Lightweight tire

Abstract

The invention relates to a tyre (1) having a radial carcass reinforcement and two working crown layers (41, 42) which are the only layers for forming a crown reinforcement (4) over at least 40% of the width L5 of the tread (5), the absolute value of the difference between the angle [alpha] 2 and the absolute value of the angle [alpha] 1 being greater than 4 DEG, the absolute value of [alpha] 2 being greater than the absolute value of [alpha] 1, the average angle alpha meets the relational expression of 20 + 164 * exp (-L / 100) lt; [alpha] [lt]; and 23 + 164 * exp (-L / 100). According to the invention, the rubber mixture of the at least one inner liner layer constituting the at least one working crown layer comprises a composition comprising 60 phr to 80 phr of a reinforcing filler comprising at least 10 phr of pyrolytic carbon black.

Description

TECHNICAL FIELD

[0001] The present invention relates to a tire having a radial carcass reinforcement, and more particularly to a tire intended to be mounted on a vehicle (such as, for example, a truck, a tractor, a trailer or a bus) that carries heavy loads and travels at a constant speed. BACKGROUND ART

[0002] Generally, in tires for heavy-duty vehicles, the carcass reinforcement is anchored in the two bead regions on both sides and is covered radially by a crown reinforcement composed of at least two superimposed layers formed by filaments or cords, the filaments or cords being parallel within each layer and crossing from one layer to another, forming an angle between 10° and 45° with the circumferential direction. The working layer forming the working reinforcement may also be covered by at least one layer called a protection layer, the protection layer being formed by reinforcing elements (called elastic reinforcing elements) that are advantageously metallic and extensible. It may also include a layer of metallic filaments or cords having low extensibility, the metallic filaments or cords forming an angle between 45° and 90° with the circumferential direction, and this ply is called a chafer ply and is located radially between the carcass reinforcement and the first crown ply (called the working ply), the carcass reinforcement and the first crown ply being formed by parallel filaments or cords with an absolute value of the angle of at most 45°. The chafer ply and at least the working ply together form a chafer reinforcement, the chafer reinforcement having little or no deformation under the various stresses to which it is subjected, and the chafer ply being substantially used to absorb the transverse compressive forces applied to all the reinforcing elements in the tire crown region.

[0003] When a cord shows a relative elongation of at most 0.2% under a tensile force equal to 10% of the breaking force, the cord is called inextensible.

[0004] When a cord shows a relative elongation of at least 3% and a maximum tangent modulus of less than 150 GPa under a tensile force equal to the breaking load, the cord is called elastic.

[0005] A circumferential reinforcing element is a reinforcing element that forms an angle within the range of +2.5° to -2.5° (relative to 0°) with the circumferential direction.

[0006] The circumferential direction or longitudinal direction of the tire is the direction that is tangent to the outer circumference of the tire and is defined by the direction of travel of the tire.

[0007] The lateral direction or axial direction of the tire is parallel to the axis of rotation of the tire.

[0008] The radial direction is the direction that intersects and is perpendicular to the axis of rotation of the tire.

[0009] The axis of rotation of a tire is the axis about which the tire rotates during normal use.

[0010] A radial plane or a meridional plane is a plane containing the axis of rotation of the tire.

[0011] The circumferential midplane or the equatorial plane is a plane perpendicular to the axis of rotation of the tire and dividing the tire into two halves.

[0012] The "modulus of elasticity" of a rubber compound should be understood as the secant modulus of elongation at 10% elongation and ambient temperature.

[0013] For a rubber composition, the secant modulus of elasticity at 10% elongation is the modulus of elasticity measured for the compound at an elongation value of 0.1 (i.e., 10% elongation, expressed as a percentage) during a uniaxial tensile test. A uniaxial tension is applied to the specimen at a constant rate, and the elongation and the force are measured. The measurement is carried out using an INSTRON-type tensile testing machine at a temperature of 23 °C and a relative humidity of 50% (ISO 23529 standard). The conditions for measuring and using the results to determine the elongation and the stress are as described in NF ISO 37 standard: 2012-03. The stress at 0.1 elongation is determined, and the secant modulus of elasticity at 10% elongation is calculated by determining the ratio of this stress value to the elongation value. A person skilled in the art will know how to select and adjust the dimensions of the specimen according to the available and usable amount of the compound, particularly in the case where the specimen is taken from a finished product such as a tire.

[0014] Due to the improvement of the road network and the expansion of the global highway network, some tires today called "road tires" are designed to travel longer distances at higher speeds. Since the wear on the tires is reduced, this combination of conditions for the tires to travel undoubtedly enables an increase in the number of kilometers traveled; on the other hand, the durability of such tires, particularly the durability of the crown reinforcement, is adversely affected.

[0015] This is because there are stresses in the crown reinforcement, more specifically shear stresses between the crown layers, and these stresses, combined with a non-negligible increase in the operating temperature at the ends of the shortest axial crown layer, result in the following: cracks appear in the rubber and propagate at the said ends.

[0016] In order to improve the durability of the crown reinforcement of the type of tire under study, solutions have been proposed related to the structure and quality of the rubber compound layer and / or the forming element arranged between and / or around the ends of the ply (more specifically, the ends of the shortest axial ply).

[0017] It is a well-known practice to introduce a layer of rubber compound between the ends of the working ply in order to create a decoupling between said ends and thus limit the shear stress. However, this decoupling layer needs to have very good cohesion. For example, such a layer of rubber compound is described in patent application WO 2004 / 076204.

[0018] In order to improve the resistance to deterioration of the rubber compound located near the edge of the crown reinforcement, patent FR 1 389 428 proposes using a rubber forming element in combination with a low hysteresis tread, said rubber forming element covering at least the sides and the edge of the crown reinforcement and being made of a rubber compound with low hysteresis.

[0019] In order to avoid separation between the plies of the crown reinforcement, patent FR 2 222 232 teaches covering the ends of the reinforcement with a rubber pad, the Shore A hardness of which is different from that of the tread covering said reinforcement and is greater than the Shore A hardness of the forming element of the rubber compound arranged between the edge of the carcass reinforcement and the plies of the crown reinforcement.

[0020] The tyres thus produced can effectively improve the performance, especially in terms of durability.

[0021] Moreover, in order to produce tyres with a very wide tread or in order to give a greater load-bearing capacity to tyres of a given size, it is a known practice to introduce a layer of circumferential reinforcing elements. For example, patent application WO 99 / 24269 describes the presence of such a layer of circumferential reinforcing elements.

[0022] The layer of circumferential reinforcing elements generally consists of at least one metal cord, said metal cord being wound so as to form a coil with a laying angle relative to the circumferential direction of less than 2.5°.

