A preliminary numerical investigation on the influence of material variability in the early-age cracking behavior of restrained concrete

The restraint of drying, autogenous, or thermal shrinkage can result in the development of tensile residual stresses. If the residual stresses that develop are large enough, they may cause cracking in the concrete. Substantial research has focused on the development of test methods to assess stress development and the corresponding potential for cracking. These test methods frequently focus on the determination of material properties that can be used in deterministic computer programs to simulate stress development and cracking. While these models are a great step forward, variability is inherent in the material properties, the construction processes, and the environmental conditions (i.e., temperature and relative humidity). This paper presents results of considering variability in a model for predicting the time of shrinkage cracking. A Monte Carlo simulation procedure has been adopted to account for variability in material properties. It has been found that a log-logistic function can accurately describe variability that can be expected in the time of cracking.     

基于应变分解方法的钢筋混凝土开裂模型

为了克服传统弥散裂缝模型的不足,采用应变分解的方法,推导了钢筋混凝土单元的开裂模型;通过假定裂缝面法向和切向变形解耦,采用混凝土非线性断裂力学的基本理论分别构造裂缝面法向和切向的本构关系;对于混凝土单元中的钢筋,在开裂后不仅考虑其轴向刚度,同时采用弹性地基梁模型考虑其横向作用对开裂混凝土应力传递的影响;采用FORTRAN语言编制程序,通过与经典梁、板构件试验结果的比较,表明该模型的合理性和有效性;可用于钢筋混凝土结构非线性和极限承载力的分析。     

Non-linear model for R/C tensile members strengthened by FRP-plates

Transverse cracking in reinforced concrete (R/C) members strengthened by FRP plates and subjected to axial loads is analyzed. A non-linear model is developed, where cohesive stresses in concrete across cracks and non-linear bond–slip law between steel bars and concrete are used. The non-linear governing equations are solved via finite difference method. Comparisons with experimental results confirm the validity of the model. Numerical examples are also presented, simulating tests on plated and unplated R/C members with displacement, force, or crack opening control. The examples show that external FRP-plating is effective in reducing crack width and, consequently, in increasing axial stiffness of tensile members.     

The effect of residual thermal stresses on transverse cracking in cross-ply laminates: an application of the coupled criterion of the finite fracture mechanics

A model to predict transverse cracking in cross-ply laminates in the presence of residual thermal stresses is developed here. This model is based on the coupled criterion of the finite fracture mechanics. This criterion has been successfully used for different materials, structures and scales to predict crack initiation. It is based on two main hypotheses: (i) crack initiation occurs as a finite-length crack onset and (ii) the crack onset requires that both stress and energy criteria are fulfilled simultaneously. The present model is developed under the generalized-plane-strain hypotheses combining the results obtained using the laminate theory and a boundary element code. The present analysis shows that the residual thermal stresses affect both the stress and the energy criteria in the form of adding a residual elastic-strain to the strain imposed by external mechanical loads. An explicit expression for this residual elastic-strain is provided. For certain composite materials as carbon/epoxy the value of this residual elastic-strain is shown to be relatively large in comparison with the nominal critical transverse strain of the material. The comparison with experiments shows that considering the residual thermal stresses using the strategy proposed here improves drastically the accuracy of the model predictions.     

A plasticity model and algorithm for mode-I cracking in concrete

A class of plasticity models which utilize Rankine's (principal stress) yield locus is formulated to simulate cracking in concrete and rock under monotonic loading conditions. The formulation encompasses isotropic and kinematic hardening/softening rules, and incremental (flow theory) as well as total (deformation theory) formats are considered. An Euler backward algorithm is used to integrate the stresses and internal variables over a finite loading step and an explicit expression is derived for a consistently linearized tangent stiffness matrix associated with the Euler backward scheme. Particular attention is paid to the corner regime, that is when the two major principal stresses become equal. A detailed comparison has been made of the proposed plasticity-based crack formulations and the traditional fixed and rotating smeared-crack models for a homogeneously stressed sample under a non-proportional loading path. A comparison between the flow-theory-based plasticity crack models and experimental data has been made for a Single Edge Notched plain concrete specimen under mixed-mode loading conditions.     

