Modelling of mixed mode debonding in externally FRP reinforced beams

In this paper a refined model able to analyze edge debonding problems in beams strengthened with externally bonded composite laminated plates, is presented. The structural system is viewed as composed by three physical different components: the base beam (made of steel or concrete), the adhesive layer and the bonded plate. Each component may be comprised by one or several mathematical layers which adopts the first-order shear deformation laminate theory. Bonding and continuity conditions between different layers are simulated by using the interface modelling technique. Strong and collapsed interface models are introduced in order to capture stress singularities and to reduce the complexity of the analysis, respectively. Governing equations for displacement fields complemented with boundary and continuity conditions, are obtained by a variational approach. According to a fracture mechanics approach, the analysis is carried out by evaluating the total and individual mode components of energy release rate (ERR).Applications for typical strengthened systems, carried out by numerical integration procedures, are proposed in which the energy release rates are evaluated by means of interface displacement jumps, leading to a very efficient numerical procedure. The approximations introduced in the model with respect to the adopted number of mathematical layers are analyzed and comparisons with existent models are given. For the simpler two-layer model of the structure, comparisons are given with the closed-form solutions obtained in [Greco F, Nevone Blasi P, Lonetti P. An analytical investigation of debonding problems in beams strengthened using composite plates. Eng Fract Mech 2006, in press]. The convergence to the results from continuum analysis is investigated when a refined assembly of layers is adopted, by means of comparisons with predictions from very careful FE solutions. Finally, the effect of different debonding modes on the overall behaviour of the structural system is analyzed. These results show the capability and the accuracy of the proposed approach to predict debonding failure behaviour in both steel and concrete strengthened beams. As a matter of fact, the proposed approach involves reduced computational cost with respect to FE solutions based on 2D continuum elements and the use of a multi-layer structural model leads to avoid some complexities related to the classical elasticity theory for bimaterial interface cracks.     

Interfacial debonding behavior of composite beam/plates with PZT patch

This paper studies interfacial debonding behavior of composite beams which include piezoelectric materials, adhesive and host beam. The focus is put on crack initiation and growth of the piezoelectric adhesive interface. Closed-form solutions of interface stresses and energy release rates are obtained for adhesive layer in the piezoelectric composite beams. Finite element analyses have been carried out to study the initiation and growth of interfaces crack for piezoelectric beams with interface element by ANSYS, in which the interface element of FE model is based on the cohesive zone models to characterize the fracture behavior of the interfacial debonding. The results have been compared with analytical solution, and the influence of different geometry and material parameters on the interfacial behavior of piezoelectric composite beams have been discussed.     

Interface stress redistribution in FRP-strengthened reinforced concrete beams using a three-parameter viscoelastic foundation model

External bonding of FRP plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP–concrete interface are critical to the effectiveness of this technique because high stress concentration along the FRP–concrete interface can lead to the FRP debonding from the concrete beam. In this study, a novel analytical solution has been developed to predict the interface stress redistribution of FRP-strengthened reinforced concrete beams induced by the viscoelastic adhesive layer. Both the FRP plate and the RC beam are modeled as Timoshenko’s beams, connected through the adhesive layer. The adhesive layer is modeled as a three-parameter viscoelastic foundation (3PVF) using Standard Linear Solid model. The 3PVF model satisfies the equilibrium equation of the adhesive layer and the zero shear-stress boundary condition at the free edge. Closed-form expressions of the time-dependent interface stresses and deflection of the beam are obtained using Laplace transform. Finite element analysis is also conducted to verify the analytical solution using a subroutine UMAT based on the Standard Linear Solid model. Numerical results suggest that the stress concentrations within the FRP–concrete interface relax with time. The axial force in the FRP plate also reduces with time due to the creep of the adhesive layer. However, this relaxation is limited to a small zone close to the end of the FPR plate.     

Experiments and analytical comparison of RC beams strengthened with CFRP composites

This paper deals with strengthening, upgrading, and rehabilitation of existing reinforced concrete structures using externally bonded composite materials. Five strengthened, retrofitted, or rehabilitated reinforced concrete beams are experimentally and analytically investigated. Emphasis in placed on the stress concentration that arises near the edge of the fiber reinforced plastic strip, the failure modes triggered by these edge effects, and the means for the prevention of such modes of failure. Three beams are tested with various edge configurations that include wrapping the edge region with vertical composite straps and special forms of the adhesive layer at its edge. The last two beams are preloaded up to failure before strengthening and the ability to rehabilitate members that endured progressive or even total damage is examined. The results reveal a significant improvement in the serviceability and strength of the tested beams and demonstrate that the method is suitable for the rehabilitation of severely damaged structural members. They also reveal the efficiency of the various edge designs and their ability to control the characteristic brittle failure modes. The analytical results are obtained through the Closed-Form High-Order model and are in good agreement with the experiment ones. The analytical and experimental results are also used for a preliminary quantitative evaluation of a fracture mechanics based failure criterion for the strengthened beam.     