[0023] In addition, the use of tyres on heavy-duty vehicles of the "job site supply" type means that the tyres are subjected to impact loads when driving over stony ground. These impact loads of course have an adverse effect on the performance in terms of durability.

[0024] For a person skilled in the art, it is also a known practice to increase the number of plies constituting the crown reinforcement in order to improve the durability of the tyre with respect to these impact loads.

[0025] The presence of one or more additional reinforcing element layers results in a greater tyre mass and a higher tyre manufacturing cost.

[0026] It is also known from document WO 2017 / 149222 a tyre in which the crown reinforcement of the tyre is lightened while also improving the durability properties of the tyre with respect to such impact loads. However, the inventors have found that when driving on a ground that exerts a great stress on the tyre, the durability performance of such a tyre may be reduced (especially at the shoulders of the tyre), for example under particularly severe driving conditions combining vehicle speed, the load borne by the tyre and the nature of the ground. In fact, for example, a reduction in durability performance can be observed when driving at a relatively high speed on a ground of the type supplied to construction sites, which is very demanding on the tyre. Summary of the invention

[0027] Therefore, the inventors have set themselves the task of providing a tyre for "heavy-duty" vehicles (such as vehicles of the "construction site supply" type), which tyre has a limited overall mass and whose durability performance with respect to the impact loads experienced by the tread is improved regardless of the nature of the ground and the driving conditions.

[0028] According to the invention, this object is achieved by a tyre comprising a radial carcass reinforcement intended to be mounted on a deep groove rim of the 15° deep groove type, said tyre comprising a crown reinforcement which comprises two working crown layers, each working crown layer being formed by reinforcing elements which are inserted between two surface layers of rubber compound, cross from one layer to the other and form an angle (α1, α2) greater than 8° with the circumferential direction, the angles α1 and α2 being oriented on either side of the circumferential direction respectively, a rubber compound layer C being arranged between at least the ends of said at least two working crown layers, the crown reinforcement being radially covered by a tread which is connected to two beads via two sidewalls, said two working crown layers and said at least one circumferential reinforcement element layer being the only layers used to form the crown reinforcement over at least 40% of the axial width of the crown reinforcement, the absolute value of the angle α2 formed by the reinforcing elements of the radially outermost working layer with the circumferential direction being greater than the angle α1 formed by the reinforcing elements of the radially innermost working layer with the circumferential direction, the absolute value of the difference between the absolute values of the angles α2 and α1 being greater than 4°, the average angle α satisfying the following relationship:

[0029] 12 + 131*exp(-L / 100) < α < 20 + 164*exp(-L / 100),

[0030] α is defined by the relationship α = Arctan((tan(|α1|)*tan(|α2|)) 1 / 2 ) where L is the maximum width of the tyre measured in the axial direction and expressed in mm, and the rubber compound composition of at least one surface layer forming at least one working crown layer comprises 60 phr to 80 phr of reinforcing filler, said reinforcing filler comprising at least 10 phr of pyrolytic carbon black.

[0031] Within the meaning of the present invention, a deep groove rim of the 15° deep groove type or a safety bulge deep groove rim is a one-piece rim as defined in the ETRTO, wherein the base intended to receive the tyre bead has a truncated conical shape, the angle formed with the axial direction being substantially equal to 15°. These bases are also extended by a rim flange with a reduced height compared to the flange of a flat base rim (the rim base of which has a substantially cylindrical shape).

[0032] The expression "parts by weight / hundred parts by weight of elastomer" (or phr) should be understood to mean parts by mass / hundred parts by mass of elastomer or rubber (the two terms being synonymous).

[0033] In certain embodiments, the composition comprises 60 phr to 80 phr of a reinforcing filler, the reinforcing filler being pyrolytic carbon black. Thus, it should be understood that the composition comprises pyrolytic carbon black as the sole reinforcing filler (thus, the composition does not comprise any inorganic reinforcing fillers and other organic reinforcing fillers).

[0034] The reinforcing filler can be as described below.

[0035] Within the meaning of the present invention, the term "pyrolytic carbon black" is understood to mean carbon black produced by the pyrolysis process (for example in the case of the recycling of such a material) of a material comprising at least one carbon-based polymer and carbon black (hereinafter referred to as the material to be pyrolysed). Whatever its form, whether powder, granule, strip or any other form, and whether in a crosslinked state or not, the physical state of the material to be pyrolysed provided is not important.

[0036] Preferably, the material to be pyrolysed can be recovered from manufactured articles or products produced during their manufacture / production (such as by-products or waste); these manufactured articles can be selected from pneumatic tyres, non-pneumatic tyres, industrial conveyor belts, conveyor belts, rubber gaskets, rubber hoses, shoe soles and windscreen wipers. Even more preferably, the pyrolytic carbon black usable within the scope of the present invention is carbon black obtained by the pyrolysis process of a material to be pyrolysed derived from manufactured articles selected from pneumatic tyres and non-pneumatic tyres.

[0037] Within the scope of the present invention, pyrolysis means any type of thermal decomposition carried out under anaerobic conditions, the raw material thereof being the material to be pyrolysed as defined above. Thus, pyrolytic carbon black differs from so-called industrial carbon black and / or ASTM grade carbon black in that the carbon-based raw material used for pyrolysis is a material comprising at least a carbon-based polymer and carbon black, rather than a material derived from petroleum fractions or from oils of coal or natural origin.

[0038] The pyrolytic carbon black that can be used within the scope of the present invention differs from known carbon blacks (such as industrial carbon blacks, especially "furnace process" carbon blacks) particularly in that its ash content is higher than that of the "furnace process" carbon black. The ash content of the "furnace process" carbon black is less than 1% by weight relative to the total weight of the "furnace process" carbon black.

[0039] Preferably, the ash content of the pyrolytic carbon black that can be used within the scope of the present invention ranges from 5% by weight to 30% by weight relative to the total weight of the pyrolytic carbon black, more preferably less than 25% by weight, and even more preferably less than 22% by weight.

[0040] Preferably, the sulfur content of the pyrolytic carbon black that can be used within the scope of the present invention is greater than 1.5% by weight relative to the total weight of the pyrolytic carbon black, preferably greater than 2% by weight, and more preferably ranges from 2.5% by weight to 5% by weight.

[0041] The sulfur content of the "furnace process" carbon black is less than 1.2% by weight relative to the total weight of the "furnace process" carbon black.

[0042] Preferably, the zinc content of the pyrolytic carbon black that can be used within the scope of the present invention is greater than or equal to 2% by weight relative to the total weight of the pyrolytic carbon black, and preferably ranges from 2.5% by weight to 8% by weight.

