FRP加固梁的FRP-混凝土界面脱胶分析

为了研究纤维增强聚合物(fiber reinforced polymer, FRP) 加固梁的FRP-混凝土界面脱胶破坏过程,本文将混凝土梁和FRP 板均视为线弹性的欧拉-伯努利梁(Euler-Bernoulli beams), 且两者通过粘结层胶结在一起. 对于FRP-混凝土结构,有两种形式的脱胶破坏：板端脱胶破坏和跨中裂缝导致的脱胶破坏.对于FRP-混凝土梁,利用合理的粘结模型按第2 种脱胶失效形式,详细讨论了FRP-混凝土界面的脱胶过程,得到了不同阶段的胶结滑移、界面剪应力和FRP 轴向力的解析解. 实验研究验证了理论分析的结果,参数研究进一步探讨了胶结长度和粘结层厚度对于FRP-混凝土界面脱胶行为的影响.     

Process of debonding in RC beams shear-strengthened with FRP U-strips or side strips

Reinforced concrete (RC) beams may be strengthened for shear using externally bonded fiber reinforced polymer (FRP) composites in the form of side bonding, U-jacketing or complete wrapping. The shear failure of almost all RC beams shear-strengthened with side bonded FRP and the majority of those strengthened with FRP U-jackets, is due to debonding of the FRP. The bond behavior between the externally-bonded FRP reinforcement (referred to as FRP strips for simplicity) and the concrete substrate therefore plays a crucial role in the failure process of these beams. Despite extensive research in the past decade, there is still a lack of understanding of how debonding of FRP strips in such a beam propagates and how the debonding process affects its shear behavior. This paper presents an analytical study on the progressive debonding of FRP strips in such strengthened beams. The complete debonding process is modeled and the contribution of the FRP strips to the shear capacity of the beam is quantified. The validity of the analytical solution is verified by comparing its predictions with numerical results from a finite element analysis. This analytical treatment represents a significant step forward in understanding how interaction between FRP strips, steel stirrups and concrete affects the shear resistance of RC beams shear-strengthened with FRP strips.     

Debonding analysis of FRP–concrete interface between two balanced adjacent flexural cracks in plated beams

A cohesive interface modeling approach to debonding analysis of adhesively bonded interface between two balanced adjacent flexural cracks in conventional material (e.g., concrete or wood) beams strengthened with externally bonded FRP plates is presented. Both the strengthened beam and strengthening FRP are modeled as two linearly elastic Euler–Bernoulli beams bonded together through a thin adhesive layer. A bi-linear cohesive model, which is commonly used in the literature, is adopted to characterize the stress-deformation relationship of the FRP–concrete interface. Completely different from the single-lap or double-shear pull models in which only the axial pull force is considered, the present model takes the couple moment and transverse shear forces in both the substrates into account to study the second type of intermediate crack-induced debonding (IC debonding) along the interface. The whole debonding process of the FRP–concrete interface is discussed in detail, and closed-form solutions of bond slip, interface shear stress, and axial force of FRP in different stages are obtained. A rotational spring model is introduced at locations of the two adjacent flexural cracks to model the local flexibility of the cracked concrete beam, with which the relationship between the local bond slip and externally applied load is established and the real bond failure process of the FRP-plated concrete beam with the increasing of the externally applied load is revealed. Parametric studies are further conducted to investigate the effect of the thickness of adhesive layer on the bond behavior of FRP–concrete interface. The present closed-form solution and analysis on the local bond slip versus applied load relationship for the second type of IC debonding along the interface shed light on the bond failure process of structures externally strengthened with FRP composite plates and can be used effectively and efficiently to predict ductility and ultimate load of FRP-strengthened structures.     

Debonding of FRP-plated reinforced concrete beam,a bond-slip analysis. I. Theoretical formulation

External bonding of FRP plates or sheets has emerged as a popular method for strengthening reinforced concrete. Debonding along the FRP–concrete interface can lead to premature failure of the structure. In this study, a bond-slip model is established to study the interface debonding induced by a flexural crack in a FRP-plated concrete beam. The reinforced concrete beam and FRP plate are modeled as two linearly elastic Euler–Bernoulli beams bonded together through a thin layer of FRP–concrete interface. The interface layer is essentially modeled as a large fracture processing zone of which the stress–deformation relationship is described by a nonlinear bond-slip model. Three different bond-slip models (bi-linear, triangular and linear-damaging) are used. By dividing the debonding process into several stages, governing equations of interfacial shear and normal stresses are obtained. Closed-form solutions are then obtained for the interfacial shear and normal stresses and the deflection of the beam in each stage of debonding. In such a way, the proposed model unifies the whole debonding process, including elastic deformation, debonding initiation and growth, into one model. With such a superior feature, the proposed model provides an efficient and effective analytical tool to study FRP–concrete interface debonding.     

