Modulus Master Curves Research Articles

Modelling the time-dependent mechanical properties of thermoplastic and thermosetting polymers with Gumbel distribution functions

In this paper, we propose a simple modelling method that accurately describes the time-dependent viscoelastic behaviour of thermoplastic and thermosetting solid polymers. We performed short-term creep and stress relaxation tests on representative samples of three major classes of polymers: an amorphous, a semi-crystalline thermoplastic and a thermosetting polymer. Then, to investigate the relationship between the model parameters and the material composition, we also tested thermoplastic matrix composites with different plasticiser contents. From the short-term tests, master curves were constructed with the use of the time–temperature superposition principle. Then, the temperature dependence of the obtained shift factors was described using the Arrhenius model. The resulting creep compliance and relaxation modulus master curves were normalised and modelled with a two-parameter cumulative Gumbel distribution function (CDF) and its complementary distribution function (CCDF). For the creep and stress relaxation master curves, the median error of modelling was less than 16 % and 16.5 % in all cases, respectively. Furthermore, it was less than 2 % for the thermosetting polymer, making this model an excellent tool for describing the creep and stress relaxation behaviour of thermosetting systems. In the case of the plasticised composites, we found a strong relationship between the material composition and the location parameter of the Gumbel model. Based on this, we developed a method that can be used to estimate the evolution of the creep compliance curve for any arbitrary OLA content (between 0 wt% and 16 wt%) at any desired temperature (between 22 °C and 70 °C).

An efficient and robust method for evaluating the low-temperature performance of asphalt binder based on DSR testing

The BBR test has received growing concerns regarding its applicability to field studies and special materials due to the large amount of long-term aged asphalt binder used in preparing asphalt binder beams and the time-consuming beam preparation and testing process. In recent years, the application of a dynamic shear rheometer (DSR) to investigate the low-temperature performance of asphalt binder has attracted widespread attention because it uses significantly less asphalt binder for testing and allows for easy specimen preparation. The objective of this study was to develop an efficient and robust method to evaluate the low-temperature performance of asphalt binder based on DSR testing. Frequency sweep tests were performed on twelve asphalt binders at temperatures ranging from 0 to 25 °C using the 8-mm parallel plate geometry. Two conversions were applied to frequency sweep test data in order to predict the flexural creep stiffness and m-value of asphalt binder, namely the conversion from frequency domain to time domain and the conversion from shear loading to bending loading. The 1S2P1D model was employed to construct the master curves of storage modulus and loss modulus. Afterwards, the flexural creep stiffness was predicted using the shear creep compliance master curve model, which was derived from the 1S2P1D model using the inverse Laplace transform, and the Poisson’s ratio, which was assumed to be constant. It was found that the predicted values of S(60) and m(60) were comparable to the counterparts measured by the BBR, which well demonstrated the feasibility of the proposed DSR-BBR conversion method. In comparison to existing analysis methods, the proposed conversion method strictly complied with the linear viscoelastic theory, and it enabled efficient and robust predictions because the prediction model of flexural creep stiffness had the same parameters as those of the 1S2P1D model, thus avoiding multiple data fittings.

The Relationship Between Loading Frequency and Truck Speed on Asphalt Pavements

The mechanistic-empirical road pavement design methods necessitate knowledge of the dynamic modulus master curve of asphalt mixtures. This requires the designer to accurately define both the load frequency and the temperature of the pavement structure. The parameter of load frequency is of great importance in laboratory fatigue tests. However, it presents a challenge since road structures are loaded in the time domain, not the frequency domain. This complexity has prompted researchers to develop time-frequency conversion methods to estimate the corresponding frequency from the duration of traffic-induced stress or deformation pulses. Recent findings indicate that the time-frequency equivalence factor is considerably lower than previously assumed. In this study, we introduce a new four-parameter empirical RAMBO material model, derived from the Ramberg–Osgood equation, which offers parameters to determine the time-frequency equivalence factor for asphalt mixtures. The relationship between the moving wheel load velocity and the load impulse time is analysed, primarily based on experimental data and computational methods from existing literature. A method for determining the wavelength of the load impulse is proposed. The theoretical correlation indicates that a wheel load travelling at 100 km/h results in a dynamic deformation frequency of 10 Hz. However, for a strain impulse, the same speed corresponds to a much lower frequency of 3–4 Hz. This study offers a refined understanding of the time-frequency equivalence factor, which is of crucial importance for more accurate road pavement design and fatigue testing.

