Behaviour of the interface between concrete and FRP using serial/parallel mixing theory

Maritzabel Molina¹, Juan José Cruz², Sergio Oller³, Alex H. Barbat⁴, Lluís Gil⁵

¹ Civil Engineer, Master in Structures, Master in Numerical methods for calculation and design engineering, PhD student in Structural Analysis, Universidad Politécnica de Cataluña. Associate Professor, Universidad Nacional de Colombia. mmolinah@unal.edu.co

² Civil Engineer, PhD student in engineering of roads, canals and ports, Universidad Politécnica de Cataluña. Professor, Universidad Autónoma de Chiapas. juan.jose.cruz@upc.edu

³ Engineer of roads, canals and ports, PhD in roads, canals and ports. Professor, Universidad Politécnica de Cataluña.sergio.oller@upc.edu

⁴ Engineer of roads, canals and ports, PhD in roads, canals and ports. Professor, Universidad Politécnica de Cataluña.alex.barbat@upc.edu

⁵ Engineer of roads, canals and ports, PhD in roads, canals and ports. Professor, Universidad Politécnica de Cataluña.lluis.gil@upc.edu

ABSTRACT

Experimental research has shown that one of the key factors affecting the behaviour of reinforced concrete structures strengthened with externally-bonded fibre-reinforced polymer (FRP) is the bonding behaviour between concrete and FRP laminates. As a complement to experimentation, this paper proposed the use of serial/parallel mixing theory in numerical simulation, which is a tool for studying the behaviour of the concrete-FRP epoxy interface. An example is presented which analyses beam test simulation results and compares them with the experimental results.

Keywords: concrete, structures, serial/parallel mixing theory

Received: May 20th 2010 Accepted: October 13th 2011

Introduction

During the past decade using fibre-reinforced polymer (FRP) composites externally bonded to concrete has been increasing used as an alternative for strengthening reinforced concrete structures. Glass fibre reinforced polymer composites (GFRP) and carbon fibre polymer composites (CFRP) are usually used as FRP strengthening. Since the use of composite materials in civil engineering is relatively new, some aspects of FRP have not yet been sufficiently researched due to their complexity. Hence, it is important to improve existing tools and to discover new ways of studying the FRP behaviour in more detail, including the interaction between experiment tests and finite element simulations.

Experimental research has shown that one of the critical parameters in defining the strength of external FRP reinforcement of concrete is the bond between concrete substrate and FRP (Pendhari et al., 2007). The behaviour of the FRP-concrete interface is thus an aspect which has been most studied, although much research has been focused on experimental tests. This paper reviews the state of knowledge concerning research in the field of FRP-concrete interface behaviour. Serial/parallel mixing theory is then described (Rastellini, 2006), this being a new tool for the numerical simulation of composite materials. FRP-concrete interface behaviour obtained from a bending bond test simulation in which serial/parallel mixing theory was used is then analysed and numerical and experimental results compared.

Classifying FRP-concrete interface bonding tests

The efficacy of FRP external reinforcement of concrete structures depends on the appropriate selection of FRP configuration based upon stiffness and strength requirements and the integrity of the bond between the concrete surface and FRP (Hollaway, 2003). Several tests have been proposed for studying interface behaviour since interface strength is given by the bond between the concrete, adhesive and FRP and their performance is the key controlling factor for debonding failures in strengthened RC structures (see Figure 1). Such tests would include:

Shear bond tests: double-shear and simple shear tests (shown in Figure 1a and Figure 1d) have been the most popular bond tests so far due to the simplicity of their setups (Yao et al., 2005). Interface behaviour in these tests is similar to that developed at the ends of the FRP laminates in strengthened RC beams; however, bending effects are neglected; and

Bending bond tests: this kind of test is the same as the bond test performed for concrete beams strengthened with steel plate, in which interface behaviour is displayed by means of an artificial crack. The stress transfer mechanism at the interface is studied with these tests to research debonding failures caused by flexural or flexural-shear cracks.

The experimentally-observed interface behaviour in some research depends on the kind of bond test (Yao et al., 2005). For example, average bond stress is higher for bending bond tests than shear bond tests; moreover, the double shear test gives a higher average bond stress value than a simple shear test (Aiello and Leone, 2008). A standard test must thus be defined for objectively determining bond strength and have reliable setup indications.