Quantifying shrinkage cracking in fiber reinforced concrete using the ring test

Tensile stress can develop in concrete when rest raint prevents the concrete from shrinking freely in response to drying, chemical reaction, or temperature reduction. When these tensile stresses exceed the tensile strength of the concrete, visible cracking may be expected to occur. While several test methods have been developed to assess a material's potential for early-age shrinkage cracking, this paper describes the use of the ‘ring-test’ for assessing the performance of a fiber reinforced concrete. An equation is presented that enables the residual stress that develops in the concrete ring specimen to be estimated. This expression is used to approximate the stress that is transferred across a crack. It is shown that for conventional fiber reinforced concrete (i.e., the mixtures described in this paper) the pre-peak mechanical properties (elastic modulus, splitting tensile strength and free shrinkage) are not influenced greatly by the addition of fibers. Rather, fibers appear to influence shrinkage-cracking behavior only after the crack begins to open. To better understand the role of fibers in mitigating early-age shrinkage cracking passive acoustic emission testing was used. Acoustic emission measurements indicate microcracking due to the heterogenous nature of the concrete and the presence of moisture gradients. The acoustic emission results highlight how a single crack begins to form into a visible crack. Finally, an approach is presented for estimating crack-width based on the strain data measured from the ring test. The role of the specimen geometry is discussed for comparing the ring test with field applications.     

Origins of tensile stress-induced circumferential cracking of waterwall tubes in boilers

Abstract

The leakage and rupture of boiler tubes in power plants is a serious problem that can lead to unscheduled and costly outages. The predominant failure location of current concern is circumferential cracking on the fireside of waterwall tubes in the furnace waterwall section of a boiler. Although there is basic agreement that cracking results from a combination of thermal fatigue and corrosion, a complete explanation of the basic phenomena needed to establish the root causes of this problem is lacking. The purpose of the present study was to analyse the sources of the tensile stress responsible for initiating circumferential cracking and to identify the key parameters controlling this tensile stress. The results of analytical modelling suggested that a combination of increasing tube wall temperature with increasing thickness of internal oxide layers, and temperature spiking due to deslagging events eventually may result in tensile stresses sufficient to crack the fireside oxide and initiate the development of circumferential cracks. This scenario also led to suggestions for reducing tensile stresses in waterwall tubes which, in turn, would be expected to delay/avoid circumferential cracking and improve the reliability of waterwall tubes.     

早龄期混凝土路面板非线性温度场下温度应力的计算

给出了一种早龄期混凝土路面板非线性温度场下温度应力的解析计算方法。模型将路面板厚度方向的非线性温度分成平均温度、线性温度和非线性温度三个分项,每一分项温度引起应力分别计算,最终总应力为三部分应力的叠加。此外,由于徐变对温度应力发展具有很大影响,因此该文也对混凝土徐变对板内温度应力的影响进行了分析。模型预测结果表明:在非线性温度分布下,温度应力沿板厚也是非线性分布的,温度变化产生的最大温度应力可能出现在路面板厚度方向的任何高度上,这依赖于沿板厚方向的温度分布特征。混凝土徐变会显著的降低路面板内的温度应力。     

Investigation of thermal cracking with the cracking-frame

If the deformations due to temperature changes or shrinkage are prevented in concrete members, restraint stresses are caused which can result in cracking. In thick members the heat of hydration is thus of importance. To reduce the risk of cracking the concrete mix must be optimized. For this purpose the influence of technological parameters on thermal cracking in concrete at early ages was studied in numerous laboratory tests with the cracking-frame. In this device the restraint stresses in a concrete specimen can be measured continuously from the very start, whereby the concrete hardens under the same conditions as a member about 50 cm thick. The cracking tendency of different concretes can be estimated by the cracking temperature, which is a further result of these tests.     

