Two-layer multi-strand cables having very low, low and medium modulus

Abstract

A two-layer multi-strand cord (60) has a modulus EC such that 50 GPa≤EC≤160 GPa. The cord comprises: (a) an internal layer (CI) of the cord made up of J>1 internal strands (TI) wound in a helix having a modulus EI, each internal strand (TI) comprising: an internal layer (C1) made up of Q≥1 internal threads (F1), and an external layer (C2) made up of N>1 external threads (F2) wound around the internal layer (C1), and (b) an external layer (CE) of the cord made up of L>1 external strands (TE) wound around the internal layer (CI) of the cord, each external strand (TE) comprising: an internal layer (C1′) made up of Q′≥1 internal threads (F1′), and an external layer (C2′) made up of N′>1 external threads (F2′) wound around the internal layer (C1′).

Claims

1. A two-layer multi-strand cord having a modulus EC and comprising: an internal layer of the cord made up of J>1 internal strands wound in a helix, each internal strand comprising an internal layer made up of Q≥1 internal threads, and an external layer made up of N>1 external threads wound around the internal layer; and an external layer of the cord made up of L>1 external strands wound around the internal layer of the cord, each external strand comprising an internal layer made up of Q′≥1 internal threads, and an external layer made up of N′>1 external threads wound around the internal layer, wherein 50 GPa≤EC≤160 GPa.

2. The two-layer multi-strand cord according to claim 1, wherein, with the internal layer of the cord having a modulus EI, 25 GPa≤EI≤180 GPa.

3. The two-layer multi-strand cord according to claim 1, wherein, with the internal layer of the cord having a modulus EI, 0.60≤EC/EI≤1.20.

4. The two-layer multi-strand cord according to claim 1, wherein, with the internal layer of the cord having a modulus EI, EC/EI≤0.59 or 1.21≤EC/EI.

5. The two-layer multi-strand cord according to claim 1, wherein 50 GPa≤EC≤89 GPa.

6. The two-layer multi-strand cord according to claim 1, wherein, with the internal layer of the cord having a modulus EI, 36 GPa≤EI≤175 GPa.

7. The two-layer multi-strand cord according to claim 1, wherein 90 GPa≤EC≤130 GPa.

8. The two-layer multi-strand cord according to claim 1, wherein, with the internal layer of the cord having a modulus EI, 25 GPa≤EI≤180 GPa.

9. The two-layer multi-strand cord according to claim 1, wherein 131 GPa≤EC≤160 GPa.

10. The two-layer multi-strand cord according to claim 1, wherein, with the internal layer of the cord having a modulus EI, 78 GPa≤EI≤180 GPa.

11. The two-layer multi-strand cord according to claim 1, wherein J=2, 3 or 4.

12. The two-layer multi-strand cord according to claim 1, wherein L=7, 8, 9 or 10.

13. The two-layer multi-strand cord according to claim 1, wherein the external layer of the cord is desaturated.

14. A tire comprising the two-layer multi-strand cord according to claim 1.

15. A tire comprising a carcass reinforcement anchored in two beads and surmounted radially by a crown reinforcement which is itself surmounted by a tread, the crown reinforcement being joined to the beads by two sidewalls, and the crown reinforcement comprising at least one two-layer multi-strand cord according to claim 1.

Description

(1) The invention will be better understood on reading the following description, given solely by way of non-limiting example and with reference to the drawings.

EXAMPLE OF A TYRE ACCORDING TO THE INVENTION

(2) A frame of reference X, Y, Z corresponding to the usual respectively axial (X), radial (Y) and circumferential (Z) orientations of a tyre has been depicted in the figures.

(3) The “median circumferential plane” M of the tyre is the plane which is normal to the axis of rotation of the tyre and which is situated equidistant from the annular reinforcing structures of each bead, and passes through the middle of the crown reinforcement.

(4) FIGS. 1 and 2 depict a tyre according to the invention and denoted by the general reference 10.

(5) The tyre 10 is for a heavy vehicle of construction plant type, for example of “dumper” type. Thus, the tyre 10 has a dimension of the type 53/80R63.

(6) The tyre 10 has a crown 12 reinforced by a crown reinforcement 14, two sidewalls 16 and two beads 18, each of these beads 18 being reinforced with an annular structure, in this instance a bead wire 20. The crown reinforcement 14 is surmounted radially by a tread 22 and connected to the beads 18 by the sidewalls 16. A carcass reinforcement 24 is anchored in the two beads 18 and is in this instance wound around the two bead wires 20 and comprises a turnup 26 positioned towards the outside of the tyre 10, which is shown here fitted onto a wheel rim 28. The carcass reinforcement 24 is surmounted radially by the crown reinforcement 14.

(7) The carcass reinforcement 24 comprises at least one carcass ply 30 comprising filamentary metal carcass reinforcing elements 31 arranged substantially parallel to one another in the carcass ply 30 and extending from one bead 18 to the other so as to form an angle of between 800 and 90 with the circumferential direction Z of the tyre 10.

(8) The tyre 10 also comprises a sealing ply 32 made up of an elastomer (commonly known as “inner liner”) which defines the radially internal face 34 of the tyre 10 and which is intended to protect the carcass ply 30 from the diffusion of air coming from the space inside the tyre 10.

(9) The crown reinforcement 14 comprises, radially from the outside towards the inside of the tyre 10, a protective reinforcement 36 arranged radially on the inside of the tread 22, a working reinforcement 38 arranged radially on the inside of the protective reinforcement 36 and an additional reinforcement 50 arranged radially on the inside of the working reinforcement 38. The protective reinforcement 36 is thus interposed radially between the tread 22 and the working reinforcement 38. The working reinforcement 38 is interposed radially between the protective reinforcement 36 and the additional reinforcement 50.

(10) The protective reinforcement 36 comprises first and second protective plies 42, 44, the first ply 42 being arranged radially on the inside of the second ply 44. Each first and second protective ply 42, 44 respectively comprises first and second filamentary metal protective reinforcing elements 43, 45 arranged substantially parallel to one another in each first and second protective ply 42, 44. Each first and second filamentary metal protective reinforcing element 43, 45 makes an angle at least equal to 10°, preferably ranging from 10° to 35° and preferentially from 15° to 30°, with the circumferential direction Z of the tyre.

(11) The working reinforcement 38 comprises first and second working plies 46, 48, the first ply 46 being arranged radially on the inside of the second ply 48. Each ply 46, 48 comprises at least one cord 60. Each first and second working ply 46, 48 respectively comprises first and second filamentary metal working reinforcing elements 47, 49 arranged substantially parallel to one another in each first and second working ply 46, 48. Each first and second filamentary metal working reinforcing element 47, 49 is formed here by a cord 60 described hereinafter.

(12) Each first and second filamentary metal working reinforcing element 47, 49 makes an angle at most equal to 60°, preferably ranging from 15° to 40°, with the circumferential direction Z of the tyre 10. Optionally, the first and second filamentary metal working reinforcing elements 47, 49 are crossed from one working ply to the other.

(13) The additional reinforcement 50, also referred to as the limiting block, the function of which is to partially react the mechanical stresses of inflation, comprises first and second additional plies 52, 54, each first and second additional ply 52, 54 respectively comprising first and second additional filamentary metal reinforcing elements 53, 55 arranged substantially parallel to one another in each first and second additional ply 52, 54. Each first and second additional filamentary metal reinforcing element 53, 55 makes an angle at most equal to 10°, preferably ranging from 5° to 10°, with the circumferential direction Z of the tyre 10. The additional filamentary metal reinforcing elements are, for example, as described in FR 2 419 181 or FR2419182.

(14) Cord According to a First Embodiment of the Invention

(15) FIG. 3 depicts the cord 60 according to a first embodiment of the invention.

(16) The cord 60 is metal and of the multi-strand type with two cylindrical layers. Thus, it will be understood that there are two layers, not more, not less, of strands of which the cord 60 is made. The layers of strands are adjacent and concentric. The cord 60 is devoid of polymer compound and of elastomer compound when it is not integrated into the tyre.

(17) The cord 60 comprises an internal layer CI of the cord 60, and an external layer CE of the cord 60. The internal layer CI is made up of J>1 internal strands TI, namely of several internal strands TI, wound in a helix. The external layer CE is made up of L>1 external strands, namely of several external strands TE wound in a helix around the internal layer CI. In this instance, J=2, 3 or 4, preferably J=3 or 4. In addition, L=7, 8, 9 or 10, preferably L=8, 9 or 10. With J=3, L=7, 8 or 9 and in this instance and here J=3, L=8.

(18) The cord 60 also comprises a wrapper F made up of a single wrapping wire.

(19) The internal layer CI is wound in a helix in a direction of winding of the internal layer of the cord, here the direction S. The internal strands TI are wound in a helix with a pitch PI such that 10 mm≤PI≤65 mm and preferably 10 mm≤PI≤45 mm. Here, PI=15 mm. The helix angle α of each internal strand TI in the internal layer CI of the cord 60 with a very low modulus ranges from 3° to 42° and in this instance α=19.8°.

(20) The external layer CE is wound in a helix around the internal layer CI in a direction of winding of the external layer of the cord that is the opposite of the direction of winding of the internal layer of the cord, here the direction Z. The external strands TE are wound in a helix around the internal strand TI with a pitch PE such that 30 mm≤PE≤65 mm and preferably 30 mm≤PE≤60 mm. Here, PE=40 mm. The helix angle α′ of each external strand TE in the external layer CE of the cord 60 ranges from 7° to 38° and, in the case of the cord 60 with a very low modulus, ranges from 13° to 38° and in this instance α′=20.0°.

(21) The wrapper F is wound around the external layer CE in a direction of winding of the wrapper, here the opposite to the direction of winding of the external layer CE, in this instance in the S-direction. The wrapping wire is wound in a helix around the external strands TE with a pitch PF such that 2 mm≤PF≤10 mm and preferably, 3 mm≤PF≤8 mm. Here, PF=5.1 mm.

(22) The assembly made up of the internal CI and external CE layers, which means to say the cord 60 without the wrapper F, has a diameter D greater than or equal to 4 mm, preferably greater than or equal to 4.5 mm, and less than or equal to 7 mm, preferably less than or equal to 6.5 mm. Here, D=6.1 mm.

(23) The internal layer CI of internal strands TI has a diameter DI. Each external strand TE has a diameter DE. In this instance, DI=3.18 mm, DE=1.46 mm.

(24) The external layer CE of the cord 60 is desaturated and completely unsaturated. The mean inter-strand distance E separating two adjacent external strands TE is therefore greater than or equal to 30 μm. As a preference, the mean inter-strand distance E separating two adjacent external strands TE is greater than or equal to 70 μm, more preferentially than/to 100 μm, more preferentially still than/to 150 μm and highly preferentially than/to 200 μm. Here, E=241 μm. The sum SIE of the inter-thread distances E of the external layer CE is greater than the diameter DE of the external strands of the external layer CE. Here, the sum SIE=8×0.241=1.93 mm, which is a value strictly greater than DE=1.46 mm.

(25) Internal Strands TI of the Cord 60

(26) Each internal strand TI has two layers. Each internal strand TI comprises, here is made up of, two layers, not more, not less.

(27) Each internal strand TI comprises an internal layer C1 made up of Q>1 internal threads F1 and an external layer C2 made up of N>1 external threads F2 wound in a helix around and in contact with the internal layer C1.

(28) Q=2, 3 or 4, preferably Q=3 or 4. N=7, 8, 9 or 10, preferably N=8, 9 or 10. With Q=3, N=7, 8 or 9, and in this instance Q=3, N=8.

(29) The internal layer C1 of each internal strand TI is wound in a helix in a direction of winding of the internal layer C1 of the internal strand TI that is identical to the direction of winding of the internal layer C1 of the cord, here in the S-direction. The Q internal threads F1 are assembled within each internal strand TI at a pitch p1 such that 2 mm≤p1≤20 mm. Here, p1=3 mm. The helix angle β of each internal thread F1 in the internal layer C1 within each internal strand TI ranges from 4° to 25°, here β=23.4°.

(30) The external layer C2 of each internal strand TI is wound around and in contact with the internal layer C1 in a direction of winding of the external layer C2 of the internal strand TI that is identical to the direction of winding of the internal layer C1 of the cord, here in the S-direction. The N external threads F2 are wound in a helix around the Q internal threads F1 and are assembled within each internal strand TI at a pitch p2 such that 4 mm≤p2≤40 mm. Here, p2=6 mm. The helix angle γ of each external thread F2 in the external layer C2 within each internal strand TI ranges from 6° to 31°, here γ=30.2°.

(31) 11°≤2α+β+γ≤110° and because Q>1, 16°≤2α+β+γ≤110°. In the embodiment of the cord 60 with a very low modulus with Q>1, 23°≤2α+β+γ≤110°. In this particular instance, 2α+β+γ=93.2°.

(32) Each internal F1 and external F2 thread of each internal strand TI respectively has a diameter D1, D2. Each diameter of the internal threads D1 and external threads D2 of each internal strand TI ranges from 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40 mm. Each internal thread F1 of each internal strand TI has a diameter D1 greater than or equal to, here equal to, the diameter D2 of each external thread F2 of each internal strand TI.

(33) In this instance, D1=D2=0.35 mm.

(34) Because of the relatively short pitch p2, the external layer C2 of each internal strand TI is desaturated and incompletely unsaturated. The inter-thread distance I2 of the external layer C2 which on average separates the N external threads is greater than or equal to 5 μm. The inter-thread distance I2 is preferably greater than or equal to 15 μm and is here equal to 29 μm. The sum SI2 of the inter-thread distances I2 of the external layer C2 is greater than the diameter d2 of the external threads F2 of the external layer C2. Here, the sum SI2=8×0.029=0.23 mm, which is a value strictly less than D2=0.35 mm.

(35) Also, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤180 GPa and in the embodiment of the cord 60 with a very low modulus, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤175 GPa. Here, the internal layer has a relatively low modulus and 25 GPa≤EI≤94 GPa, preferably 36 GPa≤EI≤94 GPa. In this instance, EI=53 GPa.

(36) External Strands TE of the Cord 60

(37) Each external strand TE has two layers. Thus, each external strand TE comprises, here is made up of, two layers, not more, not less.

(38) Each external strand TE comprises an internal layer C1′ made up of Q′≥1 internal threads F1′ and an external layer C2′ made up of N′>1 external threads F2′ wound in a helix around and in contact with the internal layer C1′.

