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Project # 12 – Multiscale modelling
Denis Davydov (PhD student)
Milan Jirásek (supervisor)
Bruno Capra (industrial partner)
Henrik Stang (academic partner)
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Multiscale modelling
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July 10th, 1983
Born in Perm city, Russia (USSR)
Sept. 1998 – June 2000 Lyceum of Perm State Technical University,
Russia.
Sept. 2000 – June 2004 Bachelor degree in Applied Mathematics and
Computer Science, Department of Mathematical Modeling of
Systems and Processes, Perm State Technical University,
Russia. Graduation thesis on “Model for superplasticity”.
Distinction: cum laudae.
Sept. 2004 – June 2006 Master degree in Applied Mathematics and
Computer Science, Department of Mathematical Modeling of
Systems and Processes, Perm State Technical University,
Russia. Graduation thesis on “Uniaxial strain stability study
problem of the nonlinear viscous material”.
Distinction: cum laudae.
Feb. 2007 – present
PhD research at Faculty of Civil
Engineering, Czech Technical University, Prague. MC-RTN
Project nr 12. “MULTISCALE MODELLING”
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Multiscale modelling
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Objectives:
•
Analysis of the role of loading rate in nanoindentation test,
understanding and evaluation of the visco-elastic properties from
nanoindentation.
•
Extension of models for micromechanical properties of cement paste
to time-dependent behavior. FEM approach as a homogenization
technique at the scale of cement paste.
Extension of multiscale model for concrete to time-dependent
behavior. This includes analytical homogenization at the scale of
mortar and concrete.
Preliminary study on possible extension to inelastic phenomena such
as cracking and plastic deformation.
•
•
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Multiscale modelling
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Date
Placement
Brief description
12.2007-04.2008
CTU
Micromechanical creep simulations; homogenization at the
level of cement paste. Methodology for determination of
viscoelastic properties
05.2008-07.2008
Oxand
Extension of multiscale model to viscoelastic behavior
08.2008-02.2009
CTU
Comparison between analytical and numerical
homogenization techniques. Verification of predicted
viscoelastic properties
03.2009-07.2009
DTU
Preliminary investigation of possible extension of
micromechanical models to fracture analysis
08.2009-01.2010
CTU
Preparation and defense of PhD dissertation
Deliverables:
•Procedures for evaluation of nanoindentation tests taking into account the influence of
loading rate.
•Numerical FEM simulation tool for viscoelastic properties of cement paste.
•Multiscale model for viscoelastic properties of mortar and concrete. Extension of the
homogenization analytical techniques for the visco-elastic deformation.
•Recommendations for further investigation of inelastic properties of cement paste.
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Multiscale modelling
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Accomplishment during the first reporting period is
Literature survey on:
• Chemistry, morphology, hydration kinetic
• Creep and shrinkage effects
• Models of the CSH structure and creep theories
• Creep modeling from engineering point of view
• Thermo-chemo-mechanical couplings
• Homogenization, Eshelbian approach, multiscale models
• Analytical solutions for indentation problem and dimensionless
analysis
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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What is the error of Oliver-Pharr procedure of extracting elastic properties
induced by experimental hypothesis of half-space homogeneous media?
Force
Difference between
E0 and E1
|E0-Eop|/E0 - error
E0
R
E1
P
h/R -
tang
|E0-E1|/E0 -
dimensionless depth
Difference between
E0 and E1
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Multiscale modelling
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Numerical modelling of the nanoindentation experiment
Too deep!!! (1.5micron)
homogenized respond of
surrounding rather then some
phase of interest
experiment
0.008
N/2 PI (appl. load in axisymmetric case)
0.007
experiment
0.006
0.005
experiment
0.003
0.002
0.001
0
-0.005
0
0.005
0.01
0.015
0.02
0.025
10^(-4)m
Norton’s visco-plastic model
Penetration depth nanometres
0.004
Kelvin-Maxwell-Voight
visco-elastic model
0.003
experiment
0.0025
E=229.026 nu=0.2 yld=1.7816
0.002 m=0.272606 K=19.3281 (Tc=6281.7174)
N / 2*PI
time sec
0.0015
0.001
0.0005
0
-0.002
0
0.002
0.004
0.006
0.008
0.01
0.012
10^(-4) m
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Multiscale modelling
“matrix” approach to
the indentation
measurements
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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1) Perform
nanoindentation
experiments into
specific places of
cement paste to better
capture intrinsic
properties
2) Use different loading
rates to distinguish
better between
viscous and plastic
deformation and have
several cycles
3) Try analytical and
numerical fitting
nanoindentation
curves with viscoelastic creep and
visco-plastic Norton
model. Compare the
results
4) Estimate a minimum
area of the phase
needed for reliable
results
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Multiscale modelling
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All products
(matrix)
HD-CSH only
(manual)
Indent. Module M=E/(1-nu^2)
C3S Alite
grain
force
All products
HD-CSH
mean
30.877
37.017
Std. dev.
