Viscoplastic response and modeling of asphalt-aggregate mixes

The strain response of asphalt-aggregate mixes to applied stresses is decomposed additively into a viscoelastic part and a viscoplastic part. The paper focuses on the response and modeling of the viscoplastic component; it includes the development of a multiaxial constitutive formulation that is capable of generating: (i) strain hardening when the loading is applied in one direction; (ii) strain softening immediately after stress reversals; (iii) volumetric changes under uniaxial conditions or isotropic conditions, or both; and (iv) directional non-symmetry. In order to investigate the model’s capabilities, four tests were performed sequentially on one asphalt sample. The tests were limited to pre-peak conditions and one temperature and consisted of creep and recovery sequences in uniaxial tension, uniaxial compression, isotropic compression and uniaxial tension-compression. Analysis of the results showed that the new theory, once calibrated, was able to adequately reproduce the viscoplastic strain component; its forecastability, however, was found limited.     

Predicting the tensile relaxation modulus of asphalt mixes based on the mix design and environmental factors

The main objective of this study was to predict the tensile relaxation modulus of asphalt mixes, without having to perform the common relaxation modulus tests, by developing a predictive model based on the mix characteristics, ageing condition, temperature and loading time. To this end, cylindrical asphalt mixture specimens containing crushed stone aggregates with 60/70 penetration asphalt binder were fabricated using two aggregate gradations, two binder contents, two air void levels and three ageing conditions with four replicates. Uniaxial tensile relaxation modulus tests were conducted on the specimens at four temperatures using the trapezoidal loading pattern at a low level of strain. Tensile relaxation modulus master curves of all the experimental combinations were constructed by the sigmoidal model. Statistical analysis of variance and regression analysis was performed on the test data and a predictive model was developed. Finally, the predictive model was verified using a group of measured values other than those used for the development of the model, and it was found that the predicted values correlated well with the measured ones.     

A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete

An existing viscoelastic constitutive model which accounts for the effects of rate-dependent damage growth is described and applied successfully to characterize the uniaxial stress, constant strain rate behavior of asphalt concrete. The special case of an elastic continuum damage model with multiaxial loading, which is based upon thermodynamics of irreversible processes with internal state variables, is first reviewed and then it is shown how this model has been extended to a corresponding viscoelastic damage model through the use of an elastic-viscoelastic correspondence principle. The general mathematical model is next specialized to uniaxial loading. A rate-type evolution law, similar in form to a crack growth law for a viscoelastic medium, is adopted for describing the damage growth within the body. Results from laboratory tests of uniaxial specimens under axial tension at different strain rates are then shown to be consistent with the theory. The discussion of data analysis describes the specific procedure used here to obtain the material parameters in the constitutive model for uniaxial loading and how the method may be generalized for multiaxial loading.     

Effect of waste plastic bottles on the stiffness and fatigue properties of modified asphalt mixes

Nowadays, the use of recycled waste materials as modifier additives in asphalt mixes could have several economic and environmental benefits. The main purpose of this research was to investigate the effect of waste plastic bottles (Polyethylene Terephthalate (PET)) on the stiffness and specially fatigue properties of asphalt mixes at two different temperatures of 5 and 20 °C. Likewise, the effect of PET was compared to styrene butadiene styrene (SBS) which is a conventional polymer additive which has been vastly used to modify asphalt mixes. Different PET contents (2–10% by weight of bitumen) were added directly to mixture as the method of dry process. Then the resilient modulus and fatigue tests were performed on cylindrical specimens with indirect tensile loading procedure. Overall, the mix stiffness reduced by increasing the PET content. Although stiffness of asphalt mix initially increased by adding lower amount of PET. Based on the results of resilient modulus test, the stiffness of PET modified mix was acceptable and warranted the proper deformation characteristics of these mixes at heavy loading conditions. At both temperatures, PET improved the fatigue behavior of studied mixes. PET modified mixes revealed comparable stiffness and fatigue behavior to SBS at 20 °C. However, at 5 °C the fatigue life of SBS modified mixes was to some extent higher than that of PET modified ones especially at higher strain levels of 200 microstrain.     

