Discrete fracture modeling of asphalt concrete

A heterogeneous fracture approach is presented for modeling asphalt concrete that is composed of solid inclusions and a viscous matrix, and is subjected to mode-I loading in the fracture test configuration. A heterogeneous fracture model, based on the discrete element method (DEM), is developed to investigate various fracture toughening mechanisms of asphalt materials using a high-resolution image processing technique. An energy-based bilinear cohesive zone model is used to model the crack initiation and propagation of materials, and is implemented as a user-defined model within the discrete element method. Experimental fracture tests are performed to investigate various fracture behavior of asphalt concrete and obtain material input parameters for numerical models. Also, bulk material properties are necessary for each material phase for heterogeneous numerical models; these properties are determined by uniaxial complex modulus tests and indirect tensile strength tests. The main objective of this study is to integrate the experimental tests and numerical models in order to better understand the fracture mechanisms of asphaltic heterogeneous materials. Experimental results and numerical simulations are compared at different test conditions with excellent agreement. The heterogeneous DEM fracture modeling approach has the potential capability to understand various crack mechanisms of quasi-brittle materials.     

Fractal effect and anisotropic constitutive model for concrete

An elasto-anisotropic damage constitutive model for concrete is developed in this work. Disregarding the coupling between the isotropic and the anisotropic damage, the isotropic damage variables are defined as functions of the microcrack fractal dimension, and the anisotropic parts are expressed by the lengths of cracks in concrete which various in different directions. The Helmholtz free energy is decomposed into the elastic deforming, damage and irreversible deforming components, with the last component used to replace the plastic deformation. Therefore the damage constitutive formulas for concrete are derived based on continuum damage mechanics. Evolution laws for both isotropic and anisotropic damage variables are derived, in which the anisotropic parts are obtained by modifying an empirical model. The critical fracture stress and the fracture toughness are investigated for materials with a single fractal crack based on the fractal geometry and the Griffith fracture criterion. Numerical computation is conducted for concrete under the uniaxial and the biaxial compression. The results indicate that the material stiffness degradation can be well addressed when the anisotropic damage is incorporated; the irreversible deformation is greatly related to the behavior of the descending branch beyond the peak load. The validation of the presented model is proofed by comparing results with the experimental data. This model provides an approach to link the macro properties of a material with its micro-structure change.     

Strain strengthening effects in Witwatersrand quartzite

A series of uniaxial compression specimens were tested over a range of applied ram displacement rates of 8.9 × 10⁻⁴ to 8.9 mm/sec to elucidate the effects of loading rate on the uniaxial compressive fracture stress of Witwatersrand quartzite. It was demonstrated that even within standard loading rate ranges, considerable scatter in the fracture strength (under uniaxial compression) existed in this particular quartzite rock. Nevertheless, a definite trend of increasing fracture resistance with increasing monotonic loading rate was evident inasmuch that increasing the loading rate (strain rate) by four orders of magnitude increase the fracture strength by almost 2.8 times. Prior fatigue loading also produced a significant strain strengthening as the uniaxial compressive fracture stress tended to increase in a sigmoidal fashion with increasing number of fatigue cycles prior to testing. Indeed, the fracture strength of quartzite was almost doubled in value after 10⁻ cycles. Plane strain fracture toughness tests utilising three point bend specimens were conducted and an average of K_lc = 1.7 MPa√m was realized. In both the uniaxial compression tests and the fracture toughness tests, failure occurred by crack extension predominantly by a transgranular flat cleavage-like mode through pure quartzite (silica) regions. However, crack extension was also observed to occur in an intergranular “ductile-like” mode through areas associated with inclusions prevalent in the quartzite.     

Effect of Randomness of Interfacial Properties on Fracture Behavior of Concrete Under Uniaxial Tension

Interfacial transition zones(ITZs) between aggregates and mortar are the weakest parts in concrete. The random aggregate generation and packing algorithm was utilized to create a two-phase concrete model, and the zero-thickness cohesive elements with different normal distribution parameters were used to model the ITZs with random mechanical properties. A number of uniaxial tension-induced fracture simulations were carried out, and the effects of the random parameters on the fracture behavior of concrete were statistically analyzed. The results show that, different from the dissipated fracture energy, the peak load of concrete does not always obey a normal distribution, when the elastic stiffness, tensile strength, or fracture energy of ITZs is normally distributed. The tensile strength of the ITZs has a significant effect on the fracture behavior of concrete, and its large standard deviation leads to obvious diversity of the fracture path in both location and shape.     

