The Virtual Cement and Concrete Testing The Virtual Cement and Concrete Testing Laboratory: A modeling example from the Laboratory: A modeling example from the

world of portland cement concreteworld of portland cement concrete

Edward J. GarbocziMaterials and Construction Research Division

Building and Fire Research LaboratoryNational Institute of Standards and Technology

OutlineOutline• Materials background• The VCCTL• Micrometer scale binder – cement paste

– Microstructure formation– Mechanical properties

• Millimeter scale - aggregates– Aggregate shape and structure– Rheology of fresh concrete

• Summary and Prospectus

Concrete

• PCC = your ordinary, everyday, random, complex, multi-scale, time-dependent composite material

• Asphaltic concrete (AC) = similar• Most of PCC research dominated by

empiricism, due to complicated nature of material

• Much of AC research = similar ?

Empiricism to science• Metals, ceramics, and polymers were once thought

to be “messy, craft” materials• Key to transforming the study of metals, ceramics,

and polymers was the availability of enough condensed matter theory (physics and chemistry) being applied to complex microstructures

• Key for random materials like PCC and AC?

Computational materials science based on sound materials science experiments

m

mm μm

nm

The Length Scales of ConcreteThe Length Scales of Concrete

Main NIST materials research

Note: Durability predictionNote: Durability predictionrequires information at all requires information at all length scaleslength scales

Earlystageresearch

Structuralengineering

Å

Focus of NIST research in concreteFocus of NIST research in concrete

• The Virtual Cement and Concrete Testing Laboratory (VCCTL)

• Vision: Just as significant modern structures are not designed without finite element programs, so we desire that significant material design of concrete will not be done without computer-aided assistance like VCCTL

• Durability prediction = our end goal

VCCTL• Internet-based and menu driven• Predicts properties based on detailed microstructure

simulations of well-characterized starting materials• Goal is to reduce number of physical concrete tests,

thus expediting R&D process• Based on NIST modeling effort over last 16 years

– Brings together basic research on processing (cement chemistry), microstructure (multi-scale), and properties (physical and chemical)

• Industrial consortium members: W.R. Grace, SIKA, ATILH, MBT, VDZ, PCA, NSSGA/ICAR, NRMCA

Simulation of a physical Simulation of a physical testing laboratorytesting laboratory

• Cement and aggregate databases– instead of bins and hoppers

• Material combination and concrete curing models– instead of mixers and molds

• Software interface – instead of a cart to take materials and samples

around the laboratory• Accurate models for performance prediction

– instead of instrumented testing machines

Micrometer scale binder Micrometer scale binder -- cement pastecement paste

(1) Microstructure formation

(2) Mechanicalproperties

Tricalcium Silicate (idealized)

DissolutionCa3SiO5 + 3 H2O → 3 Ca2+ + H2SiO4

2- + 4 OH-

Growth of C-S-Hx Ca2+ + H2SiO4

2- + 2(x-1) OH- → CaOx–SiO2–H2O

Growth of PortlanditeCa2+ + 2 OH- → Ca(OH)2

Value of x depends on local pore solution chemistry, reality is much more complicated

Modeling Challenges: Cement ChemistryModeling Challenges: Cement ChemistryModeling Challenges: Cement Chemistry

Modeling Challenges: MicrostructureModeling Challenges: MicrostructureModeling Challenges: Microstructure

MicroMicro--scalescale

75 µm75 µm

Kinetic ImplicationsKinetic Implications•• Nucleation sitesNucleation sites•• CC--SS--H growth = diffusion barrierH growth = diffusion barrier•• Water availabilityWater availability

Ca

Si

K

AlK

… X-ray elementmaps …

… segment image into phases …

SEM/BSE Image…

Measure autocorrelation fns on majority phases

… Particle Size Distribution …

Cement CharacterizationCement Characterization

A model that:• captures chemistry, physics, and microstructure of

hydration• is based on real material thermodynamic and

kinetic parameters• has intrinsic time scaling and correct length scaling• simulates diffusion, dissolution, nucleation, and

growth using only real material parameters• converges to known rate laws for diffusion and

chemical reactions• changes material sets as easily as changing lines in a

database

What do we really want?What do we really want?