The state of knowledge regarding the numerical simulation of an FRP-concrete interface

Given the complex behaviour of an FRP-concrete interface, then it is clear that further experimentation should use numerical simulation for evaluating strengthened elements' structural behaviour so as to improve the development of design guidelines and ensure FRP efficiency as reinforcement for concrete structures (Karbhari, 2001). Although several numerical studies have been carried out during the last decade for analysing cracked RC beams which were strengthened with FRP plates, few have been successful in simulating debonding failures, due to the high computational cost involved in the problem's complexity (Perera et al., 2004, Yang et al., 2003). Researchers are currently emphasising non-linear analysis of FRP-concrete interface finite elements, aimed at simulating debonding between FRP and concrete (Lu et al., 2005). The advance of finite element analysis regarding FRP-concrete interface behaviour has been associated with the simulation of crack propagation in concrete adjacent to the interface, unless the adhesive is rather weak. Two major approaches have been developed in this area:

Discrete crack models (Yang et al., 2003, Niu et al., 2006). Crack direction and position are predetermined in this methodology, where the finite element mesh needs to be changed at each load step to accommodate the propagation of a crack. This kind of approach ensures proper simulation accuracy regarding crack development and propagation, but remeshing involves a high computational cost; and

Smeared crack models (Wu and Yin, 2003, Lu et al., 2005; Ebead and Neale, 2007). Crack propagation is approached through nonlinear constitutive equations in a continuous finite element mesh. The cracks are phenomeno logically simulated as local discontinuities which are distributed throughout a particular domain. However, this method cannot model individual macrocracks because it does not localise crack development.

Researchers using crack models have studied the debonding between FRP and concrete taking into account that failure occurs by sliding fracture and/or a fracture opening up in the interface. They simulate interface behaviour through a constitutive law specified for the interface elements which have zero thickness (Yang et al., 2003, Niu et al., 2006), or specific dimensions (Wu and Yin, 2003: Ebead and Neale, 2007). Alternatively, debonding is simulated by modelling the cracking and failure of the elements in the concrete adjacent to the adhesive layer (Lu et al., 2005); this approach requires a fine mesh in the strengthened area, without using interface elements.

Constitutive models of damage and plasticity have recently been applied to nonlinear simulation for studying FRP-concrete interface degradation behaviour (Perera et al., 2004, Coronado and Lopez, 2007). This strategy is being developed and has a very broad scope for studying strengthened concrete structure debonding.

Despite degradation study of the interface near concrete cracks having been suggested in greater detail, recent simulations have only considered concrete damage and few researchers have modelled the adhesive. Furthermore, they avoid the fact that epoxy can have nonlinear behaviour as a response to concrete damage or that it can be susceptible to damage and/or plasticity.

The serial/parallel mixing theory regarding composite materials

Mixing theory, managing several constitutive models regarding composites' material components, is a tool which can be applied within the finite element method for properly simulating these materials' behaviour. However, new tools such as serial/parallel mixing theory should be used as they improve overall and local numerical simulation of elements strengthened with FRP, thereby more accurately depicting composites' actual behaviour and providing information which cannot be measured in experimental tests (Molina et al., 2010).

Serial/parallel mixing theory (Rastellini, 2006) is based on classical mixing theory developed by Trusdell and Topin (1960). Classical mixing theory is applied in continuum mechanics using the principle of the interaction of the compounding substances that constitute a particular material. It follows the hypothesis that all material components participate in parallel in each infinitesimal volume of a composite material. It also supposes that each substance participates in the behaviour of the composite in the same proportion as its volumetric participation (Oller, 2003). Nevertheless, this theory presents a restriction for use in various composite materials, since it is assumed that components coexisting at a point are parallel and have the same strain field (Car et a/., 2000)., Rastellini has proposed serial/parallel mixing theory as an alternative for simulating composite materials (Rastellini, 2006).

The fundamentals of serial/parallel mixing theory

Serial/parallel mixing theory considers that material components perform in parallel in the direction of the fibre (iso-strain condition) and that they behave in serial regarding transversal directions (iso-stress condition). This theory is based on the following hypotheses:

– All material components participate in each infinitesimal volume of a composite material, so that they are considered to be homogeneously distributed;

– Composite component materials are subjected to the same strain in parallel direction and they have the same stress in serial direction;

– The bond between composite components is perfect; and

– Component materials' contribution in composite material response is directly related to component volume fractions.

• Definition of strain and stress tensor serial and parallel components (Rastellini et al., 2008)

Strain tensor e is broken up into serial part ε_s and another parallel part ε_p; stress tensor σ is also split into its serial σ_s and parallel σp components:

These tensors decompose through fourth-order projector tensors (P_p, P_s) in parallel and serial, respectively

NP being the second-order parallel projector tensor, I the fourth-order identity tensor and e1 the director vector determining fibre direction, namely, parallel direction.