An alternative approach for characterization of the linear viscoelastic behavior of asphalt binders

This study aimed to develop an alternative approach to characterise the linear viscoelastic behaviour of asphalt binders. A rheogram model was firstly proposed based on the Carreau–Yasuda model; its accuracy was substantiated by high R 2 values. The dynamic shear modulus master curve model was then obtained using the relationship between the magnitude of complex viscosity and dynamic shear modulus and the two definitions of the time-temperature shift factor. Afterwards, the phase angle master curve model was derived according to the approximate Kramers–Kronig relation. The proposed approach was demonstrated to be capable of accurately characterising the linear viscoelastic behaviour of selected asphalt binders. In addition, the predicted zero shear viscosity (ZSV) could be potentially employed to evaluate the asphalt binder rutting resistance. Compared with the widely-used Christensen-Anderson-Marasteanu (CAM) model, the developed master curves models were better at constructing the phase angle master curves of selected asphalt binders.

Investigation of Dynamic Viscoelastic Asymmetric Response of PA6 Film Based on Fractional Rheological Model.

Polyamide 6 (PA6) film as a typical viscoelastic material, satisfies the time-temperature superposition (TTS), and demonstrates obvious dynamic strain amplitude and frequency correlation under dynamic load. The investigation of the dynamic mechanical behavior of PA6 film is essential to ensure the safety of these materials in practical applications. In addition, dynamic mechanical property testing under conventional experimental conditions generally focuses on the short-term mechanical performance of materials. Therefore, the dynamic viscoelasticity of PA6 film was tested using a dynamic thermo-mechanical analyzer (DMA) in this study, and the complex modulus master curve was constructed based on time-temperature superposition (TTS) to realize the accelerated characterization of long-term mechanical properties. Furthermore, according to experimentally obtained asymmetric characteristics of the Cole-Cole diagram and the loss modulus master curve of the PA6 film, the parameter distribution of the fractional Zener model and the modified fractional Zener model were compared, and the asymmetric dynamic viscoelastic response of PA6 film under different conditions was systematically investigated using these models. The results indicate that the modified fractional Zener model can truly describe the dynamic asymmetric characteristics of PA6 film, verify the feasibility and advantages of the modified fractional rheological model, and provide some theoretical guidance for exploring the tensile rheological mechanism of PA6 film.

Establishment and evaluation of dynamic viscoelasticity constitutive model for asphalt mixtures based on PCA model: Utilizing coal-based synthetic natural gas slag and phosphogypsum whisker as substitute fillers