(39) Q′=2, 3 or 4, preferably Q′=3 or 4. N′=7, 8, 9 or 10, preferably N′=8, 9 or 10. With Q′=3, N′=7, 8 or 9, and in this instance Q′=3, N′=8.

(40) The internal layer C1′ of each external strand TE is wound in a helix in a direction of winding of the internal layer C1′ of the external strand TE that is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. The Q′ internal threads F1′ are assembled within each external strand TE at a pitch p1′ such that 2 mm≤p1′≤20 mm, preferably 5 mm≤p1′≤20 mm. Here, p1′=10 mm. The helix angle β of each internal thread F1′ in the internal layer C1′ within each external strand TE ranges from 4° to 25°, preferably from 4° to 17°, here β′=7.3°.

(41) The external layer C2′ of each external strand TE is wound around and in contact with the internal layer C1′ in a direction of winding of the external layer C2′ of the external strand TE that is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. The N′ external threads F2′ are wound in a helix around the Q′ internal threads F1′ and are assembled within each external strand TE at a pitch p2′ such that 4 mm≤p2′≤40 mm. Here, p2′=20 mm. The helix angle γ′ of each external thread F2′ in the external layer C2′ within each external strand TE ranges from 5° to 31°, here γ′=9.8°.

(42) 23°≤2α′+β′+γ′≤97° and because Q′>1, 28°≤2α′+β′+γ′≤97° and, in the embodiment of the cord 60 with a very low modulus, 43°≤2α′+β′+γ′≤97°. In this particular instance, 2α′+β′+γ′=57.1°.

(43) Each internal F1′ and external F2′ thread of each external strand TE respectively has a diameter D1′, D2′. Each diameter of the internal threads D1′ and external threads D2′ of each external strand TE ranges from 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40 mm. Each Q′ internal thread F1′ of each external strand TI′ has a diameter D1′ greater than or equal to, here equal to, the diameter D2′ of each external thread F2′ of each external strand TE. In this instance, D1′=D2′=0.35 mm.

(44) The external layer C2′ of each external strand TE is desaturated and completely unsaturated. The inter-thread distance I2′ of the external layer C2′ which on average separates the N′ external threads is greater than or equal to 5 μm. The inter-thread distance I2′ is preferably greater than or equal to 15 μm, more preferentially greater than or equal to 35 μm, more preferentially still greater than or equal to 50 μm and highly preferentially greater than or equal to 60 μm and is here equal to 69 μm. The sum SI2′ of the inter-thread distances I2′ of the external layer C2′ is greater than the diameter D2 of the external threads F2′ of the external layer C2′. Here, the sum SI2′=8×0.069=0.55 mm, which is a value strictly greater than D2′=0.35 mm.

(45) Each thread F1, F2, F1′, F2′ has a breaking strength, denoted Rm, such that 2500 S Rm S 3100 MPa. The steel for these threads is said to be of SHT (“Super High Tensile”) grade. Other threads may be used, for example threads of an inferior grade, for example of NT (“Normal Tensile”) or HT (“High Tensile”) grade, just as may threads of a superior grade, for example of UT (“Ultra Tensile”) or MT (“Mega Tensile”) grade.

(46) 51°≤2α+β+γ+2α′+β′+γ′≤184° and because Q>1 et Q′>1, 68°≤2α+β+γ+2α′+β′+γ′≤184°. In the embodiment of the cord 60 with a very low modulus, 85°≤2α+β+γ+2α′+β′+γ′≤184° and because Q>1 and Q′>1, 110°≤2α+β+γ+2α′+β′+γ′≤184°. In this particular instance, 2α+β+γ+2α′+β′+γ′=150.3°.

(47) 1.21≤EC/EI, preferably 1.21≤EC/EI≤3.00 and here EC/EI=1.62.

(48) Also, 50 GPa≤EC≤160 GPa and in the embodiment of the cord 60 with a very low modulus, 50 GPa≤EC≤89 GPa. Here, EC=86 GPa.

(49) Method for Manufacturing the Cord According to the Invention

(50) The cord according to the invention is manufactured using a method comprising steps well known to those skilled in the art.

(51) In a step for manufacturing the internal strands using the following steps, preferably carried out in line and continuously: first of all, a first step of assembling, by twisting, the Q internal threads F1 of the internal layer C1 at the pitch p1 and in the S-direction to form the internal layer C1 at a first assembling point; followed by a second step of assembling, by twisting, the N external threads F2 around the N internal threads F1 of the internal layer C1 at the pitch p2 and in the S-direction to form the external layer C2 and each internal strand TI at a second assembling point; preferably a final twist-balancing step.

(52) In a step for manufacturing the external strands using the following steps, preferably carried out in line and continuously: first of all, a first step of assembling, by twisting, the Q′ internal threads F1′ of the internal layer C1′ at the pitch p1′ and in the Z-direction to form the internal layer C1′ at a first assembling point; followed by a second step of assembling, by twisting, the N′ external threads F2′ around the N′ internal threads F1′ of the internal layer C1′ at the pitch p2′ and in the Z-direction to form the external layer C2′ and each external strand TE at a second assembling point; preferably a final twist-balancing step.

(53) What is meant here by “twist balancing” is, as is well known to those skilled in the art, the cancellation of the residual twist torques (or the elastic return of the twist) applied to each thread of the strand, in the intermediate layer as in the external layer.

(54) After this final twist-balancing step, the manufacture of each strand is complete. Each strand is wound onto one or more receiving reels, for storage, prior to the later operation of assembling the elementary strands in order to obtain the multi-strand cord.

(55) In order to manufacture the multi-strand cord of the invention, the method, as is well known to those skilled in the art, is to cable together the strands previously obtained, using cabling machines rated for assembling strands.

(56) In a step of manufacturing the internal layer C1, the Q internal strands TI are assembled by cabling at the pitch PI and in the S-direction to form the internal layer C1 at a first assembling point. In the embodiments in which the pitch PI is relatively short and therefore in which α is relatively high, the Q internal strands TI are assembled by twisting in order to limit the risk of instability of the internal layer C1 of the strands TI.

(57) Then, in a later manufacturing step, the L external strands TE are assembled by cabling around the internal layer C1 at the pitch PE and in the Z-direction to form the assembly of the layers C1 and CE. In the embodiments in which the pitch PE is relatively short and therefore in which α′ is relatively high, the L external stands TE are assembled by twisting in order to limit the risk of instability of the external layer CE of the strands TE.

(58) In a second manufacturing step, the wrapper F is wound, at the pitch PF and in the S-direction, around the assembly previously obtained.

(59) The cord is then incorporated by skimming into composite fabrics formed from a known composition based on natural rubber and carbon black as reinforcing filler, conventionally used for manufacturing crown reinforcements of radial tyres. This compound essentially contains, in addition to the elastomer and the reinforcing filler (carbon black), an antioxidant, stearic acid, an extender oil, cobalt naphthenate as adhesion promoter, and finally a vulcanization system (sulfur, accelerator and ZnO).

(60) The composite fabrics reinforced by these cords have an elastomer compound matrix formed from two thin layers of elastomer compound which are superposed on either side of the cords and which have a thickness of between 1 and 4 mm inclusive, respectively. The skim-coating pitch (the pitch at which the cords are laid in the elastomer compound fabric) ranges from 4 mm to 8 mm.

(61) These composite fabrics are then used as working ply in the crown reinforcement during the method of manufacturing the tyre, the steps of which are otherwise known to a person skilled in the art.

(62) Cord According to a 2.sup.nd Embodiment of the Invention

(63) A low-modulus cord 61 according to a second embodiment of the invention will be described. Elements similar to those of the first embodiment are denoted by identical references.

(64) Amongst the differences between the cords 60 and 61, it will be noted that the low-modulus cord 61 is such that the helix angle α ranges from 3° to 36° and in this instance α=10°, and that the helix angle α′ ranges from 9° to 27° and in this instance α′=16.1°.

(65) It will also be noted that, in the case of the cord 61 with a low modulus, 13°≤2α+β+γ≤110° and because Q>1, 16°≤2α+β+γ≤110°. In this particular instance, 2α+β+γ=46.2°.

(66) It will also be noted that, in the embodiment of the cord 61 with a low modulus, 25 GPa≤EI≤180 GPa, preferably 64 GPa≤EI≤180 GPa. Because the internal layer has a relatively high modulus, 95 GPa≤EI≤180 GPa. In this instance, EI=148 GPa.

(67) It will also be noted that, in the case of the cord 61 with a low modulus, 31°≤2α′+β′+γ′≤71° and because Q′>1, 39°≤2α′+β′+γ′≤71°. In this particular instance, 2α′+β′+γ′=54.3°.

(68) It will also be noted that, in the case of the cord 61 with a low modulus, 65°≤2α+β+γ+2α′+β′+γ′≤153° and because Q>1 and Q′>1, 79°≤2α+β+γ+2α′+β′+γ′≤153°. In this particular instance, 2α+β+γ+2α′+β′+γ′=100.5°.

(69) It will be noted that 0.60≤EC/EI≤1.20 and here EC/EI=0.86.

(70) It will be noted that, in the embodiment of the cord 61 with a low modulus, 90 GPa≤EC≤130 GPa. Here, EC=127 GPa.

(71) Cord According to a 3.sup.rd Embodiment of the Invention

(72) FIG. 6 depicts a medium-modulus cord 62 according to a third embodiment of the invention. Elements similar to those of the cords already described are denoted by identical references.

(73) Amongst the differences between the cords 60 and 62, it will be noted that the helix angle α of each internal strand TI in the internal layer C1 of the cord 62 with a medium modulus ranges from 3° to 24° and in this instance α=9.1°. It will also be noted that the helix angle α′ of each external strand TE in the external layer CE of the cord 62 with a medium modulus ranges from 7° to 22° and in this instance α′=16.2°.

(74) It will also be noted that, in the case of the cord 62 with a medium modulus, 11°≤2α+β+γ≤64° and because Q>1, 16°≤2α+β+γ≤63° and in this instance 2α+β+γ=29.6°.

(75) It will also be noted that, in the embodiment of the cord 62 with a medium modulus, 78 GPa≤EI≤180 GPa, preferably 100 GPa≤EI≤180 GPa. Here, the internal layer has a relatively high modulus, 95 GPa≤EI≤180 GPa and in this instance EI=173 GPa.

(76) It will also be noted that, in the embodiment of the cord 62 with a medium modulus, 23°≤2α′+β′+γ′≤58° and because Q′>1, 27°≤2α′+β′+γ′≤58°. In this particular instance, 2α′+β′+γ′=49.5°.

(77) It will also be noted that, in the embodiment of the cord 62 with a medium modulus, 45°≤2α+β+γ+2α′+β′+γ′≤108° and because Q>1 and Q′>1, 60°≤2α+β+γ+2α′+β′+γ′≤108°. In this particular instance, 2α+β+γ+2α′+β′+γ′=79.1°.

(78) It will also be noted that 0.60≤EC/EI≤1.20, preferably 0.80≤EC/EI≤1.15 and here, EC/EI=0.86.

(79) It will be noted, in the embodiment of the cord 62 with a medium modulus, that 131 GPa≤EC≤160 GPa. Here, EC=149 GPa.

(80) Cord According to a 4.sup.th Embodiment of the Invention

(81) A very low-modulus cord 63 according to a fourth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(82) Amongst the differences between the cords 60 and 63, it will be noted that, because the internal layer has a relatively high modulus, 95 GPa≤EI≤180 GPa, preferably 95 GPa≤EI≤175 GPa. In this instance, EI=158 GPa.

(83) It will also be noted that EC/EI≤0.59, preferably 0.40≤EC/EI≤0.59 and here EC/EI=0.50.

(84) Cord According to a 5.sup.th Embodiment of the Invention

(85) A very low-modulus cord 64 according to a fifth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(86) Amongst the differences between the cords 62 and 64, it will be noted that the cord 64 is such that J=4 and L=9 and that each thread F1, F1′, F2, F2′ is such that D1=D1′=D2=D2′=0.40 mm.

(87) Cord According to a 6.sup.th Embodiment of the Invention

(88) A low-modulus cord 65 according to a sixth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(89) Amongst the differences between the cords 61 and 65, it will be noted that, because the internal layer has a relatively low modulus, 25 GPa≤EI≤94 GPa and in this instance, EI=59 GPa.

(90) It will also be noted that, in the embodiment of the cord 65, 1.21≤EC/EI, preferably 1.21≤EC/EI≤3.00 and here EC/EI=1.63.

(91) Cord According to a 7.sup.th Embodiment of the Invention

(92) A medium-modulus cord 66 according to a seventh embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(93) Amongst the differences between the cords 62 and 66, it will be noted that the cord 66 is such that J=4 and L=10 and that each thread F1, F1′, F2, F2′ is such that its diameter D1, D1′, D2, D2′ ranges from 0.25 mm to 0.40 mm and here D1=D1′=D2=D2′=0.35 mm.

(94) Cord According to a 8.sup.th Embodiment of the Invention

(95) FIG. 8 depicts the cord 160 according to an eighth embodiment of the invention.

(96) The cord 160 is metal and of the multi-strand type with two cylindrical layers. Thus, it will be understood that there are two layers, not more, not less, of strands of which the cord 160 is made. The layers of strands are adjacent and concentric. The cord 160 is devoid of polymer compound and of elastomer compound when it is not integrated into the tyre.

(97) The cord 160 comprises an internal layer C1 of the cord 160, and an external layer CE of the cord 160. The internal layer C1 is made up of J>1 internal strands TI, namely of several internal strands TI, wound in a helix. The external layer CE is made up of L>1 external strands, namely of several external strands TE wound in a helix around the internal layer C1. In this instance, J=2, 3 or 4, preferably J=3 or 4. In addition, L=7, 8, 9 or 10, preferably L=8, 9 or 10. With J=3, L=7, 8 or 9 and in this instance and here J=3, L=8.

(98) The cord 160 also comprises a wrapper F made up of a single wrapping wire.

(99) The internal layer CI is wound in a helix in a direction of winding of the internal layer of the cord, here the direction S. The internal strands TI are wound in a helix with a pitch PI such that 10 mm≤PI≤65 mm and preferably 10 mm≤PI≤45 mm. Here, PI=20 mm. The helix angle α of each internal strand TI in the internal layer CI of the cord 160 ranges from 4° to 41° and, in the embodiment of the cord 160 with a low modulus, from 4° to 31°, in this instance α=13.4°.

