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

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

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

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

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

6MCRTN meeting, Lausanne, January 2008

Inverse analysis on meso-scale

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

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

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

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

11MCRTN meeting, Lausanne, January 2008

Down sizing of the WST – using of Aramis

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

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

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

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

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

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.