Debonding analysis of fiber-reinforced-polymer strengthened beams: Cohesive zone modeling versus a linear elastic fracture mechanics approach

A linear elastic fracture mechanics (LEFM) approach and a cohesive interface (cohesive zone) modeling approach to the debonding analysis of concrete beams strengthened with externally bonded fiber-reinforced-polymer (FRP) strips are studied and compared. The analytical models that are based on the two approaches are presented and discussed. The cohesive interface model is formulated using a potential function and it takes into account the shear effects, the effect of the peeling stresses, and the coupling of the shear and the peeling effects. This model takes the form of a set on nonlinear differential equations. The LEFM model combines stress analysis using the high order theory and fracture analysis using the concepts of the energy release rate and the J-integral. In addition, an algorithm that converts the results of the LEFM model into the equilibrium path of the debonding process is developed. The main advantages and disadvantages of the two approaches are also discussed. The two approaches are compared in terms of their applicability to quantify and describe the debonding process in various cases that include a single shear test, an edge peeling test, and a beam specimen strengthened with FRP.     

Cohesive zone model for the prediction of interfacial shear stresses in a composite-plate RC beam with an intermediate flexural crack

In this paper, an analytical method is developed to predict the distribution of interfacial shear stresses in concrete beams strengthened by composite plates. Accurate predictions of such stresses are necessary when designing to prevent debonding induced by a central flexural crack in a FRP-plated reinforced concrete (RC) beam. In the present analysis, a new theoretical model based on the bi-linear cohesive zone model for intermediate crack-induced debonding is established, with the unique feature of unifying debonding initiation and growth. Adherent shear deformations have been included in the present theoretical analyses by assuming a parabolic shear stress through the thickness of the adherents, verifying the cubic variation of the longitudinal displacement function, whereas all existing solutions neglect this effect. The results obtained for interfacial shear stress distribution near the crack are compared to the Jialai Wang analytical model and the numerical solutions are based on finite element analysis. Parametric studies are carried out to demonstrate the effect of the mechanical properties and thickness variations of FRP, concrete and adhesive on interface debonding. Indeed, the softening zone size is considerably larger than that obtained by other models which neglect adherent shear deformations. However, loads at the limit of the softening and debonding stages are larger than those calculated without the thickness effect. Consequently, debonding at the interface becomes less apparent and the lifespan of our structure is greater.     

Structural behavior and inter-layer displacements in CFRP plated steel beams – Optical measurements,analysis, and comparative verification

The linear elastic structural behavior of steel beams strengthened with externally bonded composite materials is experimentally and analytically investigated. The paper focuses on the full-field inter-layer relative displacements between the beam and the FRP layer. Such displacements result from the interaction between the adhesively bonded components and it is the integrated outcome of the interfacial conditions and the deformability of the adhesive. As such, it is commonly adopted as the state variable in simplified bond shear stress–slip representations. This aspect, as well as other aspects of the global and localized structural response, is analytically and experimentally quantified. The experiment includes a simply supported steel beam strengthened with a CFRP plate. A 3D image correlation technique with sequential measurements is used for the assessment of the full-field inter-layer displacements along the beam. The analysis adopts a high order modeling approach that accounts for the 2D stress and displacement fields through the depth of the adhesive and a 1D shear stress–slip approach using only a linear increasing branch. The comparison between the results provides validation of the analytical and experimental capabilities with emphasis on the inter-layer effects. One of the interesting findings which is discussed and explained in this paper is the fact that the slip values calculated with the shear stress–slip approach are notably different from the ones that can be measured experimentally and determined by the high order model.     

