Constitutive modeling of the nonlinearly viscoelastic response of asphalt binders; incorporating three-dimensional effects

A dynamic shear rheometer is again used to characterize the nonlinearly viscoelastic properties of asphalt binders at intermediate or high temperatures. In our previous work, the dynamic shear rheometer test results showed that, under certain conditions, a compressive normal force was generated in an axially constrained specimen subjected to cyclic torque histories. This normal force could not be solely attributed to the Poynting effect and was also related to the tendency of the asphalt binder to dilate when subjected to shear loads. The generated normal force changed the state of stress and interacted with the shear behavior of asphalt binder. This effect was considered to be an “interaction nonlinearity” or “three-dimensional effect.” The concept is explored further in this paper by developing a fundamental approach to modeling the observed behavior. In this approach, the octahedral shear stress is used to represent the three-dimensional stress state in Schapery’s model of nonlinearly viscoelastic behavior. The model was successfully validated for several different loading histories. These results highlight the importance of modeling the mechanical behavior of asphalt binders based on the three-dimensional stress state of the material.     

Modelling the nonlinear viscoelastic response of asphalt binders

In a recent article, Narayan et al. [Narayan, S.P.A., et al., 2012b. Nonlinear viscoelastic response of asphalt binders: experimental study of relaxation of torque and normal force in torsion. Mechanics Research Communications, 43, 66–74] recorded both torque and normal force in torsional relaxation experiments on asphalt binders. The data are three-dimensional and thus, require interpretation using three-dimensional constitutive relations. In this article, we develop such a three-dimensional nonlinear viscoelastic model for asphalt binder. The predictions of the model fit the experimental data reasonably well. While there are already some three-dimensional constitutive relations available in the literature for asphalt binders which can describe the normal forces that are developed during torsion, they do not capture the relaxation behaviour presented by Narayan et al. (2012b). This new model, however, captures most of the key features of the experimental data including the development of normal forces in torsion and the relaxation behaviour. In this respect, the new model performs considerably better than the existing models.     

Using the poker-chip test for determining the bulk modulus of asphalt binders

The properties of asphalt binders strongly influence the overall mechanical response of asphalt mixture composites. A thorough understanding of the mechanistic behavior of asphalt binders is important in order to fully and accurately characterize the behavior of the asphalt mixture. The mechanical properties of the asphalt binder, the matrix in the asphalt mixture composite, are time and temperature dependent and have a lower stiffness compared to the inclusions (aggregate particles). However, computational methods used to model the micromechanics of asphalt mixtures typically assume a constant bulk modulus or Poisson’s ratio for asphalt binders. This research investigates the time-dependence of the bulk modulus of asphalt binders. Several approaches for measuring the bulk modulus were explored and the poker-chip geometry was found to be the most suitable one. The boundary value problem for the poker-chip geometry was solved to determine the bulk modulus and Poisson’s ratio of asphalt binders as a function of time. The findings from this research improve our understanding of the viscoelastic behavior of asphaltic materials, and also guide important assumptions that are typically made during computational modeling of asphaltic materials.     

A nonlinear constitutive relationship for asphalt binders

A nonlinear constitutive relationship was developed for asphalt binders. Two binders, one polymer modified and one unmodified, were tested in shear using creep and recovery loading. Five different stress levels and four loading times were considered, to capture the response of the binders in the linear and nonlinear viscoelastic range. The creep response of the binders was successfully modeled with a nonlinear power law function. The modified superposition principle was unable to predict the recovery phase of the testing data. A nonlinear constitutive relationship composed of a nonlinear viscous part plus a linear viscoelastic part was developed. The constitutive relationships successfully predicted the binders’ response in creep and recovery. The predictions of the constitutive relationships matched accurately the response of the binders subjected to the Multiple Stress Creep and Recovery loading pattern.     

