Multiscale Analysis of Multiple Damage Mechanisms Coupled with Inelastic Behavior of Composite Materials

Thermodynamically consistent constitutive equations are derived here in order to investigate size effects on the strength of composite, strain, and damage localization effects on the macroscopic response of the composite, and statistical inhomogeneity of the evolution-related damage variables associated with the representative volume element. This approach is based on a gradient-dependent theory of plasticity and damage over multiple scales that incorporates mesoscale interstate variables and their higher order gradients at both the macro- and mesoscales. This theory provides the bridging of length scales. The interaction of the length scales is a paramount factor in understanding and controlling material defects such as dislocation, voids, and cracks at the mesoscale and interpreting them at the macroscale. The behavior of these defects is captured not only individually, but also the interaction between them and their ability to create spatiotemporal patterns under different loading conditions. The proposed work introduces gradients at both the meso- and macroscales. The combined coupled concept of introducing gradients at the mesoscale and the macroscale enables one to address two issues simultaneously. The mesoscale gradients allow one to address issues such as lack of statistical homogeneous state variables at the macroscale level such as debonding of fibers in composite materials, cracks, voids, and so forth. On the other hand, the macroscale gradients allow one to address nonlocal behavior of materials and interpret the collective behavior of defects such as dislocations and cracks. The capability of the proposed model is to properly simulate the size-dependent behavior of the materials together with the localization problem. Consequently, the boundary-value problem of a standard continuum model remains well-posed even in the softening regime. The enhanced gradient continuum results in additional partial differential equations that are satisfied in a weak form. Additional nodal degrees of freedom are introduced that leads to a modified finite-element formulation. The governing equations can be linearized consistently and solved within the incremental iterative Newton-Raphson solution procedure.     

Thermal Cracking of Viscoelastic Asphalt-Concrete Pavement

This paper studies the thermal cracking of asphalt-concrete pavements using a semianalytical model that accounts for the multiscale nature of the thermal cracking phenomenon, the viscoelasticity of asphalt-concrete, and the frictional constraint on the pavement interface. This paper extends previous work to include the effects of asphalt-concrete viscoelasticity and to include a study of the effects of the major parameters. Numerical simulations lead to almost uniformly spaced thermal cracks, similar to field observations of real flexible pavement structures. A parameter study shows that material homogeneity, asphalt-concrete ductility, frictional constraint on the interface, and rate of cooling significantly influence the thermal cracking of asphalt-concrete pavements.     

Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress

Modeling of the evolution of distributed damage such as microcracking, void formation, and softening frictional slip necessitates strain-softening constitutive models. The nonlocal continuum concept has emerged as an effective means for regularizing the boundary value problems with strain softening, capturing the size effects and avoiding spurious localization that gives rise to pathological mesh sensitivity in numerical computations. A great variety of nonlocal models have appeared during the last two decades. This paper reviews the progress in the nonlocal models of integral type, and discusses their physical justifications, advantages, and numerical applications.     

Cohesive Fracturing and Stresses Caused by Hydration Heat in Massive Concrete Wall

Avoidance of cracking damage due to hydration is an important objective in the design of nuclear reactor containments. Assessment of the safety against cracking requires a realistic material model and its effective numerical implementation. Toward this goal, the paper develops a comprehensive material model which includes approximate simulation of cracking based on the principles of cohesive fracture mechanics, as well as an up-to-date creep formulation with aging and temperature effects. A standard heat conduction model is incorporated in the analysis as well. Since the crack width is the most important characteristic of cracking damage, particular attention is paid to crack spacing which governs crack width. The results of stability analysis of parallel crack systems based on fracture mechanics are used to estimate the spacing of open cracks as a function of their depth. Numerical simulations clarifying various aspects of hydration heat effects are presented.     

