The interface between asphalt binder and mineral aggregate directly affects the service life of pavement because the defects and stress concentration occur more easily there. The interaction between asphalt binder and mineral aggregate is the main cause of forming the interface. This paper presents an extensive review on the test technologies and analysis methods of interfacial interaction, including molecular dynamics simulation, phase field approach, absorption tests, rheological methods and macro mechanical tests. All of the studies conducted on this topic clearly indicated that the interfacial interaction between asphalt binder and mineral aggregate is a physical-chemical process, and can be qualitatively characterized by microscopical technique (such as SEM and AFM), and also can be quantitatively evaluated by rheological methods and interfacial mechanical tests. Molecular dynamics simulation and phase field approach were also demonstrated to be effective methods to study the interfacial behavior and its mechanism.
Highway construction and development play an important supporting role in the national economic growth. The asphalt pavement is pleasant to drive on and easy to maintain, which has become the main material for road surface [1]. However, the service life is far shorter than the designed life, and there are early damages all around [2]. In the highway construction, it is an important subject to improve road performance and service life.
According to the theory of composite materials, asphalt mixture is multiphase composite material composed of asphalt, aggregate and mineral powder [3]. The structural stability is subject to framework support and interfacial adhesion. Therefore, the performance is not only influenced by the elemental material, but also associated with the interfacial behavior between different materials. The interface between asphalt and mineral aggregate refers to the interface between the asphalt phase and the mineral aggregate phase, which is a transitional thin-layer with special properties different from the matrix on both sides. The interfacial interaction between asphalt and mineral aggregate refers to the complex physical and chemical processes occurred on the interface, such as adsorption, infiltration, and diffusion. It is influenced by the material composition, surface properties, temperature and other factors, which determines the performance of asphalt mastics or asphalt mixture. Compared with aggregate, mineral powder has a large specific surface area, which is dispersed in asphalt and forms the asphalt mastics system. In the mixture, it is cemented with aggregate, and forms the asphalt mixture. Therefore, according to the different scales, the interfacial research in asphalt mixture can be divided into two grades: the interface between asphalt and aggregate, and the interface between the asphalt and mineral powder. The aggregate and the mineral powder are referred to as the mineral aggregate.
In traditional interfacial research, it performs qualitative analysis through the adsorption of the aggregate, or performs quantitative research through pull-out force test, surface energy test and so on. However, these researches fail to analyze the adhesion mechanism and influencing factors from the perspective of the interaction, and also fail to establish relationship between the interaction and the performance. The adhesion characteristics of the mastics formed by asphalt and filler have an important effect on the strength of mixture. The early studies on mastics were generally performed from the perspective of macro rheological properties, which cannot explain the interaction mechanism of asphalt mixture.
The research on the mechanism of the interfacial interaction between asphalt and mineral aggregate not only depends on the accurate evaluation of interaction ability, but also needs the help of Micro/Nano Characterization Techniques (such as SEM or AFM), or physical/chemical testing methods. However, at present, these technologies are generally used in oil extraction, and preliminarily used in road engineering. Along with the development of the computer, molecular simulation technique is becoming a research method of micro kinetics and thermodynamics, providing a method for the research on the micro-mechanism of interfacial interaction.
Through a variety of technologies such as molecular simulation, micro-characterization, and macro-mechanical analysis, from the aspects of nano, micro and macro, this research studies the mechanism and evaluation methods of interaction between asphalt and mineral aggregate, and explores the multi-scale correlation, providing theoretical basis to fully understand the interfacial behavior between materials inside the asphalt mixture.
Molecular dynamics simulation on the adsorption behavior of asphalt on the surface of mineral aggregate
There are many interfaces in asphalt mixture, and the performance of the interface directly affects the overall performance of asphalt mixture. Interface cracking is generally caused by the defect of the micromorphology. However it is difficult to directly obtain nanoscale details of the interface cracking. It is also difficult to simulate molecular interaction or capture chemical bond information through the finite element simulation technique. Therefore, the interfacial failure mechanism between asphalt and aggregate, or the interaction in micro scale, has not been clearly recognized. As a result, the researchers begin to adopt atomic modeling to study the micro mechanical behavior of materials. And molecular dynamics simulation has been recognized as an effective tool.