Dynamic mechanical characterization of asphalt concrete mixes with modified asphalt binders

The primary objective of this work is to characterize and compare the dynamic mechanical behavior of asphalt concrete mixes with styrene butadiene styrene (SBS) polymer and crumb rubber modified asphalt binders with the behavior of mixes with unmodified viscosity grade asphalt binders. Asphalt binders are characterized for their physical and rheological properties. Simple performance tests like dynamic modulus, dynamic and static creep tests are carried out at varying temperatures and time. Dynamic modulus master curves constructed using numerical optimization technique is used to explain the time and temperature dependency of modified and unmodified asphalt binder mixes. Creep parameters estimated through regression analysis explained the permanent deformation characteristics of asphalt concrete mixes. From the dynamic mechanical characterization studies, it is found that asphalt concrete mixes with SBS polymer modified asphalt binder showed significantly higher values of dynamic modulus and reduced rate of deformation at higher temperatures when compared to asphalt concrete mixes with crumb rubber and unmodified asphalt binders. From the concept of energy dissipation, it is found that SBS polymer modification substantially reduces the energy loss at higher temperatures. Multi-factorial analysis of variance carried out using generalized liner model showed that temperature, frequency and asphalt binder type significant influences the mechanical response of asphalt concrete mixes. The mechanical response of SBS polymer modified asphalt binders are significantly correlated with the rutting resistance of asphalt concrete mixes.     

Development of mechanomutable asphalt binders for the construction of smart pavements

A new generation of asphalt binders with mecanomutable properties has been developed, with the aim of obtaining smart materials able to adapt their mechanical performance to the real changing load conditions that occur during their service life. These materials are composed of a bituminous matrix that has been modified with magnetic particles that are able to change the mechanical behavior of the binder when they are activated by a magnetic field. This study examines the main variables that govern the mechanical behavior of these materials. The mechanomutable performance of different binders has been demonstrated under various concentrations of magnetic particles. In particular, these binders could increase their stiffness and perform elastically when they are activated by a magnetic field (even at high temperatures), which, once removed, enables the initial properties of the binders to be recovered. The changes induced in the properties of the binder depend on the amount of magnetic particles, the intensity of the magnetic field, and the type of bituminous matrix. The findings open up the possibility of a wide field of applications for its implementation in smart infrastructures, with special interest in the construction, rehabilitation, and maintenance of asphalt pavements.     

Development of a stress-mode sensitive viscoelastic constitutive relationship for asphalt concrete: experimental and numerical modeling

Asphalt binder is responsible for the thermo-viscoelastic mechanical behavior of asphalt concrete. Upon application of pure compressive stress to an asphalt concrete specimen, the stress is transferred by mechanisms such as aggregate interlock and the adhesion/cohesion properties of asphalt mastic. In the pure tensile stress mode, aggregate interlock plays a limited role in stress transfer, and the mastic phase plays the dominant role through its adhesive/cohesive and viscoelastic properties. Under actual combined loading patterns, any coordinate direction may experience different stress modes; therefore, the mechanical behavior is not the same in the different directions and the asphalt specimen behaves as an anisotropic material. The present study developed an anisotropic nonlinear viscoelastic constitutive relationship that is sensitive to the tension/compression stress mode by extending Schapery’s nonlinear viscoelastic model. The proposed constitutive relationship was implemented in Abaqus using a user material (UMAT) subroutine in an implicit scheme. Uniaxial compression and indirect tension (IDT) testing were used to characterize the viscoelastic properties of the bituminous materials and to calibrate and validate the proposed constitutive relationship. Compressive and tensile creep compliances were calculated using uniaxial compression, as well as IDT test results, for different creep-recovery loading patterns at intermediate temperature. The results showed that both tensile creep compliance and its rate were greater than those of compression. The calculated deflections based on these IDT test simulations were compared with experimental measurements and were deemed acceptable. This suggests that the proposed viscoelastic constitutive relationship correctly demonstrates the viscoelastic response and is more accurate for analysis of asphalt concrete in the laboratory or in situ.     