Thermal fatigue failure induced by delamination in thermal barrier coating

The paper presents the experimental and theoretical investigation on the thermal fatigue failure induced by delamination in thermal barrier coating system. Laser heating method was used to simulate the operating state of TBC (thermal barrier coating) system. The non-destructive evaluation such as acoustic emission (AE) detect was used to study the evolution of TBC system damage. Micro-observation and AE detect both revealed that fatigue crack was in two forms: surface crack and interface delamination. It was found that interface delamination took place in the period of cooling or heating. Heating or cooling rate and temperature gradient had an important effect on interface delamination cracking propagation. A theoretical model on interface delamination cracking in TBC system at operating state is proposed. In the model, a membrane stress P and a bending moment M are designated the thermal loads of the thermal stress and temperature gradient in TBC system. In this case, the coupled effect of plastic deformation, creep of ceramic coating as well as thermal growth oxidation (TGO) and temperature gradient in TBC system was considered in the model. The thermal stress intensity factors (TSIFs) in non-FGM (functional gradient material) thermal barrier coating system is analytical obtained. The numerical results of TSIFs reveal some same results as obtained in experimental test. The model is based on fracture mechanics theory about heterogeneous materials and it gives a rigorous explanation of delaminations in TBC system loaded by thermal fatigue. Both theoretical analysis and experimental observation reveal an important fact: delaminations are fatigue cracks which grow during thermal shocks due to compressive stresses in the loading, this loads the delaminations cracks in mixed I and II mode.     

On the feasibility of using phase change materials (PCMs) to mitigate thermal cracking in cementitious materials

Temperature changes driven by hydration reactions and environmental loading are a leading cause of thermal cracking in restrained concrete elements. This work describes preliminary investigations on the use of microencapsulated phase change materials (PCMs) as a means to mitigate such thermal cracking. Special attention is paid to quantify aspects of: heat absorption and release, the development of unrestrained/restrained thermal stresses and strains and the mechanical properties including: compressive strength, elastic modulus and fracture behavior. First, PCMs incorporated in cementitious systems absorb and release heat, which scales as a function of their dosage and enthalpy of phase change. Second, for restrained and unrestrained conditions and for equal temperature change, the thermal deformation and stresses developed are noted to be similar to a plain cement system independent of the PCM dosage. However, PCM additions are noted to reduce the rate of deformation and stress development so long as the phase transition is active. Third, while the presence of PCMs does depress the compressive strength and elastic modulus (in increasing proportion with dosage), the fracture toughness is impacted to a lesser degree. While of a preliminary nature, the studies highlight a novel means of exploiting phase transitions to control thermal stress evolutions in restrained elements.     

Stress distribution and crack formation in full-scaled ultra-high strength concrete columns

Full-scaled model columns were placed both in summer and winter with an ultra-high strength concrete with a compressive strength more than 150?MPa, and stress distribution and cracking were experimentally evaluated. Specimens placed in summer exhibited cracks around the steel reinforcements which sometimes joined together. Specimens placed in winter showed, in addition to the cracks around the reinforcement, an internal crack perpendicular to the column axis as well as at the specimen surface. These cracks were found to be dependent on the temperature history due to hydration heat liberation and associated autogenous shrinkage strains. It was shown that the autogenous shrinkage of concrete increased when temperature after mixing was low and the maximum temperature during temperature history was high. This accounts for the numerous cracks found in the specimen placed in winter. Strain perpendicular to the axial direction was smaller than that of the axial direction implying the tensile stress due to autogenous shrinkage acting perpendicular to the axial direction as far as the autogenous shrinkage is isotropic. Finite element analysis confirmed the lateral stress due to autogenous shrinkage. Possible influences of autogenous shrinkage of ultra-high strength concrete on the structural performance include (1) early spalling of cover concrete and degradation of flexural strength, (2) degradation of bond and shear strength, and (3) prospect of longitudinal crack in center of the column and degradation of flexural strength.     

