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.     

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.     

Measurement of viscoelastic properties of tissue-mimicking material using longitudinal wave excitation

This paper presents an experimental framework for the measurement of the viscoelastic properties of tissuemimicking material. The novelty of the presented framework is in the use of longitudinal wave excitation and the study of the longitudinal wave patterns in finite media for the measurement of the viscoelastic properties. Ultrasound is used to track the longitudinal motions inside a test block. The viscoelastic parameters of the block are then estimated by 2 methods: a wavelength measurement method and a model fitting method. Connections are also made with shear elastography. The viscoelastic parameters are estimated for several homogeneous phantom blocks. The results from the new methods are compared with the conventional rheometry results.     

Relationship between lifetime under creep and constant stress rate for polymer-matrix composites

The present article reviews two existing theoretical approaches for creep failure criteria of viscoelastic materials. One criterion is based on the continuum damage mechanics (CDM) and the other is based on the fracture mechanics extended to viscoelastic materials. Although both theoretical frameworks are based on different physical concepts, the deduced lifetime expressions turn out to be equivalent even though its parameters have different physical interpretation. It is proved that both theoretical frameworks, when extended to variable stress loading cases, imply the linear cumulative damage (LCD) law. Additionally the relationship obtained between the creep–rupture and constant stress rate until failure is very simple. Moreover this simple relationship is obtained independently by two different cumulative damage laws, which do not obey the LCD law, and by experimental evidence using published data for two different polymer-matrix composites (PMC). Finally a micromechanical model, used for creep–rupture of unidirectional composites, is extended for constant stress rate until failure to corroborate the simple relationship obtained between the creep–rupture and constant stress rate until failure.     

Fatigue resistance potential for hot mix asphalt using viscoelastic continuum damage analysis

This paper describes testing and evaluation of the fatigue resistance potential of hot‐mix asphalt mixtures using viscoelastic continuum damage analysis, which is based on dynamic modulus determination, a state‐variable approach and damage calculation. The dynamic modulus test for stiffness characterization and the direct tension test for fatigue resistance characterization were used in the testing procedure. The state‐variable approach can be used for numerical computation of a viscoelastic convolution integral. A Nelder–Mead simplex search was used in this study to determine the damage parameter of a stiffness reduction function. The fatigue resistance was evaluated as a function of loading rate, asphalt binder content, modifier (e.g. usage of hydrated lime), and temperature, and was found experimentally to have a strong dependence on these factors.     

A viscoelastic Unitary Crack-Opening strain tensor for crack width assessment in fractured concrete structures

A post-processing technique which allows computing crack width in concrete is proposed for a viscoelastic damage model. Concrete creep is modeled by means of a Kelvin–Voight cell while the damage model is that of Mazars in its local form. Due to the local damage approach, the constitutive model is regularized with respect to finite element mesh to avoid mesh dependency in the computed solution (regularization is based on fracture energy).The presented method is an extension to viscoelasticity of the approach proposed by Matallah et al. (Int. J. Numer. Anal. Methods Geomech. 34(15):1615–1633, 2010) for a purely elastic damage model. The viscoelastic Unitary Crack-Opening (UCO) strain tensor is computed accounting for evolution with time of surplus of stress related to damage; this stress is obtained from decomposition of the effective stress tensor. From UCO the normal crack width is then derived accounting for finite element characteristic length in the direction orthogonal to crack. This extension is quite natural and allows for accounting of creep impact on opening/closing of cracks in time dependent problems. A graphical interpretation of the viscoelastic UCO using Mohr’s circles is proposed and application cases together with a theoretical validation are presented to show physical consistency of computed viscoelastic UCO.     

