1. 1 MCRTN meeting, Lausanne, January 2008 Project 11 – Fracture mechanics: Measurements and modeling Jan Skoček, DTU Henrik Stang, DTU Gilles Chanvillard, Lafarge Amor Guidoum, EPFL Petr Kabele, CTU

2. 2 MCRTN meeting, Lausanne, January 2008 Introduction Czech 2001 – 2006 Faculty of Civil Engineering, CTU in Prague Thesis: On the Application of the Mori-Tanaka Method for Woven Composites 2006 – 2009 PhD at DTU : Fracture Mechanics: Measurements and modeling

3. 3 MCRTN meeting, Lausanne, January 2008 Objectives of the project -> Part of 15 NanoCem projects: “Fundamental understanding of cementitious materials for improved chemical physical and aesthetic performance” -> To advance the understanding of experimental and theoretical fracture mechanics of fine mortars and cement pastes - qualitative - quantitative -> To establish a test set-up and test evaluation to obtain fracture properties of investigated material -> To investigate an influence of mixture properties and curing conditions to final fracture properties -> To find a relation between fracture properties and microstructure

4. 4 MCRTN meeting, Lausanne, January 2008 Theoretical background Stress x ftft a lplp wcwc w Smooth crack closure Softening curve The fictitious crack model Hinge model / standard FEA – meso-scale analysis

5. 5 MCRTN meeting, Lausanne, January 2008 Theoretical background Micro-scale –3D model is needed to truthful the micromechanics –complicated geometry – micro-structure, phase distribution, porosity –large ration between a size of a specimen (~cm) and micro- structural details needed to be modelled (~10 μm) –continuum mechanics based analysis goes into troubles with memory (too many DOFs) and with too many material parameters => Lattice models

6. 6 MCRTN meeting, Lausanne, January 2008 Inverse analysis on meso-scale

7. 7 MCRTN meeting, Lausanne, January 2008 Inverse analysis on meso-scale Tri- and quad-linear softening curves provide more accurate simulations Determination of properties of penta-linear curves failed due to problems with local minima Verified by FEM simulation

8. 8 MCRTN meeting, Lausanne, January 2008 Evolution of the fracture properties of cp Aalborg white cement paste, w/c = 0.4, no aggregates or plasticizer added Sealed immediately after casting, tested between 6 and 24 hours

9. 9 MCRTN meeting, Lausanne, January 2008 Evolution of the fracture properties of cp E [MPa]ft [MPa]Gf [J/m2] 6 hours1098.40.223922.3424 9 hours4582.90.424725.033 24 hours6335.20.792596.1678 Results from preliminary inverse analysis of the WST

10. 10 MCRTN meeting, Lausanne, January 2008 Down sizing of the WST – using of Aramis optical system Aramis based on correlation of stereo images provides strain tensor and displacement field -> CMOD and crack profile can be used as input for IA

11. 11 MCRTN meeting, Lausanne, January 2008 Down sizing of the WST – using of Aramis

12. 12 MCRTN meeting, Lausanne, January 2008 Down sizing of the WST – using of Aramis Comparison of measured and modeled CODs and Crack Tip Positions FEM simulations seems to provide better data for close to peak loads Hinge model seems to perform better in ultimate stages of loading

13. 13 MCRTN meeting, Lausanne, January 2008 Down sizing of the WST - Lattice model SEM μic 2D 3D Simple elements (12 DOFs per el. in 3D) Simple material behavior – brittle beams can provide overall softening

14. 14 MCRTN meeting, Lausanne, January 2008 Down sizing of the WST - Lattice model Double-notched tensile specimen 150x150x75 mm made out of concrete Aggregates 4-8 mm, 40 % of area filled 2D analysis FEM 110 000 nodes => 220 000 DOFs Lattice 949 nodes => 2847 DOFs

15. 15 MCRTN meeting, Lausanne, January 2008 Down sizing of the WST - Lattice model Double-notched tensile specimen 150x150x75 mm made out of concrete Aggregates 4-8 mm, 40 % of area filled 2D analysis

16. 16 MCRTN meeting, Lausanne, January 2008 Conclusions and future plans Increase of lines in the softening curves leads to higher accuracy of the simulation Inverse analysis based on the hinge model is stable up to penta-linear softening curve when troubles with local minima appears Optical deformation analysis system is an alternative and reliable way of data acquisition Various accuracy of FEM and Hinge analysis in various stages of loading Meso-scale WST (100x100x100 mm) is suitable for testing of early- age cement paste Lattice model should be able to truthful the micromechanics of the cement paste

17. 17 MCRTN meeting, Lausanne, January 2008 Conclusions and future plans cont. Comparison of lattice model and continuum model in 2D and 3D Modeling of the fracture process in hardened cement paste using 3D lattice model Lattice model and real microstructure generated my a hydration model WST on microscale in ESEM chamber Identification of fracture properties from the WST using the lattice model Stay in Lafarge – investigation of influences on the fracture properties – mixture properties, curing condition, microstructure, loading rate etc.