Linking asphalt binder fatigue to asphalt mixture fatigue performance using viscoelastic continuum damage modeling

Fatigue cracking is a major form of distress in asphalt pavements. Asphalt binder is the weakest asphalt concrete constituent and, thus, plays a critical role in determining the fatigue resistance of pavements. Therefore, the ability to characterize and model the inherent fatigue performance of an asphalt binder is a necessary first step to design mixtures and pavements that are not susceptible to premature fatigue failure. The simplified viscoelastic continuum damage (S-VECD) model has been used successfully by researchers to predict the damage evolution in asphalt mixtures for various traffic and climatic conditions using limited uniaxial test data. In this study, the S-VECD model, developed for asphalt mixtures, is adapted for asphalt binders tested under cyclic torsion in a dynamic shear rheometer. Derivation of the model framework is presented. The model is verified by producing damage characteristic curves that are both temperature- and loading history-independent based on time sweep tests, given that the effects of plasticity and adhesion loss on the material behavior are minimal. The applicability of the S-VECD model to the accelerated loading that is inherent of the linear amplitude sweep test is demonstrated, which reveals reasonable performance predictions, but with some loss in accuracy compared to time sweep tests due to the confounding effects of nonlinearity imposed by the high strain amplitudes included in the test. The asphalt binder S-VECD model is validated through comparisons to asphalt mixture S-VECD model results derived from cyclic direct tension tests and Accelerated Loading Facility performance tests. The results demonstrate good agreement between the asphalt binder and mixture test results and pavement performance, indicating that the developed model framework is able to capture the asphalt binder’s contribution to mixture fatigue and pavement fatigue cracking performance.     

Study on viscosity of conventional and polymer modified asphalt binders in steady and dynamic shear domain

This study focuses on evaluating the flow behavior of conventional and polymer modified asphalt binders in steady- and dynamic-shear domain, for a temperature range of 20–70 °C, using a Dynamic Shear Rheometer (DSR). Steady-shear viscosity and frequency sweep tests were carried out on two conventional (VG 10 and VG 30) and two polymer (SBS and EVA) modified asphalt binders. Applicability of the Cox–Merz principle was evaluated and complex viscosity master curves were analyzed at five different reference temperatures. Cross model was used to simulate the complex viscosity master curves at different temperatures.It was found that asphalt binders exhibited shear-thinning behavior at all the test temperatures. The critical shear rate increased with increase in temperature and was found to be lowest for plastomeric modified asphalt binder. The Cox–Merz principle was found to be valid in the zero-shear viscosity (ZSV) domain and deviated at higher frequency/shear rate for all the binders. Results from the study indicated that the ratio of ZSV can be successfully used as shift factors for construction of master curves at different reference temperatures. Cross model was found to be suitable in simulating the complex viscosity master curves at all the test temperatures. Analysis of model parameters indicated that a strong relationship exists between ZSV and the critical shear rate. ZSV and critical shear rate varied exponentially with temperature. This relationship was used to propose a simple equation for assessing the shift factors for construction of master curves.     

Linear and nonlinear viscoelastic and viscoplastic analysis of asphalt binders with warm mix asphalt additives

Warm-Mix Asphalt (WMA) is a widely used product, which proved a contribution to the reduction in asphalt mixing and compaction temperatures. This reduction leads to lower fuel consumption and smoke emission in asphalt plants. Most of the characterisation of binders used in WMA has focused in the past on measuring linear viscoelastic properties and associated Superpave parameters. Several studies have shown that the average stresses and strains of the asphalt mixture remain mostly within the linear viscoelastic response. However, localised strains in the binder phase of the mixture could reach values high enough to induce nonlinear viscoelastic and viscoplastic deformations. Therefore, this study focuses on an experimental and analytical evaluation of linear, nonlinear viscoelastic and viscoplastic responses of selected binders modified for use in WMA. The first part of the paper analyses the linear viscoelastic material properties and their ability to evaluate permanent deformation resistance. Then, the non-recoverable creep compliance parameter obtained from the Multiple Stress Creep Recovery (MSCR) test is analysed to assess the nonlinear response and permanent deformation of asphalt binders. The paper utilises a nonlinear plasto-viscoelastic (NPVE) approach to assess and quantify the nonlinear plasto-viscoelastic response of binders by separating the recoverable and irrecoverable strains measured in the MSCR test. Two WMA additives were included in this study by mixing them with polymer-modified and unmodified asphalt binders. Analysis of results showed that the NPVE approach captured a higher percentage of recovery than the NLVE approach. However, binder’s performance evaluation and ranking did not change by adopting the NPVE approach. The nonlinear viscoelastic parameters provided insight on the behaviour of asphalt binders mixed with WMA additives during loading cycles. Sasobit showed higher influence than Advera on binders in resisting permanent deformation by increasing the recoverable strain during the unloading phase.     

