Application of the Casson model to thixotropic waxy crude oil

The rheological behavior of a waxy crude oil was investigated using a coaxial cylinder viscometer. Experimental flow curves were fitted with the Casson equation. The Casson model was modified to interpret the hysteresis between upward and downward curves obtained in a series of consecutive runs. At the same shear rate, the mean axial ratio of the flow unit related to a down-curve (↓) is smaller than that related to an equilibrium up-curve (↑). This results in a decrease of the Casson yield stress τ_c↓ with respect to τ_c↑. A certain ξ coefficient describing departure from the equilibrium mean axial ratio was introduced into the model. Values of ξ calculated from the Casson yield stresses agreed satisfactorily with the theoretically predicted ones. Deviations from the Casson model at low shear rates were also explained. Received: 28 July 1998 Accepted: 18 February 1999     

A thermodynamic consistent damage and healing model for self healing materials

Thermodynamics of the damage and the healing processes for viscoplastic materials is discussed in detail and constitutive equations for coupled inelastic-damage-healing processes are proposed in a thermodynamic consistent framework. Small deformation state is utilized and the kinematic and the isotropic hardening effects for the damage and healing processes are introduced into the governing equations. Two new yield surfaces for the damage and healing processes are proposed that take into account the isotropic hardening effect. The computational aspect for solving the coupled elasto-plastic-damage-healing problem is investigated, and the mechanical behavior of the proposed polymeric based self healing system is obtained. Uniaxial compression tests are implemented on a shape memory polymer based self healing system and the damage and the healing are captured by measurement of the changes in the modulus of elasticity. It is concluded that the proposed constitutive equations can model the damage and healing effectively and the mechanical behavior of a shape memory polymer based self healing system can be precisely modeled using this formulation.     

A generalized rheological model of thixotropic materials

Summary A generalization of the rheological model of thixotropic materials, presented previously, was carried out. In the generalized rheological equation of state the yield stress depending on the structural parameter was introduced. In the generalized rate equation the difference in the destruction and recovery rates of the material structure was taken into account. A procedure leading to the determination of nine rheological parameters of the generalized model was worked out. The model was checked experimentally for a thixotropic paint.

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Zusammenfassung Eine früher dargestellte Theorie thixotroper Stoffe wird verallgemeinert, wobei eine von dem Strukturparameter abhängige Fließspannung eingeführt wird. Weiterhin wird der Unterschied zwischen der Zerstörungs-und der Wiederaufbaugeschwindigkeit der Stoffstruktur berücksichtigt. Eine Methode zur Bestimmung der neun benötigten Stoffparameter wird ausgearbeitet. Das Modell wird am Beispiel einer thixotropen Farbe experimentell geprüft.

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Notation a rheological parameter in eq. [26], s^–1 - A rheological parameter in eq. [16] - b rheological parameter in eq. [26] - c function in eq. [21] - averaged value of functionc in eq. [28] - c function in the rate equation [23], defined by eq. [21] - G function [1] defining material of the rate type - h function [2] determining the state of thixotropic fluid - k rheological parameter in the Herschel-Bulkley equation [17] or, in special case, in eq. [8], Ns ⁿ /m² - K function in eq. [18], Ns ^m /m² - m rheological parameter in eq. [18] or, in special case, in eq. [10] - n rheological parameter in the Herschel-Bulkley model [17] or, in special case, in eq. [8] - s rheological parameter in eq. [16] - t time, s - x arbitrary real variable - rheological parameter in eq. [9], s - shear rate, s^–1 - structural parameter, defined by eq. [2] - substantial derivative of structural parameter, s^–1 - _e function [6] describing the equilibrium curve in the coordinate system ( ) - ₀ initial value of structural parameter (att = 0) - natural time function of the thixotropic material, defined by eq. [22] - shear stress, N/m² - substantial derivative of shear stress, N/m² s - _e function describing equilibrium flow curve in the coordinate system ( ) - ₀ equilibrium yield stress, defined by eq. [12], N/m² - _y function of structural parameter describing the yield stress - function in eq. [11] Notation used in the algorithm:(Appendix) i,j,k integer - k _e (i) ordinal number of the experimental point at which the line of _i = const intersects the equilibrium flow curve - l _i number of the experiments of the type stepchange of the shear rate - l _j number of experimental points in one experiment of the type step-change of the shear rate - n _e number of experimental points on the equilibrium flow curve - n _k number of experimental points on the line of constant - n _y number of lines of constant - t(j) measured time interval (from the moment of the step-change of shear rate) - abscissa of the experimental point of ordinal numberk on the line of _i = const, in the coordinate system ( ) - abscissa of the experimental point of ordinal numberi on the equilibrium flow curve, in the coordinate system ( ) - shear rate at which the experiment of the type step-change of shear rate was carried out - _e (i) ordinate of the experimental point of ordinal numberi on the equilibrium flow curve, in the coordinate system ( ) - _y (i) value of yield stress at = _i - _s (i,j) experimental value of shear stress at constant value of shear rate (2i) for time intervalt(j) - (i,k) ordinate of the experimental point of ordinal numberk on the line of _i = const, in the coordinate system ( ) - ₀ the admissible value of the difference between the experimental and theoretical value of shear stress With 4 figures and 1 table     

