Vertical Shift Factors Research Articles

Advances in the Rheology of Synthetic Binder for Sustainable Road Pavements: An Improved Protocol for DSR Testing

Bituminous binders are thermal-dependent visco-elastic materials commonly used in pavement engineering. However, synthetic binders represent quite a new family of products that can be used in the substitution of conventional binders with various purposes. Among them, clear synthetic resins recently experienced a quick diffusion since they can be employed in the production of sustainable road pavements (which address aesthetic concerns, thermal aspects, etc.). Since specific studies addressing the rheological modeling of clear synthetic binders cannot be found in the literature, the purpose of this research is setting up an advanced rheological protocol to characterize such materials, bridging the existing knowledge gap. An extensive laboratory investigation with the dynamic shear rheometer was carried out in oscillatory mode (amplitude and frequency sweeps) to analyze the stress–strain state of such binders. An innovative test at a constant strain rate was used to construct non-linear master curves, overcoming various criticisms about the stress state of the binder when subjected to time-dependent deformations. Results indicated that, using non-linear data, horizontal and vertical shift factors (functions of temperature and strain rate) can be modeled through power law equations to obtain the master curves. This method was considered suitable for depicting the rheological response of the binders displaying such complex behaviors.

The Stiffness Behavior of Asphalt Mixtures with Different Compactness under Variable Confinement.

The dynamic modulus is a key property determining the short- and long-term performance of asphalt pavement, and its strong dependence on confining pressure and material density (mixture compactness) has been clearly indicated in the literature. It is always challenging to reproduce three-dimensional in situ stress conditions in the laboratory. To alleviate this difficulty, in this study, a convenient experimental setup was developed, in which the lateral confinement was made present and variable as a concomitant reaction of the surrounding materials to the vertical loading. Three dense-graded mixtures were prepared to a set of four different densities and then subjected to the confined dynamic modulus test. The results indicated a significant dependence of the confined modulus on the three factors of temperature, frequency, and compactness and that the mixture with coarser gradation demonstrated a less sensitivity to these parameters. A mathematical model was developed for the dynamic modulus master curve unifying these factors by means of horizontal shifting due to the time-temperature superposition principle (validated against the variable confinement at different compactness) and the vertical shift factor as a function of reduced frequency and compactness. The adequacy of the model was demonstrated using the experimental data, and its potential application in field pavement compaction was discussed.

Linear viscoelastic shear and bulk relaxation moduli in poly(tetramethylene oxide) (PTMO) using united-atom molecular dynamics

A quantitative understanding and prediction of the viscoelastic relaxation behavior of polymer melts is required to build up predictive multiscale models, which can be utilized for the practical design of viscoelastic materials. We report the application of the Green–Kubo method to compute the common shear relaxation modulus and the rarely reported bulk relaxation modulus for a realistic united atom model of poly(tetramethylene oxide) (PTMO), which is one key components of the segmented polyurethane (PU) elastomers. The temperature and molecular weight dependent viscoelastic behavior is investigated in detail by computing the bulk relaxation modulus K(t) along with shear relaxation modulus G(t). Our results provide new rheological data for PTMO melt based on the united atom model, which incorporates the chemical details of the polymer backbone. The predicted stress relaxation are mapped onto master curves using the time–temperature superposition principle with horizontal and vertical shift factors. The computed shift factors agree with the Williams–Landel–Ferry equation and appear to be similar for the shear and bulk relaxation modulus. The underlying dynamics for the shear and bulk relaxation modulus appear to stem from the same mechanistic origin as both processes seem to sample similar kinetic signature of the reference time scale of the underlying thermally activated processes in the liquid. Our results demonstrate furthermore, that MD simulations with the chemical details beyond coarse-grained models can sample the Rouse dynamics and the transitions towards entanglement, which is evident by the emergence of a plateau in shear relaxation modulus and scaling relations in the diffusion behavior of the monomer at larger molecular weights.

