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Prediction of Concrete Fracture Mechanics Behavior and Size Effect using Cohesive Zone Modeling

Prediction of Concrete Fracture Mechanics Behavior and Size Effect using Cohesive Zone Modeling. Kyoungsoo Park , Glaucio H. Paulino, Jeffery R. Roesler. Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign.

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Prediction of Concrete Fracture Mechanics Behavior and Size Effect using Cohesive Zone Modeling

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  1. Prediction of Concrete Fracture Mechanics Behavior and Size Effect using Cohesive Zone Modeling Kyoungsoo Park, Glaucio H. Paulino, Jeffery R. Roesler Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign Center of Excellence for Airport Technology, UIUC Federal Aviation Administration

  2. Concept of Cohesive Zone Model • Stage I • Elastic behavior • Stage II • Crack initiation • Tensile strength • Stage III • Non-linear cohesive law • Bi-linear softening curve for concrete • Stage IV • Traction-free macro-crack IV III II I Penalty stiffness

  3. Determination of the Cohesive Law • Cohesive strength : ft’ • Splitting test • Initial fracture energy : Gf • Size effect method (SEM) • Two-parameter fracture model (TPFM) • Total fracture energy: GF • Hillerborg’s work-of-fracture method • The stress ratio of the kink point : ψ • Peterson : 1/3 • Wittmann : 0.25 • Bazant : 0.15~0.33 Bi-linear softening curve Penalty stiffness Kink point

  4. FEA Implementation • Principle of Virtual Work • Virtual Internal Work = External Virtual Work • FEA Formulation

  5. ABAQUS User Element (UEL) Transformation Matrix ( ) Nodal coordinates Local coordinate system Numerical Integration Crack opening width ( ) UEL Properties ( ,thickness) Bi-linear softening curve ( ) Global coordinate system Element stiffness matrix Load vector Element stiffness matrix ( ) Load vector ( )

  6. Three-Point Bending Test • Obtain fracture parameters • Compare load-CMOD curves • Size effect [mm]

  7. Experimental Results • Fresh and Hardened Properties of the Concrete • Fracture Parameters

  8. Specimen Geometry and FE Mesh Cohesive elements

  9. Numerical Simulation of TPB

  10. Concrete Fracture Simulation (TPB)

  11. Numerical Validation – Small Beam D = 63 (mm) ft’ = 4.15 (MPa) Gf = 56.6 & 52.1 (N/m) GF = 119 (N/m) Ψ = 0.25

  12. Numerical Validation – Intermediate Beam D = 150 (mm) ft’ = 4.15 (MPa) Gf = 56.6 & 52.1 (N/m) GF = 164 (N/m) Ψ = 0.25

  13. Numerical Validation – Large Beam D = 250 (mm) ft’ = 4.15 (MPa) Gf = 56.6 & 52.1 (N/m) GF = 167 (N/m) Ψ = 0.25

  14. Initial fracture energy • Tensile strength Load • Stress ratio of the kink point • Total fracture energy CMOD Model Sensitivity Tensile strength Total fracture energy Stress ratio of the kink point

  15. Experimental data Numerical Result TPFM SEM * Size Effect D = 63mm D = 250mm D = 150mm

  16. Summary • Predict Load-CMOD Curve • Bi-linear softening cohesive zone model • Without calibration of the fracture parameters. • Investigate Size Effect • Cohesive Zone Model with bi-linear softening • Experiment results from Three-point bending tests • Size effect expression: • Good agreement between the results from the three methods.

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