Complex Modulus Master Curves Research Articles

Study on the constitutive model of NEPE propellant based on indentation creep

AbstractThe significance of the mechanical properties of solid propellant during the curing process lies in their contribution to stress‐strain calculations of viscoelastic engineering materials and the analysis of structural integrity of solid rocket motor charges. In order to study the Constitutive equation of the nitrate ester plasticized polyether (NEPE) propellant during the curing process, indentation creep tests were carried out on the NEPE propellant, and the viscoelastic constitutive model of propellant with curing reaction at 50 °C and atmospheric pressure was studied. Firstly, based on the viscoelastic theory, the experimental principle of indentation creep test is deduced, and indentation creep tests are carried out for propellants with different curing degrees. Then, based on 2S2P1D (2 Springs, 2 Parabolic elements, 1 Dashpot) model and time‐temperature equivalence principle, the indentation test data are processed, and the complex modulus master curve of propellant with different curing degrees is established, and the influence of curing reaction on viscoelastic properties of propellant is analyzed, so as to better understand the response characteristics of propellant system during curing. The results show that the 2S2P1D model has a good fitting effect for the master curve in low frequency period, the fitting error is controlled within 10 %, and the correlation coefficients are all above 0.95. With the curing reaction, the complex modulus gradually increases, while the change rate gradually decreases. And it tends to be stable on the seventh day.

Laboratory Investigation of Storage Stability and Aging Resistance of Slightly SBS-Modified Bitumen Binders

Slightly SBS-modified bitumen binders have been applied for the asphalt concrete impermeable layer of pumped storage power stations (PSPSs) in China. However, the storage stability and aging resistance of slightly SBS-modified bitumen are big concerns. In this study, three different types of slightly SBS-modified bitumen binders were evaluated by using a commonly used virgin bitumen and a normal SBS polymer-modified bitumen as references. All of the bitumen binders were subjected to short-term and long-term aging that were simulated by using a 5 h and 24 h thin film oven test (TFOT), respectively. A Fourier transform infrared (FTIR) spectroscopy test, storage stability test, dynamic shear rheological test, stress relaxation test, and direct tensile (DT) test were carried out to obtain insight into the storage stability and aging resistance. FTIR analysis indicated that slightly SBS modified bitumen exhibited serious aging of base bitumen together with higher polymer degradation. The aging indexes obtained from the carbonyl index and the polybutadiene (PB) index can well rank the aging resistance. Slightly SBS-modified bitumen binders had excellent storage stability, and even after a long-term period of 7 days of storage, the complex modulus and phase angle remained fairly constant. The rheological master curves were constructed to investigate the effects of short-term and long-term aging. Slightly modified bitumen binders were well identified by the plateau of the phase angle master curves. The aging resistance was well distinguished by the deviation of the complex modulus master curve using unaged bitumen as a baseline. It was found that three types of slightly SBS-modified bitumen binders exhibited inconsistent aging resistance in terms of rheological aging index. The relative change of the initial instantaneous modulus and the modulus relaxation rate was able to explain the relaxation properties. With respect to the direct tensile test, the increase in stiffness modulus and the loss of ultimate tensile strain can be used to evaluate the susceptibility of bitumen aging. An attempt was made to establish the relationship of the aging index between FTIR analysis, rheological properties, and low-temperature performance. It was found that the relationship among these aging indexes was weak. In general, slightly SBS modified bitumen should be well designed to obtain good aging resistance and low-temperature performance. Highly modified bitumen is foreseen to be promising in the case of extremely low temperatures and long-term durability.