5.252
2.074
Experimental programs to use:
Turned out to be Belite
time
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
Fit model on one experiment
And check on another!
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NEW IDEAS :
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Deviatoric creep (same for LD and HD)
LD and HD CSH
+
Self-Consistent
Upscaling with
Eshelby Solution
=
Like a
Granular
Media
Porosity (different for LD and HD)
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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NEW IDEAS :
Force
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Indentation experiment:
UPSCALING (Self-Consistent Scheme)
Deviatoric creep (same for LD and HD)
LD and HD CSH
+
Self-Consistent
Upscaling with
Eshelby Solution
=
Like a
Granular
Media
Porosity (different for LD and HD)
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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NEW IDEAS :
Force
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Indentation experiment:
Volumetric & deviatoric creep
UPSCALING (Self-Consistent Scheme)
Deviatoric creep (same for LD and HD)
LD and HD CSH
+
Self-Consistent
Upscaling with
Eshelby Solution
=
Like a
Granular
Media
Porosity (different for LD and HD)
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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NEW IDEAS :
Force
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Indentation experiment:
Volumetric & deviatoric creep
Use of elaborated analytical
Solution based on one,
published by Vandamme to
fit Deviatoric creep properties
From LD and HD CSH
Indentation experiments
UPSCALING (Self-Consistent Scheme)
Deviatoric creep (same for LD and HD)
LD and HD CSH
+
Self-Consistent
Upscaling with
Eshelby Solution
=
Like a
Granular
Media
Porosity (different for LD and HD)
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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NEW PROBLEMS : machine precision
Before:
Points to indent
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After:
Real indents (with shift!)
Unhydrated grain
Hope to have HD CSH here
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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NEW PROBLEMS : hard to identify/indent HD
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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NEW IDEAS (2):
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Use another indentation machine with higher precision,
with AFM, but with bad optics
Find “good” grains in advance using BSE/electron microscope.
BSE
BSE
AFM
indent
AFM gradient map
End ofNanocem-RTN
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10-2007 Madrid
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Effect of the not straight surface:
tan   2.79
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Force

  70 .3
Contact square has changed,
So the Oliver-Pharr procedure
Will give inappropriate results.
Is it possible at all to use that
Procedure in such a case???
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Recent work:
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Recent work (2):
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?
Is it good quality mix/clinker!?
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Recent work (3):
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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MATRIX
vs
MANUAL
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Is it possible at all to access
Properties of the phase of
Interest by matrix method?
Does it worth trying to chose right indents
from big matrix?
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
Success will probably depend
on ratio between characteristic
size of the phase and distance
between the indents.
BUT
in order to have indents close
to each other one has to do
small depths, which, from the
morphological point of view for
CSH, has to be greater then
100nm
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Multiscale modelling
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Perspectives:
1. Have more reliable procedure for nanoindentation of cement phase
(with manual method or with choosing indents from a “matrix” method)
2. Better understand viscous and plastic behaviour during loading phase
of indentation using different indentation rates
3. Have reliable results for cyclic loading by manual choice of indentation
points and maximum penetration depth
4. Come up with a reliable model to describe the indentation experiment
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Multiscale modelling
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Questions (Chemistry and Sample preparation/mixing):
1. What is the good C/S ratio for HD/LD CSH?
2. It is necessary to have a fresh, very well mixed and vibrated cement in quite a
big amount (for good mixing) to provide “homogenous” hydrated paste without
air bubbles, bunches of agglomerated aggregates. It is very important for good
polishing.
3. Presence of Phosphor??
4. Lots of Portlondite in paste??
5. The best cement for that purpose?? (white/gray/…)
Questions (Mechanical/Mathematical):
1. HD CSH zone and indents are often situated on the slope. Corrections to
Oliver-Pharr?
2. Statistical lack of experimental curves in manual method to be representative,
very time consuming.
3. Do properties of the CSH change in time?? What is right age to make
indents??? According to some experiments (??) after one year the creep is
recoverable absolutely.
4. Problems with manual indentation, machine precision or HD CSH finding
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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Thank you for you attention!
Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid
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