(100) The external layer CE is wound in a helix around the internal layer CI in a direction of winding of the external layer of the cord that is the opposite of the direction of winding of the internal layer of the cord, here the direction Z. The external strands TE are wound in a helix around the internal strand TI with a pitch PE such that 30 mm≤PE≤65 mm and preferably 30 mm≤PE≤60 mm. Here, PE=40 mm. The helix angle α′ of each external strand TE in the external layer CE of the cord 160 ranges from 130 to 360 and, in the embodiment of the cord 160 with a low modulus, from 13° to 32°, in this instance α′=19.1°.

(101) The wrapper F is wound around the external layer CE in a direction of winding of the wrapper, here the opposite to the direction of winding of the external layer CE, in this instance in the S-direction. The wrapping wire is wound in a helix around the external strands TE with a pitch PF such that 2 mm≤PF≤10 mm and preferably 3 mm≤PF≤8 mm. Here, PF=5.1 mm.

(102) The assembly made up of the internal CI and external CE layers, which means to say the cord 160 without the wrapper F, has a diameter D greater than or equal to 4 mm, preferably greater than or equal to 4.5 mm, and less than or equal to 7 mm, preferably less than or equal to 6.5 mm. Here, D=6 mm.

(103) The internal layer C1 of internal strands TI has a diameter DI. Each external strand TE has a diameter DE. In this case, DI=2.83 mm, DE=1.58 mm.

(104) The external layer CE of the cord 160 is desaturated and incompletely unsaturated.

(105) Here, the mean inter-strand distance E separating two adjacent external strands TE is such that E=29 μm. The sum SIE of the inter-thread distances E of the external layer CE is less than the diameter DE of the external strands of the external layer CE. Here, the sum SIE=8×0.029=0.23 mm, which is a value strictly less than DE=1.58 mm.

(106) Internal Strands TI of the Cord 160

(107) Each internal strand TI has three layers. Each internal strand TI comprises, here is made up of, three layers, not more, not less.

(108) Each internal strand TI comprises an internal layer C1 made up of Q>1 internal threads F1, an intermediate layer C2 made up of P>1 intermediate threads F2 wound in a helix around and in contact with the internal layer C1, and an external layer C3 made up of N>1 external threads F3 wound in a helix around and in contact with the intermediate layer C2.

(109) Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or 11 and more preferentially here Q=1, P=6 and N=11.

(110) In the instance in which Q>1, the internal layer C1 of each internal strand TI is wound in a helix in a direction of winding of the internal layer C1 of the internal strand TI that is identical to the direction of winding of the internal layer C1 of the cord, here in the S-direction. Here, the Q=1 internal thread F1 is assembled within each internal strand TI at an infinite pitch such that β=0.

(111) The intermediate layer C2 of each internal strand TI is wound around and in contact with the internal layer C1 in a direction of winding of the intermediate layer C2 of the internal strand TI that is identical to the direction of winding of the internal layer CI of the cord, here in the S-direction. The P intermediate threads F2 are wound in a helix around the Q=1 internal thread F1 and are assembled within each internal strand TI at a pitch p2 such that 5 mm≤p2≤20 mm. Here, p2=7.7 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 6° to 30°, here δ=12.2°.

(112) The external layer C3 of each internal strand TI is wound around and in contact with the intermediate layer C2 in a direction of winding of the external layer C3 of the internal strand TI that is identical to the direction of winding of the internal layer CI of the cord, here in the S-direction. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=15.4 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 7° to 30°, here γ=12.1°.

(113) 25°≤3α+β+γ+γ≤158° and here, because Q=1, 25°≤3α+β+δ+γ≤140°. In this particular instance, in this first embodiment of the cord 160 with a low modulus, 25°≤3α+β+δ+γ≤125° and here, because Q=1, 25°≤3α+β+δ+γ≤120°. In the case of the cord 160, 3α+β++γ=64.5°.

(114) Each internal F1, intermediate F2 and external F3 thread of each internal strand TI respectively has a diameter D1, D2, D3. Each diameter of the internal threads D1, intermediate threads D2 and external threads D3 of each internal strand TI ranges from 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40 mm. Each internal thread F1 of each internal strand TI has a diameter D1 greater than or equal to, here equal to, the diameter D2 of each intermediate thread F2 of each internal strand TI. Each internal thread F1 of each internal strand TI has a diameter D1 greater than or equal to, here equal to, the diameter D3 of each external thread F3 of each internal strand TI. Each intermediate thread F2 of each internal strand TI has a diameter D2 equal to the diameter D3 of each external thread F3 of each internal strand TI. In this instance, D1=D2=D3=0.26 mm.

(115) The intermediate layer C2 of each internal strand TI is saturated. Here, the distance I2 is approximately equal to 0.

(116) The external layer C3 of each internal strand TI is desaturated and completely unsaturated. The inter-thread distance I3 of the external layer C3 which on average separates the N external threads is greater than or equal to 5 μm. The inter-thread distance I3 is preferably greater than or equal to 15 μm and is here equal to 30 μm. The sum SI3 of the inter-thread distances I3 of the external layer C3 is greater than the diameter D3 of the external threads F3 of the external layer C3. Here, the sum SI3=11×0.030=0.33 mm, which is a value strictly greater than D2=0.26 mm.

(117) Also, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤180 GPa and, in the embodiment of the cord 160 with a low modulus, 25 GPa≤EI≤180 GPa, preferably 64 GPa≤EI≤180 GPa. Here, the internal layer has a relatively high modulus, so 95 GPa≤EI≤180 GPa. In this instance, EI=147 GPa.

(118) External Strands TE of the Cord 160

(119) Each external strand TE has three layers. Thus, each external strand TE comprises, here is made up of, three layers, not more, not less.

(120) Each external strand TE comprises an internal layer C1′ made up of Q′>1 internal threads F1′, an intermediate layer C2′ made up of P′>1 intermediate threads F2′ wound in a helix around and in contact with the internal layer C1′, and an external layer C3′ made up of N′>1 external threads F3′ wound in a helix around and in contact with the intermediate layer C2′.

(121) Q′=1, P′=5 or 6 and N′=10, 11 or 12, preferably Q′=1, P′=5 or 6, N′=10 or 11 and more preferentially here Q′=1, P′=6 and N′=11.

(122) In the instance in which Q′>1, the internal layer C1′ of each external strand TE is wound in a helix in a direction of winding of the internal layer C1′ of the external strand TE that is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. Here, the Q′=1 internal thread F1′ is assembled within each external strand TE at an infinite pitch p1′ such that β′=0.

(123) The intermediate layer C2′ of each external strand TE is wound around and in contact with the internal layer C1′ in a direction of winding of the intermediate layer C2′ of the external strand TE that is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. The P′ intermediate threads F2′ are wound in a helix around the Q′=1 internal thread F1′ and are assembled within each external strand TE at a pitch p2′ such that 5 mm S p2′≤20 mm. Here, p2′=7.7 mm. The helix angle δ′ of each intermediate thread F2′ in the intermediate layer C2′ within each external strand TE ranges from 6° to 22°, here δ′=15.5°.

(124) The external layer C3′ of each external strand TE is wound around and in contact with the intermediate layer C2′ in a direction of winding of the external layer C3′ of the external strand TE that is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. The N′ external threads F3′ are wound in a helix around the P′ intermediate threads F2′ and are assembled within each external strand TE at a pitch p3′ such that 10 mm s p3′≤40 mm. Here, p3′=15.4 mm. The helix angle γ′ of each external thread F3′ in the external layer C3′ within each external strand TE ranges from 7° to 22°, here γ′=14.6°.

(125) 48°≤3α′+β+δ′+γ′≤154° and here, because Q′=1, 48°≤3α′+β′+δ′+γ′≤145°.

(126) In this particular instance, in this first embodiment of the cord 160 with a low modulus, 54°≤3α′+β′+δ′+γ′≤123°, and here, because Q′=1, 54°≤3α′+β′+δ′+γ′≤118°. In the case of the cord 160, 3α′+β+′+γ′=87.4°.

(127) Each internal F1′, intermediate F2′ and external F3′ thread of each external strand TE respectively has a diameter D1′, D2′, D3′. Each diameter of the internal threads D1′, intermediate threads D2′ and external threads D3′ of each external strand TE ranges from 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40 mm. Each Q′ internal thread F1′ of each external strand TE has a diameter D1′ greater than or equal to the diameter D2′ of each intermediate thread F2′ of each external strand TE. Each Q′ internal thread F1′ of each external strand TE has a diameter D1′ greater than or equal to the diameter D3′ of each external thread F3′ of each external strand TE. Each N′ intermediate thread F2′ of each external strand TE has a diameter D2′ equal to the diameter D3′ of each external thread F3′ of each external strand TE. In this instance, D1′=0.38 mm>D2′=D3′=0.30 mm.

(128) The intermediate layer C2′ of each external strand TE is desaturated and incompletely unsaturated. The inter-thread distance I2′ of the intermediate layer C2′ which on average separates the P′ intermediate threads is greater than or equal to 5 μm. The inter-thread distance I2′ is preferably greater than or equal to 15 μm and is here equal to 32 μm. The sum SI2′ of the inter-thread distances I2′ of the intermediate layer C2′ is greater than the diameter D2 of the intermediate threads F2′ of the intermediate layer C2′. Here, the sum SI2′=6×0.032=0.19 mm, which is a value strictly less than D2′=0.30 mm. In addition, the sum SI2′ of the inter-thread distances I2′ is such that SI2′<D3′ and even SI2′<0.8×D3′.

(129) The external layer C3′ of each external strand TE is desaturated and completely unsaturated. The inter-thread distance I3′ of the external layer C3′ which on average separates the N′ external threads is greater than or equal to 5 μm. The inter-thread distance I3′ is preferably greater than or equal to 15 μm, more preferentially greater than or equal to 35 μm, more preferentially still greater than or equal to 50 μm, and here is equal to 52 μm. The sum SI3′ of the inter-thread distances I3′ of the external layer C3′ is greater than the diameter D3′ of the external threads F3′ of the external layer C3′. Here, the sum SI3′=11×0.052=0.57 mm, which is a value strictly greater than D3′=0.30 mm.

(130) Each thread F1, F2, F3, F1′, F2′, F3′ has a breaking strength, denoted Rm, such that 2500≤Rm≤3100 MPa. The steel for these threads is said to be of SHT (“Super High Tensile”) grade. Other threads may be used, for example threads of an inferior grade, for example of NT (“Normal Tensile”) or HT (“High Tensile”) grade, just as may threads of a superior grade, for example of UT (“Ultra Tensile”) or MT (“Mega Tensile”) grade.

(131) 84°≤3α+β+γ+γ+3α′+β′+δ′+γ′≤280°. In this particular instance, because Q=1 and Q′=1, 84°≤3α+β+γ+γ+3α′+β′+δ′+γ′≤246°. In the embodiment of the cord 160 with a low modulus, 107°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤211° and because Q=1 and Q′=1, 107°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤197° and here 3α+β+δ+γ+3α′+β′+δ′+γ′=151.9°.

(132) 0.60≤EC/EI≤1.20 and here EC/EI=0.70.

(133) Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 160 with a low modulus, 90 GPa≤EC≤130 GPa. Here, EC=103 GPa.

(134) Cord According to a 9.sup.th Embodiment of the Invention

(135) A low-modulus cord 161 according to a second embodiment of the invention will now be described. Elements similar to those of the cord 160 are denoted by identical references.

(136) Amongst the differences between the cords 160 and 161, it will be particularly noted that the cord 161 is such that J=4 and L=10 and that each thread F1, F1′, F2, F2′, F3, F3′ is such that its diameter D1, D1′, D2, D2′, D3, D3′ is such that D1=D2=D3=0.40 mm and D1′=D2′=D3′=0.30 mm.

(137) Cord According to a 10.sup.th Embodiment of the Invention

(138) A low-modulus cord 162 according to a third embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(139) Amongst the differences between the cords 160 and 162, Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10, N=13, 14 or 15 and here Q=3, P=8 and N=13. The Q internal threads F1 are wound in a helix within each internal strand TI at a pitch p1 such that 5 mm≤p1≤15 mm. Here, p1=8 mm. The helix angle β of each internal thread F1 of the internal layer within each internal strand TI ranges from 4° to 17°, here β=6.7°. The P intermediate threads F2 are wound in a helix around the Q internal threads F1 and are assembled within each internal strand TI at a pitch p2 such that 10 mm≤p2≤20 mm. Here, p2=15 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 8° to 22°, here δ=9.8°. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=20 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 9° to 25°, here γ=11.9°.

(140) It will also be noted that, because Q>1, 36°≤3α+β+γ+γ≤158°, and in the embodiment of the cord 162 with a low modulus, 36°≤3α+β+γ+γ≤125° and here 3α+β+δ+γ=108.5°.

(141) It will also be noted that, because the internal layer of the cord 162 has a relatively low modulus, 25 GPa≤EI≤94 GPa, preferably 64 GPa≤EI≤94 GPa and here EI=82 GPa.

(142) It will also be noted that Q′>1, Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13, 14 or 15 and here Q′=3, P′=8 and N′=13. The Q′ internal threads F1′ are wound in a helix within each external strand TE at a pitch p1′ such that 5 mm≤p1′≤15 mm. Here, p1′=12 mm. The helix angle β of each internal thread F1′ of the internal layer within each external strand TE ranges from 4° to 20°, here β′=4.5°. The P′ intermediate threads F2′ are assembled within each external strand TE at a pitch p2′ such that 10 mm≤p2′≤20 mm. Here, p2′=18 mm. The helix angle δ′ of each intermediate thread F2′ of the intermediate layer C2′ within each external strand TE ranges from 8° to 22°, here δ′=8.1°. The N′ external threads F3′ are assembled within each external strand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here, p3′=25 mm. The helix angle γ′ of each external thread F3′ in the external layer C3′ within each external strand TE ranges from 9° to 25° here γ′=9.6°.

(143) It will also be noted that, because Q′>1, 61°≤3α′+β′+δ′+γ′≤154°, and in the case of the cord 162 with a low modulus, 65°≤3α+β+δ+γ≤123° and here 3α′+β′+δ′+γ′=71.4°.