Analysis of thermal susceptibility and rheological properties of asphalt binder modified with microwave activated crumb rubber

Using crumb rubber (CR) as an asphalt modifier not only realizes the recycling of waste tire resources, but also significantly improves the asphalt pavement performance. However, crumb rubber modified asphalt (CRA) prepared by wet process has poor thermal storage stability and microwave activation is an effective way to improve thermal stability. The main purpose of this paper is to compare the temperature susceptibility and rheological characteristics of microwave-activated crumb rubber modified asphalt (MCRA) and CRA. The scanning electron microscopy (SEM) was used to characterize micro morphology of CR particles after various microwave radiation time. The frequency sweep test, multiple stress creep and recovery (MSCR) test, and linear amplitude sweep (LAS) test were conducted and Cole-Cole diagram, Black diagram as well as master curve also were used to analyze rheological properties of modified asphalt. And the modified asphalt segregation experiment and solubility were also performed to verify the improvement effect of microwave activation. The results show that microwave activation makes CR surface rough and increases its specific surface area. And the Cole-Cole diagram and Black diagram both show that CR/MCR improve the elasticity of base asphalt, and the elasticity of MCRA is lower than CRA, as well as the h value proves that the microwave activation strengthens the polymeric network of asphalt. Solubility and storage stability experiments directly demonstrate that microwave activation can promote the dissolution of CR and reduce the segregation of CR in asphalt. The phase angle master curve is more sensitive to the variation of the internal structure of CRA/MCRA than complex modulus master curve, and the plateau zone in phase angle master curve illustrates the entanglement and interaction within the modified asphalt. The addition of CR/MCR reduce the thermal sensitivity of modified asphalt, and improve high-temperature anti-rutting and medium-temperature anti-fatigue properties. Considering high temperature and fatigue characteristics, the optimal content of MCR in MCRA is 20%–25%.

Experimental characterization of the oxidative kinetic aging behavior of rejuvenated asphalt binder

• Rejuvenated binders were subjected to over-aging at various temperature and time. • The effect of temperature, duration and rejuvenator dosage on the oxidative aging mechanisms of rejuvenated binders were revealed. • Oxidative aging increased the viscoelastic behavior of rejuvenated binders while rejuvenator reduced. • The effect of rejuvenator on viscoelastic behavior of rejuvenated binders weakened gradually during oxidative aging. Rejuvenator is commonly used in reclaimed asphalt pavement (RAP) to improve the properties of the blended binder. However, the rejuvenated binder would experience aging again and cause the rejuvenated asphalt mixture prone to durability issues. This study focused on evaluating the impact of oxidative aging on the chemical and rheological properties of rejuvenated binder (RB) by means of Fourier Transform Infrared Spectroscopy and Dynamic Shear Rheometer. First, the aged binders blended with waste engine oil used as the rejuvenator at 0%, 3%, 6%, and 9% by total weight of binder. Then, laboratory oven aging procedures were employed to the RB binders at different aging temperatures and periods. Carbonyl content were determined to understand the effect of temperature and duration on the oxidative aging mechanisms of RB binders. Each RB binder had its specific fast and constant oxidative rates. With the increase of rejuvenator dosage, the temperature sensitivity of RB binders decreased in the constant rate stage and increased in the fast rate stage. The high-temperature true performance grade (HTPG) of RB binders increased with the aging time and temperature, and the effect of rejuvenator dosage on HTPG decreased gradually with aging duration. Based on the master curves of complex modulus and phase angle, the aging time and aging temperature increased the viscoelastic behavior of RB binders, and rejuvenator reduced the viscoelastic behavior, but the effect of rejuvenator lowered gradually during oxidative aging. The crossover frequency, rheological index and Cole-Cole plot demonstrated the aging decreased the viscous components and increased the elastic behavior of the RB binders. As the rejuvenator dosage increased, the viscous component of the aged RB binders increased, and the elastic behavior decreased as well as more transition behavior from viscous to elastic.

Evaluation for Low Temperature Performance of SBS Modified Asphalt by Dynamic Shear Rheometer Method

