Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas

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1 San Miguel de Tucuman, Argentina September 14 th, 2011 Seminary on Análisis Computacional del Comportamiento de Falla de Hormigón Reforzado con Fibras Metálicas Antonio Caggiano 1, Guillermo Etse 2, Enzo Matinelli 3 1 Ph.D.. Student, University of Salerno and National University of Tucuman, Bi-national co-supervised Thesis ancaggiano@unisa.it 2 Professor of Structural Mechanics, Universities of Buenos Aires and Tucuman, ARGENTINA, getse@herrera.unt.edu.ar 3 Assistant Professor, Department of Civil Engineering, University of Salerno, ITALY, e.martinelli@unisa.it

2 Overview 1. Introduction; 2. ; Structural FEM meso-scale ; 5.

3 Mesoscopic level composed by mortar, aggregates and mortar-aggregate interfaces Real material and BVP Mortar elements with fibers Fibers located along Non-linear Interface elements Mixture Theory to interfaces Elastic continuum elements

4 Cohesive-frictional interface model for FRCC

5 General assumptions Considered schemes for mixed mode failure analysis. Test setup (Hassanzadeh, 1990). Continuum linear elastic elements: 4 nodes. Zero-tickness Nonlinear Interface element.

6 Joint Model with Fiber Effects Considering a displacement vector at the interface (u): u // u = u. n = u. n axial displacement of the fiber (in direction n) transversal displacement of the fiber Consequently, the axial and angular fiber strains are given, respectively: ε = u l γ = u / l f // // / f The incremental stress-displacement relation can be expressed in compact form as: t & = E ep. u& Figure 1. Schematic configuration of joint crossed by one fiber with a general inclined angle. the stress tensor rate t& = [ & σ, & τ ] t constitutive tangent second-order tensor ep i ep f ep t f ep = ρ + g( ρ ) E f / l f + g( k ) G f / l f ( ) E C n n n n ρ # is a volumetric fraction of each component t

7 Zero Thickness Interface Model (Carol et al., 1997) As in Plasticity Theory, the relative displacement rate is decomposed into an elastic part and a plastic (cracking) part: a cracking surface, within the stress space, defining the stress level at which the cracks (in the joint element) begin; a flow rule giving an incremental crack displacement

8 a softening rules depending on the work spent during the fracture process c 0,, tgφ 0, c, χ, tg φ, α c = 2.0 α c = 1.5 α c = 0 χ 0 α c = -1.5 α c =

9 Fiber bond slip behavior Conventional Strength Mortar (CSM) - Equilibrium: - Constitutive law High Strength Mortar (HSM) - Bond-slip law Model results (continuous lines) vs. experimental data by Shannag et al of the pullout behavior of steel fibers from CSM and HSM. E f

10 Dowel action Basic equation of the model: λ [1/length] - when l f > 2 π /λ seminfinite BEF - k coefficient ranges from 75 to 450 N/mm 3 for RC (Dei Poli et al., 1992). Equivalent shear elastic modulus Dowel force at ultimate limit state, Dulacska,1972.

11 Nonlinear numerical results at material level

12 Evaluation of the model for plain concrete Test setup (Hassanzadeh, 1990). Experimental test by Hassanzadeh, 1990 Parameters of Interface kn = 500MPa / mm k t = 200MPa / mm tgφ = 0.6 χ = 2.8MPa c = 10 M Pa G I f = 0.08N / mm G IIa f I f = 10G

13 General assumptions Interface-based Discrete Crack Approach Prototype F u F Test setup (Li et al. 1998).

14 General assumptions Considered schemes for uniaxial case: Test setup (Li et al. 1998). Continuum linear elastic elements: 4 nodes. Zero-tickness Nonlinear Interface element.

15 Type of fibers Tensile tests vs. numerical predictions (a) l f [mm] d f [mm] σ y,d [GPa] E s [GPa] Dramix Harex x Calibration of the model ( q th exp,i exp,i ) q = argmin σ ε ; σ q i = 1 MODEL PARAMETERS E = 37GPa ν = 0.18 n 2 Continuum elements (b) k = k = 1000 MPa / mm n t tg φ = 0.6 χ = 4 MPa G = 0.12 N / mm I f IIa f c = G = 10 G I f 7 Interface elements MPa = 0.15 α χ σ dil = 10 MPa σ σ = y, d y, s d Es 3 = 450 / H dow = 0MPa k N mm 1-D bond slip model E = H f = 0MPa Dowel model Experimental data (Li et al., 1998) and numerical prediction for uniaxial tensile tests with (a) Dramix and (b) Harex Fibers.

16 Tensile tests vs. numerical predictions. Experimental data (Li and Li, 2001) and numerical prediction for uniaxial tensile tests with (a) Dramix Fibers.