Delamination of thin bonded cement-based overlays: analytical analysis

This paper deals with an analytical approach for the prediction of debonding initiation between cement-based overlay and old concrete substrate under monotonous mechanical loading. Based on the linear elastic fracture mechanics, an available analytical model has been used. The calculations take into account the interlocking between two crack surfaces in the overlay. To validate the model, three point static bending tests on composite specimens were carried out. Assuming that the debonding initiation just occurs after the crack cutting the overlay layer reaches the overlay–substrate interface, the stress intensity factor of the debonding tip can be calculated, allowing prediction of stress fields near the interface debonding tip. Then with a criterion of debonding initiation and propagation depending on the interface tensile strength, the load associated could be determined and might be interesting for the design of thin bonded cement-based overlays. The adequateness of this analytical approach was verified by both experimental data and finite element calculations.     

Static strength tests of steel plate strengthened concrete beams

The behaviour of damaged concrete beams strengthened by externally bonded steel plates is experimentally investigated. The study includes an investigation of the mode of failure, including flexural failure and the interface separation of the steel plate. Simply supported beams under monotonically increasing loads are considered exclusively. A total of five plain concrete beams externally reinforced with bonded steel plates were tested under static loads to determine their strength and behaviour. The variables tested were the thickness of the external steel plate, length and location of the interfacial crack, and the degree of surface preparation of the steel plate. In all five beams the thickness of adhesive was kept constant. The results indicate that (i) the behaviour of a damaged open sandwich beam is similar to that of a singly reinforced concrete beam when no debonding occurs between the concrete and the adherent steel plate; (ii) when debonding occurs, the failure is sudden and at loads smaller than for a case where failure is either by yielding of steel or crushing of concrete; (iii) the case with an interfacial crack between the steel and the adhesive is more critical than the case when the interfacial crack is between the adhesive and the concrete; and (iv) the failure load and the mode of failure are dependent on the degree of surface preparation of the steel plate. Analytical investigation to predict the interfacial debonding is summarized, and the results suggest that linear elastic fracture mechanics is suited for predicting the failure load for open sandwich beams which fail by interface debonding.     

Time-dependent behavior of RC beams strengthened with externally bonded FRP plates: interfacial stresses analysis

External bonding of fibre reinforced polymer (FRP) composites has becomes a popular technique for strengthening concrete structures all over the world. An important failure mode of such strengthened members is the debonding of the FRP plate from the concrete due to high interfacial stresses near the plate ends. For correctly installed FRP plate, failure will occur within the concrete. Accurate predictions of the interfacial stresses are prerequisite for designing against debonding failures. In particular, the interfacial stresses between a beam and soffit plate within the linear elastic range have been addressed by numerous analytical investigations. In this study, the time-dependent behavior of RC beams bonded with thin composite plate was investigated theoretically by including the effect of the adherend shear deformations. The time effects considered here are those that arise from shrinkage and creep deformations of the concrete. This paper presents an analytical model for the interfacial stresses between RC beam and a thin FRP plate bonded to its soffit. The influence of creep and shrinkage effect relative to the time of the casting and the time of the loading of the beams is taken into account. Numerical results from the present analysis are presented to illustrate the significance of time-dependent of adhesive stresses.     

Viscoelastic analysis of FRP strengthened reinforced concrete beams

External bonding of FRP plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP-concrete interface are critical to the effectiveness of this technique because high stress concentration along the FRP-concrete interface can lead to the FRP debonding from the concrete beam. Although the short-term stress distribution along the FRP-concrete interface has been studied extensively, very few studies have been conducted on the long-term stress distribution, which closely simulates the behavior of the structure during the service-life. In this study, we develop a viscoelastic solution for the long-term interface stress distribution in a FRP plate strengthened reinforced concrete beam. In this solution, the RC beam and the FRP plate are modeled as elastic materials; while the adhesive layer is modeled as a viscoelastic material using the Standard Linear Solid model. Closed-form expressions of the interface stresses and deflection of the beam are obtained using Laplace transform and calculated using the Zakian’s numerical method. The validation of this viscoelastic solution is verified by finite element analysis using a subroutine UMAT based on the Standard Linear Solid model.     

Stress analysis of steel beams strengthened with a bonded hygrothermal aged composite plate

In this paper, the problem of interfacial stresses in steel beams strengthened with bonded hygrothermal aged composite laminates is analyzed using linear elastic theory. The analysis is based on the deformation compatibility approach developed by Tounsi (Int. J. Solids Struct. 43:4154–4174, 2006) where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The adopted model takes into account the adherend shear deformations by assuming a linear shear stress through the depth of the steel beam. This solution is intended for application to beams made of all kinds of materials bonded with a thin composite plate. For steel I-beam section, a geometrical coefficient ξ is determined to show the effect of the adherend shear deformations. This research is helpful for the understanding on mechanical behaviour of the interface and design of such structures.     

