2.4. THE MARIN MODIFICATION FACTORS 15
For bending cyclic loading:
For steel,
S
0
e
D
8
<
:
0:5S
ut
S
ut
< 1400 Mpa .200 ksi/
700 .Map/ .100 ksi/ S
ut
1400 Mpa .200 ksi/:
(2.4)
For iron,
S
0
e
D
8
<
:
0:4S
ut
S
ut
< 400 Mpa .60 ksi/
160 .Map/ .24 ksi/ S
ut
400 Mpa .60 ksi/:
(2.5)
For aluminum,
S
0
e
D
8
<
:
0:4S
ut
S
ut
< 330 Mpa .48 ksi/
130 .Map/ .19 ksi/ S
ut
330 Mpa .48 ksi/:
(2.6)
For copper alloy,
S
0
e
D
8
<
:
0:4S
ut
S
ut
< 280 Mpa .40 ksi/
100 .Map/ .14 ksi/ S
ut
280 Mpa .40 ksi/:
(2.7)
For axial cyclic loading:
For steel,
S
0
e
D 0:45S
ut
: (2.8)
For cyclic torsional loading:
For steel,
S
0
e
D 0:29S
ut
: (2.9)
For iron,
S
0
e
D 0:32S
ut
: (2.10)
For copper alloy,
S
0
e
D 0:22S
ut
: (2.11)
2.4 THE MARIN MODIFICATION FACTORS
Material fatigue strength data are typically obtained from fatigue tests on standard rotating-
beam bending specimen under fully reversed cyclic bending stress. e fatigue specimens are
designed according to the fatigue test standards. For example, the rotating-beam bending stress
specimen has a polish surface finish and a curved cylindrical shape with a smallest diameter
0.300
00
in the middle of the specimen. e fatigue tests are typically under a fully reversed cyclic
bending stress at the room temperature. For fatigue design, a component under consideration
16 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
will have a different surface finish, different dimension, and different types of cyclic loading.
Different surface finish will have quite different initial defects or cracks on the surfaces. A com-
ponent with a bigger dimension means that it will have a much higher likelihood of more initial
defects inside components. e maximum stress’ area of a component due to bending, torsion,
and axial loading are quite different. For a component under bending, the maximum stress will
happen on the uppermost and lowermost layers. For a component under torsion, the maximum
stress will appear on the outer surface. However, a component under axial loading, the maxi-
mum stress will appear on the whole cross-section. erefore, component fatigue strength will
be different from the material fatigue strength obtained from fatigue specimen tests. is differ-
ence of fatigue strength between fatigue test specimen and a component is typically considered
by several Marin modification factors [2, 6, 7]. ose modifications on the material fatigue test
data are based on the rotating-beam bending fatigue test under a fully reversed cyclic bending
stress. e following equation can calculate component endurance limit S
e
at the critical section:
S
e
D k
a
k
b
k
c
S
0
e
; (2.12)
where S
0
e
is the material endurance limit obtained from fatigue test on the fatigue test spec-
imen. k
a
is the surface finish modification factor. k
b
is the size modification factor. k
c
is the
loading modification factor. A mechanical component might have several different component
endurance limits at different critical section due to the different size modification factors.
Component fatigue strength S
f
at a given fatigue life N can be obtained through the
following equation:
S
f
D k
a
k
b
k
c
S
0
f
; (2.13)
where S
0
f
is material fatigue strength at the fatigue life N , which is the number of cycles at
failure in the fatigue test. For fatigue design, the component fatigue strength S
f
is not one value
and will have a different value at different given fatigue life N . e rests in Equation (2.13) are
the same as those in Equation (2.12).
e surface finish modification factor k
a
can be treated as a normally distributed random
variable. Its mean
k
a
[7] will be calculated by the following equations:
k
a
D
8
ˆ
ˆ
ˆ
ˆ
ˆ
<
ˆ
ˆ
ˆ
ˆ
ˆ
:
16:45
.
S
ut
/
0:7427
For hot-rolled component
39:9
.
S
ut
/
0:995
For as-forged component
2:7
.
S
ut
/
0:2653
For machined surface component
1:34
.
S
ut
/
0:0848
For ground surface component;
(2.14)
where S
ut
is material ultimate tensile strength in the unit of ksi.
2.4. THE MARIN MODIFICATION FACTORS 17
Its standard deviation
k
a
will be calculated by using an estimated coefficient of variance
k
a
[7] of the surface finish modification factor k
a
by the following equations:
k
a
D
8
ˆ
ˆ
ˆ
ˆ
ˆ
<
ˆ
ˆ
ˆ
ˆ
ˆ
:
0:098 For hot-rolled component
0:078 For as-forged component
0:06 For machined surface component
0:131 For ground surface component
(2.15)
k
a
D
k
a
k
a
: (2.16)
e size modification factor k
b
will be treated as a deterministic and can be calculated by the
following equation [7]:
k
b
D
8
ˆ
<
ˆ
:
d
0:3
0:1133
For bending or torsion load with 0.11
00
d 2
00
1 For axial load;
(2.17)
where d is the diameter (or equivalent diameter) of the component in the unit of inch at the
critical section.
e load modification factor k
c
can be treated as a normally distributed random variable.
Its mean
k
c
can be calculated by the following equation [7]:
k
c
D
8
ˆ
<
ˆ
:
1 For bending load
0:774 For axial load
0:583 For torsional load:
(2.18)
Its standard deviation
k
c
will be calculated by using an estimated coefficient of variance
k
c
[7]
of the load modification factor k
c
by the following equations:
k
c
D
8
ˆ
ˆ
<
ˆ
ˆ
:
0 For bending load
0:163 For axial load
0:123 For torsional load
(2.19)
k
c
D
k
c
k
c
: (2.20)
In Equation (2.19), the coefficient of variance
k
c
for bending loads is zero, and the mean value
k
c
is 1. is result is because the fatigue strength test data comes from cyclic bending loading.
Example 2.2
A machined bar with a diameter 1.5
00
is subjected to a cyclic torsion loading. Its ultimate material
strength is 61.5 ksi. If the fatigue test data are obtained from rotating-beam specimen under
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