Modeling of the Behavior of Concrete Tension Members Reinforced with FRP Rods

The paper is devoted to the analysis of cracking and deformability of concrete tension members reinforced with fiber-reinforced polymer (FRP) rods. A theoretical nonlinear model, derived from a cracking analysis founded on slip and bond stresses, is adopted for evaluating the crack width, crack spacing, and elongation of tension members. The procedure takes into account the local bond-slip law, experimentally determined by means of pullout tests, and allows us to evaluate the influence of tensile stiffening. The analysis is performed with considering all parameters influencing the behavior of tension members, such as the concrete strength, the kind of FRP rebars, the surface treatment of FRP rebars, and the concrete cover thickness. The theoretical predictions are compared with available experimental results, obtained on cylindrical concrete specimens reinforced with carbon FRP (CFRP) rods, and with predictions of the traditional models usually adopted for design purposes.     

A finite element model for hygrothermal analysis of masonry walls with FRP reinforcement

Modeling of moisture migration and heat transfer in fiber reinforced polymer (FRP) composite upgraded masonry structures is of great importance, since the interfacial adhesive between the reinforcing FRP laminate and the host masonry is prone to moisture damages. In this paper, a generic theoretical formulation was first developed to model moisture and heat transport in a layered structure consisting of distinct materials. This formulation was based on the framework of the hygrothermal model presented by Philip and De Vries for a monolithic porous medium. Finite element implementation of the formulation was subsequently used to model moisture and heat transport in an FRP reinforced masonry block. Analytical results were then compared with experimental data to validate the model. Parametric studies were then performed for a concrete block with a reinforcing FRP laminate partially covering one surface. The results showed that changing temperature gradient affects the moisture distribution considerably. This effect was found particularly significant at the concrete/FRP interface where a drastic change in local temperature gradient is present.     

Effects of Moisture and Stresses on the Structure and Properties of Polyester Resin

The results of a complex study of structural changes in a cured Norpol 440 polyester resin under the action of damp environment and mechanical loading are presented. A considerable effect of absorbed moisture on the structure and some characteristics of the material is revealed by using thermophysical methods and X-ray diffractometry. The joint effect of moisture and mechanical stress is estimated by investigating the creep in stationary and nonstationary moisture conditions. The anisotropy of the material structure formed during creep is evaluated from the results of dilatometric measurements. It is found that the degree of anisotropy of the material after creep accompanied by moisture sorption is higher than that after creep in the conditions of moisture equilibrium with atmosphere. It is established that the aftercure and relaxation of the residual creep deformation come to an end at heating to 80-85°C. At a further rise in temperature and repeated heating, changes in the material structure are not observed.     

Tensile Characterization of FRP Rods for Reinforced Concrete Structures

The application of FRP rods as an internal or external reinforcement in new or damaged concrete structures is based on the development of design equations that take into account the mechanical properties of FRP material systems.The measurement of mechanical characteristics of FRP requires a special anchoring and protocol, since it is well known that these characteristics depend on the direction and content of fibers. In this study, an effective tensile test method is described for the mechanical characterization of FRP rods. Twelve types of glass and carbon FRP specimens with different sizes and surface characteristics were tested to validate the procedure proposed. In all, 79 tensile tests were performed, and the results obtained are discussed in this paper. Recommendations are given for specimen preparation and test setup in order to facilitate the further investigation and standardization of the FRP rods used in civil engineering.     

Load-deflection analysis of concrete elements reinforced with FRP rebars

The behavior of fiber reinforced plastic (FRP) concrete elements under service conditions is analyzed. Taking into account the real constitutive law of materials and local bond-slip law which adequately describes the interaction between the FRP reinforcement and concrete, a numerical procedure is proposed for obtaining moment-curvature relationships for a cracked beam element. Using the moment-curvature laws, the load-deflection analysis of FRP concrete beams is carried out. To study the influence of geometric and mechanical parameters, a numerical investigation was carried out and the results obtained were compared with those from other methods and Codes. The results of the experimental investigation are described and compared with those of the proposed procedure; the comparison shows good agreement between the theoretical and experimental results.     