(144) It will also be noted that, because Q>1 and Q′>1, 101°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°, and in the embodiment of the cord 162 with a low modulus, 120°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤211° and here 3α+β+δ+γ+3α′+β′+δ′+γ′=179.9°.

(145) Also, 1.21≤EC/EI and preferably 1.21≤EC/EI≤3.00 and in the embodiment of the cord 162 with a low modulus, 1.21≤EC/EI≤3.00 and here EC/EI=1.29.

(146) Cord According to a 11.sup.th Embodiment of the Invention

(147) A very low-modulus cord 163 according to a fourth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(148) Amongst the differences between the cords 160 and 163, it will be noted that the helix angle α of each internal strand TI in the internal layer CI of the cord 163 with a very low modulus ranges from 6° to 41°, in this instance α=24.6°.

(149) It will also be noted that the helix angle α′ of each external strand TE in the external layer CE of the cord 163 with a very low modulus from 14 to 36°, in this instance α′=16.3°.

(150) It will also be noted that Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10, N=13, 14 or 15 and here Q=3, P=8 and N=13. The Q internal threads F1 are wound in a helix within each internal strand TI at a pitch p1 such that 5 mm≤p1≤15 mm. Here, p1=5 mm. The helix angle β of each internal thread F1 of the internal layer within each internal strand TI ranges from 4° to 17°, here β=12.4°. The P intermediate threads F2 are wound in a helix around the Q internal threads F1 and are assembled within each internal strand TI at a pitch p2 such that 10 mm≤p2≤20 mm. Here, p2=10 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 8° to 22°, here δ=16.6°. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=15 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 9° to 25°, here γ=18°.

(151) It will also be noted that, in this embodiment of the cord 163 with a very low modulus, 29°≤3α+β+δ+γ≤158° and here because Q>1, 42°≤3α+β+δ+γ≤158°. In the case of the cord 163, 3α+β+δ+γ=120.8°.

(152) It will also be noted that, in the case of the cord 163 with a very low modulus having an internal layer with a relatively low modulus, 25 GPa≤EI≤94 GPa, preferably 36 GPa≤EI≤94 GPa, and in this instance, EI=74 GPa.

(153) It will also be noted that, in the embodiment of the cord 163 with a very low modulus, 65°≤3α′+β′+δ′+γ′≤153° and here because Q′=1, 65°≤3α′+β′+δ′+γ′≤143° and in this instance, 3α′+β′+δ′+γ′=91.8°.

(154) It will also be noted that, because Q>1 and Q′=1, 96°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤261°. In the embodiment of the cord 163 with a very low modulus, 138°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280° and because Q>1 and Q′=1, 144°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤261° and here 3α+β+δ+γ+3α′+β′+δ′+γ′=212.6°.

(155) It will be noted that, in the embodiment of the cord 163 with a very low modulus, 0.60≤EC/EI≤1.20 and here EC/EI=1.08.

(156) Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 163 with a very low modulus, 50 GPa≤EC≤89 GPa. Here, EC=80 GPa.

(157) Cord According to a 12.sup.th Embodiment of the Invention

(158) A very low-modulus cord 164 according to a fifth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(159) Amongst the differences between the cords 163 and 164, it will be noted that the internal layer has a relatively high modulus and is such that 95 GPa≤EI≤180 GPa, preferably 95 GPa≤EI≤175 GPa. In this instance, EI=157 GPa.

(160) It will also be noted that Q′>1, Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13, 14 or 15 and here Q′=3, P′=8 and N′=13. The Q′ internal threads F1′ are wound in a helix within each external strand TE at a pitch p1′ such that 5 mm≤p1′≤15 mm. Here, p1′=8 mm. The helix angle β of each external thread F1′ of the internal layer within each external strand TE ranges from 4° to 20°, here β′=7.8°. The P′ intermediate threads F2′ are assembled within each external strand TE at a pitch p2′ such that 10 mm≤p2′≤20 mm. Here, p2′=15 mm. The helix angle δ′ of each intermediate thread F2′ of the intermediate layer C2′ within each external strand TE ranges from 8° to 22°, here δ′=11.2°. The N′ external threads F3′ are assembled within each external strand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here, p3′=20 mm. The helix angle γ′ of each external thread F3′ in the external layer C3′ within each external strand TE ranges from 9° to 25°, here γ′=13.7°.

(161) It will be noted that 48°≤3α′+β′+δ′+γ′≤154° and here because Q′>1, 61°≤3α′+β′+δ′+γ′≤154°. In this particular instance, in this embodiment of the cord 164 with a very low modulus, 65°≤3α′+β′+δ′+γ′≤153° and here because Q′>1, 78°≤3α′+β′+δ′+γ′≤153°. In the case of the cord 164, 3α′+β′+δ′+γ′=130.8°.

(162) It will be noted that 84°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°. In this particular instance, because Q>1 and Q′>1, 101°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°. In the embodiment of the cord 164 with a very low modulus, 138°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280° and because Q>1 and Q′>1, 144°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280° and here 3α+β+δ+γ+3α′+β′+δ′+γ′=190.1°.

(163) It will also be noted that EC/EI≤0.59, preferably 0.40≤EC/EI≤0.59 and here EC/EI=0.49.

(164) Cord According to a 13.sup.th Embodiment of the Invention

(165) Avery low-modulus cord 165 according to a sixth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(166) Amongst the differences between the cords 163 and 165, it will be noted that Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or 11 and more preferentially here Q=1, P=6 and N=11 and that the Q=1 internal thread F1 is assembled within each internal strand TI at an infinite pitch such that β=0. The P intermediate threads F2 are wound in a helix around the Q=1 internal thread F1 and are assembled within each internal strand TI at a pitch p2 such that 5 mm≤p2 S 20 mm. Here, p2=15 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 6° to 30°, here δ=9.6°. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=25 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 7° to 30°, here γ=11.4°.

(167) It will also be noted that 25°≤3α+β+δ+γ≤158° and here because Q=1, 25°≤3α+β+δ+γ≤140°. In this particular instance, in this embodiment of the cord 165 with a very low modulus, 29°≤3α+β+γ+γ≤158° and here because Q=1, 29°≤3α+β+γ+γ≤140°.

(168) In the case of the cord 165, 3α+β+δ+γ=120.9°.

(169) It will also be noted that Q′>1, Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13, 14 or 15 and here Q′=3, P′=8 and N′=13. The Q′ internal threads F1′ are wound in a helix within each external strand TE at a pitch p1′ such that 5 mm≤p1′≤15 mm. Here, p1′=12 mm. The helix angle β of each external thread F1′ of the internal layer within each external strand TE ranges from 4° to 20°, here β′=5.2°. The P′ intermediate threads F2′ are assembled within each external strand TE at a pitch p2′ such that 10 mm≤p2′≤20 mm. Here, p2′=18 mm. The helix angle δ′ of each intermediate thread F2′ in the intermediate layer C2′ within each external strand TE ranges from 8° to 22°, here δ′=9.4°. The N′ external threads F3′ are assembled within each external strand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here, p3′=25 mm. The helix angle γ′ of each external thread F3′ in the external layer C3′ within each external strand TE ranges from 9° to 25°, here γ′=11°.

(170) It will be noted that 48°≤3α′+β′+δ′+γ′≤154° and here because Q′>1, 61°≤3α′+β′+δ′+γ′≤154°. In this particular instance, in this embodiment of the cord 165 with a very low modulus, 65°≤3α′+β′+δ′+γ′≤153°, and here because Q′>1, 78°≤3α′+β′+δ′+γ′≤153°. In the case of the cord 165, 3α′+β′+δ′+γ′=85.9°.

(171) It will be noted that 84°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°. In this particular instance, because Q=1 and Q′>1, 88°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤254°. In the embodiment of the cord 165 with a very low modulus, 138°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280° and because Q=1 and Q′>1, 148°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤254°, and here 3α+β+δ+γ+3α′+β′+δ′+γ′=206.8°.

(172) It will also be noted that 1.21≤EC/EI, preferably 1.21≤EC/EI≤3.00 and here EC/EI=1.44.

(173) Cord According to a 14.sup.th Embodiment of the Invention

(174) A medium-modulus cord 166 according to a seventh embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(175) Amongst the differences between the cords 160 and 166, it will be noted that the helix angle α of each internal strand TI in the internal layer CI of the cord 166 ranges, in the embodiment of the cord 166 with a medium modulus, from 4° to 22°, in this instance α=17.9°. The helix angle α′ of each external strand TE in the external layer CE of the cord 166 ranges, in the embodiment of the cord 166 with a medium modulus, from 11° to 21°, in this instance α′=13.2°.

(176) It will also be noted that, in the first embodiment of the cord 166 with a medium modulus, 25°≤3α+β+δ+γ≤97°. In the case of the cord 166, 3α+β+δ+γ=91°.

(177) Also, in the case of the cord 166 with a medium modulus, 78 GPa≤EI≤180 GPa, preferably 100 GPa≤EI≤180 GPa. Because the internal layer of the cord 166 has a relatively high modulus, 95 GPa≤EI≤180 GPa and here EI=96 GPa.

(178) It will also be noted that Q′>1, Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13, 14 or 15 and here Q′=3, P′=8 and N′=13. The Q′ internal threads F1′ are wound in a helix within each external strand TE at a pitch p1′ such that 5 mm≤p1′≤15 mm. Here, p1′=12 mm. The helix angle β of each internal thread F1′ of the internal layer within each external strand TE ranges from 4° to 20°, here β′=4.5°. The P′ intermediate threads F2′ are assembled within each external strand TE at a pitch p2′ such that 10 mm≤p2′≤20 mm. Here, p2′=18 mm. The helix angle δ′ of each intermediate thread F2′ in the intermediate layer C2′ within each external strand TE ranges from 8° to 22°, here δ′=8.1°. The N′ external threads F3′ are assembled within each external strand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here, p3′=25 mm. The helix angle γ′ of each external thread F3′ in the external layer C3′ within each external strand TE ranges from 9° to 25°, here γ′=9.6°.

(179) It will also be noted that, in the case of the cord 166 with a medium modulus, 48°≤3α′+β′+δ′+γ′≤89° and here because Q′>1, 61°≤3α′+β′+δ′+γ′≤89° and here 3α′+β′+δ′+γ′=61.8°.

(180) It is noted that, in the embodiment of the cord 166 with a medium modulus, 84°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤161° and because Q=1 and Q′>1, 88°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤153° and here 3α+β+δ+γ+3α′+β′+δ′+γ′=152.8°.

(181) Also, 1.21≤EC/EI, preferably 1.21≤EC/EI≤3.00 and here EC/EI=1.48.

(182) Also, in this embodiment of the cord 166 with a medium modulus, 131 GPa≤EC≤160 GPa. Here, EC=141 GPa.

(183) Cord According to a 15.sup.th Embodiment of the Invention

(184) FIG. 9 depicts the low-modulus cord 260 according to a fifteenth embodiment of the invention.

(185) The cord 260 is metal and of the multi-strand type with two cylindrical layers. Thus, it will be understood that there are two layers, not more, not less, of strands of which the cord 260 is made. The layers of strands are adjacent and concentric. The cord 260 is devoid of polymer compound and of elastomer compound when it is not integrated into the tyre.

(186) The cord 260 comprises an internal layer CI of the cord 260, and an external layer CE of the cord 260. The internal layer CI is made up of J>1 internal strands TI, namely of several internal strands TI, wound in a helix. The external layer CE is made up of L>1 external strands, namely of several external strands TE wound in a helix around the internal layer CI. In this instance, J=2, 3 or 4, preferably J=3 or 4. In addition, L=7, 8, 9 or 10, preferably L=8, 9 or 10. With J=3, L=7, 8 or 9 and in this instance and here J=3, L=8.

(187) The cord 260 also comprises a wrapper F made up of a single wrapping wire.

(188) The internal layer CI is wound in a helix in a direction of winding of the internal layer of the cord, here the direction S. The internal strands TI are wound in a helix with a pitch PI such that 10 mm≤PI≤65 mm and preferably 10 mm≤PI≤45 mm. Here, PI=20 mm. The helix angle α of each internal strand TI in the internal layer CI of the cord 260 ranges from 3° to 36° and, in the case of the cord 260 with a low modulus, from 3° to 31° and in this instance α=13.6°.

(189) The external layer CE is wound in a helix around the internal layer CI in a direction of winding of the external layer of the cord that is the opposite of the direction of winding of the internal layer of the cord, here the direction Z. The external strands TE are wound in a helix around the internal strand TI with a pitch PE such that 30 mm≤PE≤65 mm and preferably 30 mm≤PE≤60 mm. Here, PE=40 mm. The helix angle α′ of each external strand TE in the external layer CE of the cord 260 ranges from 10 to 34 and, in the case of the cord 260 with a low modulus, from 10° to 31° and in this instance α′=19.1°.

(190) The wrapper F is wound around the external layer CE in a direction of winding of the wrapper, here the opposite to the direction of winding of the external layer CE, in this instance in the S-direction. The wrapping wire is wound in a helix around the external strands TE with a pitch PF such that 2 mm≤PF≤10 mm and preferably 3 mm≤PF≤8 mm. Here, PF=5.1 mm.

(191) The assembly made up of the internal CI and external CE layers, which means to say the cord 260 without the wrapper F, has a diameter D greater than or equal to 4 mm, preferably greater than or equal to 4.5 mm, and less than or equal to 7 mm, preferably less than or equal to 6.5 mm. Here, D=6.03 mm.

(192) The internal layer CI of internal strands TI has a diameter DI. Each external strand TE has a diameter DE. In this case, DI=2.87 mm, DE=1.58 mm.

(193) The external layer CE of the cord 260 is desaturated and incompletely unsaturated.

(194) The mean inter-strand distance E separating two adjacent external strands TE is greater than or equal to 30 μm. Here, the mean inter-strand distance E separating two adjacent external strands TE is such that E=43 μm. The sum SIE of the inter-thread distances E of the external layer CE is less than the diameter DE of the external strands of the external layer CE. Here, the sum SIE=8×0.043=0.34 mm, which is a value strictly less than DE=1.58 mm.

(195) Internal Strands TI of the Cord 260

(196) Each internal strand TI has two layers. Each internal strand TI comprises, here is made up of, two layers, not more, not less.

(197) Each internal strand TI comprises an internal layer C1 made up of Q≥1 internal threads F1 and an external layer C2 made up of N>1 external threads F2 wound in a helix around and in contact with the internal layer C1.