[0043] The zinc content of the "furnace process" carbon black is substantially zero and particularly less than 0.5% by weight relative to the total weight of the "furnace process" carbon black.

[0044] Preferably, the ST SA specific surface area of the pyrolytic carbon black that can be used within the scope of the present invention, measured according to standard ASTM D6556 - 2021, is in the range of 20 m 2 / g to 200 m 2 / g, and more preferably in the range of 30 m 2 / g to 90 m 2 / g.

[0045] Preferably, the void volume of the pyrolytic carbon black that can be used within the scope of the present invention, measured according to standard ASTM D7854 (2018) at a pressure of 50 MPa, is in the range of 30 ml / 100 g to 60 ml / 100 g, and more preferably in the range of 35 ml / 100 g to 55 ml / 100 g.

[0046] The ash content is determined by calcination in a platinum dish in a muffle furnace at 825 °C according to the following protocol. Before each series of measurements, the platinum dish is pre-determined and the tare weight of the platinum dish is weighed to within 0.1 mg accuracy, and the mass is designated as P0. A 5 g sample of pyrolytic carbon black accurately weighed to within 0.1 mg is placed in the platinum dish; this mass is designated as P1. The platinum dish and its contents are pre-calcined using a Bunsen burner until fumes appear and the product ignites. After the combustion of the product is complete, the platinum dish and its contents are placed in a muffle furnace heated to 825 °C for 1 h. After 1 h, the platinum dish is removed from the furnace and immediately placed in a desiccator at ambient temperature. When the platinum dish and the ash have returned to ambient temperature, the platinum dish is weighed again to obtain the mass P2. Finally, the ash content (ash %) can be obtained using the following formula:

[0047]

[0048] After the sample is calcined, the ash is absorbed in an acidic medium and the zinc content in the pyrolytic carbon black is determined by ICP-AES (Inductively Coupled Plasma Atomic Emission Spectrometry) analysis. The ash is obtained by performing the above protocol. Approximately 100 mg of ash (test sample) is taken and placed in a PFA (Perfluoroalkoxy) tube for a HotBlock hot plate. Then 8 ml of 37% concentrated hydrochloric acid, 3 ml of 65% concentrated nitric acid and 0.5 ml of 40% hydrofluoric acid are added. The tube is closed with a tube stopper and heated at 130 °C for 2 h. After cooling, the contents are then transferred to a 100 ml PTFE (Polytetrafluoroethylene) volumetric flask that already contains 2 g of boric acid (for neutralizing hydrofluoric acid) using ultrapure water. Ultra-pure water is added up to the calibration mark. The solution obtained is diluted 100 times by taking 1 ml of the solution and placing it in a 100 ml PFTE volumetric flask that already contains 8 ml of 37% concentrated hydrochloric acid, 3 ml of 65% concentrated nitric acid, 0.5 ml of 40% hydrofluoric acid and 2 g of boric acid. Then, before analysis by Inductively Coupled Plasma Atomic Emission Spectrometry (ICP-AES), the diluted solution is filtered through a 0.45 μm GHP syringe filter. Before analyzing the diluted solution, at least 5 standard samples with zinc concentrations of 0 mg / l, 0.5 mg / l, 1 mg / l, 2 mg / l and 5 mg / l are analyzed by ICP-AES. These standard samples are prepared by diluting a commercial solution with a certified zinc concentration of 1 g / l in a 100 ml volumetric flask.

[0049] These volumetric flasks already contain 8 ml of 37% concentrated hydrochloric acid, 3 ml of 65% concentrated nitric acid, 0.5 ml of 40% hydrofluoric acid, and 2 g of boric acid. The standard solution was analyzed by ICP - AES at a wavelength of λZn = 202.613 nm. For each standard concentration (c), the intensity of the zinc signal IZn was plotted on the IZn = f(c) curve, which corresponds to a calibration line (of the y = ax + b type). Then, the sample solution of unknown concentration (diluted solution) was measured under the same conditions as the standard samples. The measured intensity was related to the concentration using the previously obtained calibration line. Since the sample and volume were pre - recorded, the concentration [c] was directly obtained by the software. 灰分 (in mass %). The zinc concentration [c] in the pyrolytic carbon black was obtained by the following equation 炭黑 (in mass %):

[0050] [c] 炭黑 = [c] 灰分 * 100 * ash content %

[0051] The sulfur content in the pyrolytic carbon black was determined by a LECO furnace. The LECO sulfur analyzer is designed to measure the sulfur content in organic materials and / or inorganic materials, especially by combustion and non - dispersive infrared detection. Before measuring the sulfur content in the sample, the boat was cleaned and the furnace was calibrated. The boat used for the LECO furnace was pre - cleaned: this involved analyzing an empty boat under the same conditions as the sample. A calibration curve was prepared based on a commercial standard sample called "BBOT" (whose purity is greater than 99.99% and ensures the contents of carbon (C), hydrogen (H), nitrogen (N), oxygen (O), and sulfur (S)). These contents are as follows: C% 72.52; H% 6.09; N% 6.51; O% 7.43 and S% 7.44. Weigh approximately 10 ± 3 mg, 20 ± 3 mg, and 40 ± 3 mg of BBOT on the boat. The standard sample / boat assembly was placed into the combustion furnace and adjusted to 1350 °C under pure oxygen. The combination of the furnace temperature and the analysis flow rate caused the combustion of the sample and the release of sulfur and / or carbon in the form of SO2(g). After 20 s, oxygen began to flow through the lance, thus accelerating the combustion of materials that are difficult to burn. Sulfur and / or carbon in the form of SO2(g) was entrained by the oxygen flow through the infrared detection unit. The software of the instrument plotted a straight line that related the mass of the introduced standard sample to the response (area) observed on the detector. Thus, the calibration line was obtained. After thoroughly cleaning the sampling equipment, approximately 80 ± 5 mg of pyrolytic carbon black was weighed and placed into the boat used for the LECO furnace.

[0052] The area of the SO2 peak observed was related to the concentration by the calibration line. The software of the instrument then calculated the weight % of sulfur in the sample based on the weight of the sample placed in the boat.

[0053] Pyrolytic carbon black is sold, for example, by BlackBear under the reference number "BBCT30" or by Scandinavian EnviroSystems under the reference number "P550".

[0054] According to ETRTO, the maximum width L of the tyre is measured on a tyre mounted on its nominal rim and inflated to its nominal pressure and is expressed in millimetres.

[0055] The angles α1 and α2 (expressed in degrees) are measured in the cross-section of the tyre. According to the invention, the angles are measured in the circumferential median plane.