Field Investigations of Cracking on Concrete Pavements

This paper presents the results of several investigations to identify the underlying causes of longitudinal cracking problems in Portland cement concrete (PCC) pavement. Longitudinal cracking is not intended and detrimental to the long-term performance of PCC pavement. Longitudinal cracking problems in five projects were thoroughly investigated and the findings indicate that longitudinal cracking was caused by: (1) late or shallow saw cutting of longitudinal joints; (2) inadequate base support under the concrete slab; and (3) the use of high coefficient of thermal expansion (CTE) aggregates. When the longitudinal cracks were caused by late or shallow saw cutting of longitudinal joints, cracks developed at a very early stage. However, when there was adequate base support, the longitudinal cracks remained relatively tight even after decades of truck trafficking. Another cause of longitudinal cracking was inadequate base support, and cracking due to this mechanism normally progressed to rather wide cracks. Some cracks were as wide as 57?mm. Evaluations of base support by dynamic cone penetrometer in areas where longitudinal cracks were observed indicate quite weak subbase in both full-depth repaired areas and surrounding areas. This implies that the current requirements for the subbase preparation for the full-depth repair are not adequate. Another cause of longitudinal cracking was due to the use of high CTE aggregate in concrete. Large volume changes in concrete when coarse aggregate with high CTE is used could cause excessive stresses in concrete and result in longitudinal cracking. To prevent longitudinal cracking, attention should be exercised to the selection of concrete materials (concrete with low CTE) and the quality of the construction (timely and sufficient saw cutting and proper selection and compaction of subbase material).     

New Directions in Concrete Health Monitoring Technology

The NSF-sponsored Center for Advanced Cement-Based Materials is actively involved in research aimed at the development of technologies for health monitoring and nondestructive evaluation of the concrete infrastructure. This paper summarizes pertinent research performed at the center. Basic findings from several new laboratory-based nondestructive evaluation techniques for concrete are reported. The described techniques are based on measurements of mechanical waves that propagate in the concrete. First, ultrasonic longitudinal wave (also called the L-wave or P-wave) signal transmission (attenuation) measurements are shown to be sensitive to the presence of damage in the form of distributed cracking in concrete. Next, experimental procedures that enable practical one-sided wave signal transmission measurements to be performed on concrete structures are described. The utility of the signal transmission measurement is demonstrated by two experimental test series; the depths of surface-opening cracks in concrete slabs are estimated and the extent and nature of autogenous healing in concrete disks are studied. Finally, an approach by which fatigue-induced damage in concrete structures is nondestructively monitored is described. Vibration frequencies are shown to be sensitive to the presence of fatigue-induced cracking in concrete specimens; changes in the vibration frequency of a concrete specimen during fatigue tests are related to the remaining fatigue life of the test specimens.     

Unified DSC Constitutive Model for Pavement Materials with Numerical Implementation

Need for unified and mechanistic constitutive models for pavement materials for evaluation of various distresses has been recognized; however, such models are not yet available. There have been efforts to develop unified models; however, they have been based usually on ad hoc combinations of models for special properties such as elastic, plastic, creep and fracture, often without appropriate connections to various coupled responses of bound and unbound materials, they may result and in a large number of parameters, often without physical meanings. The disturbed state concept (DSC) provides a modeling approach that includes various responses such as elastic, plastic, creep, microcracking and fracture, softening and healing under mechanical and environmental (thermal, moisture, etc.) within a single unified and coupled framework. A brief review is presented to identify the advantages of the DSC compared to other available models. The DSC has been validated and applied to a wide range of materials: geologic, asphalt, concrete, ceramic, metal alloys, and silicon. It allows for evaluation of various distresses such as permanent deformations (rutting), microcracking and fracture, reflection cracking, thermal cracking, and healing. The DSC is implemented in two- and three-dimensional finite-element (FE) procedures, which allow static, repetitive, and dynamic loads including elastic, plastic, creep, microcracking leading to fracture and failure. A number of examples are solved for various distresses considering flexible (asphalt) pavements; however, the DSC model is applicable to rigid (concrete) pavements also. It is felt that the DSC and the FE computer programs provide unique and novel approaches for pavement engineering. It is desirable to perform further research and applications including validation with respect to simulated and field behavior of pavements.     

