Microstructure Variability and Macroscopic Composite Properties of High Performance Fiber Reinforced Cementitious Composites

Victor C. Li and Shuxin Wang

Advanced Civil Engineering Materials

Research Laboratory

The University of Michigan

2

High Performance Fiber Reinforced Cementitious Composites

High strength High durability Self-compacting High tensile failure resistance

3

HPFRCC Characteristics: Strain-Hardening

Concrete FRC

HPFRCC

4

Engineered Cementitious Composites

Composite response in uniaxial tension

20 m

m

Damage

Fiber volume fraction 2%

0

1

2

3

4

5

0 1 2 3 4 5 6Strain (%)

Ten

sile

Str

ess

(MP

a)

0

20

40

60

80

100

Cra

ck W

idth

(m

)

Concrete Strain 10 times expanded

ECC

5

Mihara Bridge in HokkaidoOpen to traffic: April, 2005Length: 1000 m, span: 340 mDeck area: 20,000 sq. m.; ECC layer thickness: 38 mm

Composite ECC-Steel DeckSuper light-weight 40% reductionExpected service life: 100 yrs

6

Bridge-deck Link Slab RetrofitMichigan, 2005

Conventional Bridge Joint

Durable ECC Link Slab

ECC Link Slab

Lspan Lspan

Llink slab = 0.1 x Lspan

7

Variation of Tensile Behavior

PVA fiber reinforced ECC, Vf = 2%

Extreme variability case

8

Microstructure Inhomogeneity

Matrix flaws

Fiber distribution10 mm

9

Scale Linking

Le

aP

z

Single fiber pullout behavior Crack initiation at flaw

Bridging stress vs. crack opening Multiple-cracking process

Composite stress vs. strain

Steady State Cracking Requirement Crack Saturation Requirement

10

Single Fiber Modeling

idfy dAGdWdWdW ++=

Le

a

€

=4τ 0a 1+ η( )

d f+

8GdE f 1+ η( )

d f

Le

€

=τ 0 1+ β δ −δc( ) / d f( ) Le −δ +δ c( ) / d f

€

c =2τ 0Le

2 1+ η( )

E f d f+

8Gd Le2 1+ η( )

E f d f

Debonding Pullout

Fiber parameters

Interface parameters

11

Modeling of Fiber Randomness

( ) ( ) ( ) φφφ dzdzpzPVA ff

,,1

∫=

( ) ( ) ( )φφ pzpzp =,

( )fl

zp1

=22ff l

zl

≤≤−

( ) ( )D

Dp

2

3

/2

sin

⎩⎨⎧

=π

φφ

20

πφ ≤≤

12

Conditions for Strain-hardening

ss

Jb’ complementary energy

Jtip crack tip fracture energy

ss

ss

€

J tip ≤ σ oδo − σ (δ )dδ ≡ Jb'

0

δ o

∫

Variability of Jtip, Jb’ ?Matrix parameter

13

Effect of Initial Flaw Size on Cracking Strength(Computed)

Matrix intrinsic tensile strength 5 MPa

14

Tailoring of Flaw Size Distribution for Saturated Multiple Cracking

flaw size ccmc

p(c)

flaw size c cmc

p(c)

artificial flaw distribution

natural flaw distribution

Superimpose artificial flaws with prescribed sizes Artificial flaws: plastic, bubbles, lightweight aggregates,

etc.

Activated flawsactivated flaws

15

Flaw Size Tailoring in PVA-ECC

lightweight aggregatessize: 3.5 mm

4mm plastic beads

16

Lightweight Aggregates as Artificial Flaws

s/c = 0.8, fa/c = 0.8, w/b = 0.24, PVA Vf = 2.0%

lightweight aggr.: 7 vol%w/o lightweight aggr.

17

Plastic Beads as Artificial Flaws

s/c = 0.8, fa/c = 1.2, w/b = 0.24, PVA Vf = 2.0%

w/ 7 vol% beadsw/o beads

18

Open Issues

Further understand linkages between randomness of microstructures and variability in composite behaviors

Capture and quantify randomness of critical microstructures

Incorporate probabilistic models in ECC theoretical framework

19

Multiple Cracking Process

20

Conclusions

Microstructure variability significantly influences ductility of ECC materials

Control of key microstructure variability is critical to achieve robust strain-hardening behavior Ensure enough margin between Jtip and Jb’

Implantation of artificial flaws with controlled size

Further work in characterization and modeling of microstructure randomness is needed