EP0725871B1

EP0725871B1 - Metal fiber with optimized geometry for reinforcing cement-based materials

Info

Publication number: EP0725871B1
Application number: EP95915725A
Authority: EP
Inventors: Nemkumar Banthia; Madhavaro Krishnadev
Original assignee: Universite Laval
Current assignee: Universite Laval
Priority date: 1994-08-31
Filing date: 1995-04-21
Publication date: 2000-06-28
Anticipated expiration: 2015-04-21
Also published as: KR100353732B1; MX9601504A; DE69517668T2; DE69517668D1; WO1996006995A1; ATE194198T1; AU688031B2; AU2251795A; CA2131212C; DK0725871T3; ES2151059T3; KR960706001A; MX192955B; EP0725871A1

Abstract

A metal fiber (10) for reinforcing cement-based materials comprises an elongated, substantially straight central portion (12) and sinusoid shaped end portions (14, 14'). The sinusoid at each end portion (14, 14') has an optimum amplitude Ao,opt defined by: Ao,opt = [k1( sigma c)<k>2] [ sigma u< alpha > epsilon f< beta >] [Af/Pf], where k1 = 2.025 x 10<-2>, 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<2>, 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.

Description

TECHNICAL FIELD

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

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 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 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 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

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.
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 A_o,opt defined by: Ao,opt = [k1(σc)k 2] [σu α εf β] [Af/Pf] where

k₁: = 2.025 x 10^-2,
σ_c: = compressive strength of the cement-based material in MPa,
k₂: = 3.19 x 10^-1,
σ_u: = ultimate tensile strength of the metal in MPa,
α: = 6.60 x 10^-1,
ε_f: = ductility of the metal in percent, and
β: = 3.20 x 10^-1,
A_f: = cross-sectional area of the fiber in mm², and
P_f: = perimeter of the fiber in mm.

_s

Ls = (Lf - Lm)/2

L_f: = length of the fiber,
L_m: = length of the fiber central portion,

_f

_m

_f

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 σ_c ranging from about 30 to about 60 MPa, the value of k₁(σ_c)^k ₂ in equation (1) then ranges from about 6 x 10^-2 to about 7.5 x 10^-2. A preferred value of k₁(σ_c)^k ₂ which provides an optimum amplitude A_o,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  = tan-1 4(Ao,opt ) 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 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 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.
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

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

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 2πχ Ls 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 . 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).

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:

Steel Type and Properties (bulk)	Optimum Amplitude, A_o,opt
Steel A: type C1018 (σ_u = 1030 MPa; ε_f = 0.60%)	≈ 0.7 mm
Steel B: Martensite Steel (σ_u = 1550 MPa; ε_f = 1%)	≈ 1.2 mm
Steel C: HSLA Steel (σ_u = 1350 MPa; ε_f = 3.5%)	≈ 1.5 mm

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.

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 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:

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

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:

Post Crack Strength at beam displacement of span/m, PCS_m	Plain Concrete (σ_c = 40 MPa; E_c = 39 GPa)	Concrete with F1 Fibers (σ_c = 43 MPa; E_c = 39 GPa)
PCS ₃₀₀₀	0	6.3-6.5 MPa
PCS
₁₅₀₀	0	6.0-6.5 MPa
PCS
₆₀₀	0	5.8-6.0 MPa
PCS
₄₀₀	0	5.5-5.8 MPa
PCS
₃₀₀	0	5.0-5.3 MPa
PCS
₂₀₀	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

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.
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.

Claims

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:. Ao,opt = [k1(σc)k 2] [σu α εf β] [Af/Pf] where