Application of the molecular simulation in road engineering
At present, in the field of road engineering, the researchers generally take the molecular simulation technique to study asphalt and other materials. Domestic researchers build simple models, generally taking a typical molecular to represent the asphalt material. However, actual asphalt material has complex molecular composition, and the research has certain limitation.
In the United States, Jennings and others put forward typical molecular structure in the SHRP (Strategic Highway Research Program), which can represent the complex asphalt composition [4], Pauli and others use Atomic Force Microscope (AFM) to verify the rationality of the representative molecular structure [5]. Subsequently, Zhang and Greenfield simplified the asphalt composition, and proposed several representative molecular models to represent similar chemical compositions in the asphalt material: asphaltene, colloid, Naphthene aromatics, and Polar aromatics, and they performed simulation through the molecular simulation technique. In addition, they studied the influence of adding polystyrene chains on the overall performance of asphalt (such as thermal expansion coefficient and bulk modulus). Also, they analyzed the temperature dependency of viscosity, through the relaxation time and diffusion coefficient of the components [6–8].
In addition to the simulation research on comprehensive performance of asphalt materials, the molecular dynamics method is also applied in the deicing mechanism of the asphalt pavement, the compound modification of asphalt materials, and the performance degradation of materials under the condition of light and oxygen.
Application of molecular simulation in interfacial interaction
The molecular dynamics has been successfully applied in interfacial simulation of the polymer molecular. Clancy and Mattice take molecular dynamics to study the interface and the thin layer surface of polyolefin. They obtained the theoretical values such as cohesive energy density and solubility parameter. Also they found molecular relaxation, providing a reasonable explanation for interfacial interaction between heterogeneous polymers [9]. At the film interface, the method based on the Continuum Mechanics is no longer applicable, at the same time, testing and characterization technique at submicron scale is not developed enough. Based on these problems, Deng and others take molecular simulation technique to study the performance of multilayer film materials system, and evaluate the interfacial strength and mechanical properties in a smaller scale [10].
Although the molecular simulation technique is not used that much in the research on the interfacial interaction in asphalt mixture, but the research results of the adsorption and diffusion of heavy crude oil on the soil surface with organic matters have certain reference value. Murgich and others take molecular dynamics simulation technique to calculate interaction of asphaltene and colloid on kaolin surface under vacuum, and the results show that Van Der Waals interaction has larger proportion (60% – 70%), and the Coulomb interaction has smaller proportion (20% – 30%). In addition, in the crude oil adsorption on kaolin, hydrogen bond has the contribution of 10% or less [11]. However, in the research above, it takes a single molecule to represent the component, and studies the interaction with the surface of organic peroxide. However, in actual situation, asphalt has multi-components, and each component has multi-molecule. Therefore, the mutual interference between the molecules has influence on the result of simulation, which can not be ignored. Norinaga, Andrews, He and others use the molecular dynamics method to perform multi-molecule simulation on the four components of asphalt, and calculate the indices such as mobility, diffusion coefficient, and concentration distribution. It is found that through slightly increasing the number of simulated molecules, the results can be ideal. The simulation results comply with the test results [12–14]. Therefore, it is feasible and has considerable research significance to use molecular simulation technique, build typical asphalt molecules and crystal structures, and simulate the interaction between the two.
Experimental research on the absorption behavior of asphalt binder on the surface of mineral aggregate
Experimental researches on the interaction mechanism between asphalt and mineral aggregate are generally performed from the perspective of adsorption and desorption of asphalt components, and characterize the composition migration through X-ray photoelectron spectroscopy, infrared spectral analysis technique, and so on. Curtis, Scott, Fritschy and Papirer found that polar components (e.g., asphaltenes) are more likely to be adsorbed on the surface of mineral aggregate, and Curtis found that among polar components, sulfoxide, carboxylic acid, pyridine, and phenol are the most likely to be adsorbed [15–17].
