(19) |
|
|
(11) |
EP 0 725 871 B1 |
(12) |
EUROPEAN PATENT SPECIFICATION |
(45) |
Mention of the grant of the patent: |
|
28.06.2000 Bulletin 2000/26 |
(22) |
Date of filing: 21.04.1995 |
|
(51) |
International Patent Classification (IPC)7: E04C 5/01 |
(86) |
International application number: |
|
PCT/CA9500/225 |
(87) |
International publication number: |
|
WO 9606/995 (07.03.1996 Gazette 1996/11) |
|
(54) |
METAL FIBER WITH OPTIMIZED GEOMETRY FOR REINFORCING CEMENT-BASED MATERIALS
METALLFASER MIT OPTIMIERTER GEOMETRIE ZUR VERSTÄRKUNG VON ZEMENTMATERIALIEN
FIBRE METALLIQUE A GEOMETRIE OPTIMISEE POUR RENFORCEMENT DES MATERIAUX A BASE DE CIMENT
|
(84) |
Designated Contracting States: |
|
AT BE CH DE DK ES FR GB GR IE IT LI LU MC NL PT SE |
(30) |
Priority: |
31.08.1994 CA 2131212
|
(43) |
Date of publication of application: |
|
14.08.1996 Bulletin 1996/33 |
(73) |
Proprietor: UNIVERSITE LAVAL |
|
Quebec,
Quebec G1K 7P4 (CA) |
|
(72) |
Inventors: |
|
- BANTHIA, Nemkumar
Burnaby, British Columbia V5A 2T9 (CA)
- KRISHNADEV, Madhavaro
Sainte-Foy, Quebec G1W 1S7 (CA)
|
(74) |
Representative: Casalonga, Axel |
|
BUREAU D.A. CASALONGA - JOSSE
Morassistrasse 8 80469 München 80469 München (DE) |
(56) |
References cited: :
BE-A- 892 468 US-A- 4 585 487
|
US-A- 2 677 955
|
|
|
|
|
|
|
|
|
Note: Within nine months from the publication of the mention of the grant of the European
patent, any person may give notice to the European Patent Office of opposition to
the European patent
granted. Notice of opposition shall be filed in a written reasoned statement. It shall
not be deemed to
have been filed until the opposition fee has been paid. (Art. 99(1) European Patent
Convention).
|
TECHNICAL FIELD
[0001] 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 and the cement-based materials reinforced
with these fibers.
BACKGROUND ART
[0002] 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.
[0003] 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 impulsive loadings. This energy absorption
attribute of fiber reinforced concrete is often termed "toughness".
[0004] 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.
[0005] 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.
[0006] 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 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.
[0007] 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 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.
DISCLOSURE OF INVENTION
[0008] It is therefore an object of the present invention to relate the fiber geometry to
the properties of both the matrix and fiber materials, with a view to optimizing the
overall composite toughness.
[0009] 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.
[0010] 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 A
o,opt defined by:
where
- k1
- = 2.025 x 10-2,
- σc
- = compressive strength of the cement-based material in MPa,
- k2
- = 3.19 x 10-1,
- σu
- = ultimate tensile strength of the metal in MPa,
- α
- = 6.60 x 10-1,
- εf
- = ductility of the metal in percent, and
- β
- = 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 L
s defined by:
where
- Lf
- = length of the fiber,
- Lm
- = length of the fiber central portion,
and wherein 0.5 L
f < L
m < 0.75 L
f.
[0011] 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.
[0012] Where use is made of a cement-based material having a compressive strength σ
c ranging from about 30 to about 60 MPa, the value of k
1(σ
c)
k2 in equation (1) then ranges from about 6 x 10
-2 to about 7.5 x 10
-2. A preferred value of k
1(σ
c)
k2 which provides an optimum amplitude A
o,opt in the concrete compressive strength range of 30-60 MPa is about 7 x 10
-2.
[0013] The fiber according to the invention preferably has an end angle θ less than 20°,
the angle θ being defined by
The angle θ preferably ranges from about 12° to about 15°. Such a small end angle
θ prevents the fibers from undergoing balling so that there is no problem with mixing.
