Advanced XFEM Simulation of Pull-out and Debonding of Steel Bars and FRP-Reinforcements in Concrete Beams

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1 Amerian Journal of Engineering and Applied Sienes Original Researh Paper Advaned XFEM Simulation of Pull-out and Debonding of Steel Bars and FRP-Reinforements in Conrete Beams Niola Orlando and Elena Benvenuti Department of Engineering, University of Ferrara, I-44122, Ferrara, Italy Artile history Reeived: Revised: Aepted: Corresponding Author: Niola Orlando Department of Engineering, Institute/Organization: University of Ferrara, I-44122, Ferrara, Italy Abstrat: An innovative three-dimensional model is applied to the pull-out of steel bars and the debonding of FRP plates from onrete speimens. The shearing and opening modes at the interfae of debonding is fully aptured. The model is based on an innovative variant of the regularized extended Finite Element Method (XFEM) developed by the authors. In this method, the displaement disontinuity at the debonding surfae is regularized and an internal length parameter is introdued. Besides smoothing the debonding, the regularized XFEM is partiularly suitable for modelling steel fiber reinfored beams. Keywords: Pull-Out, Debonding, XFEM, Bending Test, 3D, Mixed-Mode Introdution In this study, an innovative three-dimensional (3D) approah for modelling the bond behavior of steel bars embedded in onrete bloks and FRP plates glued to onrete beams is presented. The approah adopted is based on a reently developed proedure alled regularized extended Finite Element Method (regularized XFEM) Benvenuti et al. (2016), that extends a previous two-dimensional (2D) formulation for ohesive-like interfaes, Benvenuti et al. (2012), Benvenuti et al. (2013). The regularized XFEM is a variant of the extended Finite Element Method developed by Belytshko et al. (2009), Moës et al. (1999). Reent appliations of XFEM in ivil engineering an be found in Jaśkowie (2015) and in Huo et al. (2015). However, the appliations of XFEM to the simulation of the debonding of FRP plates from onrete beams subjeted to bending are rather few. An example is the work by Dror and Rabinovith (2016). In the approah proposed in the present paper, the displaement disontinuities are regularized introduing an additional internal length parameter. Moreover, a suitable variational formulation is adopted, based on the onept of Eshelby's equivalent eigenstrain Eshelby (1957), as shown in Benvenuti (2014). A wide range of loading ases and types of reinforement is onsidered to prove the generality and the reliability of the present approah. In partiular, the following experimental tests have been modelled: Pull-out test of steel bars embedded in onrete bloks Three point bending tests of Steel-Fibers Reinfored Conrete (SFRC) beams strengthened with flexural FRP reinforements Four point bending test of steel Reinfores Conrete (RC) beams strengthened with flexural FRP reinforements The detahment of FRP plates from supports made of quasi-brittle materials is ommonly modelled as 2D plane stress problems replaing the FRP-onrete over with an equivalent non-linear one-dimensional bond stress-slip law. Relevant appliations to FRP-reinfored onrete bloks subjeted to shear tests an be found in Turon et al. (2007) and Toti et al. (2013). It has been demonstrated in Czaderski et al. (2010), Martinelli et al. (2011), Subramaniam et al. (2011), that the detahment of FRP reinforement from onrete supports involves the development of a 3D strain/stress distribution and ours in a mixed debonding mode. These aspets annot be aptured using 2D models that aount for the only shear debonding mehanisms. 3D effets have been studied by Neto et al. (2014). The presented approah takes into aount both the mixed mode debonding and 3D effets. The latter aspet has been disussed in Benvenuti et al. (2016) for the ase of single-lap shear tests. In this study, the fous is on the former aspet, namely on the mixedmode debonding Niola Orlando and Elena Benvenuti. This open aess artile is distributed under a Creative Commons Attribution (CC-BY) 3.0 liense.