A three-dimensional eigenfunction expansion approach for singular stress field near an adhesively-bonded scarf joint interface in a rigidly-encased plate

A three-dimensional eigenfunction expansion approach for determination of the singular stress field in the vicinity of an adhesively-bonded scarf joint interface in a plate, with its top and bottom surfaces being encased, fully or partially, between infinitely rigid blocks is presented. The plate is subjected to extension/bending (mode I) and in-plane shear/twisting (mode II) far-field loading. Both the adhesive layer and plate materials are assumed to be isotropic and elastic. The boundary conditions that are prescribed on the end-faces (free, fixed and lubricated) of the plate as well as those, prescribed at the bottom or top surface of the scarf-bonded plate on either side of the interface between the plate and adhesive layer materials (fixed-fixed, free-fixed and fixed-free), are exactly satisfied. Numerical results include the dependence of the lowest eigenvalue (or most severe stress singularity) on the wedge aperture angle of the plate material. Variation of the same with respect to the shear moduli ratio of the constituent plate and adhesive layer materials is also an important part of the present investigation. Hitherto unobserved interesting and physically meaningful conclusions in regards to the fixed edge singularity and delamination type flaw sensitivity of an adhesively bonded plate surface are also presented. Finally, hitherto unavailable results, pertaining to the through-width variations of stress intensity factors corresponding to symmetric and skew-symmetric sinusoidal loads that also satisfy the boundary conditions on the end-faces of the adhesively bonded plate, in the vicinity of the scarf joint interface, under investigation, bridge a longstanding gap in the bonded joint stress singularity/fracture mechanics literature.     

Thin plate bending of dissimilar half-planes with interface debonding emanating from an elliptical hole

The problem of thin plate bending of two bonded dissimilar half-planes containing an elliptical hole on the interface with debonding emanating on both sides is presented. The external load is a uniformly distributed bending moment applied at infinity perpendicular to the interface. An analytical solution is obtained using the complex stress function approach and the rational mapping function technique. Stress distributions on the interface, the boundaries of the hole and in the vicinity of the debonded tips are obtained. The stress intensity of debonding is obtained for aribitrary lengths of debonding, all possible hole dimensions and rigidity ratios.     

On the reduce of interfacial shear stresses in fiber reinforced polymer plate retrofitted concrete beams

One major problem when using bonded fiber reinforced polymer (FRP) plate is the presence of high interfacial shear stresses near the end of the composite (edge effect) which might govern the failure of the strengthening schedule. It is known that the decrease of plate thickness reduces the magnitude of stress concentration at plate ends. Another way is to use a plate end tapering. In this paper, the analytical solution of interfacial shear stresses obtained has been extended by a numerical procedure using the modal analysis of finite element method (FEM) in a retrofitted concrete (RC) beam with the FRP plate with tapered end, which can significantly reduce the stress concentration. This approach allows taking into consideration the variation of elastic properties of adhesive and plate as well as the complicated geometrical configurations and effects of thermal loads.     

碳纤维布加固RC梁中粘结性能的非线性有限元分析

碳纤维布加固钢筋混凝土(RC)梁中,碳纤维布与梁底混凝土的剥离破坏使碳纤维布的强度不能得到充分发挥。分析碳纤维布与梁底混凝土的粘结应力,是研究碳纤维布加固剥离破坏承载力的基础问题。根据4根碳纤维布加固RC梁的试验研究结果,采用商业有限元程序MSC.Marc建立有限元模型,进行了非线性计算分析。通过分离总粘结应力中的局部粘结应力,得到粘结延伸长度范围内的锚固粘结应力分布,并结合试验数据对其分布规律进行了研究。根据分析和试验结果,引入了“有效锚固粘结长度”和“锚固粘结应力”的概念,给出了极限荷载下锚固粘结应力的计算建议。     

Fracture characterization of Carbon fiber-reinforced polymer-concrete bonded interfaces under four-point bending

