Modulus Of Mixtures Research Articles

Micromechanics-based dynamic modulus prediction of polymeric asphalt concrete mixtures

Hot-mix asphalt (HMA) mixtures are widely used in the surface layer of flexible pavements. HMA mixtures are a kind of polymer matrix composite composed of polymeric asphalt mastic with the inclusion of particulate-filled media and air voids. Nowadays, more and more petroleum-based polymers (epoxy, resin) have been widely used in the HMA mixtures, in which the polymer matrix accounts for around 10–20% by volume. The properties of polymer matrix play a key role in the performance of flexible pavements. Dynamic modulus (∣ E ∗∣) of HMA mixtures is one of the fundamental engineering properties measured by the simple performance tester (SPT) and has been incorporated as a basic input in the American Association of State Highway and Transportation Officials (AASHTO) Mechanistic-Empirical Design Guide for flexible pavements. Although direct laboratory testing and empirical equations (such as the Witczak model and the Hirsch model) provide two ways to obtain the values of dynamic modulus of HMA mixtures, a predictive model based on the microstructure of HMA mixtures is more desirable. This paper presents a micromechanical model to predict the dynamic modulus of HMA mixtures. In this model, HMA mixtures are treated as a composite by embedding the mastic-coated aggregate particles into the equivalent medium of HMA mixtures. Based on the proposed model, closed-form equations were derived to predict the dynamic modulus value of HMA mixtures. The equations were able to take into account aggregate gradation and air void size distribution. In addition, laboratory experiments were conducted to verify the developed model. The dynamic modulus values of mastics and HMA mixtures were obtained through direct laboratory testing. The dynamic modulus of mastic was then used to predict the dynamic modulus of laboratory-prepared HMA mixtures with the newly developed model. It was found that the predicted dynamic moduli agreed reasonably well with the measured ones at high frequencies. The reasons for the discrepancy between measured and predicted dynamic moduli and the factors affecting the dynamic modulus were also explored in the paper.

Polymer-bridged gels of nanoparticles in solutions of adsorbing polymers

We use a combination of polymer mean field theory and Monte Carlo simulations to study the polymer-bridged gelation, clustering behavior, and elastic moduli of polymer-nanoparticle mixtures. Polymer self-consistent field theory is first numerically implemented to quantify both the polymer induced interparticle interaction potentials and the conformational statistics of polymer chains between two spherical particles. Subsequently, the formation and structure of polymer-bridged nanoparticle gels are examined using Monte Carlo simulations. Our results indicate a universality in the fractal structure for the polymer-bridged networks over a wide range of parametric conditions. Explicitly, near the gelation transition, the fractal dimension d(f) ranges between 2.2 and 2.5, and above the gelation thresholds, the elastic moduli are found to follow a universal power law G(') proportional, variant(eta-eta(c))(nu(eta) ) with a critical exponent nu(eta) approximately 1.82. The latter suggests strong similarities between polymer-bridging induced percolation and classical elastic resistor network percolation. Our results show a very good agreement with the experimental results for polymer-particle mixtures and suggest a possible framework for experimentally distinguishing the origins of gelation phenomena observed in polymer-particle mixtures.

Practical Procedure for Developing Dynamic Modulus Master Curves for Pavement Structural Design

A dynamic modulus master curve for asphalt concrete is a critical input for flexible pavement design in the mechanistic-empirical pavement design guide developed in NCHRP Project 1-37A. The recommended testing to develop the modulus master curve is presented in AASHTO Provisional Standard TP62-03, Standard Method of Test for Determining Dynamic Modulus of Hot-Mix Asphalt Concrete Mixtures. It includes testing at least two replicate specimens at five temperatures between 14°F and 130°F (-10°C and 54.4°C) and six loading rates between 0.1 and 25 Hz. The master curve and shift factors are then developed from this database of 60 measured moduli using numerical optimization. The testing requires substantial effort, and there is much overlap in the measured data, which is not needed when numerical methods are used to perform the time-temperature shifting for the master curve. This paper presents an alternative to the testing sequence specified in AASHTO TP62-03. It requires testing at only three temperatures be...

