of this work was to develop a mathematical model to investigate the rheological characteristics of viscoelastic pulp-fibre composite materials. The rheological properties of High-Yield Pulp (HYP) reinforced bio-based Nylon 11 (Polyamide 11) (PA11) composite (HYP/PA11) were investigated using a capillary rheometer. Novel predicted multiphase rheological-model-based polymer, fibre, and interphasial phases were developed. Rheological characteristics of the compo-site components influence the development of resultant microstructures;this in turn affects mechanical characteristics of a multiphase composite. The main rheological characteristics of polymer materials are viscosity and shear rate. Experimental and theoretical test results of HYP/PA11 show a steep decrease in apparent viscosity with increasing shear rate, and this melt-flow characteristic corresponds to shear-thinning behavior in HYP/PA11. The non-linear mathematical model to predict the rheological behavior of HYP/PA11 was validated experimentally at 200°C and 5000 S-1?shear rate. Finally, predicted and experimental viscosity results were compared and found to be in a strong agreement.

Rheological catastrophic model for soft clays

A brief review of the former studies on the mechanisms of soil rheology and microstructure is presented. Then a microstructure model and a set of rheological constitutive relations for soft clays, which describe how the rheological consolidation settlement develops, are established in the framework of the catastrophe theory. The validity of this model is verified by a series of rheological consolidation experiments with different loading rates. The experimental data show that creep deformation can be clearly observed in these tests, and the consolidation settlement is loading rate dependent. The characteristics of the deformation can be explained and reproduced successfully using the model. It can be concluded that only the biggest set of voids would collapse for one load increment. Parameters in the model, k and η, are gained by curve fitting. With only two free parameters, good fits of the data are achieved.

Study on Theoretical Modeling of Semi-Active Electro-Rheological Fluid Damper

This paper emphases on analyzing and investigating the mechanical behavior of electro-rheological fluid (ERF) semi-active damper. Theoretical model was developed to describe the relationship between electric field and the resistance force of ERF flowing through two parallel plane electrodes. In the model, the pressure drop along electrodes was supposed to consist of two parts: one related with viscosity and the other related with dynamic yield shear stress. The concept of yield stress influence factor was developed in deriving the theoretical formula for calculating the pressure drop in the damper. The influences of some other factors, such as, non-ideal Newtonian fluid and temperature have also been taken into account. Numerical and experimental work have been performed to prove the validity of the proposed model. The comparison of both results shows that the developed model is quite effective and practicable .

High temperature and high pressure rheological properties of high-density water-based drilling fluids for deep wells

To maintain tight control over rheological properties of high-density water-based drilling fluids, it is essential to understand the factors influencing the theology of water-based drilling fluids. This paper examines temperature effects on the rheological properties of two types of high-density water-based drilling fluids （fresh water-based and brine-based） under high temperature and high pressure （HTHP） with a Fann 50SL rheometer. On the basis of the water-based drilling fluid systems formulated in laboratory, this paper mainly describes the influences of different types and concentration of clay, the content of a colloid stabilizer named GHJ-1 and fluid density on the rheological parameters such as viscosity and shear stress. In addition, the effects of aging temperature and aging time of the drilling fluid on these parameters were also examined. Clay content and proportions for different densities of brine-based fluids were recommended to effectively regulate the rheological properties. Four theological models, the Bingham, power law, Casson and H-B models, were employed to fit the rheological parameters. It turns out that the H-B model was the best one to describe the rheological properties of the high-density drilling fluid under HTHP conditions and power law model produced the worst fit. In addition, a new mathematical model that describes the apparent viscosity as a function of temperature and pressure was established and has been applied on site.

Rheological behaviors of coal slime produced by filter-pressing

It is an effective way to use coal slime as fuel for circulating fluidized bed boilers, which will not only solve its pollution to the environment, but also turn waste to treasure. In order to provide basic technical information for transportation of coal slime from the coal preparation plant to the boiler, this paper experimentally studied the rheological behaviors of coal slime produced by filter-pressing. By using a rotational viscometer, the influences of water content, temperature, and shear time on the rheological behaviors of coal slime were investigated. Experimental results show that the coal slime will behave like Bingham plastics with low water content and like Bingham pseudo-plastics with 37.5% water content,while like pseudo-plastics with 40% water content. This indicates that the water content of coal slime must be controlled in consideration of both transportation resistance and combustion efficiency. Study results also show that, the apparent viscosity of coal slime at 5℃ is about 1.5–1.7 times of that at 40℃ for water contents 32%–37.5%, while the influence of temperature can be neglected when the water content is 40%. With increasing of water content, the influences of shear time on the apparent viscosity of coal slime becomes less. When the water content is more than 30%, the effect of shear time is negligible. It indicates that water content has the most important influence on the rheological behaviors of coal slime. There must be an optimal water content in considering conveying resistance and combustion efficiency. The environmental temperature must also be considered in coal slime transportation.

Traction rheological properties of simulative soil for deep-sea sediment

The traction capacity of the mining machine is greatly in?uenced by the traction rheological properties of the deep-sea sediments. The best simulative soil was prepared for substituting the deep-sea sediment based on the deep-sea sediment collected from the Paci?c C-C mining area. Traction rheological properties of the simulative soil were studied by a home-made test apparatus. In order to accurately describe the traction rheological properties and determine traction rheological parameters, the Newtonian dashpot in Maxwell body of Burgers model was replaced by a self-similarity spring-dashpot fractance and a new rheological constitutive model was deduced by fractional derivative theory. The results show the simulative soil has obvious non-attenuate rheological properties. The transient creep and stable creep rate increase with the traction, but they decrease with ground pressure. The fractional derivative Burgers model are better in describing non-attenuate rheological properties of the simulative soil than the classical Burgers model. For the new traction rheological constitutive equation of the simulative soil, the traction rheological parameters can be obtained by ?tting the tested traction creep data with the traction creep constitutive equation. The ground contact length of track and walking velocity of the mining machine predicted by the traction rheological constitutive equation can be used to take full advantages of the maximum traction provided by the soil and safely improve mining effciency.

Rheological properties of oil-based drilling fluids at high temperature and high pressure

The rheological properties of two kinds of oil-based drilling fluids with typically composition were studied at pressures up to 138 MPa and temperatures up to 204 ℃ using the RheoChan 7400 Rheometer.The experimental results show that the apparent viscosity,plastic viscosity and yield point decrease with the increase of temperature,and increase with the increase of pressure.The effect of pressure on the apparent viscosity,plastic viscosity and yield point is considerable at ambient temperature.However,this effect gradually reduces with the increase of temperature.The major factor influencing the rheological properties of oil-based drilling fluids is temperature instead of pressure in the deep sections of oil wells.On the basis of numerous experiments,the model for predict the apparent viscosity,plastic viscosity and yield point of oil-based drilling fluids at high temperature and pressure was established using the method of regressive analysis.It is confirmed that the calculated data are in good agreement with the measured data,and the correlation coefficients are more than 0.98.The model is convenient for use and suitable for the application in drilling operations.