[0056] According to a preferred embodiment of the invention, the rubber compound of the calendered surface layer of the two working tread plies has a composition comprising 60 phr to 80 phr of reinforcing filler, said reinforcing filler having at least 10 phr of pyrolytic carbon black.

[0057] According to a preferred embodiment of the invention, at least one calendered surface layer of at least one working tread ply is an elastomeric compound based on natural rubber or on synthetic polyisoprene mainly having cis-1,4 bonds and optionally based on at least one other diene elastomer, in the case of a blend, the content of natural rubber or synthetic polyisoprene being present in a major amount relative to the one or more other diene elastomers used.

[0058] Among the diene elastomers which can be used in blend with natural rubber or synthetic polyisoprene mainly having cis-1,4 bonds, mention may be made preferably of polybutadiene (BR) mainly having cis-1,4 bonds, styrene-butadiene copolymers (SBR) in solution or emulsion, butadiene-isoprene copolymers (BIR) and styrene-butadiene-isoprene terpolymers (SBIR). These elastomers can be elastomers modified during the polymerization process or after polymerization by branching agents (such as divinylbenzene) or star branching agents (such as carbonates, tin halides or silicon halides), or are elastomers modified by functionalizing agents such that, for example, by the action of dimethylaminobenzophenone or diethylaminobenzophenone, an oxycarbonyl or carboxyl functional group or an amine functional group is grafted onto the chain or the chain ends. In the case of a blend of natural rubber or synthetic polyisoprene mainly having cis-1,4 bonds with one or more of the above diene elastomers, natural rubber or synthetic polyisoprene is preferably used in a major amount, more preferably in an amount greater than 70 phr.

[0059] Also preferably, in addition to pyrolytic carbon black, the at least one surface layer of at least one working tread ply further comprises a reinforcing filler consisting of:

[0060] a) Carbon black used in an amount between 30 phr and 70 phr, preferably between 40 phr and 60 phr,

[0061] b) Or a white filler of the silica and / or alumina type having SiOH and / or AlOH surface functional groups with a BET specific surface area between 30 m 2 / g and 260 m 2 / g, said white filler being selected from precipitated silica or pyrogenic silica, alumina or aluminosilicate, or carbon black modified during or after synthesis, and used in an amount between 30 phr and 70 phr, preferably between 40 phr and 60 phr,

[0062] c) Or a blend of the carbon black described in (a) and the white filler described in (b), wherein the total filler content is between 30 phr and 70 phr, preferably between 40 phr and 60 phr.

[0063] The BET specific surface area is measured by the Brunauer, Emmet and Teller method described in “The Journal of the American Chemical Society” (Volume 60, page 309, February 1938), which corresponds to the NFT 45007 standard of November 1987.

[0064] If a transparent filler or a white filler is used, a coupling agent and / or a covering agent selected from reagents known to those skilled in the art must be used. As examples of preferred coupling agents, mention may be made of alkoxysilane sulfides of the bis(3-trialkoxysilylpropyl) polysulfide type, in particular bis(3-triethoxysilylpropyl) tetrasulfide sold by Degussa under the names Si69 (pure liquid product) and X50S (solid product (blended with N330 carbon black in a 50 / 50 weight ratio)). As examples of covering agents, mention may be made of fatty alcohols, alkylalkoxysilanes (such as hexadecyltrimethoxysilane or hexadecyltriethoxysilane sold by Degussa under the names Si116 and Si216 respectively), diphenylguanidine, polyethylene glycol or silicone oils optionally modified by OH or alkoxy functional groups. The covering agent and / or the coupling agent is used in a weight ratio of ≥1 / 100 and ≤20 / 100 relative to the filler, preferably between 2 / 100 and 15 / 100 when the transparent filler constitutes all of the reinforcing filler, and between 1 / 100 and 20 / 100 when the reinforcing filler consists of a blend of carbon black and a transparent filler.

[0065] As further examples of reinforcing fillers having the above morphology and SiOH and / or AlOH surface functional groups of silica and / or alumina type materials and which can be used as partial or total substitutes for these materials according to the invention, mention may be made of carbon blacks which are modified during synthesis by adding compounds of silicon and / or aluminium to the feedstock oil of the furnace or, after synthesis, by adding an acid to an aqueous suspension of the carbon black in a sodium silicate and / or sodium aluminate solution, so as to at least partially cover the surface of the carbon black with SiOH and / or AlOH functional groups. As non-limiting examples of carbon-based fillers of this type having SiOH and / or AlOH functional groups on the surface, mention may be made of the CSDP type fillers described in document No. 24 of the ACS Rubber Division Meeting (Anaheim, California, 6-9 May 1997), and those fillers in patent application EP-A-0799 854.

[0066] When using a transparent filler as the only reinforcing filler, hysteresis properties and cohesion properties are obtained by using precipitated silica or fumed silica or precipitated alumina or aluminosilicate having a BET specific surface area between 30 m 2 / g and 260 m 2 / g. As non-limiting examples of fillers of this type, mention may be made of silica KS404 from Akzo, Ultrasil VN2 or VN3 and BV3370GR from Degussa, Zeopol 8745 from Huber, Zeosil 175MP or Zeosil 1165MP from Rhodia, HI-SIL 2000 from PPG, etc.

[0067] The results obtained with the tyres according to the invention have effectively demonstrated that, regardless of the nature of the ground and the driving conditions, the performance in terms of durability can be improved in the case of weight reduction of the tyre crown reinforcement. Moreover, the weight reduction of the tyre crown reinforcement is accompanied by a simplification of the manufacturing process and a reduction in the manufacturing cost.

[0068] Unexpectedly, the results effectively show that the weight of the tyres according to the invention can be reduced by reducing the number of layers constituting the tyre crown reinforcement, while improving the durability of the tyre crown, in particular with respect to the impact loads to which the tyre edges (especially at the shoulders of the tyre) are subjected, regardless of the nature of the ground and the driving conditions.

[0069] In particular, those skilled in the art are aware that, in order to improve the durability performance of tyre crown reinforcements with respect to this type of impact load, the usual practice is to increase the number of layers of reinforcing elements and the stiffness of the compounds used.

[0070] The inventors believe that these results can be explained by the fact that the angle formed with the circumferential direction by the reinforcing elements of the radially innermost working crown layer is an angle of less absolute value than the angle formed by the reinforcing elements of the radially outermost working crown layer, and by the presence of pyrolytic carbon black used as filler in at least one surface layer of at least one working crown layer. They have found that the smaller angle of the reinforcing elements of the radially innermost working crown layer seems to delay the absorption of the tensile forces by the reinforcing elements in the event of such impact loads. Moreover, the inventors have demonstrated that the presence of pyrolytic carbon black in the rubber compound constituting at least one surface layer of at least one working crown layer gives said rubber compound a value of elongation at break that is higher than that of more conventional compounds. In general, if the impact load is similar to that observed when driving over stony ground, more specifically on the shoulder of the tire, the rupture of the reinforcing elements, if such a rupture occurs, is found in the radially innermost layer, more specifically at its ends. These observations seem to indicate that, facing this type of attack, the angular difference in the reinforcing elements between two working crown layers and the presence of pyrolytic carbon black in the rubber compound constituting at least one skin layer of at least one working crown layer make it possible to improve the endurance performance of the tire while reducing the number of layers in the crown reinforcement.