Understanding thixotropic and antithixotropic behavior of viscoelastic micellar solutions and liquid crystalline dispersions. I. The model

A simple model consisting of the Upper Convected Maxwell constitutive equation and a kinetic equation for destruction and construction of structure, first proposed by Fredrickson in 1970, is used here to reproduce the complex rheological behavior of viscoelastic systems that also exhibit thixotropy and rheopexy under shear flow. The model requires five parameters that have physical significance and that can be estimated from rheological measurements. Several steady and unsteady flow situations were analyzed with the model. The model predicts creep behavior, stress relaxation and the presence of thixotropic loops when the sample is subjected to transient stress cycles. Such behavior has been observed with surfactant-based solutions and dispersions. The role of the characteristic time for structure built up, λ, in the extent and shape of the thixotropic loops is demonstrated.     

A unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids

A constitutive model for elasto-viscoplastic thixotropic materials is proposed. It consists of two differential equations, one for the stress and the other for the structure parameter, a scalar quantity that indicates the structuring level of the microstructure. In contrast to previous models of this kind, the structure parameter varies from zero to a positive and typically large number. The lower limit corresponds to a fully unstructured material, whereas the upper limit corresponds to a fully structured material. When the upper limit is finite, the model represents a highly shear-thinning, thixotropic, and viscoelastic liquid that possesses an apparent yield stress. When it tends to infinity, the behavior of a true yield-stress material is achieved. Predictions for rheometric flows such as constant shear rate tests, creep tests, SAOS, and large-amplitude oscillatory shear (LAOS) are presented, and it is shown that, in all cases, the trends observed experimentally are faithfully reproduced by the model. Within the framework of the model, simple explanations are given for the avalanche effect and the shear banding phenomenon. The LAOS results obtained are of particular importance because they provide a piece of information that so far is absent in the literature, namely a quantitative link between the Lissajous–Bowditch curve shapes and rheological effects such as elasticity, thixotropy, and yielding.     

Nanoporous metal organic framework materials for hydrogen storage

Hydrogen is expected to play an important role in future transportation as a promising alternative clean energy source to carbon-based fuels.One of the key challenges to commercialize hydrogen energy is to develop appropriate onboard hydrogen storage systems,capable of charging and discharging large quantities of hydrogen with fast enough kinetics to meet commercial requirements.Metal organic framework (MOF) is a new type of inorganic and organic hybrid nanoporous particulate materials.Its diverse networks can enhance hydrogen storage through tuning the structure and property of MOFs.The MOF materials so far developed adsorb hydrogen through weak disperston interactions,which allow significant quantity of hydrogen to be stored at cryogenic temperatures with fast kinetics.Novel MOFs are being developed to strengthen the interactions between hydrogen and MOFs in order to store hydrogen under ambient conditions.This review surveys the development of such candidate materials,their performance and future research needs.     

A viscoelastic fluid model for describing the mechanics of a coarse ligated plasma clot

Thrombi are formed at the end of a series of complex biochemical processes. There are various types of thrombi, and their rheological properties change depending on the conditions during clot formation. In this paper, a model for a particular type of clot, formed from human plasma, is proposed within a thermodynamic framework that recognizes that viscoelastic fluids possess multiple natural configurations.     

