Numerical characterization of compressive response and damage evolution in laminated plates containing a cutout

A micromechanical constitutive model [Liang Z, Lee HK, Suaris W. Micromechanics-based constitutive modeling for unidirectional laminated composites. Int J Solid Struct 2006;43:5674–89], based on the concept of the ensemble-volume average for laminated composites, is implemented into a finite element program to numerically characterize the compressive response and damage evolution in laminated plates containing a cutout. Prior to the implementation of the model into the finite element program, the predicted moduli of laminated composites are compared with analytical bounds and experimental data for the validation and verification of the constitutive model. A series of numerical simulations for a uniaxial test of laminated plate specimens containing a cutout are conducted using the implemented constitutive model. The predictions are compared with experimental data [Lessard LB, Chang FK. Damage tolerance of laminated composites containing an open hole and subjected to compressive loadings: Part II-Experiment. J Compos Mater 1991;25:44–64; Chang FK, Lessard LB. Damage tolerance of laminated composites containing an open hole and subjected to compressive loadings: Part I-Analysis. J Compos Mater 1991;25:2–43] to verify the accuracy of the implemented constitutive model. A parametric study is also carried out to illustrate the influence of the geometry of the specimens on the behavior of laminated plates. It is shown that the implemented constitutive model is suitable for the analysis of the constitutive behavior of laminated plates having a dilute or moderate fiber volume fraction.     

Compressive behavior of concrete cylinders confined by narrow strips of CFRP with spacing

Application of carbon fiber-reinforced polymer (CFRP) is one of the effective strengthening methods for structural members such as reinforced concrete columns and beams. However, air voids and debonds between CFRP and concrete due to poor workmanship may degrade the structural performance otherwise expected by the strengthening. In order to minimize such debonds and ease the installation, the authors propose to wrap compressive concrete members with narrow strips of CFRP laminates with spacing. This paper focuses on an experimental study to investigate the effectiveness of applying the narrow strips of CFRP laminates. In this study, 60 concrete cylinders wrapped with CFRP strips having different spacings and widths are tested under compression load. The effects of several key parameters such as spacing, spliced length, number of layers, and section area of the CFRP laminates are investigated. In addition, stress–strain curves of pre-damaged specimens wrapped with CFRP laminates are also focused. Based on the experimental results, constitutive models of concrete confined by narrow strips of CFRP laminates are proposed.     

Numerical model for CFRP confined concrete elements subject to monotonic and cyclic loadings

Uniaxial cyclic and monotonic compression tests were carried out on partially and fully wrapped concrete cylinders with Carbon Fibre Reinforced Polymer (CFRP) wet lay-up sheets. The influence of the concrete compressive strength, CFRP stiffness, geometric confinement arrangement and loading type on the compressive behaviour of reinforced concrete column elements of circular cross-section up to their failure was assessed. A uniaxial stress–strain constitutive model is proposed, and the results obtained from the experimental tests were used to calibrate some of the parameters of this model, and to appraise the model performance. This model allows the simulation of reinforced concrete members by using Timoshenko one-dimensional elements, in the context of the finite element method (fibre model). Good agreement was obtained between numerical simulations and experimental results for both monotonic and cyclic loading tests.     

A damage mechanics model of crack-weakened,chopped fiber composites under impact loading

A micromechanical approach recently proposed by Lee and Simunovic [Compos. Part B: Engng. 31 (2000) 77] is introduced to develop analytical and numerical models that efficiently predict the behavior of chopped fiber based composites containing microcracks under impact loading. Based on the ensemble-volume averaging process and the first-order effects of eigenstrains due to the existence of chopped fibers and microcracks, an effective yield criterion of the composites is derived. Microcracks in the matrix are considered by employing the Eshelby's equivalence principle and their influence on the stress–strain relations of the composites is investigated. Further, the Weibull's probabilistic function is used to model the varying probability of progressive partial fiber debonding. The developed micromechanical constitutive model is then implemented into the finite element code DYNA3D to perform impact simulation of the composites. Finally, numerical simulations for cantilever beam test and composite contact test are carried out to validate the finite element implementation and predict the impact behavior of composite structures.     

