Fatigue Crack Paths 2003

where N is the number of expected fibres, Ac is the concrete cross section, Af is the

fibre cross section area, D is a constant that depends on the distribution of the fibres and

it is equal as 0.5 for uniformly distributed fibres (the theoretical numbers of fibres

bridging the cross section for the materials adopted is reported in Figure 4d). This large

scatter of experimental results was somehow expected because of the low volume

fraction of fibres adopted. Results from hybrid fibres (made of 0.32% of Macro fibres

and 0.32% of Meso1fibres) are shown in Figure 5c; it can be noticed the slightly higher

number of cycles and, in particular, the lower scatter of the experimental results (in term

of number of cycles). In fact, the smaller diameter of meso (and micro) fibres favours a

more uniform fibre distribution. It was already found the remarkable influence of the

fibre density in the cracked area; however, this parameter is even more important for

fatigue behaviour.

L

PLCAOIND

M A C R O

0

50

100

150

200

250

12505000

12505000

C O D 1

C O D 1 4 8 1

C O D 2

C O D 1 4 8 2

C O D 1 4 8 3

O A D [d a N ]

C O D1 4 8 1 B

Dd[ a N ]

L O A

0

0

50

100

150

200

250

C O D

(a)

(b)

M A C R OM+E S O C D 100 150

L

0

50

200

250

Specimen

nmax

nmacrofibres

nmesofibres

12505000

COD1O521CDOD15122 5 2 3

Macro-A 5401

41

-

Macro-B

23

27

-

AdNDa[ ]

Macro-C

n.a.

0

-

theoretical

-

27.0

-

HyFRC1-A 75

18

38

O

HyFRC1-B 109

15

35

20

HyFRC1-C 130

51

theoretical

-

13.5

30.4

n.a. = not available

(c)

(d)

Figure 4. Experimental results from uniaxial tensile tests: static test on plain concrete

(a); cyclic tests on cylinders with macrofibres (b) and cyclic tests on cylinders with

hybrid fibres (c); maximumnumber of cycles (nmax) and of fibres crossing the cracked

section (d).