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.     

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.     

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.     

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.     

Improved theoretical solution for interfacial stresses in concrete beams strengthened with FRP plate

In this paper, an improved theoretical interfacial stress analysis is presented for simply supported concrete beam bonded with a FRP plate. The adherend shear deformations have been included in the present theoretical analyses by assuming a linear shear stress through the thickness of the adherends, while all existing solutions neglect this effect. Remarkable effect of shear deformations of adherends has been noted in the results. Indeed, the resulting interfacial stresses concentrations are considerably smaller than those obtained by other models which neglect adherent shear deformations. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. This research is helpful for the understanding on mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

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。     

Mechanics and fracture of crack tip deformable bi-material interface

Novel interface deformable bi-layer beam theory is developed to account for local effects at crack tip of bi-material interface by modeling a bi-layer composite beam as two separate shear deformable sub-layers with consideration of crack tip deformation. Unlike the sub-layer model in the literature in which the crack tip deformations under the interface peel and shear stresses are ignored and thus a “rigid” joint is used, the present study introduces two interface compliances to account for the effect of interface stresses on the crack tip deformation which is referred to as the elastic foundation effect; thus a flexible condition along the interface is considered. Closed-form solutions of resultant forces, deformations, and interface stresses are obtained for each sub-layer in the bi-layer beam, of which the local effects at the crack tip are demonstrated. In this study, an elastic deformable crack tip model is presented for the first time which can improve the split beam solution. The present model is in excellent agreements with analytical 2-D continuum solutions and finite element analyses. The resulting crack tip rotation is then used to calculate the energy release rate (ERR) and stress intensity factor (SIF) of interface fracture in bi-layer materials. Explicit closed-form solutions for ERR and SIF are obtained for which both the transverse shear and crack tip deformation effects are accounted. Compared to the full continuum elasticity analysis, such as finite element analysis, the present solutions are much explicit, more applicable, while comparable in accuracy. Further, the concept of deformable crack tip model can be applied to other bi-layer beam analyses (e.g., delamination buckling and vibration, etc.).     

Finite element analysis of interfacial stresses in FRP–RC hybrid beams

The interfacial stresses in fiber reinforced plastic (FRP)–reinforced concrete (RC) hybrid beams were studied by the finite element method. The mesh sensitivity test shows that the finite element results for interfacial stresses are not sensitive to the finite element mesh. The finite element analysis then is used to calculate the interfacial stress distribution and evaluate the effect of the structural parameters on the interfacial behavior. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. This research is helpful for the understanding on mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

碳纤维布加固混凝土梁的解析分析

根据弹性理论和部分组合截面假定，分析碳纤维布加固混凝土梁体系，建立单位长度粘结界面剪力表达式和碳纤维布轴向拉力微分方程，从而推导出碳纤维布拉力、混凝土梁正截面弯矩和粘结界面剪应力解析解的一般形式，满足实际应用．结合算例指出：碳纤维布轴向拉力和粘结界面剪应力分布不均匀，在端部区段应力集中，可能导致加固失效，应采取措施加强锚固．     

FRP-混凝土界面粘结行为的参数影响研究

FRP-混凝土界面的粘结性能对FRP加固混凝土结构力学行为和破坏模式有着重要影响。本文对表征FRP-混凝土界面粘结性能的三个重要参数(界面初始刚度、最大剪应力、界面破坏能)开展研究,通过13个单剪试件的试验考察了混凝土强度、胶层厚度和粘结长度等因素对界面粘结行为的影响,根据试验结果拟合了界面破坏能、最大剪切应力与胶层剪切刚度、混凝土强度之间的函数关系。在试验研究基础上,构建了外贴FRP-混凝土界面粘结的有限元模型。通过有限元分析考察了界面破坏能等三个参数不变的前提下,不同的局部粘结滑移本构关系对界面粘结行为的影响;进而研究了其中一个参数变化时引起的界面粘结性能改变。研究结果表明:界面粘结承载力随着胶层厚度增加而逐渐提高;胶层厚度与界面破坏能成正比,与峰值剪应力成反比;当界面破坏能等三个参数保持不变时,局部粘结滑移本构关系对FRP-混凝土界面粘结性能的影响较小;三个参数中的一个增大时将延缓界面破坏的过程。     

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。     

Modelling of stresses and strains in bonded concrete overlays subjected to differential volume changes

The differential volume changes between repair material and substrate concrete induces stresses in concrete overlays. These stresses could cause the repair material cracking or the interface delamination, which facilitate the penetration of harmful substances into concrete and hence accelerate the deterioration of concrete overlays. In order to investigate the characteristics of these stresses, an analytical model has been developed based on the plate theory and the assumption of the linear relation between shear stress and slip at the interface. This model is able to calculate the tensile stress in the repair material, shear and normal stresses at the interface and the corresponding strains. With this model, the influence of the interface shear stiffness, the dimension of the concrete overlay, and the elastic moduli of two materials on stresses and strains was studied.     