A combined analytical and experimental approach is presented to characterize both mode-II and mixed mode fracture of Carbon fiber-reinforced polymer-concrete bonded interfaces under four-point bending load, and closed-form solutions of compliance and energy release rate of the mode-II (four-point symmetric end-notched flexure) and mixed (four-point asymmetric end-notched flexure) mode fracture specimens are provided. The transverse shear deformation in each sub-layer of bi-material bonded beams is included by modeling each sub-layer as an individual first order shear deformable beam, and the effect of interface crack tip deformation on the compliance and energy release rate are taken into account by applying the interface deformable bi-layer beam theory (i.e., the flexible joint model). The improved accuracy of the present analytical solutions for both the compliance and energy release rate is illustrated by comparing with the solutions predicted by the conventional rigid joint model and finite element analysis. The fracture of Carbon fiber-reinforced polymer-concrete bonded interface is experimentally evaluated using both the four-point symmetric and asymmetric end-notched flexure specimens, and the corresponding values of critical energy release rates are obtained. Comparisons of the compliance rate-changes and resulting critical energy release rates based on the rigid joint model, the present theoretical model, and numerical finite element analysis demonstrate that the crack tip deformation plays an important role in accurately characterizing the mixed mode fracture toughness of hybrid material bonded interfaces under four-point bending load. The improved solution of energy release rates for the four-point symmetric and asymmetric end-notched flexure specimens by the flexible joint model can be used to effectively characterize hybrid material interface, and the fracture toughness values obtained for the Carbon fiber-reinforced polymer-concrete interface under mode-II and mixed mode loading can be employed to predict the interface fracture load of concrete structures strengthened with composites.     

Fracture-mechanics failure criteria for RC beams strengthened with FRP strips––a simplified approach

A simplified approximation approach for the evaluation of a fracture mechanics based criterion for the edge delamination failure of reinforced concrete beams strengthened with externally bonded composite materials is presented. The proposed approach is based on evaluation of the energy release rate (ERR) through the virtual crack extension method using various analytical and numerical stress analysis models. The investigated models include the high-order model, two types of “elastic foundation” or “springs” models, a simplified beam model, and finite elements analysis. The stress and displacement fields, the governing equations and their closed form solutions, and the expressions for the release rate of the total potential energy of the various models are presented. The proposed approach sets up the basis for an energetic failure criterion, in which the ERR is compared to the specific fracture energy of the bonded system. This criterion replaces the traditional allowable stress approach in describing the initiation and stable or unstable growth of the delamination crack. The capabilities of the proposed approach and its ability to evaluate the ERR through simplified and approximated models is investigated numerically. The accuracy of the simplified approach is numerically examined through comparison with the J-integral formulation. Numerical results in terms of stresses near the edge of the bonded strip, the ERR associated with initiation and growth of the interfacial crack, and the critical loads and crack lengths are presented. The paper closes with a summary and conclusions.     

Debonding of a thin rubberised and fibre-reinforced cement-based repairs: Analytical and experimental study

An analytical approach for the prediction of debonding initiation between a rubberised cement-based overlay and old concrete substrate under monotonous mechanical loading was applied. Based on the linear elastic fracture mechanics, a model has been developed taking into account the interlocking between two crack surfaces in the overlay. Assuming that the debonding initiation just occurs after the crack cutting the overlay layer reaches the overlay–substrate interface, the stress intensity factor of the debonding tip can be calculated, allowing prediction of stress fields near the interface debonding tip. Then with a criterion of debonding initiation and propagation depending on the interface tensile strength, the load associated could be determined and might be interesting for the design of thin bonded cement-based overlays. The adequateness of this analytical approach was verified by both experimental data and finite element calculations. It has been used to show the relevance of a cement-based material with low modulus of elasticity combined with a high residual post crack strength to achieve sustainable repairs.     

Reinforcement delamination of metallic beams strengthened by FRP strips: Fracture mechanics based approach

The delamination failure of metallic beams reinforced by externally bonded fibres reinforced polymers (FRP) is addressed in this paper and a simplified fracture mechanics based approach for the edge delamination of the reinforcement strips is illustrated. The criterion is based on the evaluation of the energy release rate (ERR) using both analytical and numerical models. The analytical models consist of a simplified version of a “two parameters elastic foundation” and “transformed section” model while the numerical analyses refer to the modified virtual crack closure technique (MVCCT). The main aim of the paper is to establish a fracture mechanics failure criterion based on the ERR and the specific fracture energy of the bonded strips. The criterion is an alternative approach to the well known stress based method to asses the load carrying capacity of the adhesive joint. The accuracy of the simplified approaches is shown through a numerical example which refers to a steel beam strengthened by carbon fibres reinforced polymers (CFRP).