Finding an alternative or supplementary test method to evaluating the low temperature performance of asphalt is an area of considerable interest. This paper tries to explore the possibility of using the dynamic shear rheometer (DSR) method for assessing the low temperature properties of styrenebutadienestyrene (SBS) modified asphalt. In the study, 60/80 and 80/100 pen grade asphalt binders, named binder A-70, binder B-70 and binder C-90, are used to produce the SBS modified asphalt samples. After that, the low temperature performance of the asphalt binders is characterized by using bending beam rheometer (BBR) test. The results indicate that the low temperature performance of the different binders is related to the source of the binder. The low temperature performance of asphalt could be improved with the addition of the SBS. The DSR test is used to develop the complex modulus master curves for binders. Based on the principle of time–temperature conversion, the glass transition temperature of asphalt is calculated by the Williams–Landel–Ferry (WLF) equation. The glass transition temperatures (Tg) of base asphalt and the SBS modified asphalt are determined by the viscoelastic parameters of the master curve and the WLF equation coefficients based on the time–temperature superposition principle. By establishing the relationship between the critical temperature and the Tg of the asphalt binder, the effectiveness of the method established in this paper is verified. The advantage of this method is the ability to use the DSR test for the rapid evaluation of the low temperature performance of asphalt, which is able to reduce testing materials and save testing time as well. The glass transition temperature of the SBS modified asphalt is closely associated with aging degree, asphalt source and the SBS content.

Laboratory Evaluation on Performance of Recycled Asphalt Binder and Mixtures under Short-Term Aging Conditions

As asphalt materials are exposed to very high temperatures before construction, such as in the transportation stage or the storage stage, short-term aging of asphalt material occurs. At these stages, diffusion or blending between RAP (reclaimed asphalt pavement) binder and virgin binder may occur. In this study, recycled blends, incorporating SBS modified binder, RAP binder and recycling agents, were prepared with incremental RAP binders of up to 40%, and RTFO (Rolling Thin-Film Oven) tests in condition times of 300 and 600 min were conducted on the recycled blends. Characterization tests included ΔTcr, complex modulus master curve, a G-R (Glover-Rowe) parameter on recycled blends, and dynamic modulus, fracture test, and midpoint bending fatigue tests on mixtures. The ΔTcr and the G-R parameter results showed that aging time significantly affected the cracking resistance of the recycled blends. Compared to the virgin SBS modified asphalt binder, the recycled blends tended to be more sensitive to the aging process. The complex modulus master curve of binders and the dynamic modulus and phase angle results of mixtures show that the binder/mixtures appear to be stiffer with an increase in the RAP binder dosage. Generally, the low temperature cracking and fatigue cracking resistance of virgin mixtures is better than that of RAP mixtures, especially for high RAP binder dosage mixtures, and longer aging times have a negative impact on the cracking resistance of mixture. However, when we extend RTFO aging time, the higher dosage of RAP mixtures show better cracking resistance than the lower dosage of RAP mixtures. The reason for this could be that the chemical process may occur between the virgin SBS modified asphalt binder and the RAP binder at high temperatures.

Evaluation of the Response Analysis Approach Used in the Mechanistic-Empirical Pavement Design Guide

Asphalt concrete (AC) is a typical viscoelastic material exhibiting rate-dependent behavior. The rate-dependency of AC should be properly taken into consideration in pavement response analysis to accurately evaluate pavement performance and life. In the Mechanistic-Empirical Pavement Design Guide (MEPDG), the dynamic modulus master curve is used to account for the rate-dependency of the dynamic modulus of AC. However, the rate-dependent phase angle is ignored and a constant phase angle of 0 is assumed. The partial characterization of rate-dependent properties of AC in the MEPDG may lead to inaccurate results. This study compares the pavement responses computed using the MEPDG approach and the layered viscoelastic theory (LVET) which utilizes the complex modulus master curve to fully characterize the rate-dependent properties of AC. Typical three-layer pavement structures were analyzed at three temperatures (−10°C, 20°C and 50°C) and four speeds (10, 40, 80 and 120 km/h). The results show that the horizontal tensile stresses at the bottom of cement-treated base layer obtained from the two approaches are almost the same, and for other responses analyzed, the results obtained from the MEPDG approach are larger than those from the LVET approach, especially for the responses in the AC layer. The normalized difference of the vertical compressive strain at the mid-depth of the AC layer between the two approaches can be up to 100% and that for the horizontal tensile strain at the bottom of the AC layer can be more than 50%.

Establishment of Complex Modulus Master Curves Based on Generalized Sigmoidal Model for Freeze-Thaw Resistance Evaluation of Basalt Fiber-Modified Asphalt Mixtures.