Improvement of surface quality on peritectic steel slabs

Peritectic steel grades are very sensitive to microcracking along austenitic grain boundaries in continuous casting. Irsid and Aktiengesellschaft der Dillinger Hüttenwerke (DH) have combined laboratory studies and industrial trials to improve surface quality on these sensitive grades. Laboratory studies at Irsid confirmed the hypothesis that a very thin layer of ferrite along austenitic grain boundaries is detrimental for cracking and indicate that the risk of cracking decreases as soon as ferrite ratio is above 10 %. Dilatometric investigations demonstrate that there is a strong shift between thermodynamic equilibrium and beginning of γ→α phase transformation under casting conditions. Furthermore, at the slab surface, there is no cyclic transformation γ→α→γ induced by thermal cycling in front of spray nozzles and supporting rolls. DH performed trials with various cooling strategies on its new vertical caster No. 5. No cracks appear with intensive cooling whereas microcracks are present with soft cooling. These results are in agreement with laboratory studies. Intensive cooling is the standard condition at DH. With this process, microcracking is avoided for all slab formats.     

Stiffness Degradation and Time to Cracking of Cover Concrete in Reinforced Concrete Structures Subject to Corrosion

Corrosion-induced cracks in reinforced concrete (RC) structures degrade the stiffness of the cover concrete. The stiffness degradation is mainly caused by the softening in the stress-strain relation in the cracked concrete. Limited efforts have been made to model the cracking and the corresponding effects on the cover concrete, despite of its importance in assessing and modeling the behavior of RC structures. This paper proposes a stiffness degradation factor to model the stiffness degradation of the cover concrete subject to cracking. The proposed factor is computed in terms of the cracking strain corresponding to the maximum opening of the concrete cracks based on an energy principle applied to a fractured RC structure. The time to cracking of the cover concrete is then determined as the time from the corrosion initiation needed by the crack front to reach the outer surface of the cover concrete. The proposed stiffness degradation factor and the method to compute the time to cracking are illustrated through two numerical examples. The times to cracking of the cover concrete that are predicted using the proposed method are in agreement with the measured values from laboratory experiments.     

Toward a Physical Damage Variable for Concrete

Continuum damage mechanics models, while elegant and useful, suffer from what are typically highly idealized relationships between model and material. In this technical note, using three-dimensional (3D) measurements of internal cracking, direct, albeit simple relationships were made between the quantity of cracking and a corresponding scalar damage variable. Geometric properties of internal cracks were measured through 3D image analysis of in situ microtomographic scans of small concrete specimens subject to compression. A scalar damage variable was determined from the changes in stiffness measured in successive loading cycles. Results showed a nearly linear relationship between the damage variable and the volume of new cracks formed. In contrast, results showed a nonlinear relationship between the damage variable and the crack surface area. Such relationships can potentially lead to a more physical basis for continuum damage formulations.     

Permeability due to the Increase of Damage in Concrete: From Diffuse to Localized Damage Distributions

Experimental tests exhibit a strong interaction between material damage and transport properties of concrete. There are at least two asymptotic cases where some theoretical modeling exists: in the case of diffuse cracking, the material permeability should be controlled by damage, e.g., by the decrease of average stiffness due to microcracking. In the case of localized microcracking, and after a macrocrack has formed, permeability should be controlled by a power function of the crack opening (Poiseuille flow). For quasi-brittle materials with evolving microstructure due to mechanical loads, a transition regime on the evolution of permeability between these two asymptotic cases is expected. In this contribution, we define a relationship between permeability and damage that is consistent with the two above configurations. One of the key issues is to relate the crack opening to the state variables in the continuum approach, so that the two asymptotic cases are expressed in the same variable system and can be matched. A simplified approach is used for this purpose. The permeability law is then derived using a mixing formula that weights each asymptotic regime with damage. To illustrate the influence of the matching law on structural response, finite-element simulations of a Brazilian splitting test and a comparison with existing test data are presented.     

