A unified approach for the static and dynamic analyses of intermediate debonding in FRP-strengthened reinforced concrete beams

A spectral method is proposed for solving static and dynamic problems in FRP-strengthened reinforced concrete beams in a unified way. In order to appropriately simulate the debonding failure a mechanical model considering nonlinear stress–strain relationships for concrete and steel is used. The FRP-to-concrete interface is modelled using a realistic bilinear local bond-slip law. Numerical results with the proposed model for the interfacial shear stress distribution and the load–displacement response are derived for beams statically tested. Using the same spectral model the influence of interfacial delaminations on the dynamic characteristics of the structures is studied. The feasibility of the proposed method for performing dynamic analyses for high frequency excitations in a very simple and non-expensive way makes this study very useful in non-destructive testing analyses as a tool for diagnoses and detection of debonding in its initial stage by monitoring the change in dynamic characteristics.     

Experimental and numerical investigation of the debonding interface between an old concrete and an overlay

The paper focuses on debonding propagation along an interface, notably on the major influence of the interlocking between the two faces of the debonding interface. The aim of the study is to obtain the data necessary for relevant and efficient debonding modelling. The work associates experiment and simulation with the purpose of quantifying the interlocking along the interface. The overlay material investigated was a fibre reinforced mortar (FRM). Direct tension tests of notched FRM specimens were firstly conducted to obtain the tensile strength and the residual normal stress—crack width relationship. Its Young's modulus was determined from compression tests. The substrate-overlay interface was investigated by direct tension tests and flexure tests performed on composite substrate-overlay specimens. The direct tension tests provided the interface tensile strength and the relationship between debonding-opening and residual normal tensile stress. Three point flexural static tests informed on the structural behaviour of the interface. The debonding interface propagation was monitored using a video-microscope with a maximum enlargement of ×175. Using the identified and quantified parameters, modelling of the above mentioned static tests was carried out by the finite elements method using CAST3M code developed in France by CEA (Centre for Atomic Energy). The comparison of modelling and experiment results shows a good coherence and proves the important role of interlocking on the debonding mechanism.     

A superimposed cohesive zone model for investigating the fracture properties of concrete–asphalt interface debonding

A cohesive zone model is proposed to simulate the interface debonding, a preponderant cause of failure for bonded concrete overlay of asphalt (BCOA). The model is constructed by superimposing four root models, each representing the mechanism of one subcritical failure at the interface zone observed in laboratory experiments. The model parameters are established through an inverse analysis of wedge splitting tests performed on BCOA specimens. These inputs are mainly a function of the materials at the interface zone, such as microtexture and macrotexture, and thus can be expected to be applicable to the numerical simulation of a full scale BCOA slab. For modeling across scales, the impact of specimen size, milling depth and initial flaw size on the model, in terms of peak traction and fracture energy, is also discussed.     

A fracture-based model for FRP debonding in strengthened beams

This paper presents an experimental and analytical research study aimed at understanding and modeling of debonding failures in fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beams. The experimental program investigated debonding failure modes and mechanisms in beams strengthened in shear and/or flexure and tested under monotonic loading. A newly developed fracture mechanics based model considers the global energy balance of the system and predicts the FRP debonding failure load by characterizing the dominant mechanisms of energy dissipation during debonding. Validation of the model is performed using experimental data from several independent research studies and a design procedure is outlined.     

An experimental and numerical study on omega stringer debonding

Omega stringers offer interesting structural capabilities and are expected on future aircraft fuselages. In postbuckling mode, the final failure of these structures may occur by stringer debonding between stringer flanges and the skin of the fuselage. In this study, it is demonstrated that the use of fracture mechanics allows to predict skin/omega stringer separation under multiple load cases. Three different load cases and experiments are presented allowing a debonding to start at different locations: at free flange edges or at the inner radius of the omega. Firstly, a skin/stringer configuration subjected to three point bending following the longitudinal axis of the stringer was tested. For this configuration, a numerical study was made and shows the influence of a refined mesh taking into account resin fillets. Secondly, new specimens were obtained by cutting into slices the longitudinal specimen. Those specimens were subjected to four points bending. It has been shown that the upper rolls position of the test jig could modify the debonding location. Numerical models have allowed to determine accurately the debonding location and the associated load level. For some specimens, resin fillets were removed from the flange tips and their effect were assessed numerically and experimentally.     

