DE69517668T2 - METAL FIBER WITH OPTIMIZED GEOMETRY FOR REINFORCING CEMENT MATERIALS - Google Patents

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

FIELD OF TECHNOLOGY

The present invention relates to improvements in the field of fiber-reinforced cement-based materials. More specifically, the invention relates to a metal fiber with an optimized geometry for reinforcing cement-based materials and to the cement-based material reinforced with these fibers.

STATE OF THE ART

All cement-based materials are weak in tensile stress. Furthermore, these materials have very low elongation, which places them in a brittle class with other brittle materials such as glass and ceramics. It is well known that concrete and other Portland cement-based materials can be reinforced with short, randomly distributed steel fibers to improve their mechanical properties. It is also known that for any improvement in tensile strength, the fiber volume fraction must exceed a certain critical value.

After matrix rupture, fibers form stress transfer bridges and hold matrix cracks together so that further crack propagation causes the fibers to undergo pull-out from the matrix. Since pull-out processes are energy-intensive, steel fiber reinforced concrete exhibits a stable load-deflection behavior in the region after matrix rupture, placing these materials in a class of pseudoplastic or tough materials such as steel and polymers. Therefore, while a simple unreinforced matrix fails in a brittle manner when tensile stresses occur, the tensile fibers in fiber reinforced concrete continue to accommodate stresses after matrix rupture, resulting in helps to maintain structural integrity and cohesion in the material. Furthermore, fibers, when suitably designed, undergo pull-out processes and the friction work required for pull-out results in a significantly improved energy absorption capacity. Therefore, fiber-reinforced concrete exhibits better behavior not only under static and quasi-static applied loads, but also under fatigue, impact and shock loads. This energy absorption property of fiber-reinforced concrete is often referred to as "toughness."

Concrete is a material that softens during cold deformation and forms microcracks. In steel fiber-reinforced cement-based composite materials, a fiber bridging effect begins even before the perceived macrocracking of the matrix occurs. The critical fiber volume fraction or the magnitude of the increase in strength at a certain fiber volume fraction therefore depends on the geometry of the fiber. Furthermore, the pull-out resistance of an individual fiber from the cementitious matrix around it depends on the geometry, which in turn determines the shape of the load-deflection diagram after matrix cracking and the achievable improvement in the toughness of a composite material.

Improving the strength of the composite at a given fiber volume fraction, or in other words reducing the required critical fiber volume fraction, is possible by over-deforming the fiber. However, this may lead to too good fiber anchoring in the matrix and causes a brittle cracking pattern in the area after matrix rupture. Toughness reductions in the case of over-deformed fibers can therefore be significant. The other possible way is to reduce the number of fibers in the composite by reducing the size of the This solution is known to cause extreme difficulties in terms of concrete mixing and workability, and uniform fiber distribution often becomes impossible because the fibers tend to clump together, resulting in a highly uneven distribution.

In U.S. Patent No. 4,585,487, which proposes a concrete reinforcing fiber with uniform undulating corrugations distributed along its entire length, the only fiber performance characteristic considered for optimization is fiber pullout. The same is true with respect to Canadian Patents No. 926,146 and No. 1,023,395, which disclose concrete reinforcing fibers having a straight center section with shaped ends. Some fibers have ends that are thicker; others have ends that are hooked. All of these features are intended to improve the anchoring of the fiber in the concrete.

For fibers used as reinforcement randomly distributed in a moldable concrete matrix, the property of interest is the overall toughness of the composite material. The toughness of the composite material, although it depends on the pull-out resistance of the fibers, cannot be quantitatively derived from the results of an ideal fiber pull-out test in which the fiber is aligned with respect to the load direction, since in a real composite material, once the brittle cementitious matrix ruptures, the fibers are not only embedded at different depths on either side of the matrix, but also inclined at different angles with respect to the load direction. Furthermore, fibers pulled out as bundles exhibit very different behaviour compared to a single fibre, which is mainly due to fibre-fibre interaction. Furthermore, in a real composite material, the contribution from the matrix as fibres are pulled out (as assumed in an ideal pull-out test) is not completely absent due to aggregate entanglement, void tearing and crack zones. Therefore, the idealised single fibre pull-out test, with the fibre oriented with respect to the load direction, is not a realistic representation of what happens in a real composite material. No attempt has been made to date to reasonably optimise the fibre geometry with respect to the properties of the matrix material, i.e. concrete, and the fibre material, i.e. steel or other metal.

DISCLOSURE OF THE INVENTION

It is therefore an object of the present invention to combine the fiber geometry with the properties of both the matrix and the fiber material with a view to optimizing the overall toughness of the composite material.