To promote the secondary utilization of solid waste in asphalt pavement and reduce resource waste and environmental damage, the fine solid waste powder from the secondary treatment of solid waste was used as a substitute filler to prepare asphalt mixtures. To more precisely characterize the effects of filler type and substitution ratio on the dynamic viscoelastic mechanical characteristics of asphalt mixtures, the dynamic modulus test was conducted on asphalt mixtures, while the dynamic modulus master curve of asphalt mixtures was established based on the time-temperature equivalent principle and the Sigmoidal function. The improved generalized Sigmoidal (IGS) model, five-parameter fractional Zener (FFZ) model, six-parameter fractional Zener (SFZ) model and ten-parameter fractional Zener (TFZ) model were used to construct the shrinkage frequency curves of different asphalt mixtures under different constitutive relationships, whereas the applicability of the constitutive models was further evaluated by the principal component analysis (PCA) model. The research results showed that the dynamic modulus and phase angle of the mixture exhibited a similar change rule with the variation of temperature and frequency, and the use of solid waste-based fillers could effectively reduce the effect of frequency variation on the viscoelasticity of the mixture. The dynamic modulus master curve constructed by Sigmoidal function could accurately describe the functional relationship between the dynamic modulus with loading frequency and temperature, and the variation trend of dynamic modulus in a wider frequency range was flattened with the increase in frequency, and this change rule was not affected by the substitution ratio of the filler, while the use of solid waste-based filler could reduce the dependence of the mixture on the temperature. Compared to several fractional constitutive models, the IGS model exhibited a higher fitting accuracy for the dynamic viscoelasticity of several mixtures, and with the use of solid waste-based fillers, the deviation of fitting curves gradually decreased. A comparative study showed that the fractional constitutive model was difficult to accurately describe the dynamic viscoelasticity of the mixture, and the IGS model was preferred to be recommended as a calculation model to investigate the constitutive relationship on the dynamic viscoelasticity of the mixture.

Investigation on rheological properties and aging mechanism of asphalt under multiple environmental conditions

Under climatic conditions such as high temperature plus ultraviolet radiation and water, the mechanical properties of asphalt pavement will be significantly attenuated. Present research mainly focused on thermal oxidation and ultraviolet radiation aging, and there were many controversies about the effect of water on the aging performance of asphalt. In addition, the relationship between the aging behavior of asphalt under complex environments and the standard PAV test needs to be further clarified. This research comprehensively evaluated the rheological properties, microscopy, and functional group of matrix asphalt, SBS, and high viscosity modified asphalt under different climatic conditions. Compared with thermal oxidation aging, daily exposure to UV radiation can increase the aging degree of matrix and modified asphalt by about 5 % and 1.5 %, respectively. Compared with thermal oxidation aging, the presence of water and the coupling effect of UV and water can reduce the aging degree of asphalt by 3.5 % and 2.6 %, respectively. After 5 days of thermal oxidation and UV coupling, the aging degree was close to or even greater than that of the PAV experiment. Asphalt aging caused an upward shift in the complex modulus master curve, and a downward shift in the phase angle master curve of matrix asphalt and high viscosity modified asphalt. Due to the synergistic effects of hardening and polymer degradation, the phase angle master curve of SBS modified asphalt showed an upward trend in the low frequency range. Under the influence of climatic conditions, the polymer of asphalt would degrade, the particle size of the polymer phase decreased, and the brightness of fluorescent image became darker. The rich polymer phase structure of high viscosity modified asphalt enabled it to maintain excellent mechanical properties even after long-term aging.

Modeling the Fundamental Viscoelastic Properties of Polylactic Acid (PLA) and PLA/Nanocomposites in a Unified Manner.

The description of various loading types within the frame of viscoelasticity, such as creep-recovery and stress relaxation in a wide time scale, by means of the same model and similar model parameters is always an interesting topic. In the present work, a viscoelastic model that was analyzed in previous works has been utilized to describe the main standard loading types of viscoelasticity with the same set of model parameters. The relaxation function of this model includes a distribution function followed by the energy barriers that need to be overcome by the molecular domains when a stress field is applied. This distribution function attains a decisive role in the analysis and it was shown that it can be determined on the basis of the loss modulus master curve experimental results. Thereafter, requiring no additional parameters, the creep compliance, the relaxation modulus of poly-lactic acid (PLA) in a wide time scale, as well as creep-recovery at various stresses could be predicted. It was also found that by employing the distribution function associated with the PLA matrix, the creep-recovery experimental data of PLA/hybrid nanocomposites could subsequently be predicted. Therefore, the proposed analysis was shown to be a useful method to predict the material's viscoelastic response.

Study on the Application of Kramers-Kronig Relation for Polyurethane Mixture.