Prediction of intermediate crack debonding failure in FRP-strengthened reinforced concrete beams

The present paper addresses with intermediate crack (IC) debonding failure modes in FRP-strengthened reinforced concrete beams; a non-linear local deformation model, derived from a cracking analysis based on slip and bond stress, is adopted to predict the stresses and strains distribution at failure. Local bond-slip laws at the longitudinal steel-to-concrete and FRP-to-concrete interfaces, as well as the tension stiffening effect of the reinforcement (steel and FRP) to the concrete, are considered. Model predictions are compared to experimental results available in the literature together with predictions of other models. Reasonable agreement with experimentally measured IC debonding loads and FRP strains is observed for all examined strengthened beams. Results of a parametric analysis, varying geometrical and mechanical parameters involved in the physical problem are also presented and discussed.     

复合材料或钢板加固RC梁的板端剥离破坏承载力

 对受拉表面粘贴纤维增强复合材料( Fibre reinforced polymer/ plastic , FRP)或钢板的抗弯加固钢筋混凝土(Reinforced concrete , RC)梁的板端剥离破坏承载力进行了较为细致的研究。在分析关键参数、 试验数据及现 有计算模型的基础上 , 提出了一个简单、 合理的板端剥离破坏承载力计算新模型。该模型首先给出板端位于纯弯 区的弯曲剥离和板端位于弯矩为零或接近于零的主剪区的剪切剥离的承载力计算公式 , 进而采用简洁的相关曲线 确定板端在弯2剪共同作用区的剥离承载力。新模型通过包含未加固梁的抗剪承载力和几个物理意义明确的重要 参数 , 充分反映了抗弯加固梁的剥离破坏机制 , 与试验结果吻合良好 , 使用方便 , 可供制订规范和实际加固工程 设计时参考应用。     

含面芯界面缺陷的蜂窝夹芯板侧向压缩破坏模式

为了对含面芯层间脱胶缺陷的蜂窝夹芯板在侧向压缩载荷作用下的典型破坏模式进行数值预报, 建立了基于蔡-希尔破坏准则和粘结模型的计算模型。该计算模型是建立在对蜂窝夹芯板的双悬臂梁(DCB)和单臂梁(SLB) 试验中所发现的一种新的破坏模式的分析基础之上的。对蜂窝夹芯板的侧向压缩破坏行为的数值预报中, 发现一种新的破坏模式: 位于脱胶区域的面板首先发生局部屈曲失稳, 随后面板内部靠近芯子的45°/0°层间出现分层, 与此同时最靠近芯子的45°铺层发生断裂, 伴随着45°/0°层间分层的扩展, 面板发展成为对称性整体屈曲失稳。与侧向压缩试验测试结果对比发现, 计算模型模拟中所预报的破坏模式在实验测试中也得到了很好的验证。      

A numerical study of inclusion-matrix debonding in the presence of a nearby crack

Debonding of an inclusion from the surrounding matrix in the presence of a nearby crack tip is studied numerically. Finite element models of symmetric three-point bend configurations are implemented in conjunction with a stiffness degradation method and the maximum tensile stress criteria to investigate the influence of debonding on crack tip parameters. The geometry considered is a single edge cracked beam having a symmetrically positioned stiff or soft cylindrical inclusion ahead of the crack tip. The numerical model is first validated by interferometric measurements on an edge cracked epoxy specimen with a glass inclusion. The measured quantities namely, the crack mouth opening displacement, crack mouth compliance, energy release rate, dominant strain, are all successfully captured by the adopted numerical methodology, before and after the inclusion debonds from the matrix. Subsequently, the effects of parameters such as the distance between the crack tip and inclusion center (L), the inclusion diameter (d), and the Young’s modulus ratio between the inclusion and the matrix, are studied using the model. A stiff inclusion of constant (d/L) ratio debonds from the matrix at higher load levels when the inclusion interface is farther away from the crack tip. The increase in the crack driving force due to debonding is the highest when the inclusion proximity parameter ρ is approximately 0.4 and it decreases when ρ is increased or decreased relative to this value. However, when d/L ratio is varied, higher crack driving forces due to debonding are observed for larger size inclusions due to a greater loss of crack tip shielding and reinforcement. The influence of the modulus ratio (E_i/E_m) due to debonding is most prominent in the range 0-1 for fixed d/L and ρ values. Additionally, a stiffer inclusion tends to debond from the matrix at lower loads for a constant interfacial strength.     

基于激光超声二次谐波技术检测纤维增强树脂复合材料加固混凝土结构剥离损伤

纤维增强树脂(FRP)复合材料加固混凝土结构的早期剥离损伤往往趋向于闭合状态,传统线性超声技术对这种剥离损伤不敏感.本文提出了基于连续激光激发窄带超声波技术结合非线性超声二次谐波法检测FRP复合材料加固混凝土剥离损伤的方法,该方法通过强度调制激光技术在加固结构的表面激励窄带超声表面波,在超声波的扰动下,依据弹簧模型的接...     