It is a further object of the invention to provide a metal fiber with an optimized geometry for reinforcing cement-based materials such that the fiber fully exploits matrix anchorage without tearing in the region before macrocracking of the matrix and is pulled out with the maximum pull-out resistance in the region after macrocracking of the matrix, giving the highest possible toughness.

In accordance with the present invention, there is therefore provided a metal fiber for reinforcing cement-based materials, which has an elongated, substantially straight central portion and sinusoidal end sections. The sinusoidal shape at each end section has an optimal amplitude Ao,opt, which is defined by:

Ao,opt = [k1 (σc)k2][σuαεfβ][Af/Pf] (1)

where

k&sub1; = 2.025 x 10⁻²,

&sigma;c = compressive strength of the cement-based material in MPa,

k&sub2; = 3.19 x 10⁻¹,

σu = tensile strength of the metal in MPa,

&alpha; = 6.60 x 10⁻¹,

εf = ductility of the metal in percent, and

&beta; = 3.20 x 10⁻¹,

Af = cross-sectional area of the fibre in mm², and

Pf = circumference of the fiber in mm.

The sinusoidal shape also has a wavelength Ls, which is defined by:

Ls = (Lf - Lm)/2 (2)

where

Lf = length of the fibre,

Lm = length of the middle section,

and where 0.5 Lf < Lm < 0.75 Lf.

As can be seen from equation (1), both the tensile strength and ductility of the fiber material and the compressive strength of the cement-based material are important factors in defining the optimal amplitude. The equation further takes into account the cross-sectional area and circumference of the fiber. It is therefore possible to design the fiber geometry according to the properties of the chosen fiber and matrix materials and ultimately the toughness of the composite material, which is desired in a real structure.

Furthermore, where a cement-based material having a compressive strength σc ranging from about 30 to about 60 MPa is used, the value of k1(σc)k2 in equation (1) ranges from about 6 × 10⁻² to about 7.5 × 10⁻². A preferred value of k1(σc)k2 which provides an optimum amplitude Ao,opt in the concrete compressive strength range of 30-60 MPa is about 7 × 10⁻².

The fiber according to the invention preferably has an end angle θ which is less than 20°, the angle θ being defined by

? = tan⁻¹ 4(Ao,opt) / Ls. (3)

The angle θ preferably ranges from about 12º to about 15º. Such a small final angle θ prevents the fibers from undergoing agglomeration, so that there is no problem in mixing.

The fibers of the invention which have sinusoids only at the end portions provide better reinforcement than those which have sinusoids along the entire length thereof, as in the case of U.S. Patent No. 4,585,487. In a crack where fibers form stress transfer bridges and are subjected to pull-out forces, those with deformations over the entire length transfer the entire pull-out force immediately through the anchorage back to the matrix. In the case of fibers which are deformed only at the extreme ends, the stresses are slowly transferred from the crack surface to the interior of the matrix, with the main Force transfer occurs only at the extreme ends. Such gradual transfer of stresses avoids possible fracture and splitting of the matrix at the fracture surface, which is usually observed in fibers deformed along their entire length. It is due to the fracture and splitting of the matrix that fibers, when in a group, adversely affect each other's ability to reinforce and the overall toughness of the composite material is seriously reduced. Due to the fact that the optimum amplitude of the sinusoidal end portions of the fibers of the invention is defined as a function of both the tensile strength and stretchability of the fiber material and the compressive strength of the matrix material, such amplitude is generally less than 5% of the fiber length. The low fiber amplitude results in a more gradual transfer of stresses back to the matrix and therefore less fracture and splitting of the matrix around the fibers.

A particularly preferred 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 wavelength Ls of the sinusoid at each end portion of the fiber is about 12.5 mm.

A fiber-reinforced concrete containing the fibers of the invention can be used in non-basement floor slabs, shotcrete, exposed concrete, prefabricated products, coastal structures, structures in earthquake zones, major and minor repairs, guard rails, foundations, hydraulic structures and many other applications.

SHORT DESCRIPTION OF THE DRAWING

Further features and advantages of the invention will become more apparent from the following description of preferred embodiments, with reference to the accompanying drawings, in which:

Fig. 1 is a side view of a steel fiber according to the invention;

Fig. 2 is a load-deflection diagram comparing the toughness of concrete reinforced with the fiber shown in Fig. 1 with that of concrete reinforced with conventional fibers; and

Fig. 3 is a graph showing the relationship between the strength after failure and the beam center deflection, expressed as a fraction of the span, for the same fibers.