[0071] However, the use of pyrolytic carbon black in at least one skin layer of at least one working crown layer results in a reduction in the stiffness of said at least one skin layer of at least one working crown layer. This lower stiffness compared to more common compounds is a factor detrimental to the durability of this radially innermost working crown layer when subjected to high stresses, such as when driving at sustained speed.

[0072] A more common tire design in practice provides that the surface layer of the working crown layer has a secant modulus of elasticity at 10% elongation greater than 10 MPa. Such a modulus of elasticity is required in order to be able to limit the compression of the reinforcing elements of the working crown layer, in particular when the vehicle moves along a winding route, in a parking lot or when passing through a circuitous route. This is because the shearing action in the axial direction acting on the tread in the area of contact with the ground leads to compression of the reinforcing elements of the working crown layer.

[0073] The relatively low stiffness compound based on pyrolytic carbon black of said at least one skin layer of at least one working crown layer contributes to limiting the temperature rise that occurs when it is subjected to shear stresses.

[0074] Furthermore, the reduction in weight of the crown reinforcement allows the overall thickness of the crown of the tyre to be reduced. The inventors have also demonstrated that, when running at sustained speed, the temperature of the crown of the tyre is lower than that of a tyre of more conventional design.

[0075] The inventors have also been able to demonstrate that the cohesion of the at least one calendered skin of at least one working crown layer according to the invention remains satisfactory.

[0076] Within the meaning of the present invention, a cohesive rubber compound is a rubber compound that is particularly resistant to cracking. Thus, the cohesion of the compound is evaluated by means of a fatigue cracking test carried out on "PS" (pure shear) specimens. The test consists in determining the variation of the crack propagation rate "Vp" (nm / cycle) as a function of the energy release rate "E" (J / m 2 ) over the experimental range covered by the measurements, which is a temperature range from -20 °C to +150 °C, using an atmosphere of air or nitrogen. The stress on the specimens is a dynamic displacement with an amplitude between 0.1 mm and 10 mm applied in the form of a pulsed stress load ("half-sine" tangent signal), where the pause time is equal to the pulse duration; the frequency of the signal is on average about 10 Hz.

[0077] The measurements consist of three parts:

[0078] · Adaptation of the "PS" specimens for 1000 cycles at 27% deformation.

[0079] · Energy characterization to determine the "E" = f(deformation) law. The energy release rate "E" is equal to W0*h0, where W0 = the energy supplied to the material per cycle and per unit volume, and h0 = the initial height of the specimen. Thus, the acquisition of "force / displacement" data gives the relationship between "E" and the amplitude of the stress load.

[0080] · Measurement of the crack after notching the "PS" specimen. The data collected are used to determine the variation of the crack propagation rate "Vp" as a function of the applied stress load level "E".

[0081] The inventors have shown in particular that the combination of weight reduction of the crown reinforcement and a compound of lower stiffness based on pyrolytic carbon black in at least one surface layer of at least one working crown ply contributes to reducing the variation in cohesion of at least one surface layer of at least one working crown ply. This is because more conventional tire designs particularly include surface layers of working crown plies with an elastic secant modulus greater than 10 MPa at 10% elongation, which causes a variation in the cohesion of the rubber compound layer arranged between the ends of the working crown ply, and the cohesion tends to become weaker. The inventors have noticed that the combination of weight reduction of the crown reinforcement and a compound of lower stiffness based on pyrolytic carbon black in at least one surface layer of at least one working crown ply limits the temperature rise and results in a slight variation in the cohesion of at least one surface layer of at least one working crown ply. Thus, the inventors consider that the cohesion of layer C (which is less than that found in more conventional tire designs) is satisfactory in the tire design according to the present invention.

[0082] The combination of the weight-reduced crown reinforcement according to the invention and the lower-stiffness pyrolysis-carbon-black-based compound (the pyrolysis-carbon-black-based compound seems to be able to impair the durability of the tire under extreme use conditions) of at least one surface layer of at least one working crown layer actually enables the durability performance of the tire to be maintained or even improved. The inventors believe that this result can be explained by the fact that on the one hand, the weight-reducing design of the crown reinforcement and on the other hand, the presence of the lower-stiffness pyrolysis-carbon-black-based compound in at least one surface layer of at least one working crown layer, which seem to reverse the expected effect on durability, have a cumulative effect on the tire crown temperature.

[0083] Advantageously according to the invention, the fracture potential index F2 / FR2 of the radially outermost working layer is less than 1 / 6, where:

[0084] FR2 is the breaking force of each cord of the radially outermost working layer under uniaxial extension,

[0085] F2 = p2*Tc*[(tan(|α1|) / (tan(|α1|)+tan(|α2|))) / cos 2 (|α2|)+C F , where

[0086] Tc = 0.078*P*Rs*(1-(Rs 2 -R L 2 ) / (2*Rt*Rs)),

[0087] P is the nominal inflation pressure of the tire according to ETRTO,

[0088] C F = 0.00035*(min((L - 80) / sin(|α1|),(L - 80) / sin(|α2|),480)-480),

[0089] p2 is the pitch of the laying of the reinforcing elements of the radially outermost working crown layer, the pitch being measured perpendicular to the reinforcing elements in the circumferential mid-plane,

[0090] Rs = Re - Es,

[0091] Re is the outer radius of the tire, measured at the radially outermost point on the tread surface of the tire, the surface being extrapolated to fill any voids that may be present,

[0092] Es is the radial distance between the radially outermost point of the tire and its orthogonal projection on the radially outer surface of the reinforcing elements of the radially innermost working crown layer,

[0093] R Lis the average value of the radii of the axially outermost points of the main part of the carcass reinforcement layer on each side of the tire.

[0094] Rt is the radius of the circle passing through three points located on the outer tread surface outside the void and defined at axial distances from the shoulder end equal to 1 / 4, 1 / 2, and 3 / 4 of the axial width of the tread, respectively.

[0095] The thickness Es and the spacing p2 are measured in the cross-section of the tire and are expressed in millimeters.