k₁

= 2.025 x 10^-2,

σ_c

= compressive strength of the cement-based material in MPa,

k₂

= 3.19 x 10^-1,

σ_u

= ultimate tensile strength of the metal in MPa,

α

= 6.60 x 10^-1,

ε_f

= ductility of the metal in percent, and

β

= 3.20 x 10^-1,

A_f

= cross-sectional area of the fiber in mm², and

P_f

= perimeter of the fiber in mm,

said sinusoid further having a wavelength L_s defined by: Ls = (Lf - Lm)/2 where

L_f

= length of the fiber,

L_m

= length of the central portion,

and wherein 0.5 L_f < L_m < 0.75 L_f.
A fiber according to claim 1, wherein the length L_f of the fiber ranges from about 25 to about 60 mm.
A fiber according to claim 1, wherein said central portion (12) and said end portions (14,14') have a uniform rectangular cross-section.
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 L_f of the fiber is about 50 mm and the length L_m of the central portion (12) is about 25 mm.
A fiber according to claim 1, wherein said central portion (12) and said end portions (14,14') have a uniform circular cross-section.
A fiber according to claim 1, wherein the cement-based material has a compressive strength σ_c ranging from about 30 to about 60 MPa and wherein k₁(σ_c)^k ₂ ranges from about 6 x 10^-2 to about 7.5 x 10^-2.
A fiber according to claim 6, wherein k₁(σ_c)^k ₂ is about 7 x 10^-2.
A fiber according to claim 7, wherein the cross-sectional area A_f and the perimeter P_f of the fiber are such that A_f/P_f = 1.33 x 10^-1 mm.
A fiber according to claim 8, wherein said metal is steel.
A fiber according to claim 9, wherein said steel is of type C1018 having an ultimate tensile strength σ_u of about 1030 MPa and a ductility ε_f of about 0.60%, and wherein said sinusoid has an optimum amplitude A_o,opt of about 0.7 mm.
A fiber according to claim 9, wherein said steel is a martensite steel having an ultimate tensile strength σ_u of about 1550 MPa and a ductility ε_f of about 1%, and wherein said sinusoid has an optimum amplitude A_o,opt of about 1.2 mm.
A fiber according to claim 9, wherein said steel is a high strength low aluminum steel having an ultimate tensile strength σ_u of about 1350 MPa and a ductility ε_f of about 3.5%, and wherein said sinusoid has an optimum amplitude A_o,opt of about 1.5 mm.
A fiber according to claim 1, wherein said end portions (14,14') each have an end angle  below 20°, the angle  being defined by:  = tan-1 4(Ao,opt ) Ls .
A fiber according to claim 13, wherein said angle  ranges from about 12° to about 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: Ao,opt = [k1(σc)k 2] [σu α εf β] [Af/Pf] where

k₁

= 2.025 x 10^-2,

σ_c

= compressive strength of the cement-based material in MPa,

k₂

= 3.19 x 10^-1,

σ_u

= ultimate tensile strength of the metal in MPa,

α

= 6.60 x 10^-1,

ε_f

= ductility of the metal in percent, and

β

= 3.20 x 10^-1,

A_f

= cross-sectional area of the fiber in mm², and

P_f

= perimeter of the fiber in mm,

said sinusoid further having a wavelength L_s defined by: Ls = (Lf - Lm)/2 where

L_f

= length of the fiber,

L_m

= length of the central portion,

and wherein 0.5 L_f < L_m < 0.75 L_f.
A metal fiber reinforced cement-based material according to claim 15, wherein the length L_f of the fibers (10) range from about 25 to about 60 mm.
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.
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 L_f of the fibers (10) is about 50 mm and the length L_m of the central portion (12) is about 25 mm.
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.
A metal fiber reinforced cement-based material according to claim 15, wherein the cement-based material has a compressive strength σ_c ranging from about 30 to about 60 MPa and wherein k₁(σ_c)^k ₂ ranges from about 6 x 10^-2 to about 7.5 x 10^-2.
A metal fiber reinforced cement-based material according to claim 20, wherein k₁(σ_c)^k ₂ is about 7 x 10^-2.
A metal fiber reinforced cement-based material according to claim 21, wherein the cross-sectional area A_f and the perimeter P_f of the fibers (10) are such that A_f/P_f = 1.33 x 10^-1 mm.
A metal fiber reinforced cement-based material according to claim 22, wherein said metal is steel.
A metal fiber reinforced cement-based material according to claim 23, wherein said steel is of type C1018 having an ultimate tensile strength σ_u of about 1030 MPa and a ductility ε_f of about 0.60%, and wherein said sinusoid has an optimum amplitude A_o,opt of about 0.7 mm.
A metal fiber reinforced cement-based material according to claim 23, wherein said steel is of martensite steel having an ultimate tensile strength σ_u of about 1550 MPa and a ductility ε_f of about 1%, and wherein said sinusoid has an optimum amplitude A_o,opt of about 1.2 mm.
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 σ_u of about 1350 MPa and a ductility ε_f of about 3.5%, and wherein said sinusoid has an optimum amplitude A_o,opt of about 1.5 mm.
A metal fiber reinforced cement-based material according to claim 15, wherein said end portions (14,14') each have an end angle  below 20°, the angle  being defined by:  = tan-1 4(Ao,opt ) Ls .
A metal fiber reinforced cement-based material according to claim 27, wherein said angle  ranges from about 120 to about 15°.