This study aims to study the freeze–thaw (F–T) resistance of asphalt mixture incorporating styrene–butadiene–styrene (SBS) polymer and basalt fiber by using the established complex master curves of the generalized Sigmoidal model. Asphalt mixture samples incorporating styrene–butadiene–styrene (SBS) polymer and basalt fiber were manufactured following the Superpave gyratory compaction (SGC) method and coring as well as sawing. After 0–21 F–T cycles processing, a complex modulus test asphalt mixture specimen was performed to evaluate the influence of the F–T cycle. Besides, according to the time–temperature superposition principle, the master curves of a complex modulus were constructed to reflect the dynamic mechanical response in an extended range of reduced frequency at an arbitrary temperature. The results indicated that the elastic and viscous portions of asphalt mixture incorporating SBS and basalt fiber have decreased overall. It could be observed from the dynamic modulus ratio that the dynamic modulus ratios of specimens were more affected by the F–T cycle at low frequency or high temperature. Thus, in the process of asphalt pavement design and maintenance, attention should be paid to seasonal frozen asphalt pavement under low frequency and high temperature.

Master Curve Establishment and Complex Modulus Evaluation of SBS-Modified Asphalt Mixture Reinforced with Basalt Fiber Based on Generalized Sigmoidal Model.

Basalt fiber has been proved to be a good modified material for asphalt mixture. The performance of basalt fiber modified asphalt mixture has been widely investigated by extensive researches. However, most studies focused on ordinary static load tests, and less attention was paid to the dynamic mechanical response of asphalt mixture incorporating with basalt fiber. This paper aims to establish the master curve of complex modulus of asphalt mixture incorporating of styrene-butadiene-styrene (SBS) polymer and basalt fiber using the generalized Sigmoidal model. Both loading frequency and temperature were investigated for dynamic mechanical response of asphalt mixture with basalt fiber. In addition, based on the time-temperature superposition principle, the master curves of complex modulus were constructed to reflect the dynamic mechanical response at an extended reduced frequency range at an arbitrary temperature. Results indicated that the generalized Sigmoidal model in this paper could better reflect the dynamic mechanical response accurately with correlation coefficients above 0.97, which is utilized to predict the dynamic mechanical performances accurately. Simultaneously, the modulus values exhibit an increasing trend with loading frequency and decrease versus temperature. However, the phase angle values showed different trends with frequency and temperature.

Tridimensional linear viscoelastic properties of bituminous mixtures produced with crumb rubber added by dry process

ABSTRACT The influence of the addition of Crumb Rubber (CR) by dry process on the tridimensional linear viscoelastic properties of bituminous mixtures was studied. Advanced complex modulus tests were performed on two bituminous mixtures: a classical one used as reference material and a similar bituminous mixture with 3% of CR (in the mass of the mixture). CR with a continuous 3/6 mm grain size distribution replaced coarse aggregates. Complex modulus and complex Poisson’s ratio were determined from sinusoidal tension/compression loading tests. Experimental data were modelled with the 2S2P1D model. Results show that Time-Temperature Superposition Principle is valid for the mixture containing CR. Similar shift factors were used to obtain master curves of complex modulus and complex Poisson’s ratio of both mixtures. Lower values of norm of complex modulus at high frequencies/low temperatures were found for the mixture with CR. Curves of normalised complex modulus and complex Poisson’s ratio of both mixtures overlap.

Rheological Behavior and Its Chemical Interpretation of Crumb Rubber Modified Asphalt Containing Warm-Mix Additives

The microstructure and chemical composition of asphalt binders have a significant effect on their rheological properties and, therefore, their performance as road paving binders. This study aims to investigate the effects of warm-mix asphalt (WMA) additives, organic type and chemical type, on the rheological properties and chemical internal structure of base asphalt and crumb rubber modified asphalt (CRMA). A set of dynamic shear rheometer (DSR) tests was conducted to obtain the rheological parameters (e.g., complex viscosity, complex modulus, phase angle) of asphalt binders. The flow activation energy was calculated from Arrhenius equation based on viscosity data to rank the thermal susceptibility. Black diagrams and master curves of complex modulus and phase angle were utilized to analyze the rheological properties. The molecular weight distributions of asphalt binders were inverted from the phase angle master curve to evaluate the molecular weight characteristics. It was found that the the addition of crumb rubber into base asphalt improves the rheological properties of enhanced modulus and elasticity. Organic and chemical types of WMA additives have different chemo-physical effects on both base asphalt and CRMA. Phase angle inversion method provides a powerful tool to monitor the molecular structure change and, therefore, the chemo-physical interactions of asphalt binders induced by modifications. Finally, there is a good correlation between flow activation energy and molecular weight.