一种基于材料细观特征量的PBX拉伸强度理论模型

为给塑性黏结炸药(PBX)的力学强度设计提供支撑、探索材料细观特征量与材料强度之间的定量规律,应用微裂纹扩展区理论,将PBX炸药的单轴拉伸过程中力学响应特征的变化归结为扩展裂纹取向角度的增加,将扩展裂纹最大取向角与拉伸强度相关联,构建了基于材料细观特征量的拉伸强度理论模型,并采用不同温度的单轴拉伸实验验证了该理论模型的有效性。研究表明:该拉伸强度理论模型可以实现对PBX炸药拉伸强度与炸药微裂纹密度、颗粒/黏结剂界面性能以及颗粒/黏结剂体系的表观杨氏模量、泊松比等细观特征量之间关系的定量描述。     

Constitutive relationship of brittle rock subjected to dynamic uniaxial tensile loads with microcrack interaction effects

A micromechanical model is proposed to describe both stable and unstable damage evolution in microcrack-weakened brittle rock material subjected to dynamic uniaxial tensile loads. The basic idea of the present model is to classify the constitution relationship of rock material subjected to dynamic uniaxial tensile loads into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The influence of all microcracks with different sizes and orientations are introduced into the constitutive relation by using the statistical average method. Effects of microcrack interaction on the complete stress-strain relation as well as the localization of damage for microcrack-weakened brittle rock material are analyzed by using effective medium method. Each microcrack is assumed to be embedded in an approximate effective medium that is weakened by uniformly distributed microcracks of the statistically-averaged length depending on the actual damage state. The elastic moduli of the approximate effective medium can be determined by using the dilute distribution method. Micromechanical kinetic equations for stable and unstable growth characterizing the ‘process domains’ of active microcracks are taken into account. These ‘process domains’ together with ‘open microcrack domains’ completely determine the integration domains of ensemble averaged constitutive equations relating macro-strain and macro-stress. Theoretical predictions have shown to consistent with the experimental results.     

Fractal analysis of fracture in concrete

Experimental results indicate that propagation paths of cracks in concrete are often irregular, producing rough fracture surfaces which are fractal. Based on dynamic analysis of microcrack coalescence, this paper presents a statistical fractal model to describe the damage evolution of concrete. The model demonstrates that the mechanism of fracture surfaces formed in concrete is closely related to the dynamic processes of the cascade coalescence of microcracks. A unimodal relation between the fractal dimension and the coalescence threshold can qualitatively explain the relation between fractal dimension and fracture energy.     

Fracture initiation associated with chemical degradation: observation and modeling

The fracture initiation in engineering thermoplastics resulting from chemical degradation is usually observed in the form of a microcrack network within a surface layer of degraded polymer exposed to a combined action of mechanical stresses and chemically aggressive environment. Degradation of polymers is usually manifested in a reduction of molecular weight, increase of crystallinity in semi crystalline polymers, increase of material density, a subtle increase in yield strength, and a dramatic reduction in toughness. An increase in material density, i.e., shrinkage of the degraded layer is constrained by adjacent unchanged material results in a buildup of tensile stress within the degraded layer and compressive stress in the adjacent unchanged material due to increasing incompatibility between the two. These stresses are an addition to preexisting manufacturing and service stresses. At a certain level of degradation, a combination of toughness reduction and increase of tensile stress result in fracture initiation. A quantitative model of the described above processes is presented in these work. For specificity, the internally pressurized plastic pipes that transport a fluid containing a chemically aggressive (oxidizing) agent is used as the model of fracture initiation. Experimental observations of material density and toughness dependence on degradation reported elsewhere are employed in the model. An equation for determination of a critical level of degradation corresponding to the offset of fracture is constructed. The critical level of degradation for fracture initiation depends on the rates of toughness deterioration and build-up of the degradation related stresses as well as on the manufacturing and service stresses. A method for evaluation of the time interval prior to fracture initiation is also formulated.     

Velocity field equations and strain localization

The velocity field equations of a hypo-elastic material are derived using arbitrary curvilinear coordinates in the actual configuration of the body, and emphasizing “higher order” terms which would disappear in an infinitesimal strain theory. As an example, bifurcation analyses are carried out with the help of the velocity field equations, for the thin rod and the thin plate under uniaxial tension. The results agree with those from the literature, at least if the “higher order” terms are disregarded. Differences may result from the way these terms are incorporated in the hypo-elastic approach.     