A thermo-elastoplastic model for soft rocks considering structure

In the fields of nuclear waste geological deposit, geothermy and deep mining, the effects of temperature on the mechanical behaviors of soft rocks cannot be neglected. Experimental data in the literature also showed that the structure of soft rocks cannot be ignored. Based on the superloading yield surface and the concept of temperature-deduced equivalent stress, a thermo-elastoplastic model for soft rocks is proposed considering the structure. Compared to the superloading yield surface, only one parameter is added, i.e. the linear thermal expansion coefficient. The predicted results and the comparisons with experimental data in the literature show that the proposed model is capable of simultaneously describing heat increase and heat decrease of soft rocks. A stronger initial structure leads to a greater strength of the soft rocks. Heat increase and heat decrease can be converted between each other due to the change of the initial structure of soft rocks. Furthermore, regardless of the heat increase or heat decrease, a larger linear thermal expansion coefficient or a greater temperature always leads to a much rapider degradation of the structure. The degradation trend will be more obvious for the coupled greater values of linear thermal expansion coefficient and temperature. Lastly, compared to heat decrease, the structure will degrade more easily in the case of heat increase.     

A thermodynamic approach to analyze shear localization in semi-solid materials

A theoretical framework of the shear localization analysis was developed for semi-solid materials taking into account a non-equilibrium relationship between viscous deformation, pressure and interfacial surface energy. Considering a shear layer model, the necessary condition of perturbation growth and subsequent shear localization was derived. The results revealed that the localization phenomenon in the semi-solid deformation strongly depends on the difference between irreversible viscous work done on pores and grains and the reversible viscous deformational work stored as the interfacial surface energy. This thermodynamic quantity indicates the possibility of a perturbation growth or decade in terms of the process parameters such as dilatancy, permeability and also the fraction of the solid skeleton.     

A model system for thixotropy studies

Many constitutive equations have been proposed for thixotropic materials but the supporting experimental evidence has usually been rather fragmentary. To a large extent this is due to the difficulties involved in measuring thixotropic systems. These systems normally display various phenomena that result in poor accuracy and poor reproducibility of the measurements. Therefore, it has been attempted here to formulate a robust thixotropic system that allows accurate measurements and that would be suitable for detailed studies of thixotropy. The system that has been developed is based on a matrix liquid that consists of a high boiling paraffin oil and a low molecular weight poly(isobutylene). A suitable type of fumed silica is used as the dispersed phase. The various rheological parameters of the material can be altered by varying the concentration of the components and, if necessary, the molecular weight of the polymer. The relative humidity around the sample turns out to be an important factor in controlling the yield stress, and its effect is shown to be reversible. The selected system can be measured accurately over a wide range of measurement conditions. These include stress jump measurements, which can be used to separate viscous and elastic contributions. The highest possible shear rate is limited by the occurrence of a peculiar phenomenon that shows up in the normal stresses.     

A structural model for thixotropy of colloidal dispersions

The present study proposes a structural model to describe the thixotropic behavior of colloidal dispersions. This model uses structural viscosity and elasticity as internal parameters, and predicts the evolution of shear stress when shear rate varies over time. Viscosity represents the structural level of colloidal aggregates and is dependent upon their alignment. Changes in alignment are linked to changes in shear rate, are regarded as instantaneous and are not believed to cause thixotropic behavior. Only changes in the structural level or structural viscosity and in the elastic deformation of colloidal aggregates cause measurable thixotropic behavior. Variations in structural viscosity over time, and at a fixed shear rate, follow a first-order kinetic equation based on two characteristic thixotropic times. This model incorporates several parameters, which are fitted independently by the appropriate rheological tests, in order to avoid any mathematical coupling. This model has been tested in 3 wt% Laponite aqueous dispersions using different ionic strengths.     

A new microstructure-based constitutive model for human blood

A new constitutive equation for whole human blood is derived using ideas drawn from temporary polymer network theory to model the aggregation and disaggregation of erythrocytes in normal human blood at different shear rates. Each erythrocyte is represented by a dumbbell. The use of a linear spring law in the dumbbells leads to a multi-mode generalized Maxwell equation for the elastic stress and both the relaxation times and viscosities are functions of a time-dependent structure variable. An approximate constitutive equation is derived by choosing a single mode corresponding to the cell aggregate size where the largest number of cells are to be found. This size is identified in the case of steady flows. The model exhibits shear-thinning, viscoelasticity and thixotropy and these are clearly related to the microstructural properties of the fluid. Agreement with the experimental data of Bureau et al. [M. Bureau, J.C. Healy, D. Bourgoin, M. Joly, Rheological hysteresis of blood at low shear rate, Biorheology 17 (1980) 191–203] in the case of a simple triangular step shear rate flow is convincing.     

