Wire Ropes, Elements and Definitions - Wire Ropes: Tension, Endurance, Reliability - page 19

Fig. 1.14 Tensile strength
amplitude for wires with
diameters d = 1.17-4.2 mm
and nominal tensile strength
R 0 = 1,570-1,960 N/mm 2 ,
Unterberg ( 1967 )

0.4

˃ t , A
R m

mean

0.3

0.2

0.1

˃ t , A
R m

min

0

0 0.2 0.4

˃ t,m / R m

0.6 0.8 1.0

¼ 0 : 251 R m 0 : 199 r t ; lower :

r t ; A R 0 ¼ 1,770; d ¼ 2 : 7

The standard deviation is large. As a lower limit for this tensile strength amplitude
Unterberg gave the Goodman-line

¼ 0 : 2 R m 0 : 2 r t ; m :

r t ; A ; min R 0 ¼ 1,770; d ¼ 2 : 7

From his reverse bending tests, Unterberg ( 1967 ) found the mean relative bending
strength amplitude

¼ 0 : 271 R m 0 : 170 r t ; m :

r b ; A R 0 ¼ 1,770; d ¼ 2 : 7 ð 1 : 3a Þ

The bending strength amplitude ( 1.3a ), is a little smaller than the tensile strength
amplitude ( 1.3a ). The deviation of the bending strength is also a little smaller than
that of the tension strength to be seen in Fig. 1.14 . The bending length l = 80 mm
in relation to the smaller tensile stressing length l = 15-35 mm in case of tensile
fatigue tests may be the reason for that. For the middle stress r m = 0 and the
tensile R m = 1,770 N/mm 2 , strength the mean bending strength amplitude

(alternate bending amplitude) is r b ; Alt ¼ 0 : 271 R m ¼ 480 N/mm 2 and the mean

tensile strength amplitude is r t ; Alt ¼ 0 : 313 R m ¼ 554 N/mm 2 .
In any case, if the theory of stress gradient effect is valid, there should be an
advantage for the bending strength. However there is no such advantage to be
found in the test results. According to the theory of stress gradient effect,
Faulhaber ( 1933 ), Hempel ( 1957 ) and Siebel ( 1959 ), the fatigue strength of the
wire should be the greater, the greater the stress gradient in the wire cross-section
is. The theory of stress gradient means that if the stress gradient is large, the outer
highly stressed lay can be supported by the less stressed layer below. However the
bending strength amplitude according to ( 1.3a ) is not at all greater than the tensile