Experimental study on RC beams with FRP strips bonded with rubber modified resins

This paper presents the effects of adhesive properties on structural performance of reinforced concrete (RC) beams strengthened with carbon fiber reinforced plastic (CFRP) strips. The epoxy adhesives modified with liquid rubber of different content were used to bond the CFRP strips, and four point bending experiments were carried out on RC beams. The experimental results show that different CFRP strip thickness of 0.22 and 0.44 mm resulted in a transition of failure mechanism from interfacial debonding along the CFRP-concrete interface to concrete cover separation starting from the end of CFRP strips in the concrete. Moreover, it is suggested that no matter interfacial debonding or concrete cover separation, the rubber modifier enhanced the structural performance by increasing the maximum load-carrying capacity and the corresponding ductility, compared with the beams bonded with a neat epoxy resin. The improvement of structural performance due to modified adhesive was associated with the modification of stress profiles along the CFRP-concrete interface especially the stress concentration at the end of FRP, and the enhanced interlaminar fracture toughness. Rubber modified epoxy therefore is worth further studying in practical repair applications.     

Efficacy of CFRP-based techniques for the flexural and shear strengthening of concrete beams

Near surface mounted (NSM) and externally bonded reinforcement (EBR) strengthening techniques are based on the use of carbon fiber reinforced polymer (CFRP) materials and have been used for the structural rehabilitation of concrete structures. In the present work, the efficacies of the NSM and EBR techniques for the flexural and shear strengthening of reinforced concrete beams are compared carrying out two experimental groups of tests. For the flexural strengthening, the efficacy of applying CFRP laminates according to NSM is compared to those resulting from applying CFRP laminates and wet lay-up CFRP sheets according to EBR technique. The influences of the equivalent reinforcement ratio (steel and laminates) and spacing of the laminates on the efficiency of the NSM technique for the flexural strengthening is also investigated. A numerical strategy is implemented to analyze the applicability of the FRP effective strain concept, proposed by ACI and fib in the design of FRP systems for the flexural strengthening. To assess the efficacy of the NSM technique for the shear strengthening of concrete beams, four beam series of distinct depth and longitudinal tensile steel reinforcement ratio are tested. Each series is composed of one beam without any shear reinforcement and one beam using the following shear reinforcing systems: conventional steel stirrups; strips of wet lay-up CFRP sheet of U configuration applied according to EBR technique; and laminates of CFRP embedded into vertical or inclined (45°) pre-cut slits on the concrete cover of the beam lateral faces, according to the NSM technique. Using the obtained experimental results, the performance of the analytical formulations proposed by ACI, fib and Italian guidelines is appraised.     

Contribution to the understanding of the mechanical behaviour of CFRP-strengthened RC beams subjected to fire: Experimental and numerical assessment

Recent experimental tests and numerical simulations about the fire resistance behaviour of CFRP-strengthened RC beams proved that CFRP strengthening systems are able to attain considerable fire endurance, provided that adequate fire protection systems are used. In a fire event, even though a CFRP laminate may rapidly debond from the central part of the beam in which it is installed, if sufficiently thick insulation is applied in the anchorage zones, the laminate transforms into a “cable” fixed at the extremities, thus maintaining a considerable contribution to the mechanical response of the strengthened beam. This paper presents experimental and numerical investigations on CFRP-strengthened RC beams with the objective of understanding in further depth their fire resistance behaviour, namely the influence of the above mentioned “cable” mechanism on the mechanical response of the beams. The experimental campaign, performed at ambient temperature, comprised 4-point bending tests on RC beams strengthened with CFRP laminates according to either the EBR or the NSM techniques, in both cases fully or partially (only at the anchorages, thus simulating the cable mechanism) bonded to the soffit of the beams. For the test conditions used in this study, for both types of strengthening systems, partially bonding the CFRP laminates did not affect the stiffness of the beams and caused only a slight reduction of their strength (6–15%). The numerical study comprised the simulation of the structural response of all beams tested. Non-linear finite element models were developed in Atena commercial package, in which a smeared cracked model was adopted to simulate concrete and appropriate bond-slip constitutive relations were defined for the CFRP-concrete interfaces. A very good agreement was obtained between experimental data and numerical results, providing further validation to the “cable” mechanism and the possibility of taking it into account when designing fire protection systems for CFRP-strengthened RC beams.     

