The article deals with the analysis of influence of carbon-fibre reinforced polymer (CFRP) on stress distribution in a steel reinforced concrete beam loaded by four-point bending flexural test. Simulation of the delamination is modelled by FEM with a cohesion zone material model. Distribution of cracks with CFRP strengthening is analysed, too. Finally, the fatigue life tests analysis was executed for the steel specimen (W.Nr. 1.0429 – concrete steel), which was used in the reinforced concrete beam. The fatigue test results are used to plot the fatigue life curve

M. Močilan

P. Kopas

P. Novák

P. Pastorek

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Finite element analysis of bond behavior in a steel reinforced concrete structure strengthened carbon fibre reinforced polymer (CFRP) strips

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405METALURGIJA 56 (2017) 3-4, 405-408P. PASTOREK, P. NOVÁK, P. KOPAS, M. MOČILANFI NITE ELEMENT ANALYSIS OF BOND BEHAVIOR IN A STEEL REINFORCED CONCRETE STRUCTURE STRENGTHENED CARBON FIBRE REINFORCED POLYMER (CFRP) STRIPSReceived – Primljeno: 2016-12-15Accepted – Prihvaćeno: 2017-05-10Preliminary Note – Prethodno priopćenjeP. Pastorek, P. Novák, P. Kopas, M. Močilan, University of Žilina, Fac-ulty of Mechanical Engineering, Department of Applied Mechanics, Žilina, Slovak RepublicThe article deals with the analysis of influence of carbon-fibre reinforced polymer (CFRP) on stress distribution in a steel reinforced concrete beam loaded by four-point bending flexural test. Simulation of the delamination is mod-elled by FEM with a cohesion zone material model. Distribution of cracks with CFRP strengthening is analysed, too. Finally, the fatigue life tests analysis was executed for the steel specimen (W.Nr. 1.0429 – concrete steel), which was used in the reinforced concrete beam. The fatigue test results are used to plot the fatigue life curve.Key words: steel, strengthened, polymer strip, stress, finite element method (FEM)INTRODUCTIONIn the past decades, the use of composites for strengthening and repairing concrete structures has gained significant importance in civil engineering [1-3]. There are a large number of new, innovative building ma-terials on the market. In order to avoid a drastic impact of building materials now or in the future, these materials as well as their manufacture and use must comply with the ecological standards. The trend of developing new build-ing materials is not characterised by inventing something new, but rather by improving something long-existing. The aim of this study is to create a model to simulate a four-point bending loading experiment on a reinforced concrete beam with and without carbon-fibre reinforced polymer.FEM SIMUL ATION OF A REINFORCED CONCRETE BEAM Experimental measurements of four-point bending of a reinforced concrete beam were carried out in our labo-ratory. Figure 1 show that the contact between the load and the beam, as well as the contact between the supports and the beam. The surface representing half profile of the T-beam is divided into smaller areas, borderlines of which will be used later to create a mesh of link/beam elements forming the steel reinforcement. The element Solid65 was used for discretization the steel reinforce-ment. The dimensions of the full-size beams are 3600 mm x 350 mm x 400 mm and the span between the sup-ports was 3310 mm. Moreover, the lower part of the beam includes a milled groove in the covering layer. ISSN 0543-5846METABK 56(3-4) 405-408 (2017)UDC – UDK 669.14.018.001.7:678.7-621.41:620.518.1=111The groove is 4 mm wide, 20 mm deep, and 3 000 mm long, positioned symmetrically in relation to the trans-verse plane of the beam symmetry (Figure 2).Figure 1  Experimental stand for four-point bending testFigure 2  Geometric model of the reinforced concrete beam with a gap or the  composite lamella406P. PASTOREK et al.: FI NITE ELEMENT ANALYSIS OF BOND BEHAVIOR IN A STEEL REINFORCED CONCRETE... METALURGIJA 56 (2017) 3-4, 405-408modulus E = 200 GPa, ductility  = 0,005, Poisson’s rate μ = 0,3.Composite lamella: the simulated composite lamel-la is made by the BASF company. Its trade name is MBRACE CFK 150/2 000. The composite lamella di-mensions are 20 x 1,4 x 3000 mm. For this lamella type, the manufacturer states the Young’s modulus larger than 165 GPa, Poisson’s number μ = 0,2 and the recommend-ed design tensile strength is 51,8 kN, which means that the uniaxial tension stress is 1 850 MPa at the lamella cross-section of 28 mm2.High-strength epoxy glue: to affix the lamella into the groove in the beam we use high-strength epoxy adhe-sive with a high glass transition temperature for the MBRACE lamella system by BASF, with the trade name MBRACE Laminate Adhesive HT. Its bond strength is >14 MPa, compressive strength is 73 MPa, bending elas-tic modulus is 4263 MPa, glass transition temperature is ≥ 40°, shrinkage/ expansion is ≤ 0,1 % [5].ANALYSIS OF THE