METAL FIBER WITH OPTIMIZED GEOMETRY FOR REINFORCING CEMENT-BASED MATERIALS

FIBRE METALLIQUE A GEOMETRIE OPTIMISEE POUR RENFORCER LES MATERIAUX A BASE DE CIMENT

English Abstract

A metal fiber for reinforcing cement-based materials comprises an elongated, substantially straight central portion and sinusoid shaped end portions. The sinusoid at each end portion has an optimum amplitude Ao, opt defined by: Ao, opt = [k1(?c)k2] [?u.alpha. .epsilon.f.beta.] [Af/Pf] where k1 = 2.025 x 10-2, ?c = compressive strength of the cement-based material in MPa, k2 = 3.19 x 10-1, ?u = ultimate tensile strength of the metal in MPa, .alpha. = 6.60 x 10-1, .epsilon.f = ductility of the metal in percent, and .beta. = 3.20 x 10-1, Af = cross-sectional area of the fiber in mm, and Pf = perimeter of the fiber in mm. The sinusoid further has a wavelength Ls defined by: Ls = (Lf - Lm)/2 where Lf = length of the fiber, Lm = length of the central portion, and wherein 0.5 Lf < Lm < 0.75 Lf. Since the optimum amplitude is defined as a function of the ultimate tensile strength and ductility of the fiber material as well as of the compressive strength of the matrix material, it is possible to tailor the fiber geometry according to the properties of the fiber and matrix materials chosen, and ultimately to the composite toughness desired in an actual structure.

French Abstract

Une fibre métallique pour renforcer les matériaux à base de ciment qui comprend une partie centrale allongée et substantiellement droite, ainsi que des extrémités sinusoïdales. La sinusoïde de chaque extrémité présente une amplitude optimale Ao, opt définie par Ao, opt = [k1(sigma c)k2] [sigma u alpha epsilon f bêta] [Af/Pf], où k1 = 2,025 x 10 à la -2; sigma c = résistance du matériau à base de ciment en compression en MPa; k2 = 3,19 x 10 à la -1; sigma u = résistance à la traction du métal en MPa; alpha = 6,60 x 10 à la -1; epsilon f = ductilité du métal en pourcentage; bêta = 3,20 x 10 à la -1; Af = l'aire de la section transversale de la fibre en mm2.