Reinforcing DNA Supramolecular Hydrogel with Polymeric Multiple-Unit Linker

Reinforcing DNA Supramolecular Hydrogel with Polymeric Multiple-Unit Linker

Effect of Cross-Linking Density on Horizontal and Vertical Shift Factors in Linear Viscoelastic Functions of Epoxy Resins

Epoxy resins are an important class of thermosetting resins, and their network structure, obtained by the curing reaction of epoxy and amine compounds, plays an important role in the material properties. We here revisited a time–temperature superposition (TTS) principle applied to the dynamic viscoelastic functions of epoxy resins, in which the network was well defined and systematically varied on the basis of the length of n-alkyl diamine. The superimposition of isothermal curves in the frequency domain required not only a horizontal shift but also a vertical shift, regardless of the length of n-alkyl diamine. The temperature dependence of the horizontal shift factor, aT, could be well expressed by the Williams–Landel–Ferry equation. The fitting parameter, called C2, increased with decreasing alkyl chain length of the diamine, meaning that the thermal expansion of the free volume was suppressed due to greater cross-linking density. This was qualitatively confirmed by a full-atomistic molecular dynamics (MD) simulation. Meanwhile, the vertical shift factor, bT, increased with increasing temperature, and the extent was smaller with increasing cross-linking density. This can be explained in terms of the entropic contribution to the modulus in the temperature region above the glass transition temperature. The entropy change estimated using the isobaric molar heat capacity from the MD simulation strongly supported this hypothesis. The knowledge here obtained should be useful for a better design of thermosetting polymers as well as for the prediction of long-term durability.

Development of healing model and simplified characterization test procedure for asphalt concrete

Fatigue cracking is one of the major distresses in asphalt pavement. Numerous and significant efforts have been undertaken to predict the fatigue life of pavements. One of the mechanisms that affects fatigue life is healing, and thus, including healing in fatigue performance prediction models is necessary. For this study, twelve healing tests at three temperatures and four rest periods were conducted to evaluate the healing characteristics of asphalt materials. The percentage of healing (%Hs) used in this study is defined as the ratio of the internal state variable (S) before the rest period to the incremental internal state variable due to the rest period. A %Hs mastercurve was constructed by applying the time–temperature superposition (t-TS) principle to the %Hs versus rest period curves and thereby proved that the t-TS principle works for healing. The %Hs mastercurves at different damage levels were shifted vertically to construct one reference %Hs mastercurve. The amount of vertical shifting is referred to as the vertical healing shift factor. The reference %Hs mastercurve with the vertical healing shift factor and t-TS principle led to the proposed shift healing model as a function of rest period, temperature, and damage level. A test protocol to calibrate the model also is suggested in this work. The protocol requires only three specimens, and thus, testing can be completed within a day. The proposed shift healing model characterized by the suggested protocol test was implemented successfully in twelve healing tests to predict the healing behavior of the test specimens, which indicates the prediction capability of the suggested model and test protocol.

Entropic and Energetic Elasticities of Natural Rubber with a Nanomatrix Structure.

The entropic and energetic elasticities of natural rubber with a nanomatrix structure are investigated by measuring the viscoelastic properties of deproteinized natural rubber (DPNR)-graft-polystyrene (PS). A nanomatrix structure is formed by graft copolymerization of styrene onto the surface of natural rubber particles, followed by coagulation. The morphology of the nanomatrix structure is observed with transmission electron microscopy. Natural rubber particles with about 1 μm diameter are well dispersed in a nanomatrix of PS. The horizontal shift factor (aT) and vertical shift factor (bT) are determined by superposition to create a master curve according to the time-temperature superposition principle. The positive slope of DPNR appears in the plot of bT versus temperature, suggesting that entropic elasticity occurs. In contrast, the slopes of DPNR-graft-PS are negative at lower temperatures but positive at higher temperatures. The negative slope, which suggests entropic elasticity, may be attributed to the formation of a nanomatrix structure. Natural rubber with a nanomatrix structure realizes both energetic elasticity and entropic elasticity.