Polyurethane (PU) mixture, which is a new pavement mixture, exhibits different dynamic properties compared to a hot-mixed asphalt mixture (HMA). This paper analyzed whether the Kramers-Kronig (K-K) relation and thermorheologically simple properties applied to the PU mixture. Based on the results, the PU mixture exhibited thermorheologically simple properties within the test conditions. The time-temperature superposition principle (TTSP) was applicable for the PU mixture to construct a dynamic modulus master curve using the standard logistic sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak-Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The core-core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K-K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results with the test temperatures and loading frequencies. The phase angle of the PU mixture at extremely high or low test temperatures cannot be derived from the dynamic modulus data.

Investigation of the Properties of High-Viscosity Modified Asphalt Binder under Hygrothermal Environments.

High-viscosity modified asphalt binder (HVMA) is used widely as a polymer-modified binder in porous asphalt pavement because it can improve the cohesiveness of the asphalt mixture. However, because of the high voidage in the mixture, HVMA is vulnerable to aging induced by temperature, oxygen, water, sunlight, and other climatic conditions, which degrades the performance of pavement. The properties of asphalt binder are affected adversely by the effects of hygrothermal environments in megathermal and rainy areas. Therefore, it is essential to study the aging characteristics of HVMA under the influence of hygrothermal environments to promote its application as a high-viscosity modifier. A hygrothermal cycle aging test (HCAT) was designed to simulate the aging of HVMA when rainwater was kept inside of the pavement after rainfall in megathermal areas. One kind of base bitumen and three kinds of HVMA (referred to as SBS, A, and B, respectively) were selected in this study. Short-term aging tests, hygrothermal cycling aging tests, and long-term aging tests were performed on the base bitumen and three kinds of modified asphalt binder. Fourier-transform infrared spectroscopy (FTIR), thermo-gravimetric analysis (TGA), and dynamic shear rheological (DSR) tests were used to evaluate the properties of the binders on the micro and macro scales. By comparing the index variations of the four binders before and after aging, the effects of the hygrothermal environment on the properties of HVMA were studied. It was found that the effects of the hygrothermal environment expedited the decomposition of the polymer and the formation of carbonyl groups compared with the TFOT and PAV test, which TGA confirmed further. Moreover, the thermal stability of the samples was improved after HCAT. In addition, the master curves of the complex modulus showed that hygrothermal cycles made the high-temperature rutting resistance of asphalt binder increase significantly. All of the results above verified that the effect of hygrothermal cycling could accelerate the aging of HVMA and shorten its service life.

Construction and examination of temperature master curve for asphalt with different aging extents

Master curve is widely applied to assess the rheological properties of asphalt. The traditional master curve describes the variation of asphalt rheological properties with frequency. However, compared to frequency, the influence of temperature on asphalt properties is of greater concern. This study attempted to establish a method to transform the traditional master curve into temperature master curve. To this end, asphalt binder with different aging extents were prepared using aging simulation tests, and traditional complex shear modulus master curves of asphalt binder were established based on frequency sweep test. These were then transformed into temperature master curves using the established temperature-frequency equation. Furthermore, the accuracy of the temperature master curve was assessed through temperature sweep tests. The results showed that the temperature-frequency equation obtained based on Williams Landel Ferry equation effectively described the relationship between temperature and reduced frequency. The temperature master curve demonstrated good applicability for asphalt at different aging levels, with the differences between complex shear modulus values calculated by temperature master curve and the experimental values generally within 20%. The temperature master curve accurately characterized the trend of complex shear modulus with temperature. However, this accuracy and applicability were primarily focused on the mid-temperature and high-temperature ranges. The temperature master curve had obvious deficiency in predicting the complex shear modulus at low temperature. The findings provide new methods and insights into the relationship between asphalt rheological properties and temperature.