MODES FOR CARRYING OUT THE INVENTION

As shown in Fig. 1, the illustrated steel fiber, which is generally designated by reference numeral 10, comprises an elongated, substantially straight central portion 12 with sinusoidal end portions 14 and 14'. The sinusoidal shape at each end portion is defined by

where the coordinate system is constructed as shown in Fig. 1 and Ao is the amplitude of the sinusoid. Also shown in Fig. 1 are the length Lf of the fiber 10, the length Lm of the middle section 12 and the length Ls of the end sections 14, 14' as well as the end angle θ. The length Lf of the fiber 10 can vary from about 25 to about 60 mm. As explained in the present document, the fiber geometry is optimized by giving the sinusoid an optimal amplitude Ao,opt as defined in equation (1).

For example, the optimal amplitudes for the following three steels with different mechanical properties are given in Table 1, where σc = 40 MPa and Af/Pf = 1.33 10-1 mm:

TABLE 1 Steel type and properties (solid base material) Optimal amplitude, Ao,opt

Steel A: Type C1018 (εu = 1030 MPa; εf = 0.60%) 0.7 mm

Steel B: Martensitic steel (σu = 1550 MPa; εf = 1%) 1.2 mm

Steel C: HSLA steel σu = 1350 MPa; εf = 3.5%) 1.5 mm

* high strength with low aluminium content

In the embodiment shown in Fig. 1, the fiber 10 has a uniform rectangular cross-section. Such a fiber can also have a circular cross-section.

Fibers with optimized geometry at a dosage of 40 kg/m³ were used to reinforce concrete matrices with an unreinforced compressive strength of 40 MPa. Beams made from the fiber-reinforced concrete were tested for third-point deflection together with their unreinforced accompanying materials. Beam displacements were measured using a frame around the specimen such that the disturbance component of load point displacement due to the subsidence of bearings was automatically eliminated. The resulting load-deflection diagrams are presented in Fig. 2, comparing the toughness of concrete reinforced with the fibers of the invention (F1) with that of concrete reinforced with conventional fibers (F2 to F5). The conventional fibers tested for comparison purposes were the following: TABLE 2

The graphs were analyzed using both conventional techniques (ASTM - C1018; JSCE SF-4) and the PCS technique described by J.-F. Trottier, "Toughness of Steel Reinforced Cement-Based Composites", PhD thesis, Laval University, 1993, with a view to determining the toughness parameters. The results are given in Table 3 and shown in Fig. 3: TABLE 3

In Table 3, Ec is the elastic modulus of concrete according to ASTM C-469. The JSCE-SF-4 technique takes the entire area (elastic and plastic) under the curve up to a Deflection of a span/150 and converts it into an equivalent strength after failure.

The fibers of the invention, even at a low dosage of 40 kg/m³, lead to a strength increase in the system, as can be seen from the increase in load-bearing capacity in the simple, unreinforced matrix. Furthermore, the composite material is able to absorb approximately the same level of stress after matrix rupture as at matrix rupture, and thus a very high toughness is derived. The composite material behaves almost in an elastoplastic manner.

A slight increase (about 7%) in the compressive strength of concrete as a result of fiber addition indicates that appropriate fiber distribution and mix compaction have been achieved.

As can also be seen from Figs. 2 and 3, the inventive fiber with optimized geometry performs superiorly to existing commercial fibers and provides higher flexural toughness. It is believed that the fiber geometry fully exploits the potential of steel as well as that of the cement matrix to produce an optimized composite material.

Claims (28)

