Cohesive-bridging zone model of FRP-concrete interface debonding

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, a combined cohesive/bridging zone model is presented to simulate the debonding procedure between the FRP and concrete interface. In this model, the crack processing zone of the interface is modeled by a cohesive zone model and the particle interlocking zone of the interface is modeled by a bridging zone model. Two different linearly softening bond stress-slip laws are used to describe these two different zones. Closed-form solutions of interfacial stress, FRP stress and ultimate load are obtained for a typical single-lap specimen and verified with experimental results. The pulling force applied to the FRP plate is found to be proportional to the square root of the energy release rate at the debonding tip for this model. Such a relationship is then extended to any general shapes of bond stress-slip law through J-integral method. A new approach to experimentally determine the bond stress-slip law is also proposed.     

Numerical simulation of interface debonding with a combined damage/friction constitutive model

 Experimental studies for pull-out tests in fiber-reinforced composites reveal a softening behaviour due to interface crack growth between fiber and matrix followed by a contact friction behaviour on the cracked area. In this contribution this debonding process is modelled within the framework of interface damage mechanics, where the displacement discontinuities during the progressive decohesion are related to constitutive equations extended by an anisotropic damage model. The contact/friction behaviour after complete separation is described by a friction model analogously to the classical theory of plasticity. The simulation of the load-displacement curve in the pull-out test with the drop-off behaviour is achieved by introducing a Hermite polynomial. The numerical simulations are performed for glas/polystyrol fiber-reinforced composites, thus illustrating the progressive debonding and friction between both constituents and demonstrating a good agreement with experimental data of a pull-out test. Received 18 November 1999     

The interface crack with a contact zone

An analytical method is applied to the contact zone model of the finite length interface crack problem. The results are valid for small contact zone lengths due to interpenetration of the crack faces. Qualitative results obtained in [1] are confirmed. Also where possible numerical comparisons are made with the work of Comninou et al. [2, 3, 4, 5] and reasonable agreement is obtained.

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Résumé On a appliqué une méthode analytique au modèle de zône de contact dans le cas d'un problème de fissure d'interface de longueur finie. Les résultats sont valables pour des longueurs de la zône de contact faibles, dues à une interpénétration des faces de la fissure. Des résultats qualitatifs obtenus dans la référence [1] sont confirmés. En outre, il a été possible de procéder à des comparaisons numériques avec les travaux de Comninou et al. [Réf. 2 à 5] et un accord raisonnable a été obtenu.

     

The interaction of mode I crack with multi-inclusions in a three-phase model

An approximately close form solution has been developed for mode I crack interacting with multi-inclusions in composite materials. The crack-tip stress intensity factor is evaluated in a three-phase model, which combines the present knowledge that the inclusions only in the immediate neighborhood of the crack-tip have strong effect on the stress intensity factor and that the far inclusions have an overall effects which can be estimated by effective properties of the composites. As validated by numerical examples, the solution has good accuracy for a wide range of the modulus ratios between the inclusion and matrix material.     

The interaction between a crack and an inclusion

A numerical method described recently[1] is used here to obtain the stress intensity factor for a crack near an inclusion. Results for the variation of the stress intensity factor with the distance of the crack tip from the inclusion, are shown graphically.     

Reinitiation of a crack reaching an interface

We consider here a bi-material made of two layers bonded together by an interface. The specimen is loaded in tension parallel to the interface and the existence of a mode I crack is assumed. The crack initiated in just one layer reaches the interface normally. We then study the second of the two possible cases: the crack crosses the interface and goes straight into the second layer, in mode I also; or the crack debonds the interface before reinitiating in the second layer at the debond tip.In the present study the conditions of the reinitiation of the crack in the second layer after debonding of the interface are presented. The maximum debond distance is calculated by means of a Shear Lag analysis associated with a damage constitutive equation.Qualitative rules for design are pointed out to make the interface a location of crack arrest or at least of crack growth delay. These rules are mainly: small thickness of the possibly cracked layer, strong interface and tough substrate.     