沥青混合料低温临界开裂温度的确定

为了同时考虑沥青混合料在降温过程中温度应力的累积和松弛作用,确定临界开裂温度,对试件进行了线收缩系数试验,并利用间接拉伸试验确定其抗拉强度和蠕变柔量,由蠕变柔量和松弛模量的关系得到松弛模量的Prony系列表达式;由Boltzmann叠加原理,得到温度应力公式,计算出不同降温速率下产生的温度应力,根据低温抗拉强度曲线,确定出沥青混合料的临界开裂温度,并对结果予以验证。结果表明:该方法考虑了应力累积和松弛二者的综合作用,能够较好地反映沥青混合料的低温开裂特性,其计算结果与约束试件温度应力试验结果相近;该方法不仅适用于恒定降温速率,还适用于现场连续变速降温工况;随温度的降低或降温速率的增加沥青混合料内部温度应力累积速度加快,临界开裂温度随降温速率增加而升高。      

Bonded aircraft repairs under variable amplitude fatigue loading and at low temperatures

Bonded repairs can replace mechanically fastened repairs for aircraft structures. Compared to mechanical fastening, adhesive bonding provides a more uniform and efficient load transfer into the patch, and can reduce the risk of high stress concentrations caused by additional fastener holes necessary for riveted repairs. Previous fatigue tests on bonded Glare (glass‐reinforced aluminium laminate) repairs were performed at room temperature and under constant amplitude fatigue loading. However, the realistic operating temperature of ?40 °C may degrade the material and will cause unfavourable thermal stresses. Bonded repair specimens were tested at ?40 °C and other specimens were tested at room temperature after subjecting them to temperature cycles. Also, tests were performed with a realistic C‐5A Galaxy fuselage fatigue spectrum at room temperature. The behaviour of Glare repair patches was compared with boron/epoxy ones with equal extensional stiffness. The thermal cycles before fatigue cycling did not degrade the repair. A constant temperature of ?40 °C during the mechanical fatigue load had a favourable effect on the fatigue crack growth rate. Glare repair patches showed lower crack growth rates than boron/epoxy repairs. Finite element analyses revealed that the higher crack growth rates for boron/epoxy repairs are caused by the higher thermal stresses induced by the curing of the adhesive. The fatigue crack growth rate under spectrum loading could be accurately predicted with stress intensity factors calculated by finite element modelling and cycle‐by‐cycle integration that neglected interaction effects of the different stress amplitudes, which is possible because stress intensities at the crack tip under the repair patch remain small. For an accurate prediction it was necessary to use an effective stress intensity factor that is a function of the stress ratio at the crack tip R_{crack tip} including the thermal stress under the bonded patch.     

预应力混凝土箱梁开裂后的刚度损伤评估

箱梁容易在支座、1/4跨及跨中位置出现裂缝,箱梁开裂病害与箱梁过量下挠相互耦合,其作用机理较为复杂,评估箱梁过量下挠的难点在于箱梁裂后的刚度分布特性研究。为了有效评估箱梁裂后刚度,制作了大比例尺预应力混凝土连续箱梁模型,开展了反复荷载作用下的箱梁破坏性试验,分别采用两种方法开展了箱梁裂后刚度分布特性研究。第一种方法,结合试验数据,基于Levenberg-Marquardt优化算法,对已测试得到的不同开裂程度下的挠度进行刚度分布反演;第二种方法,基于模型试验测试的荷载挠度曲线直接建立刚度折减评估参数,对开裂后箱梁的刚度损伤分布进行统计分析。对比分析了两种方法计算得到的箱梁裂后刚度纵向分布特征,验证了评估结果的有效性。研究结果表明:箱梁裂后开裂区域的刚度折减系数以加载位置为参考点,其余部位的刚度损伤沿箱梁纵向呈线性分布。提出了箱梁裂后刚度损伤计算方法。该研究可对开裂后箱梁的服役性能评估提供了理论参考。     

Progress in failure analysis of constrained shrinkage cracking in reinforced concretes

Shrinkage-induced cracking in constrained concrete slabs is an important failure mode for concrete structures. Several empirical relations have been reported in earlier studies. This paper develops a mechanics-based relationship for shrinkage-induced cracking through a shear-lag model that can be used to analyze the stress field, crack width, and the final crack spacing for cracked concrete slabs. The present model prediction is observed to be close to the empirical relation based on long-term observations.     

