STEEL FIBERS FROM CEMENTITIOUS

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29 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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MODELLING THE PULLOUT OF HOOKED
STEEL FIBERS FROM CEMENTITIOUS
MATRIX

Edmunds Zīle
, Olga Zīle

Institute of Polymer Mechanics

Riga, Latvia

Introduction

Concrete is brittle material with low fracture toughness in
tension

Addition of short, randomly distributed fibers greatly improve the fracture
toughness. The fibers bridge discrete cracks and thereby provide increased
control of the fracture process

2

What affects performance of FRC?


Fiber material

3



Fiber volume fraction



Fiber shape



Fiber aspect ratio



Fiber strength

Objectives

1.
Testing of some commercially available hooked
-
end steel fibers.



2.
Development of simple analytical model for the effect of fiber geometry on

the pullout behavior suitable for practical use.




4

Single fiber pullout specimens

HE+ 1/60 and HE 75/50

hooked steel fibers

produced by ArcelorMittal

5

Properties of the fibers

Fiber

type

σ
Y

(
MPa
)

r
(mm)

l
e

(mm)

l

(mm)

ρ

(mm)

θ

(
rad
)

HE 75/50

1100

0.35

2.0

2.1

1.7

0.62

HE+ 1/60

1450

0.45

1.9

1.4

2.2

0.66

6

Experiment: pullout of straight fibers

7

Experiment: pullout of
hooked

fibers

8

Modeling of the fiber pullout process

P
ullout load
P

of mechanically deformed fiber can be split into two components
:

C
omponent due to the plastic bending

of the fiber in the curved matrix ducts

C
omponent due to the frictional sliding

of fiber

through straight matrix ducts

where
L
s

is total lenght of straight matrix ducts and

τ

is frictional shear stress

Frictional shear stress can be obtained from straight fiber pullout tests

9

Bending of fiber under tension


2
Y Y
T T r
 
 
The following assumptions are made:


1.
The material is isotropic and strain
-
rate independent.


2.
The elastic strains are small in comparison with the plastic strains and can be
neglected. Hence, the material is assumed to be rigid, perfectly plastic.


3.
The damage of
cementitious

matrix around the mechanically deformed fiber during the
pullout is neglected.


If f
iber is subjected to a tension force less than the yield tension

10

Increase of the tension

1.
As the fiber bends at
A

and unbends at
B

there will be an increase in tension.

2.
The tension will increase as the fiber slides against friction between
A

and
B
.

11

Increase of the tension

The plastic work done on the

fiber element by deforming it at
A
:

The external work:

I
ncrease of the tension

at
A
:

The tension in the fiber after bending at
A
:

12

Friction in the curved matrix duct

13


B A
T T e


Due to friction
the tension in the fiber

before unbending at
B
:

where

μ

is

coefficient

of

friction

Tension in the fiber after curved matrix duct

Tension in the fiber

after
un
bending at
B
:




in
out in
T T T T
T
T T T e T


 

  



1
1
i
i i
T T T T
T
T T T e T




 

  
or

T
ension in the fiber after
i
th curved duct
:

14

Pullout of hooked
-
end fibers: stage 1

L
ength of embedded part of the fiber without

hook before pullout process

15

Fiber segments in curved ducts
C
1

and
C
2

subjected to
plastic bending.


Fiber segments in straight ducts
S
1
,
S
2

and
S
3

subjected to frictional sliding.

Pullout of hooked
-
end fibers: stage 2

16

Length of the fiber segment in the curved duct
C
1

decreases, which causes gradual reduction of pullout force
component due to plastic bending.


Fiber segment in curved duct
C
2

subjected to plastic
bending.


Fiber segments in straight ducts
S
2

and
S
3

subjected to
frictional sliding.

Pullout of hooked
-
end fibers: stage 3

17

Fiber segment in curved duct
C
2

subjected to plastic
bending.


Fiber segments in straight ducts
S
2

and
S
3

subjected to
frictional sliding.

Pullout of hooked
-
end fibers: stage 4

18

Length of the fiber segment in the curved duct
C
2

decreases, which causes gradual reduction to zero of
pullout force component due to plastic bending.


Fiber segment in straight duct
S
3

subjected to frictional
sliding.

Pullout of hooked
-
end fibers: stage 5

19

Pullout force is only due to frictional sliding of fiber
segment in straight duct
S
3
.

Comparison with experiment

Model proposed by
Alwan et al.*

20

Proposed model

* J.M. Alwan, A.E. Naaman, P. Guerrero
,
Concrete Science and Engineering
, 1 (1999) 15
-
25.

Conclusions


1.
A simple model is developed to simulate the mechanical contribution of fiber geometry
to the pullout response. It is assumed that fiber geometry is composed of straight and
curved segments. The mechanical contribution depends on the amount of plastic work
required to straighten the fiber during pullout and friction in the curved ducts. The
plastic work is a function of geometrical parameters and yield stress of the fiber. The
damage of
cementitious

matrix during pullout is neglected.


2.
The model provides a reasonably good description of experimental pullout data of

hooked
-
end steel fibers.



21

22

This work was supported by ERAF via project

Nr. 2010/0293/2DP/2.1.1.1.0/10/APIA/VIAA/073