Analysis of dielectric response of epoxy-mica insulation with temperature normalization

To decrease equipment costs and facilitate the simple and convenient on-site frequency dielectric spectroscopy (FDS) testing of epoxy-mica insulation of stator coils, specimens from a stator coil, subjected to 623 hours of 48 kV AC electrical ageing, were tested at temperatures from 0 to 120°C and frequencies from 10−1 to 107 Hz. The master curves and shift factors of the real and imaginary susceptibility components were obtained by the temperature normalization method. According to the horizontal shift factor, the complex susceptibility of the insulation increased exponentially with temperature. Regarding the vertical shift factor, the characteristic peak of the imaginary component of the complex susceptibility, representing the interface polarization of the epoxy-mica insulation, increased exponentially with temperature, and its movement can be expressed by the Arrhenius equation. The master curves of the temperature from 20 to 100°C and the frequency from 1 to 103 Hz can be fitted to the six-degree Debye relaxation model and Havriliak-Negami function. Through the shift factors and master curves, FDS data from 20 to 100°C can be estimated without temperature control.

Temperature effect on viscoelastic properties of anisotropic magnetorheological elastomers under compression

Magnetorheological elastomers (MREs) are a class of smart materials composed of an elastomer and micron-sized magnetic particles. Besides the loading amplitude and frequency, the elastic and rheological properties of MREs are also dependent on the external magnetic field and temperature. Previous studies focused on the influences of external magnetic field, strain amplitude and frequency on the dynamic properties, however, the temperature effect was rarely reported. In this paper, dynamic mechanical analysis (DMA) tests were carried out to investigate the viscoelastic properties of the anisotropic MRE samples under various temperatures and magnetic fields. A transition behavior of the anisotropic MRE samples was observed at about 50 °C for the dynamic modulus. The storage modulus initially decreased with the increasing of the temperature up to 50 °C and then increased or maintained a stable value when the temperature increased up to 60 °C. The time-temperature superposition (TTS) principle was extended to construct the dynamic modulus master curve of the MREs by using the horizontal shift factor and the vertical shift factor. The good correlations between the measured and predicted data were confirmed by performing statistical analysis for the goodness of fit. The constructed master curve and shift factors can be used to predict the viscoelastic properties of the MREs beyond the DMA experiment’s range of temperatures and frequencies.

Time-temperature equivalence in a PVA dual cross-link self-healing hydrogel

Hydrogels consisting of permanent chemical bonds plus transient physical bonds are known to have self-healing properties, high toughness, and to be highly viscoelastic. These mechanical responses derive from the ability of the physical bonds to break and reform during deformation. The rate of bond breaking and reformation is found experimentally to be independent of stress but is expected to depend on temperature. Using a poly(vinyl alcohol) hydrogel with chemical and physical cross links, the temperature dependence of the mechanical response is measured using large strain load/unload tension tests and torsional rheometry for temperatures from 13 to 50 °C. The rheometry data show that time-temperature superposition can be used to condense the data to a master curve. It is found that allowing the model parameters to be temperature dependent, a previously developed constitutive model fits the tension and rheometry data well. Horizontal (time) and vertical (amplitude) shift factors calculated directly from the rheometer test data and from tension test data agree well with each other showing that the constitutive model describes the mechanical behavior well over the temperature range explored and that the material closely follows simple time-temperature superposition.Hydrogels consisting of permanent chemical bonds plus transient physical bonds are known to have self-healing properties, high toughness, and to be highly viscoelastic. These mechanical responses derive from the ability of the physical bonds to break and reform during deformation. The rate of bond breaking and reformation is found experimentally to be independent of stress but is expected to depend on temperature. Using a poly(vinyl alcohol) hydrogel with chemical and physical cross links, the temperature dependence of the mechanical response is measured using large strain load/unload tension tests and torsional rheometry for temperatures from 13 to 50 °C. The rheometry data show that time-temperature superposition can be used to condense the data to a master curve. It is found that allowing the model parameters to be temperature dependent, a previously developed constitutive model fits the tension and rheometry data well. Horizontal (time) and vertical (amplitude) shift factors calculated directly from t...