预应力钢绞线锈胀及混凝土开裂预测

针对钢绞线锈蚀导致混凝土开裂现象,开展了不同应力状态下混凝土的锈胀开裂试验,基于红外和热重分析研究了预应力钢绞线锈蚀产物的膨胀率,分析了预应力对保护层临界开裂时间和裂缝宽度的影响,综合考虑预应力、铁锈膨胀率和混凝土开裂损伤等因素,建立了开裂初始和发展全过程的锈胀裂缝预测模型,并通过试验结果进行了验证。结果表明:预应力会加速混凝土的锈胀开裂,在钢绞线抗拉强度75%的预应力水平下,保护层初始开裂时间降低了22%,裂缝扩展速率增加了9%;建立的模型具有较好的精度,可以合理地预测预应力混凝土的锈胀开裂。     

Crack development in concrete structures due to imposed strains—Part II: Parametric study of a wall fully restrained at the base

Crack development due to imposed strains in concrete walls fully restrained at the base is studied in order to improve control of cracking. In this second paper the influence of reinforcement and concrete properties as well as geometry on crack width and crack spacing is studied. In a first paper a two-dimensional FE-method is described, with closing forces in cracks concentrated to spring elements. Temperatures changes are used as load and the calculations are performed stepwise with opening of nodes and implementation of spring elements. It is shown that the two-dimensional behaviour of the wall only gives about half the crack widths compared to a one-dimensional bar with the same percentage of reinforcement. The reason is that the restraint along the base will effectively facilitate distribution of cracking along the wall. The two-dimensional analysis shows that the crack widths are limited also by low reinforcement ratios. For the same reinforcement ratio the crack width will increase with tensile strength of the concrete. The geometry of the wall has very little influence on the cracking behaviour unless the wall is very short. Bond stiffness and bar diameter have a limited effect on the crack width in the wall.     

An elastic strip with periodic surface cracks under thermal shock

The problem of two periodic edge cracks in an elastic infinite strip located symmetrically along the free boundaries under thermal shock is investigated. It is assumed that the infinite strip is initially at constant temperature. Suddenly the surfaces containing the edge cracks are quenched by a ramp function temperature change. Very high tensile transient thermal stresses arise near the cooled surface resulting in severe damage. The degree of the severity for a subcritical crack growth mode is measured by determining the stresses intensity factors. The thermoelastic problem is treated as uncoupled quasi-static. The superposition technique is used to solve the problem. The thermal stresses obtained from the uncracked strip with opposite sign are utilized as the only external loads to formulate the perturbation problem. By expressing the displacement components in terms of finite and infinite Fourier transforms, a hypersingular integral equation is derived with the crack surface displacement as the unknown function. Numerical results for stress intensity factors are carried out and presented as a function of time, cooling rate, crack length, and periodic crack spacing.     

Modeling the cracks opening–closing and possible remedial sawing operation of AAR-affected dams

A significant number of existing concrete dams are at present deteriorated by chemo-mechanical processes known as Alkali-Aggregate Reactions (AAR). This phenomenon is responsible for cracking and expansion of the material which lead to mechanical degradation of the structures operability and safety. Its chemo-mechanical modeling has been already dealt with by considering the influence of temperature, humidity, stiffness reduction and stress in the development of expansion. This modeling has first been developed as valid only for continuous media. In order to widen the field of modeling applicability, this paper describes a novel procedure for modeling displacement discontinuities in AAR-affected concrete structures, mainly to take into account two phenomena: firstly, the modeling of significant isolated cracks opening–closing that result from interactions between expansion and mechanical behavior of the structure; and secondly, the evaluation of the potential efficiency of stress release (e.g. sawing of dams), the procedure of which consists in the creation of slot cutting in the structure for release of excessive compressive stresses. The elaborated model, aimed to possibly combine contact elements and non-linear volume coupled models of durability mechanics related to AAR modeling, was applied to the 3D simulations of a simplified model ideally representing a part of a dam and also to a real gravity dam. Displacements and stresses at the contact elements zone were computed and compared with results of the dam computations without contact elements. The results show that the creation of the slot cutting leads to decrease of the compressive stresses in the structure, which confirms a favorable effect of this stress release technique in order to deal with AAR affected structures.