Project # 12 – Multiscale modelling

1 Nanocem-RTN T0+20 Semi-Annual Meeting 10-2007 Madrid

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Project # 12 – Multiscale modelling

Denis Davydov (PhD student)

Milan Jirásek (supervisor)

Bruno Capra (industrial partner)

Henrik Stang (academic partner)


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Multiscale modelling

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”


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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.


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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.

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


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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


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P

Force

E0

E1

R

What is the error of Oliver-Pharr procedure of extracting elastic propertiesinduced by experimental hypothesis of half-space homogeneous media?

Diff

ere

nce

be

twe

en

E

0 a

nd

E1

|E0-Eop|/E0 - error

h/R - dimensionless depthtang

Difference between E0 and E1

|E0-E1|/E0 -


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Kelvin-Maxwell-Voight visco-elastic model

time secP

enet

rati

on

dep

th n

ano

met

res


Numerical modelling of the nanoindentation experiment

experiment

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

-0.005 0 0.005 0.01 0.015 0.02 0.025

10^(-4)m

N/2

PI (

appl

. loa

d in

axi

sym

met

ric c

ase)

experiment

experiment

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012

10^(-4) m

N / 2

*PI

experiment

E=229.026 nu=0.2 yld=1.7816m=0.272606 K=19.3281 (Tc=6281.7174)

Norton’s visco-plastic model

Too deep!!! (1.5micron)homogenized respond ofsurrounding rather then somephase of interest


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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 visco-elastic creep and visco-plastic Norton model. Compare the results

4) Estimate a minimum area of the phase needed for reliable results

“matrix” approach tothe indentation measurements


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Indent. Module M=E/(1-nu^2)

All products(matrix)

HD-CSH only(manual)

All products HD-CSH

mean 30.877 37.017

Std. dev. 5.252 2.074

time

force

Experimental programs to use:

C3S Alitegrain

Turned out to be Belite

Fit model on one experimentAnd check on another!


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NEW IDEAS :

Deviatoric creep (same for LD and HD)

Porosity (different for LD and HD)

+Self-ConsistentUpscaling with Eshelby Solution

=Like a GranularMediaLD and HD CSH


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NEW IDEAS :

Force

UPSCALING (Self-Consistent Scheme)




=Like a GranularMedia

Indentation experiment:

LD and HD CSH


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NEW IDEAS :

Force




Volumetric & deviatoric creep




LD and HD CSH


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NEW IDEAS :

Force




Volumetric & deviatoric creep



Use of elaborated analyticalSolution based on one, published by Vandamme tofit Deviatoric creep propertiesFrom LD and HD CSH Indentation experiments


LD and HD CSH


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NEW PROBLEMS : machine precision

Before: After:

Hope to have HD CSH hereUnhydrated grain

Points to indentReal indents (with shift!)


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NEW PROBLEMS : hard to identify/indent HD


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NEW IDEAS (2):

Use another indentation machine with higher precision, with AFM, but with bad optics Find “good” grains in advance using BSE/electron microscope.

AFM gradient map

BSE

BSE

AFM

grainEnd of HD zone

indent


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Effect of the not straight surface:

3.70

Force

79.2tan

Contact square has changed,So the Oliver-Pharr procedureWill give inappropriate results.Is it possible at all to use that Procedure in such a case???


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Recent work:


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Recent work (2):

?

Is it good quality mix/clinker!?


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Recent work (3):


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MATRIX vs MANUAL

Is it possible at all to access Properties of the phase of Interest by matrix method?

Success will probably depend on ratio between characteristicsize of the phase and distancebetween the indents.BUTin order to have indents close to each other one has to do small depths, which, from themorphological point of view for CSH, has to be greater then 100nm

Does it worth trying to chose right indents from big matrix?


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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


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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


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Thank you for you attention!

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Project # 12 – Multiscale modelling

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