Damage characterization and modeling of a 7075-T651 aluminum plate

In this paper, the damage-induced anisotropy arising from material microstructure heterogeneities at two different length scales was characterized and modeled for a wrought aluminum alloy. Experiments were performed on a 7075-T651 aluminum alloy plate using sub-standard tensile specimens in three different orientations with respect to the rolling direction. Scanning electron microscopy was employed to characterize the stereology of the final damage state in terms of cracked and or debonded particles. A physically motivated internal state variable continuum model was used to predict fracture by incorporating material microstructural features. The continuum model showed good comparisons to the experimental data by capturing the damage-induced anisotropic material response. Estimations of the mechanical stress–strain response, material damage histories, and final failure were numerically calculated and experimentally validated thus demonstrating that the final failure state was strongly dependent on the constituent particle morphology.     

Fatigue behavior and modeling of short fiber reinforced polymer composites including anisotropy and temperature effects

Effects of anisotropy and temperature on cyclic deformation and fatigue behavior of two short glass fiber reinforced polymer composites were investigated. Fatigue tests were conducted under fully-reversed (R = −1) and positive stress ratios (R = 0.1 and 0.3) with specimens of different thicknesses, different fiber orientations, and at temperatures of −40 °C, 23 °C, and 125 °C. In samples with 90° fiber orientation angle, considerable effect of thickness on fatigue strength was observed. Effect of mold flow direction was significant at all temperatures and stress ratios and the Tsai–Hill criterion was used to predict off-axis fatigue strengths. Temperature also greatly influenced fatigue strength and a shift factor of Arrhenius type was developed to correlate fatigue data at various temperatures, independent of the mold flow direction and stress ratio. Micromechanisms of fatigue failure at different temperatures were also investigated. Good correlations between fatigue strength and tensile strength were obtained and a method for obtaining strain–life curves from load-controlled fatigue test data is presented. A fatigue life estimation model is also presented which correlates data for different temperatures, fiber orientations, and stress ratios.     

Effect of aggregate shape on the mechanical properties of a simple concrete

The influence of aggregate shape on the fracture energy, tensile strength and elasticity modulus in concrete is considered. For this purpose, eight simple cement-based composites were designed, manufactured and tested, with two purposes: to provide experimental data that can throw some light on this involved problem and help in the design of future cement-based composites, and supply information that can be used as a benchmark for checking numerical models of concrete failure, as this simple composite is amenable to being modelled quite easily. Thirty-six notched beams were tested and values of the fracture energy and elasticity modulus were recorded. The tensile strength was measured from indirect standard tensile tests. Comparison with available experimental data is also included and discussed. Fracture was modelled using a cohesive crack with a bilinear softening function; data of the softening function inferred from the experimental measurements are also provided and discussed.     

Creep and drying shrinkage characteristics of concrete produced with coarse recycled concrete aggregate

Laboratory tests are performed to investigate the effects of a new method of mixture proportioning on the creep and shrinkage characteristics of concrete made with recycled concrete aggregate (RCA). In this method, RCA is treated as a two component composite material consisting of residual mortar and natural aggregate; accordingly, when proportioning the concrete mixture, the relative amount and properties of each component are individually considered. The test variables include the mixture proportioning method, and the aggregate type. The results show that the amounts of creep and shrinkage in concretes made with coarse RCA, and proportioned by the new method, are comparable to, or even lower than, those in similar concretes made entirely with natural aggregates. Furthermore, it is demonstrated that by applying the proposed “residual mortar factor” to the existing ACI and CEB methods for calculating creep or shrinkage of conventional concrete, these methods could be also applied to predict the creep and shrinkage of RCA-concrete.     