• Equilibrium and compatibility equations regarding composite layers

The numerical implementation of the theory was developed to split up composite c in a certain number of layers neap, so that each layery is made up of a matrix and a fibre group f having the same orientation (Molina et a/., 2010). Based on the hypothesis so described, the following equilibrium and strain compatibility equations are given in each composite layer y (Martinez et a/., 2008)

– Parallel behaviour

– Serial behaviour

• Constitutive equations for composite layers' material components

Once composite strain tensor ce has been found, each layer's stress and strain state component agreement with equilibrium and compatibility equations is assessed and then composite stress state is worked out. Each component's state is described by a constitutive equation depicting its behaviour. When plasticity theory is used, the constitutive equation is written as (Martínez et al., 2008):

so that     is the constitutive tensor of the matrix m or fibres   of layer  .

• Serial/parallel mixing theory algorithm

figure 2 shows this theory's algorithm for composite layery.

• Equilibrium equation regarding composite layer

After each composite layer has been analysed, composite ^cσ stress tensor is calculated by adding the stress tensor for all composite layers ncap according to the volumetric participation of each layer   (Molina, 2009).

Analysis of concreteepoxy-FRP interface behaviour

The literature about comparisons between experimental results for bending bond test and numerical simulations is limited; such comparisons have only been made with two-dimensional models. Perera et al., adopted this approach when analysing a bending test with hinge (Figure 1e); they indicated that local failure was mainly due to localised high shear bond stresses transmitted to the concrete from the laminate. They pointed out that interface shear strength is thus an important factor in the behaviour of strengthening reinforced concrete beams with FRP (Perera et al., 2004). Leung et al., carried out a bending bond test with steel fixture (Figure 1f); they showed that the debonding failure mechanism led to loss of interface strength, followed by reduction in shear stress. They indicated that the initial drop in strength was caused by loss of cohesion between interface materials, while stress decreased due to the combined effects of continual sliding and damage occurring at the interface (Leung et al., 2006).

The PLCDYN finite element program (CIMNE, 2010) was used in the following numerical simulation of a bending bond test using serial/parallel theory to analyse concrete-epoxy-CFRP interface nonlinear behaviour.

Bending bond test geometry

Figure 3 shows the bending test's geometry and setup where the CFRP laminate is attached to the underside of the blocks. Only the block having the short laminate was simulated using a 10,940 8-node hexahedral elements mesh. The model involved five simple materials; their properties are shown in Table 1. It should be noted that Poisson's ratio was not considered in composite reinforcing materials so as not to overestimate the stresses of their matrices.

Regarding serial/parallel theory, the composite materials' matrices are concrete and polymer matrix in reinforced concrete and CFRP, respectively, while steel and carbon fibres provide the reinforcement. Moreover, it was taken into account that the steel bars and carbon fibres were orientated at 0 degrees for the load direction applied when considering composite anisotropy. Figure 4 shows the four composite materials assigned to the model and Table 2 contains the volumetric share of each composite material's components.

Description of material constitutive models

Kachanov's damage model was considered in the integral analysis of interface behaviour concerning concrete, epoxy and polymeric matrix in line with the principle that interface damage causes a reduction in component materials' mechanical properties (Molina, 2009). Likewise, an elasto-plastic model was used regarding steel and a linear elastic model for carbon fibre, based on a hypothesis that all materials had no initial damage and that there was a perfect bond during initial interface state re concrete -epoxy adhesive, epoxy adhesive-CFRP and concrete-steel.

The maximum load obtained in the bond test and its simulation was 17.75kN; a ductile failure occurred in both cases. Figure 5 shows composite strains according to strain gauge location; these were installed every 0.05m on the specimen from the end where the strengthening was attached. Note the similarity between strain evolution measured experimentally and that calculated along the laminate in the numerical simulation. This Figure shows that there was a linear increase in strain in line with initial load level; this linearity became sequentially lost as load increased as a result of progressive damage to the concrete and adhesive from the free end of the attached laminate (0.05m) to the other end (0.35m). This pattern agreed with the findings of Leung et al.

One of the advantages of using serial/parallel mixing theory is that the evolution of internal variables, such as damage or plastic hardening in the composite and its components, can be studied by assigning a constitutive model for each composite component. This allows the simulation to improve the integral analysis of the interface failure mechanism. The laminate debonding happened on the 0.35m side and the concrete became detached at the block end during the test, as shown in Figure 6a. Concrete damage occured along the strengthening area, as seen in Figure 6b, being higher on the lateral sides; the damage to the concrete surface spread from the end block to 0.40m inside the block, i.e. 0.05m beyond the attached laminate. Figure 6c shows that the detached part of the concrete in the test had a shape similar to the deformed section in the numerical model. Furthermore, there was evidence that the damage caused by high concrete stress induced laminate peeling, an effect that has also been observed by Casas and Pascual (Casas and Pascual, 2007); this kind of failure occurs in localised areas adjacent to flexural cracks and the transition region toward the free end where the FRP is attached (Perera et al., 2004)_. Figure 6d shows that the epoxy had a higher level of damage at the end where the concrete became detached and reduced toward the inside of the reinforced area.