(198) Q=2, 3 or 4, preferably Q=3 or 4. N=7, 8, 9 or 10, preferably N=8, 9 or 10. With Q=4, N=7, 8 or 9 and in this instance Q=4, N=9.

(199) The internal layer C1 of each internal strand TI is wound in a helix in a direction of winding of the internal layer C1 of the internal strand TI that is identical to the direction of winding of the internal layer C1 of the cord, here in the S-direction. The Q internal threads F1 are assembled within each internal strand TI at a pitch p1 such that 5 mm≤p1≤20 mm. Here, p1=7.7 mm. The helix angle β of each internal thread F1 in the internal layer C1 within each internal strand TI ranges from 4° to 17°, here β=9.9°.

(200) The external layer C2 of each internal strand TI is wound around and in contact with the internal layer C1 in a direction of winding of the external layer C2 of the internal strand TI that is identical to the direction of winding of the internal layer C1 of the cord, here in the S-direction. The N external threads F2 are wound in a helix around the Q internal threads F1 and are assembled within each internal strand TI at a pitch p2 such that 5 mm≤p2≤40 mm. Here, p2=15.4 mm. The helix angle γ of each external thread F2 in the external layer C2 within each internal strand TI ranges from 7° to 20°, here γ=11.8°.

(201) 16°≤2α+β+γ≤105° and because Q>1, 20°≤2α+β+γ≤105°. In this particular instance, in the case of the cord 260 with a low modulus. 16°≤2α+β+γ≤86° and because Q>1, 19°≤2α+β+γ85° and here 2α+β+γ=48.9°.

(202) Each internal F1 and external F2 thread of each internal strand TI respectively has a diameter D1, D2. Each diameter of the internal threads D1 and external threads D2 of each internal strand TI ranges from 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40 mm. Each internal thread F1 of each internal strand TI has a diameter D1 greater than or equal to, here equal to, the diameter D2 of each external thread F2 of each internal strand TI. In this instance, D1=D2=0.30 mm.

(203) Because of the relatively short pitch p2, the external layer C2 of each internal strand TI is desaturated and completely unsaturated. The inter-thread distance I2 of the external layer C2 which on average separates the N external threads is greater than or equal to 5 μm. The inter-thread distance I2 is preferably greater than or equal to 15 μm, more preferentially greater than or equal to 35 μm and here equal to 46 μm. The sum SI2 of the inter-thread distances I2 of the external layer C2 is greater than the diameter d2 of the external threads F2 of the external layer C2. Here, the sum SI2=9×0.046=0.41 mm, which is a value strictly greater than D2=0.30 mm.

(204) Also, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤180 GPa and in the case of the cord 260 with a low modulus which has an internal layer with a relatively high modulus, 95 GPa≤EI≤180 GPa. In this instance, EI=148 GPa.

(205) External Strands TE of the Cord 260

(206) Each external strand TE has three layers. Thus, each external strand TE comprises, here is made up of, three layers, not more, not less.

(207) Each external strand TE comprises an internal layer C′ made up of Q′>1 internal threads F1′, an intermediate layer C2′ made up of P’>1 intermediate threads F2′ wound in a helix around and in contact with the internal layer C1′, and an external layer C3′ made up of N′>1 external threads F3′ wound in a helix around and in contact with the intermediate layer C2′.

(208) Q′=1, P′=5 or 6 and N′=10, 11 or 12, preferably Q′=1, P′=5 or 6, N′=10 or 11 and more preferentially here Q′=1, P′=6 and N′=11.

(209) In the instance in which Q′>1, the internal layer C1′ of each external strand TE is wound in a helix in a direction of winding of the internal layer C1′ of the external strand TE, the direction of winding of the internal layer C1′ of the external strand TE is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. Here, the Q′=1 internal thread F1′ is assembled within each external strand TE at an infinite pitch p1′ such that β′=0.

(210) The intermediate layer C2′ of each external strand TE is wound around and in contact with the internal layer C1′ in a direction of winding of the intermediate layer C2′ of the external strand TE that is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. The P′ intermediate threads F2′ are wound in a helix around the Q′=1 internal thread F1′ and are assembled within each external strand TE at a pitch p2′ such that 5 mm≤p2′≤20 mm. Here, p2′=7.7 mm. The helix angle δ′ of each intermediate thread F2′ in the intermediate layer C2′ within each external strand TE ranges from 6° to 22°, here γ′=15.5°.

(211) The external layer C3′ of each external strand TE is wound around and in contact with the intermediate layer C2′ in a direction of winding of the external layer C3′ of the external strand TE that is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. The N′ external threads F3′ are wound in a helix around the P′ intermediate threads F2′ and are assembled within each external strand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here, p3′=15.4 mm. The helix angle γ′ of each external thread F3′ in the external layer C3′ within each external strand TE ranges from 7° to 22°, here γ′=14.6°.

(212) 47°≤3α′+β′+δ′+γ′≤147° and in the case of the cord 260 with a low modulus, 54°≤3α′+β′+δ′+γ′≤125° and because Q′=1, 54≤3α′+β′+δ′+γ′≤120°. In this particular instance, 3α′+β′+δ′+γ′=87.4°.

(213) Each internal F1′, intermediate F2′ and external F3′ thread of each external strand TE respectively has a diameter D1′, D2′, D3′. Each diameter of the internal threads D1′, intermediate threads D2′ and external threads D3′ of each external strand TE ranges from 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40 mm. Each Q′ internal thread F1′ of each external strand TI′ has a diameter D1′ greater than or equal to the diameter D2′ of each intermediate thread F2′ of each external strand TE. Each Q′ internal thread F1′ of each external strand TE has a diameter D1′ greater than or equal to the diameter D3′ of each external thread F3′ of each external strand TE. Each N′ intermediate thread F2′ of each external strand TE has a diameter D2′ equal to the diameter D3′ of each external thread F3′ of each external strand TE. In this instance, D1′=0.38 mm>D2′=D3′=0.30 mm.

(214) The intermediate layer C2′ of each external strand TE is desaturated and incompletely unsaturated. The inter-thread distance I2′ of the intermediate layer C2′ which on average separates the P′ intermediate threads is greater than or equal to 5 μm. The inter-thread distance I2′ is preferably greater than or equal to 15 μm and is here equal to 32 μm. The sum SI2′ of the inter-thread distances I2′ of the intermediate layer C2′ is greater than the diameter D2 of the intermediate threads F2′ of the intermediate layer C2′. Here, the sum SI2′=6×0.032=0.19 mm, a value strictly less than D2′=0.30 mm. In addition, the sum SI2′ of the inter-thread distances I2′ is such that SI2′<D3′ and even SI2′<0.8×D3′.

(215) The external layer C3′ of each external strand TE is desaturated and completely unsaturated. The inter-thread distance I3′ of the external layer C3′ which on average separates the N′ external threads is greater than or equal to 5 μm. The inter-thread distance I3′ is preferably greater than or equal to 15 μm, more preferentially greater than or equal to 35 μm, more preferentially still greater than or equal to 50 μm, and here is equal to 52 μm. The sum SI3′ of the inter-thread distances I3′ of the external layer C3′ is greater than the diameter D3′ of the external threads F3′ of the external layer C3′. Here, the sum SI3′=11×0.052=0.57 mm, which is a value strictly greater than D3′=0.30 mm.

(216) Each thread F1, F2, F1′, F2′, F3′ has a breaking strength, denoted Rm, such that 2500≤Rm≤3100 MPa. The steel for these threads is said to be of SHT (“Super High Tensile”) grade. Other threads may be used, for example threads of an inferior grade, for example of NT (“Normal Tensile”) or HT (“High Tensile”) grade, just as may threads of a superior grade, for example of UT (“Ultra Tensile”) or MT (“Mega Tensile”) grade.

(217) 84°≤2α+β+γ+3α′+β′+δ′+γ′≤226° and because Q>1 et Q′=1, 88°≤2α+β+γ+3α′+β′+δ′+γ′≤206°. In the case of the cord 260 with a low modulus, 87°≤2α+β+γ+3α′+β′+δ′+γ′≤172° and because Q>1 and Q′=1, 90°≤2α+β+γ+3α′+β′+δ′+γ′≤165°. In this instance 2α+β+γ+3α′+β′+δ′+γ′=136.3°.

(218) 0.60≤EC/EI≤1.20 and here EC/EI=0.69.

(219) Also, 50 GPa≤EC≤160 GPa and in this embodiment 90 GPa≤EC≤130 GPa. Here, EC=102 GPa.

(220) Cord According to a 16.sup.th Embodiment of the Invention

(221) A low-modulus cord 261 according to a second embodiment of the invention will now be described. Elements similar to those of the cord 260 are denoted by identical references.

(222) Amongst the differences between the cords 260 and 261, it will be noted that Q=1, N=5 or 6, and here Q=1, N=6.

(223) It will also be noted that the N external threads F2 are wound in a helix around the Q=1 internal thread F1 and are assembled within each internal strand TI at a pitch p2 such that 5 mm≤p2≤30 mm. Here, p2=7.7 mm. The helix angle γ of each external thread F2 in the external layer C2 within each internal strand TI ranges from 5° to 26°, here γ=12.9°.

(224) It will also be noted that 16°≤2α+β+γ≤105° and because Q=1, 16°≤2α+β+γ≤86° and here 2α+β+γ=26.5°.

(225) It will be noted that, because Q=1 and Q′=1, 84°≤2α+β+γ+3α′+β′+δ′+γ′≤199°.

(226) In the case of the cord 261 with a low modulus, with Q=1 and Q′=1, 87°≤2α+β+γ+3α′+β′+δ′+γ′≤160°. In this instance 2α+β+γ+3α′+β′+δ′+γ′=136.3°.

(227) It will be noted that EC/EI≤0.59, and preferably 0.40≤EC/EI≤0.59 and here EC/EI=0.56.

(228) Cord According to a 17.sup.th Embodiment of the Invention

(229) A low-modulus cord 262 according to a third embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(230) Amongst the differences between the cords 260 and 262, it will be noted that, because the internal layer of the cord 262 with a low modulus has a relatively low modulus, 25 GPa≤EI≤94 GPa, preferably 64 GPa≤EI≤94 GPa. In this instance, EI=71 GPa.

(231) It will be noted that 1.21≤EC/EI and preferably 1.21≤EC/EI≤3.00 and in the case of the cord 262 with a low modulus, 1.21≤EC/EI≤2.82, and here EC/EI=1.33.

(232) Cord According to a 18.sup.th Embodiment of the Invention

(233) A very low-modulus cord 263 according to a fourth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(234) Amongst the differences between the cords 260 and 263, it will be noted that the helix angle α of each internal strand TI in the internal layer CI of the cord 263 ranges, in the case of the cord 263 with a very low modulus, from 5° to 36° and in this instance α=10°. It will also be noted that the helix angle α′ of each external strand TE in the external layer CE of the cord 263 ranges, in the case of the cord 263 with a very low modulus, from 14 to 34 and in this instance α′=14.5°.

(235) It will also be noted that, in the case of the cord 263 with a very low modulus, 20°≤2α+β+γ≤105° and because Q>1, 27°≤2α+β+γ≤105° and here 2α+β+γ=53.6°.

(236) It will be noted that, in the case of the cord 263 with a very low modulus, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤175 GPa. In the case of the cord 263 that has an internal layer with a relatively high modulus, 95 GPa≤EI≤180 GPa, preferably 95 GPa≤EI≤175 GPa. In this instance, EI=130 GPa.

(237) It will be noted that, in the case of the cord 263 with a very low modulus and because Q′=1, 66°≤3α′+β′+δ′+γ′≤147°. In this particular instance, 3α′+β′+δ′+γ′=.sup.930.5°.

(238) It will also be noted that, in the case of the cord 263 with a very low modulus, 146°≤2α+β+γ+3α′+β′+δ′+γ′≤226° and because Q>1 and Q′=1, 1300 S 2α+β+γ+3α′+β′+δ′+γ′≤206°. In this instance 2α+β+γ+3α′+β′+δ′+γ′=147.1°.

(239) In the case of the cord 263 with a very low modulus, 0.60≤EC/EI≤1.20 and here EC/EI=0.64.

(240) It will also be noted that, in this embodiment of the cord 263 with a very low modulus, 50 GPa≤EI 89 GPa. Here, EC=84 GPa.

(241) Cord According to a 19.sup.th Embodiment of the Invention

(242) A very low-modulus cord 264 according to a fifth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(243) Amongst the differences between the cords 263 and 264, it will be noted that, in the case of the cord 264 with a very low modulus that has an internal layer with a relatively low modulus, 25 GPa≤EI≤94 GPa, preferably 36 GPa≤EI≤94 GPa. In this instance, EI=42 GPa.

(244) It will be noted that Q′>1, and here Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13, 14 or 15 and here Q′=3, P′=8 and N′=13.

(245) It will be noted that the Q′ internal threads F1′ are wound in a helix within each external strand TE at a pitch p1′ such that 5 mm≤p1′≤15 mm. Here, p1′=12 mm. The helix angle β of each internal thread F1′ of the internal layer within each external strand TE ranges from 4° to 20°, here β′=6°. The P′ intermediate threads F2′ are assembled within each external strand TE at a pitch p2′ such that 10 mm≤p2′≤20 mm. Here, p2′=18 mm. The helix angle δ′ of each intermediate thread F2′ in the intermediate layer C2′ within each external strand TE ranges from 8° to 22°, here δ′=10.9°. The N′ external threads F3′ are assembled within each external strand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here, p3′=25 mm. The helix angle γ′ of each external thread F3′ in the external layer C3′ within each external strand TE ranges from 9° to 25°, here γ′=12.8°.

(246) It will also be noted that, in the case of the cord 264 with a very low modulus and because Q′>1, 75°≤3α′+β′+δ′+γ′≤140°. In this particular instance, 3α′+β′+δ′+γ′=95.7°.

(247) It will be noted that, in the case of the cord 264 with a very low modulus and because Q>1 and Q′>1, 146°≤2α+β+γ+3α′+β′+δ′+γ′≤226°. In this particular instance, 2α+β+γ+3α′+β′+δ′+γ′=188.9°.

(248) It will be noted that, in the case of the cord 264 with a very low modulus, 1.21≤EC/EI and preferably 1.21≤EC/EI≤3.00 and here EC/EI=1.72.