Ardebrant and Pugh found that Langmuir isotherm and Freundlich isotherm can be used to describe the adsorption of the asphalt on the surface of the mineral aggregate, and different functional groups in asphalt have different degrees of adsorption on the surface of the mineral aggregate [18]. Gonzalez and Middea found that the adsorption of asphalt on the surface of the mineral aggregate can be described through Langmuir isotherm, which complies with the monolayer adsorption hypothesis [19]. However, Acevedo and others found the asphalt composition on the surface of mineral aggregate belongs to the multilayer adsorption hypothesis, and the Freundlich isotherm is applicable to describe. The subsequent research detailed this conclusion, and it is found that asphaltene with weak aromatic compounds belongs to monolayer adsorption, and asphaltene with strong aromatic compounds belongs to multilayer adsorption [20,21]. Abudu and Goual recently found that Langmuir isotherm is more applicable for mineral aggregate with silica or alumina, and the Freundlich isotherm is more applicable for mineral aggregate with dolomite and calcite. Also, it is proved that asphaltene is the main ingredient adsorbed on the surface of the mineral aggregate, with the thickness of adsorption layer 2–3 nm [22].
Solvent molecules have a certain degree of interference on the adsorption behavior of asphalt molecules on the surface of the mineral aggregate, and the selection of suitable medium can provide more valuable conclusions. The researchers need to attach importance to reduce the effect of solvent, increasing the adsorption accuracy. Ekholm and others measured the adsorption of resin n-heptane solution on the surface of metal. It is found that resin strictly complies with the monolayer adsorption. The adsorption strength is high, and difficult to remove. However, compared with the asphaltene, the adsorption quantity is smaller. In mixed solvent, the adsorption quantity is reduced. And in toluene, the adsorption quantity is 0. In subsequent studies, it is found that the adsorption quantity of asphaltene increases along with the concentration of asphalt- toluene solution, which belongs to multilayer adsorption [23]. Goual found asphaltene can be continuously adsorbed at the interface between water and oil, and soft asphalt has saturation limitation [24]. Acevedo takes ultraviolet spectroscopy to study the adsorption of asphaltene and resin on the surface of the organic matrix (hot asphaltene) and the inorganic matrix (silica). Results show that with the toluene solution, asphaltene on the inorganic matrix surface can have monolayer or multilayer adsorption. The adsorption of resin on the surface of the silica is rare. The adsorption quantity of asphaltene on the organic surface is at least 10 times of the adsorption quantity on inorganic surface, and it is generally multilayer adsorption. After changing the solvent, it is found that the resin can have multilayer distribution on the asphaltene surface. However, the interaction between resin and asphaltene is obviously less than the interaction between asphaltene and asphaltene [16].
With the progress of science and technique, using advanced characterization technique together with adsorption and desorption tests, we can achieve more valuable conclusions. Balabin and Syunyaev use near infrared spectroscopy (NIR) to study the adsorption of petroleum asphaltene and resin on the surface of different minerals. It is found that the adsorption rate is subject to the matrix type, the adsorption rate is higher than the desorption rate, and the adsorption rate of resin is higher than the adsorption rate of asphaltene. At the same time, it proved that the NIR is applicable for evaluation [25,26]. Labrador takes ellipsometry to measure the adsorption of asphaltene on the glass surface. Asphalt film has the thickness 20 nm–300 nm, and the thickness increases along with the concentration of asphalt- toluene solution. The author thinks that the adsorption of asphaltene on the glass surface is physical action, because there are no covalent bonds and ionic bonds between components [27]. Turgman-Cohen also takes the technique to measure the thickness of the self-assembly layer. It is found that the interaction between the asphaltene and the silicone polar component is stronger, and the interaction between the asphaltene and the self-assembled monolayer component is not obvious [28]. Saraji and others use UV/VIS spectrometer to measure the adsorption of asphaltene on porous medium, and it is found that the adsorption is subject to the type of the mineral aggregate. Compared with quartz and dolomite, the calcite has larger adsorption quantity, with the thickness of adsorption layer 1.6 nm – 3.9 nm [29].