RESULTSFigure 3 shows the maximum deflection in the mid-dle of the reinforced concrete beam with a lamella, and it reaches the value wmax = 7,57 mm. This value is slightly reduced compared with the model with CFRP lamella [6]. Due to bending, the free end of the beam behind the support is displaced upwards by 0,89 mm. Figure 4 shows the first principal stress in the concrete. This val-ue indicates the sites that are critical for the concrete deterioration due to a high tensile stress, which concrete naturally “does not like”. High values are present in the beam lower side. The maximum is reached due to con-crete deterioration consideration, and it appears near the steel reinforcement.Due to the lamella groove, and the lamella with a high elasticity modulus, concentration of stresses oc-curs near the original beam/groove interface. The maxi-MODELLING THE LAMELLA AND ITS BONDING WITH THE CONCRETEBonding the lamella with the concrete is modelled using the conta173 contact elements, considering the contact with adhesive bonding (bonded always con-tact), and using a cohesive material model (CZM – Co-hesive Zone Material). We used the data provided by the manufacturer of the glue. We assumed a dominant shear mode of breaking the bonded joint. This material model requires entering τmax = 12 MPa (maximum equivalent contact shear stress), δt = 1 mm (tangential displacement after debonding). This value is not stated by the manufac-turer and must be obtained through an experiment [4].In the post-processing, for the contact defined in the above manner, we can evaluate the generally known data, such as contact status, contact gap, contact pres-sure, as well as the following variables:DPARAM – debonding parameter – this parameter takes a value from 0 to 1, where the value 1 corresponds with the breaking of the bonded joint, and the value 0 corresponds with the initial unbroken joint, DTSTARI – the time step at which debonding oc-curred.BOUNDARY CONDITIONS The solution is significantly influenced also by the manner used for the beam positioning modelling. In or-der to prevent the formation of stress concentrators, we modelled a plane support with a width corresponding to the experiment, and a joint in the support width centre. The above was done using shell elements – shell181. The nodes in the support width centre were removed of all degrees of freedom for displacement, and we re-tained all degrees of freedom for rotation. Contact with the beam was done using the conta173 and target170 contact elements. A support modelled in this manner has no longer caused the formation of stress concentra-tors in its vicinity; therefore no cracks occurred in this area [5].The load acting on the beam in its upper part was created as a quarter of the total force  F = 110 kN acting on the small area formed by the experiment require-ments. The small area is 150 mm wide and its distance from the beam centre is 500 mm [6].MATERIAL PROPERTIESCon crete: the concrete according to STN EN 206-1 was used (Concrete STN EN 206-1- C35/45-Cl0, 04-Dmax16-S3). The material properties of the concrete are: Young’s concrete elasticity modulus E = 34 GPa, ductility stated by the manufacturer cu = 0,035, Pois-son’s rate μ = 0,2, the concrete density ρ = 2 400 kg.m-3. Steel reinforcement: the concrete steel B500 B ac-cording to STN EN 10027 was used: strength Rc = 500 MPa, ultimate tensile strength  Rm = 550 MPa, Young’s Figure 3  Displacement of the reinforced concrete beam with a lamellaFigure 4  First principal stress in the concrete407P. PASTOREK et al.: FI NITE ELEMENT ANALYSIS OF BOND BEHAVIOR IN A STEEL REINFORCED CONCRETE...METALURGIJA 56 (2017) 3-4, 405-408mum value dropped and moved to this area from the steel reinforcement site.Figure 5 shows the third principal stress in the con-crete. This value shows the areas where concrete crush-ing might occur in case of exceeding the concrete com-pressive strength.The maximum reached value is - 28,1 MPa is below the used concrete compressive strength, therefore there should be no crushing. The stress value was higher compared to the previous case and, like in the first principal stress, the value moved from the steel reinforcement to the site of the lamella groove [6].   