Viscoelastic Master Curves Research Articles

Investigating the effects of reducing the number of temperatures and frequencies on the development of master curves for viscoelastic properties of bituminous composite

This study aimed to assess the feasibility of substituting temperature sweep tests for frequency sweep tests and explore the potential of utilizing fewer temperatures and frequencies in dynamic modulus tests to formulate viscoelastic properties master curves. The results indicated that master curves derived from temperature sweep tests mirrored the trends and values obtained from frequency sweep tests, presenting a viable alternative for constructing viscoelastic properties master curves of bitumen. Furthermore, models fitted to dynamic modulus test results at three temperatures and three frequencies exhibited comparable primary parameters, values, and trends to those derived from the complete dataset. The model fitted on reduced data demonstrated robust performance with correlation and R-squared values exceeding 0.95. Considering a marginal increase of about 5% in Residual Standard Error (RSE) values when using the reduced dataset, generating master curves with fewer test results underscored the feasibility and reliability of the original master curves.

Viscoelastic Characteristics and Mechanical Performances of Asphalt Mastic and Mixtures with Fly Ash from Municipal Solid Waste Incineration Residues

Viscoelastic Characteristics and Mechanical Performances of Asphalt Mastic and Mixtures with Fly Ash from Municipal Solid Waste Incineration Residues

Characterization of viscoelastic behavior of basalt fiber asphalt mixtures based on discrete and continuous spectrum models.

In order to analyze the differences between the master curves of relaxation modulus E(t) and creep compliance J(t) obtained from discrete and continuous spectrum models, and to comprehensively evaluate the effect of basalt fiber content on the viscoelastic behavior of asphalt mixtures, complex modulus tests were conducted for asphalt mixtures with fiber content of 0%, 0.1%, 0.2% and 0.3%, respectively. Consequently, the master curves of Viscoelastic Parameters of asphalt mixtures were constructed according to the generalized Sigmoidal model(GSM) and the approximate Kramers-Kronig (K-K) relationship. Then, transformation of master curves using discrete and continuous spectrum models to obtain the models of E(t) and J(t) containing all viscoelastic information. Also, the accuracy of the models of E(t) and J(t) was evaluated. The results show that the addition of basalt fibers improves the strength, stress relaxation and deformation resistance of asphalt mixtures. It is worth noting that basalt fibers achieve the improvement of asphalt mixtures by changing their internal structure. Considering the different viscoelastic master curves at four dosages, the optimum fiber dosage was 0.2%. In addition, both discrete and continuous model conversion methods can obtain high accuracy conversion results.

Brownian dynamics simulation on the parallel superposition rheology of a colloidal gel

Parallel superposition rheology has been explored using Brownian dynamics simulations on a model colloidal gel by imposing a small amplitude probing oscillation parallel to the main shear flow. This study aims to investigate the constituting principles behind the material functions in parallel superposition rheometry (PSR) and to elucidate the principles behind the structure responses. The viscoelastic spectra under frequency sweeps show that in a high-frequency region, each curve can be superimposed onto a single master curve using horizontal shift factors equal to viscosity which is a reminiscence of time-shear rate superposition in orthogonal superposition rheometry. This corresponds to the region where a parallel superposition analysis can be adequately performed as the shear rate controls the viscoelastic spectra of the gel independently from probing perturbation. On the other hand, in the low-frequency region, this principle breaks down and even negative storage modulus is observed due to the strong flow coupling effect, which is also found in experiments. By introducing the spatial moduli, it is found that the negative modulus originates from the attractive potential region. In the flow conditions where negative modulus occurs, the shear force is strong enough to break down every surface bond between the particles. In this state, the increase in structural factor in response to the rise in the shear rate dominates particle stress, even within the attractive potential region. This arises because the isolated particles have more opportunities to interact with other particles as the shear rate of the imposed perturbation increases. This structural response, influenced by the attractive potential, results in a negative storage modulus and a positive loss modulus after performing Fourier transformation. This paper, for the first time by a simulation approach, demonstrates the essential characteristics of the material functions obtained using PSR. Also, this study is expected to enhance our understanding on the flowing materials and suggest a criterion for the reliable application of superposition rheology using a viscoelastic master curve.