Claims

The embodiments of the invention, in which an exclusive
property or privilege is claimed are defined as follows:
1. A metal fiber for reinforcing cement-based materials,
which comprises an elongated, substantially straight central
portion and sinusoid shaped end portions, the sinusoid of
each end portion having an optimum amplitude Ao, opt defined
by:
Ao,opt = [k1 (?c) k2] [?u.alpha. .epsilon.f.beta.] [Af/Pf]
where
k1 = 2.025 x 10-2,
?c = compressive strength of the cement-based
material in MPa,
k2 = 3.19 x 10-1,
?u = ultimate tensile strength of the metal in MPa,
.alpha. = 6. 60 x 10-1,
.epsilon.f = ductility of the metal in percent, and
.beta. = 3.20 x 10-1,
Af = cross-sectional area of the fiber in mm2, and
Pf = perimeter of the fiber in mm,
said sinusoid further having a wavelength Ls defined by:
Ls = (Lf - Lm)/2
where
Lf = length of the fiber,
Lm = length of the central portion,
and wherein 0.5 Lf < Lm < 0.75 Lf.
2. Fiber according to claim 1, wherein the length Lf of the
fiber ranges from about 25 to about 60 mm.
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3. Fiber according to claim 1, wherein said central portion
and said end portions have a uniform rectangular cross-
section.
4. Fiber according to claim 3, wherein said central portion
and said end portions have a thickness of about 0.4 mm and a
width of about 0.8 mm, and wherein the length Lf of the fiber
is about 50 mm and the length Lm of the central portion is
about 25 mm.
5. Fiber according to claim 1, wherein said central portion
and said end portions have a uniform circular cross-section.
6. Fiber according to claim 1, wherein the cement-based
material has a compressive strength ?c ranging from about 30
to about 60 MPa and wherein k1(?C)k2 ranges from about 6 x
10-2 to about 7.5 x 10-2.
7. Fiber according to claim 6, wherein k2(?C)k2 is about 7 x
10-2.
8. Fiber according to claim 7, wherein the cross-sectional
area Af and the perimeter Pf of the fiber are such that
Af/Pf = 1.33 x 10-1 mm.
9. Fiber according to claim 8, wherein said metal is steel.
10. Fiber according to claim 9, wherein said steel is of
type C1018 having an ultimate tensile strength ?µ of about
1030 MPa and a ductility .epsilon.f of about 0.60%, and wherein said
sinusoid has an optimum amplitude Ao,opt of about 0.7 mm.
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11. Fiber according to claim 9, wherein said steel is a
martensite steel having an ultimate tensile strength ?u of
about 1550 MPa and a ductility .epsilon.f of about 1%, and wherein
said sinusoid has an optimum amplitude Ao,opt of about
1.2 mm.
12. Fiber according to claim 9, wherein said steel is a high
strength low aluminum steel having an ultimate tensile
strength ?u of about 1350 MPa and a ductility .epsilon.f of about
3.5%, and wherein said sinusoid has an optimum amplitude
Ao,opt of about 1.5 mm.
13. Fiber according to claim 1, wherein said end portions
each have an end angle .theta. below 20°, the angle .theta. being defined
by:
.theta. = tan-1 <IMG> .
14. Fiber according to claim 13, wherein said angle .theta. ranges
from about 12° to about 15°.
15. A metal fiber reinforced cement-based material, which
comprises a cement-based material in admixture with metal
fibers, said metal fibers each having an elongated,
substantially straight central portion and sinusoid shaped
end portions, the sinusoid of each end portion having an
optimum amplitude Ao,opt defined by:
Ao,opt = [k1(?c)k2] [?u.alpha. .epsilon.f.beta.] [Af/Pf]
where
k1 = 2.025 x 10-2,
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.sigma.c = compressive strength of the cement-based
material in MPa,
k2 = 3.19 x 10-1,
.sigma.u = ultimate tensile strength of the metal in MPa,
.alpha. = 6.60 x 10-1,
.epsilon.f = ductility of the metal in percent, and
.beta. = 3.20 x 10-1,
Af = cross-sectional area of the fiber in mm, and
Pf = perimeter of the fiber in mm,
said sinusoid further having a wavelength LS defined by:
LS = (Lf - Lm)/2
where
Lf = length of the fiber,
Lm = length of the central portion,
and wherein 0.5 Lf < Lm < 0.75 Lf.
16. A metal fiber reinforced cement-based material as
claimed in claim 15, wherein the length Lf of the fibers
range from about 25 to about 60 mm.
17. A metal fiber reinforced cement-based material as
claimed in claim 15, wherein said central portion and said
end portions have a uniform rectangular cross-section.
18. A metal fiber reinforced cement-based material as
claimed in claim 17, wherein said central portion and said
end portions have a thickness of about 0.4 mm and a width of
about 0.8 mm, and wherein the length Lf of the fibers is
about 50 mm and the length Lm of the central portion is about
25 mm.
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19. A metal fiber reinforced cement-based material as
claimed in claim 15, wherein said central portion and said
end portions have a uniform circular cross-section.
20. A. metal fiber reinforced cement-based material as
claimed in claim 15, wherein the cement-based material has a
compressive strength ?c ranging from about 30 to about 60 MPa
and wherein k1(?c)k2 ranges from about 6 x 10-2 to about 7.5 x
10-2.
21. A metal fiber reinforced cement-based material as
claimed in claim 20, wherein k1(?c)k2 is about 7 x 10-2.
22. A metal fiber reinforced cement-based material as
claimed in claim 21, wherein the cross-sectional area Af and
the perimeter Pf of the fibers are such that Af/Pf = 1.33 x
10-1 mm.
23. A metal fiber reinforced cement-based material as
claimed in claim 22, wherein said metal is steel.
24. A metal fiber reinforced cement-based material as
claimed in claim 23, wherein said steel is of type C1018
having an ultimate tensile strength ?u of about 1030 MPa and
a ductility .epsilon.f of about 0.60%, and wherein said sinusoid has
an optimum amplitude, Ao,opt of about 0.7 mm.
25. A metal fiber reinforced cement-based material as
claimed in claim 23, wherein said steel is of martensite
steel having an ultimate tensile strength ?u of about
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1550 MPa and a ductility .epsilon.f of about 1%, and wherein said
sinusoid has an optimum amplitude, Ao,opt of about 1.2 mm.
26. A metal fiber reinforced cement-based material as
claimed in claim 23, wherein said steel is a high strength
low aluminum steel having an ultimate tensile strength ?u of
about 1350 MPa and a ductility .epsilon.f of about 3.5%, and wherein
said sinusoid has an optimum amplitude, Ao,opt of about
1.5 mm.
27. A metal fiber reinforced cement-based material as
claimed in claim 15, wherein said end portions each have an
end angle ? below 20°, the angle ? being defined by:
? = tan-1 <IMG>
28. A metal fiber reinforced cement-based material as
claimed in claim 27, wherein said angle ? ranges from about
12° to about 15°.
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Description