A thermodynamic model of physical gels

Physical gels are characterized by dynamic cross-links that are constantly created and broken, changing its state between solid and liquid under influence of environmental factors. This restructuring ability of physical gels makes them an important class of materials with many applications, such as in drug delivery. In this article, we present a thermodynamic model for physical gels that considers both the elastic properties of the network and the transient nature of the cross-links. The cross-links’ reformation is captured through a connectivity tensor M at the microscopic level. The macroscopic quantities, such as the volume fraction of the monomer ?, number of monomers per cross-link s, and the number of cross-links per volume q, are defined by statistic averaging. A mean-field energy functional for the gel is constructed based on these variables. The equilibrium equations and the stress are obtained at the current state. We study the static thermodynamic properties of physical gels predicted by the model. We discuss the problems of un-constrained swelling and stress driven phase transitions of physical gels and describe the conditions under which these phenomena arise as functions of the bond activation energy E_a, polymer/solvent interaction parameter χ, and external stress p.     

基于SiPESC通用试验设计和代理模型算法构架

基于面向服务的开放软件平台SiPESC,针对试验设计和代理模型共性特征,采用面向服务插件编程的设计方法和软件设计模式,研发了试验设计和代理模型通用算法构架。构架的核心思想是将算法、数据模型和任务管理相分离,形成独立的服务,从而实现算法通用性。整个构架中,试验设计和代理模型分别由五个基本服务构成。重点阐述基本插件所代理功能的抽象过程和通用接口的设计思想,给出算法构架的使用步骤及扩展方式。利用该构架试验设计开发了均匀试验设计、正交试验设计、析因试验设计及中心复合试验设计;代理模型实现了响应面模型、径向基函数模型及Kriging模型,并对部分算法进行数值验证。研究工作表明,算法构架适用于通用试验设计和代理模型算法,可方便进行动态扩展,具备良好的开放性和重用性。     

A unified residual-based thermodynamic framework for strain gradient theories of plasticity

A unified thermodynamic framework for gradient plasticity theories in small deformations is provided, which is able to accommodate (almost) all existing strain gradient plasticity theories. The concept of energy residual (the long range power density transferred to the generic particle from the surrounding material and locally spent to sustain some extra plastic power) plays a crucial role. An energy balance principle for the extra plastic power leads to a representation formula of the energy residual in terms of a long range stress, typically of the third order, a macroscopic counterpart of the micro-forces acting on the GNDs (Geometrically Necessary Dislocations). The insulation condition (implying that no long range energy interactions are allowed between the body and the exterior environment) is used to derive the higher order boundary conditions, as well as to ascertain a principle of the plastic power redistribution in which the energy residual plays the role of redistributor and guarantees that the actual plastic dissipation satisfies the second thermodynamics principle. The (nonlocal) Clausius-Duhem inequality, into which the long range stress enters aside the Cauchy stress, is used to derive the thermodynamic restrictions on the constitutive equations, which include the state equations and the dissipation inequality. Consistent with the latter inequality, the evolution laws are formulated for rate-independent models. These are shown to exhibit multiple size effects, namely (energetic) size effects on the hardening rate, as well as combined (dissipative) size effects on both the yield strength (intrinsic resistance to the onset of plastic strain) and the flow strength (resistance exhibited during plastic flow). A friction analogy is proposed as an aid for a better understanding of these two kinds of strengthening effects. The relevant boundary-value rate problem is addressed, for which a solution uniqueness theorem and a minimum variational principle are provided. Comparisons with other existing gradient theories are presented. The dissipation redistribution mechanism is illustrated by means of a simple shear model.     

A thermodynamic approach to model the caloric properties of semicrystalline polymers

It is well known that the crystallisation and melting behaviour of semicrystalline polymers depends in a pronounced manner on the temperature history. If the polymer is in the liquid state above the melting point, and the temperature is reduced to a level below the glass transition, the final degree of crystallinity, the amount of the rigid amorphous phase and the configurational state of the mobile amorphous phase strongly depend on the cooling rate. If the temperature is increased afterwards, the extents of cold crystallisation and melting are functions of the heating rate. Since crystalline and amorphous phases exhibit different densities, the specific volume depends also on the temperature history. In this article, a thermodynamically based phenomenological approach is developed which allows for the constitutive representation of these phenomena in the time domain. The degree of crystallinity and the configuration of the amorphous phase are represented by two internal state variables whose evolution equations are formulated under consideration of the second law of thermodynamics. The model for the specific Gibbs free energy takes the chemical potentials of the different phases and the mixture entropy into account. For simplification, it is assumed that the amount of the rigid amorphous phase is proportional to the degree of crystallinity. An essential outcome of the model is an equation in closed form for the equilibrium degree of crystallinity in dependence on pressure and temperature. Numerical simulations demonstrate that the process dependences of crystallisation and melting under consideration of the glass transition are represented.     