Research on the evaluation methods for the interaction between asphalt binder and mineral fillers
Evaluation methods for the interfacial interaction between asphalt and mineral fillers
(1) Rheological mechanical method
The mineral fillers are extremely small, so it is extremely difficult to directly measure the adhesion strength between asphalt and mineral fillers, from the perspective of mechanics. Therefore, the researchers often study the interfacial behavior between asphalt and mineral powder indirectly through measuring the mechanical properties of asphalt mastics under different filler-asphalt ratio.
In 1971, David systematically studied the mechanical properties of asphalt mastics. The results show that the interfacial behavior between asphalt and mineral powder has a great influence on the mechanical behavior of mastics [30]. In 2009, Wu from Harbin Institute of Technique found that the temperature, the type of asphalt, the acid-base properties of filler, and the size of fillers have significant impacts on the interaction ability [31]. Tan and Guo quantified the interfacial thickness and the degree of interaction between asphalt binder and mineral fillers by using the thermodynamics and rheological methods, respectively. They also studied the effect of fillers on the phase behavior of asphalt mastic, used surface free energy method to study the cohesion and adhesion of asphalt mastic. Multiscale results showed that the interaction dictated the adhesion property between asphalt and aggregate and further influenced the moisture damage resistance of asphalt mixtures [32–36]. Zhang et al. proposed the evaluation indicator of interaction based on the complex modulus and phase angle, and studied the effects of aggregate chemical composition on asphalt–aggregate interactions. They found that the effects of CaO are greater than SiO2 due to the stronger interaction between asphalt binder and CaO analytical reagents [37,38]. In another similar study, Miljković and Radenberg demonstrated that the interfacial interaction between the binder and the sand in the localised contact regions influenced on fracture behaviour of the bitumen emulsion mortar (BEM) mixtures [39].
(2) Microscopic test
Shao et al. from Harbin Institute of Technique are the first researches to use scanning electron microscope (SEM) to study microscopic interface of the asphalt mastics [40], and the micromorphology of asphalt mastics interface is shown in Fig. 1. Tan & Guo analyzed the mechanism of interfacial interaction between asphalt binder and mineral fillers by using the physical and chemical test methods (e.g. dynamic mechanics analysis – DMA, differential scanning calorimetry – DSC and Fourier transform infrared spectroscopy – FTIR) and micro/nano scale measurement techniques (e.g., atomic force microscope – AFM). They found that physical interaction was greater than chemical interaction and influenced significantly by the specific surface area of fillers [41]. Wang and Sha studied the micromorphology of cement emulsified asphalt interface. It is concluded that the interfacial micromorphology affects the overall performance of concrete, and cement can obviously improve the interfacial micromorphology [42].
Khattak and others take overlap shear test and scanning electron microscope to study the adhesion of different asphalt and aggregate under the condition of low temperature. The results show that adhesive strength loss under the condition of low temperature is the main reason for the damage in asphalt mixture [43]. Shinhe and others use devices such as Differential Scanning Calorimeter (DSC) to measure the adhesion between asphalt and mineral powder, and obtained the structure characteristics of the interface between asphalt and mineral aggregate [44].