Transverse Thermal Expansion of FRP Bars Embedded in Concrete

Fiber reinforced polymers (FRPs) have a thermal expansion in the transverse direction much higher than in the longitudinal direction and also higher than the thermal expansion of hardened concrete. The difference between the transverse coefficient of thermal expansion of FRP bars and concrete may cause splitting cracks within the concrete under temperature increase and, ultimately, failure of the concrete cover if the confining action of concrete is insufficient. This paper presents the results of an experimental investigation to analyze the effect of the ratio of concrete cover thickness to FRP bar diameter (c/db) on the strain distributions in concrete and FRP bars, using concrete cylindrical specimens reinforced with a glass FRP bar and subjected to thermal loading from ?30?to?+80°C. The experimental results show that the transverse coefficient of thermal expansion of the glass FRP bars tested in this study is found to be equal to 33 (×10?6?mm/mm/°C), on average and the ratio between the transverse and longitudinal coefficients of thermal expansion of these FRP bars is equal to 4. Also, the cracks induced by high temperature start to develop on the surface of concrete cylinders at a temperature varying between +50 and +60°C for specimens having a ratio of concrete cover thickness to bar diameter c/db less than or equal to 1.5. A ratio of concrete cover thickness to glass fiber reinforced polymers (GFRP) bar diameter c/db greater than or equal to 2.0 is sufficient to avoid cracking of concrete under high temperature up to +80°C. The analytical model, presented in this paper, is in good agreement with the experimental results, particularly for negative temperature variations.     

A crystallographic study of fatigue damage in titanium

Large grain specimens with average grain size of 0.0127 m made from commercial purity titanium were subjected to a torsional cyclic strain at two different amplitudes: ±0.008 and =0.003. Fatigue damage was studied by scanning electron microscopy and crystal orientations were determined by X-ray diffraction and surface trace analysis. It was found that cyclic strain amplitude influenced the deformation mode and the nature of the macroscopic crack propagation. At high strain amplitudes the normal slip processes were observed and microcracking was observed on the (0001), and {1100} slip planes. The macroscopic crack propagation was dominated by the Stage I shear mode; however, some Stage II tensile mode propagation was observed after extensive Stage I propagation. At low strain amplitude twin plane cracking was observed on the {1011}, {1010}, and {1123} planes in addition to normal slip plane cracking, and the macroscopic crack propagation was dominated by the Stage II tensile mode. However, microscopic examination showed the macroscopic tensile mode cracks to be composed of microscopic shear mode cracks along slip planes and twin planes. At both low and high strain amplitudes cracking was observed on the {1120} plane which is neither a slip or twin plane in titanium. It is proposed that this cracking mode was a result of a dislocation reaction forming sessile dislocations on the {1120} plane.     

Study of the Behavior of Concrete under Triaxial Compression

An experimental study of the confined compression behavior of concrete has been performed using 150×300?mm cylindrical specimens subjected to hydrostatic pressure in a triaxial cell and axial loading through a servo-hydraulic testing machine. A confining stress range of 0 to 60 MPa (about twice the uniaxial compressive strength) was employed to obtain the brittle-ductile transition behavior of the material. The increase in confining pressure leads to a change in the mode of failure and an increase in the maximum axial load-carrying capacity. It is seen that, at zero or low confinement, there is distributed microcracking and several macrocracks, and the response exhibits a well-defined peak and subsequent softening. At high confinements, relatively large axial and transversal strains of over 10% have been obtained, with monotonically increasing loads leading to horizontal plateaus. There is no distributed cracking and failure occurs with the propagation of few macrocracks. In general, the observed trends confirm and extend previous results reported in the literature. Optical microscopy shows extensive microcracking, especially in the aggregates, and pore collapse at high confinement. A preliminary interpretation of the results based on the theory of elastoplasticity is also presented.     