A non-local criterion for modelling unbalanced woven ply laminates with stress concentrations

A non-local ply scale criterion [Hochard C, Lahellec N, Bordreuil C. A ply scale non-local fibre rupture criterion for CFRP woven ply laminated structures. Compos Struct 2007;80:321–26] was previously developed for predicting the failure of balanced woven ply structures with stress concentrations. This non-local criterion was based on the mean values determined over a Fracture Characteristic Volume (FCV) corresponding to a cylinder with a circular area and the same thickness as the ply. This non-local approach along with a ply scale continuum damage behavioural model was implemented in the ABAQUS Finite Element Code. The behavioural model was developed from a classical Continuum Damage Mechanics (CDM) model [Ladevèze P. A damage computational method for composite structures. Comput Struct 1992;44:79–87]. In the present study, this approach was extended to the case of unbalanced woven ply. The FCV approach and the CDM behavioural model are presented and comparisons are made between the experimental data and the modelling predictions obtained on plates with open holes, notches and saw cuts.     

On the design and optimization of hybrid carbon fiber reinforced polymer-steel cable system for cable-stayed bridges

This paper addresses the effective use of carbon fiber reinforced polymeric (CFRP) materials in the cable system. As the span length of cable-stayed bridges increases, several technical challenges become more dominant with traditional material. This paper mainly focuses on improving the aerodynamic performance through implementing CFRP composites in the cable system in combination with steel. In order to maximize the improvement, a genetic algorithm (GA)-based optimization procedure is developed to optimize the distribution of CFRP and steel. A numerical example is presented and the results suggest the typical composition of an optimized CFRP-steel cable system for long-span cable-stayed bridges.     

Ductile strengthening using externally bonded and near surface mounted composite systems

Externally bonded fiber reinforced polymers (FRP) has been established as an effective technique for strengthening concrete members. Other techniques, like near surface mounted (NSM) FRP bars, and steel reinforced polymers (SRP) have emerged as viable alternatives. In this study, four composite-based strengthening systems were used to provide equivalent flexural performance, namely: externally bonded CFRP sheets, NSM prefabricated CFRP strips, externally bonded SRP sheets and NSM stainless steel bars. The strengthening design was based on achieving approximately 38% increase in flexural capacity over the unstrengthened control beams. The mode of failure by design was brittle failure controlled by concrete crushing at 0.003 strain. However, the experimental program was designed to demonstrate the effectiveness of transverse anchoring reinforcement to control premature debonding failure modes and fully utilize the high strength of the composite systems. A more ductile behavior was also observed as a result of transverse strengthening and concrete confinement effects. Accordingly, an increase of approximately 50% in flexural strength is accomplished.     

Long-term moisture effects on the interfacial shear strength between surface treated carbon fiber and epoxy matrix

In recent years, carbon fiber reinforced polymer (CFRP) composites have found increasing applications in marine and offshore area, where the CFRP components are subjected to a persistent attack of moisture. The performance degradation of composites under those critical service conditions becomes a key issue. In this work, silane coating and multiwalled carbon nanotubes were applied on carbon fibers to enhance the fiber/matrix interfacial bonding strength. The long-term effects of moisture on the interfacial shear strength (IFSS) of the composites in underwater environments, such as de-ionized water and simulated seawater, have been studied using single fiber microbond method. The silane coating and carbon nanotube-modified silane coating are found to contribute 14.5% and 26.3% increase in IFSS of the CFRP in dry air, and well maintain this improvement during a 120-day immersion test in de-ionized water and simulated seawater.     