The interface crack with a contact zone (an analytical treatment)

An analytical treatment is made of the problem of an interface crack with a contact zone. It is shown that the unrealistic oscillatory singularities are removed independent of the contact zone size. The model of Comninou [1, 2, 3, 4] leads to an equation for the contact zone length with possibly an infinity of solutions. However, only the largest of these appears to satisfy all the subsidiary conditions of the problem posed i.e. that of a single contact region. The singular shear stress field at the crack tip is effectively independent of the precise (small) contact zone length. An alternative model, illustrated in Fig. 3, is suggested. Each of these models leads to the same energy release rate.

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Résumé On a traité par voie analytique le problème d'une fissure d'interface avec une zone de contact. On montre que les singularités oscillatoires non réalistes peuvent être otées indépendamment de la dimension de la zone de contact. Le modèle de Comninou conduit à une équation pour la longueur de la zone de contact avec une possibilité d'une infinité de solutions. Toutefois seul leur plus grand nombre paraît apte à satisfaire toutes les conditions subsidiaires du problème posé c'est-à-dire de la région de simple contact. Le champ singulier de containte de cisaillement à l'extrémité de la fissure est effectivement indépendant de la longueur de la zone à laquelle s'effectue le contact précis. On suggère un modèle de rechange illustré à la fig. 3. Chacun de ces modèles conduit à la même vitesse de relaxation de l'énergie.

     

A mechanical model for fiber reinforced composite materials with elasto-plastic matrix and interface debonding

The behaviour of fiber-reinforced composites is examined through the formulation of a non-linear constitutive law obtained through a physical-based approach. The elasto-plastic macro constitutive equations for such a class of materials, composed by a matrix phase with elasto-plastic behaviour and several fiber-reinforcing phases, is obtained by considering an imperfect bounds between the matrix and the fibers, i.e. a certain amount of sliding is assumed to be present at the matrix–fiber interface. The fibers are assumed to have only axial stiffness with negligible relative matrix–fiber displacements orthogonal to the fiber's axis. The amount of sliding has been determined through energetic considerations by taking into account the evolution of the shear stress distribution along a single fiber during an increasing load history applied to the composite. The mechanical constitutive law has been implemented in a F.E. code and some numerical simulation have been performed in order to assess the reliability of the proposed model.     

The interaction between a screw dislocation and a nano-inhomogeneity with a semi-infinite wedge crack penetrating the interface

The interaction between a screw dislocation and a circular nano-inhomogeneity with a semi-infinite wedge crack penetrating the interface is investigated. By using Riemann-Schwartz’s symmetry principle integrated with the analysis of singularity of complex functions and the conformal mapping technique, the analytical expressions of the stress field in both the circular nano-inhomogeneity and the infinite matrix, the image force acting on the screw dislocation and the stress intensity factor at the crack tip are obtained. The influence of elastic mismatch of materials, inhomogeneity size, interface stress, wedge crack opening angle and the relative location of dislocation on the image force and on the equilibrium position of the screw dislocation and the shielding effect of the screw dislocation are discussed in detail. The results show that interface stress has a significant impact on the movement of dislocations near the interface, and the effect of interface stress enhances when the inhomogeneity radius decreases. With the decrease in the wedge crack opening angle, the influence of interface stress on the movement of the screw dislocation and on the SIF enhances. With the increment of the relative shear modulus, the influence of interface stress weakens with the screw dislocation locating in the inhomogeneity and strengthens with the screw dislocation locating in the matrix. When the screw dislocation is located in the inhomogeneity, the positive (negative) interface stress increases (decreases) the shielding effect, while this phenomenon is opposite when the screw dislocation locates in the matrix.     

Interaction between an interface crack and a parallel subinterface crack

In this paper, the pseudo-traction method addressed thoroughly in homogeneous cases is combined with the edge dislocation method to solve the interaction problem of an interface crack with a parallel subinterface crack. After deriving the fundamental solutions for a typical interface crack loaded by the normal and tangential concentrated tractions on both crack surfaces and the fundamental solutions for an edge dislocation beneath the interface, the interaction problem is reduced to a system of singular integral equations which can be solved numerically with the aid of the Chebyshev polynomial technique. Numerical results for the stress intensity factors are shown in the figures in which six kinds of material combinations presented by Hutchinson et al. [1] are considered.     