[0096] According to the invention, the meridian cross-section of the tire is defined such that the centroids of the bead wires form an axially oriented straight line, the distance between said centroids being equal to the width of the nominal rim J increased by 20 mm and minus twice the distance measured axially between the centroid of the bead wire and the point on the outer surface of the tire.

[0097] The inventors have also found that by choosing the absolute value of the difference between the absolute values of the above-mentioned angles α1 and α2 in combination with the average angle α and the fracture potential index F2 / FR2 (as defined for this advantageous embodiment according to the invention), it is possible to dispense with the protective layer that is usually mounted radially on the outside of the other layers of the crown reinforcement. Such a layer is usually present so that it can be sacrificed in the case where the tire is subjected to an attack of the cutting type, which can compromise the integrity of the metal reinforcement elements through corrosion phenomena related to the fatigue of the reinforcement elements. The inventors have actually found that when the tire is inflated or when it is used in normal running, the reinforcement elements of the radially outermost working crown layer of the tire according to the invention are subjected to less stress than the reinforcement elements of the radially outermost working crown layer of a more conventional tire; said more conventional tire shows a smaller angular difference in absolute value between the reinforcement elements of the different working layers, the absolute value of the angle formed by the reinforcement elements of the radially innermost working layer being greater than or equal to the angle formed by the reinforcement elements of the radially outermost working layer, and a higher fracture potential index F2 / FR2. Therefore, the reinforcement elements of the radially outermost working crown layer of the tire according to the invention have significantly better durability than more conventional tires; thus, the inventors have found that the protective layer can be omitted, thereby contributing to reducing the weight of the tire and limiting the temperature rise in the crown area of the tire.

[0098] According to a preferred embodiment of the invention, the absolute value of the difference between the absolute values of the angles α2 and α1 is greater than or equal to 10°, preferably greater than 14°. According to this embodiment and according to the explanations provided above, it is possible to further improve the durability performance of the reinforcement elements of the radially outermost working layer and / or further improve the performance of the tire with respect to impact loads (such as those suffered when driving over stony ground).

[0099] Preferably, the absolute value of the difference between the absolute values of the angles α2 and α1 is less than 25°, more preferably less than 20°. Above these values, the tire is prone to uneven wear under certain usage conditions.

[0100] Advantageously according to the invention, the fracture potential index F2 / FR2 of the radially outermost working layer is less than 1 / 8. Such a fracture potential index F2 / FR2 further contributes to improving the durability of the reinforcing elements of the radially outermost working layer during tire use.

[0101] Preferably according to the invention, the fracture potential index F1 / FR1 of the radially innermost working layer is less than 1 / 3, where:

[0102] FR1 is the breaking force of each cord of the radially innermost working layer under uniaxial extension.

[0103] F1 = p1 * Tc * [(tan(|α2|) / (tan(|α1|)+tan(|α2|))) / cos 2 (|α1|)+C F , where

[0104] p1 is the pitch of the laying of the reinforcing elements of the radially innermost working crown layer, the pitch being measured perpendicular to the reinforcing elements in the circumferential mid-plane.

[0105] Also preferably, the fracture potential index F1 / FR1 of the radially innermost working layer is at least 30% higher than the fracture potential index F2 / FR2 of the radially outermost working layer.

[0106] According to an advantageous embodiment of the invention, the axially widest working crown layer is located radially inside another working crown layer.

[0107] According to a preferred embodiment of the invention for optimizing the weight reduction of the tire crown, the two working crown layers are the only layers used to form the crown reinforcement over the entire axial width of the crown reinforcement.

[0108] The metal element is preferably a steel cord.

[0109] According to a preferred embodiment of the invention, the reinforcing elements of the working crown layer are non-extendable metal cords. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] By reference to the description of the exemplary embodiments of the invention given in the accompanying drawings, other details and advantageous features of the invention will become apparent hereinafter, the drawings showing a meridional view of a tire design according to an embodiment of the invention.

[0111] For the sake of easier understanding, the attached drawings are not drawn to scale. The attached drawings only show a half view of the tire, which extends symmetrically about an axis XX', which represents the circumferential median plane or the equatorial plane of the tire. Detailed Description

[0112] In the attached drawings, the size of the tire 1 is 275 / 80R 22.5. The tire 1 includes a radial carcass reinforcement 2 anchored in two beads (not shown in the figures). The carcass reinforcement is formed of a single layer of metal cords. This carcass reinforcement 2 is hoop-reinforced by a crown reinforcement 4, which is formed radially from the inside out by:

[0113] - A first working layer 41, which is formed of metal cords oriented at an angle equal to 18°,

[0114] - A second working layer 42 formed of metal cords, which are oriented at an angle equal to 30° and cross the metal cords of layer 41. The cords of each of the working layers 41, 42 are oriented on both sides of the circumferential direction respectively.

[0115] The metal cords of the reinforcing elements constituting the two working layers are cords of formula 9.35. They are distributed within each working layer at a distance equal to 2 mm between the reinforcing elements, and this distance is measured along a direction perpendicular to the bisector of the cords.

[0116] The crown reinforcement itself is covered by a tread 5.

[0117] The tire is inflated to a pressure of 8.5 bar.

[0118] The axial width L of the first working layer 41 41 is equal to 220 mm.

[0119] The axial width L of the second working layer 42 42 is equal to 200 mm.

[0120] The axial width L5 of the tread is equal to 215 mm.

[0121] The maximum axial width L is equal to 302 mm.

[0122] The combined mass of the two working layers 41, 42 and the circumferential reinforcing element layer 43 (including the mass of the metal cords and the surface compound) thus totals 10.1 kg.

[0123] According to the present invention, the calendered surface layer of the working crown layers 41, 42 is made of an elastomeric compound containing pyrolytic carbon black.

[0124] The difference between the angle formed by the cords of the first working crown layer and the circumferential direction and the angle formed by the cords of the second working crown layer and the circumferential direction is equal to 12°.

[0125] The average angle is equal to 23.4°, and is clearly between 20.4° and 28.0°.

[0126] The measured value of Re is equal to 541.7 mm.

[0127] The measured value of Es is equal to 22.3 mm.

[0128] The average value R of the measured radius L is equal to 410 mm.

[0129] The value Rt determined on the tire is equal to 900 mm.

[0130] The calculated value of Tc is equal to 362 N / mm.

[0131] C F The calculated value of is equal to -0.01.

[0132] The value of F1 is equal to 514.4 N.

[0133] The value of F2 is equal to 311.2 N.

[0134] The breaking forces FR1 and FR2 of the reinforcing elements of the working crown ply are equal to 2600 N.

[0135] The breaking potential index F2 / FR2 is equal to 12%.

[0136] The breaking potential index F1 / FR1 is equal to 19.8%.