An analysis of moisture diffusion according to Fick’s law and the tensile mechanical behavior of a glass-fabric-reinforced composite

The properties of moisture diffusion parameters and their effect on the tensile mechanical behavior of a fabric composite (glass fiber/epoxy resin) in the warp and weft directions were investigated. The water up take by specimens conditioned in a humid environment under different relative humidities (0, 60, and 96% RH) at a constant temperature of 60°C was evaluated by weight gain measurements. The water absorption followed Fick’s diffusion law in the fabric composite. A comparison between the values obtained for the moisture diffusion coefficient and the equilibrium moisture content at the laboratory and those given by Loos and Springer showed that the parameters depended not only on the nature of materials, but also on environmental conditions. The effect of moisture absorption on tensile characteristics of the composite, which was tested in uniaxial tension in the warp and weft directions at constant imposed displacement rates up to failure, showed a significant reduction in the ultimate tensile strength of the specimens conditioned at 96% RH. Russian translation in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 43, pp. 479-488, May-June, 2009.     

Cracking Analysis of FRP-Reinforced Concrete Flexural Members

The paper is dedicated to the cracking analysis of FRP (Fiber-Reinforced Polymer)-reinforced concrete elements. A general nonlinear calculation procedure, based on the slip and bond stresses, is described and adopted for the prediction of the crack width and crack spacing in FRP-reinforced concrete beams. An analytical expression of the bond-slip law is estimated using the corresponding experimental results available in the literature. A numerical investigation is carried out and the influence of the mechanical and geometrical parameters of the material (bond-slip law, reinforcement ratio, concrete strength, diameter of rebars, etc.) on the crack formation is investigated. Referring to glass-FRP-reinforced concrete beams, a comparison between the theoretical predictions and experimental results is made. The results obtained are presented and discussed.     

Load-deflection analysis of concrete elements reinforced with FRP rebars

The behavior of fiber reinforced plastic (FRP) concrete elements under service conditions is analyzed. Taking into account the real constitutive law of materials and local bond-slip law which adequately describes the interaction between the FRP reinforcement and concrete, a numerical procedure is proposed for obtaining moment-curvature relationships for a cracked beam element. Using the moment-curvature laws, the load-deflection analysis of FRP concrete beams is carried out. To study the influence of geometric and mechanical parameters, a numerical investigation was carried out and the results obtained were compared with those from other methods and Codes. The results of the experimental investigation are described and compared with those of the proposed procedure; the comparison shows good agreement between the theoretical and experimental results.Department of Materials Science, University of Lecce, Via per Arnesano, 73100 Lecce, Italy. Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 163–172, March–April, 1999.     

Temperature dependence of stress–fatigue life data of FRP composites

Polymer-matrix composites are viscoelastic materials, and their mechanical properties are significantly influenced by temperature. The present study develops a power-law stress–fatigue life relation which takes into account the effect of temperature on the fatigue strength of fibre-reinforced polymer (FRP) composites. The validity of the relation is evaluated on the basis of various sets of experimental data found in the literature, and the estimated fatigue lives obtained are found to be in good agreement with the experiments.     

Effect of anisotropy on the cyclic deformation and heating of SVAM-type glass-reinforced plastics

The effect of anisotropy of the mechanical properties on the cyclic deformation and heating of 1:1 and 5:1 SVAM-type glass laminates has been investigated for symmetrical tension-compression and pulsating tension and compression. It is shown that on the main part of the fatigue curve, depending on the anisotropy and the cyclic stress level, the temperature may be stabilized. At the same time, fracture is invariably accompanied, under fixed experimental conditions, by a rise in temperature to a certain value that depends only on the anisotropy property of the glass-reinforced plastic, the strain also reaching critical values that are determined by the cycle asymmetry and the anisotropy property of the material.Institute of Mathematics and Mechanics, Academy of Sciences of the Armenian SSR, Erevan. Translated from Mekhanika Polimerov, No. 5, pp. 898–903, September–October, 1971.     