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The present invention pertains to improvements in the
field of fiber reinforced cement-based materials. More
particularly, the invention relates to a metal fiber having
an optimized geometry for reinforcing cement-based materials.
All cement-based materials are weak in tension. In
addition, these materials have a very low strain capacity
which places them in a brittle category with other brittle
materials such as glass and ceramics. It is well known that
concrete and other portland cement-based materials may be
reinforced with short, randomly distributed fibers of steel
to improve upon their mechanical properties. It is also known
that for any improvement in the tensile strength, fiber
volume fraction has to exceed a certain critical value.
Beyond matrix cracking, fibers form stress transfer
bridges and hold matrix cracks together such that a further
crack opening or propagation causes the fibers to undergo
pull-out from the matrix. Pull-out processes being energy
intensive, steel fiber reinforced concrete exhibits a stable
load-deflection behavior in the region beyond matrix-cracking
which places these materials in a category of pseudo-plastic
or tough materials such as steel and polymers. Thus, while a
plain unreinforced matrix fails in a brittle manner at the
occurrence of cracking stresses, the ductile fibers in fiber
reinforced concrete continue to carry stresses beyond matrix
cracking which helps maintaining structural integrity and
cohesiveness in the material. Further, if properly designed,
fibers undergo pull-out processes and the frictional work
needed for pull-out leads to a significantly improved energy
absorption capability. Therefore, fiber reinforced concrete
exhibits better performance not only under static and quasi-
; statically applied loads but also under fatigue, impact and
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,~ ,
impulsive loadings. This energy absorption attribute of fiber
reinforced concrete is often termed "toughness".
Concrete is a strain-softening, micro-cracking material.
In steel fiber reinforced cement-based composites, fiber
bridging action sets in even prior to the occurrence of the
perceived matrix macro-cracking. The critical fiber volume
fraction or the magnitude of strength improvement at a
certain fiber volume fraction, therefore, depends upon the
geometry of the fiber. Also dependent upon the geometry is
the pull-out resistance of an individual fiber from the
cementitious matrix around it, which in turn, governs the
.,. ,._ ., ~.
~ shape of the load-deflection plot beyond matrix cracking and
the achievable improvement in composite toughness.
An improvement in the strength of the composite at a
certain fiber volume fraction or, in other words, a reduction
in the required critical fiber volume fraction, is possible
by excessively deforming the fiber. However, this may lead to
too good a fiber anchorage with the matrix and causes a
brittle mode of fracture in the post-matrix cracking region.
Toughness reductions in the case of excessively deformed
fibers, therefore, can be significant. The other possible way
is to increase the number of fibers in the composite by
reducing the size of the fibers. This solution is known to
cause extreme difficulties in terms of concrete mixing and
workability, and uniform fiber dispersion often becomes
impossible as the fibers tend to clump together giving a
highly non-uniform distribution.
In US Patent N 4,585,487 which proposes a concrete-
reinforcing fiber having uniform wave shaped corrugations
distributed over its entire length, the sole fiber
performance characteristics considered for optimization is
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the fiber pull-out performance. The same also applies in
respect of Canadian Patent Nos. 926,146 and 1,023,395 which
disclose concrete-reinforcing fibers having a straight
central portion with shaped ends. Some fibers have ends which
are formed thicker; others have ends which are hooked. All
these characteristics are intended to improve anchoring of
the fiber in the concrete.
For fibers that are used as a reinforcement distributed
randomly in a moldable concrete matrix, the property of
interest is the overall composite toughness. The composite
toughness, although dependent on the pull-out resistance of
fibers, cannot quantitatively be derived from the results of
an ideal fiber pull-out test where the fiber is aligned with
respect to the load direction, since in a real composite,
~ once the brittle cementitious matrix cracks, the fibers are
_ ~ not only embedded to various depths on both sides of the
matrix but also inclined at various angles with respect to
the loading direction. Further, fibers pulling out as a
bundle have a very different performance as compared to a
single fiber owing primarily to fiber-fiber interaction.
Also, in a real composite, the contribution from the matrix
is not entirely absent while fibers are pulling out (as
assumed in an ideal pull-out test) due to aggregate
interlocking, discontinuous cracking and crack bands. Thus,
the idealistic single fiber pull-out test with the fiber
aligned with respect to the loading direction is not a
realistic representation of what is happening in a real
i- composite. So far, no attempt has been made to rationally
- optimize the fiber geometry with respect to the properties of
the matrix material, i.e. concrete, and the fiber material,
i.e. steel or other metal.
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It is therefore an object of the present invention to
relate the fiber geometry to the properties of both the
matrix ar.d fiber materials, with a view to optimizing the
overall composite toughness.
It is another object of the invention to provide a metal
fiber with an optimized geometry for reinforcing cement-based
materials such that the fiber fully utilizes matrix anchoring
without fracturing in the pre-matrix macro-cracking region
and pulls out at the maximum pull-out resistance in the post-
matrix macro-cracking region giving the highest possible
toughness.
In accordance with the present invention, there is thus
provided a metal fiber for reinforcing cement-based
materials, which comprises an elongated, substantially
straight central portion and sinusoid shaped end portions.
The sinusoid at each end portion has an optimum amplitude
Ao/ opt defined by
Ao,opt = [kl (aC) k2] [aU ~f~] [Af/Pf] (1)
where
kl = 2.025 x 10-2,
= compressive strength of the cement-based
material in MPa,
k2 = 3.19 x 10-1,
au = ultimate tensile strength of the metal in MPa,
= 6.60 x 10-1,
= ductility of the metal in percent, and
~ = 3.20 x 10-1,
Af = cross-sectional area of the fiber in mm2, and
Pf = perimeter of the fiber in mm.
The sinusoid further has a wavelength Ls defined by:
Ls = (Lf - Lm)/2 (2)

