1 mcrtn meeting, lausanne, january 2008 project 11 – fracture mechanics: measurements and modeling...
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![Page 1: 1 MCRTN meeting, Lausanne, January 2008 Project 11 – Fracture mechanics: Measurements and modeling Jan Skoček, DTU Henrik Stang, DTU Gilles Chanvillard,](https://reader034.vdocuments.mx/reader034/viewer/2022051215/56649ebc5503460f94bc5cd2/html5/thumbnails/1.jpg)
1MCRTN 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
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2MCRTN 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
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3MCRTN 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
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4MCRTN meeting, Lausanne, January 2008
Theoretical background
f
tf
w w
F
w
F t
chF
t
w
G w dw
E G f
lEG
f
c
( )
( )
, ,
( )
0
2
Stress
x
ft
alp
wc
w w( )w
w w( )
Smooth crack closure
Softening curve
FG
The fictitious crack model
Hinge model / standard FEA – meso-scale analysis
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5MCRTN 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
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6MCRTN meeting, Lausanne, January 2008
Inverse analysis on meso-scale
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7MCRTN 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
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8MCRTN 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
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9MCRTN meeting, Lausanne, January 2008
Evolution of the fracture properties of cp
E [MPa] ft [MPa] Gf [J/m2]
6 hours 1098.4 0.22392 2.3424
9 hours 4582.9 0.42472 5.033
24 hours 6335.2 0.79259 6.1678
• Results from preliminary inverse analysis of the WST
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10MCRTN 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
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11MCRTN meeting, Lausanne, January 2008
Down sizing of the WST – using of Aramis
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12MCRTN 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
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13MCRTN 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
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14MCRTN 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
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15MCRTN 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
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16MCRTN 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
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17MCRTN 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.