Double-layer multi-strand cable having improved bending endurance
A multi-strand cord ( 50 ) comprises an internal layer (CI) of the cord made up of K=1 three-layer (C1, C2, C3) internal strand (TI), with the internal layer (C1) being made up of Q internal metallic threads (F1), the intermediate layer (C2) being made up of M intermediate metallic threads (F2) and the external layer (C3) being made up of N external metallic threads (F3), and an external layer (CE) of the cord made up of L>1 three-layer (C1′, C2′, C3′) external strands (TE) wound around the internal layer (CI) of the cord, with the internal layer (C1′) being made up of Q′ internal metallic threads (F1′), the intermediate layer (C2′) being made up of M′ intermediate metallic threads (F2′) and the external layer (C3′) being made up of N′ external metallic threads (F3′). The cord ( 50 ) has an endurance criterion SL≤40 000 MPa·mm with S L = max ( Δ σ bending _ CI Cp ; Δ σ bending _ CE C r × Cp ) ; and a size criterion Ec≥0.46 with Ec=Sc/Se.
1 . A two-layer multi-strand cord comprising:
an internal layer of the cord made up of K=1 three-layer internal strand comprising:
an internal layer made up of Q=1, 2, 3 or 4 internal metallic threads of diameter d1;
an intermediate layer made up of M intermediate metallic threads of diameter d2 wound around the internal layer; and
an external layer made up of N external metallic threads of diameter d3 wound around the intermediate layer; and
an external layer of the cord made up of L>1 three-layer external strands wound around the internal layer of the cord comprising:
an internal layer made up of Q′=1, 2, 3 or 4 internal metallic threads of diameter d1′;
an intermediate layer made up of M′ intermediate metallic threads of diameter d2′ wound around the internal layer; and
an external layer made up of N′ external metallic threads of diameter d3′ wound around the intermediate layer,
wherein the cord has a bending endurance criterion SL≤40 000 MPa·mm with
SL
=
max
(
Δ
σ
bending
_
CI
Cp
;
Δ
σ
bending
_
CE
C
r
×
Cp
)
,
and a size criterion Ec≥0.46 with Ec=Sc/Se, where:
Δσ bending CI =Msteel×Max(d1; d1′; d2; d2′)/2 in MPa·mm is a maximum bending stress per unit curvature seen by the internal threads of the internal and external strands or intermediate threads of the internal and external strands,
Δσ bending_CE =Msteel×Max(d3; d3′)/2 in MPa·mm is a maximum bending stress per unit curvature seen by the external metallic threads of the internal and external strands,
M steel — 210 000 MPa is the modulus of the steel,
d1, d1′, d2, d2′, d3 and d3′ are expressed in mm,
Cp
=
CpIT
+
CpTE
2
,
Cp is a penetration coefficient for the cord with Cp IT an inter-strand penetration coefficient and Cp TE a penetration coefficient for the external strands with:
Cp IT =0.4 when the inter-strand distance E of the external strands of the external layer E<30 μm; or
Cp IT =1.0 when E>70 μm; or
CP IT =0.015×E−0.05 when 30 μm≤E≤70 μm; and
CpTE
=
CpC
3
′
+
min
(
CpC
2
′
;
CpC
3
′
)
2
,
where CpC2′ is a penetration coefficient for the intermediate layer of the external strand and CpC3′ is a penetration coefficient for the external layer of the external strand such that:
Cp C2′=0.4 when the inter-thread distance I2′ of the intermediate metallic threads of the intermediate layer I2′<10 μm; or
Cp C2′=1.0 when I2′>40 μm; or
Cp C2′=0.02×I2′+0.2 when 10 μm≤I2′≤40 μm; and
Cp C3′=0.4 when the inter-thread distance I3′ of the external metallic threads of the external layer I3′<10 μm; or
Cp C3′=1.0 when I3′>40 μm; or
Cp C3′=0.02×I3′+0.2 when 10 μm≤I3′≤40 μm;
Cr is a dimensionless performance coefficient of the cord with
C
r
=
1
-
(
sin
(
∝
f
)
d
3
×
d
3
′
×
(
∑
i
=
1
Q
′
+
M
′
+
N
′
F
mi
)
×
sin
(
α
t
)
N
×
Cste
)
where:
d3 and d3′ are expressed in mm,
αf is an angle of contact between the external metallic threads of the internal strand and the external metallic threads of the external strands expressed in radians,
αt is a helix angle of each external strand expressed in radians;
∑
i
=
1
Q
′
+
M
′
+
N
′
F
mi
is a sum of forces at break for the Q′+M′+N′ threads of an external strand in Newtons;
Cste=1500 N·mm −2 ;
D is a diameter of the cord in mm; and
Sc is a compacted surface area in mm 2 with Sc=[Q×(d1/2) 2 +M×(d2/2) 2 +N×(d3/2) 2 +L×(Q′×(d1′/2) 2 +M′×(d2′/2) 2 +N′×(d3′/2) 2 )]×π and Se is the surface area of the cord in mm 2 Se=π×(D/2) 2 .
2 . The cord according to claim 1 , wherein SL≤37 500 MPa·mm.
3 . The cord according to claim 1 , wherein SL≥25 000 MPa·mm.
4 . The cord according to claim 1 , wherein Ec≥0.47.
5 . The cord according to claim 1 , wherein Ec≤0.65.
6 . The cord according to claim 1 , wherein αf is greater than or equal to 0°.
7 . The cord according to claim 1 , wherein αf is less than or equal to 25°.
8 . The cord according to claim 1 , wherein αt is greater than or equal to 0°.
9 . The cord according to claim 1 , wherein αt is less than or equal to 20°.
10 . The cord according to claim 1 , wherein the external layer of the cord is desaturated so that an inter-strand distance of the external strands, defined, on a section of the cord perpendicular to the main axis of the cord, as being the shortest distance separating, on average, circular envelopes in which two adjacent external strands are inscribed, is greater than or equal to 30 μm.
11 . The cord according to claim 1 , wherein the external layer of each external strand is desaturated.
12 . The cord according to claim 1 , wherein the penetration coefficient for the cord Cp is greater than or equal to 0.60.
13 . The cord according to claim 1 , wherein the cord is extracted from a polymer matrix.
14 . A reinforced product comprising a polymer matrix and at least one cord according to claim 1 .
15 . A tire comprising at least one cord according to claim 1 .