FRP-to-concrete interfaces between two adjacent cracks: Theoretical model for debonding failure

External bonding of fibre reinforced polymer (FRP) composites has become a popular technique for strengthening concrete structures all over the world. The performance of the interface between FRP and concrete is one of the key factors affecting the behaviour of the strengthened structure. Existing laboratory research has shown that the majority of reinforced concrete (RC) beams strengthened with a bonded FRP soffit plate fail due to debonding of the plate from the concrete. Two types of debonding failures have been commonly observed: plate end debonding and intermediate crack induced debonding. In order to understand and develop methods to predict such debonding failures, the bond behaviour between concrete and FRP has been widely studied using simple shear tests on FRP plate/sheet-to-concrete bonded joints and a great deal of research is now available on the behaviour of these bonded joints. However, for intermediate crack induced debonding failures, the debonding behaviour can be significantly different from that observed in a simple shear test. Among other factors, the most significant difference may be that the FRP plate between two adjacent cracks is subject to tension at both cracks. This paper presents an analytical solution for the debonding process in an FRP-to-concrete bonded joint model where the FRP plate is subject to tension at both ends. A realistic bi-linear local bond-slip law is employed. Expressions for the interfacial shear stress distribution and the load–displacement response are derived for different loading stages. The debonding process is discussed in detail. Finally, results from the analytical solution are presented to illustrate how the bond length affects the behaviour of such bonded joints. While the emphasis of the paper is on FRP-to-concrete joints, the analytical solution is equally applicable to similar joints between thin plates of other materials (e.g. steel and aluminium) and concrete.     

弹性地基双层梁理论下的混凝土路面力学分析

为建立混凝土路面结构受力分析计算模型,以Winkler弹性地基梁模型为基础,推导出了弹性地基双层梁理论的表达式;给定边界条件,利用MATLAB软件获得了无限长弹性地基梁在集中力作用下的挠度表达式。将混凝土路面结构简化为弹性地基上的双层梁,当车辆荷载作用于混凝土路面时,在集中载荷的作用下,建立了面层与基层的微分平衡方程。应用广义“初参数”法,得到了双层梁位移和应力的解析解。通过算例,对面层及基层的变形和应力进行了分析,结果表明:增大面层、基层的轴惯性矩和地基的弹性常数,可以有效地减少面层和基层的变形量,降低最大应力数值,但抗弯刚度对基层和面层的弯矩受力影响不大。最后将结果与ANSYS分析结果进行了比较,佐证了解的可靠性,研究结果可为混凝土路面结构设计提供依据。     

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.     

Flexural time-dependent cracking and post-cracking behaviour of FRP strengthened concrete beams

The time-dependent flexural cracking behaviour of reinforced concrete beams strengthened with externally bonded composite materials is investigated with a focus on the creep effects. A theoretical model is developed, which accounts for the creep of the different materials involved, and which also accounts for the time-dependent cracking and the tension-stiffening phenomenon. The deformability of the adhesive layer in shear and through its thickness, as well as its ability to transfer shear and vertical normal stresses, is considered in the model. The incremental governing equations are formulated via the variational principle of virtual work based on an incremental exponential algorithm for the creep modelling. The capabilities of the model are demonstrated through numerical examples including a comparison with test results available in the literature. The results show that creep causes a significant redistribution of the internal forces and the interfacial stresses at the adhesive interfaces with time, which should be carefully considered in the design of FRP strengthened members.     

Exact static solutions to piezoelectric smart beams including peel stresses. II. Numerical results,comparison and discussion

This part presents the numerical results, comparisons and discussion for the exact static solutions of smart beams with piezoelectric (PZT) actuators and sensors including peel stresses presented in Part I. (International Journal of Solids and Structures, 39, 4677–4695) The actuated stress distributions in the adhesive and the adhesive edge stresses varying with the thickness ratios are firstly obtained and presented. The actuated internal stress resultants and displacements in the host beam are then calculated and compared with those predicted by using the shear lag model. The stresses in the adhesive caused by an applied axial force, bending moment and shear force are calculated, and then used to compute the sensing electric charges for comparison with those predicted using the shear lag model. The numerical results are given for the smart beam with (a) one bonded PZT and (b) two symmetrically bonded PZTs, with a comparison to those predicted using the shear lag model. Novel, simple and more accurate formulas for the equivalent force and bending moment induced by applied electric field are also derived for the host beam with one PZT or two symmetrically bonded PZTs. The symmetric shear stress and the anti-symmetric peel stress components caused by a shear force are discussed. In addition, in the case of PZT edge debonding, the stress redistribution in the adhesive and the self-arresting mechanism are also investigated.