Interfacial stress analysis of a thin plate bonded to a rigid substrate and subjected to inclined loading

The so-called peel test, in which a thin plate bonded to a substrate is subjected to an inclined pulling force, has been widely used to characterise the bond behaviour of adhesives. This paper presents an analytical solution for the interfacial normal and shear stresses in such a peel test to provide an improved understanding of its underlying mechanism. An approximate closed-form solution is also presented. The effect of the peel angle (i.e. the angle between the applied force and the substrate) on the interfacial stresses is discussed. Apart from being a widely used test for quantifying adhesive characteristics, the process of debonding in a peel test resembles that of intermediate flexural-shear or shear crack induced debonding in flexurally strengthened RC members, where a relative vertical displacement exists between the two sides of the crack, leading to an angle between the external plate and the concrete substrate. Therefore, the results of this study also offer some insight into the latter failure mode which is very important in the flexural strengthening design of RC members.     

A three-parameter elastic foundation model for interface stresses in curved beams externally strengthened by a thin FRP plate

Externally bonding of fiber reinforced polymer (FRP) plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP–concrete interface are of great importance to the effectiveness of this type of strengthening because high stress concentration along the FRP–concrete interface can lead to the FRP debonding from the concrete beam. In this study, we develop an analytical solution of interface stresses in a curved structural beam bonded with a thin plate. A novel three-parameter elastic foundation model is used to describe the behavior of the adhesive layer. This adhesive layer model is an extension of the two-parameter elastic foundation commonly used in existing studies. It assumes that the shear stress in the adhesive layer is constant through the thickness, and the interface normal stresses along two concrete/adhesive and adhesive/FRP interfaces are different. Closed-form solutions are obtained for these two interfacial normal stresses, shear stress within the adhesive layer, and beam forces. The validation of these solutions is confirmed by finite element analysis.     

THEORETICAL MODEL ON INTERFACE FAILURE MECHANISM OF REINFORCED CONCRETE CONTINUOUS BEAM STRENGTHENED BY FRP

Fiber reinforced polymer （FRP） composites are increasingly being used for the re-pair and strengthening of deteriorated concrete structural components through adhesive bonding of prefabricated strips/plates and the wet lay-up of fabric. Interfacial bond failure modes have attracted the attention of researchers because of the importance. The objective of the present study is to analyse the interface failure mechanism of reinforced concrete continuous beam strength-ened by FRP. An analytical solution has been firstly presented to predict the entire debonding process of the model. The realistic bi-linear bond-slip interfacial law was adopted to study this problem. The crack propagation process of the loaded model was divided into four stages （elastic,elastic-softening,elastic-softening-debonded and softening-debonded stage）. Among them,elastic-softening-debonded stage has four sub-stages. The equations are solved by adding suitable stress and displacement boundary conditions. Finally,critical value of bond length is determined to make the failure mechanism in the paper effective by solving the simultaneously linear algebraic equations. The interaction between the upper and lower FRP plates can be neglected if axial stiffness ratio of the concrete-to-plate prism is large enough.     

碳纤维布与钢板复合加固梁剥离破坏研究

通过12根碳纤维布与钢板复合加固钢筋混凝土梁的抗弯性能研究,结果表明复合加固方式能有效地改善被加固构件的受力性能,但常由于复合加固层的剥离可能导致加固效果的降低。复合加固层与被加固构件之间的剥离是由于薄弱截面在剪应力及正应力的集中作用下而产生的,文中对复合加固层与混凝土之间的粘结剪应力及剥离正应力的计算公式分别进行推导,并进一步对碳纤维布与钢板复合加固的剥离机理进行分析,为工程应用提供依据。     

CFRP-混凝土界面粘结的疲劳性能试验研究

外贴FRP是重要的混凝土结构加固技术,但目前对外贴FRP加固混凝土结构的疲劳性能研究尚不充分,尤其对FRP-混凝土粘结界面的疲劳退化规律和破坏模式的研究更为缺乏。本文采用双面剪切试件,通过2个静载试件和4个疲劳试件的试验研究,考察了粘结长度和胶层厚度等因素对FRP-混凝土界面粘结疲劳性能的影响。通过分析沿粘结长度的FRP应变分布在疲劳循环过程中和疲劳后静载过程中的变化情况,讨论了不同粘结长度和粘结胶层厚度条件下的粘结界面疲劳退化规律和疲劳后静载性能。试验结果表明:胶层树脂-混凝土粘结界面是发生疲劳剥离破坏的薄弱环节;胶层厚度增大时,由于疲劳引起的界面损伤累积发展显著减小,疲劳后静载中胶层厚度较大试件的粘结承载力也更大;粘结长度增大时,界面粘结呈现更为明显的损伤退化,但由于试验粘结长度小于有效粘结长度,疲劳后的静粘结承载力仍更大。     