CEMHYD3D (NIST) CEMHYD3D (NIST) (works well in many ways)(works well in many ways)

• Digital image basis• Accurate microstructure representationBut:• Rule-based to mimic reaction and diffusion• Little or no kinetic information• Difficult to change materials

Existing Cement Hydration ModelExisting Cement Hydration ModelExisting Cement Hydration Model

• Discretize on regular grid• Stochastic methods for diffusion and reaction• Algorithms are mechanistically based, and

converge to standard PDE rate equations• Applies to general aqueous mineral systems• Micrometer level

• Note: Microstructure and chemistry are being simultaneously simulated

New Model: HydratiCANew Model: HydratiCANew Model: HydratiCA

Mesh Class

Node Classneighbors, volume, materials,methods for transport and rx

Base Material Class

(Liquid, Solid, Gel, Crystal, Solute)

Ion Database Class

ID, mol wt, radius, intrinsic diffusivity, charge(immutable)

Dimensions, resolution, clock, phase stats, thermal condition, moisture conditions, databases

ID, composition, ρ, Ω, Cp, porosity, mobility, virtual methods for material-specific behavior

Derived Material Classes

Methods for material-specific behaviorencoded here

Material Database Class

Reaction Database ClassID, reactants, products, molar stoichiometric coefficients, reaction enthalpy, activation enthalpy, equilibrium constant baseline rate constant

C++, object-oriented modular construction

HydratiCA: Chemical ReactionsHydratiCA: Chemical ReactionsHydratiCA: Chemical Reactions

• Reaction events are localized within a node• List of available reactants is generated and

compared against reaction database• Unit reaction is executed (n cells of A and

m cells of B are removed, p cells of C are added) on a probabilistic basis

• Probability proportional to rate constant k

a A + b B a A + b B →→ c Cc Ck

HydratiCA: Modeling EquilibriumHydratiCA: Modeling EquilibriumHydratiCA: Modeling Equilibrium

a A + b B a A + b B →→ c Cc Ckf

c C c C →→ a A + b Ba A + b Bkr

d{C}dt

= k f {A}a{B}b d{C}dt

= −kr{C}c

At equilibrium:At equilibrium:At equilibrium: kr{C}c = k f {A}a{B}b

k f

kr

={C}c

{A}a{B}b = Keq

HydratiCA: Chemical EquilibriumHydratiCA: Chemical EquilibriumHydratiCA: Chemical Equilibrium

Equilibrium

Precipitation

Dissolution

Ca(OH)2 Ca2+ + 2OH-kf

kr

kf = 2.17x10-7 moles/m2/skr = 3.29x10-3 moles/m2/s

Nucleation from a single seed

Surface nucleation

Elastic properties of allmajor phases known.Typical size is 1003 = 106 elements

Each voxel is a tri-linear finite element

4

Mechanical properties of cement paste binderMechanical properties of cement paste binder

w/c=0.25

28 day microstructures

w/c=0.30 w/c=0.35 w/c=0.40

w/c=0.45 w/c=0.50 w/c=0.55 w/c=0.60

0

5

10

15

20

25

30

35

0.2 0.3 0.4 0.5 0.6 0.7

14 d Holcim (modified)

E(exp)E(mod)G(exp)G(mod)

E,G

(GP

a)

w/c

results

Note: Large FEM simulationsNote: Large FEM simulations

• Using MPI, large FEM simulations are possible on Linux cluster

• Have done linear elastic simulations with over 200,000,000 tri-linear cubic elements

(1)Aggregate shapeand structure

(2) Rheology of fresh concrete

Millimeter scale Millimeter scale -- aggregatesaggregates

Tomograph courtesy of FHWA

Spherical harmonic analysis• Measure r(θ, φ) from center of mass to surface

• Compute anm by inverting r(θ, φ) = Σn,m anm Ynm(θ, φ)

– Ynm = spherical harmonic function

• Random shape will be analytically known – just like simple shapes like spheres and ellipsoids

• All shape and size information for particle is in the (N+1)2

coefficients

How to get 3-D surface points: X-ray computed tomography

X-raysX-rays

Emitter Detector

Picked up from a stream bed on a family hike

n=0

n=30

AMRL fine aggregate for HMA

ASTM C-33 sand

L = 3.85

W = 3.17

T = 1.0

ASTM D 4791L = lengthW = widthT = thickness

W-5 0.0W-4 0.0 0.0W-3 0.3 0.2 0.0W-2 4.5 1.4 0.6 0.0W-1 63.4 27.1 2.2 0.0 0.0

L-1 L-2 L-3 L-4 L-5

ASTM C-33 sand

W-5 0.0W-4 0.0 0.0W-3 0.5 1.3 0.0W-2 8.5 8.9 3.8 0.0W-1 32.4 37.4 6.7 0.4 0.2

L-1 L-2 L-3 L-4 L-5

Sand for hot-mix asphalt

Cement paste

Concrete – truck and rheometer

Mortar

MultiMulti--scale approach to scale approach to experimental rheologyexperimental rheology