The role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals

The mechanical response of engineering materials evaluated through continuum fracture mechanics typically assumes that a crack or void initially exists, but it does not provide information about the nucleation of such flaws in an otherwise flawless microstructure. How such flaws originate, particularly at grain (or phase) boundaries is less clear. Experimentally, “good” vs. “bad” grain boundaries are often invoked as the reasons for critical damage nucleation, but without any quantification. The state of knowledge about deformation at or near grain boundaries, including slip transfer and heterogeneous deformation, is reviewed to show that little work has been done to examine how slip interactions can lead to damage nucleation. A fracture initiation parameter developed recently for a low ductility model material with limited slip systems provides a new definition of grain boundary character based upon operating slip and twin systems (rather than an interfacial energy based definition). This provides a way to predict damage nucleation density on a physical and local (rather than a statistical) basis. The parameter assesses the way that highly activated twin systems are aligned with principal stresses and slip system Burgers vectors. A crystal plasticity-finite element method (CP-FEM) based model of an extensively characterized microstructural region has been used to determine if the stress–strain history provides any additional insights about the relationship between shear and damage nucleation. This analysis shows that a combination of a CP-FEM model augmented with the fracture initiation parameter shows promise for becoming a predictive tool for identifying damage-prone boundaries.     

Tensile failure of micro-concrete: from mechanical tests to FE meso-model with the help of X-ray tomography

In this work, concrete is studied at meso-scale (aggregates, macro-pores and mortar matrix), where the local failure mechanisms are known to drive the macroscopic behaviour of the material. In order to highlight the impact of the mechanical and morphological properties of each phase (along with their interfaces), micro-concrete specimens are prepared with rather small dimensions compared to the size of the heterogeneities. X-ray tomography is used to reliably obtain the morphology of the heterogeneous meso-structure, which is then given as an input to a 3D FE meso-model with enhanced discontinuities. A uniaxial tensile numerical simulation is performed as a first application. To validate the numerical model, a uniaxial tensile test of the same micro-concrete specimen is performed inside the X-ray scanner and the in-situ evolution of the micro-structure is followed. Thus, both a direct validation of the model and a valuable insight of the 3D fracture mechanisms while the load progresses are obtained. After identification of the numerical parameters, comparison of experimental and numerical results reveals the capability of the meso-model to reproduce the actual material response (in terms of macroscopic strength, Young’s modulus and fracture patterns), with the explicit representation of the meso-scale heterogeneities being its key feature. To further challenge the meso-model, a new morphology coming from an X-ray scan of another characteristic micro-concrete specimen is introduced and its macroscopic behaviour is computed without a priori numerical identification. Starting from an X-ray scan in meso-scale, it is shown that the 3D meso-model is capable to predict the macroscopic behaviour and the failure patterns of the material.

     

Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials: A 3D study

In a recent publication (Yang et al., 2009. Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials. Int. J. Solids Struct. 46 (17) 3222–3234), we developed a finite element method capable of modelling complex two-dimensional (2D) crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. The present study extends the method to model three-dimensional (3D) problems. First, 3D cohesive elements are inserted into the initial mesh of solid elements to model potential crack surfaces by a specially designed, flexible and efficient algorithm and corresponding computer program. The softening constitutive laws of the cohesive elements are modelled by spatially-varying 3D Weibull random fields. Monte Carlo simulations are then carried out to obtain statistical information of structural load-carrying capacity. A concrete cube under uniaxial tension was analysed as an example. It was found that as the 2D heterogeneous model, the 3D model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. Increasing heterogeneity in terms of the variance in the tensile strength random fields resulted in lower mean and higher standard deviation of peak loads. Due to constraint effects and larger areas of unsmooth, non-planar fracture surfaces, 3D modelling resulted in higher mean and lower standard deviation of peak loads than 2D modelling.     

An application of a damage constitutive model to concrete at high temperature and prediction of spalling

A characteristic feature of concrete under uniaxial compression is the development of cracks parallel to the loading direction. A damage constitutive model proposed by Ortiz [Ortiz, M., 1985. A constitutive theory for the inelastic behaviour of concrete. Mech. Mater. 4, 67–93] can predict the transverse tensile stress responsible for these cracks by considering the interaction between the aggregate and the mortar and the development of damage in the latter. When concrete is exposed to high temperature, as is the case during fire, the failure mode is thermal spalling. In order to improve the prediction of the stresses involved in this failure Ortiz’s model is extended to account for the effects of high temperature. Published experimental results for uniaxial and biaxial compression at high temperatures are used to calibrate the temperature dependence of some of the material properties. The transient creep strain is accounted for by modifying the constrained thermal strain. The stress analysis is coupled with hygro-thermal analysis of heat, mass transfer and pore pressure build-up. The effect of pore pressure on the damage evolution is modeled by applying a body force in the stress analysis module proportional to the pressure gradient. A numerical example of concrete under fire is solved and the computed results are discussed. Spalling is predicted when the damage variable reaches its maximum value of unity. The predicted depth and time of spalling for a range of variation of permeability and initial liquid water content are presented. They are in good agreement with published experimental results.     