Investigating the Fundamental Effects of Binders on Pharmaceutical Tablet Performance

For solid dosage forms, a better understanding of the fundamental properties of the binders helps in developing better formulations and products. The objective of this study was to determine the effects of binder toughness and plastic flow on tablet hardness, friability, and capping. The characteristic of binder toughness was determined, and the correlation between the ejection force of the tablet and the toughness of the binder was established. Evaluation was conducted using acetaminophen tablets with different kinds of binders (i.e., hydroxypropylcellulose, methylcellulose [MC], povidone [PVP], starch, etc.). A rotary tablet press was used for tableting at three different speeds. The properties of binders and acetaminophen tablets were determined using a diametral compression test. The toughness was measured as the curve of the area under the load versus deflection. The microbehavior of these binders was also studied. The acetaminophen tablets with the binders were subjected to predetermined loads and then examined under a scanning electron microscope. The tablets that contained hydroxypropylcellulose as a binder showed the highest toughness and had the lowest ejection force. The ejection force of tablets decreased with increasing concentrations of hydroxypropylcellulose in the dosage forms. The tablets that contained other binders failed by capping and random cracking in the middle. These results show that hydroxypropylcellulose, a thermoplastic polymer, provides the best physical characteristics for the tablets. This effect could help in improving tablet manufacturing conditions (e.g., compression force and speed).     

Investigating the Fundamental Effects of Binders on Pharmaceutical Tablet Performance

For solid dosage forms, a better understanding of the fundamental properties of the binders helps in developing better formulations and products. The objective of this study was to determine the effects of binder toughness and plastic flow on tablet hardness, friability, and capping. The characteristic of binder toughness was determined, and the correlation between the ejection force of the tablet and the toughness of the binder was established. Evaluation was conducted using acetaminophen tablets with different kinds of binders (i.e., hydroxypropylcellulose, methylcellulose [MC], povidone [PVP], starch, etc.). A rotary tablet press was used for tableting at three different speeds. The properties of binders and acetaminophen tablets were determined using a diametral compression test. The toughness was measured as the curve of the area under the load versus deflection. The microbehavior of these binders was also studied. The acetaminophen tablets with the binders were subjected to predetermined loads and then examined under a scanning electron microscope. The tablets that contained hydroxypropylcellulose as a binder showed the highest toughness and had the lowest ejection force. The ejection force of tablets decreased with increasing concentrations of hydroxypropylcellulose in the dosage forms. The tablets that contained other binders failed by capping and random cracking in the middle. These results show that hydroxypropylcellulose, a thermoplastic polymer, provides the best physical characteristics for the tablets. This effect could help in improving tablet manufacturing conditions (e.g., compression force and speed).     

基于拟力法的钢支撑非线性滞回行为模拟

钢支撑在轴力作用下会同时发生材料非线性和几何非线性,复杂的力与变形关系是数值模拟过程中的重点与难点。该文基于拟力法的基本理论,提出了支撑非线性滞回行为的计算模型,通过塑性转动铰来模拟由屈曲行为引起的塑性弯曲变形;通过滑动铰来模拟由拉伸屈服和增长效应产生的轴向塑性伸长行为,模型中计及了弹性弯曲变形本身的几何非线性行为。该模型物理意义简单、力学行为明确,在模拟支撑非线性滞回行为的过程中保持初始刚度不变,塑性铰的变形可直观地衡量支撑的屈曲程度。数值模拟与试验结果对比验证了该方法的精确性与适用性。将该模型应用于某钢框架-支撑结构地震反应分析中,计算结果表明:该方法可以模拟支撑在复杂荷载作用下的非线性行为,具备拟力法所特有的精确、高效及稳定等优点。     