A thermodynamic model for electrical current induced damage

Electromigration-induced damage, which is in principal an irreversible mass diffusion under high current density, has been a concern for VLSI design for a long time. Miniaturization of electronic device sizes down to nano-scale will make electromigration a concern for all conducting components. This paper uses thermodynamics, statistical mechanics and mass transport (diffusion) principals to propose a model for electromigration process and a damage evolution model to quantify the degradation in microelectronics (and micro electromechanical system) solder joints subjected to high current densities. Entropy production in the system is used as a damage metric. The irreversible thermodynamic damage model utilized in this work has previously been successfully applied to thermo-mechanical fatigue of microelectronic solder joints. In this paper we extend this model to electromigration-induced degradation.Electromigration process is modeled by the atomic vacancy flux (mass diffusion) process. The proposed unified model is compared with several existing analytical and empirical models. A comparison of the damage evolution model proposed in here agrees well with empirical models proposed in the literature.     

A void nucleation and growth based damage framework to model failure initiation ahead of a sharp notch in irradiated bcc materials

A continuum damage framework is developed and coupled with an existing crystal plasticity framework, to model failure initiation in irradiated bcc polycrystalline materials at intermediate temperatures. Constitutive equations for vacancy generation due to inelastic deformation, void nucleation due to vacancy condensation, and diffusion-assisted void growth are developed. The framework is used to simulate failure initiation at dislocation channel interfaces and grain boundaries ahead of a sharp notch. Evolution of the microstructure is considered in terms of the evolution of inelastic deformation, vacancy concentration, and void number density and radius. Evolution of the damage, i.e., volume fraction of the voids, is studied as a function of applied deformation. Effects of strain rate and temperature on failure initiation are also studied. The framework is used to compute the fracture toughness of irradiated specimens for various loading histories and notch geometries. Crack growth resistance of the irradiated specimens are computed and compared to that of virgin specimens. Results are compared to available experimental data.     

A unified framework for modeling hysteresis in ferroic materials

This paper addresses the development of a unified framework for quantifying hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials. Because the mechanisms which produce hysteresis vary substantially at the microscopic level, it is more natural to initiate model development at the mesoscopic, or lattice, level where the materials share common energy properties along with analogous domain structures. In the first step of the model development, Helmholtz and Gibbs energy relations are combined with Boltzmann theory to construct mesoscopic models which quantify the local average polarization, magnetization and strains in ferroelectric, ferromagnetic and ferroelastic materials. In the second step of the development, stochastic homogenization techniques are invoked to construct unified macroscopic models for nonhomogeneous, polycrystalline compounds exhibiting nonuniform effective fields. The combination of energy analysis and homogenization techniques produces low-order models in which a number of parameters can be correlated with physical attributes of measured data. Furthermore, the development of a unified modeling framework applicable to a broad range of ferroic compounds facilitates material characterization, transducer development, and model-based control design. Attributes of the models are illustrated through comparison with piezoceramic, magnetostrictive and shape memory alloy data and prediction of material behavior.     

Three-dimensional phenomenological thermodynamic model of pseudoelasticity of shape memory alloys at finite strains

The familiar small strain thermodynamic 3D theory of isotropic pseudoelasticity proposed by Raniecki and Lexcellent is generalized to account for geometrical effects. The Mandel concept of mobile isoclinic, natural reference configurations is used in order to accomplish multiplicative decomposition of total deformation gradient into elastic and phase transformation (p.t.) parts, and resulting from it the additive decomposition of Eulerian strain rate tensor. The hypoelastic rate relations of elasticity involving elastic strain rate are derived consistent with hyperelastic relations resulting from free energy potential. It is shown that use of Jaumann corotational rate of stress tensor in rate constitutive equations formulation proves to be convenient. The formal equation for p.t. strain rate , describing p.t. deformation effects is proposed, based on experimental evidence. Phase transformation kinetics relations are presented in objective form. The field, coupled problem of thermomechanics is specified in rate weak form (rate principle of virtual work, and rate principle of heat transport). It is shown how information on the material behavior and motion inseparably enters the rate virtual work principle through the familiar bridging equation involving Eulerian rate of nominal stress tensor.

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