Influencing factors of the interfacial interaction between asphalt binder and mineral fillers
Traditional researches on the interfacial behavior between the asphalt and mineral powder are generally performed from the perspective of asphalt mastics system. Therefore, the influencing factors of interfacial behavior are generally about the influence of materials on the performance of the mastics. Back in 1915, Richardson studied the influence of filler on the stiffness of mastics asphalt. And it is believed that the stiffness of mastics would be influenced by the geometry of filler, the interaction between fillers, and the thickness of the adsorption layer [45]. In 1932, Miller and Traxler put forward the theory that the size distribution, shape, texture, gap, and specific surface area of the filler, are important physical properties affecting the mastics [46]. In 1939, Mitchell and Lee put forward that mineral powder’s “bulk settle volume” is the important index influencing the performance of mastics [47]. Then in 1947, Rigden put forward that mineral powder’s fractional voids is a very important index influencing the performance of mastics, because it is related to the size distribution, shape, and texture. Also, he put forward the concept of critical filler concentration [48]. However, in 1998, Shashidhar and Romero found that the fractional voids failed to take some factors in to consideration, such as agglomeration, dispersion, and interaction between asphalt and filler. Thus the fractional voids need further improvement. At the same time, it is found that the maximum packing factor and the physical/chemical interaction have great impact on the interfacial performance [49].
In 1961, Kallas and Puzinauskas found the importance of filler gradation on the interaction between asphalt and mineral aggregate, and found that the interaction could provide more reasonable explanation for the observed stiffness enhancement model of asphalt mastics [50]. In 1962, Tunnicliff found the importance of the size distribution of the mineral fillers, and put forward the concept of adsorption layer (Fig. 2). He believes the surface of filler can absorb asphaltene, making the asphalt soft, improving the crack resistance [51].
In 1971, Heukelom and Wijga put forward the equation of relative viscosity, volume concentration, shear rate, and sol. He considered the interaction between mineral fillers, and put forward the sol and gel state model [52].
Relationship between the performance and the interfacial interaction between asphalt and mineral fillers
At present, the researches on the influence of interfacial behavior between asphalt and mineral powder on the performance are generally perform from the perspective of stiffness modulus of asphalt mastics. Back in 1956, Einstein established the performance (such as viscosity and modulus) enhancement model (as shown in Eq. (1)) of the asphalt mastics along with the filler volume fraction growth, and there is a linear relation between the two [53].
——Performance (such as viscosity, modulus of elasticity, and modulus of shearing) enhancement ratio;
k——Einstein coefficient;
——Filler volume fraction.
In subsequent research, it is found that this equation is only applicable when the filler volume fraction is less than 0.1, and it is not subject to the size distribution, the acid-base properties of filler, and the shape of mineral fillers. However, when the filler volume fraction is greater than 0.1, the equation is not applicable, and the specific surface area and size distribution become influential.
In 1965, based on the defect of Einstein’s equation, Thomas put forward the experience Equation with high concentration of the filler [54], as shown in Eq. (2).
where is Einstein coefficient, usually taken as 2.5. and are other enhancement coefficients, subject to the selected theory.
In many subsequent researches, the equation was tested. Shenoy found when the power of was elected, the model result and the test result have error around 10%, and when the elected power gets higher, the error gets smaller [55].
In order to overcome the defect of empirical equation, the subsequent researchers studied the semi empirical equation. In 1951, Mooney put forward semi-empirical equation as shown in Eq. (3), and the equation is appliable when the concentration of filler is high [56].
Later, Maron and Pierce put forward semi-empirical Equation appliable for wide range of concentration, shown in Eq. (4) [57].
In 1969, Halpin and others considered the influence of mineral fillers and properties of matrix materials, and put forward general semi-empirical equation, as shown in Eq. (5) [58].
In the Equation, the parameter A is subject to the Poisson’s ratio of the filler shape and matrix material, and parameter B is related to matrix modulus and filler modulus.
In 1994, based on the micro mechanical field equation and stochastic filler interaction, Ju and Chen simplified the mineral fillers into spherical fillers, and put forward two phase composite modulus prediction method which contains random elastic spherical filler distribution [59], shown in Eq. (6).
Researches on micromechanical model of asphalt mastics have many forms, mainly divided into the following three categories: (1) macro phenomenon analysis- correspondence principle; (2) based on the variation principle; (3) based on the generalized self-consistent theory. Among them, the last one is most applied, which considers the influence of interfacial behavior. In 1999, Buttlar studied the mechanical properties of asphalt mastics through the method, and thought the stiffness enhancement is caused by volume filling enhancement, physical/chemical enhancement, and filler enhancement. Using the calibration model, he calculated the thickness of adsorption layer as 20 nm–100 nm [60–63].