Torsion fatigue behavior of unidirectional carbon/epoxy and glass/epoxy composites

This paper presents results of the feasibility of carbon/epoxy composites (CFRP) as a future helicopter flexbeam material. Torsional behaviors of unidirectional CFRP and glass/epoxy composites (GFRP) with the same resin matrix were investigated. The initial torsional rigidity of CFRP was almost identical to that of GFRP. The torsional rigidities calculated using finite element analyses (FEA) agreed with the experimental results: the torsional rigidities are governed mainly by the material’s shear stiffness. Torsion fatigue tests were also conducted by controlling the angle of twist of the sinusoidal wave under a constant tensile axial load. No catastrophic failure occurred with either GFRP or CFRP, although decreased amplitudes of torque and torsional rigidities were observed according to the number of cycles. Results of X-ray CT inspections and numerical calculation by FEA revealed that degradation of a torsional rigidity is caused mainly by splitting crack propagation along the fiber direction. The torsion fatigue life of CFRP was superior to that of GFRP. Consequently, results confirmed that CFRP exhibits excellent properties as a torsional element of a helicopter flexbeam in terms of torsional rigidity and tension–torsion fatigue behaviors.     

Flexural and shear strengthening of RC beams with composite materials – The influence of cutting steel stirrups to install CFRP strips

Experimental, numerical and analytical investigations have revealed that Carbon Fibre Reinforced Polymer (CFRP) strips with larger cross section height improve the effectiveness of the Near Surface Mounted (NSM) technique for the flexural strengthening of existing reinforced concrete (RC) beams. However, this height is limited to the concrete cover thickness of the longitudinal steel bars, since the application of strips of cross section height larger than the cover thickness requires that the bottom arm of the steel stirrups be cut. This work aims to assess the influence, in terms of shear resistance, of cutting the bottom arm of steel stirrups to install NSM strips for the flexural strengthening of RC beams. The obtained results showed that, for monotonic loading, cutting the bottom arm of steel stirrups led to a decrease of the beam’s load carrying capacity of less than 10%. Due to the high effectiveness of the adopted NSM flexural strengthening systems, shear can be a predominant failure mode for these beams. To avoid this type of failure mode, strips of wet lay-up CFRP sheets with U configuration were used, resulting in effective strengthening solutions for RC beams. In the present paper the experimental program is described, and the obtained results are presented and discussed.     

Nonlinear finite element modeling of concrete deep beams with openings strengthened with externally-bonded composites

This paper aims to develop 3D nonlinear finite element (FE) models for reinforced concrete (RC) deep beams containing web openings and strengthened in shear with carbon fiber reinforced polymer (CFRP) composite sheets. The web openings interrupted the natural load path either fully or partially. The FE models adopted realistic materials constitutive laws that account for the nonlinear behavior of materials. In the FE models, solid elements for concrete, multi-layer shell elements for CFRP and link elements for steel reinforcement were used to simulate the physical models. Special interface elements were implemented in the FE models to simulate the interfacial bond behavior between the concrete and CFRP composites. A comparison between the FE results and experimental data published in the literature demonstrated the validity of the computational models in capturing the structural response for both unstrengthened and CFRP-strengthened deep beams with openings. The developed FE models can serve as a numerical platform for performance prediction of RC deep beams with openings strengthened in shear with CFRP composites.     

