Highly compressible open reinforcing cord
A cord ( 50 ) comprises a single layer ( 52 ) made up of N helically wound metal filamentary elements ( 54 ) having an outer diameter D, the metal filamentary elements ( 54 ) defining an internal enclosure ( 58 ) of the cord of diameter Dv. Each metal filamentary element ( 54 ) has a diameter Df and a helix radius of curvature Rf. With this cord ( 50 ), D, Dv, Df and Rf being expressed in millimeters: 0.10≤Jr≤0.25, 9≤Rf/Df≤30, and 1.60≤Dv/Df≤3.20, where Jr=N/(π*(D−Df))×(Dh×Sin(π/N)−(Df/Cos(α×π/180))) and α is the helix angle, expressed in degrees, of each metal filamentary element ( 54 ).
1. A cord comprising a single layer made up of N helically wound metal filamentary elements having an outer diameter D, each metal filamentary element describing, when the cord extends in a substantially rectilinear direction, a helical path about a main axis substantially parallel to the substantially rectilinear direction, such that, in a section plane substantially perpendicular to the main axis, a distance between a center of each metal filamentary element and the main axis is equal to half a helix diameter Dh and is substantially constant and identical for all the metal filamentary elements, the metal filamentary elements defining an internal enclosure of a cord of diameter Dv, each metal filamentary element having a diameter Df and a helix radius of curvature Rf defined by Rf=P/(π×Sin(2α)), where P is a pitch of each metal filamentary element expressed in millimeters and α is a helix angle of each metal filamentary element,
wherein, with Dh, D, Dv, Df and Rf being expressed in millimeters:
0.10≤ Jr≤ 0.25
9≤ Rf/Df≤ 30, and
1.60≤ Dv/Df≤ 3.20,
where Jr=N/(π*(D−Df))×(Dh×Sin(π/N)−(Df/Cos(α×π/180))), α is the helix angle, expressed in degrees, of each metal filamentary element and Dv=Dh−Df.
2. The cord according to claim 1 , wherein 0.14≤Jr≤0.25.
3. The cord according to claim 1 , wherein 9≤Rf/Df≤25.
4. The cord according to claim 1 , wherein 1.70≤Dv/Df≤3.20.
5. The cord according to claim 1 , wherein the helix radius of curvature Rf is such that 4.10 mm≤Rf≤5.30 mm.
6. The cord according to claim 1 , wherein the helix diameter Dh of each metal filamentary element is such that 0.70 mm≤Dh≤1.60 mm.
7. The cord according to claim 1 , wherein Df is such that 0.10 mm≤Df≤0.50 mm.
8. The cord according to claim 1 , wherein Dv is such that Dv≥0.50 mm.
9. The cord according to claim 1 , wherein each metal filamentary element is wound at a pitch P such that 3 mm≤P≤15 mm.
10. The cord according to claim 1 , wherein D≤2.10 mm.
11. The cord according to claim 1 , wherein a ratio K of the pitch P to the diameter Df of each metal filamentary element, P and Df being expressed in millimeters, is such that 19≤K≤44.
12. The cord according to claim 1 , wherein the helix angle α is such that 13°≤α≤30°.
13. The cord according to claim 1 , wherein the cord has a structural elongation As such that As≥1.5%, the structural elongation As being determined by applying the standard ASTM D2969-04 of 2014 to the cord so as to obtain a force-elongation curve, the structural elongation As being equal to elongation, in %, corresponding to a projection onto an elongation axis of intersection between a tangent to a structural portion of the force-elongation curve and a tangent to an elastic portion of the force-elongation curve.
14. The cord according to claim 1 , wherein the cord has, once embedded in a crosslinked standard elastomeric matrix having a modulus in extension at 10% elongation ranging from 5 MPa to 10 MPa, a modulus of elasticity in extension greater than or equal to 100 GPa, the modulus of elasticity in extension at 10% elongation being determined according to the standard ASTM D2969-04 of 2014.
15. A tire comprising the cord according to claim 1 , the cord embedded in an elastomeric matrix.