A coupled cohesive zone model for transient analysis of thermoelastic interface debonding

A coupled cohesive zone model based on an analogy between fracture and contact mechanics is proposed to investigate debonding phenomena at imperfect interfaces due to thermomechanical loading and thermal fields in bodies with cohesive cracks. Traction-displacement and heat flux–temperature relations are theoretically derived and numerically implemented in the finite element method. In the proposed formulation, the interface conductivity is a function of the normal gap, generalizing the Kapitza constant resistance model to partial decohesion effects. The case of a centered interface in a bimaterial component subjected to thermal loads is used as a test problem. The analysis focuses on the time evolution of the displacement and temperature fields during the transient regime before debonding, an issue not yet investigated in the literature. The solution of the nonlinear numerical problem is gained via an implicit scheme both in space and in time. The proposed model is finally applied to a case study in photovoltaics where the evolution of the thermoelastic fields inside a defective solar cell is predicted.     

A discrete spectral model for intermediate crack debonding in FRP-strengthened RC beams

One of the common failure modes of reinforced concrete (RC) beams strengthened in flexure with a bonded fibre-reinforced polymer (FRP) is intermediate crack (IC) debonding, which is originated at a critical section in the vicinity of flexural cracks and propagates to a plate end. Despite considerable research over the last years, few reliable and simplified IC debonding strength models have been developed. This paper firstly presents a one-dimensional model based on the discrete crack approach for concrete and the spectral element method for the numerical simulation of the IC debonding process. The progressive formation of flexural cracks and subsequent concrete–FRP interfacial debonding is formulated by the introduction of a new element able to represent both phenomena simultaneously without perturbing the numerical procedure. Furthermore, with the proposed model, high frequency dynamic response for these kinds of structures can also be obtained in a very simple and non-expensive way, which makes this procedure very useful as a tool for diagnoses and detection of debonding in its initial stage by monitoring the change in local dynamic characteristics.     

Williams' blister test analyzed as an interface crack problem

A model is constructed to analyze more carefully the energy release rate for Williams' blister test. The model, which consists of an interface crack between two elastic layers, is loaded by uniform internal pressure. The singular integral equations for the dislocation densities are derived and solved using numerical quadrature and the energy release rate is calculated directly from the dislocation densities. Both the two-dimensional and axisymmetric penny-shaped crack problems are considered, and it is noted that there are significant differences between these two cases. It is found that in some cases crack propagation will not be catastrophic.

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Résumé On établit un modèle mathématique en vue d'analyser de manière plus soignée le taux de relaxation d'énergie dans le test de coupelle proposé par Williams. Le modèle représente une fissure d'interface entre deux couches clastiques, et est soumis à une pression interne uniforme. On déduit les intégrales singulières caractérisant les densités de dislocation, et on les résoud par quadrature numérique, pour ensuite calculer les taux de relaxation d'énergie directement à partir de ces densités de dislocation. Sont à la fois considérés les problèmes de fissures circulaires bidimensionnelle, et axisymétrique. On observe des différences significatives entre ces deux variantes. On trouve également que, dans certains cas, la propagation d'une fissure peut ne pas être brutale.

     

Time-dependent boundary element analysis for an interface crack in a two-dimensional unidirectional viscoelastic model composite

Interfacial stress singularities in a unidirectional two-dimensional laminate model consisting of an elastic fiber and a viscoelastic matrix have been investigated using the time-domain boundary element method. First, the interfacial singular stresses between the perfectly bonded fiber and the matrix of a unidirectional laminate subjected to a uniform transverse tensile strain have been investigated near the free surface, but without any edge crack. Such stress singularity might lead to fiber-matrix debonding or an edge crack. Then, the overall stress intensity factor for the case of a small interfacial edge crack of length a has been computed. The numerical procedure does not permit calculation of the limiting case for which the edge crack length vanishes.     