Viscoelastic parametric conversions and mechanical response analysis of asphalt mixtures

In this study, dynamic modulus, dynamic resilience modulus, and creep compliance tests were conducted to characterize and quantify the effects of viscoelastic parameters of asphalt mixtures on the mechanical response of pavement structures. From the laboratory testing under different loading waveforms, master curves were generated to computed the viscoelastic parameters that were used as input for ANSYS modeling. In general, the corresponding results indicated that the stress magnitude had a significant influence on the evolution of master curves for the viscoelastic parametric conversions from creep compliance and that all the mechanical responses (namely stress, strains, and deformations) tended to increase with temperature. For the asphalt mixtures evaluated, the relaxation modulus transformed from the creep compliance was largely indifferent whilst those converted from the dynamic modulus did not exceed 15% from the actual values. In terms of the loading mode, the highest fitting accuracy for the viscoelastic parameters and master curves was obtained for the half-sine waveform. Overall, the study results indicated that ensuring good interlayer bonding is imperative for minimizing the compressive/shear stresses and strains in pavement structures to mitigate shear failure, debonding, delamination, etc. Additionally, the study also demonstrated that use of modified asphalt mixtures was critical to mitigate high compressive and shear strains arising for heavy traffic loading in high temperature climatic conditions.

The hidden hierarchical nature of soft particulate gels

Soft particulate gels are composed of a small amount of particulate matter dispersed in a continuous fluid phase. The solid components assemble to form a porous matrix, providing rigidity and control of the mechanical response, despite being the minority constituent. The rheological response and gel elasticity are direct functions of the particle volume fraction. However, the diverse range of different functional dependencies reported experimentally has challenged efforts to identify general scaling laws. Here we reveal a hidden hierarchical organization of fractal elements that controls the viscoelastic spectrum, and which is associated with the spatial heterogeneity of the solid matrix topology. The fractal elements form the foundations of a viscoelastic master curve, constructed using large-scale three-dimensional (3D) microscopic simulations of model gels, which can be described by a recursive rheological ladder model over a range of particle volume fractions and gelation rates. The hierarchy of the fractal elements provides the missing general framework required to predict the gel elasticity and the linear viscoelastic response of these complex materials. Colloidal gels consist of particles embedded in a fluid. It is now found that a gel’s viscoelastic spectrum, relating mechanical properties and deformation frequencies, can be understood by modelling these gels as networks of fractal viscoelastic units, connected hierarchically.

Investigation into Rheological Behavior of Warm-Mix Recycled Asphalt Binders with High Percentages of RAP Binder

The rheological properties of warm-mix recycled asphalt binders are critical to enhancing design quality and interpreting the performance mechanisms of the corresponding mixtures. This study investigated the rheological behavior of warm-mix recycled asphalt binders with high percentages of RAP binder. The effects of two warm-mix additives [wax-based Sasobit (S) and surfactant-based Evotherm-M1 (E)], a rejuvenating aging [ZGSB (Z)], four RAP binder contents (0%, 30%, 50% and 70%), and three aging states (unaged, short-term aged and long-term aged) were evaluated in detail using the dynamic shear rheometer (DSR), bending beam rheometer (BBR) and Brookfield rotational viscometer tests as well as conventional performance tests over the whole range of temperatures. The results showed that the rejuvenating agent Z effectively alleviated the aging effect of the RAP binder; however, it could hardly eliminate entirely this negative impact, especially at higher RAP binder contents. The addition of S remarkably lowered the apparent viscosity of the warm-mix recycled binders by up to 35.0%, whereas E had little influence on the binder viscosity due to its surfactant nature. Besides, S performed much better in improving rutting resistance (with the increase of up to 411.3% in |G*|/sinδ) than E, while E exhibited superior fatigue performance (with the reduction of up to 42.3% in |G*|·sinδ) to that of S. In terms of the thermal cracking resistance, E had very slight influence and S even yielded an adverse impact (with the increase of up to 70.2% in Sa and the decrease of up to 34.1% in m-value). Further, S broadened the ranges of pavement service temperatures by about 12 °C, whereas E almost did not change the PG grades of the binders. Finally, regarding the characteristics of viscoelastic master curves, S considerably improved the dynamic modulus and lowered the phase angle of the binders over a wide range of frequencies and temperatures but led to the failure of the time-temperature superposition principle due to its thermorheologically complex nature. Nevertheless, in this regard, the effect of E was found very mild.

Fractional Calculus Approach to Reproduce Material Viscoelastic Behavior, including the Time-Temperature Superposition Phenomenon.