17 Tensile tests vs. numerical predictions. Experimental data (Li and Li, 2001) and numerical prediction for uniaxial tensile tests with (a) Dramix Fibers.

18 Tensile tests vs. numerical predictions. Experimental data (Li and Li, 2001) and numerical prediction for uniaxial tensile tests with (a) Dramix Fibers.

19 Structural FEM meso-scale scale

20 Future Developments: Non-linear Finite Element Analysis Notched beam in three-point bending Displacement-based control test Plane stress state 2000 mm Non-linear elastoplastic FRC joints 200 mm 100 mm Linear elastic continuum elements without FRC interfaces 20 mm

21 MODEL PARAMETERS E = 31.9GPa ν = 0.20 k = k = 1000 MPa / mm n tg φ = 0.6 c t = 10 M Pa G 0.06 N / mm I f Continuum elements Interface elements χ = 3.6 MPa σ = 30 MPa dil = IIa G f = 10 G I f

22 FE Analysis - 3 Points Beam (Carpinteri & Brighenti data 2010) Displacement-based control test 3-points beam with 1 notch (having width of 2 mm) Plane stress state FIRST SCHEME 360 mm 400 mm Non-linear elastoplastic FRM joints Non-linear elastoplastic coarse aggregatesmortar joints 100 mm 30 mm Linear elastic FRC elements Linear elastic coarse aggregates elements Linear elastic FRM elements

23 FE Analysis - 3 Points Beam (Carpinteri & Brighenti Displacement-based control test Brighenti data 2010) 3-points beam with 1 notch (having width of 2 mm) 140 mm Plane stress state SECOND SCHEME 20 mm 210 mm Non-linear elastoplastic FRM joints Non-linear elastoplastic coarse aggregatesmortar joints 100 mm 30 mm Linear elastic FRC elements Linear elastic coarse aggregates elements Linear elastic FRM elements

24 FE Analysis - 3 Points Beam (Carpinteri & Brighenti data 2010) FIRST SCHEME SECOND SCHEME

25 FE Analysis - 3 Points Beam (Carpinteri & Brighenti data 2010) Carpinteri & Brighenti FIRST SCHEME Brighenti, 2010 SECOND SCHEME vs. Meso-mechanical Analyses Applied Load [N] PB-0.0% with centroidal notch 3PB-0.5% with centroidal notch 3PB-0.0% with eccentrical notch 3PB-0.5% with eccentrical notch Deflection [mm]

26 Comments and future developments

27 An extended experimental campaign is ongoing at DiCiv (UniSA) about the Post-cracking fracture behavior of pre-notched beams reinforced with mixed short/long steel fibers Super plasticizers Fibers Cement Steel Fiber Reinforced Concrete Fine Aggregates Water Coarse Aggregates Test's labels 10 SFRC mixture types + 1 plain concrete as reference Mixture Type L = 100 % S = 0 % L = 75 % S = 25 % L = 50 % S = 50 % L = 25 % S = 75 % L = 0 % S = 100 % Fiber Contents 1.0 L L LS S S ρf (%] 0.5 L L LS S S

28 then the specimens have been cured under water during 28 days

29 2nd Workshop - The new boundaries of structural concrete Università Politecnica delle Marche September, 15-16, compressive strength@mpad Rcm (MPa) compressive strength@mpad Compressive strength f cube-28 (EN 206-1) L % white % compressive strength@mpad LS 50 compressivestrength@mpad S % 10 white 0.5 % S LS LS50-05 L75-05 L S100-1 S75-1 LS50-1 S 100L75-1 L white SFRC % white 0.5 % Ç 1.0 % white 0.5 % e e e compressivestrength@mpad e 1.0 % white 0.5 % e

30 UNI Part II: Test method for determining the First Crack Strength and The Ductility Indexes

31 applied Experimental graphics: P CTODm 28 days L % redo the paste L100 1% 0.5% D flexurale Strength [kn] applied L75 applied LS50 applied % % 0.5% applied S % 0.5% D S100 REF S S75-05 LS50-05 L75-05 L S100-1 S75-1 LS50-1 L75-1 L100-1 [kn] D 0.5% 1.0 % 0.5% D D

32 Conclusions A numerical model based on the described interface elements has been presented in the present work. The model is particularly suited to model the stress-strain behavior of FRC in tension, capturing the fiber effect in bridging the crack opening, by means of two main mechanisms, such as bonding strength and dowel action in axial and transverse direction, respectively. Discontinuous interface approach is particularly suitable for mesoscale failure. The numerical simulations, presented in this work, may conclude that the constitutive proposals mainly capture the fundamental behaviors of fibrous concretes. Further are required.

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