In 1973, Ziegel and Romanov put forward the concept of interaction, and they thought that the volume fraction of filler shall be the corrected through interaction parameter, shown in Eqs. (7) and (8).
B——Interaction parameter;
——Thickness of adsorption layer (m);
——Equivalent particle diameter (m);
Lipatov and others think the B value is subject to the filler volume fraction and it is questionable [64].
Research on the evaluation methods for the interaction between asphalt binder and mineral aggregate
At present, the development of high performance additives and the optimization of structural design provide the asphalt pavement with excellent performance. However, under the condition of complex climate and load, the asphalt pavement still has problems such as rut, crack, and aging. Under the effect of overloading, there are nonlinear structure behaviors. The classical viscoelastic mechanics is limited in the characterization of the pavement properties, such as destruction, fatigue and aging. It is necessary to perform systemic research on the interfacial characteristics, and the influence on complex viscoelastic behaviors and failure mechanism. Zhu et al. studied the meso mechanical model of the effective macro performance of the composite material with multiple inclusions and weak interfaces, and he believed that there is a state of weak interface between asphalt mastics and aggregate [65].
At present, researches on the interface between asphalt and aggregate in the asphalt mixture are mainly focused on the cohesion and adhesion performance of asphalt and aggregate (see Fig. 3). With poor adhesion, under the influence of water, temperature, and traffic load, the aggregate may be peeled off, and the performance of the mixture decreases. On the one hand, it brings in new problems, making the pavement pitted and loose. On the other hand, it makes the existing problems worse. Therefore, it is of great significance to study the interfacial behaviors between asphalt and aggregate.
At present, the research on interface behavior between asphalt and aggregate are generally performed from the perspective of adhesive and cohesive properties. It performs qualitative evaluation through the degree of adsorption, or it performs quantitative evaluation through macro mechanical test. For adhesion test, it adsorbs the asphalt on the surface of the mineral aggregate, and places the mineral aggregate into the water. It measures the adhesion of asphalt through the analysis on desorption quantity. The general test methods include boiling method, immersion method, shearing adhesion test, desorption test, surface energy method, etc.
In addition to the above-mentioned test methods, the researches also take numerical simulation for the research on the interfacial behavior between asphalt and aggregate. For example, Gong from Harbin Institute of Technique built micromorphology model of asphalt mixture. Taking the interface strength into consideration, it studies the influence of fine micromorphology on the crack resistance of interface and mastics [66].
In the traditional research, it is believed that the adhesion between asphalt and aggregate is most related to water damage resistance of the asphalt mixture. And there are not that much researches on the relation between interfacial behavior and other aspects of the performance. Ribeiro and others found that the interaction between asphalt and aggregate has effect on the mechanical properties of asphalt mixture, and the influence is subject to the composition of the aggregate [67].
Due to the significant economic advantages and environmental benefits, the warm mix regeneration technique becomes popular in the research on road. Some researches believe, when paving the regeneration asphalt pavement, warm mix technique and hot mix technique can provide similar pavement performance [68,69]. However, more researchers found that, when paving the regeneration asphalt pavement using warm mix technique, there will be problems such as water damage, rutting, temperature crack [70–72]. Although researchers have done a lot in this aspect, they somehow failed to make sure the mechanism of the performance differences. Mohajeride and others characterized the interfacial transition area between regenerated asphalt and new asphalt in the regenerated asphalt mixture, through the nano-indentation, nano-computed tomography, and optical microscope technique, and they believe the area will affect the overall mechanical properties [73]. Therefore, the research on the interfacial performance between the asphalt and the regeneration aggregate can provide theoretical basis for improving warm mix regeneration technique.