Toward the constitutive modeling of epoxy matrix: Temperature-accelerated quasi-static molecular simulations consistent with the experimental test

Abstract We propose an efficient simulation-based methodology to characterize the quasi-static (experimental low strain rate) yield stress of an amorphous thermoset polymer, which has generally been considered a limitation of molecular dynamics (MD) simulations owing to the extremely short time steps involved. In an effort to overcome this limitation, the temperature-accelerated method – in which temperature is treated as being equivalent to time in deformation kinetics – is employed to explore the experimental strain rate conditions. The mechanical tensile behavior of a highly crosslinked polymer is then investigated with MD simulations by considering different strain rates and temperatures below the glass transition temperature. The derived yield stress represents the time- and temperature-dependent characteristics, showing that the yield stress decreases with increasing temperature and decreasing strain rate. Changeable vertical and horizontal shift factors are introduced for the first time to reflect nonlinear characteristics of the yield stress across a broad range of strain rates and to quantify the correlation between increasing temperatures and decreasing strain rates. With the proposed method, the Eyring plot, which describes the rate effect on yield from quasi-static to high-rate conditions, is predicted from MD simulations, and agrees well with macroscopic experimental results. From the constructed Eyring plot, the experimentally validated quasi-static stress-strain response is also estimated by using linear elastic model and Ludwick's hardening model. The proposed method provides new avenues for the design of glassy polymers using only fully atomistic MD simulations, thus overcoming the existing temporal scale limitations.

The development of the Scaled Accelerated Loading Simulator facility and transfer functions to the full-scale pavement using theory of similitude by finite element analysis

The purpose of this study is to investigate the relationship of the vertical deformation between the scaled-down pavement test and full-scale pavement structure according to the theory of similitude-based analysis procedure. Finite element analysis used to investigate and establish the relationship between the scaled-down and full-scale models. Four scaled-down models with scaling factors of 0.9, 0.75, 0.6, and 0.45 with two types of constitutive models of asphalt concrete materials, elastic and viscoelastic, are considered. The results show that the vertical deformation in the full-scale model achieved by applying a vertical shift to the vertical deformation in the scaled-down model. The vertical shift factor varies linearly in normal and logarithm scale with the scaling factor from 0.9 to 0.45 for linear elastic and viscoelastic material, respectively. Moreover, this study proposes a systematic analysis procedure to determine the testing temperature in the SALS test at a specific loading speed by using the time–temperature superposition principle. This study contributes considerably to preliminary understanding of the relationship between the scaled-down tester in the laboratory and the full-scale model according to the theory of similitude.

A quantitative correlation between polyethylene/graphene interfacial viscoelastic dissipation and deformation parameters: A molecular simulation study

In this study, the influence of applied tensile stretching rate and temperature on amorphous polyethylene/graphene (PE/G) and polyethylene/amino functionalized graphene (PE/aFG) interfaces were studied via molecular dynamics (MD) simulations. The simulations results indicated that the interfacial adhesion during stretching process was increased with increasing the stretching rate (V) while decreased with increasing the temperature (T). This behavior can be connected to changing the polymer chains friction arisen from inadequate reorientation time, which especially happened at the higher stretching rates and lower temperatures. Furthermore, the amino functionalization of G strengthened both the thermodynamic work of adhesion and interfacial viscoelastic energy dissipation function, φ (V, T), in the interface deformation process. In fact, relying the chains on aFG surface with stronger interfacial interactions also increased the required energy for the chains to disentangle and reorient on the surface. Moreover, the stretching rate dependency of the φ value well follows a power law at all the stretching temperatures. The effect of stretching rate and temperature on φ value was simultaneously investigated utilizing the time-temperature superposition principle. Master curves of the simulation data, φ (aTV), was obtained for PE/G and PE/aFG interfaces on which the horizontal (aT) and vertical shift factor (bT) were calculated using Williams-Landel-Ferry (WLF) equation and Bueche-Rouse theory, respectively.