拉伸载荷下混凝土体分形内聚模型

在综合考虑混凝土试件微断裂面分形分布及断面分形演化基础上,提出了体分形内聚模型,用于描述混凝土试件在准静态拉伸载荷作用下的破坏行为。数值计算结果与现有实验数据吻合较好。此外,采用该模型分析了混凝土骨料级配对材料软化性质的影响。结果表明,在拉伸载荷作用下,混凝土骨料级配越均匀,材料的软化特征越明显。     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.     

The Three-Stage Model Based on Strain Strength Distribution for the Tensile Failure Process of Rock and Concrete Materials

A three-stage model is introduced to describe the tensile failure process of rock and concrete materials.Failure of the material is defined to contain three stages in the model,which include elastic deformation stage,body damage stage and localization damage stage.The failure mode change from uniform body damage to localization damage is expressed.The heterogeneity of material is described with strain strength distribution.The fracture factor and intact factor,defined as the distribution function of strain strength,are used to express the fracture state in the failure process.And the distributive parameters can be determined through the experimental stress-strain curve.     

混凝土率型内时损伤本构模型

混凝土是一种典型的率敏感材料,为了更好地描述混凝土结构在动力、冲击荷载作用下的强度和变形特征,本文结合内时理论和损伤理论建立了一种考虑混凝土率效应的内时损伤本构模型。该模型的特点:将混凝土材料的受力软化效应分解为密实状态的塑性效应和由微裂缝扩展引起的刚度退化效应。前者由内时理论来描述,这使该模型摆脱了一般弹塑性模型中屈服面的概念,从而更符合混凝土的变形特性,并且简化了非线性计算过程;后者由损伤理论来描述,根据混凝土的动力试验结果建立了增量型的损伤演变方程,从而使该模型能够较好地反映混凝土的动力特性。最后,应用本文建议的模型对一钢筋混凝土简支梁进行了非线性分析,结果表明:当结构承受快速荷载作用时,应变率对结构的受力性能影响较大,在进行结构分析时必须予以考虑。     

Meso-scale approach to modelling the fracture process zone of concrete subjected to uniaxial tension

A meso-scale analysis is performed to determine the fracture process zone of concrete subjected to uniaxial tension. The meso-structure of concrete is idealised as stiff aggregates embedded in a soft matrix and separated by weak interfaces. The mechanical response of the matrix, the inclusions and the interface between the matrix and the inclusions is modelled by a discrete lattice approach. The inelastic response of the lattice elements is described by a damage approach, which corresponds to a continuous reduction of the stiffness of the springs. The fracture process in uniaxial tension is approximated by an analysis of a two-dimensional cell with periodic boundary conditions. The spatial distribution of dissipated energy density at the meso-scale of concrete is determined. The size and shape of the deterministic FPZ is obtained as the average of random meso-scale analyses. Additionally, periodicity of the discretisation is prescribed to avoid influences of the boundaries of the periodic cell on fracture patterns. The results of these analyses are then used to calibrate an integral-type nonlocal model.     

Initiation and stable growth of penny-shaped crack in aging viscoelastic transversally isotropic material

Considered is the long-term cracking of an aging transversally isotropic material containing a Mode I penny-shaped crack under remotely applied tensile stress. The aging material properties are described by the Boltzmann–Volterra’s linear theory for integral operators with non-difference kernels. It applied to wood, concrete, some polymers and rocks. Only the symmetric case is considered where the crack lies in the plane of isotropy. The modified Leonov–Panasyuk–Dugdale’s crack model is used with a constant process zone assuming that the critical opening displacement is the fracture criterion. Volterra’s principle is applied to derive the equations of subcritical crack growth. Numerical calculations are made for subcritical crack growth for the specific example of transversally isotropic material simulating the behavior of reinforced concrete.     

Tensile fracture behavior of heterogeneous materials based on fractal geometry

Many of heterogeneous structural materials, like concrete, have different behavior under tensile stresses in comparison to their behavior under compressive stresses. The aim of this paper is to interpret behavior of such materials subjected to tensile stresses, by using newly introduced concept of fractal geometry. In the first part of this paper, tensile behavior of granular composites has been studied by using fractal geometry. It is shown that the fractality of the cross section in this kind of composites can be used to interpret the size effect on tensile strength. In fact, this work is a modification with innovations on the previous studies on fractal based size effect.This hypothesis that the fracture surfaces of quasi-brittle materials are fractals has been verified by several investigations. Accordingly, in the other part of this paper, softening process in heterogeneous materials is studied. Resulting from presented approach, a new softening curve for quasi-brittle materials is proposed. This new softening curve is denominated “Quasi-fractal softening curve” and is consisted of two parts, a linear portion in beginning part and an exponential portion in rest of the curve. This makes it very compatible to the pre-existing softening curves.