Direct determination of cohesive stress transfer during debonding of FRP from concrete

Interface cohesive stress transfer between FRP and concrete during debonding is typically obtained using measured surface strains on the FRP, along the direction of the fibers. The cohesive material law is derived under a set of assumptions which include: (a) the bending stiffness of the FRP laminate is insignificant with respect to that of the concrete test block; (b) the strains in the bulk concrete produced by debonding are negligible, thus concrete substrate can be considered rigid; (c) there is stress transfer between FRP and concrete through the FRP–concrete interface which is of zero thickness; and (d) the axial strain in the FRP composite is uniform across its thickness. In this paper, a test procedure for directly obtaining the through-thickness strains in the FRP and the concrete substrate during cohesive stress transfer associated with debonding is presented. The displacement and strain fields are measured on the side of a direct-shear specimen with the FRP strip attached on the edge. Based on the experimental results, the influence of the assumptions which have been introduced to determine the cohesive law is discussed. Within the stress transfer zone there is a sharp gradient in the shear strain. The location of the interface crack within the stress transfer zone and the cohesive stress transfer during the propagation of the interface crack are determined.     

Thin bonded cement-based overlays: numerical analysis of factors influencing their debonding under monotonic loading

After a period in service, the degradation of concrete structures is unavoidable. For large concrete areas, thin bonded cement-based overlay is a suitable rehabilitation technique. However, the durability of such repairs sometimes remains difficult to predict, especially because of the variable conditions inherent in the work site. The present paper, associating experiment and simulation approaches, focuses on some key parameters influencing debonding propagation along the concrete overlay–substrate interface under static loading. Based on the cohesive crack concept, a model using identified and quantified parameters was built and validated by comparing numerical and experimental results. Different factors having an impact on the interface debonding were then investigated. For the overlay material, the parameters analysed were autogenous shrinkage, Young’s modulus, tensile strength and types of fibre-reinforcement. For the curing conditions, the relative humidity of the surroundings was taken into account. Concerning the overlay–substrate interface, the fracture energy and bond defects were considered. The model predictions allowed the influence of each factor to be evaluated. In particular, the effect of shrinkage on the durability of the composite specimens was clarified. The importance of the capacity of fibres to control debonding by restraining crack opening was proved.     

Multi-level experimental and numerical analysis of composite stiffener debonding. Part 2: Element and panel level

In the framework of test analysis pyramid, large specimens were studied. To represent the bending behaviour during postbuckling, specimens composed of a plate with a stiffener were supported on five points and loaded transversely by two points, thus being subjected to “seven point” bending. By modifying the positions of the two loading points, symmetrical and antisymmetrical buckles that led to interface failure between the flange and the skin could be simulated. First a global numerical model of the test was made in order to assess the efficiency of the approach developed in the first part of this study. Predictions were in accordance with experiments despite strong scatter. Then, a global/local test method was considered. In this method, the global model considered shell elements although the local model used volume elements. The onset of delamination was correctly predicted at local level. Finally, the method was applied to two large stiffened panels subjected to compression and shear.     

Numerical simulation of rebar/concrete interface debonding of FRP strengthened RC beams under fatigue load

The aim of this paper is to simulate the rebar/concrete interface debonding of FRP strengthened RC beams under fatigue load and also, to ascertain the influence of design parameters such as the elastic modulus, thickness and length of the FRP plate on the debonding performance. In order to simplify the simulation, some basic equilibrium equations are formulated and then the stresses of the rebar and FRP plate are numerically solved, and stress intensity factor is avoided in the simulation by fundamentals of fracture mechanics because of its complexity around the crack tip of bi-material interface. With the combination of finite element method and difference approximation, authors program the degradation model of coefficient of friction, debond criterion, propagation law and loop of load process into a commercial finite element code to investigate the fatigue debonding. The relationships between the debond length as well as other fatigue parameters and number of cyclic load are obtained and discussed.     

A bilinear cohesive zone model tailored for fracture of asphalt concrete considering viscoelastic bulk material

A bilinear cohesive zone model (CZM) is employed in conjunction with a viscoelastic bulk (background) material to investigate fracture behavior of asphalt concrete. An attractive feature of the bilinear CZM is a potential reduction of artificial compliance inherent in the intrinsic CZM. In this study, finite material strength and cohesive fracture energy, which are cohesive parameters, are obtained from laboratory experiments. Finite element implementation of the CZM is accomplished by means of a user-subroutine which is employed in a commercial finite element code (e.g., UEL in ABAQUS). The cohesive parameters are calibrated by simulation of mode I disk-shaped compact tension results. The ability to simulate mixed-mode fracture is demonstrated. The single-edge notched beam test is simulated where cohesive elements are inserted over an area to allow cracks to propagate in any general direction. The predicted mixed-mode crack trajectory is found to be in close agreement with experimental results. Furthermore, various aspects of CZMs and fracture behavior in asphalt concrete are discussed including: compliance, convergence, and energy balance.     