Study on the characterization method of dynamic modulus for asphalt mixture under multi-factor coupling conditions

In the actual service process of asphalt pavement, the dynamic response of the pavement structure layer is induced by vehicle loads. The dynamic modulus is a crucial parameter for analyzing the mechanical response of asphalt pavement. Due to significant influences from temperature and loading frequency on test measurements, along with its time-temperature equivalence, it becomes imperative to investigate the behavior of dynamic modulus under different temperature frequencies. Furthermore, laboratory loading modes also exert substantial effects on dynamic modulus. Employing different loading modes during measurement often leads to significantly varied stress states in specimens, yielding distinct values for dynamic modulus. Therefore, this study conducts dynamic modulus tests using direct tension, uniaxial compression, and indirect tension under five test temperatures and six loading frequencies while examining its variations under different stress states and temperature frequencies. The corresponding master curves and prediction models of dynamic modulus are derived, providing a valuable reference for predicting the dynamic modulus under wide-area test conditions. Through comparative analysis of dynamic modulus values at different stress levels, the stress level is incorporated into the master curve to establish corresponding master curves of dynamic modulus. By applying relevant theories and research on time-temperature equivalence, we obtained dynamic modulus master curves for three loading modes by fitting and analyzing dynamic modulus test data at various temperatures and loading frequencies. Combining the Sigmoid model and Williams-Landel-Ferry(WLF) equation, we derived prediction models for dynamic modulus under three loading modes. Comparative analysis of dynamic modulus values under these three loading modes allowed us to establish transformation equations for the prediction models in different loading scenarios. Finally, representative dynamic modulus values for permanent deformation in typical pavement structure layers were predicted based on laboratory test results and the derived models. The research findings presented in this paper have significant implications in eliminating the influence of loading modes on dynamic modulus predictions, establishing a unified prediction model, and providing essential parameters for predicting permanent deformation and fatigue life equivalent temperature.

Study on Viscoelastic Properties of Various Fiber-Reinforced Asphalt Binders.

This study analyzed the viscoelastic properties of asphalt binders reinforced with various fibers, such as modified asphalt binder, modified asphalt binder reinforced with lignin fibers (LFs), polyester fibers (PFs), and polypropylene fibers (PPFs), using dynamic shear rheological (DSR) testing. Then, the experiment generated data on the dynamic modulus and phase angle, which described the dynamic rheological characteristics at varying temperatures. The generalized Maxwell model was employed to select the appropriate element, and the test curve was fitted into a discrete time spectrum based on the time-temperature equivalence principle (TTSP). The master curves of the relaxation modulus and creep compliance were established to predict the relaxation and creep properties of various asphalt binders. The analysis indicated that fiber-reinforced binders offer superior resistance to high temperatures and long-term deformation, while being less sensitive to temperature and having a more significant elastic characterization. The binders reinforced with PPFs and LFs exhibited superior performance in high-temperature settings and long-term durability, respectively. On the other hand, the binder reinforced with PFs displayed exceptional high-temperature elastic properties. Additionally, based on the experimental data and corresponding discussion, it appears that the 13-element GM model is more appropriate for fitting the data.

Study of the matrix–particle interactions of polymer nanocomposites in the low‐frequency regime

AbstractIn this study, the dynamic moduli, in a wide frequency scale, of two series of polymer nanocomposites were qualitatively discussed. The dynamic mechanical analysis experimental results of polylactic acid (PLA)/silica nanocomposites, as well as PLA/graphene oxide‐carbon nanotubes hybrid nanocomposites, were employed. The study has been focused on the low‐frequency regime, estimating the terminal incline of the storage and loss modulus. In addition, the relative position of the two dynamic moduli was examined and results about the nanofiller's dispersion quality, as well as their interaction with the matrix were extracted. The consequence of nanofiller kind, loading, and distribution quality on the mechanical enhancement was thoroughly studied. In addition, the storage modulus master curves could be simulated by a model from the literature, considering the topological constraints of an entangled polymer reinforced by nanoparticles. It was shown that by adopting the linear contribution of the free and adsorbed chains to the relaxation function, the details of the master curves could be captured in the entire frequency range, quite effectively. The estimated model parameter values confirmed the analysis of the matrix–particle interactions.Highlights The SiO2 size effect on the terminal zone slope of the dynamic moduli. Successful description of the dynamic moduli by the tube reptation concept. Analysis of the physical meaning of the model parameter values. Relation between SiO2 dispersion quality and molecular motion restriction. Matrix‐particle interactions is the governing mechanism of enhancement.