(249) Cord According to a 20.sup.th Embodiment of the Invention

(250) A medium-modulus cord 265 according to a sixth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(251) Amongst the differences between the cords 260 and 265, it will be noted that the helix angle α of each internal strand TI in the internal layer CI of the cord 265 with a medium modulus ranges from 3° to 20° and in this instance α=6.8°. It will also be noted that the helix angle α′ of each external strand TE in the external layer CE of the cord 265 with a medium modulus ranges from 100 to 220 and in this instance α′=15.3°.

(252) It will also be noted that Q=1, N=5 or 6 and here Q=1, N=6. The N external threads F2 are wound in a helix around the Q=1 internal thread F1 and are assembled within each internal strand TI at a pitch p2 such that 5 mm≤p2≤30 mm. Here, p2=5 mm. The helix angle γ of each external thread F2 in the external layer C2 within each internal strand TI ranges from 5° to 26°, here γ=19.4°.

(253) It will be noted that, in the case of the cord 265 with a medium modulus, 16°≤2α+β+γ≤68° and because Q=1, 16°≤2α+β+γ≤56° and here 2α+β+γ=33°.

(254) It will also be noted that, in the case of the cord 265 with a medium modulus, 78 GPa≤EI≤180 GPa, preferably 100 GPa≤EI≤180 GPa, and in the case of the cord 265 that has an internal layer with a relatively high modulus, 95 GPa≤EI≤180 GPa and, in this instance, EI=165 GPa.

(255) It will be noted that, in the case of the cord 265 with a medium modulus, 47°≤3α′+β′+δ′+γ′≤89° and because Q′=1, 47°≤3α′+β′+δ′+γ′≤86°. In this particular instance, 3α′+β′+δ′+γ′=71.4°.

(256) It will be noted that, in the case of the cord 265 with a medium modulus, 84°≤2α+β+γ+3α′+β′+δ′+γ′≤136°, and because Q=1 and Q′=1, 84°≤2α+β+γ+3α′+β′+δ′+γ′≤112°. In this particular instance, 2α+β+γ+3α′+β′+δ′+γ′=104.2°.

(257) It will also be noted that, in the case of the cord 265 with a medium modulus, in the case of the cord 265 with a medium modulus, 0.60≤EC/EI≤1.20, preferably 0.80≤EC/EI≤1.15 and here EC/EI=0.90.

(258) Also, 50 GPa≤EC≤160 GPa and in the embodiment of the cord 265 with a medium modulus, 131 GPa≤EC≤160 GPa. Here, EC=148 GPa.

(259) Cord According to a 21.sup.st Embodiment of the Invention

(260) A medium-modulus cord 266 according to a seventh embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(261) Amongst the differences between the cords 265 and 266, it will be noted that Q=2, 3 or 4, preferably Q=3 or 4. N=7, 8, 9 or 10. With Q=3 and N=7, 8 or 9 and here Q=3, N=8.

(262) It will be noted that the Q internal threads F1 are assembled within each internal strand TI at a pitch p1 such that 5 mm≤p1≤20 mm. Here, p1=12 mm. The helix angle β of each internal thread F1 in the internal layer C1 within each internal strand TI ranges from 4° to 17°, here β=6°. The N external threads F2 are wound in a helix around the Q internal threads F1 and are assembled within each internal strand TI at a pitch p2 such that 5 mm≤p2≤40 mm. Here, p2=18 mm. The helix angle γ of each external thread F2 in the external layer C2 within each internal strand TI ranges from 7° to 20°, here γ=10.9°.

(263) It will be noted that, in the case of the cord 266 with a medium modulus, because Q>1, 20°≤2α+β+γ≤68° and here 2α+β+γ=26.9°.

(264) It will also be noted that Q′>1, and here Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13, 14 or 15 and here Q′=3, P′=8 and N′=13.

(265) It will be noted that the Q′ internal threads F1′ are wound in a helix within each external strand TE at a pitch p1′ such that 5 mm≤p1′≤15 mm. Here, p1′=12 mm. The helix angle β of each external thread F1′ of the internal layer within each external strand TE ranges from 4° to 20°, here β′=4.5°. The P′ intermediate threads F2′ are assembled within each external strand TE at a pitch p2′ such that 10 mm≤p2′≤20 mm. Here, p2′=18 mm. The helix angle δ′ of each intermediate thread F2′ in the intermediate layer C2′ within each external strand TE ranges from 8° to 22°, here δ′=8.1°. The N′ external threads F3′ are assembled within each external strand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here, p3′=25 mm. The helix angle γ′ of each external thread F3′ in the external layer C3′ within each external strand TE ranges from 9° to 25°, here γ′=9.6°.

(266) It will be noted that, in the case of the cord 266 with a medium modulus and because Q′>1, 620≤3α′+β′+δ′+γ≤89° and here 3α′+β′+δ′+γ′=77.1°.

(267) Cord According to a 22.sup.nd Embodiment of the Invention

(268) FIG. 10 depicts the cord 360 according to a sixth embodiment of the invention.

(269) The cord 360 is metal and is of the multi-strand type with two cylindrical layers. Thus, it will be understood that there are two layers, not more, not less, of strands of which the cord 360 is made. The layers of strands are adjacent and concentric. The cord 360 is devoid of polymer compound and of elastomer compound when it is not integrated into the tyre.

(270) The cord 360 comprises an internal layer CI of the cord 360, and an external layer CE of the cord 360. The internal layer CI is made up of J>1 internal strands TI, namely of several internal strands TI, wound in a helix. The external layer CE is made up of L>1 external strands, namely of several external strands TE wound in a helix around the internal layer CI. In this instance, J=2, 3 or 4, preferably J=3 or 4. In addition, L=7, 8, 9 or 10, preferably L=8, 9 or 10. With J=3, L=7, 8 or 9 and in this instance and here J=3, L=8.

(271) The cord 360 also comprises a wrapper F made up of a single wrapping wire.

(272) The internal layer CI is wound in a helix in a direction of winding of the internal layer of the cord, here the direction S. The internal strands TI are wound in a helix with a pitch PI such that 10 mm≤PI≤65 mm and preferably 10 mm≤PI≤45 mm. Here, PI=20 mm. The helix angle α of each internal strand TI in the internal layer CI of the cord 360 ranges from 4° to 36° and in the embodiment of the cord 360 with a low modulus from 4° to 27° and in this instance α=13.4°.

(273) The external layer CE is wound in a helix around the internal layer CI in a direction of winding of the external layer of the cord that is the opposite of the direction of winding of the internal layer of the cord, here the direction Z. The external strands TE are wound in a helix around the internal strand TI with a pitch PE such that 30 mm≤PE≤65 mm and preferably 30 mm≤PE≤60 mm. Here, PE=40 mm. The helix angle α′ of each external strand TE in the external layer CE of the cord 360 ranges from 10° to 32° and, in the embodiment of the cord 360 with a low modulus, from 11° to 31° and in this instance α′=18.6°.

(274) The wrapper F is wound around the external layer CE in a direction of winding of the wrapper, here the opposite to the direction of winding of the external layer CE, in this instance in the S-direction. The wrapping wire is wound in a helix around the external strands TE with a pitch PF such that 2 mm≤PF≤10 mm and preferably 3 mm≤PF≤8 mm. Here, PF=5.1 mm.

(275) The assembly made up of the internal CI and external CE layers, which means to say the cord 360 without the wrapper F, has a diameter D greater than or equal to 4 mm, preferably greater than or equal to 4.5 mm, and less than or equal to 7 mm, preferably less than or equal to 6.5 mm. Here, D=5.7 mm.

(276) The internal layer CI of internal strands TI has a diameter DI. Each external strand TE has a diameter DE. In this case, DI=2.83 mm, DE=1.46 mm.

(277) The external layer CE of the cord 360 is desaturated and incompletely unsaturated. The mean inter-strand distance E separating two adjacent external strands TE is greater than or equal to 30 μm, preferably greater than or equal to 70 μm and more preferentially greater than or equal to 100 μm. Here, the mean inter-strand distance E separating two adjacent external strands TE is such that E=117 μm. The sum SIE of the inter-thread distances E of the external layer CE is less than the diameter DE of the external strands of the external layer CE. Here, the sum SIE=8×0.117=0.94 mm, which is a value strictly less than DE=1.46 mm.

(278) Internal Strands TI of the Cord 360

(279) Each internal strand TI has three layers. Each internal strand TI comprises, here is made up of, three layers, not more, not less.

(280) Each internal strand TI comprises an internal layer C1 made up of Q>1 internal threads F1, an intermediate layer C2 made up of P>1 intermediate threads F2 wound in a helix around and in contact with the internal layer C1, and an external layer C3 made up of N>1 external threads F3 wound in a helix around and in contact with the intermediate layer C2.

(281) Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or 11 and more preferentially here Q=1, P=6 and N=11.

(282) In the instance in which Q>1, the internal layer C1 of each internal strand TI is wound in a helix in a direction of winding of the internal layer C1 of the internal strand TI that is identical to the direction of winding of the internal layer C1 of the cord, here in the S-direction. Here, the Q=1 internal thread F1 is assembled within each internal strand TI at an infinite pitch such that β=0.

(283) The intermediate layer C2 of each internal strand TI is wound around and in contact with the internal layer C1 in a direction of winding of the intermediate layer C2 of the internal strand TI that is identical to the direction of winding of the internal layer CI of the cord, here in the S-direction. The P intermediate threads F2 are wound in a helix around the Q=1 internal thread F1 and are assembled within each internal strand TI at a pitch p2 such that 5 mm≤p2≤20 mm. Here, p2=7.7 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 6° to 30°, here δ=12.2°.

(284) The external layer C3 of each internal strand TI is wound around and in contact with the intermediate layer C2 in a direction of winding of the external layer C3 of the internal strand TI that is identical to the direction of winding of the internal layer CI of the cord, here in the S-direction. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=15.4 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 7° to 30°, here γ=12.1°.

(285) 26°≤3α+β+δ+γ≤162° and here because Q=1, 26°≤3α+β+δ+γ≤140°. In this particular instance, in this first embodiment of the cord 360 with a low modulus, 26°≤3α+β+δ+γ≤128° and here because Q>1, 26°≤3α+β+γ+γ≤113°. In the case of the cord 360, 3α+β+δ+γ=64.5°.

(286) Each internal F1, intermediate F2 and external F3 thread of each internal strand TI respectively has a diameter D1, D2, D3. Each diameter of the internal threads D1, intermediate threads D2 and external threads D3 of each internal strand TI ranges from 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40 mm. Each internal thread F1 of each internal strand TI has a diameter D1 greater than or equal to, here equal to, the diameter D2 of each intermediate thread F2 of each internal strand TI. Each internal thread F1 of each internal strand TI has a diameter D1 greater than or equal to, here equal to, the diameter D3 of each external thread F3 of each internal strand TI. Each intermediate thread F2 of each internal strand TI has a diameter D2 equal to the diameter D3 of each external thread F3 of each internal strand TI. In this instance, D1=D2=D3=0.26 mm.

(287) The intermediate layer C2 of each internal strand TI is saturated. Here, the distance I2 is approximately equal to 0.

(288) The external layer C3 of each internal strand TI is desaturated and completely unsaturated. The inter-thread distance I3 of the external layer C3 which on average separates the N external threads is greater than or equal to 5 μm. The inter-thread distance I3 is preferably greater than or equal to 15 μm and is here equal to 30 μm. The sum SI3 of the inter-thread distances I3 of the external layer C3 is greater than the diameter D3 of the external threads F3 of the external layer C3. Here, the sum SI3=11×0.030=0.33 mm, which is a value strictly greater than D2=0.26 mm.

(289) Also, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤180 GPa. In the case of the cord 360 with a low modulus, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤175 GPa. Here, the internal layer has a relatively high modulus, so 95 GPa≤EI≤180 GPa. In this instance, EI=147 GPa.

(290) External Strands TE of the Cord 360

(291) Each external strand TE has two layers. Thus, each external strand TE comprises, here is made up of, two layers, not more, not less.

(292) Each external strand TE comprises an internal layer C1′ made up of Q′≥1 internal threads F1′ and an external layer C2′ made up of N′>1 external threads F2′ wound in a helix around and in contact with the internal layer C1′.

(293) Q′=2, 3 or 4, preferably Q′=3 or 4. N′=7, 8, 9 or 10, preferably N′=8, 9 or 10. With Q′=3, N′=7, 8 or 9 and in this instance Q′=3, N′=8.

(294) The internal layer C1′ of each external strand TE is wound in a helix in a direction of winding of the internal layer C1′ of the external strand TE that is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. The Q′ internal threads F1′ are assembled within each external strand TE at a pitch p1′ such that 5 mm≤p1′≤20 mm. Here, p1′=7.7 mm. The helix angle β of each internal thread F1′ in the internal layer C1′ within each external strand TE ranges from 4° to 17°, here β′=9.4°.

(295) The external layer C2′ of each external strand TE is wound around and in contact with the internal layer C1′ in a direction of winding of the external layer C2′ of the internal strand TE that is identical to the direction of winding of the external layer CE of the cord, here in the Z-direction. The N′ external threads F2′ are wound in a helix around the Q′ internal threads F1′ and are assembled within each external strand TE at a pitch p2′ such that 5 mm≤p2′≤40 mm. Here, p2′=15.4 mm. The helix angle γ′ of each external thread F2′ in the external layer C2′ within each external strand TE ranges from 7° to 20°, here γ′=12.7°.

(296) 28°≤2α′+β′+γ′≤960 and here because Q′>1, 34°≤2α′+β′+γ′≤96°. In this particular instance, in this first embodiment of the cord 360 with a low modulus, 28°≤2α′+′+γ′≤89 and here because Q′=1, 36°≤2α′+β′+γ′≤89°. In the case of the cord 360, 2α′+β+γ′=59.3°.

(297) Each internal F1′ and external F2′ thread of each external strand TE respectively has a diameter D1′, D2′. Each diameter of the internal threads D1′ and external threads D2′ of each external strand TE ranges from 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40 mm. Each Q′ internal thread F1′ of each external strand TI′ has a diameter D1′ greater than or equal to, here equal to, the diameter D2′ of each external thread F2′ of each external strand TE. In this instance, D1′=D2′=0.35 mm.