Figure 7 shows the evolution of damage in the concrete and the epoxy over an area adjacent to a lateral side of the laminate. Regarding concrete damage, Figure 7a shows uniform distribution (maximum 67%) and there was 20% damage 0.02 m beyond the laminate end for post-peak load as an indicator of reinforced area capacity loss. Concerning the epoxy damage shown in Figure 7b, the maximum damage occurred towards the block end of the attached reinforcement. Such local damage was caused by stress concentration in which FRP deflection on the blocks' separation joint induced tearing effects into the adhesive epoxy, apart from pulling effects. This proved the importance of simulating the adhesive epoxy, taking into account that its behaviour was not linear and inelastic because it was susceptible to damage, despite having greater strength than the concrete, contrary to that assumed by other studies (Leung et al., 2006, Yang et al., 2003, Lu et al., 2005).

Interface normal and shear stresses

Since the failure occurred in the strengthening area, concrete, epoxy and CFRP axial and shear stress trends were analysed in the area adjacent to the laminate's lateral side.

Figure 8 shows the concrete's axial and shear stresses. Regarding the axial, Figure 8a shows a sign of debonding failure, the greater stresses due to load increase arose at different points throughout the reinforced area towards the CFRP end. Post-maximum load stress occurred within 0.03 m from the laminate end (2.69 MPa). Concerning the shear stresses shown in Figure 8b, it can be seen that the greater stresses for load levels up to 15.92 kN happened at the free end where the CFRP was attached, reaching a maximum 1.72 MPa stress. The stress threshold changed position for higher loads at different points along the interface.

Figure 9 shows epoxy axial and shear stresses at the interface with the laminate because they were related to a higher rate of damage. Figure 9a shows that the greatest axial stress occurred 0.02m from the free end until load was 15.92 kN; then, as load increased, the greatest stress happened at 0.01m. Shear stress distribution in epoxy was almost parabolic (as seen in Figure 9b). The greatest stresses were present 0.02 m from the block end at the start until a 14.06 kN load was applied; then, as the load increased, the curve changed in line with the greater stresses towards the other end of the reinforced area.

According to CFRP axial and shear stress shown in Figure 10, the laminate remained in the elastic range. The axial stress indicated in Figure 10a had an almost linear trend up to 14.06 kN load. Stress distribution was semi-parabolic with higher load levels, and greatest stresses arose 0.01 m from the block end (493.0 Mpa maximum value). The greatest shear stress was around 10.3 Mpa (Figure 10b).

As regards the interface, the behaviour of concrete and epoxy resulted from a combination of axial and shear stresses, while FRP behaviour was due to axial stress. Three-dimensional simulation revealed that axial and shear stress contributions were different from that indicated in studies involving plane stress state by analysing the behaviour of concrete, adhesive and FRP; this agreed with that observed by Chen and Pan in a three-dimensional model of a simple shear test(Chen and Pan, 2006).

Conclusions

Serial/parallel mixing theory is a versatile numerical tool for analysing the behaviour of composite materials and their components. It allows each composite component to be ascertained by a constitutive equation which is suitable for predicting their behaviour (elasticity, plasticity, damage, etc) and it can calculate composite performance by combining its components' mechanical behaviour. This numerical tool thus led to a better analysis of structures involving composite materials;

This work studied CFRP-concrete interface behaviour in a bending bond test using serial/parallel mixing theory and the results were compared to those obtained experimentally. The three-dimensional model gave a good approximation of the experimental interface, thereby validating the use of serial/parallel mixing theory and showing the importance of three-dimensional models, since they allow failure mechanism to be fully analysed; and

The numerical simulation of the bond test showed the need for modelling adhesive epoxy taking into account its nonlinear behaviour, being susceptible to damage and interacting with concrete failures. Furthermore, the epoxy adhesive simulation showed the local effect at the FRP end, produced by a combination of peeling and pulling on the laminate, thereby affecting both the concrete and the adhesive.

Acknowledgements

This work has been financed by the following projects: the Spanish Ministry of Science and Innovation "RECOMP", Ref. BIA2005 -06952, "DECOMAR", Ref. MAT2003-08700-C03-02 and "DELCOM", Ref. MAT2008-02232/MAT; Spanish Ministry of Public Works project "Retrofitting and Reinforcement of Reinforced Concrete structures with Composite Materials"; European Union for Latin-America Alban Scholarships Programme, Ref. E06D101053C0; the Mexican Secretariat of Public Education, Under-secretariat for Higher Education's Teacher Improvement Programme (PROMEP), scholarship folio UACHIS-160; International Centre for Numerical Methods in Engineering (CIMNE), Spain; and Universitat Politècnica de Catalunya Department of Materials' Strength and Structural Engineering (ETSEIAT) and its laboratory (CER-LITEM), Spain.

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