Assessment of transmission of the shear stress in potted anchors for composite rods 1. Sleeve of constant thickness

The key problem facing the application of fiber-reinforced polymer (FRP) stay cables and tendons is the anchorage. Potted (bond-type) anchors have been used more extensively than anchors of any other type. The main aim in the design of anchors is to minimize the peak shear stress at the FRP rod-pottant interface. To this end, parametric analyses of the stress state in the anchors are carried out. Since parametric studies can not be easily performed by the finite-element method, an analytical model of the anchor is proposed. The model involves significant simplifying assumptions and allows one to obtain a relatively simple analytical solution for shear-stress distributions at the FRP rod-pottant interface. The use of this solution at various boundary conditions and various geometrical and mechanical parameters of anchor components enables one to search for and evaluate, at least qualitatively, different methods for decreasing the peak interfacial shear stress in the anchor. In this part of the investigation, an anchor consisting of a sleeve of constant thickness is considered. Russian tanslation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 321-346, May-June, 2009.     

Computational mechanical analysis of composite bondlines under environmental moisture loads

A combined moisture diffusion and mechanical computational analysis methodology was developed as part of an independent research program at Lockheed to enhance our understanding of nonlinear and coupled physical processes in materials. The physical behavior of interest is the mechanical response of composite material systems to environmental conditions which can change the materials' moisture content. In particular, it is desirable to know what set of environmental conditions will affect the integrity of a partial adhesive bondline when a bondline gap (no adhesive) is present. The Lockheed proprietary finite element analysis code DIAL was modified to analyze this phenomena in two stages. First, the temporal moisture partial pressures in the materials are calculated from initial and environmental boundary conditions and second, these partial pressures are then passed to a quasi-static mechanical analysis where the moisture data at each time step is treated as a dilatation (swelling) load. The resulting stress and strain state is then calculated, as well as gap closure, if any.Demonstration of this methodology was on a relatively simple 2-dimensional axisymmetric example problem. The results show primarily compressive stresses caused by the positive dilatation (swelling) induced by moisture intrusion of the structure. The stresses concentrate at adhesive bondlines, and bondline gap behavior (i.e., the absence of a contiguous adhesive bond at material interfaces) is correctly simulated. It should be noted that the behavior of the gap and any resultant stress/strains due to a change in moisture is problem dependent, and this example problem is meant as a demonstration of methodology.     

Long-Term Creep of Hybrid Aramid/Glass-Fiber-Reinforced Plastics

The results of experimental investigation of the long-term creep of SVM aramid fibers, EDT-10 epoxy resin, aramid-epoxy FRP (fiber-reinforced plastics), glass-epoxy FRP, and aramid/glass-epoxy hybrid FRP with different volume fractions of aramid and glass fibers are presented. The long-term tests were continued for 50,000 h (5.7 years). A structural approach for predicting the long-term creep from the properties and content of the components is considered. The effect of hybridization (partial replacement of the aramid fibers by glass fibers) on the inelastic deformation of hybrid FRP is discussed. The redistribution of stresses in the components during long-term creep of the hybrid composites is analyzed.     

Effect of shear stiffness and concrete wedge cone failure on fracture of a fiber-reinforced plastic rod at an intersection with a concrete crack

Experimental results of model speciments in which FRP rods fractured due to local deformation at a crack intersection in a concrete member were analyzed by a 3D nonlinear finite element method in which orthogonal anisotropy of the FRP rod was considered. The analytical results indicated that accurate prediction of shear modulus of the FRP rod and size of concrete wedge cone failure around the FRP rod was significant to predict deformation and fracture of the FRP rod. FRP rods as reinforcement in concrete members, the small shear modulus, because of the orthogonal anisotropy and the wedge cone failure, may prevent the FRP rod from fracturing at a very low tensile stress due to the local deformation at the crack intersection.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 21, No. 2, pp. 158–166, March–April, 1996.     