The design of modern products and processes cannot prescind from the usage of viscoelastic materials that provide extreme design freedoms at relatively low cost. Correct and reliable modeling of these materials allows effective use that involves the design, maintenance, and monitoring phase and the possibility of reuse and recycling. Fractional models are becoming more and more popular in the reproduction of viscoelastic phenomena because of their capability to describe the behavior of such materials using a limited number of parameters with an acceptable accuracy over a vast range of excitation frequencies. A particularly reliable model parametrization procedure, using the poles–zeros formulation, allows researchers to considerably reduce the computational cost of the calibration process and avoid convergence issues typically occurring for rheological models. The aim of the presented work is to demonstrate that the poles–zeros identification methodology can be employed not only to identify the viscoelastic master curves but also the material parameters characterizing the time–temperature superposition phenomenon. The proposed technique, starting from the data concerning the isothermal experimental curves, makes use of the fractional derivative generalized model to reconstruct the master curves in the frequency domain and correctly identify the coefficients of the WLF function. To validate the methodology, three different viscoelastic materials have been employed, highlighting the potential of the material parameters’ global identification. Furthermore, the paper points out a further possibility to employ only a limited number of the experimental curves to feed the identification methodology and predict the complete viscoelastic material behavior.

Experimental and numerical investigation on the effect of material models of tire tread composites in rolling tire noise via coupled acoustic-structural finite element analysis

Tire noise has received enormous attention for its importance in vehicle noise, vibration, and harshness (NVH) along with noise regulation. This study demonstrates a numerical prediction of the rolling tire noises considering tread composite material models in the coupled acoustic-structural finite element analysis. The viscoelastic master curves were developed for the frequency-dependent damping in the structural vibrations of the tire. It was numerically found that the tread composites with 230.4% and 1,428% larger storage (E’) and loss moduli (E”), respectively, resulted in 1.16–9.79% louder structure-borne noises. Moreover, the elastic modulus (E) of the tread composites was proportionally related to the tire noises, suggesting that reduced elastic and viscoelastic moduli are desired for low-noise tires. This study can contribute to thoroughly understanding how the composite material properties, particularly viscoelasticity, can be designed to control structural noise and vibration in next-generation structures such as autonomous electric vehicles and urban air mobility.

An ultrasound method for characterization of viscoelastic properties in frequency domain at small deformations

Background The ultrasound technique, usually based on the transmission mode, is capable of providing the viscoelastic properties of polymers. Further techniques involving pulse-echo methods were also described in literature, but they still exhibit inaccuracies in the evaluation of the acoustic properties. Objective The manuscript focuses on an innovative approach for the characterization of the viscoelastic behavior of polymers employing the ultrasound methodology. The proposed procedure is based on the pulse-echo method in order to overcome possible inaccuracies in acoustic properties evaluation and in issues related to transmitter mode applications. Methods Starting from the pulse-echo method adopted for the acquisition, a novel formulation for data processing has been developed and described, allowing to determine the wave attenuation coefficient, in comparison to the commonly employed procedures involving ultrasound in polymers characterization, based on transmitter mode inspections. To carry out the study, a specifically designed ultrasound bench has been set up and three different polymers have been tested in the temperature range of interest. Results According to the proposed methodology, the loss factor towards the temperature is determined starting from the data acquired considering the identified attenuation coefficient and the measured sound velocities. The trustworthiness of the novel procedure has been proved comparing the obtained viscoelastic loss factor quantities to the reference master curves obtained by the standard Dynamic Mechanical Analysis characterizations carried out on the same polymer specimens. Conclusions A novel methodology involving ultrasound technology aiming to evaluate the viscoelasticity of the polymers using non-destructive approach has been developed. The results obtained are agreement with the standard viscoelastic master curves determined through the DMA.

Dynamic Modulus Characteristics of Mixtures Containing Recycled Asphalt Pavements, Warm Mix Additives, and Antistrip Agents

Abstract The utilization of reclaimed asphalt pavement (RAP) has proven to be a promising technology to solve some of the environmental issues and resource shortages in many parts of the world. The objective of this study was to investigate dynamic modulus and phase angle of surface type mixtures using two warm mix asphalt (WMA) technologies (i.e., warm mix additive E and foaming), and two liquid antistripping agents (ASAs). A total of 20 mixtures were designed and tested. Viscoelastic master curve modeling, statistical analysis, as well as continuous relaxation spectrums were conducted to obtain a better understanding of the properties of the mixtures. The results implied that RAP or WMA technologies had significant effects on mechanical performances, which should be carefully considered during mix design, but ASA agents, statistically, did not have such effects. In addition, the influence of RAP depended on WMA technology type, and the effects of ASA agents relied on aggregate and RAP source. The rheological index showed that both WMA technologies and ASA materials had negative impacts on the rheological properties of the mixtures, but the addition of RAP mitigates this impact only for mixtures containing ASA additives. Furthermore, the continuous relaxation spectrum confirmed the negative influences of WMA technologies and no obvious effects of ASA materials.