Evaluation of a Predicted Dynamic Modulus for Florida Mixtures

The new 2002 AASHTO guide for the design of pavement structures is based on mechanistic principles and requires the dynamic modulus as input to compute stress, strain, and rutting and cracking dama ...

A Study on the Manufacture of Clinker Using Low Grade Limestone and Waste Paper Sludge

This study was carried out to manufacture portland cement clinker using low grade limestone and waste paper sludge. Waste paper sludges were added to supply CaO component in low grade limestone, because low grade limestone contains relatively poor CaO. The cement raw materials such as limestone, clay and iron-ore were obtained in Ssangyong cement in Donghae, waste paper sludge in Samil paper. Composition and texture of raw materials and cement mineral phases were investigated by XRF, XRD and DTA etc..Portland clinker was made as follows. Modulus of mixture of raw materials was fixed in LSF = 94.0, SM = 2.4 and IM = 1.7. Raw materials are crushed, mixed and ground to fine powder, then put into furnace where it is heated to burning temperature. In here, CaF2 as a fluxing agent was used to facilitate burning.From the experimental results it appears CaF2 promotes that produces C2S at relatively low temperature of 1, 100°C. Cement minerals were produced as C2S at 1, 100°C and C3S at 1, 200°C. Also it was found that when water is added to cement minerals, there follows formation of cement hydrates such as C-S-H and ettringite.

Effect of temperature and pressure on the speed of sound and isentropic bulk modulus of mixtures of biodiesel and diesel fuel

AbstractThe density and speed of sound of blends of biodiesel with No. 2 and No. 1 diesel fuels were measured from atmospheric pressure to 32.46 MPa at temperatures of 20 and 40°C. The isentropic bulk modulus was calculated from these quantities. The results show that the density and isentropic bulk modulus can be accurately modeled as having a linear variation with blend percentage. Speed of sound is better correlated by a second‐order equation. Correlation equations are given and a blending rule is developed that allows the density, speed of sound, and isentropic bulk modulus of blends to be calculated from the properties of the biodiesel and diesel fuel.

Damping and elastic properties of binary powder mixtures

Damping and elastic properties of binary powder mixtures were investigated by a dynamic measurement method using vibration. Experiments were performed on a range of binary powder mixtures comprised of glass sphere, sand, polyethylene and rubber powders. Loss factor and Young's modulus of binary mixtures were calculated from the experimental data. The calculated loss factors were dependent upon the mixing fraction, but almost independent of compressive stress and packing conditions. In order to describe the properties of binary mixtures, a simple two-phase model has been developed and compared with experimental data. Reasonable agreement between the model and the experimental data was obtained.

Characteristics of crumb rubber modified (CRM) asphalt concrete

The mix design for CRM asphalt concrete with the Marshall method and laboratory tests to evaluate low temperature behaviors and temperature susceptibilities of CRM asphalt concrete are presented. The mix design was performed using one asphalt cement (120/150 penetration grade), five aggregate gradations for three rubber contents (0, 3, and 5% by weight of aggregate) and both pretreated and untreated crumb rubber (passenger tire). All mixtures satisfied the Marshall mix design criteria. For laboratory tests, two asphalt cements (85/100 and 120/150 penetration grade), three aggregate gradations for three rubber contents (0, 3, and 5% by weight of aggregate) and two types of pretreated crumb rubber (passenger and industrial tires) were used. The addition of crumb rubber did not significantly affect the overall temperature susceptibility of the mixtures. It did, however, substantially decrease the mixture modulus at any given temperature. The decrease in modulus was accentuated as the content of crumb rubber increased. The potential for thermal cracking decreased with the amount of crumb rubber. This demonstrated that a CRM asphalt mixture could relieve stress build up by its ability to strain.