Rheological characterisation of modified binders at mixing and compaction temperature

The mixing temperature for binders is normally chosen by the pavement engineer based on a specific ‘viscosity’ required during hot mix asphalt production. Majority of the unmodified binders exhibit Newtonian behaviour at the mixing temperature and hence the determination of the same is straight-forward. However, when modified binders are used, experiments using a rotational viscometer indicate that the binder exhibits viscoelastic non-Newtonian fluid characteristic even at very high temperature. Consequently, the ‘viscosity’ varies with time and the location where it is measured, and hence is not a unique property of the material. In this work, a thermodynamically consistent, frame-invariant viscoelastic non-Newtonian fluid model was developed to characterise the rheological properties of the binders tested in a rotational viscometer. In the investigation reported here, two types of modified binders, polymer and crumb rubber, and one unmodified binder were used. These binders were subjected to steady and variable shear rate experiments in a rotational viscometer. The viscoelastic non-Newtonian model developed was able to predict reasonably the response of binders subjected to various protocols. In addition, bituminous mixtures were fabricated at different mixing and compaction temperatures using these binders, and the evolution of volumetric properties was investigated. The experimental investigation on mixtures showed that for identical aggregate gradation, the apparent viscosity of the binders played a critical role on the final volumetric properties obtained.     

Effects of recycled asphalt pavements on the fatigue life of asphalt under different strain levels and loading frequencies

Fatigue lives of Hot Mix Asphalt (HMA) and binder have been studied separately for a long time. However, fatigue lives of HMA containing Recycled Asphalt Pavement (RAP) and the binder extracted from the same HMA containing RAP have not been studied yet. This study examines the effects of RAP, loading frequency and strain level on the fatigue lives of asphalt mixtures and binders. In addition, the relationship between the fatigue lives of asphalt mixture and binder is determined. Beam fatigue tests were conducted to determine the fatigue behaviors of two asphalt mixtures: one with 35% RAP and the other without RAP. To evaluate binder’s fatigue behavior, binders were extracted and recovered from these two mixtures. Then, fatigue lives of these two binders were determined using time sweep and Linear Amplitude Sweep (LAS) tests. Results show that presence of RAP in mixture causes a decrease in the mixture’s fatigue life, whereas it causes an increase in the fatigue life of binder. As expected, an increase in loading frequency results in an increase in the fatigue lives of asphalt mixture as well as binder. In addition, increase in strain level causes a decrease in the fatigue lives of both mixtures and binders. Fatigue lives of binders from time sweep and LAS tests show a good correlation with the mixture’s fatigue life by the beam fatigue test.     

The use of natural rubber latex as a renewable and sustainable modifier of asphalt binder

Natural rubber (NR) powder as a bio-modifier of asphalt binder has been shown to have some beneficial effects. However, there is limited research into the use of the liquid form of NR, i.e. concentrated NR latex, as an asphalt binder modifier. Compared to NR powder, NR latex is cheaper and more accessible in some countries, and potentially creates viscosity-reducing foams in the modified binder during mixture production. In this research, asphalt binders modified with different amount of NR latex were systematically studied, including the rotational viscosities, rutting resistance, fatigue resistance, low-temperature behaviour and temperature sensitivity. The dispersion of the NR latex in the modified binders was examined using fluorescence microscope and atomic force microscope. Test results indicate that the addition of NR latex increases the viscosity and elastic recovery of the modified binders and potentially enhances asphalt pavements’ resistance to rutting, thermal cracking and fatigue damage. The NR latex also reduces the temperature sensitivity of the modified binders. The optimum NR latex content was found to be 7% of the total mass of the modified binder. A network of extensive microstructures mixed with bubbles was identified in the modified binders under heat. As a renewable and sustainable material, NR latex has the potential to be used as an effective asphalt modifier.     