Cooling cycle effects on low temperature cracking characteristics of asphalt concrete mixture

The effect of cooling cycles on the low temperature behavior of asphalt concrete mixtures is investigated using a recently developed acoustic emission (AE) test device. In an attempt to link the local AE response of the asphalt mixtures to the pavement global response obtained through mechanical tests, the AE-based results were validated using traditional mechanical pavement performance testing methods namely, the disk-shaped compact tension [DC(T)] test and the indirect tensile test (IDT) method. Field-aged pavement cores, which were expected to have a gradient in binder aging properties (more aging near the surface of the pavement), were collected and tested. Test results revealed that significant damage resulted from cyclic cooling, effecting the fracture energy and stress relaxation ability of the asphalt mixture. The AE results collected were consistent with the results obtained using the DC(T) and the IDT test methods. The so-called Felicity effect was observed by evaluating AE activity occurring in a sample subjected to multiple cooling cycles and an AE based healing index was introduced to evaluate the amount of healing that resulted from warming cycles. Low temperature induced microdamage was also investigated using X-ray computer micro-tomography, in an effort to better understand the physical nature of microcracking in asphalt mixtures at low temperatures and the source of AE emissions detected.     

Numerical analysis of lamb wave generation in piezoelectric composite IDT

An equivalent, single-layer model for Lamb wave generation by interdigital transducer (IDT) on composite host structures is developed. The additional complexities generally encountered while launching the surface acoustic wave (SAW) on composite structure, such as the coupling between the Lamb wave modes, the complicated nature of the electromechanical actuation etc. are considered. The model of infinite IDT is extended to deal with the finite IDT with edge discontinuities. The effect of electromechanical actuation on the wavelength shifts with respect to the passive case is investigated. The problem of electrically driven instability within the IDT is analyzed. Numerical results are reported by considering a model of the IDT integrated with the host structure, which shows that there are significant deviations from the conventional design estimates while launching a targeted mode. The proposed approach may enable one to obtain new designs in material systems and geometry that avoid mode-mixing, or to introduce it by choice.     

Influence of water and temperature on mechanical properties of selected asphalt pavements

One of the main causes of distress in asphalt pavements is water damage. The purpose of this paper is to compare different test methods to evaluate moisture susceptibility. This is of special importance because of the insufficient effectiveness of the test procedures currently used. In this research, experiments were conducted to investigate the effects of water and temperature on mechanical properties of mixtures with different, air void content. The evaluation of such properties concentrates on the following three approaches: innovative (Coaxial Shear Test), traditional, (Indirect Tensile Test) and empirical (Cantabro Test). Specimens were prepared by means of Superpave Gyratory Compactor (SGC) and divided in two different subsets for controlled dry and wet conditioned testing. Test results indicated that the Indirect Tensile Test (IDT) is not able to discriminate between wet and dry condition as the Coaxial Shear Test (CAST) does. The CAST method reproduces closest the real field conditions and indicates clearly the risk of water damage for open graded mixtures (high air void content). Dense graded mixtures (low air void content) showed less influence probably due to the reduced amount of penetrating water. Cantabro Tests (CAT) provided also significant results in good correlation with air void content and material properties of asphalt mixes.     

The use of stress sweep tests for asphalt mixtures nonlinear viscoelastic and fatigue damage responses identification

Asphaltic materials are known to present a behavior that can be approximated by the theory of viscoelasticity. For these materials it is essential to characterize fatigue damage. An important aspect therein is the separation between nonlinear viscoelastic and fatigue damage responses. This is a complex issue, since both nonlinearity and damage have a similar effect on the overall material mechanical behavior, i.e. decrease in the stiffness and increase in the phase angle. This paper presents an experimental and a mathematical procedure to separate the nonlinear viscoelastic from the fatigue damage response for asphaltic materials. Stress sweep tests were used to characterize a hot mixture asphalt at nine conditions (three temperatures and three frequencies). Once all strain values were obtained in a stress controlled sweep test, a statistical analysis was used to find the maximum stress that can be applied to the material without invoking the damage response. The results showed that the transition stress value is directly associated with material properties, the stiffness being an important factor in this result. Consequently, stress, temperature and frequency determine together the mechanical response of the material (linear or nonlinear viscoelastic, fatigue damage and/or plastic deformation). Results from this study can be associated with other fatigue damage approaches in order to better select the stress or strain amplitude that should be used in fatigue tests, and to eliminate the amount of energy that is dissipated in the nonlinear viscoelastic region.     

