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Purdue University School of Civil Engineering West 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

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purdue university school of civil engineering west west lafayette indiana

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

introduction

Introduction

We Typically use ‘Effective Properties’

equivalent strain e composite
( = 1.405, C1= 0.25)Equivalent Strain (eComposite)
  • 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 e composite
Equivalent Elastic Modulus (EComposite)
  • 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 s composite
Equivalent Residual Stress (sComposite)
  • 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

sComposite= ECompositeeComposite

eSH-Paste-100 me

EPaste= 20 GPa, EAgg= 40 ~ 200 GPa

scope of this research and objectives
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
Paste

L

DL’

L’

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)

HomogenousPaste

L

Externally

Unrestrained

Externally

Restrained

Paste

No stress

(epaste)

Stress

(spaste=Epasteepaste)

residual stress in a heterogenous system
DL’’

L”

L

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

Heterogeneous

Agg.

L

Externally

Unrestrained

Externally

Restrained

s

?

d

Stress ( s ?)

Under External +

Internal Restraint

Internal Stress

sInternal ?

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)

A Model to Investigate the Residual Stress Fields

EPaste=20 GPa, nPaste=0.2, EAgg=200 GPa, nAgg=0.3

eSH-Paste =-100 me

single aggregate prism model externally unrestrained sample
Single Aggregate Prism Model- Externally Unrestrained Sample -
  • Externally unrestrained sample is nearly axi-symmetric

Internal Stress

( s1: MPa )

single aggregate prism model externally unrestrained sample1
Single Aggregate Prism Model- Externally Unrestrained Sample -
  • Externally unrestrained sample has stress fields which are nearly axi-symmetric

Internal Stress

( s1: MPa )

single aggregate prism model externally restrained sample
Single Aggregate Prism Model- Externally Restrained Sample -
  • Externally restrained sample exhibits different behavior

( s1: MPa )

single aggregate prism model externally restrained sample1
Single Aggregate Prism Model- Externally Restrained Sample -
  • Externally restrained sample exhibits different behavior

( s1: MPa )

comparing single aggregate prism models
Comparing Single Aggregate Prism Models

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
Agg.

Agg.

Agg.

Void

B

H

Single Aggregate Prism Model(Bond Condition)

Externally Restrained

Stress Localization

Externally Unrestrained

No

Stress

Void

Perfectly Bonded/Unbonded

Externally Restrained

(Vertical Direction)

Perfectly

Bonded

Perfectly

Unbonded

consider models with more than one aggregate

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 Models(Finite Element Analysis)
  • Unit Cell Composite Model

Externally Unrestrained

Externally Restrained

( s: MPa )

unit cell composite model externally unrestrained
Unit Cell Composite Model- Externally Unrestrained -
  • 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
Unit Cell Composite Model- Externally Restrained -
  • 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
Comparing the Heterogenous Stress and the Homogenous Stress
  • 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

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
Preliminary Observation

BOND CONDITION – MICROCRACKING (Key issue)

(Example: Restrained Boundary Condition)

Microcracking

Cracking

nist oof simulation
NIST - OOF Simulation
  • Procedure

Concrete

Saw Cut

Polishing

Concrete Specimen

phenolphthalein

Polished Surface

Image Analysis

Surface Treatment

Mesh

Material

Properties

Define phases

Meshed image

nist oof simulation 2 phase agg paste
NIST - OOF Simulation (2-Phase: Agg. & Paste)
  • Apply boundary condition, shrinkage strain onto cement paste phase

(Example: Externally restrained B.C.)

Strain Analysis e1

Stress Analysis s1

467 me

25 MPa

0 me

- 435 me

12 MPa

Before cracking

After Cracking

0 MPa

Cracked image

After cracking

nist oof simulation 3 phase agg paste interface
NIST - OOF Simulation (3-Phase: Agg., Paste, Interface)
  • Interface  Bond Condition

3-Phase Strain Analysise1

3-Phase Analysis

1000 me

0 me

- 435 me

2-Phase Analysis

Paste

Aggregate

Interface

conclusions
Conclusions
  • The Existence of Aggregate

Provides Internal Restraint  Higher Internal Stress Development (sMax-Internal > sComposite)

  • 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:

HigherVAgg, EAgg Higher sMax.-Internal

- Externally Restrained:

Not Clear (But, small changes when EAgg/Epaste > 2)

conclusions1
Conclusions
  • Equivalent Stress vs. Maximum Internal Stress

1) sMax-Internal > sComposite

2) The increase of VAgg : sComposite Decreases

sMax-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

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