A theoretical model for roughness induced crack closure

A theoretical model for the effects of grain size on the magnitude of roughness induced crack closure (RICC) at fatigue crack growth threshold has been proposed. With the basic configuration of a crack propagating incrementally along planar slip bands and deflecting at grain boundaries, an idealized zig-zag crack path is considered. The effective slip band length is considered to be equal to grain size. It is assumed that the dislocations emitted from the crack tip upon loading to form the pile-up are completely irreversible to produce a comnined mode I and mode II displacement at the crack tip. The assumption of continuously distributed dislocations in the pile-up facilitated the calculation of crack tip sliding displacement (CTSD) along the slip plane from which the mode I closure disregistry just behind the crack tip can be calculated. The closure stress intensity factor at threshold, K _el,th could then be expressed as a function of critical resolved shear stress, average macroscopic yield stress, angle subtended by the slip plane with the crack plane and the length of the slip band. Comparisons of the predicted trends with experimental data from various alloy systems indicate good agreement.

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Résumé On propose un modèle théorique pour décrire les effets de la taille du grain sur l'importance de la rugosité associée à la fermeture d'une fissure lors du franchissement du seuil de propagation en fatigue. On considère un chemin de fissuration en zig-zag idéalisé, avec une configuration de base d'une fissure qui se propage par incréments le long des bandes de glissements et par déviations aux frontières des grains. La longueur effective d'une bande de glissement est prise comme égale à la taille du grain. On suppose que les dislocations émises de l'extrémité de la fissure sous charge et qui forment l'empilement, sont totalement irréversibles au point de produire un déplacement combiné de mode-I et de mode-II à cette même extrémité. L'hypothèse de dislocations continûment distribuées dans l'empilement facilite le calcul du dèplacement par glissement de l'extrémité de la fissure le long du plan de glissement, à partir duquel on peut établir les conditions de fermeture en mode-I juste derrière l'extrémité de la fissure. Le facteur d'intensité de contraites de seuil peut dès lors être exprimé en fonction de la contrainte critique de cisaillement, de la limite élastique macroscopique moyenne, de l'angle entre le plan de glissement et le plan de la fissure, et de la longueur de la bande de glissement. Un bon accord est trouvé entre les tendances prévues et les données expérimentales, dans le cas de divers alliages.

     

Closed interface crack with singular spring stiffness model

The singularity of the stress field at the tip of a partially closed interface crack is discussed based on a non-uniform spring stiffness model that includes an inverse function of the radial distance from the crack edge. The stress singularity is found to be governed by the coefficient of the inverse function, henceforth referred to as “stiffness intensity” due to its resemblance to the well-known stress intensity factor. Two distinct non-oscillatory singular stress fields, corresponding to Modes I and II deformations, respectively, are found to coexist. An oscillatory singularity may also appear, but only when the two stiffness intensities are close to each other. This means that the oscillatory singularity exists when the normal and tangential interactions between the upper and lower crack faces are close.     

Thermal crack problems for a bimaterial with an interface crack and internal defects subjected to a heat source

The interaction between internal defects and an interface crack in a bimaterial subjected to a thermal load, in particular a heat source, is examined. Attention is focused on the construction of the associated integral equations.     

Thermal crack problems for a bimaterial with an interface crack and internal defects subjected to a heat source

The interaction between internal defects and an interface crack in a bimaterial subjected to a thermal load, in particular a heat source, is examined. Attention is focused on the construction of the associated integral equations.     

Stress solution for a crack at an arbitrary angle to an interface

Two-dimensional elasticity solution and the stress intensity factors are determined for a finite crack in one of the materials of a bimaterial composite. The crack has an arbitrary orientation and distance from the straight interface. The solution for general stress boundary conditions on the crack surface is presented in the form of coupled Fredholm integral equations of the second kind. Numerical values of the stress intensity factors are computed for various crack orientations, distances from the interface, and different combinations of material properties when the boundary conditions are uniform pressure and uniform shear stress.