4 S-N Curves

4.1 Basic S-N curves

4.1.1 Capacity

The capacity of welded steel joints and steel base material with respect to fatigue strength is defined by S-N curves which provide the relationship between the stress range applied to the detail and the number of constant amplitude load cycles to failure.

4.1.2 Design S-N curves

The fatigue assessment is based on use of S-N curves which are obtained from fatigue tests. The design S-N curves are established at two standard deviations below the mean S-N curves corresponding to 50% of probability of survival for relevant experimental data. Design S-N curves given in Table 2 and Table 3 correspond to a probability of survival of 97.7%.

Table 1 : Welded joints: thickness exponents

No	Joint category description	Condition	n
1	Cruciform joints, transverse T-joints, plates with transverse attachments	As-welded	0.25
1		Weld toetreatedby post-weld improvement method	0.2
2	Transverse butt welds	As-welded	0.2
2	Transverse butt welds	Ground flush or weld toe treated by post-weld improvement method	0.1
3	Longitudinal welds or attachments to plate edges	Any	0.1
3	Longitudinal welds or attachments to plate edges	Weld toe treated by post-weld improvement method	0.1
4	Longitudinal attachments on the flat bar or bulb profile	Any	0
4	Longitudinal attachments on the flat bar or bulb profile	Weld toe treated by post-weld improvement method ⁽¹⁾	0
5	Longitudinal attachments and doubling plates	As-welded	0.2
5	Longitudinal attachments and doubling plates	Weld toetreated by post-weld improvement method	0.1
6	Longitudinal attachments and doubling plates supported longitudinally	As-welded	0.1
6		Weld toetreated by post-weld improvement method ⁽¹⁾	0
(1) No benefit applicable for post-weld treatment of longitudinal end connections.

4.1.3 S-N curve scope of application

The S-N curves are applicable to normal and high strength steels up to a specified minimum yield stress equal to 390 N/mm².

4.1.4 In-air environment

The basic design curves in-air environment shown in Figure 3 are represented by linear relationships between log (Δσ) and log (N) as follows:

log (N) = log (K₂) – m ⋅ log (Δσ)

where:

l log(K₂) = log (K₁) − 2 ⋅ log(δ).

K₁ : Constant related to mean S-N curve, as given in Table 2.

K₂ : Constant related to design S-N curve, as given in Table 2.

δ : Standard deviation of log (N), as given in Table 2.

Δσ_q : Stress range at N = 10⁷ cycles related to design S-N curve, in N/mm², as given in Table 2.

Table 2 : Basic S-N curve data, in-air environment

Class	K₁		m	Standard deviation δ	K₂	Design stress range at 10⁷cycles	Design stress range at 2×10⁶cycles
Class	K₁	log₁₀K₁	m	log₁₀δ	K₂	Δσ_qN/mm2	N/mm²
B	2.343E15	15.3697	4.0	0.1821	1.01E15	100.2	149.9
C	1.082E14	14.0342	3.5	0.2041	4.23E13	78.2	123.9
D	3.988E12	12.6007	3.0	0.2095	1.52E12	53.4	91.3

Figure 3 : Basic design S-N curves, in-air environment

4.1.5 Corrosive environment

The basic design curves for corrosive environment shown in Figure 4 are represented by linear relationships between log(Δσ) and log(N) as follows:

log (N) = log (K₂) – m ⋅ log (Δσ)

N : Predicted number of cycles to failure under stress range Δσ.

K₂ : Constant related to design S-N curve as given in Table 3.

Table 3 : Basic S-N curve data, corrosive environment

Class	K₂	m	Design stress range at 2×10⁶ cycles, N/mm²
B_corr	5.05 x 10¹⁴	4.0	126.1
C_corr	2.12 x 10¹³	3.5	101.6
D_corr	7.60 x 10¹¹	3.0	72.4

Figure 4 : Basic design S-N curves, corrosive environment

4.2 Selection of S-N curves

4.2.1 Welded joints

For fatigue assessment of welded joints exposed to in-air environment, S-N curve D as defined in Table 2 is to be used. For corrosive environment, S-N curve D_corr as defined in Table 3 is to be used.

4.2.2 Base material free edge

For fatigue assessment of base material at free edge exposed to in-air environment, S-N curves B or C as defined in Table 2 are to be used. For corrosive environment, S-N curves B_corr or C_corr as defined in Table 3 are to be used.

4.2.3 Surface finishing factor

The S-N curve C is applicable to most of non-welded locations taking into account the likelihood of some notching from corrosion, wear and tear in service with surface finishing factor as given in Table 4.

Higher surface finishing quality may be applied in using S-N curve B as given in Table 4, provided adequate protective measures are taken against wear, tear and corrosion and finite element analysis according to Ch 9, Sec 5, [2] is carried out.

Table 4 : Non-welded joints: thickness exponent and surface finishing factor

Joint configuration, fatigue crack location and stress direction		Edge cutting process	Edge treatment	Surface finishing	n	K_sf	S-N curve
1	Rolled or extruded plates and sections as well as seamless pipes, no surface or rolling defects	N/A	N/A	No surface nor roll defect ^{(1) (2)}	0	0.94	B
2	Cut edges	Machine- cutting e.g. by a thermal process or sheared edge cutting	Cutting edges chamfered or rounded by means of smooth grinding, groove direction parallel to the loading direction	Smooth surface free of cracks and notches ^{(1) (2)}	0.1	1.00	B
			Cutting edges broken or rounded	Smooth surface free of cracks and notches ^{(1) (2)}	0.1	1.07	B
			No edge treatment	Surface free of cracks and severe notches (inspection procedure) ^{(1) (2)}	0.1	1.0	C
		Manually thermally cut e.g. by flame cutting	No edge treatment	Surface free of cracks and severe notches (inspection procedure) ^{(1) (2)}	0.1	1.24	C
(1) Stress increase due to geometry of cut-outs to be considered. (2) Fine mesh FE analysis according to Ch 9, Sec 5, [2].