2 Niola Orlando and Elena Benvenuti / Amerian Journal of Engineering and Applied Sienes 2016, 9 (3): Main Features of the Regularized XFEM The proposed approah models the mehanial behavior of displaement disontinuities in brittle materials. A briefly review of the approah has been reported hereinafter. More details about the proposed approah an be found in Benvenuti (2014), Benvenuti et al. (2016). An additional internal length governing the width of the proess zone is introdued. The adopted regularization avoids the possible mesh-dependeny indued by softening damaging laws. Moreover, a smooth ontinuousdisontinuous transition is obtained, Benvenuti and Tralli (2012). The approah is based on a damage proedure that an orretly reprodue mixed-mode debonding, as shown in the single-lap shear tests previously presented. Let the displaement field u be disontinuous aross the failure surfae defined aording the mehanial problem R 3 of normal n S. Within a single element of nodal degrees of freedom U e and A e interpolated by the usual FE interpolation funtions N e, the regularized XFEM displaement u e of element is: e e e e u = NU +H e NA, (1) where, H is the regularized Heaviside funtion (Fig. 1). This regularized funtion approximates the Heaviside funtion for vanishing regularization parameter. The vetor A e ollets the jump omponents along, and for the finite element. H is assumed a funtion of the signed distane from the level-set surfae. By ompatibility, the strain field is: e ε = ε + ε + δ, (2), e ε =BU e e ε = H BA e e ( n S ) (2a) (2b) δ = γ NA, (2) where, B e = N e is the standard FE ompatibility matrix and = H (implying that H = H n S = n S ). Strains ε and ε represent respetively the deformation of the bulk in absene of regularized and the spatial variation of the disontinuity intensity A e. Strain δ orresponds to the strain loalized over the regularization volume. Steel bars, FRP plates and adhesive layers are usually modelled as linear elasti materials. At eah Gauss point, the damage variables D and D for the onrete are introdue. Then, with E =E/, the stresses are omputed as: ( 1 ) E (1 ) E, (3) = D + D e σ ε ε σ = e ( 1 D ) E δ. (4) Fig. 1. Regularized Heaviside funtion The stress σ pertains to the bulk material and is governed by the onstitutive matrix E and the damage variable D. In partiular, the damage ranges from 0 (material sound) up to the ritial value D, when the evolution of damage of D is dropped. D is governed by the Galileo-Rankine riterion: σ = Eε, { σ σ σ } σ = max,, (5) The exponential elasto-damaging law (Fig. 2) is assumed: If σ f, t f t σ f t D= min Dr,1 exp 2H, σ f t (6) where, 0 is a softening parameter and is the tensile strength of the onrete. The funtion has a non-ompat support. The ontribution of points whose distane is larger than 20 from the disontinuity surfae is negleted. As soon as the damage reahes the ritial value in an element inside the regularization volume of height 40 entered on the rak, the regularization is ativated for the element. In partiular, two ases an our: The size of the mesh is smaller than the value of 40, whih leads to a thik proess zone The size of the mesh is larger than the value of 40, whih leads to a thin proess zone 747

3 Niola Orlando and Elena Benvenuti / Amerian Journal of Engineering and Applied Sienes 2016, 9 (3): Fig. 2. Exponential Rankine elasto-damaging law adopted When the regularization is ativated, the evolution of damage in the element is linked to the variable. The salar equivalent stress σ related to the evolution of is omputed as: ase of thin proess zone Eδ σ =, γ E δase of thik proess zone (7) σ = max,,, { σ1 σ 2 σ3 } The damage is governed by the same softening law used for the bulk: if σ f, t f t σ f t D = max Dr,1 exp 2 H, σ ft (8) The mixed-mode debonding is modelled through the adoption of a loal level-set defined at the Gauss point level. In the onstitutive model, n S represents the normal unit vetor of the disontinuity surfae. The damage is affeted by n S. While for mode I disontinuities n S has to be orthogonal to the surfae disontinuity, it has be found that for desribing mixed-mode debonding a different orientation of the vetor is required. Let us imagine that the regularized layer an be regarded as a series of inlined trusses as shown in Fig. 3. For the mixed loading mode of Fig. 3, the vetor n S has to be aligned along the diretion of the trusses in the deformed onfiguration. Noteworthy, the loal level-set is imposed a priori, but the final diretions of the jump vetors A e at the nodes are omputed by the nonlinear iterative-inremental proedure and will not generally oinide with that of the superimposed n S. Fig. 3. Example of loal level-set for mixed-mode debonding. The mehanial behaviour of the disontinuity surfae is shematized with the trusses In the numerial results shown in the forthoming setions, tetrahedral elements have been used. Pull-Out In this setion, the pull-out test on a steel rebar embedded in a onrete blok has been investigated by means of the proposed regularized XFEM approah. As referene results, the experimental findings of Xiao and Falkne (2007) have been onsidered, where two sets of pull-out tests were performed using plain and deformed bars for the speimens shown in Fig. 4. The mehanial properties of the onrete are: ompressive strength = 43.52, Young s modulus = 34.2 and Poisson ratio = 0.2. The plain and the deformed steel rebars have Young s modulus = 210, Poisson ratio = 0.3 and respetively a yield strength equals to y = 300 and = 420. The load was applied by a testing mahine to the end of the rebar, while the slip at the free end of the rebar was reorded. In the simulations, the material parameters of the damage law have been alibrated. In partiular, for the plain bar = 7.0 and = have been used, while, for the deformed bar, = 13.5 and = have been imposed. For both the appliations, the regularization parameter have been set to = mm, enrihing only one layer of finite elements having mesh size h = 1 mm (thin proess zone). The threshold value of damage have been set to = In this way, the damaging proess ours in the enrihed elements. The numerial and the experimental results are ompared in Fig. 5, where the grey zone with the dashed profiles indiates the experimental results. To redue the omputational burden, only a quarter of the speimen have been meshed (Fig. 6). 748