Cracking on the interface: a phase field approach
Cracking, as one of the most serious distresses in pavements, needs to be carefully studied and evaluated. The commonly seen cracks in pavements are macro-scale, while actually they are starting from the very small cracks and fracture occurs on the interface. There have been many researches in pavement cracking and recently, phase-field method has emerged as a very powerful tool to study the cracking on the interface.
Kuhn et al. discovered that the phase field can be used to analyze the brittle fracture in a continuum approach [74]. In their model, the local free energy was considered as a quadratic function and the energy caused by external loadings is neglected. In the simulation, they considered the equilibrium condition without volume forces. The numerical results showed that the proposed phase field model is capable to simulate the brittle fracture in materials with comparison to the Classic Fracture Mechanics.
The dynamic fracture has always been a problem for the materials engineers. The instable crack propagation is very hard to be depicted using the traditional fracture mechanics theory. To solve this problem, Henry et al. studied the dynamic instabilities of fracture using a classical Karma-Kessler-Levine phase field model [75]. They represented the elastic materials by the elastic displacement field and the phase field variable. Simulation results showed that, for elastic fracture, different instabilities considering the crack propagation could be captured. They also proposed that microscopic interaction should be considered for future studies.
Karma et al. numerically investigated the unsteady crack motion and branching in Mode III brittle fracture, which further approached the cracking in real materials [76].
Eastgate et al. presented a continuum fracture model by using the phase field method [77]. In their simulation, the whole mass is conservative and the phase field is proportional to the mass density. To conveniently track the interface evolution during cracking, the phase field approach smooth the original mathematical sharp interface. They current employed a two-dimensional model where Possion’s ratio is 0<n<1 and for three-dimensional expansion, the Possion’s ratio is 0<n<1/2. It is observed that for both cases, this approach can be used for asphalt and asphalt-based materials.
Schlüter et al. further considered a more complex case: the dynamic brittle [78]. They used this method mainly due to the drawbacks of a sharp interface description of cracks by some traditional approaches. Considering that the dynamic effects have a significant impact on the cracking process in the actual engineering applications, they further developed the previous quasi-brittle model by adding the dynamic coupled terms. The 2-D simulation was developed to approximately describe the cracking process by using a variational formulation and the coupled Euler-Lagrange field equations. Their results indicated that the crack nucleation due to superposition of reflected elastic waves could be simulated where the previous researches cannot.
Takaishi et al. proposed a phase field model for anti-plane shear crack growth [79]. Their work significantly advanced the researches of cracking in isotropic materials since the rarely studied mode III (torsion) cracking is modelled. Moreover, they considered the model as a gradient follow of the Francfort-Marigo type free energy where in most cases Gibbs free energy is employed. Takaishi et al.’s progress provides a new way to define the free energy formulation in the phase field model for materials cracking analysis.
Schänzel et al. evaluated the cracking in rubber-like materials using the phase-field-type fracture based on the operator split techniques [80]. The results were validated using a double-edge-notch-tension specimen. By comparing with the experimental results, it was found that phase field method can solve the cracking problems in composite materials.
Wang et al. studied the material defects and deformation at the interface based on the phase field modeling [81]. They suggested that the phase-field-crystal model can describe the atomic configurations of defects and deformation at the interface. To bridge the microscale and macroscale, the mesoscale tool coarse grained phase field models were employed to predict the microstructure evolution. Their results show that phase field model can capture the interfacial behavior while considering the chemical interactions.
Song et al. suggested that the crack tip domain was the most important region during the cracking process and therefore the corresponding mechanical loading and electric loading should be taken into consideration for ferroelectrics stress concentration analysis [82].
Levitas et al. conducted researches in the fracture in liquid using phase field modeling [83]. Their studies revealed the development of the overdriven fracture in liquid in tensile pressure wave. They further pointed out that for fracture in liquid, the gradient energy terms, which was expressed as the function of phase field variable, should not be included in the phase field equations considering the material instability. Levitas et al.’s work significantly improve the study on interfacial evolution in liquid fracture area. Especially for asphalt, it may change into the viscous liquid state at high temperature and meanwhile there still exist cavitation problems.