Temperature dependent dynamic mechanical properties of Magnetorheological elastomers: Experiment and modeling

Magnetorheological elastomers (MREs) are a group of smart composite materials which are composed of magnetic particles dispersed in an elastomeric matrix. The controllable dynamic properties of these materials rely on many factors, in which temperature is a significant influencing factor requiring further investigations. In this paper, the dynamic mechanical analysis (DMA) tests have been performed to determine the viscoelastic properties of MREs with different test conditions. Based on the experiment results, the dynamic properties of MREs is modelled respectively by fractional Maxwell model (FMM) and generalized Maxwell model (GMM), and then the master curve of complex modulus is constructed using the time–temperature superposition (TTS) principle. The results show that the transition behavior of the silicon rubber based MRE samples under uniaxial compression occurs at about 50 °C. The storage modulus exhibits two different trends with the temperature variation: It first decreases rapidly and then increases slightly or maintains a stable value with increasing temperature.

Investigation of Prony series model related asphalt mixture properties under different confining pressures

The objective of this paper is to investigate linear viscoelastic properties of asphalt mixtures measured under different confining pressures with respect to master curves of complex modulus, relaxation time and modulus of Prony series model. A modified collocation method is utilized to calculate the relaxation modulus of Prony series representation after the relaxation time is selected. The relaxation moduli of two asphalt mixtures under different confining pressures are compared at a wide range of reduced loading times. Finite element simulation is employed to fully investigate the effect of confining pressure on mechanical responses of asphalt pavement. The results show that the construction method of master curves of complex moduli is effective and reliable. The relaxation modulus calculated from the smoothed experimental storage and loss moduli of the same complex moduli are slightly different, and it is impossible to obtain the accurate relaxation time and modulus to well agree with the test data of storage and loss moduli simultaneously at the full range of reduced angular frequencies. As the confining pressure increases, the relaxation modulus does not always increase at the full range of reduced loading time due to the effect of phase angle. As the confining pressure increases, the tensile strains and shear strains in the asphalt layer decrease in the practical speeds of vehicular loading.

Comparisons of asphalt pavement responses computed using layer properties backcalculated from dynamic and static approaches

The falling weight deflectometer (FWD) testing is widely used as a nondestructive technique to backcalculate layer properties of in-situ asphalt pavement structures. Traditionally, static backcalculation methods based on the layered elastic theory (LET) are employed to analyze FWD data. However, the static method can not take into consideration the dynamic effects of the impulse loading generated in FWD testing, as well as the viscoelastic behaviour of asphalt concrete (AC). Therefore, the layer properties backcalculated from the static approach and the pavement responses computed using these layer properties are questionable. In this study, FWD tests were conducted on two asphalt pavements, one with a flexible base and the other with a semi-rigid base. The field FWD data were backcalculated using the traditional static approach and the dynamic approach which uses the spectral element method as the forward analysis engine. The elastic modulus of each layer was obtained from the static backcalculation, while in the dynamic backcalculation, the complex modulus master curve, which is the fundamental property of viscoelastic materials, was obtained for each AC layer, and elastic moduli were obtained for other layers. The two sets of backcalculated results were employed to analyze pavement responses to moving vehicular loading using the LET and layered viscoelastic theory, respectively. The results show that responses from the viscoelastic analyses are significantly larger than those from the elastic analyses except for the vertical strain at the asphalt treated base layer at high speeds. At a low speed of 16 km/h, most of the responses from the viscoelastic analyses are more than two times those from the elastic analyses. The results presented in this study pose a serious concern over the traditional approach in which both the backcalculation of FWD data and computation of pavement response to traffic loading are based on the LET.