[0014] 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 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.
[0015] 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
L
f of about 50 mm and a length L
m of about 25 mm. The wavelenth L
s of the sinusoid at each end portion of the fiber is about 12.5 mm.
[0016] Fiber reinforced concrete incorporating the fibers of the invention can be used in
slabs on grade, shotcrete, architectural concrete, precast products, offshore structures,
structures in seismic regions, thin and thick repairs, crash barriers, footings, hydraulic
structures and many other applications.
BRIEF DESCRIPTION OF DRAWINGS
[0017] 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.
MODES FOR CARRYING OUT THE INVENTION
[0018] 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
where the coordinate system is as illustrated in Fig. 1 and A
o is the amplitude of the sinusoid. Also illustrated in Fig. 1 are the length L
f of the fiber 10, the length L
m of the central portion 12 and the length L
s of the end portions 14,14', as well as the end angle θ. The length L
f 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 sinusoid an optimum amplitude A
o,opt as defined in equation (1).
[0019] For example, the optimum amplitudes for the following three steels with different
mechanical properties are given in Table 1, where σ
c = 40 MPa and A
f/P
f = 1.33 x 10
-1 mm:
TABLE 1
Steel Type and Properties (bulk) |
Optimum Amplitude, Ao,opt |
Steel A: type C1018 (σu = 1030 MPa; εf = 0.60%) |
≈ 0.7 mm |
Steel B: Martensite Steel (σu = 1550 MPa; εf = 1%) |
≈ 1.2 mm |
Steel C: HSLA* Steel (σu = 1350 MPa; εf = 3.5%) |
≈ 1.5 mm |
* High Strength Low Aluminum |
[0020] In 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.
[0021] Fibers with optimized geometry at a dosage rate of 40 kg/m
3 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 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
Fiber Designation |
Geometry |
Cross-Section Shape |
Length (mm) |
Size (mm) |
Tensile Strength (MPA) |
Weight (g.) |
Number per kg |
F2 |
Hooked-end |
Circular |
60 |
0.8 diam. |
1115 |
0.263 |
3800 |
F3 |
Twin-cone |
Circular |
62 |
1.0 diam. |
1198 |
0.403 |
2480 |
F4 |
Crimped |
Circular |
60 |
1.0 diam. |
1037 |
0.420 |
2380 |
F5 |
Crimped |
Crescent |
52 |
2.3 x 0.55 |
1050 |
0.393 |
2540 |
[0022] 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 determining the toughness parameters. The results are given in Table 3 and
plotted in Figure 3:
TABLE 3
Post Crack Strength at beam displacement of span/m, PCSm |
Plain Concrete (σc = 40 MPa; Ec = 39 GPa) |
Concrete with F1 Fibers (σc = 43 MPa; Ec = 39 GPa) |
PCS3000 |
0 |
6.3-6.5 MPa |
PCS1500 |
0 |
6.0-6.5 MPa |
PCS600 |
0 |
5.8-6.0 MPa |
PCS400 |
0 |
5.5-5.8 MPa |
PCS300 |
0 |
5.0-5.3 MPa |
PCS200 |
0 |
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 |
I10 |
1.0 |
9.0-9.5 |
I20 |
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 |
[0023] In Table 3, E
c 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.
[0024] The fibers of the inventions even at a low dosage of 40 kg/m
3 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.
[0025] 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.
[0026] 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.
1. A metal fiber (10) for reinforcing cement-based materials, which comprises an elongated,
substantially straight central portion (12) and sinusoid shaped end portions (14,14'),
the sinusoid of each end portion (14,14') having an optimum amplitude A
o,opt defined by:.
where
k1 = 2.025 x 10-2,
σc = compressive strength of the cement-based material in MPa,
k2 = 3.19 x 10-1,
σu = ultimate tensile strength of the metal in MPa,
α = 6.60 x 10-1,
εf = ductility of the metal in percent, and
β = 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 L
s defined by:
where
Lf = length of the fiber,
Lm = length of the central portion,
and wherein 0.5 L
f < L
m < 0.75 L
f.