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.

Application of dynamic complex stiffness modulus master curves of HMA with recycled materials in the mechanistic-empirical design of road pavement structures

The main objective of the paper is to present the possibilities and advantages of advanced methods for determining the viscoelastic properties of asphalt mixtures produced using recycled materials in individual mechanistic-empirical pavement design. The use of various types of materials in asphalt mixture production can significantly alter their functional parameters, such as the dynamic stiffness modulus. In addition, this parameter changes with the change in the temperature of the road pavement and the speed of vehicles. In order to determine the durability of the pavement structure in an informed manner and minimize the risk of error, it is necessary to investigate and describe as precisely as possible this variability in the behavior of asphalt layers as a result of changes in the properties of input materials, e.g. by the addition of recycled materials and under the influence of changes in temperature and load velocity of the pavement. The most effective approach involves the application of master curves of the dynamic complex stiffness modulus of asphalt mixture, constructed based on research results conducted at different temperatures and loading frequencies. This allows for the determination of stress and deformation states of the pavement construction under various climatic conditions, utilizing seasonal or average monthly temperatures and considering the specific characteristics of pavement operation, such as different vehicle speeds for main routes, connectors, or street intersections. The paper compares the changes in dynamic modulus master curves for different types of asphalt mixtures with and without the addition of waste or recycled materials such as reclaimed asphalt pavement (RAP), rubber from used tires, or synthetic fibres and changes impact on the estimated durability of the pavement structure due to different approaches to determining climatic conditions and movement speed.

Do different chemical and rheological properties act as effective and critical indicators for efficiency evaluation of rejuvenated bitumen?

This study investigates the impacts of rejuvenator type/dosage and the aging degree of bitumen on the chemical and rheological properties of rejuvenated bitumen, and propose critical chemo-rheological indicators for evaluating rejuvenation efficiency. Moreover, the potential connections between essential chemical and rheological indices of rejuvenator-aged bitumen blends are explored. Results indicate that chemical indices show linear relationships with rejuvenator dosage and vary depending on the rejuvenator type and aging level of bitumen. All rejuvenators can regenerate certain rheological parameters of aged bitumen to varying degrees, but cannot restore the crossover modulus (Gc). Various rheological indices exhibit different correlations with rejuvenator dosage and sensitivity degrees to the discrepancy in rejuvenator type and aging degree of bitumen. Critical chemical and rheological indicators are proposed based on their sensitivity levels to influence factors, with the aromaticity index (AI), carbonyl index (CI), and sulfoxide index (SI) as effective chemical indices and the complex modulus (G*), crossover frequency (fc), and high-temperature master curve area (AMH) as critical rheological indices for rejuvenation efficiency evaluation. The study finds that the magnitude of rejuvenation efficiency for four rejuvenators is Bio-oil > Engine-oil > Naphthenic-oil > Aromatic-oil, and the linear correlations between the critical chemical and rheological indices, together with their rejuvenation percentages, are significantly affected by the rejuvenator type and aging level of bitumen.