4 Niola Orlando and Elena Benvenuti / Amerian Journal of Engineering and Applied Sienes 2016, 9 (3): Fig. 6. Pull-out: Mesh of a quarter of pull-out speimen having dofs and minimum mesh size h=1 mm Fig. 4. Pull-out: Geometries of the Xiao and Falkne (2007) speimen (dimensions in mm) (a) Fig. 5. Pull-out: Computed (ontinuous lines) and experimental (grey areas) load-slip profiles for plain bars (blue lines) and deformed bars (red lines) (see Fig. 7 for the ontour plots of damage) The ontour plots of the damage evolution of the onrete speimen during the load proess for the deformed bar have been reported in Fig. 7. (b) Fig. 7. Pull-out: Evolution of Damage during the load proess (see Fig. 5) (a) Step A (b) Step B 749

5 Niola Orlando and Elena Benvenuti / Amerian Journal of Engineering and Applied Sienes 2016, 9 (3): It is lear that the damage starts to develop from the loaded end and propagates towards the free ends of the bar. The peak load is reahed when the whole bond surfae is damaged. The agreement between the omputed and the experimental load displaement results is very satisfying for the entire load proess. FRP Flexural Strengthening This setion is devoted to investigate the debonding of FRP flexural reinforements from onrete beams using the regularized XFEM approah. Several studies on FRP strengthening tehnique are available, suh as Turon et al. (2007), Carrara et al. (2011), Toti et al. (2013), Carrara and Ferretti (2013), Neto et al. (2014). It has been proved that the debonding ours within the onrete layer few millimeters beneath the adhesive layer. In partiular, the following debonding modes (see Fig. 8) in bending, Smith and Teng (2002), Aram et al. (2008), test have been identified: Plate end debonding Debonding by flexural raks Debonding by shear raks In the present study, two different experimental ampaigns have been modelled. Three Point Bending Test As a first ase-study, the experimental program arried out by Yin and Wu (2003) on Steel Fiber Reinfored Conrete beams (SFRC) has been modeled. In their study, the onrete beam strengthened with a FRP flexural reinforement shown in Fig. 9 was subjeted to a three point bending test. A onrete with ompressive strength = 26, Young s modulus = 25 and Poisson ratio = 0.2 was employed. No standard steel reinforement bars were employed. Short steel-fibers of length = 30 mm and diameter Ø = 0.5 mm were added to the onrete mixture. In the present simulations, three different mixtures of SFRC, with fiber volume fration = 0%, 0.25%, 1.0% respetively, have been onsidered. To relate the tensile strength of the onrete to, the Job and Ananth (2007) formula: f = f + f RI + RI (8) sp 0.63( m) 0.288( m) has been adopted. In Equation 8, RI = V l / ϕ is the fiber reinfored index. The value of the softening parameter has been kept onstant to = for all the appliations. The steel-fibers at as a diffuse reinforement system. Debonding and pulling out of fibers during the raking development dissipate energy, implying a substantial inrease in toughness and strength for growing. f f f In the proposed regularized XFEM approah, the dissipation of the energy at the debonding surfae material is influened by the regularization parameter. In partiular, the bigger the higher the peak load of the load-displaement profiles. Moreover, the presene of prevents the sudden loss of stiffness at the surfae of the FRP debonding. A posteriori, the following linear relationship between the volume fration and the regularization parameters. ( V f ) = , (9) has been identified. In these simulations, the damage threshold has been set to = This hoie allows the orret development of the raks into the bulk before the ativation of the ontinuous-disontinuous transition. The omparison between numerial and experimental results are shown in Fig. 11. Exploiting the double symmetry of the test, only a quarter of the speimen have been modelled (Fig. 10). As found in the experiments, in the numerial simulations, the FRP debonding (see Fig. 16) is triggered by the onentration of the interfaial shear stress near a flexural/shear rak after the ourrene of diffused flexural raks in the onrete. Then, the debonding propagates towards the plate ends. Furthermore, the omputed loads at the rak initiation and at the debonding initiation are very similar to the experimental values reorded by Yin and Wu (2003). The experimental failure modes are orretly predited with the thik zone proess. Moreover, the agreement between experimental and numerial loaddefletion results for all the values of fiber volume fration is highly satisfying. Four Point Bending Test As a seond appliation, the experimental setup of Barros et al. (2007) has been onsidered. For this purpose, the onrete beam of Fig. 12 has been onsidered. For the onrete, the ompressive strength = 44.2, Young s modulus =34.4 and Poisson's ratio =0.2 was employed. Following Barros et al. (2007), the steel bar reinforements with diameter Ø =6.5, =627 and a =210 have been modeled. In order to reord the enhanement on ultimate load with FRP reinforement, the beam was subjeted to a four point bending test. A ontrol test on a beam without FRP flexural reinforement was also arried out. The omparison between experimental and numerial data is shown in Fig. 13. The analyses have been omputed taking the tensile strength of the onrete equals to = 3.28 and the softening parameter equal to =