(298) The external layer C2′ of each external strand TE is desaturated and completely unsaturated. The inter-thread distance I2′ of the external layer C2′ which on average separates the N′ external threads is greater than or equal to 5 μm. The inter-thread distance I2′ is preferably greater than or equal to 15 μm, more preferentially greater than or equal to 35 μm, more preferentially still greater than or equal to 50 μm and highly preferentially greater than or equal to 60 μm and is here equal to 66 μm. The sum SI2′ of the inter-thread distances I2′ of the external layer C2′ is greater than the diameter D2′ of the external threads F2′ of the external layer C2′. Here, the sum SI2′=8×0.066=0.53 mm, which is a value strictly greater than D2′=0.35 mm.

(299) Each thread F1, F2, F3, F1′, F2′ has a breaking strength, denoted Rm, such that 2500≤Rm≤3100 MPa. The steel for these threads is said to be of SHT (“Super High Tensile”) grade. Other threads may be used, for example threads of an inferior grade, for example of NT (“Normal Tensile”) or HT (“High Tensile”) grade, just as may threads of a superior grade, for example of UT (“Ultra Tensile”) or MT (“Mega Tensile”) grade.

(300) 64°≤3α+β+γ+γ+2α′+β′+γ′≤224°. In this particular instance, because Q=1 and Q′>1, 68°≤3α+β+δ+γ+2α′+β′+γ′≤220°. In the embodiment of the cord 360 with a low modulus, 74°≤3α+β+δ+γ+2α′+β′+γ′≤183° and, because Q=1 and Q′>1, 84°≤3α+β+δ+γ+2α′+β′+γ′≤168° and here 3α+β+δ+γ+2α′+β′+γ′=123.8°.

(301) 0.60≤EC/EI≤1.20 and here EC/EI=0.75.

(302) Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 360 with a low modulus, 90 GPa≤EC≤130 GPa. Here, EC=111 GPa.

(303) Cord According to a 23.sup.th Embodiment of the Invention

(304) A low-modulus cord 361 according to a second embodiment of the invention will now be described. Elements similar to those of the cord 360 are denoted by identical references.

(305) Amongst the differences between the cords 360 and 361, it will be particularly noted that Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10, N=13, 14 or 15 and here Q=3, P=8 and N=13.

(306) It will be noted that the Q internal threads F1 are wound in a helix within each internal strand TI at a pitch p1 such that 5 mm≤p1≤15 mm. Here, p1=12 mm. The helix angle β of each internal thread F1 of the internal layer within each internal strand TI ranges from 4° to 17°, here β=6°. The P intermediate threads F2 are wound in a helix around the Q internal threads F1 and are assembled within each internal strand TI at a pitch p2 such that 10 mm≤p2≤20 mm. Here, p2=18 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 8° to 22°, here δ=10.9°. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=25 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 9° to 25° here γ=12.8°.

(307) It will also be noted that, because Q>1, 36°≤3α+β+δ+γ≤162°. In this particular instance, in this embodiment of the cord 361 with a low modulus and because Q>1, 36°≤3α+β+δ+γ128° and here 3α+β+δ+γ=51.9°.

(308) It will be noted that Q′=1 and here, N′=5 or 6, preferably N′=6.

(309) It will be noted that the N′ external threads F2′ are wound in a helix around the Q′ internal threads F1′ and are assembled within each external strand TE at a pitch p2′ such that 5 mm≤p2′≤30 mm. Here, p2′=15 mm. The helix angle γ′ of each external thread F2′ in the external layer C2′ within each external strand TE ranges from 5° to 26°, here γ′=8.8°.

(310) It will be noted that, because Q′>1, 28°≤2α′+β′+γ′≤86°. In this particular instance, in this embodiment of the cord 361 with a low modulus, 28°≤2α′+β′+γ′≤85°. In the case of the cord 361, 2α′+β′+γ′=63.4°.

(311) It will be noted that, because Q>1 and Q′=1, 73°≤3α+β+δ+γ+2α′+β′+γ′≤212°.

(312) In the embodiment of the cord 361 with a low modulus, 86°≤3α+β+δ+γ+2α′+β′+γ′≤168° and here 3α+β+δ+γ+2α′+β′+γ′=115.3°.

(313) Cord According to a 24.sup.th Embodiment of the Invention

(314) A low-modulus cord 362 according to a third embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(315) Amongst the differences between the cords 360 and 362, it will be noted that 28 GPa≤EI≤94 GPa and, in the case of the cord 362 with a low modulus that has an internal layer with a relatively low modulus, 25 GPa≤EI≤94 GPa, preferably 64 GPa≤EI 94 GPa. In this instance, EI=65 GPa.

(316) It will also be noted that Q′=1, N′=5 or 6 and here preferably N′=6. The N′ external threads F2′ are wound in a helix around the Q′=1 internal thread F1′ and are assembled within each external strand TE at a pitch p2′ such that 5 mm≤p2′≤30 mm. Here, p2′=15 mm. The helix angle γ′ of each external thread F2′ in the external layer C2′ within each external strand TE ranges from 5° to 26°, here γ′=8.8°.

(317) It will be noted that, because Q′=1, 28°≤2α′+β′+γ′≤86° and, in this embodiment of the cord 362 with a low modulus, 28°≤2α′+β′+γ′≤85°. In the case of the cord 362, 2α′+β′+γ′=36.4°.

(318) It will also be noted that, because Q=1 and Q′=1, 64°≤3α+β+δ+γ+2α′+β′+Y'S 200°, and in the embodiment of the cord 362 with a low modulus, 74°≤3α+β+δ+γ+2α′+β′+γ′≤158° and here 3α+β+δ+γ+2α′+β′+γ′=148.5°.

(319) Also, 1.21≤EC/EI, and preferably 1.21≤EC/EI≤3.00 and in the embodiment of the cord 362 with a low modulus, 1.21≤EC/EI≤2.82, and here EC/EI=1.54.

(320) Cord According to a 25.sup.th Embodiment of the Invention

(321) A very low-modulus cord 363 according to a fourth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(322) Amongst the differences between the cords 360 and 363, it will be noted that the helix angle α of each internal strand TI in the internal layer CI of the cord 363 with a very low modulus ranges from 4° to 36° and in this instance α=26.7°. It will be noted that the helix angle α′ of each external strand TE in the external layer CE of the cord 363 with a very low modulus ranges from 130 to 320 and in this instance α′=16°.

(323) It will be noted that Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10, N=13, 14 or 15 and here Q=3, P=8 and N=13. The Q internal threads F1 are wound in a helix within each internal strand TI at a pitch p1 such that 5 mm≤p1≤15 mm. Here, p1=5 mm. The helix angle β of each internal thread F1 of the internal layer within each internal strand TI ranges from 4° to 17°, here β=10.7°. The P intermediate threads F2 are wound in a helix around the Q internal threads F1 and are assembled within each internal strand TI at a pitch p2 such that 10 mm≤p2≤20 mm. Here, p2=10 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 8° to 22°, here δ=14.5°. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=15 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 9° to 25°, here γ=15.7°.

(324) It will be noted that, in this embodiment of the cord 363 with a very low modulus, 35≤3α+β+δ+γ≤162° and here because Q>1, 36°≤3α+β+γ+γ≤162°. In the case of the cord 363, 3α+β+δ+γ=121°.

(325) It will also be noted that, in the case of the cord 363 having a very low modulus, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤175 GPa and, because the internal layer has a relatively low modulus, 25 GPa≤EI≤94 GPa, preferably 36 GPa≤EI≤94 GPa. In this instance, EI=73 GPa.

(326) It will be noted that, in the case of the cord 363 with a very low modulus, 34≤2α′+β′+γ′≤96° and here because Q′>1, 42°≤2α′+β′+γ′≤96 and here, 2α′+β′+γ′=65.6°.

(327) It will also be noted that, in the case of the cord 363 with a very low modulus, 10°≤3α+β+δ+γ+2α′+3′+γ′≤224° and, because Q>1 and Q′=1, 121°≤3α+β+δ+γ+2α′+β′+γ′≤224° and here 3α+β+δ+γ+2α′+β′+γ′=186.6°.

(328) It will be noted that, in the case of the cord 363 with a very low modulus, 0.60≤EC/EI≤1.20 and here EC/EI=1.14.

(329) Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 363 with a very low modulus, 50 GPa≤EC≤89 GPa. Here, EC=83 GPa.

(330) Cord According to a 26.sup.th Embodiment of the Invention

(331) A very low-modulus cord 364 according to a fifth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(332) Amongst the differences between the cords 363 and 364, it will be noted that Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or 11 and here, more preferentially Q=1, P=6 and N=11. The P intermediate threads F2 are wound in a helix around the Q=1 internal thread F1 and are assembled within each internal strand TI at a pitch p2 such that 5 mm≤p2≤20 mm. Here, p2=5 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 6° to 30°, here δ=19.4°. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=10 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 7° to 30°, here γ=18.7°.

(333) It will be noted that, because Q=1, in the embodiment of the cord 364 with a very low modulus, 35°≤3α+β+δ+γ≤140° and here, 3α+β+δ+γ≤51.9°.

(334) It will be noted that, because the cord 364 with a very low modulus has an internal layer of the cord with a relatively high modulus, 95 GPa≤EI≤180 GPa, preferably 95 GPa≤EI≤175 GPa. In this instance, EI=146 GPa.

(335) It will also be noted that Q′=1 and here, N′=5 or 6, preferably N′=6. The N′ external threads F2′ are wound in a helix around the Q′=1 internal thread F1′ and are assembled within each external strand TE at a pitch p2′ such that 5 mm≤p2′≤30 mm. Here, p2′=5 mm. The helix angle γ′ of each external thread F2′ in the external layer C2′ within each external strand TE ranges from 5° to 26°, here γ′=25.4°.

(336) It will be noted that, because Q′=1, 28°≤2α′+β′+γ′≤86 and in this embodiment of the cord 364 with a very low modulus, 34°≤2α′+β′+γ′≤86° and here 2α′+β′+γ′=64.8°.

(337) It will also be noted that, because Q=1 and Q′=1, 64°≤3α+β+δ+γ+2α′+β′+γ′≤200° and in the embodiment of the cord 364 with a very low modulus, 100°≤3α+β+δ+γ+2α′+β′+γ′≤200° and here 3α+β+δ+γ+2α′+β′+γ′=116.7°.

(338) It will also be noted that EC/EI≤0.59 and here EC/EI=0.58.

(339) Cord According to a 27.sup.th Embodiment of the Invention

(340) A medium-modulus cord 365 according to a sixth embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(341) Amongst the differences between the cords 360 and 365, it will be noted that the helix angle α of each internal strand TI in the internal layer CI ranges, in the case of the cord with a medium modulus 65, from 4° to 23° and in this instance α=11°. The helix angle α′ of each external strand TE in the external layer CE ranges, in the case of the cord with a medium modulus 65, from 10° to 27° and in this instance α′=17°.

(342) It will also be noted that Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10, N=13, 14 or 15 and here Q=3, P=8 and N=13. The Q internal threads F1 are wound in a helix within each internal strand TI at a pitch p1 such that 5 mm≤p1≤15 mm. Here, p1=8 mm. The helix angle β of each internal thread F1 of the internal layer within each internal strand TI ranges from 4° to 17°, here β=6.7°. The P intermediate threads F2 are wound in a helix around the Q internal threads F1 and are assembled within each internal strand TI at a pitch p2 such that 10 mm≤p2≤20 mm. Here, p2=15 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 8° to 22°, here δ=9.8°. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=20 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 9° to 25°, here γ=11.9°.

(343) It will also be noted that, in the case of the cord 365 with a medium modulus and because Q>1, 26°≤3α+β+δ+γ≤97° and here, 3α+β+δ+γ=61.4°.

(344) Also, in the case of the cord 365 with a medium modulus, 78 GPa≤EI≤180 GPa, preferably 100 GPa≤EI≤180 GPa. In the case of the cord 365 with a medium modulus comprising an internal layer with a relatively high modulus, 95 GPa≤EI≤180 GPa and here EI=157 GPa.

(345) It will also be noted that Q′=1, N′=5 or 6 and here preferably N′=6. The N′ external threads F2′ are wound in a helix around the Q′=1 internal thread F1′ and are assembled within each external strand TE at a pitch p2′ such that 5 mm≤p2′≤30 mm. Here, p2′=15 mm. The helix angle γ′ of each external thread F2′ in the external layer C2′ within each external strand TE ranges from 5° to 26°, here γ′=8.8°.

(346) It will be noted that, in the case of the cord 365 with a medium modulus, 30°≤2α′+β′+γ′≤64° and here because Q′=1, 30°≤2α′+β′+γ′≤62° and in this instance, 2α′+β′+γ′=44°.

(347) It will be noted that, in the case of the cord 365 with a medium modulus, 64°≤3α+β+δ+γ+2α′+β′+γ′≤135° and, because Q>1 and Q′=1, 73°≤3α+β+δ+γ+2α′+β′+γ′≤131° and here, 3α+β+δ+γ+2α′+β′+γ′=105.4°.

(348) Also, 0.60≤EC/EI≤1.20, preferably 0.80≤EC/EI≤1.15 and here EC/EI=0.91.

(349) Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 365 with a medium modulus, 131 GPa≤EC≤160 GPa. Here, EC=143 GPa.

(350) Cord According to a 28.sup.th Embodiment of the Invention

(351) A medium-modulus cord 366 according to a seventh embodiment of the invention will now be described. Elements similar to those of the cords already described are denoted by identical references.

(352) Amongst the differences between the cords 365 and 366, it will be noted that Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or 11 and here, more preferentially Q=1, P=6 and N=11. The P intermediate threads F2 are wound in a helix around the Q=1 internal thread F1 and are assembled within each internal strand TI at a pitch p2 such that 5 mm≤p2≤20 mm. Here, p2=15 mm. The helix angle δ of each intermediate thread F2 in the intermediate layer C2 within each internal strand TI ranges from 6° to 30°, here δ=8.8°. The N external threads F3 are wound in a helix around the P intermediate threads F2 and are assembled within each internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=25 mm. The helix angle γ of each external thread F3 in the external layer C3 within each internal strand TI ranges from 7° to 30°, here γ=10.3°.

(353) It will also be noted that Q′=2, 3 or 4, preferably Q′=3 or 4. N′=7, 8, 9 or 10, preferably N′=8, 9 or 10. With Q′=3, N′=7, 8 or 9, and in this instance Q′=3, N′=8.