Fire behaviour of thermally insulated RC beams strengthened with NSM-CFRP strips: Experimental study

This paper presents the results of fire resistance tests on reinforced concrete (RC) beams flexurally strengthened with carbon fibre reinforced polymer (CFRP) strips installed according to the near surface mounted (NSM) technique using two different adhesives. The beams were simultaneously subjected to a service load and the ISO 834 standard fire. Different fire protection schemes were studied, comprising a thinner insulation layer along the bottom soffit of the beams and a thicker one at the CFRP anchorage zones. The main objectives of this paper were (i) to understand in further depth the fire behaviour of NSM-strengthened RC beams, in particular the structural effectiveness of the strengthening system during fire, (ii) to evaluate the efficiency of the above-mentioned fire protection strategy in extending the CFRP mechanical contribution during fire, and (iii) to compare the fire performance of the NSM-strengthening system with that of the alternative externally bonded reinforcement (EBR) technique, recently investigated under similar test conditions. The results obtained showed that using the adopted insulation schemes (i.e., thicker insulation at the anchorage zone and thinner insulation in the current zone), even after the CFRP-concrete bond is highly damaged in the central zone of the beams, the strengthening system is able to retain its structural effectiveness through a cable mechanism: for insulation thicknesses of 25 mm (current zone) and 50 mm (anchorage zones), the fire resistance of the strengthening system was extended up to 114 min. The loss of effectiveness of the CFRP system occurred when the average temperature in the adhesive at the CFRP anchorage zones attained values ranging from 2.2 to 5.6 times its glass transition temperature (T_g). The comparison with the EBR-strengthened beams confirmed the much better performance of the NSM strengthening.     

Anchorage resistance of CFRP strips externally bonded to various cementitious substrates

This paper presents a study on the anchorage capacity of Carbon Fiber Reinforced Polymer (CFRP) strips bonded to a cementitious substrate used for concrete surface reprofiling. The structural strengthening of a large-scale prestressed concrete girder in the framework of a bridge retrofitting project by means of prestressed CFRP strips required the levelling of an initial negative camber of about 2–4 cm. Both midspan and girder end situations were investigated with lap-shear and prestress force-releasing tests. Four different solutions regarding the levelling material, i.e. three mortars applied by hand as well as dry shotcrete, were tested. The results in terms of strain, slip and total anchorage resistance are presented and compared. In the end, dry shotcrete is recommended for the girder application. In addition to a very convincing bond behavior, the application is, despite the necessity of involving a specialized company from the field, clearly less time-consuming and easier. The retained solution represents an interesting approach for future applications in bridge retrofitting when an even surface is necessary for bonding CFRP strips.     

Mechanical characteristics and strengthening effectiveness of random-chopped FRP composites containing air voids

In random-chopped fiber-reinforced polymer (FRP) composites used as a retrofit material, a high volume fraction of voids is inevitable due to the manufacturing characteristics. In this paper, the mechanical characteristics and strengthening effectiveness of random-chopped FRP composites containing air porosity are investigated through experiments and numerical analysis. Coupon-shaped specimens with various material compositions were manufactured to examine the uniaxial tensile performance, and the air voids in the composites were measured by a microscope camera. In order to predict the overall performance of the composites, a micromechanical formulation that accounts for porosity was newly developed. The derived model was incorporated into a finite element (FE) code, and the model parameters were estimated by comparing uniaxial tensile test results for various systems of random-chopped FRP composites. In addition, concrete beams strengthened with the composites were produced to evaluate their load-carrying capacity. The FE predictions of the composite structures were then compared with experimental data to verify the predictive capability of the proposed numerical framework.     