6 Niola Orlando and Elena Benvenuti / Amerian Journal of Engineering and Applied Sienes 2016, 9 (3): Fig. 8. FRP debonding main failure modes Fig. 12. Four Point Bending Test: Speimen geometries (dimensions in mm) Fig. 9. Three Point Bending Test: Geometry of the speimen (dimensions in ) Fig. 13. Four Point Bending Test: Computed and experimental load-defletion (see Fig. 16 for the deformed rak pattern) Fig. 10. Three Point Bending Test: Mesh of a quarter of the speimen having dofs and minimum mesh size h=5 (a) (b) Fig. 11. Three Point Bending Test: and experimental loaddefletion profiles (see Fig. 16 for the deformed rak pattern) Fig. 14. (a) Deformed (magnifiation fator 3) rak pattern at failure of the beam without FRP reinforement. (b) shows the partiular of the yielding of the bottom bar 751

7 Niola Orlando and Elena Benvenuti / Amerian Journal of Engineering and Applied Sienes 2016, 9 (3): Fig. 15. Pitures of the experimental failure mode obtained by Barros et al. (2006) (a) (b) () (d) Fig. 16. Comparison of FRP debonding failure modes between three and four point bending test (magnifiation fator 3). (a) Debonding initiation in three point test (b) Debonding initiation in four point test () Debonding failure by shear raks (d) plate end debonding failure Aording to the experimental evidenes, suh as Smith and Teng (2002), Barros et al. (2007), Aram et al. (2008), the surfae of the debonding has been imposed between onrete over and steel reinforement. The regularization parameters has been kept equals to =0.375 mm (thik zone proess). Only a quarter of the speimen has been meshed to redue the omputational burden of the analyses. A mesh with dofs and minimum mesh size h=5mm has been used. In Fig. 14 the deformed rak pattern at failure of the beam without the FRP reinforement has been reported. The failure of the beam was due to the yielding of the bottom steel reinforements at the flexural rak under the load appliation point. In Fig. 16 the omparison between the failure modes of the three and four point bending test has been reported. The FRP debonding mode is different from the three point bending test. In the four point test the debonding starts to propagates from the plate end of the sheet. Then the proess ontinues towards the mid-span of the beam, until the omplete detahment of the reinforement. As expeted, the load profile after the total debonding follows the strutural path of the beam without the FRP reinforement. In Fig. 15 a piture of the experimental FRP debonding is shown. It is remarkable that the experimental mode validates the performed analyses. The good agreement between numerial and experimental data is very satisfying. 752