Measuring Viscoelastic Master Curves at the Nanoscale in Polymer Composites

Measuring Viscoelastic Master Curves at the Nanoscale in Polymer Composites

Impact of interfacial properties on the viscoelastic relaxation of hard–soft block copolymers using finite element analysis

Abstract

A Novel Approach to Describe the Time-Temperature Conversion among Relaxation Curves of Viscoelastic Materials.

Time and temperature, besides pressure in a lesser extent, represent the most significant variables influencing the rheological behavior of viscoelastic materials. These magnitudes are each other related through the well-known Time–Temperature Superposition (TTS) principle, which allows the master curve referred to relaxation (or creep) behavior to be derived as a material characteristic. In this work, a novel conversion law to interrelate relaxation curves at different temperatures is proposed by assuming they to be represented by statistical cumulative distribution functions of the normal or Gumbel family. The first alternative responds to physical considerations while the latter implies the fulfillment of extreme value conditions. Both distributions are used to illustrate the suitability of the model when applied to reliable derivation of the master curve of Polyvinil–Butyral (PVB) from data of experimental programs. The new approach allows not only the TTS shift factors to be estimated by a unique step, but the whole family of viscoelastic master curves to be determined for the material at any temperature. This represents a significant advance in the characterization of viscoelastic materials and, consequently, in the application of the TTS principle to practical design of viscoelastic components.

Molecular simulation of nanocolloid rheology: Viscosity, viscoelasticity, and time-concentration superposition

A particulate molecular model in which the solvent particles are considered explicitly is developed for studying the linear viscoelasticity of nanocolloidal suspensions using molecular dynamics simulations. Nanocolloidal systems of volume fractions ranging from 0.10 to 0.49 are studied. The hydrodynamics in these model systems are governed by interparticle interactions. The volume fraction dependence of the relative zero shear viscosity exhibited by this molecular model is consistent with that reported in the literature experiments and simulations. Over the range of frequencies studied, the relative dynamic viscosity values follow the same qualitative trend as that seen in the literature experiments. The time-concentration superposition (TCS) principle is successfully applied to construct the viscoelastic master curves that span nine decades of frequency in the case of the elastic modulus and more than four decades of frequency in the case of the loss modulus. The TCS principle was observed to fail at high volume fractions that are near the glass transition concentration; this finding is consistent with the literature experimental and simulation observations. The volume fraction dependence of the shift factors used in the construction of the viscoelastic master curves is in good quantitative agreement with that of the viscosity of the nanocolloidal systems. Our results demonstrate that molecular simulations in conjunction with an explicit solvent model can be used to quantitatively represent the viscosity and the viscoelastic properties of nanocolloidal suspensions. Such particulate models will be useful for studying the rheology of systems whose properties are governed by specific chemical interactions.

Dynamic viscoelasticity of silica-filled styrene-butadiene rubber/polybutadiene rubber (SBR/BR) elastomer composites

In this study, the viscoelastic master curve allowed us to explore the effect of silica filler network and bound rubber along with the strain- and temperature-dependent viscoelastic properties. It was experimentally found along with analytical modelling that the bound rubbers improve the damping properties of the elastomer composites in the low frequency range (57%) while reducing damping properties (45%) in the high frequency range. This result indicates that the damping properties can be designed by controlling the bound rubber content in the elastomer composites, which is becoming substantially important for many structural parts such as bush or tire for electric vehicles.

Laboratory evaluation of long-term aging effect on linear viscoelastic and fatigue properties of FAM mixtures

Aging is considered as one of the major factor which causes an increase in stiffness and brittleness to asphaltic mixture. This study aimed at evaluating the effect of different aging protocol on viscoelastic and fatigue properties of Fine Aggregate Matrix (FAM) which represents the finer portion (passing 2.36 mm sieve size) of asphalt concrete mixtures. To evaluate the effect of aging on viscoelastic and fatigue properties of FAM mixtures, six different long-term aging levels (6 h at 135 °C, 12 h at 135 °C, 24 h at 135 °C, 5 days at 95 °C, and 12 days at 95 °C aging on FAM loose mixture and 5 days at 85 °C on compacted FAM specimens) were considered. Linear Visco-Elastic (LVE) limit of each FAM mixtures was initially determined by conducting strain sweep test. Viscoelastic properties (|G*| and δ) and master curve shape parameters of FAM mixtures were further determined from temperature and frequency sweep test. Fatigue properties of FAM mixtures at different aging levels were evaluated using strain controlled time sweep test. Irrespective of the aging level applied to the FAM specimen, the LVE limit was found almost constant for all FAM mixtures. Viscoelastic properties (|G*| and δ) for FAM specimen aged for 24 h at 135 °C, and 12 days at 95 °C aged FAM mixtures showed similar results from the master curve plots. The fatigue properties of FAM mixtures decreased as the aging level changed from 5 days at 95 °C to higher level aging of 12 days at 95 °C. Despite of the similar viscoelastic properties, the trend observed between FAM mixtures aged 12 days at 95 °C and 24 h at 135 °C were not found to have similar fatigue properties. Findings of this study on FAM phase can be successfully used to characterize the effect of long-term aging on performance studies of FAM mixtures.