(354) It will also be noted that the Q′ internal threads F1′ are assembled within each external strand TE at a pitch p1′ such that 5 mm≤p1′≤20 mm. Here, p1′=8 mm. The helix angle β of each internal thread F1′ in the internal layer C1′ within each external strand TE ranges from 4° to 17°, here β′=6.7°. The N′ external threads F2′ are wound in a helix around the Q′ internal threads F1′ and are assembled within each external strand TE at a pitch p2′ such that 5 mm≤p2′≤40 mm. Here, p2′=15 mm. The helix angle γ′ of each external thread F2′ in the external layer C2′ within each external strand TE ranges from 7° to 20°, here γ′=9.8°.

(355) It will be noted that, in the case of the cord 366 with a medium modulus and because Q′>1, 37°≤2α′+β′+γ′≤64° and in this instance, 2α′+β′+γ′=45.5°.

(356) It will also be noted that, in the case of the cord 366 with a medium modulus and because Q=1 and Q′>1, 68°≤3α+β+γ+γ+2α′+β′+γ′≤127° and here 3α+β+δ+γ+2α′+β′+γ′=101.5°.

(357) It will be noted that each cord described hereinabove is metal and of the multi-strand type with two cylindrical layers. Thus, it will be understood that there are two layers, not more, not less, of strands of which the cord is made. The layers of strands are adjacent and concentric. It will also be noted that the cord is devoid of polymer compound and of elastomer compound when it is not integrated into the tyre.

(358) Tables 1 to 5 below summarize the features of the cords described hereinabove and those of examples 2-1, 2-2 and 2-4 of WO2008026271 which are identified respectively by the letters T2-1, T2-2 and T2-4 in Tables 1 to 5.

(359) These Tables 1 to 5 list the measured modulus values EC of the cords. The curves of force-elongation measured in accordance with standard ASTM D2969-04 of 2014 for the cords 60, 61 and 62 according to the invention have been illustrated respectively in FIGS. 4, 5 and 7. In each of these figures, the tangent to the elastic part of the force-elongation curve, that allows the modulus values EC to be calculated, has been drawn in solid line. The structural elongations As, elastic elongations Ae, and plastic elongations Ap have also been identified.

(360) The structural elongation As is measured between the origin and the intersection of the tangent to the elastic part with the abscissa axis. The elastic elongation Ae is measured between the intersection of the tangent to the elastic part with the abscissa axis and the intersection of the tangent to the elastic part with the ordinate value corresponding to the elongation at break. The plastic elongation Ap is measured between the intersection of the tangent to the elastic part with the ordinate value corresponding to the elongation at break, and the elongation at break.

(361) Of course, the invention is not restricted to the exemplary embodiments described above.

(362) For reasons of industrial feasibility, of cost and of overall performance, it is preferable to implement the invention with linear threads, that is to say straight threads. In other words, the threads used are not pre-formed prior to being assembled.

(363) It will also be possible to combine the features of the various embodiments described or envisaged above, with the proviso that these features are compatible with one another.

(364) TABLE-US-00001 TABLE 1 Cord T2-2 60 61 62 63 64 65 66 TI Q/N 3/9 3/8 3/8 3/8 3/8 3/8 3/8 3/8 D1/D2 0.255/0.255 0.35/0.35 0.35/0.35 0.26/0.26 0.35/0.35 0.40/0.40 0.26/0.26 0.35/0.35 PI/p1/p2 (mm) 55/8/16 15/3/6 30/7.4/11.8 30/11.2/22.2 30/10/20 40/3.4/6.9 15/2.2/4.5 30/15/30 α/β/γ 4/6.6/9 19.8/23.4/30.2 10/9.8/16.4 9.1/4.8/6.6 12.3/7.3/9.8 10.6/23.6/30.1 18.3/23.7/30 12.3/4.8/6.6 2α + β + γ 23.6 93.2 46.2 29.6 41.7 74.9 90.3 36 EI (GPa) >170 53 148 173 158 76 59 164 TE Q′/N′ 3/9 3/8 3/8 3/8 3/8 3/8 3/8 3/8 D1′/D2′ 0.255/0.255 0.35/0.35 0.35/0.35 0.26/0.26 0.35/0.35 0.40/0.40 0.26/0.26 0.35/0.35 PE/p1′/p2′ (mm) 60/8/16 40/10/20 50/7.7/15.4 40/10/20 60/3/6 40/10/20 40/10/20 50/10/20 α′/β′/γ′ 9.9/6.6/9 20/7.3/9.8 16.1/9.4/12.7 16.2/7.3/9.8 14.7/23.4/30.2 24.2/7.3/9.8 16.4/7.3/9.8 17.4/7.3/9.8 2α′ + β′ + γ′ 35.4 57.1 54.3 49.5 83 65.5 49.9 51.9 J/L 3/9 3/8 3/8 4/9 4/9 4/9 4/10 4/10 2α + β + γ + 59 150.3 100.5 79.1 124.7 140.4 140.2 87.9 2α′ + β′ + γ′ EC (GPa) >160 86 127 149 79 82 96 143 EC/EI / 1.62 0.86 0.86 0.50 1.08 1.63 0.87

(365) TABLE-US-00002 TABLE 2 Cord T2-1 160 161 162 TI Q/P/N 3/9/15 1/6/11 1/6/11 3/8/13 D1/D2/D3 0.175/0.175/0.175 0.26/0.26/0.26 0.40/0.40/0.40 0.26/0.26/0.26 PI/p1/p2/p3 (mm) 50/5/10/15 20/inf/7.7/15.4 60/inf/15/25 15/8/15/20 α/β/δ/γ 4.5/7.3/9.8/10.7 13.4/0/12.2/12.1 6.9/0/9.6/11.4 26.7/6.7/9.8/11.9 3α + β + δ + γ 41.3 64.5 41.7 108.50 EI (GPa) >170 147 168 82 TE Q′/P′/N′ 3/9/15 1/6/11 1/6/11 3/8/13 D1′/D2′/D3′ 0.175/0.175/0.175 0.38/0.30/0.30 0.30/0.30/0.30 0.26/0.26/0.26 PE/p1′/p2′/p3′ (mm) 65/5/10/15 40/inf/7.7/15.4 60/inf/5/10 60/12/18/25 α′/β′/δ′/γ′ 9.3/7.3/9.8/10.7 19.1/0/15.5/14.6 17.1/0/21.7/21.2 16.4/4.5/8.1/9.6 3α′ + β′ + δ′ + γ′ 55.7 87.4 94.2 71.4 J/L 3/9 3/8 3/8 4/9 3α + β + δ + γ + 97 151.9 135.9 179.9 3α′ + β′ + δ′ + γ′ EC (GPa) >160 103 109 106 EC/EI / 0.70 0.65 1.29 Cord 163 164 165 166 TI Q/P/N 3/8/13 3/8/13 1/6/11 1/6/11 D1/D2/D3 0.30/0.30/0.30 0.40/0.40/0.40 0.40/0.40/0.40 0.26/0.26/0.26 PI/p1/p2/p3 (mm) 15/5/10/15 60/12/18/25 15/inf/15/25 15/inf/5/10 α/β/δ/γ 24.6/12.4/16.6/18 8.5/6.9/12.4/14.5 33.3/0/9.6/11.4 17.9/0/18.8/18.5 3α + β + δ + γ 120.8 59.3 120.9 91 EI (GPa) 744 157 55 96 TE Q′/P′/N′ 1/6/11 3/8/13 3/8/13 3/8/13 D1′/D2′/D3′ 0.30/0.30/0.30 0.30/0.30/0.30 0.30/0.30/0.30 0.26/0.26/0.26 PE/p1′/p2′/p3′ (mm) 60/inf/5/10 35/8/15/20 60/12/18/25 60/12/18/25 α′/β′/δ′/γ′ 16.3/0/21.7/21.2 32.7/7.8/11.2/13.7 20.1/5.2/9.4/11 13.2/4.5/8.1/9.6 3α′ + β′ + δ′ + γ′ 91.8 130.8 85.9 61.8 J/L 3/8 3/8 4/9 3/8 3α + β + δ + γ + 212.6 190.1 206.8 152.8 3α′ + β′ + δ′ + γ′ EC (GPa) 80 78 79 141 EC/EI 1.08 0.49 1.44 1.48

(366) TABLE-US-00003 TABLE 3 Cord T2-4 260 261 262 TI Q/N 3/9 4/9 1/6 3/8 D1/D2 0.175/0.175 0.30/0.30 0.30/0.26 0.26/0.26 PI/ρ1/ρ2 (mm) 45/5.5/12 20/7.7/15.4 60/inf/7.7 15/8/15 α/β/γ 3.4/6.6/8.2 13.6/9.9/11.8 6.8/0/12.9 29.6/6.7/9.8 2α + β + γ 21.6 48.9 26.5 75.7 EI (GPa) >170 148 171 71 TE Q′/P′/N′ 3/9/15 1/6/11 1/6/11 1/6/11 D1′/D2′/D3′ 0.255/0.255/0.255 0.38/0.30/0.30 0.30/0.26/0.26 0.30/0.26/0.26 PE/p1′/p2′/p3′ (mm) 55/6/12/18 40/inf/7.7/15.4 35/inf/5/10 60/inf/15/25 α′/β′/δ′/γ′ 10.3/8.8/11.9/12.9 19.1/0/15.5/14.6 25.1/0/19.4/18.7 17/0/6.7/7.7 3α′ + β′ + δ′ + γ′ 64.5 87.4 113.4 65.4 J/L 3/6 3/8 4/9 4/9 2α + β + γ + 86.1 136.3 139.9 141.1 3α′ + β′ + δ′ + γ′ EC (GPa) >160 102 97 94 EC/EI / 0.69 0.56 1.33 Cord 263 264 265 266 TI Q/N 3/8 3/8 1/6 3/8 D1/D2 0.35/0.35 0.35/0.35 0.30/0.26 0.35/0.35 PI/ρ1/ρ2 (mm) 30/5/10 15/8/15 60/inf/5 60/12/18 α/β/γ 10/14.4/19.2 35.6/9/13 6.8/0/19.4 5/6/10.9 2α + β + γ 53.60 93.20 33 26.90 EI (GPa) 130 42 165 173 TE Q′/P′/N′ 1/6/11 3/8/13 1/6/11 3/8/13 D1′/D2′/D3′ 0.39/0.35/0.35 0.35/0.35/0.35 0.30/0.26/0.26 0.26/0.26/0.26 PE/p1′/p2′/p3′ (mm) 60/inf/5/10 60/12/18/25 60/inf/7.7/15.4 45/12/18/25 α′/β′/δ′/γ′ 14.5/0/25.4/24.6 22/6/10.9/12.8 15.3/0/12.9/12.4 18.3/4.5/8.1/9.6 3α′ + β′ + δ′ + γ′ 93.5 95.7 71.4 77.1 J/L 3/8 4/9 4/9 3/8 2α + β + γ + 147.1 188.9 104.2 104 3α′ + β′ + δ′ + γ′ EC (GPa) 84 72 148 142 EC/EI 0.64 1.72 0.90 0.82

(367) TABLE-US-00004 TABLE 4 Cord T2-1 T2-2 T2-4 360 361 TI Q/P/N 3/9/15 31-19 31-19 1/6/11 3/8/13 D1/D2/D3 0.175/0.175/0.175 0.255/0.255 0.175/0.175 0.26/0.26/0.26 0.35/0.35/0.35 PI/p1/p2/p3 (mm) 50/5/10/15 55/8/16 45/5.5/12 20/inf/7.7/15.4 60/12/18/25 α/β/δ/γ 4.5/7.3/9.8/10.7 4/6.6/—/9 3.4/6.6/8.2 13.4/0/12.2/12.1 7.4/6/10.9/12.8 3α + β + δ + γ 41.3 / / 64.5 51.9 EI (GPa) >170 >170 >170 147 164 TE Q′/N′ 3/9/15 3/9 3/9/15 3/8 1/6 D1′/D2′ 0.175/0.175/0.175 0.255/0.255 0.255/0.255/0.255 0.35/0.35 0.39/0.35 PE/p1′/p2′ (mm) 65/5/10/15 60/8/16 55/6/12/18 40/7.7/15.4 35/inf/15 α′/β′/γ′ 9.3/7.3/9.8/10.7 9.9/6.6/9 10.3/8.8/11.9/12.9 18.6/9.4/12.7 27.3/0/8.8 2α′ + β′ + γ′ / 35.4 / 59.3 63.4 J/L 3/9 3/9 3/6 3/8 3/8 3α + β + δ + γ + / / / 123.8 115.3 2α′ + β′ + γ′ EC (GPa) >160 >160 >160 111 112 EC/EI / / / 0.75 0.68

(368) TABLE-US-00005 TABLE 5 Cord 362 363 364 365 366 TI Q/P/N 1/6/11 3/8/13 1/6/11 3/8/13 1/6/11 D1/D2/D3 0.39/0.35/0.35 0.26/0.26/0.26 0.30/0.26/0.26 0.26/0.26/0.26 0.39/0.35/0.35 PI/p1/p2/p3 (mm) 15/inf/5/10 15/5/10/15 60/inf/5/10 30/8/15/20 30/inf/15/25 α/β/δ/γ 20.7/0/25.4/24.6 26.7/10.7/14.5/15.7 4.6/0/19.4/18.7 11/6.7/9.8/11.9 12.3/0/8.8/10.3 3α + β + δ + γ 112.10 121 51.90 61.40 56 EI (GPa) 65 73 146 157 157 TE Q′/N′ 1/6 3/8 1/6 1/6 3/8 D1′/D2′ 0.39/0.35 0.35/0.35 0.39/0.35 0.39/0.35 0.26/0.26 PE/p1′/p2′ (mm) 50/inf/15 60/5/10 35/inf/5 45/inf/15 60/8/15 α′/β′/γ′ 13.8/0/8.8 16/14.4/19.2 19.7/0/25.4 17.6/0/8.8 14.5/6.7/9.8 2α′ + β′ + γ′ 36.4 65.6 64.8 44 45.5 J/L 2/8 4/9 3/8 3/8 3/8 3α + β + δ + γ + 148.5 186.6 116.7 105.4 101.5 2α′ + β′ + γ′ EC (GPa) 100 83 85 143 149 EC/EI 1.54 1.14 0.58 0.91 0.95