Prediction of interfacial fracture between concrete and fiber reinforced polymer (FRP) by using cohesive zone modeling

Interfacial debonding between concrete and fiber reinforced polymer (FRP) is investigated through integrating experiments and computations. An experimental program is designed to evaluate interfacial fracture parameters of mode-I through cutting and bonding specimens with an FRP sheet. The evaluated fracture parameters, i.e. the fracture energy and the bonding strength, are confirmed by predicting FRP debonding failure with the cohesive zone modeling approach. In the cohesive zone model, a traction-separation relation for FRP debonding is proposed with a shape index while providing various initial descending slopes. Computational results of the cohesive zone model agree well with three-point bending test results for both FRP debonding and plain concrete fracture. Furthermore, both experimental and computational results demonstrate that the fracture energy and the cohesive strength are essential fracture parameters for the prediction of FRP debonding behavior.     

Width effect in the interface fracture during shear debonding of FRP sheets from concrete

The increasing use of carbon fiber reinforced polymer (FRP) sheets for strengthening existing reinforced concrete beams has generated considerable research interest in understanding the debonding mechanism of failure in such systems. The influence of the width of the FRP on the load-carrying capacity is investigated in this paper. The interfacial crack propagation and strain distribution during shear debonding are studied using a full-field optical technique known as digital image correlation. The results indicate the development of high stress/strain gradients at the interface as a consequence of the relative slip between the FRP and the concrete. The interface stress transfer between the FRP and concrete produces axial strain gradients in the FRP along its length. In the vicinity of the edges along the width of the FRP, edge regions comprising of both FRP and concrete are established. The edge region is characterized by high strain gradients in a direction perpendicular to the length and is of fixed width throughout the debonding process. The size of the edge regions is also found to be quite independent of the width of the FRP. Mode-II fracture condition exists in the interface directly below the FRP away from the edge regions. The interfacial crack is shown to be associated with a cohesive stress transfer zone of fixed length. During debonding, the stress transfer zone is shown to propagate in a self-similar manner at a fixed load. The interface fracture properties obtained from the portion of FRP away from the edge regions are shown to be independent of the FRP width. It is shown that when the width of concrete is larger than that required for establishing the edge regions, the nominal stress at debonding increases with an increase in the width of FRP. The scaling in the load carrying capacity during shear debonding is shown to be the result of the edge regions which do not scale with the width of the FRP.     

Mechanistic model and numerical analysis for corrosion damage of reinforced concrete structure

Through sampling, we have conducted systematically the analyses of changing characteristics of steel bar corrosion and crack width on reinforced concrete surfaces. Based on the analyses from the sampling, we have obtained the mathematical model for outer elliptical contour and the formulas to calculate thickness of corrosion layer at any associated point on steel bars. A stress model of discrete displacement on fictitious boundary for the corrosion layer and corresponding solutions for displacement and stress on the fictitious boundary have been advanced, which solve quantitatively the stress to the structure acted by corrosion layer. Finally, under the conditions of displacement on the fictitious boundary and by applying numerical manifold method, we had performed the simulation of track for crack propagation caused by corrosion and expansion of side steel bars as time elapses in existing reinforced concrete structures. The simulation results have conformed to those of the experiment.     

A method for modeling the transition of weak discontinuities to strong discontinuities: from interfaces to cracks

Cohesive zone models are widely used to model interface debonding problems; however, these models engender some significant drawbacks, including the need for a conforming mesh to delimit the interfaces between different materials or components and that penalty or other constraint methods necessary to enforce initially perfect adhesion at interfaces degrade the critical time step for stability in explicit time integration. This article proposes a new technique based on the extended finite element method that alleviates these shortcomings by representing the transition from perfect interfacial adhesion to debonding by switching the enriched approximation basis functions from weakly discontinuous to strongly discontinuous. At this transition, the newly activated degrees of freedom are initialized to satisfy a point‐wise consistency condition at the interface for both displacement and velocity. Analysis of the stable time step for one‐dimensional elements with mass lumping is presented, which shows the increase of the stable time step compared with a cohesive zone model. Both one‐dimensional and two‐dimensional verification examples are presented, illustrating the potential of this new approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Thermal loading of a thin layer with circular debonding over a substrate

By using techniques appropriate to mixed boundary value problems, this study addresses the determination of stress intensity factors for a circular interface debonding between a thin layer and a substrate subjected to nearly uniform temperature change. The solution method involves three-dimensional equilibrium equations of thermo-elasticity under axisymmetry conditions. The stress intensity factors are obtained by solving the resulting pair of coupled singular integral equations numerically. This revised version was published online in August 2006 with corrections to the Cover Date.