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where
Lf = length of the fiber,
Lm = length of the fiber central portion,
and where-n 0.5 Lf < Lm < 0.75 Lf.
As it is apparent from equation (1), both the ultimate
tensile strength and the ductility of the fiber material as
~ well as the compressive strength of the cement-based material
- are important factors in defining the optimum amplitude. The
equation also takes into account the cross-sectional area and
perimeter of the fiber. It is therefore possible to tailor
the fiber geometry according to the properties of the fiber
and matrix materials chosen, and ultimately to the composite
toughness desired in an actual structure.
Where use is made of a cement-based material having a
compressive strength ac ranging from about 30 to about
-~ 60 MPa, the value of k1(ac)k2 in equation (1) then ranges from
about 6 x 10-2 to about 7.5 x 10-2. A preferred value of
kl(~C)k2 which provides an optimum amplitude Ao~opt in the
concrete compressive strength range of 30-60 MPa is about
7 x 10-2.
The fiber according to the invention preferably has an
end angle ~ less than 20, the angle ~ being defined by
t -1 4(Ao~opt) (3)
Ls
The angle ~ preferably ranges from about 12 to about 15.
Such a small end angle ~ prevents the fibers from undergoing
balling so that there is no problem with mixing.
The fibers of the invention which have sinusoids only at
the end portions as opposed to those that have sinusoids
along their entire length, such as in the case of US Patent
N 4,585,487, provide better reinforcing. At a crack where