Influence of non-starch polysaccharides isolated from wheat flour on the gelatinization and gelation of wheat starches

To evaluate the effects of the non-starch polysaccharide (NSP) quantity and its chemical composition on wheat starch gelatinization and gelation properties, we selected seven wheat cultivars based on their different water-insoluble (WIP) and soluble NSP (WSP) composition, and then extracted their total NSP rich fraction from wheat flour. The ratio of WIP to WSP ranged from 0.421 to 1.361. The NSP rich fraction was added to two types of isolated wheat starch having different amylose content. The effects of isolated NSP rich fraction on wheat starch gelatinization and gelation were analyzed using a Rapid Visco Analyser (RVA) and dynamic viscoelastic measurement. In RVA measurement, adding NSP increased the peak viscosity at higher concentrations, with the increment in peak viscosity depending on the wheat cultivar origin. Starch paste containing NSP had a higher breakdown than starch alone. In dynamic viscoelastic measurement, starch isolated from a low amylose line, Kanto 107, showed a clearly different time curve for the storage modulus from a normal amylose line, Norin 61. The effect of NSP on storage shear modulus differed between low amylose and normal amylose starch. In Kanto 107 starch with lower amylose content, adding the NSP rich fraction showed increased rigidity, and the storage and loss shear modulus of starch mixed with NSP rich fraction correlated with the ratio of WIP to WSP. In Norin 61 starch, adding NSP reduced the amount of solubilized starch and amylose, resulting in suppressing the storage modulus of starch and NSP mixtures.

Exact relations for effective tensors of composites: Necessary conditions and sufficient conditions

Typically the elastic and electrical properties of composite materials are strongly microstructure dependent. So it comes as a nice surprise to come across exact formulae for effective moduli that are universally valid no matter what the microstructure. Such exact formulae provide useful benchmarks for testing numerical and actual experimental data and for evaluating the merit of various approximation schemes. They can also be regarded as fundamental invariances existing in a given physical context. Classic examples include Hill's formulae for the effective bulk modulus of a two-phase mixture when the phases have equal shear moduli, Levin's formulae linking the effective thermal expansion coefficient and effective bulk modulus of two-phase mixtures, and Dykhne's result for the effective conductivity of an isotropic two-dimensional polycrystalline material. Here we present a systematic theory of exact relations embracing the known exact relations and establishing new ones. The search for exact relations is reduced to a search for matrix subspaces having a structure of special Jordan algebras. One of many new exact relations is for the effective shear modulus of a class of three-dimensional polycrystalline materials. We present complete lists of exact relations for three-dimensional thermoelectricity and for three-dimensional thermopiezoelectric composites that include all exact relations for elasticity, thermoelasticity, and piezoelectricity as particular cases. © 2000 John Wiley & Sons, Inc.

Estimation of In-Situ Strength of Cement-Treated Soils Based on a Two-Phase Mixture Model

A two-phase mixture model for predicting the stress-strain relationship of mixtures with different materials is proposed based on consideration of the stress distribution and strain energy in the mixture. Elastic moduli of mixtures with two different elastic materials are estimated by the proposed model and its validity is confirmed by comparing with the calculated results from other theories and the experimental results. In-situ cement-treated soils are regarded as a kind of two-phase mixture consisting of improved and unimproved parts, and the proposed model is applied to such in-situ treated soils. A level of mixing of the treated soils is evaluated using the improvement rate obtained from the improved area in a cross section of sampling specimen. Deformation modulus and unconfined compressive strength of the in-situ treated soil with different improvement rates are derived based on the two-phase mixture model. In order to confirm the validity of the proposed equations, laboratory model tests simulating the actual mixing process at site were conducted and the calculated results were compared with the test results. The proposed equation for estimating the in-situ strength of the treated soils was also verified by the results of the in-situ improvement tests.

Linear viscoelasticity of colloidal mixtures

In this work we develop a unifying and general method for calculating linear viscoelastic properties of multicomponent colloidal mixtures of spherical particles. Using linear response theory based on the many-body Smoluchowski diffusion equation, we derive an exact expression for the zero shear rate shear relaxation function, together with a Green-Kubo formula for the static shear viscosity. From these results, we obtain an exact expression for the high frequency elastic shear modulus of colloidal mixtures. We present, in addition, the first derivation of a self-consistent mode coupling scheme for the linear viscoelasticity of concentrated colloidal mixtures. This scheme offers the opportunity for a unified description of linear viscoelasticity and diffusion mechanisms. It accounts further for polydispersity and mixing effects, and leads naturally to a diverging shear viscosity at a glass transition point. Various limiting cases are considered to assess the accuracy of the approach. It is shown to be a valuable method for evaluating the rheological properties of concentrated colloidal mixtures.