Non-symplectic smooth circle actions on symplectic manifolds

We construct smooth circle actions on symplectic manifolds with non-symplectic fixed point sets or cyclic isotropy sets. All such actions are not compatible with any symplectic form on the manifold in question. In order to cover the case of non-symplectic fixed point sets, we use two smooth 4-manifolds (one symplectic and one non-symplectic) which become diffeomorphic after taking the products with the 2-sphere. The second type of actions is obtained by constructing smooth circle actions on spheres with non-symplectic cyclic isotropy sets, which (by the equivariant connected sum construction) we carry over from the spheres on products of 2-spheres. Moreover, by using the mapping torus construction, we show that periodic diffeomorphisms (isotopic to symplectomorphisms) of symplectic manifolds can provide examples of smooth fixed point free circle actions on symplectic manifolds with non-symplectic cyclic isotropy sets.     

Numerical Analysis of a Cyclical Loaded Construction under Corrosion Degradation

A contribution for analytical and numerical tools that permits of a deterministic evaluation of structure behavior in external conditions, under multiparameter and/or cyclic mechanical, thermal and chemical loads, is the aim of this paper. Particular structure elements undergo the plastic and corrosion degradation and they dissipate energy, which consists of irreversible contributions, like a work on the inelastic strains. The construction and its unit lifetime are estimated according to a dissipated energy criterion. The paper emphasizes the modeling and numerical implementation of degradation effects, such as cyclic plasticity, generated by mechanical and thermal loads, stress corrosion, electrochemical corrosion and low-cyclic corrosion. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical model of the anisotropy of low-cycle deformability of glass-fiber reinforced plastics

Conclusion A theoretical model is suggested for the anisotropy of low-cycle deformability of glass plastics determined by the anisotropy of the deformational properties of the material in short-term static tension (compression). The effect of the anisotropy of cyclic loss of strength of the deformational properties is taken into account by the introduction of the characterizing function which is taken to be independent of the mechanical properties of the material and of the conditions of low-cycle loading.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 437–442, May–June, 1985.     

Effects of temperature and moisture on the mechanical properties of polyester resin in tension

The effect of environment on the physical and mechanical properties of composite materials in some cases is determined by the environmental sensitivity of the binder. The results of experimental investigation of the deformability and strength of polyester resin, widely used as a binder in composites, upon the action of stationary and quasi-stationary loads, temperatures, and moisture are presented. The ranges of acceptable values of these services factors are determined. The elastic modulus and tensile strength of the material are obtained from quasi-static tests. The viscoelastic behavior of the resin is investigated in creep tests. From the results of a short-term experiment with stepwise loading up to failure, it is found that the creep of specimens with a moisture content of 0.14% can be described by a linear viscoelastic model for stresses up to 20 MPa (two thirds of the strength). The action of single loading impulses is summarized according to the Boltzmann superposition principle. The temperature and absorbed moisture are considered as factors accelerating the relaxation processes in the material. The creep activation under the action of these factors is described using the methods of time-temperature and time-moisture equivalence. The results of short-term creep tests allow us to determine the relaxation characteristics of the material in stationary conditions. The long-term creep under close-to-service conditions is predicted using these data and quite good agreement with the control test is obtained. The sensitivity of the material characteristics (strength, elastic modulus, and creep strain) to the action of temperature and moisture is estimated. The creep strain is most sensitive to the action of environmental factors. For a fully saturated material (moisture content 1.64 wt.%), after one hour creep, this strain four times exceeds that of a dry one. The same growth in deformability is caused by an 18°C increase in temperature. A quantitative comparison of the characteristics of polyester and epoxy resins allows us to choose the binder for composites and to estimate the expected environmental effect. Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 395–406, May–June, 2000.     

Finite-element modeling of the interaction of reinforcement with concrete matrix

A finite-element model of a reinforced concrete beam with rebars modeled by a 3-D deformable body has been developed. An analysis of the stress-strain state of the beam allowed us to determine the stress distribution on cross sections of the rebars and the location of zones with cracks in concrete. It is found that the break of bond between the reinforcement and concrete goes outside the areas of intensely cracked concrete matrix. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 309–316, May–June, 2008.     

Cyclic actions on compression bodies

We classify cyclic actions on compression bodies. We find necessary and sufficient arithmetic conditions for a compression body to admit aZ _p -action withp a prime number.