2. A fiber according to claim 1, wherein the length Lf of the fiber ranges from about 25 to about 60 mm.
3. A fiber according to claim 1, wherein said central portion (12) and said end portions
(14,14') have a uniform rectangular cross-section.
4. A fiber according to claim 3, wherein said central portion (12) and said end portions
(14,14') 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 (12) is about 25 mm.
5. A fiber according to claim 1, wherein said central portion (12) and said end portions
(14,14') have a uniform circular cross-section.
6. A fiber according to claim 1, wherein the cement-based material has a compressive
strength σc ranging from about 30 to about 60 MPa and wherein k1(σc)k2 ranges from about 6 x 10-2 to about 7.5 x 10-2.
7. A fiber according to claim 6, wherein k1(σc)k2 is about 7 x 10-2.
8. A 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. A fiber according to claim 8, wherein said metal is steel.
10. A fiber according to claim 9, wherein said steel is of type C1018 having an ultimate
tensile strength σu of about 1030 MPa and a ductility εf of about 0.60%, and wherein said sinusoid has an optimum amplitude Ao,opt of about 0.7 mm.
11. A fiber according to claim 9, wherein said steel is a martensite steel having an ultimate
tensile strength σu of about 1550 MPa and a ductility εf of about 1%, and wherein said sinusoid has an optimum amplitude Ao,opt of about 1.2 mm.
12. A fiber according to claim 9, wherein said steel is a high strength low aluminum steel
having an ultimate tensile strength σu of about 1350 MPa and a ductility εf of about 3.5%, and wherein said sinusoid has an optimum amplitude Ao,opt of about 1.5 mm.
13. A fiber according to claim 1, wherein said end portions (14,14') each have an end
angle θ below 20°, the angle θ being defined by:
14. A fiber according to claim 13, wherein said angle θ 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 (10), said metal fibers (10) each having an elongated,
substantially straight central portion (12) and sinusoid shaped end portions (14,14')
the sinusoid of each end portion (14,14') having an optimum amplitude A
o,opt defined by:
where
k1 = 2.025 x 10-2,
σc = compressive strength of the cement-based material in MPa,
k2 = 3.19 x 10-1,
σu = ultimate tensile strength of the metal in MPa,
α = 6.60 x 10-1,
εf = ductility of the metal in percent, and
β = 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 L
s defined by:
where
Lf = length of the fiber,
Lm = length of the central portion,
and wherein 0.5 L
f < L
m < 0.75 L
f.
16. A metal fiber reinforced cement-based material according to claim 15, wherein the
length Lf of the fibers (10) range from about 25 to about 60 mm.
17. A metal fiber reinforced cement-based material according to claim 15, wherein said
central portion (12) and said end portions (14,14') have a uniform rectangular cross-section.
18. A metal fiber reinforced cement-based material according to claim 17, wherein said
central portion (12) and said end portions (14,14') have a thickness of about 0.4
mm and a width of about 0.8 mm, and wherein the length Lf of the fibers (10) is about 50 mm and the length Lm of the central portion (12) is about 25 mm.
19. A metal fiber reinforced cement-based material according to claim 15, wherein said
central portion (12) and said end portions (14,14') have a uniform circular cross-section.
20. A metal fiber reinforced cement-based material according to claim 15, wherein the
cement-based material has a compressive strength σc ranging from about 30 to about 60 MPa and wherein k1(σc)k2 ranges from about 6 x 10-2 to about 7.5 x 10-2.
21. A metal fiber reinforced cement-based material according to claim 20, wherein k1(σc)k2 is about 7 x 10-2.
22. A metal fiber reinforced cement-based material according to claim 21, wherein the
cross-sectional area Af and the perimeter Pf of the fibers (10) are such that Af/Pf = 1.33 x 10-1 mm.
23. A metal fiber reinforced cement-based material according to claim 22, wherein said
metal is steel.