Xu et al. proposed a model to study the spatio-temporal growth of isotatic polystyrene crystals during isothermal crystallization. In their studies, an asymmetric double well local free energy density was employed [84].
In most studies, the crack propagation was considered as isotropic while in reality, it was generally anisotropic. To solve this problem, Abdollahi et al. suggested that the anisotropic fracture would interact with the material structure and resulted in a different crack propagation velocities between the radial cracks and the parallel ones using phase field simulation [85].
Based on the previous studies, Hou et al. systematically studied the asphalt-based materials using the phase field model from both macroscale and microscale and mainly include, Mode I cracking [86], Mixed mode cracking [87], asphalt self-healing [88], crack interaction [89], Mode II cracking [90], microscopic phase separation in asphalt [91], quasi-brittle fracture [92], and fractal analysis on asphalt mixture [93]. Hou et al.’s researches mainly analyzed the whole asphalt micro and macro structure from the energy aspect and therefore could provide a view of the whole structure evolution. Their main contributions can be summarized into two categories: 1) Analyze the asphalt microstructure from material re-arrangement view. In this case, the components of asphalt are simplified to three: asphaltene, resin and oil or four if wax is considered. Combining with Atomic Force Microscopy (AFM) experiments, the results show that phase separation will occur under certain thermal conditions and result in an uneven stress distribution. And, under certain conditions, asphalt self-healing occurs due to the phase kinetics; 2) Analyze the asphalt microstructure from crack/unbroken view. In this case, the asphalt microstructure is depicted using a phase-field variable which assumes positive one in the unbroken part and negative one in the cracked part. The non-conserved Allen-Cahn equation is adopted to evolve the whole coupled phase-elastic-field.
In all, the current researches on the interface evolution using the phase field method can be summarized into four categories:
(1) Crack propagation in interface. The phase field system will have the most conveniences in solving such problems. The double well potential function can be employed as the local free energy density and the elastic energy should be taken into consideration since it reflected the external loading conditions. Note the non-conserved Allen-Cahn equation should be used as the governing equation.
(2) Material re-arrangement at interface. The asphalt material mass is considered as conservative in this case while in most cracking analysis it is not. In this case, the conserved Cahn-Hillard equation should be used as the governing equation.
(3) Isotropic and anisotropic material problems. The asphalt materials can be considered as isotropic for simplicity only for two cases: first is pure asphalt binder and second is asphalt mixture with very fine aggregates. For other problems, the anisotropic properties need to consider using phase-field modeling.
(4) Fracture in solid and liquid. This is especially important for asphalt materials under different temperature conditions since asphalt behaves solid at low temperature and viscous liquid at high temperature. For the latter, the gradient energy needs to be removed from the total free energy function in phase field modeling.
Conclusions
Based on the analysis presented in this paper, the conclusions of the study are summarized as follows:
(1) In the area of road engineering, molecular simulation technology can be used to study the performance of asphalt binder and the interfacial behavior between asphalt binder and mineral aggregate. In the area of heavy crude oil or polymer, molecular simulation model of interface is idealistic, and its correlation with tests results needs to be studied further.
(2) The interfacial interaction between asphalt binder and mineral aggregate is a physical-chemical process. The selective adsorption of four components of asphalt binder is not only related to the physical properties of aggregate surface, but also related to the chemical composition of materials. Advanced characterization technologies can be used to study the mechanism of interfacial interaction between asphalt binder and mineral aggregate.
(3) The rheological methods can be used to evaluate the interfacial interaction between asphalt binder and mineral fillers. The image characterization, such as scanning electron microscope, can be used to observe the interfacial morphology qualitatively.
(4) Adhesion and cohesion are two imprtant factors influencing the performance of interface between asphalt binder and mineral aggregate. They are usually evaluated qualitatively by the wrapped degree, or studied quantitatively by macro mechanical tests.
(5) The phase field method can be used to study the crack propagation and material re-arrangement at interface, isotropic and anisotropic material problems and fracture in solid and liquid.
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