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for the rotary bending strength r
Rot
is much smaller than in the Wöhler-diagram in
Fig.
1.11
.
For both wires, the transition from the finite to the infinite life strength lies at
the number of bending cycles of about N = 300,000. This is situated in the range
between N = 150,000 and N = 500,000 that Hempel (
1957
) and Unterberg (
1967
)
previously found in rotary bending and fluctuating tensile tests.
1.1.6.4 Finite Wire Endurance
For straightened wires taken from wire ropes, Wolf (
1987
) evaluated a mean
number of rotary bending cycles for wires with diameter d = 0.8-1.0 mm
lg N
¼
21
:
708
5
:
813
lg r
rot
:
ð
1
:
2a
Þ
Briem (
2000
) and Ziegler et al. (
2005
) have also done a great number of fatigue
tests with a Stuttgart rotary bending machine. In both series of fatigue tests the
wires were new (not taken from a rope). They were only straightened before the
tests. The following endurance equations were found by regression calculation
using the test results in the finite life region Briem (
2000
):
R
0
1,770
lg N
¼
13
:
74
3
:
243
lg r
rot
0
:
30
lg d
0
:
74
lg
ð
1
:
2b
Þ
for wire diameters d
¼
0
:
8
2
:
2 mm and
for nominal strength R
0
¼
1,770; 1,960;
and 2,160 N/mm
2
:
Ziegler et al. (
2005
) found
lg N
¼
12
:
577
3
:
542
lg r
rot
0
:
072
lg d
þ
0
:
612
lg R
m
ð
1
:
2c
Þ
for wire diameters d
¼
0
:
8
1
:
8 mm and
for nominal strength R
0
¼
1,370
2,160 N/mm
2
:
The influence of the diameter of the wire and its tensile strength is different in the
two equations. Briem (
2000
) even found that the number of rotary bending cycles
is reduced when the tensile strength is increased. Only the bending stress as a main
influence may be considered as a common result because of the relatively small
range of wire diameters and tensile strength tested. Thus, the mean number of
rotary bending cycles for new wires with a diameter d = 1 mm and tensile
strength R
0
= 1,770 N/mm
2
is
lg N
¼
14
:
152
3
:
393
lg r
rot
:
ð
1
:
2d
Þ
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