24. A metal fiber reinforced cement-based material according to claim 23, wherein said
steel is of type C1018 having an ultimate tensile strength σu of about 1030 MPa and a ductility εf 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 according to claim 23, wherein said
steel is of martensite steel having an ultimate tensile strength σu of about 1550 MPa and a ductility εf 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 according to claim 23, wherein said
steel is a high strength low aluminum steel having an ultimate tensile strength σu of about 1350 MPa and a ductility εf 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 according to claim 15, wherein said
end portions (14,14') each have an end angle θ below 20°, the angle θ being defined
by:
28. A metal fiber reinforced cement-based material according to claim 27, wherein said
angle θ ranges from about 120 to about 15°.
1. Metallfaser (10) zum Verstärken eines Materials auf Zementbasis, welche einen länglichen,
im wesentlichen geraden Mittelabschnitt (12) und sinusförmige Endabschnitte (14, 14')
umfaßt, wobei die Sinusform jedes Endabschnitts (14, 14') eine optimale Amplitude
A
o,opt aufweist, welche definiert ist durch:
wobei
k1 = 2,025 × 10-2,
σc = Druckfestigkeit des Materials auf Zementbasis in MPa,
k2 = 3,19 × 10-1,
σu = Zerreißfestigkeit des Metalls in MPa,
α = 6,60 × 10-1,
εf = Streckbarkeit des Metalls in Prozent, und
β = 3,20 × 10-1,
Af = Querschnittsfläche der Faser in mm2, und
Pf = Umfang der Faser in mm,
wobei die Sinusform ferner eine Wellenlänge L
s aufweist, welche definiert ist durch:
wobei
Lf = Länge der Faser,
Lm = Länge des Mittelabschnitts,
und wobei 0,5 L
f < L
m < 0,75 L
f.
2. Faser nach Anspruch 1, wobei die Länge Lf der Faser in einem Bereich von etwa 25 bis etwa 60 mm liegt.
3. Faser nach Anspruch 1, wobei der Mittelabschnitt (12) und die Endabschnitte (14, 14')
einen einheitlichen rechteckigen Querschnitt aufweisen.
4. Faser nach Anspruch 3, wobei der Mittelabschnitt (12) und die Endabschnitte (14, 14')
eine Dicke von etwa 0,4 mm und eine Breite von etwa 0,8 mm aufweisen, und wobei die
Länge Lf des Mittelabschnitts (12) etwa 25 mm beträgt.
5. Faser nach Anspruch 1, wobei der Mittelabschnitt (12) und die Endabschnitte (14, 14')
einen einheitlichen kreisförmigen Querschnitt aufweisen.
6. Faser nach Anspruch 1, wobei das Material auf Zementbasis eine Druckfestigkeit σc aufweist, welche in einem Bereich von etwa 30 bis etwa 60 MPa liegt, und wobei k1(σc)k2 in einem Bereich von etwa 6 × 10-2 bis etwa 7,5 × 10-2 liegt.
7. Faser nach Anspruch 6, wobei k1(σc)k2 etwa 7 × 10-2 beträgt.
8. Faser nach Anspruch 7, wobei die Querschnittsfläche Af und der Umfang Pf der Faser derart festgelegt sind, daß Af/Pf = 1,33 × 10-1 mm.
9. Faser nach Anspruch 8, wobei das Metall Stahl ist.
10. Faser nach Anspruch 9, wobei der Stahl vom Typ C1018 mit einer Zerreißfestigkeit σu von etwa 1030 MPa und einer Streckbarkeit εf von etwa 0,60% ist, und wobei die Sinusform eine optimale Amplitude Ao,opt von etwa 0,7 mm aufweist.
11. Faser nach Anspruch 9, wobei der Stahl ein Martensitstahl mit einer Zerreißfestigkeit
σu von etwa 1550 MPa und einer Streckbarkeit εf von etwa 1% ist, und wobei die Sinusform eine optimale Amplitude Ao,opt von etwa 1,2 mm aufweist.