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.,
fibers form stress-transfer bridges and are subjected to
pull-out forces, those with deformations over the entire
length transmit the entire pull-out force immediately back to
the matrix through anchorage. In the case of fibers deformed
only at the extremities, the stresses are slowly transferred
from the crack face to the interior of the matrix with the
major transfer of forces taking place only at the
extremities. Such a gradual transfer of stresses averts a
possible crushing and splitting of the matrix at the crack
face which is commonly observed in fibers deformed all along
the length. It is due to the matrix crushing and splitting
that fibers unfavorably affect each others ability to
reinforce when in a group and the overall toughness of the
composite is severely reduced. Since the optimum amplitude of
the sinusoid shaped end portions of the fibers according to
the invention is defined as a function of the ultimate
tensile strength and ductility of the fiber material as well
as of the compressive strength of the matrix material, such
amplitude is generally less than 5% of the fiber length. The
low fiber amplitude leads to a more gradual transfer of
stresses back to the matrix and hence less crushing and
splitting of the matrix around the fibers.
A particularly preferred metal fiber according to the
invention has a uniform rectangular cross-section with a
thickness of about 0.4 mm and a width of about 0.8 mm, a
length Lf of about 50 mm and a length Lm of about 25 mm. The
wavelenth Ls of the sinusoid at each end portion of the fiber
is about 12.5 mm.
Fiber reinforced concrete incorporating the fibers of
the invention can be used in slabs on grade, shotcrete,
architectural concrete, precast products, offshore

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structures, structures in seismic regions, thin and thick
repairs, crash barriers, footings, hydraulic structures and
many other applications.
Further features and advantages of the invention will
become more readily apparent from the following description
of preferred embodiments, reference being made to the
accompanying drawings in which:
Figure 1 is a side elevational view of a steel fiber
according to the intention;
Figure 2 is a load deflection plot in which the
toughness of concrete reinforced with the fiber illustrated
in Fig. 1 is compared with that of concrete reinforced with
conventional fibers; and
Figure 3 is a graph showing the relationship between
post-crack strength and beam mid-span deflection expressed as
a fraction of the span for the same fibers.
As shown in Fig. 1, the steel fiber illustrated which is
generally designated by reference numeral 10 comprises an
elongated, substantially straight central portion 12 with
sinusoid shaped end portions 14 and 14'. The sinusoid at each
end portion is defined by
y = Ao sin L (4)
where the coordinate system is as illustrated in Fig. 1 and
Ao is the amplitude of the sinusoid. Also illustrated in Fig.
1 are the length Lf of the fiber 10, the length Lm f the
central portion 12 and the length Ls of the end portions
14,14', as well as the end angle ~. The length Lf of the
fiber 10 may vary from about 25 to about 60 mm. As explained
herein, the fiber geometry is optimized by giving to the