Effects of thermal aging level on the morphological structures, rheological properties and fatigue characteristics of high-viscosity asphalts

High-viscosity asphalt (HVA) provides excellent cracking and rutting resistance for ecological permeable pavement. However, HVA suffers from severe aging due to higher construction temperatures and rich porous structures, which limited its applications for urban sustainability. Currently there is still a lack of knowledge about the thermal aging effects and mechanisms of HVA. In this study, the effects of thermal aging on the morphological structures, rheological and fatigue properties of two HVAs (i.e. HVA-1 and HVA-2) at five aging levels via Simple Aging Test (SAT) are systematically investigated. HVA-1, characterized by loosen and coarse reticulated structures, undergoes significant structural changes during aging, whereas HVA-2, characterized by dense and fine reticulated structures, experiences fewer alterations. The changes in the modulus master curves of HVAs become more gradual after aging, indicating the reduced temperature sensitivity. Multiple stress creep recovery results reflect that two types of HVAs exhibit totally different dominance of oxidation or polymer degradation depending on aging level. Liner amplitude sweep (LAS) results based on damage mechanics analysis reveal that aging leads to an increase in the accumulated strain energy observed in stress-strain curves for both HVAs. As aging progresses, the proportion of elastic energy decreases due to polymer degradation, resulting in a reduction in fatigue life. Especially, the fatigue life of aged HVAs significantly decreases after SAT40. LAS results based on fracture mechanics analysis show that the crack length increases with aging due to polymer degradation and asphalt phase hardening. Aging effect on crack length was limited at initial stage but becomes more significant as crack extends. As aging deepens, the crack initial stage of HVAs tends to lengthen while the crack extension stage tends to shorten. Moreover, the crack growth process of HVAs follows a two-stage behavior of crack initiation and propagation under certain aging levels from the relationship between energy release rate and crack propagation rate. Overall, the thermal aging kinetics of various HVAs differ significantly in the structures, rheological and fatigue properties as aging deepens. HVA-2 with loosen and coarse structures exhibits greater aging resistance and lower temperature sensitivity than HVA-1 with dense and fine structures.

Rheological and Aging Characteristics of Polymer-Modified Asphalt with the Addition of Sulfur

Crosslinking agents, notably sulfur, are used in asphalt binder modification to facilitate chemical bonding between polymer chains and the asphalt binder. Despite some prior research indicating the benefits of sulfur crosslinking in enhancing polymer-modified asphalt’s (PMA) stability, there is a lack of comprehensive understanding regarding its impact on rheological properties and its anti-aging potential. This study addresses these gaps by thoroughly investigating the effects of varying the sulfur content (ranging from 0.03% to 0.5% by total weight of binder) on PMA’s rheological properties. The research assesses the effectiveness of sulfur in enhancing PMA’s resistance to aging using various methods, including the Glover-Rowe parameter, FTIR analysis, and the examination of the dynamic modulus and phase angle master curves. The results indicated that the addition of sulfur, particularly up to 0.3%, bumps the high-temperature performance grade by one level, and significantly improves elasticity, allowing the PMA to support heavier traffic without experiencing rutting, all while maintaining resistance to low-temperature cracking. Furthermore, PMA with sulfur demonstrated an increase in resistance to aging, reducing the aging potential by approximately 15% with the best sulfur formulation. This enhanced durability can reduce the frequency of maintenance activities, leading to cost savings, reduced roadwork emissions, and prolonged pavement life.

Validation of a Mathematical-Based Model for the Rheological Characterization of Asphalt Mixtures

Asphalt mixtures are viscoelastic materials whose behavior is highly dependent on temperature and loading frequency. The influence of these factors is described through master curves constructed at a given reference temperature based on the principle of frequency-temperature superposition. These curves are used as inputs in asphalt pavement design procedures based on mechanistic principles and related to their in-service pavement performance. This paper proposes the application of the Kramers-Kronig (K-K) relations to characterize the rheological properties of asphalt materials using a mathematical approach. Due to the complexity of the integration of the K-K relations, an approximate solution of the K–K relations was used to develop a Mathematical-Based Model to predict the master curves for the Dynamic Modulus |E*| and the Phase Angle f. This model was validated using the experimental results of two different asphalt mixtures with different characteristics. The results indicate that the model is accurate, and could be an effective approach to mathematically predict the master curves of the asphalt mixture viscoelastic properties in a wide range of temperatures and frequencies.