12. Faser nach Anspruch 9, wobei der Stahl ein hochfester Stahl mit niedrigem Aluminiumgehalt
mit einer Zerreißfestigkeit σu von etwa 1350 MPa und einer Streckbarkeit εf von etwa 3,5% ist, und wobei die Sinusform eine optimale Amplitude Ao,opt von etwa 1,5 mm aufweist.
13. Faser nach Anspruch 1, wobei die Endabschnitte (14, 14') jeweils einen Endwinkel θ
von unter 20° aufweisen, wobei der Winkel θ definiert ist durch:
14. Faser nach Anspruch 13, wobei der Winkel θ in einem Bereich von etwa 12° bis etwa
15° liegt.
15. Metalltaserverstärktes Material auf Zementbasis, welches ein Material auf Zementbasis
mit einer Beimischung von Metallfasern (10) umfaßt, wobei die Metallfasern (10) jeweils
einen länglichen, im wesentlichen geraden Mittelabschnitt (12) und sinusförmige Endabschnitte
(14, 14') aufweisen, wobei die Sinusform jedes Endabschnitts (14, 14') eine optimale
Amplitude A
o,opt aufweist, welche definiert ist durch:
wobei
k1 = 2,025 × 10-2,
σc = Druckfestigkeit des Materials auf Zementbasis in MPa,
k2 = 3,19 × 10-1,
σu = Zerreißfestigkeit des Metalls in MPa,
α = 6,60 × 10-1,
εf = Streckbarkeit des Metalls in Prozent, und
β = 3,20 × 10-1,
Af = Querschnittsfläche der Faser in mm2, und
Pf = Umfang der Faser in mm,
wobei die Sinusform ferner eine Wellenlänge L
s aufweist, welche definiert ist durch:
wobei
Lf = Länge der Faser,
Lm = Länge des Mittelabschnitts,
und wobei 0,5 L
f < L
m < 0,75 L
f.
16. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 15, wobei die Länge
Lf der Fasern (10) in einem Bereich von etwa 25 bis etwa 60 mm liegt.
17. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 15, wobei der Mittelabschnitt
(12) und die Endabschnitte (14, 14') einen einheitlichen rechteckigen Querschnitt
aufweisen.
18. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 17, wobei der Mittelabschnitt
(12) und die Endabschnitte (14, 14') eine Dicke von etwa 0,4 mm und eine Breite von
etwa 0,8 mm aufweisen, und wobei die Länge Lf der Fasern (10) etwa 50 mm beträgt und die Länge Lm des Mittelabschnitts (12) etwa 25 mm beträgt.
19. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 15, wobei der Mittelabschnitt
(12) und die Endabschnitte (14, 14') einen einheitlichen kreisförmigen Querschnitt
aufweisen.
20. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 15, wobei das Material
auf Zementbasis eine Druckfestigkeit σc aufweist, welche in einem Bereich von etwa 30 bis etwa 60 MPa liegt, und wobei k1(σc)k2 in einem Bereich von etwa 6 × 10-2 bis etwa 7,5 × 10-2 liegt.
21. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 20, wobei k1(σc)k2 etwa 7 × 10-2 beträgt.
22. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 21, wobei die Querschnittsfläche
Af und der Umfang Pf der Fasern (10) derart festgelegt sind, daß Af/Pf = 1,33 x 10-1 mm.
23. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 22, wobei das Metall
Stahl ist.
24. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 23, wobei der Stahl
vom Typ C1018 mit einer Zerreißfestigkeit σu von etwa 1030 MPa und einer Streckbarkeit εf von etwa 0,60% ist, und wobei die Sinusform eine optimale Amplitude Ao,opt von etwa 0,7 mm aufweist.
25. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 23, wobei der Stahl
aus Martensitstahl mit einer Zerreißfestigkeit σu von etwa 1550 MPa und einer Streckbarkeit εf von etwa 1% besteht, und wobei die Sinusform eine optimale Amplitude Ao,opt von etwa 1,2 mm aufweist.
26. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 23, wobei der Stahl
ein hochfester Stahl mit niedrigem Aluminiumgehalt mit einer Zerreißfestigkeit σu von etwa 1350 MPa und einer Streckbarkeit εf von etwa 3,5% ist, und wobei die Sinusform eine optimale Amplitude Ao,opt von etwa 1,5 mm aufweist.
27. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 15, wobei die Endabschnitte
(14, 14') jeweils einen Endwinkel θ von unter 20° aufweisen, wobei der Winkel θ definiert
ist durch:
28. Metallfaserverstärktes Material auf Zementbasis nach Anspruch 27, wobei der Winkel
θ in einem Bereich von etwa 12° bis etwa 15° liegt.
1. Fibre métallique (10) pour renforcer les matériaux à base de ciment, qui comprend
une partie centrale allongée sensiblement droite (12) et des parties d'extrémité (14,
14') en forme de sinusoïdes, la sinusoïde de chaque partie d'extrémité (14, 14') ayant
une amplitude optimum A
o,opt définie par :
où
k1 = 2,025 × 10-2,
σc = résistance à la compression du matériau à base de ciment en MPa,
k2 = 3,19 × 10-1,
σu = charge limite de rupture du métal en MPa,
α = 6,60 × 10-1,
εf = ductilité du métal en pourcents, et
β = 3,20 × 10-1,
Af = aire de la section de la fibre en mm2, et
Pf = périmètre de la fibre en mm,
ladite sinusoïde ayant en outre une longueur d'onde L
s définie par :
où
Lf = longueur de la fibre,
Lm = longueur de la partie centrale,
et où 0,5 L
f < L
m < 0,75 L
f.
2. Fibre selon la revendication 1, dans laquelle la longueur Lf de la fibre est comprise dans l'intervalle allant d'environ 25 mm à environ 60 mm.
3. Fibre selon la revendication 1, dans laquelle ladite partie centrale (12) et lesdites
parties d'extrémité (14, 14') sont de section rectangulaire uniforme.
4. Fibre selon la revendication 3, dans laquelle ladite partie centrale (12) et lesdites
parties d'extrémité (14, 14') ont une épaisseur d'environ 0,4 mm et une largeur d'environ
0,8 mm, et dans laquelle la longueur Lf de la fibre est d'environ 50 mm et la longueur Lm de la partie centrale (12) est d'environ 25 mm.
5. Fibre selon la revendication 1, dans laquelle ladite partie centrale (12) et lesdites
parties d'extrémité (14, 14') sont de section circulaire uniforme.
6. Fibre selon la revendication 1, dans laquelle le matériau à base de ciment présente
une résistance à la compression σc comprise dans l'intervalle allant d'environ 30 à environ 60 MPa et dans laquelle
k1(αc)k2 est compris dans l'intervalle allant d'environ 6 × 10-2 à environ 7,5 × 10-2.
7. Fibre selon la revendication 6, dans laquelle k1(σc)k2 vaut environ 7 × 10-2.
8. Fibre selon la revendication 7, dans laquelle l'aire Af et le périmètre Pf de la fibre sont tels que Af/Pf = 1,33 × 10-1 mm.
9. Fibre selon la revendication 8, dans laquelle ledit métal est de l'acier.
10. Fibre selon la revendication 9, dans laquelle ledit acier est de type C1018 présentant
une charge limite de rupture σu d'environ 1030 MPa et une ductilité εf d'environ 0,60 %, et dans laquelle ladite sinusoïde a une amplitude optimum Ao,opt d'environ 0,7 mm.
11. Fibre selon la revendication 9, dans laquelle ledit acier est un acier martensitique
présentant une charge limite de rupture σu d'environ 1550 MPa et une ductilité εf d'environ 1 %, et dans laquelle ladite sinusoïde a une amplitude optimum Ao,opt d'environ 1,2 mm.
12. Fibre selon la revendication 9, dans laquelle ledit acier est un acier à haute résistance
et à basse teneur en aluminium présentant une charge limite de rupture σu d'environ 1350 MPa et une ductilité εf d'environ 3,5 %, et dans laquelle ladite sinusoïde a une amplitude optimum Ao,opt d'environ 1,5 mm.