Brownian Dynamics + Momentum Conserving CollisionHydrodynamic Behavior

Concrete Rheology Model: Dissipative Particle Dynamics

Model developed by N. Martys (NIST) based on an algorithm by Hoogerbrugge and Koelman (1992)

33--D dissipative particle dynamics simulation D dissipative particle dynamics simulation of realof real--shape aggregates in simple shear flowshape aggregates in simple shear flow

Requires large parallel computers

Mix masters try to crack code for constructionResearchers are borrowing a million hours of processor time from NASA to analyze how concrete is combined—and to find the right recipe for building success

March 24, 2006

SummarySummary

• Transformation of “messy empiricism” to scientific material requires both kinds of basic materials science

– Strong support from industry via VCCTL consortium

– Cement and concrete industry sees this need• Computational materials science is

transforming concrete in the same way as the fields of ceramics, metals, and polymers have already been changed

ProspectusProspectus

• Is a Virtual Asphaltic Concrete Testing Laboratory (VACTL) on the path of progress?

– Characterize asphalt, aggregates (dust to coarse)– Model for chemistry of asphalt matrix, model for

packing of aggregates– Models for response of AC to mechanical and

chemical and thermal loads– Similar in some ways to the project that FHWA

began in the 1990’s, but more chemistry and real particle shapes now possible

Acknowledgements

• NIST – Dale Bentz, Jeff Bullard, Clarissa Ferraris, Nick Martys, Ken Snyder, Paul Stutzman

• Univ. Texas – Sinan Erdogan, David Fowler

• VCCTL – various industrial members• FHWA – Dick Livingston, Habeeb Saleh

Electronic monograph on the computational materials science of concrete

http://ciks.cbt.nist.gov/monograph/

Computation of properties and performance

MODEL

nmnm μμmm mmmmREAL

17th ACBM/NIST Computer Modeling Workshop June 26-29, 2006

HydratiCA: Modeling Aqueous DiffusionHydratiCA: Modeling Aqueous DiffusionHydratiCA: Modeling Aqueous Diffusion

• Based on a random walker algorithm• Each computational node contains a

number of “cells” of solute and water• In any time step, each cell can execute a

single step in a random direction• Probability of stepping is proportional to

the solute mobility and the time increment

p = D Δt/λ2

HydratiCA: Ionic DiffusionHydratiCA: Ionic DiffusionHydratiCA: Ionic Diffusion

• Effective mobility of a charged species is influenced by long-range Coulombicinteractions with other charged species

• Local charge neutrality is required, even though different ions have different mobilities

• HydratiCA can estimate the electrostatic potential at each time step, and include it in the electrochemical potential

• Results in biased random walk

Coupled diffusion of ionsCoupled diffusion of ionsCoupled diffusion of ions

DDCaCa = 0.7 x 10= 0.7 x 10--55 cmcm22/s/s

DDOHOH = 5.3 x 10= 5.3 x 10--55 cmcm22/s/s

x

*

Hr

Hp

ΔH*rev

ΔH*f

HydratiCA: Temperature EffectsHydratiCA: Temperature EffectsHydratiCA: Temperature Effects

Ca(OH)2 Ca2+ + 2OH-

ΔHrxo = -17.88 kJ/mole

kf

kr

lnKeq (T) = lnKeq (298) +

ΔHro

R

HydratiCA: Temperature EffectsHydratiCA: Temperature EffectsHydratiCA: Temperature Effects

1298

−1T

⎡ ⎣ ⎢

⎤ ⎦ ⎥

Need for particle shape analysis in composite materials

• Composites are affected by the shape and property contrast between phases

• Dilute limit shows shape and contrast dependence:P = P1 (1 + [P] c)

• c = volume fraction• P1 is old property• P is new property• [P] is intrinsic property

• If property contrast is small, then [P] does not depend on shape

• If property contrast is high, then [P] depends sensitively on shape

1

2

Relative ViscosityRelative Viscosity

η2 = True or absolute composite plastic viscosityη1 = True or absolute binder plastic viscosity

f(G, C) = function depending on the rheometer geometry (G) including slip effects and experimental conditions (C ).

),(),(

1

2

1

2

CGfCGf

ηη

ηη

=

Article in January/February 2006 issue

Encouragement from other materials

• Metals before dislocation theory• Polymers before molecular chain theory• Ceramics before Prof. Kingery• Were seen as “messy”• “....guiding theme (of Kingery’s work) was that

ceramics should be seen as a class of materials with common and controllable attributes rather than as the products of isolated and idiosyncratic cultures.” (R.J. Brook, Nature 406, 582 (2000)