Cohesive zone model of intermediate crack-induced debonding of FRP-plated concrete beam

External bonding of FRP plates or sheets has emerged as a popular method for strengthening reinforced concrete structures. Debonding along the FPR–concrete interface can lead to premature failure of the structures. In this study, debonding induced by a flexural crack in a FRP-plated concrete beam is analyzed through a nonlinear fracture mechanics method. The concrete beam and FRP plate are modeled as linearly elastic simple beams connected together through a thin layer of FRP–concrete interface. A bi-linear cohesive (bond-slip) law, which has been verified by experiments, is used to model the FRP–concrete interface as a cohesive zone. Thus a cohesive zone model for intermediate crack-induced debonding is established with a unique feature of unifying the debonding initiation and growth into one model. Closed-form solutions of interfacial stress, FRP stress and ultimate load of the plated beam are obtained and then verified with the numerical solutions based on finite element analysis. Parametric studies are carried out to demonstrate the significant effect of FRP thickness on the interface debonding. The bond-slip shape is examined specifically. In spite of its profound effect on softening zone size, the bond-slip shape has been found to have little effect on the ultimate load of the plated beam. By making use of such a unique feature, a simplified explicit expression is obtained to determine the ultimate load of the plated concrete beam with a flexural crack conveniently. The cohesive zone model in this study also provides an efficient and effective way to analyze more general FRP–concrete interface debonding.     

光纤传感器测量FRP加固结构的损伤

A distributed fiber optic sensor is developed for condition monitoring of civil infrastructure sys-tems. The fiber optic sensor is especially useful in applications involving structures strengthened by fiberreinforced polymer (FRP) composites. The sensor principles are simple and therefore, practical for detec-tion of cracks, debonding and deformation measurements. Structural monitoring capability of the sensor     

A fully-analytical approach for modelling the response of FRP plates bonded to a brittle substrate

Composite materials, such as fiber reinforced polymers (FRP), are more and more common as strengthening solution for existing structures. Adhesion between FRP and the existing substrate generally represents one of the main concerns on the effectiveness of these techniques. The bond behaviour of composite materials on concrete substrates (but also steel, masonry and wooden ones) are generally investigated by means of pull-out tests. The present paper, starting from the most common assumptions of the mechanical behaviour of the various materials, proposes a fully-analytical formulation for determining the response in terms of the relationship between the external force and the corresponding maximum interface slip observed in those tests. The proposed approach emphasises the key behavioural differences between “short” and “long” bonding length. The former are characterised by a softening behaviour of the relationship between the applied force and the maximum slip, while the latter exhibits a numerically challenging snap-back behaviour. All the key points of the relationship between the external force and the maximum interface slip are defined in closed-form for both the above mentioned cases. Finally, a comparison with some experimental results obtained on FRP-to-concrete pull-out tests are proposed.     

FRP-混凝土界面剥离破坏过程并行数值模拟

FRP-混凝土界面粘结性能和抗拉裂能力是外贴FRP片材加固混凝土结构技术的关键问题。基于FRP与混凝土界面面内剪切试验的结果,采用材料真实破裂过程三维并行分析(RFPA3D-Parallel)系统,对FRP-混凝土界面的粘结性能进行了三维并行数值模拟研究。数值试验再现了FRP-混凝土构件的三维破裂过程演化过程,清晰地反映了拉伸载荷作用下FRP-混凝土构件界面剥离破坏的规律,FRP-混凝土界面剥离破坏是一个细观损伤不断产生和宏观裂缝形成的渐进过程,可通过监测FRP-混凝土结构损伤演化过程的声发射来揭示FRP-混凝土结构在外载荷作用下的损伤程度。FRP片材在加载过程中的变形剥离破坏过程大致可以划分为四个阶段：(1)弹性变形阶段;(2)弹性软化阶段;(3)弹性软化剥离阶段;(4)软化剥离阶段。本文的数值计算表明RFPA3D-Parallel并行数值模拟方法为FRP片材-混凝土界面剥离破坏过程和机理研究提供了一个很好的途径,同时也为研究FRP-混凝土工程结构等的损伤断裂机理提供了一个新的分析手段,这对于土木建筑工程中FRP-混凝土结构的工程设计施工、损伤断裂控制及混凝土结构加固等研究无疑具有重要的理论指导和实践意义。     

Creep in concrete beams strengthened with composite materials

This paper investigates the creep behaviour of concrete beams strengthened with externally bonded composite materials. The challenges associated with the creep modelling of the different materials involved are discussed and a theoretical model is developed. The model derived in the paper accounts for the viscoelasticity of the materials using differential-type constitutive relations that are based on the linear Boltzman’s principle of superposition. The model also accounts for the deformability of the adhesive layer in shear and through its thickness, and for its ability to resist stresses in these directions. These aspects are not fully accounted for in the existing models. An incremental formulation of the field equations is conducted via the variational principle of virtual work, which considers the variation of the internal stresses in time and their effect on the creep response. A numerical study that examines the capabilities of the model and quantifies the response of the strengthened beam to sustained loads is presented, with special focus on the edge stresses that develop at the adhesive interfaces and which initiate debonding failures. The effect of flexural cracking of the concrete is also considered through an enhancement of the model, along with a numerical example that describes the variation with time of the forces and stresses in the concrete beam, the internal steel reinforcement, and the FRP strip at the cracked section.     