The course of axial stresses in the reinforcement is shown in Figure 6. As we can see, compressive stress occurs in the upper part of the reinforcement. The max-imum compressive stress emerged near the action of the loading pressure, and the compressive stress value in the reinforcement reached the value pmax,steel = 164,32 MPa. The maximum tensile stress emerged in the bottom part of the steel reinforcement, at the site under the load-ing force, and its value reached σtmax,steel = 424,63 MPa. This value is lowered compared with the model without the composite reinforcement, but it is still near the value of the yield strength Rc.Figure 7 shows the pink-coloured cracks formed in the concrete as a result of exceeding the concrete tensile strength. These cracks occur around the T-shaped steel stirrups.The shape and length of cracks has changed signifi-cantly compared with the case without a lamella. Al-though there is still one significantly long crack at the site under the acting load, other cracks are of approxi-mately the same length. In Figure 8 we can see the DPARAMJ and DPARA-MI values that indicate the probability of adhesion loss of the glue and the lamella.The maximum value is cca 0,94, which represents a 94 % probability of adhesion loss. According to the DT-Figure 5 Third principal stress in the concreteFigure 6 Axial stresses in the concrete beam reinforcementFigure 7 Depiction of cracks in the concreteFigure 8 The probability of adhesion loss with loading steps501502503504505501,00E+03 1,00E+04 1,00E+05 1,00E+06 1,00E+07Number of cycles to failure / log n  Stress amplitude a / Mpa      103              1 4              5               06              107  Figure 9 Wöhler curve of 1.0429 steel (bending) STARI value, this should occur in the last, 9th loading step, at the site filled with red.Finally we carried out low-frequency fatigue tests on the W. Nr. 1.0429 steel to determine fatigue life in the low-cycle fatigue domain. We gradually tested the specimen bars in a multiaxial test device for a single-axis type of loading, which was done at provided air-cooling. The resulting number of cycles prior to frac-ture, frequency of the fatigue loading, and the eccentric deviation setting value were entered into a worksheet. Figure 9 shows the measured values at low-frequency experimental testing, processed in a regression analysis [7-10].CONCLUSIONS The results obtained show that the use of the above-mentioned composite lamella changes the stress distri-bution in the concrete matrix as well as in the steel rein-forcement. This is manifested by the reduction in the 408P. PASTOREK et al.: FI NITE ELEMENT ANALYSIS OF BOND BEHAVIOR IN A STEEL REINFORCED CONCRETE... METALURGIJA 56 (2017) 3-4, 405-408maximum stress values in the tensile domain for both the concrete and the reinforcement, and in case of the concrete also by increased maximum compression stress-es, which is favourable for concrete. The maximum bending (deflection) values are very similar in the two cases. It also results from the data obtained that there will be no adhesion compromise between the concrete and the lamella (the maximum value is 94 % of the bond ultimate shear strength), but there will occur de-lamination in the concrete. The shape and size of the cracks in the concrete have changed as well. Based on the values measured in fatigue tests, the fatigue strength can be approximately determined at the number of cy-cles prior to fracture Nf = 1.107. Hence, the fatigue life of the tested material of concrete (reinforcing) steel could be around 110 MPa.AcknowledgementsThis paper was supported by the Slovak Research and Development Agency under contract No. APVV – 0736 – 12, and by the Slovak Grant Agency VEGA 1/0983/15.REFERENCES[1] E. J. Barbero, Finite Element Analysis of Composite Mate-rials Using ANSYS. CRC Press (2014), p. 334. [2] L. Dahmani, A. Khennane, S. Kaci, Crack Identification in Reinforced Concrete Beam Using ANSYS Software. Strength of Materials 42 (2010) 2, 232-240.[3] M. Žmindák, J. Meško, Z. Pelagić, A. Zrak, Finite element analysis of crack growth in pipelines. In: Manufacturing Technology, Journal for Science, Research and Produc-tion. 14/1, (2014), 116-122.[4] M. Žmindák, P. Novák, V. Dekýš, Repair of composite structure using cold sleeve with polymer filling material. Advanced Materials Research 897 (2014) 83-86. [5] A. Čavojcová, M. Moravčík, F. Bahleda, J. Jošt, Experi-mental Verification of Reinforced Concrete Member under Cyclic Loading. Procedia Engineering 92 (2014), 262-267.[6] M. Žmindák, P. Novák, P. Pastorek, Analysis of bond between reinforced concrete beam and fiber reinforced polymer lamella, In: Mechanics of Composite Materials and Structures, Sušice, 2016. [7] A. Vaško, L. Trško, R. Konečná, Fatigue behaviour of syn-thetic nodular cast irons. Metalurgija 54 (2015) 1, 19-22.[8] J. Belan, High frequency fatigue test of IN 718 alloy – mi-crostructure and fractography evaluation. Metalurgija 54 (2015) 1, 59-62.[9] M. Vaško, M. Sága, Application of fuzzy structural analysis for damage prediction considering uncertain S/N curve. Applied Mechanics and Materials 420 (2013), 21-29.[10] F. Nový, P. Kopas, O. Bokůvka, A. Savin, Fatigue durabi-lity of ductile iron in very-high-cycle region. Manufactu-ring Technology Journal for Science, Research and Pro-duction 16 (2016) 2, 406-409.Note:  The responsible translator for the En glish language is Janka Súkeníková, Sarja, Žilina, Slovakia

Finite element analysis of bond behavior in a steel reinforced concrete structure strengthened carbon fibre reinforced polymer (CFRP) strips

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