A multi-temporal scale approach to high cycle fatigue simulation

High cycle fatigue (HCF) is a failure mechanism that dominates the life of many engineering components and structures. Time scale associated with HCF loading is a main challenge for developing a simulation based life prediction framework using conventional FEM approach. Motivated by these challenges, the extended space–time method (XTFEM) based on the time discontinuous Galerkin formulation is proposed. For HCF life prediction, XTFEM is coupled with a two-scale continuum damage mechanics model for evaluating the fatigue damage accumulation. Direct numerical simulations of HCF are performed using the proposed methodology on a notched specimen of AISI 304L steel. It is shown the total fatigue life can be accurately predicted using the proposed simulation approach based on XTFEM. The presented computational framework can be extended for predicting the service and the residual life of structural components.     

单向复合材料横向裂纹黏弹性损伤演化模型

建立一个考虑基体黏弹性的纤维增强聚合物单向复合材料在产生横向裂纹时的损伤演化模型,有效地预测了单向复合材料横向拉伸行为。假设呈现威布尔分布的缺陷会在变形的驱动下演化为损伤,并以此为基础建立了单向复合材料横向损伤演化模型。通过此模型,时间-温度叠加原理（TTSP）得到了更具有物理基础的解释。最后,通过具体例子阐述了此模型的应用,并通过试验对模型预测结果进行了验证。本模型有效地预测了单向复合材料横向拉伸行为。由于单向复合材料横向性能存在脆性,此模型还无法准确预测失效和强度。      

Effective and recovery stresses in deformation studies of polyvinyl chloride and polypropylene using the modified strain transient dip test

Partitioning the applied stress into internal stress components (effective and recovery) using the modified strain transient dip test is a useful approach towards a better understanding of the viscoelastic nature of polymers. The internal stresses of polyvinyl chloride (PVC) and polypropylene (PP) were measured successfully using this test on a computer-controlled electro-servo hydraulic tensile testing machine which was designed for rapid step unloading in less than 1 s to avoid memory effects of the polymers. A power-law relationship can be used to describe the variation of the internal stress components with strain. Actual yield strains occurred at smaller values (less than 2%) than those obtained from a conventional stressstrain diagram (which for PVC and PP exceed 3.5% and 7%, respectively). This observation indicated that plastic yielding occurred much earlier and yield strains from conventional stress-strain diagrams may be overestimates. For very ductile material (PP) the activation volumes were comparable in magnitude to that obtained conventionally; whilst for less ductile material (PVC), the activation volume was four times higher. One of the main advantages of stress partitioning is for the detailed definition of the extrapolated yield point which otherwise will be missed out in a conventional plot of applied stress and strain.     

Aggregate distribution influence on the indirect tensile test of asphalt mixtures using the discrete element method

The purpose of this study is to investigate the effect of horizontal aggregate distribution, i.e. aggregate distribution in horizontal cross sections, on the indirect tensile (IDT) test of asphalt mixtures. An index of aggregate homogeneity, used to evaluate the aggregate distribution in a two-dimensional (2D) cross section, was comprehensively described; the horizontal aggregate distribution was evaluated by the index. A microstructure-based discrete element model for predicting the IDT test results was established by a discrete element program called particle flow code in two dimensions (PFC2D). Based on this model and by loading horizontal cross sections of asphalt mixtures along different directions, the effects of horizontal aggregate distribution on the splitting strength and maximum horizontal stress with regard to an IDT test were numerically simulated by means of the discrete element method; the obtained results were verified by performing an actual IDT test. Results reveal that the splitting strengths and maximum horizontal stresses in the IDT test exhibit anisotropy. Furthermore, it is revealed that there is an insignificant correlation between the horizontal aggregate distributions and the average splitting strengths and average maximum horizontal stresses, as well as a significant correlation between the horizontal aggregate distributions and the variations in the splitting strengths and maximum horizontal stresses.     

Estimation of piezoelastic and viscoelastic properties in laminated structures

An inverse method for material parameter estimation of elastic, piezoelectric and viscoelastic laminated plate structures is presented. The method uses a gradient based optimization technique in order to solve the inverse problem, through minimization of an error functional which expresses the difference between experimental free vibration data and corresponding numerical data produced by a finite element model. The complex modulus approach is used to model the viscoelastic material behavior, assuming hysteretic type damping. Applications that illustrate the influence of adhesive material interfaces and viscoelastic parameter identification are presented and a few simulated test cases aid the interpretation of results.     