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"
, .
sinusoid an optimum amplitude Ao/opt as defined in equation
(1) -
For example, the optimum amplitudes for the followingthree steels with different mechanical properties are given
in Table 1, where ac = 40 MPa and Af/Pf = 1.33 x 10-1 mm:
TABLE 1
Steel Type and Properties (bulk) Optimum Amplitude,
o,opt
Steel A: type C1018 (~u = 1030 MPa;
~ ~f = 0.60%) z 0.7 mm
- Steel B: Martensite Steel
(au = 1550 MPa; ~f = 1%) ~ 1.2 mm
Steel C: HSLA* Steel
(au = 1350 MPa; ~f = 3.5~) z 1.5 mm
* High Strength Low Aluminum
10In the embodiment illustrated in Fig. 1, the fiber 10
has a uniform rectangular cross-section. Such a fiber may
also have a circular cross-section.
Fibers with optimized geometry at a dosage rate of
40 kg/m3 were used in reinforcing concrete matrices having an
------~~~~- unreinforced compressive strength of 40 MPa. Beams made from
the fiber-reinforced concrete were tested in third point
flexure, along with their unreinforced companions. The beam
displacements were measured using a yoke around the specimen
such that the spurious component of the load point
displacement due to the settlement of supports was
automatically eliminated. The resulting load deflections
plots are set forth in Fig. 2, where the toughness of
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concrete reinforced with the fibers of the invention (F1) is
compared with that of concrete reinforced with conventional
fibers (F2 to F5). The conventional fibers investigated for
comparative purpose were the following:
TABLE 2
- FiberGeometryCross- Length Size Tensile Weight Number
Design- Section (mm) (mm) Strength (g.) per kg
ation Shape (MPA)
F2 Hooked-Circular 60 0.8 1115 0.263 3800
end diam.
F3 Twin-coneCircular 62 1.0 1198 0.403 2480
diam.
F4 CrimpedCircular 60 1.0 1037 0.420 2380
diam.
F5 CrimpedCrescent 522.3 x 1050 0.393 2540
0.55
The plots were analyzed according to conventional
techniques (ASTM - C1018; JSCE SF-4) as well as to the PCS
technique described by J.-F. Trottier, "Toughness of Steel
Reinforced Cement-Based Composites", Ph.D. Thesis, Laval
University, 1993, with a view to deterrining the toughness
parameters. The results are given in Table 3 and plotted in
Figure 3:
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~ TABLE 3
~'
Post Crack Strength Plain Concrete Concrete with Fl
- at beam displacement (~c = 40 MPa; Fibers (~c = 43 MPa;
of span/m, PCSm Ec = 39 GPa) Ec = 39 GPa)
PCS3000 6.3-6.5 MPa
1500 o 6.0-6.5 MPa
PCS600 0 5.8-6.0 MPa
PCS400 o 5.5-5.8 MPa
PCS300 5.0-5.3 MPa
PCS200 4.0-4.8 MPa
Modulus of Rupture
(MOR) 5.19 MPa 5.5-5.9 MPa
Toughness Indices
(ASTM-C1018)
I5 1.0 4.7-5.0
Ilo 1.0 9.0-9.5
1.0 17.2-20.0
I30 1.0 22.0-23.0
I60 1.0 45.0-50.0
JSCE (SF-4) Factor - 5.2-5.8 MPa
In Table 3, Ec is the elastic modulus of concrete as per
ASTM C-469. The JSCE SF-4 technique takes the total area
(elastic and plastic) under the curve up to a deflection of
span/150 and converts into an equivalent post-crack strength.
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The fibers of the inventions even at a low dosage of 40
kg/m3 lead to strengthening in the system as evident from the
increase in the load carrying capacity over the plain,
unreinforced matrix. Also, after the matrix cracking, the
composite is capable of carrying approximately the same level
of stresses as when at matrix cracking and as such very high
toughness is derived. The composite behaves almost in an
elasto-plastic manner.
A minor increase (about 7~) in the compressive strength
of concrete due to fiber addition indicates that an adequate
fiber dispersion and mix compaction were achieved.
As it is also apparent from Figs 2 and 3, the fiber with
optimized geometry according to the invention behaves
superior to existing commercial fibers and provides higher
flexural toughness. It is believed that the fiber geometry
fully utilizes the potential of steel and that of the cement
matrix to produce an optimized composite.
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