8 Niola Orlando and Elena Benvenuti / Amerian Journal of Engineering and Applied Sienes 2016, 9 (3): Conlusion The regularized 3D XFEM approah has been suessfully applied to simulate the pull-out of steel rebars and the debonding of the FRP-plates in pull-out and bending tests. In partiular, the numerial simulations have shown that: The pull-out of the rebars is orretly aptured for both plain and deformed bars, adopting a thin debonding layer of 1 mm In the three point bending tests of SFRC beams, the regularization length parameter makes it possible to apture the influene of the fiber volume ontent on the strutural response In the simulated three and four point bending tests, the proedure of ontinuous-disontinuous transition makes the orret development of the debonding behavior possible The proedure is able to model 3D mixed debonding mode In general, the strutural responses obtained agree with the experimental data These results onfirm the reliability of the model, whih an be a useful tool together and in alternative to experimental tests. Aknowledgement This researh was supported by the University of Ferrara. Author s Contributions Niola Orlando: Performed numerial analysis, interpreted data, wrote manusript and ated as orresponding author. Elena Benvenuti: Supervised development of work, helped in data interpretation and manusript evaluation. Referenes Aram, M.R., C. Czaderski and M. Motavalli, Debonding failure modes of flexural FRPstrengthened RC beams. Composites part B: Engineering, 39: DOI: /j.ompositesb Barros, J.A., S.J. Dias and J.L. Lima Effiay of CFRP-based tehniques for the flexural and shear strengthening of onrete beams. Cement Conrete Composites, 29: DOI: /j.emonomp Belytshko, T., R. Graie and G. Ventura, A review of extended/generalized finite element methods for material modeling. Modelling Simulation Materials Si. Eng., 17: Benvenuti, E. and A. Tralli, Simulation of finitewidth proess zone in onrete-like materials by means of a regularized extended finite element model. Computational Mehanis, 50: DOI: /s y Benvenuti, E., XFEM with equivalent eigenstrain for matrix inlusion interfaes. Computational Mehanis, 53: DOI: /s Benvenuti, E., G. Ventura, N. Ponara and A. Tralli, Variationally onsistent extended FE model for 3D planar and urved imperfet interfaes. Computer Methods Applied Mehanis Eng., 267: DOI: /j.ma Benvenuti, E., N. Orlando, D. Ferretti and A. Tralli, A new 3D experimentally onsistent XFEM to simulate delamination in FRP-reinfored onrete. Composites Part B: Engineering, 91: DOI: /j.ompositesb Benvenuti, E., O. Vitarelli and A. Tralli Delamination of FRP-reinfored onrete by means of an extended finite element formulation. Composites Part B: Eng., 43: DOI: /j.ompositesb Carrara, P. and D. Ferretti, A finite-differene model with mixed interfae laws for shear tests of FRP plates bonded to onrete. Composites Part B: Engineering, 54: DOI: /j.ompositesb Carrara, P., D. Ferretti, F. Freddi and G. Rosati, Shear tests of arbon fiber plates bonded to onrete with ontrol of snap-bak. Engineering Frature Mehanis, 78: DOI: /j.engframeh Czaderski, C., K. Soudki and M. Motavalli, Front and side view image orrelation measurements on FRP to onrete pull-off bond tests. J. Composites Constrution, 14: DOI: /(ASCE)CC Dror, E.B. and O. Rabinovith, Size effet in the debonding failure of FRP strengthened beams. Eng. Frature Mehanis, 156: DOI: /j.engframeh Eshelby, J.D., The determination of the elasti field of an ellipsoidal inlusion and related problems. Proeedings Royal Soiety London A: Mathematial, Physial Eng. Si., 241: DOI: /rspa Huo, Z.Y., G.X. Qian and D.J. Zheng, Seepage Analysis of the Struture with Craks Based on XFEM. Open Civil Eng. J., 9: DOI: /

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