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Purdue University School of Civil EngineeringWest West Lafayette, Indiana

Autogenous Shrinkage, Residual Stress, and Cracking In Cementitious Composites: Influence of Internal and External Restraint

Jae-Heum Moon, Farshad Rajabipour, Brad Pease, and Jason Weiss

4th International Seminar on Self-Desiccation and Its Importance in Concrete Technology

http://sports.espn.go.com/ncaa/clubhouse?collegeId=2509

Introduction

Stress Relaxation

0 7 14 21 28Age of Specimen (Days)

0

4

8

12Stress Based

On Hooke’s Law

Stress InSpecimen

Cal

cula

ted

Tens

ile S

tress

(MPa

)0 7 14 21 28

Age of Specimen (Days)

0

4

8

12Stress Based

On Hooke’s Law

Cal

cula

ted

Tens

ile S

tress

(MPa

)

Stress InSpecimen

We Typically use ‘Effective Properties’

Creep/Cracking Effect

Stress Relaxation

28

,,Etdd

Edtd SHR

SHRd

Edtd ,

Initial Specimen

Shrinkage Effect

Restraint Effect

Final Stress State

Equivalent Strain (Composite)

nAggPasteComposite )V1(

Agg

Paste1 E

EC1

1nn

( = 1.405, C1= 0.25)n

0.01 0.1 1 10 100 1000Ratio of Aggregate and

Paste Stiffnesses (EAgg/E Paste)

0.00

0.25

0.50

0.75

1.00

1.25

1.50

Shrin

kage

Exp

onen

t, n

• Equivalent Strain as determined using Pickett’s Approach from 1956

• Pickett’s equation has an awkward computation for n• Here results of simulations (hex cell)

Equivalent Elastic Modulus (EComposite)

0 20 40 60 80 100Vol. of Agg. (%)

0

40

80

120

160

200

Equi

vale

nt E

com

posi

te (G

Pa) Parallel Model

Series ModelHansen's ModelSimulation

EAgg / EPaste = 10

PasteAggAggPasteAgg

AggAggPasteAggcomposite E

E)V1(E)V1(E)V1(E)V1(

E

• T.C. Hansen developed an approach to estimate the elastic modulus using a similar approach to those described by Pickett (an aggregate sphere in a paste cell).

• Here we see hexagonal unit cell simulations which compare well

Equivalent Residual Stress (Composite)

0 20 40 60 80 100Vol. of Agg. (%)

0

0.5

1

1.5

2

2.5

Stre

ss (M

Pa)

EAgg 10EPaste 5 2

Equivalent

Externally Restrained

Composite= EComposite Composite

EPaste= 20 GPa, EAgg= 40 ~ 200 GPa

SH-Paste -100

• If we neglect creep, we could simulate the effect of restraint (using Picketts and Hansens estimates) as we increase the volume of the aggregate

• Here we can see that as the volume of aggregate increases the stresses decrease

• This would imply that the residual stress would decrease

Scope of this Research and Objectives

• Does the presence of aggregate would result in local internal stresses that are different than the stresses obtained from the ‘equivalent property approach’?

• To evaluate the role of aggregate on the residual stress development as it is influenced by both internal and external restraint

• To investigate how external restraint changes the shape of the stress field around the aggregate

• To begin to try to incorporate microcracking and cracking in the composite systems

Introduction to the Idea of Residual Stress in a Homogenous System

• Residual stress development: (For now we will assume no creep effects to keep the problem somewhat straightforward)

Externally

Unrestrained

HomogenousPaste

No stress(paste)

ExternallyRestrained

L

Paste

L’ L’

Stress(paste=Epastepaste)

L

Paste

Residual Stress in a Heterogenous System

• Residual stress development: (For now we will assume no creep effects to keep the problem somewhat straightforward)

Internal StressInternal ?

L

L” L’’

Stress ( ?)Under External +Internal Restraint

L

?

Agg.

d

Externally

Unrestrained


Heterogeneous

Externally

Unrestrained

HomogenousPaste

No stress(paste)


LL

Paste

L’ L’

PastePaste

L’ L’L’ L’

Stress(paste=Epastepaste)

L

Paste

A Model to Investigate the Residual Stress Fields

• ANSYS – FEA Model• Quadratic rectangular

eight-node elements plane-stress

• Autogenous shrinkage applied using a temperature substitution analogy

• Paste - assumed to have a modulus of 20 GPa and a Poissons ratio of 0.20

• Perfect-bond between aggregate and cement paste is assumed

• Length (5) to Width (1)EPaste=20 GPa, Paste=0.2, EAgg=200 GPa, Agg=0.3SH-Paste =-100

Single Aggregate - Unrestrained

L

H

H D

L

Single Aggregate - Restrained

Single Aggregate Prism Model - Externally Unrestrained Sample -

Internal Stress

: MPa )

• Externally unrestrained sample is nearly axi-symmetric

Single Aggregate Prism Model - Externally Unrestrained Sample -

Internal Stress

: MPa )

• Externally unrestrained sample has stress fields which are nearly axi-symmetric

0 10 20 30

Distance from an aggregate (m m )

- 2

- 1

0

1

2

3

Stre

ss (M

Pa) A

B

H

Unrestrained SingleAggregate Specimen

A

B

Single Aggregate Prism Model - Externally Restrained Sample -

: MPa )

• Externally restrained sample exhibits different behavior

Single Aggregate Prism Model - Externally Restrained Sample -

: MPa )