Effects of SARA fractions on low temperature properties of asphalt binders

Effects of the chemical fraction on the low temperature rheological behaviours of asphalt binders were explored in this study. Four fractions, namely saturate, aromatic, resin and asphaltene (SARA), were obtained from eleven asphalt binders by a novel column chromatography separation method. In addition, the viscoelastic master curves for binders and their subsets were characterised by dynamic shear rheometer (DSR) at high frequencies (low temperatures). The results showed that the complex modulus and phase angle of asphalt binders were closely related to the changes of SARA fractions. Moreover, low temperature properties of asphalt binders characterised by the creep stiffness modulus and m-value were measured using bending beam rheometer (BBR) test. The increases of asphaltene in asphalt binder resulted in the decreases of creep stiffness modulus of asphalt as well as m-value. Further, the glass transition temperature (Tg) of resins, asphaltenes and asphalt binders were measured by differential scanning calorimetry (DSC) test. The results showed that the Tg values of asphalt binders were mainly determined by saturates and aromatics fractions. However, the Tg values of the asphalt binder would increase with the increase of asphaltene content. Finally, significant relationships between SARA fractions and low temperature parameters of asphalt binder specimens were found and conducted using linear regression analysis, indicating that the SARA fractions would perform significant effects on the low temperature properties of asphalt binders.

Milligram Size Rheology of Molten Polymers

During laboratory practice, it is often necessary to perform rheological measurements with small specimens, mainly due to the limited availability of the investigated systems. Such a restriction occurs, for example, because the laboratory synthesis of new materials is performed on small scales, or can concern biological samples that are notoriously difficult to be extracted from living organisms. A complete rheological characterization of a viscoelastic material involves both linear and nonlinear measurements. The latter are more challenging and generally require more mass, as flow instabilities often cause material losses during the experiments. In such situations, it is crucial to perform rheological tests carefully in order to avoid experimental artifacts caused by the use of small geometries. In this paper, we indicate the drawbacks of performing linear and nonlinear rheological measurements with very small amounts of samples, and by using a well-characterized linear polystyrene, we attempt to address the challenge of obtaining reliable measurements with sample masses of the order of a milligram, in both linear and nonlinear regimes. We demonstrate that, when suitable protocols and careful running conditions are chosen, linear viscoelastic mastercurves can be obtained with good accuracy and reproducibility, working with plates as small as 3 mm in diameter and sample thickness of less than 0.2 mm. This is equivalent to polymer masses of less than 2 mg. We show also that the nonlinear start-up shear fingerprint of polymer melts can be reliably obtained with samples as small as 10 mg.

Modelling of rheological and chemical properties of asphalt binder considering SARA fraction

Modelling the rheological properties and chemical characteristics of asphalt material has been a hotspot. In this study, 20/40 and 60/80 pen grade asphalt binders named binder A and binder B were used to blend eleven binder samples. After that, a novel column chromatography was applied to collect sufficient SARA (Saturates, Aromatics, Resins and Asphaltenes). The Dynamic Shear Rheometer (DSR) test was used to develop the viscoelastic master curves for binders and their subsets. The Fourier Transform Infrared Spectroscopy (FTIR) test was conducted to identify and semi-quantitatively analyze the notable functional groups. Linear combination models were conducted between rheological model parameters and chemical components. It was found that the contents of Asphaltenes and Saturates increased, while those of Resins and Aromatics decreaed with the addition of binder A, resulting in the increased colloidal instability index (CII) values. In addition, the Saturates had constant value of phase angle, while the phase angle master curves of Aromatics and Resins showed plateau values of 80°. Resins containing more aromatic structures had a lower frequency (high temperature) value at this plateau value. Furthermore, the main findings were that ICC and ICH of Aromatics as well as ICH and ISO of Resins had significant relationships with binder A content. Statistically, several parameters such as CResins, CAsphaltenes, CII, ICC of Aromatics, ICH of Aromatics, ICH of Resins, and ISO of Resins had significant effects to develop multiple linear regression model on asphalt rheological properties.