Section
2 Fatigue design S-N curves
2.1 Basic design S-N curves
2.1.1 The basic design curves consist of linear relationships between
log(SB) and log(N). They are based upon a statistical analysis of
appropriate experimental data and may be taken to represent two standard deviations
below the mean line. Thus the basic S-N curves are of the form:
log(N) = log( ) – dσ – m log( )
where
|
N |
= |
the predicted number of cycles to failure under stress range 
|
 |
= |
a constant relating to the mean S-N curve |
|
d |
= |
the number of standard deviations below the mean |
|
σ |
= |
the standard deviation of log N
|
|
m |
= |
the inverse slope of the S-N curve. |
The relevant values of these terms are shown in Table 12.2.1 Details of basic S-N
curves. Table 12.2.1 Details of basic S-N
curves also shows the value of 
where
log( ) = log( ) – 2σ
which is relevant to the basic design curves (i.e. for d =
2).
2.2 Modifications to basic S-N curves
2.2.1 The factors listed in this sub-Section are to be considered when using
the basic S-N curve.
2.2.2
Unprotected joints in sea-water. For joints without adequate corrosion
protection which are exposed to sea water the basic S-N curve is reduced by a factor
of two on life for all joint classes.
NOTE
For high strength steels, i.e.  >400 N/mm2, a penalty factor of two may not be
adequate. In addition the correction relating to the numbers of small stress cycles
is not applicable.
For joints of other thicknesses, correction factors on life or stress
have to be applied to produce a relevant S-N curve. The correction on stress range
is of the form:
S = 
where
|
S |
= |
the fatigue strength of the joint under consideration |
 |
= |
the fatigue strength of the joint using the basic S-N curve |
|
t |
= |
the actual thickness of the member under consideration |
 |
= |
the thickness relevant to the basic S-N curve |
Substituting the above relationship in the basic S-N curve equation in
Pt 4, Ch 12, 2.1 Basic design S-N curves and using the equation for log ( ) in Pt 4, Ch 12, 2.1 Basic design S-N curves yields the following equation of the S-N for a
joint member thickness t:
log(N) = log – m log
A value of t = 22 mm should be used for calculating endurance
N when the actual thickness is less than 22 mm.
NOTE
This gives a benefit for nodal joints with wall thicknesses in the range
of 22 to 32 mm.
Table 12.2.1 Details of basic S-N
curves
| Class
|
|
|
m
|
Standard deviation
|
|
N/mm2
|
|
|
|
|
| B
|
2,343 x 1015
|
15,3697
|
35,3900
|
4,0
|
0,1821
|
0,4194
|
1,01 x 1015
|
100
|
| C
|
1,082 x 1014
|
14,0342
|
32,3153
|
3,5
|
0,2041
|
0,4700
|
4,23 x 1013
|
78
|
| D
|
3,988 x 1012
|
12,6007
|
29,0144
|
3,0
|
0,2095
|
0,4824
|
1,52 x 1012
|
53
|
| E
|
3,289 x 1012
|
12,5169
|
28,8216
|
3,0
|
0,2509
|
0,5777
|
1,04 x 1012
|
47
|
| F
|
1,289 x 1012
|
12,2370
|
28,1770
|
3,0
|
0,2183
|
0,5027
|
0,63 x 1012
|
40
|
| F2
|
1,231 x 1012
|
12,0900
|
27,8387
|
3,0
|
0,2279
|
0,5248
|
0,43 x 1012
|
35
|
| G
|
0,566 x 1012
|
11,7525
|
27,0614
|
3,0
|
0,1793
|
0,4129
|
0,25 x 1012
|
29
|
| W
|
0,368 x 1012
|
11,5662
|
26,6324
|
3,0
|
0,1846
|
0,4251
|
0,16 x 1012
|
25
|
| T
|
4,577 x 1012
|
12,6606
|
29,1520
|
3,0
|
0,2484
|
0,5720
|
1,46 x 1012
|
53,
see Note 1
|
| NOTES
|
| 1. Idealised hot spot stress
|
2. For example, the T curve expressed in terms of  is:
|
 (N) = 12,6606 – 0,2484d – 3 ( )
|
Figure 12.2.1 Basic design S-N curve for
non-nodal joints
Figure 12.2.2 Basic design S-N curve for
nodal joints
Figure 12.2.3 Treatment of high cyclic
stresses for the T-curve and a material with yield stress = 350
N/mm2
2.3 Treatment of low stress cycles
2.3.1 Under constant amplitude stresses there is a certain stress range, which
varies both with the environment and with the size of any initial defects, below
which an indefinitely large number of cycles can be sustained. In air and sea-water
with adequate protection against corrosion, and with details fabricated in
accordance with this Appendix, it is assumed that this non-propagating stress range,
So
. is the stress corresponding to N = 107 cycles; relevant
values of  are shown in Table 12.2.1 Details of basic S-N
curves.
2.3.3 An adequate estimate of this behaviour can be made by assuming that the
S-N curve has a change of inverse slope from m to m + 2 at N =
107 cycles. This correction does not apply in the case of unprotected
joints in sea-water.
2.4 Treatment of high stress cycles
2.4.1 For high stress cycles the design S-N curve for nodal joints (the T
curve) may be extrapolated back linearly to a stress range equal to twice the
material yield stress  .
2.4.3 A similar procedure can be adopted for non-nodal joints (Classes B-G)
where local bending or other structural stress concentrating features are involved
and the relevant stress range includes the stress concentration.
2.4.4 If the joint is in a region of simple membrane stress then the design
S-N curves may be extrapolated back linearly to a stress range given by twice the
tensile stress limitations given in these Rules.
2.4.5 For the Class W curve, extrapolation may be made back as for the
non-nodal joints but to a stress range defined by half the values given above (i.e.
with reference to shear instead of tensile stress).
|