13. Fibre selon la revendication 1, dans laquelle lesdites parties d'extrémité (14, 14')
ont chacune un angle d'extrémité θ inférieur à 20°, l'angle θ étant défini par :
14. Fibre selon la revendication 13, dans laquelle ledit angle θ est compris dans l'intervalle
allant d'environ 12° à environ 15°.
15. Matériau à base de ciment renforcé par des fibres métalliques, qui comprend un matériau
à base de ciment mélangé avec des fibres métalliques (10), lesdites fibres métalliques
(10) comprenant chacune une partie centrale allongée sensiblement droite (12) et des
parties d'extrémité (14, 14') en forme de sinusoïdes, la sinusoïde de chaque partie
d'extrémité (14, 14') ayant une amplitude optimum A
o,opt définie par :
où
k1 = 2,025 × 10-2,
σc = résistance à la compression du matériau à base de ciment en MPa,
k2 = 3,19 × 10-1,
σu = charge limite de rupture du métal en MPa,
α = 6,60 × 10-1,
εf = ductilité du métal en pourcents, et
β = 3,20 × 10-1,
Af = aire de la section de la fibre en mm2, et
P f = périmètre de la fibre en mm,
ladite sinusoïde ayant en outre une longueur d'onde L
s définie par :
où
Lf = longueur de la fibre,
Lm = longueur de la partie centrale,
et où 0,5 L
f < L
m < 0,75 L
f.
16. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
15, dans lequel la longueur Lf des fibres (10) est comprise dans l'intervalle allant d'environ 25 à environ 60 mm.
17. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
15, dans lequel ladite partie centrale (12) et lesdites parties d'extrémité (14, 14')
sont de section rectangulaire uniforme.
18. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
17, dans lequel ladite partie centrale (12) et lesdites parties d'extrémité (14, 14')
ont une épaisseur d'environ 0,4 mm et une largeur d'environ 0,8 mm, et dans lequel
la longueur Lf des fibres (10) est d'environ 50 mm et la longueur Lm de la partie centrale (12) est d'environ 25 mm.
19. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
15, dans lequel ladite partie centrale (12) et lesdites parties d'extrémité (14, 14')
sont de section circulaire uniforme.
20. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
15, dans lequel le matériau à base de ciment présente une résistance à la compression
σc comprise dans l'intervalle allant d'environ 30 à environ 60 MPa et dans lequel k1(σc)k2 est compris dans l'intervalle allant d'environ 6 × 10-2 à environ 7,5 × 10-2.
21. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
20, dans lequel k1(σc)k2 vaut environ 7 × 10-2.
22. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
21, dans lequel l'aire Af et le périmètre Pf des fibres sont tels que Af/Pf = 1,33 × 10-1 mm.
23. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
21, dans lequel ledit métal est de l'acier.
24. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
23, dans lequel ledit acier est de type C1018 présentant une charge limite de rupture
σu d'environ 1030 MPa et une ductilité εf d'environ 0,60 %, et dans lequel ladite sinusoïde a une amplitude optimum Ao,opt d'environ 0,7 mm.
25. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
23, dans lequel ledit acier est un acier martensitique présentant une charge limite
de rupture σu d'environ 1550 MPa et une ductilité εf d'environ 1 %, et dans lequel ladite sinusoïde a une amplitude optimum Ao,opt d'environ 1,2 mm.
26. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
23, dans lequel ledit acier est un acier à haute résistance et à basse teneur en aluminium
présentant une charge limite de rupture σu d'environ 1350 MPa et une ductilité εf d'environ 3,5 %, et dans laquelle ladite sinusoïde a une amplitude optimum Ao,opt d'environ 1,5 mm.
27. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
15, dans lequel lesdites parties d'extrémité (14, 14') ont chacune un angle d'extrémité
θ inférieur à 20°, l'angle θ étant défini par :
28. Matériau à base de ciment renforcé par des fibres métalliques selon la revendication
27, dans lequel ledit angle θ est compris dans l'intervalle allant d'environ 12° à
environ 15°.