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

Transcription

1 Predicion of Concree Fracure Mechanics Behavior and Size Effec using Cohesive Zone Modeling Kyoungsoo Park, Glaucio H. Paulino, Jeffery R. Roesler Deparmen of Civil and Environmenal Engineering Universiy of Illinois a Urbana-Champaign Cener of Excellence for Airpor Technology, UIUC Federal Aviaion Adminisraion

2 Concree Srucures Assembly Hall, IL. Concree Pavemen Scaling Size Effec Fracure Mechanics Arch Bridge, TN. 2

3 Fracure Mechanics Size Effec Size Effec Mehod (SEM) logσ N Energy concep Srengh Theory Equivalen elasic crack model Two size-independen fracure parameers: G f and c f Quasi-brile σ N = Bf 1+ DD 0 LEFM 1 2 log D Bazan ZP, Kazemi MT. 1990, Deerminaion of fracure energy, process zone lengh and brileness number from size effec, wih applicaion o rock and concree, Inernaional Journal of Fracure, 44, Two-Parameer Fracure Model (TPFM) Equivalen elasic crack model Two size-independen fracure parameers : K I and CTOD c Jenq, Y. and Shah, S.P. 1985, Two parameer fracure model for concree, Journal of Engineering Mechanics, 111,

4 Mechanisms of Concree Fracure Tracion-free macrocrack Bridging zone Microcrack zone Why Cohesive Zone Model? σ f w f w 4

5 Ouline Moivaion Cohesive Zone Model for Concree Finie Elemen Analysis Implemenaion Numerical Predicion of Three-poin Bending Tess Size Effec Summary 5

6 Concep of Cohesive Zone Model Sage I Elasic behavior σ f Sage II IV III II I Crack iniiaion Tensile srengh w f w Sage III Non-linear cohesive law Bi-linear sofening curve for concree σ f Penaly siffness Sage IV ψ f Tracion-free macro-crack G f G F G f w 6 w 1 w f

7 Deerminaion of he Cohesive Law Bi-linear sofening curve σ f Penaly siffness Cohesive srengh : f Spliing es Iniial fracure energy : G f Size effec mehod (SEM) Two-parameer fracure model (TPFM) ψ f G f G w 1 F Kink poin G f w f w Toal fracure energy: G F Hillerborg s work-of-fracure mehod The sress raio of he kink poin : ψ w 1 = 2G f f 2 w = G (1 ψ ) G ψ f f F f 7 Peerson : 1/3 Wimann : 0.25 Bazan : 0.15~0.33

8 FEA Implemenaion Principle of Virual Work Virual Inernal Work = Exernal Virual Work δεσdω + δwtdγ = δufdγ T T T Ω Γ c Γ c v 4 u 4 w n v 3 w v1 v2 u 1 u 3 u 2 FEA Formulaion T BEBdΩ + N NdΓ u = PdΓ c w T T Ω Γ c Γ T T w w T n = w Tn Tn w w n T 8 f w cr ( ) f w w 1 cr n = wn ψ f ( wf wk) 0 ( w < w ) 0 n cr ( w w < w ) cr n k ( wk wn < wf ) ( wn wf )

9 ABAQUS User Elemen (UEL) Nodal coordinaes Transformaion Marix ( ) R Local coordinae sysem Numerical Inegraion Crack opening widh ( w, w ) n UEL Properies ( G, G, f, ψ, w,hickness) F f cr, T T w Bi-linear sofening curve ( ) Global coordinae sysem Elemen siffness marix Load vecor R Elemen siffness marix ( N N) T Load vecor ( NT) T w T 9

10 Numerical Verificaion Double Canilever Beam (DCB) Tes P Δ 2 2h a0 a L 3EI P = a 3 0 Δ 2 P GEBh Δ = Y Z X 10

11 Three-Poin Bending Tes Obain fracure parameers Compare load-cmod curves Size effec P D S L a 0 [mm] 11

12 Experimenal Resuls Fresh and Hardened Properies of he Concree Fresh Concree Densiy Slump Air conen 2403 kg/m mm 2.8 % Hardened Concree Compressive srengh Spli srengh Modulus of elasiciy 58.3 MPa 4.15 MPa 32.0 GPa Fracure Parameers B250-80a B250-80b B250-80c B150-80a B150-80b B150-80c B63-80a B63-80b B63-80c CB63-80a CB63-80b CB63-80c Hillerborg TPFM SEM G F (N/m) K I (MPa m 1/2 ) CTOD c (mm) G f (N/m) c f (mm) N/A N/A 106 N/A N/A N/A N/A N/A

13 Specimen Geomery and FE Mesh Y Z X Cohesive elemens Y Z X 13

14 Numerical Validaion Small Beam D = 63 (mm) f = 4.15 (MPa) G f = 56.6 & 52.1 (N/m) G F = 119 (N/m) Ψ = 0.25 P D a 0 CMOD 14

15 Numerical Validaion Inermediae Beam D = 150 (mm) f = 4.15 (MPa) G f = 56.6 & 52.1 (N/m) G F = 164 (N/m) Ψ = 0.25 P D a 0 CMOD 15

16 Numerical Validaion Large Beam D = 250 (mm) f = 4.15 (MPa) G f = 56.6 & 52.1 (N/m) G F = 167 (N/m) Ψ = 0.25 P D a 0 CMOD 16

17 Model Sensiiviy Load Iniial fracure energy Tensile srengh Sress raio of he kink poin Tensile srengh Toal fracure energy CMOD Sress raio of he kink poin Toal fracure energy 17

18 Size Effec D = 63mm D = 150mm D = 250mm log ( σ Nu ) ( Pa) 1.00E+06 * Experimenal daa Numerical Resul TPFM SEM σ N = Bf 1+ DD E ( log D ) ( mm)

19 Summary Predic Load-CMOD Curve Bi-linear sofening cohesive zone model Wihou calibraion of he fracure parameers. Invesigae Size Effec Cohesive Zone Model wih bi-linear sofening Experimen resuls from Three-poin bending ess Size effec expression: σ N = Bf 1+ DD Good agreemen beween he resuls from he hree mehods. 0 19