Modeling of mixed-mode debonding in the peel test applied to superficial reinforcements

This paper focuses on modeling of the interface between a rigid substrate and a thin elastic adherend subjected to mixed-mode loading in the peel test configuration. The context in which the investigation is situated is the study of bond between fiber-reinforced polymer (FRP) sheets and quasi-brittle substrates, where FRP sheets are used as a strengthening system for existing structures. The problem is approached both analytically and numerically. The analytical model is based on the linear-elastic fracture mechanics energy approach. In the numerical model, the interface is discretized with zero-thickness contact elements which account for both debonding and contact within a unified framework, using the node-to-segment contact strategy. Uncoupled cohesive interface constitutive laws are adopted in the normal and tangential directions. The formulation is implemented and tested using the finite element code FEAP. The models are able to predict the response of the bonded joint as a function of the main parameters, which are identified through dimensional analysis. The main objective is to compute the debonding load and the effective bond length of the adherend, i.e., the value of bond length beyond which a further increase has no effect on the debonding load, as functions of the peel angle. The detailed distributions of interfacial shear and normal stresses are also found. Numerical results and analytical predictions are shown to be in excellent agreement.     

INTERFACIAL BEHAVIOR OF PIPE JOINTS UNDER TORSION LOADS

The interfacial behavior of pipe joints is studied in this paper. Firstly, through nonlinear fracture mechanics, the analytical expressions of interfacial shear stress and the loaddisplacement relationship at loaded end of pipe joints under torsion loads are obtained. Thus the shear stress propagation and the debonding process of the whole interface for different bond lengths can be predicted. Secondly, through the analytical solutions, the influences of different bond lengths on the load-displacement curve and the ultimate load are studied. The stress transfer mechanism, the interface crack propagation and the ductility behavior of the joints can be explained.     

Coupled mixed-mode cohesive zone modeling of interfacial debonding in simply supported plated beams

The development of predictive models for plate end debonding failures in beams strengthened with thin soffit plates is a topic of great practical relevance. After the early stress-based formulations, fracture mechanics approaches have become increasingly established. More recently, the cohesive zone (CZ) model has been successfully adopted as a bridge between the stress- and fracture mechanics-based treatments. However, the few studies of this nature propose complex formulations which can only be implemented numerically. To date, the only available analytical solution based on CZ modeling for the prediction of interfacial stresses/debonding in plated beams is limited to the determination of interfacial shear stresses and thus neglects the mixed-mode effects generated by the presence of interfacial normal stresses at the plate end. This paper presents a new analytical formulation based on the CZ modeling approach for the prediction of plate end debonding in plated beams. A key enhancement with respect to the previous solution is the use of a coupled mixed-mode CZ model, which enables a full account of mixed-mode effects at the plate end. The model describes the evolution of the interface after the end of the elastic regime, and predicts the value of the load at incipient debonding. The achievement of a closed-form solution for this quite complex case entails the introduction of a crucial simplifying assumption, as well as the ad hoc modeling of an effective cohesive interfacial response. The paper presents the analytical theory and compares its predictions with numerical and experimental results.     

FRP strengthened walls with delaminated regions – Geometrically nonlinear response

The paper studies the geometrically nonlinear behavior of walls that are strengthened with fiber reinforced polymer (FRP) composite materials but include pre-existing delaminated regions. The paper uses an analytical–numerical methodology. Three specially tailored finite elements that correspond to perfectly bonded regions, to delaminated regions where the debonded layers are in contact, and to delaminated regions where the debonded layers are not in contact are presented. All finite elements are based on a high order multi layered plate theory. The geometrical nonlinearity is introduced by means of the Von Karman nonlinear strains whereas the contact nonlinearity is handled iteratively. The validity and convergence of the finite element models is demonstrated for each type of element through comparison with closed form analytical solutions available for specific cases. The unified model that combines the three types of finite element is then used for studying the nonlinear behavior of a locally delaminated FRP strengthened wall under in-plane normal and in-plane shear loads. Finally, conclusions regarding the effect of the delamination on the response of the strengthening system, on the conditions that evolve in the bonded region that surrounds the delamination, and on the global response of the multi-layered structure are drawn. Additional conclusions regarding the application of the modeling approach to other delamination sensitive layered structural systems close the paper.     

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.