考虑水-温循环的SBS改性沥青复数剪切模量预估模型

为探寻季节性冻土区多次水-温循环后沥青胶结料特征官能团变化与复数剪切模量之间的关系,联合FTIR和动态剪切流变（DSR）试验,对经0、3、6、9、12、15和18次水-温循环后的苯乙烯-丁二烯-苯乙烯嵌段共聚物（SBS）改性沥青进行测试,探明了多次水-温循环下SBS改性沥青复数剪切模量和特征官能团的变化规律;采用灰色关联熵分析理论数学模型,明确了复数剪切模量与特征官能团含量变化的关联程度;基于麦夸特法和通用全局优化算法对不同温度和频率下DSR测试的SBS改性沥青复数剪切模量G*及FTIR测试官能团变化指数进行多元统计回归分析,提出了SBS改性沥青复数剪切模量的预估模型。结果表明:多次水-温循环使沥青发生了水-温老化,但SBS改性剂对沥青水-温老化具有抑制作用;随着水-温循环次数的增加,沥青FTIR图谱中亚砜基与羰基呈现出明显的增大趋势;SBS改性沥青特征官能团变化对复数剪切模量影响程度由大到小的排序为脂肪族化物 > 非对称脂肪族化物 > 芳香族化合物 > SBS含量（苯乙烯+丁二烯） > 亚砜基 > 羰基;多次水-温循环后SBS改性沥青复数剪切模量随着特征官能团含量变化呈现出多元线性关系。      

Fatigue and healing performance assessment of asphalt binder from rheological and chemical characteristics

The fatigue and healing performance of asphalt binder affect the durability of asphalt concrete and by extension, asphalt pavements. The objectives of this paper are to (1) estimate the fatigue and healing characteristics of asphalt binder by newly developed linear amplitude sweep (LAS) and LAS-based Healing (LASH) protocols, and (2) investigate the relationship between chemical composition of asphalt and engineering performance. Three neat asphalt binders (Pen-30, Pen-50 and Pen-70) and one SBS modified binder are selected for this study. Experimental results indicate that the SBS binder has advanced fatigue resistance among all tested binders and the softer neat binder with a higher penetration grade generally displays better fatigue performance. The fatigue failure occurrence is a significant threshold for healing potential comparison. The rate of healing (H^R) results suggest that the best healing potential is with Pen-70 binder in pre-failure conditions followed by the SBS binder, Pen-50 and Pen-30 binders. However, the SBS binder presents better healing performance than Pen-70 binder in post-failure condition. Further solvency fractionation, into saturates, aromatics, resins and asphaltenes, indicates that the asphaltene content is negatively proportional to the quantified binder fatigue life whereas the H^R index is found to be well correlated to the weight percents of saturates and ratio of saturates to aromatics (S/Ar). The combined use of LAS and LASH tests is recommended for effectively distinguishing and designing the fatigue-healing performance of neat and modified asphalt binders. Limiting the contents of asphaltenes would be of help to improve the binder fatigue resistance and either saturates percent or S/Ar parameter should be considered to assure the self-healing potential of asphalt binder.     

针刺C/C-SiC复合材料剪切非线性本构关系

为研究针刺C/C-SiC复合材料的剪切损伤行为,首先,进行了面内剪切加卸载实验,并利用SEM对复合材料的剪切破坏形貌进行了观测;然后,建立了一种塑性与损伤相结合的非线性本构模型描述复合材料的非线性力学行为,以幂函数描述等效塑性应变与等效应力的关系;最后,基于剪切强度的Weibull分布规律提出了一种指数型损伤变量表征剪切刚度的退化,并通过实验数据拟合得到模型中的参数。结果表明:复合材料在卸载后存在明显的残余应变,卸载模量随载荷的增加不断降低,表现出明显的剪切非线性特征;大量无纬布纤维束和纤维单丝拔出,且易在针刺部位发生破坏;由于针刺部位等缺陷的不规律分布,剪切强度存在一定的分散性,符合指数型Weibull统计分布规律;复合材料的剪切非线性主要由基体开裂和纤维/基体界面脱粘等内部损伤引起,从宏观上可以解释为塑性变形和刚度性能折减。所得结论表明本构模型能够很好地表征C/C-SiC复合材料的面内剪切非线性行为。