The effects of heterogeneity and anisotropy on the size effect in cracked polycrystalline films

A model is developed for quantifying the size effect due to heterogeneity and anisotropy in polycrystalline films. The Monte Carlo finite element calculations predict the average and standard deviation of the microscopic (local) stress intensity factors and energy release rate of a crack in a columnar aggregate of randomly orientated, perfectly bonded, orthotropic crystals (grains) under plane deformation. The boundary of the near-tip region is subjected to displacement boundary conditions associated with a macroscopic (far field or nominal) Mode-I stress intensity factor and average elastic constants calculated for the uncracked film with a large number of grains. The average and standard deviation of the microscopic stress intensity factors and energy release rate, normalized with respect to the macroscopic parameters, are presented as functions of the number of grains within the near-tip region, and the parameters that quantify the level of crystalline anisotropy. It is shown that for a given level of anisotropy, as long as the crack tip is surrounded by at least ten grains, then the expected value and standard deviation of the crack tip parameters are insensitive to the number of crystals. For selected values of crystalline anisotropy, the probability distributions of Mode-I stress intensity factor and stress ahead of the crack are also presented. The results suggest that the size effect due to heterogeneity and anisotropy is weak; crack initiation load and direction are governed only by the details of the grains in the immediate vicinity of the crack tip. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling the damage evolution due to second-phase particle fragmentation and decohesion in an Al alloy

Summary In some Al alloys, the damage observed is often associated with fragmentation and decohesion of hard particles. A non-uniform angular distribution of particles can induce an anisotropic damage evolution with respect to the strain paths. A model is-proposed based on a 3D FE simulation of the growth of cavities associated with fragmentation or decohesion. It is shown that the growth increases approximately linearly with strain, and exponentially with triaxiality. A simple phenomenological model is proposed based on the FE results, and makes use of the initial damage value as well as the initial angular distribution of particles. The predicted results are compared with experimental ones.     

Numerical computation in the viscoelastoplastic continuum damage of hot mix asphalt concrete

The objective of this paper is to develop an accurate and advanced material characterization of hot mix asphalt concrete using an existing viscoelastoplastic constitutive model that accounts for rate of loading, temperature and stress state with growing damage. The modelling strategy of viscoelastoplastic continuum damage is based on modelling strain components separately and then combining the resulting models to obtain a final integrated viscoelastoplastic model. According to this model, the initial-boundary value problem is numerically solved using the constitutive relationship expressed in the convolution integral form. The model is successful in predicting responses up to localization when microcracks start to coalesce.     

Computations of permeability tensor coefficients and anisotropy of asphalt concrete based on microstructure simulation of fluid flow

Asphalt concrete is the most widely used material for building the surface layer of pavements. It is a porous material that consists of a non-uniform arrangement of asphalt binder, aggregate particles and air voids. One of the primary factors controlling pavement performance is the fluid flow characteristics within the surface asphalt concrete layer.

This paper focuses on the numerical simulation of fluid flow in the three-dimensional (3-D) microstructure of asphalt concrete, and the calculation of permeability from the flow field. The asphalt concrete microstructure was captured using the non-destructive X-ray computed tomography (CT) technique. X-ray CT images were processed in order to identify and retain interconnected air voids and eliminate isolated voids. This image processing enhanced the efficiency of the model as it does not have to solve for flow in isolated voids that do not contribute to fluid flow. The X-ray CT images were analyzed and the results were used to determine the relationship between air void distribution and permeability directional distribution or anisotropy.

The computed permeability values were found to have good correlation with the experimental measurements. The major and minor principal directions of the permeability tensor were found to correspond to the horizontal and vertical directions, respectively. The results indicated that the non-uniform spatial distribution of air voids created more open flow paths in the horizontal directional than the vertical direction, and hence was the much higher permeability in the horizontal directions.     