Heat-Induced Interactions and Gelation of Mixtures of β-Lactoglobulin and α-Lactalbumin

The changes in protein aggregation and storage modulus of mixtures of β-lactoglobulin and α-lactalbumin were measured, by gel electrophoresis and dynamic rheology, respectively, during 60 min of heating at 75 or 80 °C in a buffer simulating the whey protein concentrate environment. The results were consistent with the formation of heat-induced hydrophobically bonded aggregates involving both α-lactalbumin and β-lactoglobulin that undergo disulfide bond interchange reactions within the aggregate as the basis for the generation of gel strands and gels. The apparent difference in response to heat treatment at 75 °C between mixtures of bovine serum albumin (BSA) and β-lactoglobulin and mixtures of α-lactalbumin and β-lactoglobulin is likely to be based on at least three factors: the different thermal transition temperatures of the three proteins; the possibility of self-initiation of thiol−disulfide interchange reactions for BSA and β-lactoglobulin, but not α-lactalbumin; and the ability of α-lactalbumin to form interprotein aggregates with each of the other two proteins prior to disulfide bond interchange and gelation. Keywords: Whey protein concentrate; hydrophobic aggregation; disulfide bonding

Temperature Correction of Backcalculated Moduli and Deflections Using Linear Viscoelasticity and Time-Temperature Superposition

New analytical procedures for temperature correction of backcalculated asphalt concrete moduli and surface deflections were developed based on the theory of linear viscoelasticity and the time-temperature superposition principle and verified using falling weight deflectometer data and field temperature measurements. The new correction procedures explicitly utilize the thermorheological properties of the asphalt mixture. The resulting temperature-modulus correction factors depend only on the relaxation modulus and time-temperature shift factor of the mixture. The temperature-deflection correction factor depends on both the material properties and the layer thicknesses of the pavement section. Emphasis has been placed on the analytical description of the mixture’s thermoviscoelasticity responsible for temperature effects on mixture modulus and pavement deflection. A mechanistic framework for dealing with temperature correction problems for asphalt pavement has been introduced.

Viscoelastic properties of ι-carrageenan/gelatin mixtures

The storage ( G′) and loss ( G′) moduli of transparent mixtures of ι-carrageenan and gelatin have been measured during gelation and melting and compared with those of gelatin and ι-carrageenan systems alone. The moduli of the mixtures were always higher than the sum of those of their components alone. Gelatin and ι-carrageenan seem to reinforce each other. Three specific temperature domains can be distinguished, delimited by the melting and helix-coil transition temperatures of gelatin and ι-carrageenan. An interpretation based on conformational changes and an attractive electrostatic interaction between the two biopolymers is suggested. The temperature dependence of G′ and G″ for mixtures has been studied as a function of thermal history (time and temperature of gel ageing), sodium chloride concentration and molecular weight of the ι-carrageenan.

Revised Predictive Model for Dynamic (Complex) Modulus of Asphalt Mixtures

Many predictive techniques for determining the dynamic modulus of asphalt concrete mixes have evolved over the past 25 years. One such model, developed at the University of Maryland, has been widely incorporated in design manuals and methods used throughout the world. However, the current predictive model only allows the determination of the dynamic modulus from the original bitumen properties among other variables. This model has been developed from dynamic (complex) modulus tests on laboratory-prepared specimens and does not take into account the hardening effects that take place during short- and long-term aging. By incorporating recent field studies on the aged viscosity of conventional asphalt cements, a revised model for the dynamic modulus of asphalt mixtures has been developed using the actual bitumen viscosity as the most important predictor variable in place of temperature. This modification now allows the model to be used to predict dynamic modulus for mixtures exhibiting any degree of binder aging. Also, by using a sigmoidal function model form, significant improvement in prediction rationality was achieved for using the model at extreme temperature conditions.