Effect of HDPEH polymer on viscoelastic properties of SBS modified asphalt

Styrene-Butadiene-Styrene (SBS) is one of the polymer that has been used for enhancing asphalt binder properties. The present work discusses the combined effect of High Density Polyethylene Homo Polymer (HDPEHP) and SBS on conventional and rheological properties of viscosity grade 30 asphalt commonly used in India. Six blends of binders were prepared using varying percentages of SBS and HDPEHP. Various rheological tests were performed on unaged, short-term aged and long-term aged binders to evaluate the effect of both polymers. Use of both polymers increased the viscosity of polymer modified blends marginally when compared to unmodified binder. Comparison of complex modulus mastercurves indicated that at lower reduced frequencies, complex modulus values were higher for polymer modified blends in relation to unmodified binder. Higher elasticity was provided by addition of HDPEHP when compared to other blends. Analysis of relaxation modulus and creep compliance mastercurves indicated combination of SBS and HDPEHP offered higher resistance under creep load and strain under long term conditions. Thus, it can be concluded that addition of HDPEHP enhances viscoelastic properties of SBS modified binder.

Rheological Properties of Modified Coal Tar Pitches

AbstractDifferent modifiers composed of polyethylene glycol, paraformaldehyde, polystyrene, and polyphosphoric acid at different ratios (designated CD-0, CD-1, CD-2. CD-3, and CD-4) were added to coal tar pitch. The resulting modified pitches were prepared and designated control D-0 and D-1, D-2, D-3, and D-4, correspondingly. The objective of this study was to evaluate the properties of the control and modified coal tar pitches by the dynamic shear rheometer (DSR) test and microscopic imaging technology. The complex shear modulus G* and phase angle δ of the modified coal tar pitches decreased with increased temperature, which indicated a decline in the gradual capacity for resistance to permanent deformation at high temperatures. There was good correlation between the Christensen-Andersen-Marasteanu (CAM) model and the complex modulus master curve of the modified coal tar pitches. The test results showed that D-4 had a higher complex viscosity η* than that of the control D-0 and the other modified coal t...

The impact of Hisingerite on asphalt shear resistance

Two Marshall-designed asphalt mixtures were developed with common coarse aggregate, added filler (1% hydrated lime) and bituminous binder (5.8% acid-modified bitumen). The target aggregate grading and overall volumetrics were not significantly different. Different fine aggregate (dust sources) were used in each asphalt mixture. Dust A contained predominantly Nontronite clay minerals while 82% of the Dust B clay minerals were identified as Hisingerite. Hisingerite is a rarely encountered and poorly studied clay mineral. Specialist geotechnical interpretation of its unique properties indicated potentially adverse impact on mastic stability and asphalt shear response. This research assessed the impact of Hisingerite clay on otherwise identical asphalt mastic, as an indicator of the impact of Hisingerite-rich dust sources on asphalt performance. Six M1000 (acid-modified) bitumen samples were each used to manufacture two mastic samples, one containing each fine aggregate. The same hydrated lime was added, and all mastic samples were manufactured with constant proportions of bitumen, added filler and fine aggregate, representative of the asphalt mixture designs. Wheel tracking, resilient modulus, tensile strength and moisture resistance testing did not indicate any detrimental effects from Hisingerite-rich Dust B nor did mastic complex modulus master curves. Multiple stress creep recovery testing found the Dust B mastic to deform less than Dust A mastic under cyclic shear. This was concluded to likely reflect the lower density and higher absorption of the Dust B fine aggregate. Despite the concerning physical properties, it was concluded that the incorporation of Hisingerite-rich fine aggregate presented no risk to asphalt performance. It follows that there is no basis for additional routine testing of potential dust sources to identify Hisingerite content. This research also highlighted the importance of controlling mastic composition during testing, with further testing at a constant ‘effective’ binder volume required. Maintaining the filler dosage constant relative to the mass (or volume) of the dust (or the bitumen) must also be considered.