Flexural strengthening of RC beams using Hybrid Composite Plate (HCP): Experimental and analytical study

Hybrid Composite Plate (HCP) is a reliable recently proposed retrofitting solution for concrete structures, which is composed of a strain hardening cementitious composite (SHCC) plate reinforced with Carbon Fibre Reinforced Polymer (CFRP). This system benefits from the synergetic advantages of these two composites, namely the high ductility of SHCC and the high tensile strength of CFRPs. In the material-structural of HCP, the ultra-ductile SHCC plate acts as a suitable medium for stress transfer between CFRP laminates (bonded into the pre-sawn grooves executed on the SHCC plate) and the concrete substrate by means of a connection system made by either chemical anchors, adhesive, or a combination thereof. In comparison with traditional applications of FRP systems, HCP is a retrofitting solution that (i) is less susceptible to the detrimental effect of the lack of strength and soundness of the concrete cover in the strengthening effectiveness; (ii) assures higher durability for the strengthened elements and higher protection to the FRP component in terms of high temperatures and vandalism; and (iii) delays, or even, prevents detachment of concrete substrate. This paper describes the experimental program carried out, and presents and discusses the relevant results obtained on the assessment of the performance of HCP strengthened reinforced concrete (RC) beams subjected to flexural loading. Moreover, an analytical approach to estimate the ultimate flexural capacity of these beams is presented, which was complemented with a numerical strategy for predicting their load-deflection behaviour. By attaching HCP to the beams' soffit, a significant increase in the flexural capacity at service, at yield initiation of the tension steel bars and at failure of the beams can be achieved, while satisfactory deflection ductility is assured and a high tensile capacity of the CFRP laminates is mobilized. Both analytical and numerical approaches have predicted with satisfactory agreement, the load-deflection response of the reference beam and the strengthened ones tested experimentally.     

Mechanics of three-dimensional braided structures for composite materials – Part II: prediction of the elastic moduli

In the first part of this series of paper [Z.X. Zang, R. Postle, Mechanics of three-dimensional braided structures for composite materials – Part I: fabric structure and fibre volume fraction, Comp. Struct. 49 (2000) 451–459], it was demonstrated that the braiding angles and fibre volume fraction can be represented as functions of the normalized pitch length introduced as a key parameter of three-dimensional braided reinforced composite materials. In the present paper, the models for the prediction of the tensile and shear moduli of three-dimensional braided composites are established by numerical simulation and mathematical modelling. Three-dimensional braided preforms are produced from the material system comprising glass/polypropylene and their moduli are measured. The results predicted from the braided composite models are supported by the experimental data.     

Near surface mounted CFRP laminates for shear strengthening of concrete beams

A Near Surface Mounted (NSM) strengthening technique was developed to increase the shear resistance of concrete beams. The NSM technique is based on fixing, by epoxy adhesive, Carbon Fiber Reinforced Polymer (CFRP) laminates into pre-cut slits opened in the concrete cover of lateral surfaces of the beams. To assess the efficacy of this technique, an experimental program of four-point bending tests was carried out with reinforced concrete beams failing in shear. Each of the four tested series was composed of five beams: without any shear reinforcement; reinforced with steel stirrups; strengthened with strips of wet lay-up CFRP sheets, applied according to the externally bonded reinforcement (EBR) technique; and two beams strengthened with NSM precured laminates of CFRP, one of them with laminates positioned at 90° and the other with laminates positioned at 45° in relation to the beam axis. Influences of the laminate inclination, beam depth and longitudinal tensile steel reinforcement ratio on the efficacy of the strengthening techniques were analyzed. Amongst the CFRP strengthening techniques, the NSM with laminates at 45° was the most effective, not only in terms of increasing beam shear resistance but also in assuring larger deformation capacity at beam failure. The NSM was also faster and easier to apply than the EBR technique. The performance of the ACI and fib analytical formulations for the EBR shear strengthening was appraised. In general, the contribution of the CFRP systems predicted by the analytical formulations was slightly larger than the values registered experimentally. Performance of the formulation by Nanni et al. for NSM strengthening technique was also appraised. Using bond stress and CFRP effective strain values obtained in pullout bending tests with NSM CFRP laminate system, the formulation by Nanni et al. predicted a contribution of this CFRP system for the beam shear resistance of 72% the experimentally recorded values.