[0137] The breaking potential index F1 / FR1 is 65% higher than the breaking potential index F2 / FR2.

[0138] Various tires according to the invention have been compared with various reference tires of the same size.

[0139] Tire I according to the invention has a surface layer of the working crown plies 41, 42 made of compound 1.

[0140] The first reference tire T1 differs from tire I1 according to the invention in the properties of the compounds for the surface layers of the working crown plies, these surface layers being made of compound R.

[0141] The various compounds used are listed below, each compound showing the secant modulus of elasticity and the elongation at break at 10% elongation.

[0142]

[0143]

[0144] The values of the components are expressed in phr (parts by weight per hundred parts of elastomer).

[0145] The pyrolysis carbon black (carbon black RCB) contains 20% ash, 1.8% sulfur and 4.5% zinc.

[0146] The carbon black N347 contains 0.5% ash, 1% sulfur and 0% zinc.

[0147] The contents of the various components in the blend I1 other than carbon black are adjusted according to the knowledge of those skilled in the art so as to obtain similar temperature and curing time conditions for various tires and to enable comparison of the properties of the tires.

[0148] The second reference tire T2 differs from the reference tire T1 in that the crown reinforcement thereof is formed radially from the inside out by:

[0149] - a triangular ply composed of two half plies and formed of non-wound 9.28 non-extensible metal cords, the metal cords being oriented at an angle equal to 65°,

[0150] - a first working ply formed of metal cords oriented at an angle equal to 26°,

[0151] - a second working ply formed of metal cords oriented at an angle equal to 18° and crossing the metal cords of the first working ply, the cords of each ply in the working ply being oriented on both sides in the circumferential direction,

[0152] - a protective ply formed of elastic 6.35 metal cords.

[0153] The metal cords of the two working plies are cords of type 9.35. They are distributed within each working ply at a distance equal to 2 mm between the reinforcing elements, the distance being measured along a direction perpendicular to the bisector of the cords.

[0154] The reference tire T2 is inflated to a pressure of 8.5 bar.

[0155] The total axial width of the triangular ply is equal to 180 mm and the width of each half ply is equal to 60 mm.

[0156] The axial width of the first working ply is equal to 220 mm.

[0157] The axial width of the second working ply is equal to 200 mm.

[0158] The axial width of the protective ply is equal to 136 mm.

[0159] The combined mass of the working ply, the protective ply and the triangular ply of the reference tire T2 (including the mass of the metal cords and the surface compound) totals 10.0 kg.

[0160] The mass of the reference tire is 62.9 kg.

[0161] The absolute value of the difference between the absolute value of the angle formed by the cords of the first working crown ply and the circumferential direction and the absolute value of the angle formed by the cords of the second working crown ply and the circumferential direction is equal to 8°.

[0162] The average angle is equal to 21.7°.

[0163] The value of F1 is equal to 320 N.

[0164] The value of F2 is equal to 392 N.

[0165] The values of F1 and F2 are obtained by finite element simulation. The large number of reinforcing plies in the crown makes it impossible to use a simple analytical model.

[0166] The breaking forces FR1 and FR2 of the reinforcing elements of the working crown ply are equal to 2600 N.

[0167] The breaking potential index F2 / FR2 is equal to 15.1%.

[0168] The breaking potential index F1 / FR1 is equal to 12.3%.

[0169] The breaking potential index F1 / FR1 is 22.7% higher than the breaking potential index F2 / FR2.

[0170] A first (especially heat - required) durability test is carried out on a testing machine. Each tire rolls in a straight line at a speed equal to the maximum speed rating (or speed index) specified for the tire under an initial load of 4000 kg. In order to shorten the duration of the test, the initial load is gradually increased.

[0171] Other (especially mechanically - required) durability tests are carried out on a testing machine. A lateral force and a dynamic over - load are applied to the tire in a cyclic manner. The tire according to the present invention is tested under the same conditions as those applied to the reference tire.

[0172] The tests thus carried out show that the distances covered by the tire according to the present invention and the reference tire in each of these tests are substantially the same.

[0173] Tests were also carried out to characterize the breaking strength of the tire crown reinforcement subjected to impact loads. These tests consisted of running a tire inflated to the recommended pressure and subjected to the recommended load on a cylindrical obstacle or indentor tool having a diameter equal to 1.5 inches (i.e., 38.1 mm), a hemispherical head, and a given height. The trajectory of the tire was adjusted so that the axis of the obstacle corresponded to the position of one of the axially outermost ribs of the tread. The breaking strength was characterized by the critical height of the indentor tool, i.e., the maximum height at which the indentor tool caused complete breakage of the crown reinforcement (i.e., breakage of all crown plies). These values represent the energy required to break the crown blocks. These values are expressed relative to a base number 100, which corresponds to the value measured for the reference tire T2.

[0174] I 125 Reference T1 120 Reference T2 100

[0175] These results show that, despite the reduction in the weight of the tire (in particular by reducing the mass of its crown reinforcement), the breaking energy of the tread surface of tires I1 and I2 according to the invention under impact loads is higher than that of the tread surface of the reference tire T2 under impact loads and higher than that of the tread surface of tire T1 under impact loads.

[0176] Final durability tests were carried out to reproduce driving conditions combining vehicle speed and particularly adverse ground. Thus, these tests reproduce the extreme conditions especially for "heavy-duty load" vehicles of the "site supply" type.

[0177] This final test includes: a stage of driving on a test track at 100 km / h for 2 hours under the load and pressure conditions indicated on the tire, followed by a stage of driving on a stony road at 35 km / h for 12 minutes, repeated 25 times.

[0178] The purpose of the stage of driving at low speed on the stony road is to have an adverse effect on durability due to repeated impact loads on the tread.

[0179] The purpose of the stage of driving at high speed on the test track is to raise the temperature of the tire. This makes the tire more sensitive to the effects of repeated impact loads on the tread and promotes the propagation of cracks initiated during the stage of driving on the stony road.

[0180] At the end of the run, the tires were inspected using speckle shearing interferometry and peeled so that any damage could be analyzed. This is a visual analysis, allowing a comparison between any cracks and crack propagation. The tires were scored and compared with each other. A score greater than 100 corresponds to a tire with less damage. The most severely damaged tire received a score of 100.

[0181] Fraction: I 120 Reference T1 100 Reference T2 100

[0182] At the end of the run, the tyres I1 and I2 according to the invention exhibit a lower degree of damage than the reference tyres T1 and T2.

[0183] During these final endurance tests, after driving for 2 hours on a circular track at 100 km / h in the first stage, the temperature of the tyre at the end of the tread block is measured.