An experimental study on the hazard assessment and mechanical properties of porous concrete utilizing coal bottom ash coarse aggregate in Korea

This study evaluates quality properties and toxicity of coal bottom ash coarse aggregate and analyzes mechanical properties of porous concrete depending on mixing rates of coal bottom ash. As a result, soundness and resistance to abrasion of coal bottom ash coarse aggregate were satisfied according to the standard of coarse aggregate for concrete. To satisfy the standard pertaining to chloride content, the coarse aggregates have to be washed more than twice. In regards to the result of leaching test for coal bottom ash coarse aggregate and porous concrete produced with these coarse aggregates, it was satisfied with the environment criteria. As the mixing rate of coal bottom ash increased, influence of void ratio and permeability coefficient was very little, but compressive and flexural strength decreased. When coal bottom ash was mixed over 40%, strength decreased sharply (compressive strength: by 11.7–27.1%, flexural strength: by maximum 26.4%). Also, as the mixing rate of coal bottom ash increased, it was confirmed that test specimens were destroyed by aggregate fracture more than binder fracture and interface fracture. To utilize coal bottom ash in large quantities, it is thought that an improvement method in regards to strength has to be discussed such as incorporation of reinforcing materials and improvement of aggregate hardness.     

Three-dimensional numerical modeling of the damage mechanism of amorphous polymer network

The objective of this work is to numerically study the damage mechanism of amorphous polymer network. A molecular polymerization algorithm is employed to generate three-dimensional (3D) amorphous polymer network, in which the entanglement and sliding points are considered. Using 3D network model and finite element method, we obtained the stress–stretch relations of the polymer network and the evolution of molecular chains with deformation. Also, the damage behavior of amorphous polymer network is investigated and discussed in detail, including the nucleation, growth and coalescence of “void” like damage and the formation of craze.     

Micromechanical modeling of damage and fracture of unidirectional fiber reinforced composites: A review

An overview of methods of the mathematical modeling of deformation, damage and fracture in fiber reinforced composites is presented. The models are classified into five main groups: shear lag-based, analytical models, fiber bundle model and its generalizations, fracture mechanics based and continuum damage mechanics based models and numerical continuum mechanical models. Advantages, limitations and perspectives of different approaches to the simulation of deformation, damage and fracture of fiber reinforced composites are analyzed.     

Coupled damage tensors and weakest link theory for the description of crack induced anisotropy in concrete

Crack induced anisotropy in concrete is modeled within the general framework of damage mechanics. The damage state, formulated by using the effective stresses, is described by two second order tensors for direct and for induced cracks, respectively. These variables are deduced from different causes of deterioration by the generalized weakest link theory. The major contributions of this paper are the development of a failure criterion in multiaxial compression loading, and the definition of a projection method for assessing the effects of an initial oriented damage in any loading direction. The model is applied to the numerical analysis of concrete structures and the results are compared to available experimental data.     

Analytical modeling and experimental study of tensile strength of asphalt concrete composite at low temperatures

In this study, analytical modeling of the tensile strength of hot-mix asphalt (HMA) mixtures at low temperatures was developed. To do this, HMA mixtures were treated as a two-phase composite material with aggregates (coarse and fine) dispersed in an asphalt mastic matrix. A two-phase composite model, which was similar to Papanicolaou and Bakos's [J. Reinforced Plast. Compos. 11 (1992) 104] model with a particle embedded in an infinite matrix, was proposed. Unlike Papanicolaou and Bakos's model, an axial stress was introduced to the fiber end to consider the load transferred from the asphalt mastic the aggregate. Efforts were also made to consider the effect of aggregate gradation, asphalt mastic degradation, and interfacial damage between the aggregates and asphalt mastic matrix on the tensile strength of the HMA mixtures. Experimental investigations were conducted to validate the developed theoretical relations. A reasonable agreement was found between the predicted tensile strength and the experimental results at low temperatures. Parameters affecting the tensile strength of asphalt mixtures were discussed based on the calculated results.     

Buckling analyses of viscoelastic structures considering ageing and damage effects

The durability of structures made of composite materials is affected by diverse factors, among which creep deformation, ageing and damage. Ageing is related to elapsed time (with different effects in different environmental conditions); damage is related to microstructural modifications due stress and/or strain inputs.The formal definition of these effects and the corresponding constitutive formulations are presented. These formulations are used to obtain analytical solutions and also to implement a Finite Element programme for viscoelastic analysis of laminar structures in a large displacement with small strains context. Then, the effects of ageing and damage on both the short and the long term stability of beam columns are analyzed. Some examples for verification of the formulation and for the comparison of effect are presented.