基于UDEC-GBM的矿物晶粒解理特征对硬岩石破坏过程的影响

基于块体离散单元数值模拟方法（UDEC-GBM）,以钾长石矿物颗粒为例,详细研究了矿物晶粒解理倾角、解理倾角围压效应及解理间距对硬质岩石力学性质、微观开裂过程及机理的影响,并探讨了解理特征在工程实际中可能带来的影响。数值研究结果表明:（1）晶粒解理具有明显倾角效应,当解理倾角由0°增加到90°时,岩石的弹性模量、单轴压缩强度及峰后脆延特征都会发生变化,穿晶总裂纹数受影响明显,主要体现在钾长石张拉穿晶裂纹显著增加,钾长石剪切裂纹数量在60°增加到最大值后减少,石英穿晶张拉裂纹数量也有明显变化,总体而言不断增加,而沿晶裂纹数量呈减少趋势,整个开裂过程仍以张拉沿晶主导;（2）晶粒解理倾角效应受围压影响,围压会导致沿晶裂纹和穿晶裂纹数量和二者比值发生变化,但不同倾角下围压对沿晶裂纹和穿晶裂纹数量和比值变化影响不一样;（3）当解理间距由2 mm增加到4 mm时,穿晶裂纹数量有增加趋势,而沿晶裂纹数量减少,总剪切和张拉裂纹数量比值不变,对岩石微观张拉、剪切破坏机制无明显影响。此外,具有解理结构的矿物晶粒含量较高且矿物晶粒本身性质对岩石性质及响应影响显著时,解理特征对板裂、岩爆等破坏的影响应给予重视。      

Mesoscale Approach to Modeling Concrete Subjected to Thermomechanical Loading

Concrete subjected to combined compressive stresses and temperature loading exhibits compressive strains, which are considerably greater than for concrete subjected to compressive stresses alone. This phenomenon is called transient thermal creep or load induced thermal strain and is usually modeled by macroscopic phenomenological constitutive laws which have only limited predictive capabilities. In the present study a mesoscale modeling approach is proposed in which the macroscopically observed transient thermal creep results from the mismatch of thermal expansions of the mesoscale constituents. The mesostructure of concrete is idealized as a two-dimensional three-phase material consisting of aggregates, matrix, and interfacial transition zones. The nonlinear material response of the phases is described by a plasticity interface model. The mesoscale approach was applied to analyze compressed concrete specimens subjected to uniform temperature histories and the analysis results were compared to experimental results reported in the literature.     

介孔二氧化硅球形孔内近场辐射换热

介孔二氧化硅基材内含不连续且均匀分布的球形孔.由于孔径小于热辐射特征波长,近场辐射作用不容忽视.本文基于涨落耗散理论和并矢格林函数,计算介孔二氧化硅球形孔内的近场辐射换热,由此得到的近场辐射的当量导热系数,将进一步用来修正介孔二氧化硅的有效导热系数.采用稀介质孔隙率加权模型耦合球形孔内近场辐射当量导热系数、孔内受限气体导热系数及介孔二氧化硅基材导热系数,得到介孔二氧化硅的有效导热系数,并进一步考察了孔径和温度的影响.研究结果表明,在介观尺度下,其辐射热流比宏观尺度下要高2-7个数量级.球形孔内近场辐射的热流及当量导热系数随着孔径的增加呈指数衰减,随着温度的升高而增大.介孔二氧化硅的有效导热系数随着孔隙率的增加逐渐减小,随着温度的升高缓慢增加.孔径越小,近场辐射的作用越显著,不容忽视.当孔径大于50 nm时,尺寸效应逐渐消失.      

Three-Dimensional Damage Model for Concrete. II: Verification

A three-dimensional damage model for concrete has been proposed in the preceding paper, Part I: Theory. This paper focuses on the application of the damage model for quasi-brittle materials such as concrete. The determination of model parameters for the evolution rule of damage is discussed. The model parameters to consider the frictional stress and the stiffness reduction under hydrostatic compression are also studied. For verification, the proposed model is applied to concrete subjected to confined compression, triaxial, loading, and cyclic loading. Consistent results, as compared with other researchers’ experimental data, were obtained, and the proposed model is considered worthy of further research work.