1. A metal fiber (10) for reinforcing a cement-based material, comprising an elongated, substantially straight central portion (12) and sinusoidal end portions (14, 14'), the sinusoidal shape of each end portion (14, 14') having an optimal amplitude Ao,opt defined by: Ao,opt = [k1 (σc)k2][σuαεfβ][Af/Pf] where k&sub1; = 2.025 x 10⁻², &sigma;c = compressive strength of the cement-based material in MPa, k&sub2; = 3.19 x 10⁻¹, σu = tensile strength of the metal in MPa, &alpha; = 6.60 x 10⁻¹, εf = ductility of the metal in percent, and &beta; = 3.20 x 10⁻¹, Af = cross-sectional area of the fibre in mm², and Pf = circumference of the fibre in mm, wherein the sinusoidal shape further has a wavelength Ls which is defined by: Ls = (Lf - Lm)/2 where Lf = length of the fibre, Ch = length of the middle section, and where 0.5 Lt < Ch < 0.75 Lf. 2. The fiber of claim 1, wherein the length Lf of the fiber is in a range of about 25 to about 60 mm. 3. Fiber according to claim 1, wherein the middle section (12) and the end sections (14, 14') have a uniform rectangular cross-section. 4. Fiber according to claim 3, wherein the central portion (12) and the 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 central portion (12) is about 25 mm. 5. Fiber according to claim 1, wherein the central portion (12) and the end portions (14, 14') have a uniform circular cross-section. 6. The fiber of claim 1, wherein the cement-based material has a compressive strength σc ranging from about 30 to about 60 MPa, and k1(σc)k2 ranging 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 circumference Pf of the fiber are set such that Af/Pf = 1.33 x 10-1 mm. 9. The fiber of claim 8, wherein the metal is steel. 10. The fiber of claim 9, wherein the steel is of type C1018 with a tensile strength σu of about 1030 MPa and a ductility εf of about 0.60%, and wherein the sinusoidal shape has an optimal amplitude Ao,opt of about 0.7 mm. 11. Fiber according to claim 9, wherein the steel is a martensitic steel having a tensile strength σu of about 1550 MPa and a stretchability εf of about 1%, and wherein the sinusoidal shape has an optimal amplitude Ao,opt of about 1.2 mm. 12. The fiber of claim 9, wherein the steel is a high strength, low aluminum content steel having a tensile strength σu of about 1350 MPa and a ductility εf of about 3.5%, and wherein the sinusoidal shape has an optimal amplitude Ao,opt of about 1.5 mm. 13. Fiber according to claim 1, wherein the end sections (14, 14') each have an end angle θ of less than 20°, the angle θ being defined by: ? = tan-14(Ao,opt) / Ls. 14. The fiber of claim 13, wherein the angle θ is in a range of about 12° to about 15°. 15. A cement-based metal fiber reinforced material comprising a cement-based material with an admixture of metal fibers (10), the metal fibers (10) each having an elongated, substantially straight central portion (12) and sinusoidal end portions (14, 14'), the sinusoidal shape of each end portion (14, 14') having an optimal amplitude Ao,opt which is defined by: Ao,opt = [k1 (σc)k2][σuαεfβ][Af/Pf] where k&sub1; = 2.025 x 10⁻², &sigma;c = compressive strength of the cement-based material in MPa, k&sub2; = 3.19 x 10⁻¹, σu = tensile strength of the metal in MPa, &alpha; = 6.60 x 10⁻¹, εf = ductility of the metal in percent, and &beta; = 3.20 x 10⁻¹, Af = cross-sectional area of the fibre in mm², and Pf = circumference of the fibre in mm, wherein the sinusoidal shape further has a wavelength Ls which is defined by: Ls = (Lf - Lm)/2 where Lf = length of the fibre, Lm = length of the middle section, and where 0.5 Lf < Lm < 0.75 Lf. 16. A cement-based metal fiber reinforced material according to claim 15, wherein the length Lf of the fibers (10) is in a range of about 25 to about 60 mm. 17. A cement-based metal fiber reinforced material according to claim 15, wherein the central portion (12) and the end portions (14, 14') have a uniform rectangular cross-section. 18. A cement-based metal fiber reinforced material according to claim 17, wherein the central portion (12) and the 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 cement-based metal fiber reinforced material according to claim 15, wherein the central portion (12) and the End sections (14, 14') have a uniform circular cross-section. 20. The metal fiber reinforced cement-based material of claim 15, wherein the cement-based material has a compressive strength σc which is in a range of about 30 to about 60 MPa, and wherein k₁(σc)k2 is in a range of about 6 x 10⁻² to about 7.5 x 10⁻². 21. A cement-based metal fiber reinforced material according to claim 20, wherein k₁(σc)k2 is about 7 x 10⁻². 22. A cement-based metal fiber reinforced material according to claim 21, wherein the cross-sectional area Af and the perimeter Pf of the fibers (10) are set such that Af/Pf = 1.33 x 10-1 mm. 23. A cement-based metal fiber reinforced material according to claim 22, wherein the metal is steel. 24. A cement-based metal fiber reinforced material according to claim 23, wherein the steel is of type C1018 with a tensile strength σu of about 1030 MPa and a ductility εf of about 0.60%, and wherein the sinusoidal shape has an optimal amplitude Ao,opt of about 0.7 mm. 25. A cement-based metal fiber reinforced material according to claim 23, wherein the steel is made of martensitic steel having a tensile strength σu of about 1550 MPa and a ductility εf of about 1%, and wherein the sinusoidal shape has an optimal amplitude Ao,opt of about 1.2 mm. 26. A cement-based metal fiber reinforced material according to claim 23, wherein the steel is a high strength steel having low aluminium content with a tensile strength % of about 1350 MPa and a ductility εf of about 3.5%, and wherein the sinusoidal shape has an optimum amplitude Ao,opt of about 1.5 mm. 27. A cement-based metal fiber reinforced material according to claim 15, wherein the end portions (14, 14') each have an end angle θ of less than 20°, the angle θ being defined by: ? = tan-14(Ao,opt) / Ls. 28. The cement-based metal fiber reinforced material of claim 27, wherein the angle θ is in a range of about 12° to about 15°.