A consistent approach for characterising asphalt concrete based on generalised Maxwell or Kelvin model

The generalised Maxwell (GM) model and generalised Kelvin (GK) model are widely used in characterising the linear viscoelastic (LVE) properties of asphalt concrete. Traditionally, the GM and GK model coefficients are determined by fitting the analytical LVE functions to pre-smoothed storage component data. The loss component data are usually disregarded primarily due to the fact that a well-accepted loss component master curve of asphalt concrete is not available to pre-smooth the experimental results. This study shows that the results obtained from the traditional approach may not satisfy some basic LVE requirements, namely the Kronig–Kramers relation between the storage and loss components, the convolution integral relation between the relaxation modulus and creep compliance and the applicability of the same time-temperature shift factor to various LVE functions. In addition, the relationships between the viscoelastic constants and model coefficients are usually neglected in the traditional approach which may lead to inconsistent LVE functions. A new procedure was proposed in this study to determine the GM and GK model coefficients using the collocation method. The experimental results are pre-smoothed using a complex modulus master curve represented by the modified Havriliak–Negami (MHN) model and then the model coefficients are solved from either the storage or loss component collocation points. The relation between viscoelastic constants and model coefficients is satisfied by introducing an additional linear equation besides those for the collocation points. It is shown that more densely spaced time constants (typically 0.5 decades apart) are necessary to eliminate any oscillation in the loss component master curves. The results show that the proposed approach effectively correct the deficiencies associated with the traditional approach. The GM model and GK model obtained from the approach are equivalent for the same material. The new approach provides a consistent and simple way for determining the coefficients of GM and GK model for asphalt concrete.

A comparative study of the influence of shift factor equations on master curve construction

This paper evaluates the applicability of different shifting techniques for constructing complex modulus master curves using the time-temperature superposition principle (TTSP). A database of complex modulus results of unmodified bitumens, polymer modified bitumens (PMBs), bitumen-filler mastics, unaged and aged bitumens was used together with a Generalized Logistic Sigmoidal Model to assess the validity of seven different shifting approaches. Except for the Laboratoire Central des Ponts et Chaussees (LCPC) method, the construction of master curves was done using the Generalised Logistic Sigmoidal Model and non-linear least squares regression optimization with the aid of the Microsoft Excel Spreadsheet Solver function. The goodness-of-fit for the various shifting techniques and functions was assessed through graphical and statistical methods. From the study, it was found that a numerical shift approach using non-linear least squares produced the best fit between experimental and predicted data in terms of both graphical and goodness-of-fit statistics. The ranking of the other shifting techniques consisted of the LCPC approach, followed by the William, Landel and Ferry (WLF), Modified Kaelble, Viscosity Temperature Susceptibility (VTS), Arrhenius and Log-Linear methods. However, most of the equations are basically empirical and they are not expected to be strictly obeyed by any materials. Discrepancies were still evident, even for the better functions, for those materials that demonstrated a deviation from the thermorheological simplicity of the rheological behaviour as found for highly structured bitumens following high degrees of polymer modification and/or oxidative ageing.

Physical Modelling and Identification of Polymer Viscoelastic Behaviour above Glass Transition Temperature and Application to the Numerical Simulation of the Hot Embossing Process

The experimental processing parameters, such as applied pressure and forming temperature have been analysed during polymer hot embossing of micro-cavities. The viscoelastic characteristics of polymer above the glass transition temperature have been investigated with the classical viscoelastic models. Generalized Maxwell Model has been used to describe polymer behaviours in the glass transition temperature range. The parameters include relaxation time, storage modulus and loss modulus of the Generalized Maxwell Model that have been introduced. The identification of polymer characteristics has been carried out through Dynamic Mechanical Analysis (DMA). The storage modulus, the loss modulus and the damping factor of the selected polymer have been obtained with different imposed frequencies. The master curve of complex modulus has been obtained by applying the time temperature superposition principle. The experimental data has been identified with optimized fitting parameters of Generalized Maxwell Model. A proper agreement between the experimental measurement and the identification of viscoelastic model is observed. The resulting constitutive equations have been implemented in finite element software in order to achieve the numerical simulation of the hot embossing process.