• Externally restrained sample exhibits different behavior

0 10 20 30


-2

-1

0

1

2

3

Stre

ss (M

Pa) A

B

Restrained SingleAggregate Specim en

H A

B

Comparing Single Aggregate Prism Models

0 10 20 30


- 2

- 1

0

1

2

3

Stre

ss (M

Pa) A

B

H

Unrestrained SingleAggregate Specimen

A

B

0 10 20 30


- 2

- 1

0

1

2

3

Stre

ss (M

Pa) A

B

Restrained SingleAggregate Specim en

H A

B

DOAA

B

We can see the stresses perpendicular to the B-Axis in the unrestrained specimen are higher than the other direction

Single Aggregate Prism Model(Bond Condition)

0 4 8 12Distance from the Agg. (mm )

1

2

3

4

5

6

Stre

ss (M

Pa)

Perfectly BondedPerfectly UnbondedAir VoidNo Agg.

Agg. Agg.

Agg.


PerfectlyBonded

PerfectlyUnbonded

Externally Unrestrained

Perfectly Bonded/Unbonded

(Vertical Direction)

Stress Localization

H

B

Void NoStress

Void


Consider Models with More than One Aggregate

• Up to now we discussed about the residual stress development in single aggregate systems

• We have also been studying hexagonal unit cell models to get a better idea of what is happening in the overall system

• These hexagonal cell models were shown to be similar to the case of restrained ‘ring’ elements in some earlier studies

Unit Cell Composite Models(Finite Element Analysis)

• Unit Cell Composite Model

Hexagonal Unit Cell Model

Single Unit Cell Equivalent Cylinder

lHex

ROP

ROA

: MPa )

Externally Unrestrained


Unit Cell Composite Model- Externally Unrestrained -

0 20 40 60 80 100Vol. of Agg. (% )

0

1

2

3

Max

. Prin

cipa

l Str

ess(

MPa

)

1 052

10 . 50 . 1

E x t e r n a l l y U n r e s t r a i n e d

E Agg/EPaste (Simulation)

• Results indicate that residual stress increases with an increase in– Aggregate Volume– Elastic Modulus of the

Aggregate• Residual stresses can be

high even though the specimen is externally unrestrained

• This is consistent with the measurement of acoustic activity which may correspond to microcracking

Unit Cell Composite Model- Externally Restrained -

0 20 40 60 80 100Vol. of Agg. (% )

0

2

4

6

Max

. Prin

cipa

l Str

ess

(MPa

)

1 052

10 . 50 . 1

E x t e r n a l l y R e s t r a i n e d ( S i m u l a t i o n )

E Agg / EPaste

• Results indicate that residual stress is similar with– Agg. Volume– Elastic Modulus of

the Aggregate• This may suggest

that while the stiffness and volume of the aggregate are important for free shrinkage they may be less critical for cases of restrained shrinkage

Comparing the Heterogenous Stress and the Homogenous Stress

0 20 40 60 80 100Vol. of Agg. (%)

0

2

4

6

Str

ess

(MP

a)

EAgg 10EPaste 5 2

Internal Equivalent

Restrained B. C.• The maximum

homogenous stress significantly varies with aggregate volume and stiffness

• The maximum heterogenous stress does not vary significantly with elastic modulus or aggregate volume

• This suggests that external restraint in a heterogenous system requires further study

The Need to Include Stable Crack Development at the Aggregate

• Up to now we discussed about the residual stress development

• It has become clear from both experimental and numerical simulations that microcracking and cracking behavior in a heterogenous composite system are important and would substantially impact modeling

• We will discuss preliminary model results though substantially more experimental and numerical studies are underway

Preliminary Observation

BOND CONDITION – MICROCRACKING (Key issue)

Microcracking Cracking

(Example: Restrained Boundary Condition)

NIST - OOF Simulation

• Procedure

Polished Surface

phenolphthalein

Define phases

Image AnalysisSurface Treatment

Mesh

Material Properties

Meshed image

ConcreteConcrete

Concrete SpecimenSaw Cut

Polishing

NIST - OOF Simulation (2-Phase: Agg. & Paste)

• Apply boundary condition, shrinkage strain onto cement paste phase

Before cracking

After cracking

Stress Analysis 1

0 MPa

25 MPa

12 MPa

Strain Analysis 1

- 435

467

0

Cracked image

After Cracking

(Example: Externally restrained B.C.)

NIST - OOF Simulation (3-Phase: Agg., Paste, Interface)

• Interface Bond Condition

3-Phase Strain Analysis 1 1000

- 435

2-Phase Analysis

0

3-Phase Analysis

Paste

Aggregate

Interface

Conclusions

• The Existence of Aggregate Provides Internal Restraint Higher Internal Stress

Development (Max-Internal > Composite)

• The Bond Condition Between Aggregate and Cement Paste

- Externally Unrestrained Little role - Externally Restrained Critical

• Role of Aggregate on the Internal Stress Development - Externally Unrestrained: Higher VAgg, EAgg Higher Max.-Internal

- Externally Restrained: Not Clear (But, small changes when EAgg/Epaste > 2)

Conclusions

• Equivalent Stress vs. Maximum Internal Stress

1) Max-Internal > Composite

2) The increase of VAgg : Composite Decreases

Max-Internal Does not vary significantly It is possible to underestimate the microcracking and

cracking potential of concrete if estimation is performed only using equivalent parameters

Further Information http://bridge.ecn.purdue.edu/~wjweiss