A multiscale approach to damage configurational forces

A two-scale homogenization method is used to construct a damage model in the framework of configurational mechanics. The upscaling procedure allows for the identification of damage configurational forces as the result of the microscopic fracture analysis. The obtained damage equation incorporates stiffness degradation, material softening, unilaterality, induced anisotropy. The balance of configurational forces naturally captures a microscopic length, leading to size effects in the overall damage response. The new approach is illustrated in the case of brittle damage, for a three point bending test. Extended finite elements are used for the numerical modeling of macro-crack initiation and growth. The influence of the microscopic size on the failure initiation stress is analyzed and it is shown that this dependence follows a Hall–Petch type rule.     

Composite toughness enhancement with interlaminar reinforcement

An experimental investigation of a newly proposed through-thickness reinforcement approach aimed to increase interlaminar toughness of laminated composites is presented. The approach alters conventional methods of creating three-dimensional fiber-reinforced polymer composites in that the reinforcing element is embedded into the host laminate after it has been cured. The resulting composite is shown to possess the benefits of a uniform surface quality and consolidation of the original unreinforced laminate. This technique was found to be highly effective in suppressing the damage propagation in delamination double-cantilever beam (DCB) test samples under mode I loading conditions. Pullout testing of a single reinforcing element was carried out to understand the bridging mechanics responsible for the improved interlaminar strength of reinforced laminate and stabilization and/or arrest of delamination crack propagation. The mode I interlaminar fracture of reinforced DCB samples was modeled using two-dimensional cohesive finite-element scheme to support interpretation of the experiments.     

Development of a viscoelastic continuum damage model for cyclic loading

A previously developed spectrum model for linear viscoelastic behavior of solids is used to describe the rate-dependent damage growth of a time dependent material under cyclic loading. Through the use of the iterative solution of a special Volterra integral equation, the cyclic strain history is described. The spectrum-based model is generalized for any strain rate and any uniaxial load history to formulate the damage function. Damage evolution in the body is described through the use of a rate-type evolution law which uses a pseudo strain to express the viscoelastic constitutive equation with damage. The resulting damage function is used to formulate a residual strength model. The methodology presented is demonstrated by comparing the peak values of the computed cyclic strain history as well as the residual strength model predictions to the experimental data of a polymer matrix composite.     

Finite element cohesive fracture modeling of airport pavements at low temperatures

Low temperature cracking induced by seasonal and daily thermal cyclic loads is one of the main critical distresses in asphalt pavements. The safety of aircraft departure and landing becomes a crucial issue in runways when thermal cracks occur in airport pavements. The low-temperature fracture behavior of airport pavements was investigated using a bilinear cohesive zone model (CZM) implemented in the finite element method (FEM). Nonlinear temperature gradients of pavement structures were estimated based on national weather data and an integrated climate prediction model. Experimental tests were conducted to obtain the numerical model inputs such as viscoelastic and fracture properties of asphalt concrete using creep compliance tests, indirect tensile strength tests (IDT), and disk-shaped compact tension (DC(T)) tests. The finite element pavement fracture models could successfully predict the progressive crack behavior of asphalt pavements under the critical temperature and heavy aircraft gear loading conditions.     

Exposing the nonlinear viscoelastic behavior of asphalt-aggregate mixes

In this study asphalt-aggregate mixes are treated as both viscoelastic and viscoplastic. Following a damage mechanics approach, a nonlinear viscoelastic constitutive formulation is generated from a linear formulation by replacing ‘applied stresses’ with ‘effective viscoelastic stresses’. A non-dimensional scalar entity called ‘relative viscoelastic stiffness’ is introduced; it is defined as the ratio of applied to effective viscoelastic stress and encapsulates different types of nonlinearities. The paper proposes a computational scheme for exposing these nonlinearities by uncovering, through direct analysis of any test data, changes experienced by the ‘relative viscoelastic stiffness’. In general terms, the method is based on simultaneous application of creep and relaxation formulations while preserving the interrelationship between the corresponding time functions. The proposed scheme is demonstrated by analyzing a uniaxial tension test and a uniaxial compression test (separately). Results are presented and discussed, unveiling and contrasting the character of viscoelastic nonlinearities in both cases. A conceptual viewpoint is offered to explain the observations, illustrating the requirements from any candidate constitutive theory.