Revised Predictive Model for Dynamic (Complex) Modulus of Asphalt Mixtures

Many predictive techniques for determining the dynamic modulus of asphalt concrete mixes have evolved over the past 25 years. One such model, developed at the University of Maryland, has been widely incorporated in design manuals and methods used throughout the world. However, the current predictive model only allows the determination of the dynamic modulus from the original bitumen properties among other variables. This model has been developed from dynamic (complex) modulus tests on laboratory-prepared specimens and does not take into account the hardening effects that take place during short- and long-term aging. By incorporating recent field studies on the aged viscosity of conventional asphalt cements, a revised model for the dynamic modulus of asphalt mixtures has been developed using the actual bitumen viscosity as the most important predictor variable in place of temperature. This modification now allows the model to be used to predict dynamic modulus for mixtures exhibiting any degree of binder aging. Also, by using a sigmoidal function model form, significant improvement in prediction rationality was achieved for using the model at extreme temperature conditions.

The rheology and microstructure of charged colloidal suspensions

The effects of electric charge interation and particle correlations on suspension rheology are examined. A one-component fluid analysis using a Smoluchowski equation for the equilibrium structure is applied to charged suspensions of spherical colloids under shear. The frequency dependent modulus and viscosity, predicted as functions of particle and added salt concentrations, are compared with published rheological measurements on model suspensions. Recent improvements in the statistical mechanical theories for the equilibrium microstructure, its nonequilibrium deformation, and the bulk shear stresses are included. The direct electrostatic interaction is found to drive the divergence in the shear viscosity near the liquid-solid phase transition. Extensions of the theory predict the elastic modulus of binary mixtures of charged colloids. Estimates of the primary electroviscous effect, hydrodynamic interactions, and errors in the Yukawa limiting form for the potential and applications of asymptotic theories are presented. Predictions for the rheology based on effective hard-sphere models are found to be reasonable when using a parameter fit from the equilibrium phase behavior. Mean-field mode coupling theories predict larger relaxation times than calculated from the Smoluchowski equation (=SE). A study of binary mixing effects on elasticity shows non-ideal behavior. It is noted that equilibrium structural information can be used to resolve discrepancies between the theoretical predictions and the measured rheology.

The Young's modulus of binary powder mixtures

Many industrial powder systems are multicomponent and the use of powder fillers is widespread. This study reports on the measurement of the Young's modulus for four model binary powder mixtures, E (mix), and tests the application and predictive capability of published equations to experimental data. Powder blends of poly(tetrafluoroethylene) (PTFE) and lactose, PTFE and calcium carbonate, poly(vinylchloride) (PVC) and lactose, and PVC and calcium carbonate, representing two polymeric matrix powders and two powder fillers, were compressed to form beam specimens over a range of compositions and porosities. The Young's modulus of mixtures, E (mix), obtained from four-point-beam-bending studies was analysed to obtain values at zero porosity, E 0(mix), which were fitted into published mixture equations. Results demonstrated that simple mixing rules did not hold. In all cases, negative deviations were obtained for plots of E 0(mix) versus volume % filler fraction, indicating that the polymeric powder components with the lower Young's modulus dominated the E 0(mix) value. The Nielsen equation was found to be the preferred mixture relationship since, unlike other tested relationships, experimental data for all systems studied were well fitted by the function and predicted values of E 0(filler) showed reasonably good agreement with figures derived from monocomponent beam specimens.

Stress relaxation behavior of binary mixtures of waxes.

Stress relaxation contributes greatly to the restriction of shrinkage of the pattern at the male portion of the die. In this study, three types of binary mixtures consisting of paraffin and another ingredient were formulated, and the effects of ingredients on stress relaxation of these mixtures were investigated.By the application of the time-temperature superposition principle for each material, relaxation curves at various temperatures were superimposed to a single master curve with good overlapping. Addition of carnauba wax to paraffin resulted in a high restriction of stress relaxation in the high temperature range. Addition of beeswax to paraffin decreased the modulus of mixtures in the low temperature range. Dammar caused no appreciable change in stress relaxation of mixtures.