Dynamic viscoelasticity of a series of poly(4-n-alkylstyrene)s and their alkyl chain length dependence

Dynamic viscoelastic measurements were performed for a series of poly(4-n-alkylstyrene)s with six different n-alkyl side chains, that is, methyl, ethyl, propyl, butyl, hexyl and octyl groups. Based on the time-temperature superposition principle, storage modulus G′, loss modulus G″ and loss tangent tan δ were shifted with horizontal shift factor aT and vertical shift factor bT, giving well superposed master curves for all the polymers. With increase of the number of carbon atoms, plateau modulus GN0, which corresponds to G′ value at minimum tan δ, decreases, while entanglement molecular weight Me(=ρRT/GN0) increases, where ρ is the polymer density, R is the gas constant and T is the absolute temperature. Degree of polymerization at onset of entanglement, Ne, which defined as Me/M0, where M0 denotes the molecular weight of each monomer, also increases with increase of n-alkyl side chain length. Packing length estimated from the empirical equation by Fetters also increases with increase of n-alkyl lengths. These results are presumably due to large polymer chain thickness caused directly by substituents on phenyl rings of styrene units.

A comparative study of the effects of cone-plate and parallel-plate geometries on rheological properties under oscillatory shear flow

In this study, the effects of cone-plate (C/P) and parallel-plate (P/P) geometries were investigated on the rheological properties of various complex fluids, e.g. single-phase (polymer melts and solutions) and multiphase systems (polymer blend and nanocomposite, and suspension). Small amplitude oscillatory shear (SAOS) tests were carried out to compare linear rheological responses while nonlinear responses were compared using large amplitude oscillatory shear (LAOS) tests at different frequencies. Moreover, Fourier-transform (FT)-rheology method was used to analyze the nonlinear responses under LAOS flow. Experimental results were compared with predictions obtained by single-point correction and shear rate correction. For all systems, SAOS data measured by C/P and P/P coincide with each other, but results showed discordance between C/P and P/P measurements in the nonlinear regime. For all systems except xanthan gum solutions, first-harmonic moduli were corrected using a single horizontal shift factor, whereas FT rheology-based nonlinear parameters (I3/1, I5/1, Q3, and Q5) were corrected using vertical shift factors that are well predicted by single-point correction. Xanthan gum solutions exhibited anomalous corrections. Their first-harmonic Fourier moduli were superposed using a horizontal shift factor predicted by shear rate correction applicable to highly shear thinning fluids. The distinguished corrections were observed for FT rheology-based nonlinear parameters. I3/1 and I5/1 were superposed by horizontal shifts, while the other systems displayed vertical shifts of I3/1 and I5/1. Q3 and Q5 of xanthan gum solutions were corrected using both horizontal and vertical shift factors. In particular, the obtained vertical shift factors for Q3 and Q5 were twice as large as predictions made by single-point correction. Such larger values are rationalized by the definitions of Q3 and Q5. These results highlight the significance of horizontal shift corrections in nonlinear oscillatory shear data.

Application of time–temperature superposition principle to Chinese fir orthotropic creep

The application of time–temperature superposition principle (TTSP) to orthotropic creep in dry Chinese fir (Cunninghamia lanceolata [Lamb.] Hook.) was investigated through a sequence of short-term tensile creep for longitudinal (L), radial (R), and tangential (T) specimens in the temperature range of 30–150 °C. A visual assessment for the validity of TTSP was carried out by applying the approximated complex plane (ACP). The results showed that TTSP was well matched for R and T specimens using horizontal shift factor to construct master curves. As for L specimen, an additional vertical shift factor was applied to construct a smooth master curve, owing to the temperature-dependent compliance. Based on the application of ACP, the creep model governed by a power law was proposed to successfully depict the master curve for each main anatomy direction. The present study partially provided the firsthand data in verifying the applicability of TTSP of the orthotropic viscoelasticity of Chinese fir wood, and successfully constructed the rheological model to predict the orthotropic creep response. More importantly, the result can function as the base to the structural safety designs for the engineering structures of Chinese fir in practice.