[0184] Temperature I 94℃ Reference T1 97℃ Reference T2 102℃

[0185] These results show that the temperature exhibited by the tyres according to the invention is not actually as high as that of the reference tyres.

Claims

1. A tire (1) comprising a radial carcass reinforcement (2) intended to be mounted on a deep groove rim of the 15° deep groove type, said tire comprising a crown reinforcement (4), said crown reinforcement (4) comprising two working crown plies (41, 42) having reinforcing elements interposed between two surface layers of rubber compound, crossing from one ply to the other and forming an angle (α1, α2) greater than 8° with the circumferential direction, said angles α1 and α2 being oriented on either side of the circumferential direction, a rubber compound layer C being arranged between at least the ends of said two working crown plies, said crown reinforcement (4) being radially covered by a tread (5), said tread being connected to two beads (3) via two sidewalls, wherein: - said two working crown plies (41, 42) are the only plies forming the crown reinforcement (4) over at least 40% of the axial width of the crown reinforcement (5), - the absolute value of the angle (α2) formed by the reinforcing elements of the radially outermost working crown ply (42) with the circumferential direction is greater than the angle (α1) formed by the reinforcing elements of the radially innermost working crown ply (41) with the circumferential direction, - the absolute value of the difference between the absolute values of the angles (α2) and (α1) is greater than 4°, - the average angle α satisfies the following relationship: 12 + 131*exp(-L / 100) < α < 20 + 164*exp(-L / 100), α is defined by the relation α = Arctan((tan(|α1|) * tan(|α2|)) 1 / 2 ), where L is the maximum width of the tyre measured in the axial direction and expressed in mm, characterized in that the rubber compound comprising the composition of at least one surface layer forming at least one working crown ply comprises 60 phr to 80 phr of reinforcing filler, said reinforcing filler comprising at least 10 phr of pyrolytic carbon black.

2. The tire according to claim 1, characterized in that The ash content of the pyrolytic carbon black ranges from 5% by weight to 30% by weight, preferably less than 25% by weight, more preferably less than 22% by weight, relative to the total weight of the pyrolytic carbon black, the ash content being determined by calcination in a platinum dish in a muffle furnace at 825 °C according to the method described in the specification.

3. The tire according to claim 1 or 2, characterized in that, The sulfur content of the pyrolytic carbon black is greater than 1.5% by weight, preferably greater than 2% by weight, preferably in the range of 2.5% by weight to 5% by weight, relative to the total weight of the pyrolytic carbon black, the sulfur content in the pyrolytic carbon black being determined by a LECO furnace according to the method described in the specification.

4. The tire (1) according to any one of claims 1 to 3, characterized in that The zinc content of the pyrolytic carbon black is greater than or equal to 2% by weight, preferably in the range of 2.5% by weight to 8% by weight, the zinc content being determined by analyzing the ash absorbed in an acidic medium after calcination of the sample and by ICP - AES (Inductively Coupled Plasma Atomic Emission Spectrometry) according to the method described in the specification.

5. The tire according to any one of the preceding claims, characterized in that, Said at least one surface layer of at least one working crown ply is an elastomeric compound based on natural rubber, or on synthetic polyisoprene mainly having cis - 1,4 bonds, and optionally based on at least one other diene elastomer, in the case of a blend, the natural rubber or synthetic polyisoprene being present in a major amount relative to the content of one or more other diene elastomers used.

6. The tire (1) according to any one of the preceding claims, characterized in that, In addition to the pyrolytic carbon black, the at least one calendered skin layer of the at least one working tread ply further comprises a reinforcing filler consisting of: a) carbon black used in an amount between 30 phr and 70 phr, preferably between 40 phr and 60 phr, b) or a white filler of the silica and / or alumina type having SiOH and / or AlOH surface functional groups with a BET specific surface area between 30 m 2 / g and 260 m 2 / g, selected from precipitated silica or pyrogenic silica, alumina or aluminosilicate, or carbon black modified during or after synthesis, and used in an amount between 30 phr and 70 phr, preferably between 40 phr and 60 phr, c) or a blend of the carbon black described in (a) and the white filler described in (b), wherein the total filler content is between 30 phr and 70 phr, preferably between 40 phr and 60 phr.

7. The tire (1) according to any one of the preceding claims, characterized in that The fracture potential index F2 / FR2 of the radially outermost working tread ply (42) is less than 1 / 6, where: FR2 is the breaking force of each cord of the radially outermost working tread ply under uniaxial extension, F2 = p2 * Tc * [(tan(|α1|) / ((tan(|α1|) + tan(|α2|))) / cos 2 (|α2|) + C F , where Tc = 0.078 * P * Rs * (1 - (Rs 2 -R L 2 ) / (2 * Rt * Rs)), P is the nominal inflation pressure of the tire according to ETRTO, C F = 0.00035 * (min((L - 80) / sin(|α1|), (L - 80) / sin(|α2|), 480) - 480), p2 is the pitch of the laying of the reinforcing elements of the radially outermost working tread ply, measured perpendicular to the reinforcing elements at the circumferential mid-plane, Rs = Re - Es, Re is the outer radius of the tire, measured at the radially outermost point on the tread surface of the tire, the surface being extrapolated to fill any voids that may be present, Es is the radial distance between the radially outermost point of the tire and its orthogonal projection on the radially outer surface of the reinforcing elements of the radially innermost working tread ply, R L is the average value of the radii of the axially outermost points on each side of the tire, Rt is the radius of the circle passing through three points located on the outer tread surface outside the void and defined by axial distances from the shoulder end equal to 1 / 4, 1 / 2, and 3 / 4 of the axial width of the tread, respectively.

8. The tire (1) according to claim 7, characterized in that, The fracture potential index F2 / FR2 of the radially outermost working tread ply (42) is less than 1 / 8.

9. The tire (1) according to any one of claims 7 and 8, characterized in that The fracture potential index F1 / FR1 of the radially innermost working tread ply (41) is less than 1 / 3, where: FR1 is the breaking force of each cord of the radially innermost working ply under uniaxial extension, F1 = p1 * Tc * [(tan(|α2|) / ((tan(|α1|)+tan(|α2|))) / cos 2 (|α1|)+C F , where p1 is the pitch of the laying of the reinforcing elements of the radially innermost working tread ply, measured perpendicular to the reinforcing elements at the circumferential mid-plane.

10. The tire (1) according to claim 9, characterized in that, The fracture potential index F1 / FR1 of the radially innermost working ply (41) is at least 30% higher than the fracture potential index F2 / FR2 of the radially outermost working ply (42).

11. The tire (1) according to any one of the preceding claims, characterized in that, The two working tread plies (41, 42) are the only plies used to form the tread reinforcement over the entire axial width of the tread reinforcement (4).

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