Application of TTSP to wood-development of a vertical shift factor

Abstract The applicability of the time-temperature superposition principle (TTSP) to wood has been investigated aiming at the prediction of long-term mechanical properties of wood by both horizontally and vertically shifting of short-term stress relaxation data obtained by experiments. The expression of TTSP considering the vertical shift factor (b T ) for wood is proposed the first time. The results showed that: (1) TTSP applied to poplar and the master curve that was obtained from 1 h of tests at 283.2, 303.2, 320.2, 343.2, and 363.2 K in a relative humidity (RH) of 60% could predict the stress relaxation behavior for approximately 42 years at 283.2 K and 60% RH. (2) There was a linear correlation between lga T and T -1, lg a T =6590.40 T -1 -23.64 (R2=0.994), which followed the Arrhenius equation well, while the apparent activation energy was 34.6 kcal mole-1. (3) The b T had a linear relationship with temperature, and the relation was lgb T =0.0013T-0.37 (R2=0.999). (4) The long-term relaxation curve of the long-term verification test had high goodness of fit with the master curve. The results can be interpreted that the TTSP expression considering the b T proposed in this paper is rational.

Bio-Based Resin Reinforced with Flax Fiber as Thermorheologically Complex Materials.

With the increase in structural applications of bio-based composites, the study of long-term creep behavior of these materials turns into a significant issue. Because of their bond type and structure, natural fibers and thermoset resins exhibit nonlinear viscoelastic behavior. Time-temperature superposition (TTS) provides a useful tool to overcome the challenge of the long time required to perform the tests. The TTS principle assumes that the effect of temperature and time are equivalent when considering the creep behavior, therefore creep tests performed at elevated temperatures may be converted to tests performed at longer times. In this study, flax fiber composites were processed with a novel liquid molding methacrylated epoxidized sucrose soyate (MESS) resin. Frequency scans of flax/MESS composites were obtained at different temperatures and storage modulus and loss modulus were recorded and the application of horizontal and vertical shift factors to these viscoelastic functions were studied. In addition, short-term strain creep at different temperatures was measured and curves were shifted with solely horizontal, and with both horizontal and vertical shift factors. The resulting master curves were compared with a 24-h creep test and two extrapolated creep models. The findings revealed that use of both horizontal and vertical shift factors will result in a smoother master curves for loss modulus and storage modulus, while use of only horizontal shift factors for creep data provides acceptable creep strain master curves. Based on the findings of this study, flax/MESS composites can be considered as thermorheologically complex materials.

Dynamic viscoelastic properties of polyvinyl chloride with physical aging

The experimental research of dynamic viscoelastic properties of polyvinyl chloride was conducted by the dynamic mechanical analysis method in this paper. And the fitting equation of dynamic modulus of polymers has been presented. Based on the time-aging time equivalent principle, horizontal shift factor and vertical shift factor of aging time are carried out, which proposes a novel method for the research on time-aging time equivalent analysis of dynamic mechanical properties of polymers during physical aging.

Coefficient of friction between a rigid conical indenter and a model elastomer: Influence of local frictional heating

We investigate the coefficient of friction between a rigid cone and an elastomer with account of local heating due to frictional dissipation. The elastomer is modeled as a simple Kelvin body and an exponential dependency of viscosity on temperature is assumed. We show that the coefficient of friction is a function of only two dimensionless variables depending on the normal force, sliding velocity, the parameter characterizing the temperature dependence as well as shear modulus, viscosity at the ambient temperature and the indenter slope. One of the mentioned dimensionless variables does not depend on velocity and determines uniquely the form of the dependence of the coefficient of friction on velocity. Depending on the value of this controlling variable, the cases of weak and strong influence of temperature effects can be distinguished. In the case of strong dependence, a generalization of the classical “master curve” procedure introduced by Grosch is suggested by using both horizontal and vertical shift factors.