3 Reference Stresses for Fatigue Assessment

3.1 Fatigue stress range

3.1.1 The fatigue stress range for each load case of each loading condition is defined in [3.1.2] for welded joints and in [3.1.3] for base material free edge.

The stress range of each loading condition (j) to be considered is the stress range obtained from the predominant load case, according to Ch 9, Sec 1, [7.1.2].

where:

Δσ_{FS, i(j)} : Fatigue stress range, in N/mm², for load case (i) of loading condition (j), as defined in [3.1.2] for welded joints and in [3.1.3] for base material free edge.

3.1.2 Welded joints

For welded joints, the fatigue stress range Δσ_FS,i(j), in N/mm², corrected for mean stress effect, thickness effect and warping effect, is taken as:

For simplified stress analysis:
For FE analysis:
- For web-stiffened cruciform joints:
- For other joints:

where:

f_W : Correction factor for the effect of stress gradient along weld line given as 0.96

f_S : Correction factor for the effect of supporting member given as 0.95

: Hot spot stress range, in N/mm², due to dynamic loads in load case (i) of loading condition (j) given in Ch 9, Sec 4, [2.1.1].

Fatigue stress range, in N/mm²,due to the principal hot spot stress range

SideL, SideR: Left and right side respectively of the line A-A as shown in Ch 9, Sec 5, Figure 15 and Ch 9, Sec 5, Figure 16.

f_{mean1, i(j)} : Correction factor for mean stress effect given in [3.2].

f_{mean2, i(j)} : Correction factor for mean stress effect given in [3.2].

f_warp : Correction factor due to warping effect, taken as:

f_warp = 1.07 for the deck longitudinal stiffener of bulk carrier, the closest to the longitudinal hatch coaming in way of the hatch corner as shown in Figure 1, except f_warp = 1.0 when OST is not the dominant load case for all loading conditions,
f_warp = 1.04 for following deck longitudinal stiffeners of bulk carrier, except f_warp = 1.0 when OST is not the dominant load case for all loading conditions:
- The closest stiffener to the longitudinal hatch coaming at one web frame away from the hatch corner, in way of the hatch opening as shown in Figure 1,
- The second closest stiffener away from the longitudinal hatch coaming in way of the hatch corner as shown in Figure 1,
f_warp = 1.0 for the other cases.

Figure 1 : Warping effect on deck longitudinal stiffeners of bulk carrier

Δσ_{HS1, i(j)}: Principal hot spot stress ranges, in N/mm2, due to dynamic loads for load case (i) of loading condition (j) which acts within ±45° of the perpendicular to the weld toe, determined in Ch 9, Sec 5, [3.1.2], Ch 9, Sec 5, [3.3.2] and Ch 9, Sec 5, [4.2.3] for the two types of shell elements (4-node or 8- node).

Δσ_{HS2, i(j)}: Principal hot spot stress ranges, in N/mm², due to dynamic loads for load case (i) of loading condition (j) which acts outside ±45° of the perpendicular to the weld toe, determined in Ch 9, Sec 5, [3.1.2], Ch 9, Sec 5, [3.3.2] and Ch 9, Sec 5, [4.2.3] for the two types of shell elements (4-node or 8- node).

3.1.3 Base material free edge

For base material free edge, the fatigue stress range, Δσ_FS,i(j) in N/mm², is taken as the local stress range at free edge, Δσ_BS,i(j), as defined in Ch 9, Sec 1, [2.4] with correction factors:

where:

K_sf : Surface finishing factor for base material given in [4.2.3].

f_material : Correction factor for material strength, taken as:

Δσ_{BS, i(j)} : Local stress range, in N/mm², due to dynamic loads in load case (i) of loading condition (j) taken as:

: Local stress, in N/mm², in load case ‘i1’ and ‘i2’ of loading condition (j), obtained by very fine mesh FE analysis specified in Ch 9, Sec 5.

3.2 Mean stress effect

3.2.1 Correction factor for mean stress effect

The mean stress correction factor to be considered for each principal hot spot stress range of welded joint, Δσ_{HS, i(j),} or for local stress range at free edge, Δ_{σBS, i(j)}, is taken as:

For welded joint:
For base material:

where:

R_eEq = max(315; R_eH)
σ_{mean i(j)} : Fatigue mean stress, in N/mm², for base material calculated according to [3.2.2] or welded joint calculated according to, [3.2.3] or [3.2.4] as applicable.

3.2.2 Mean stress for base material free edge

The fatigue mean stress for base material free edge, σ_mean,i(j), in N/mm², due to static and dynamic loads case ‘i1’ and 'i2’ of loading condition (j) is calculated by the following formula based on local stress:

3.2.3 Mean stress for simplified method

The fatigue mean stress to be considered for welded joint assessed by the simplified stress analysis is to be obtained from Ch 9, Sec 4, [2.2].

3.2.4 Mean stress for FE analysis

The fatigue mean stresses for welded joint due to static and dynamic loads, σ_{mean, i(j),pX} and σ_{mean, i(j),pY}, in N/mm₂, for load cases ‘i1’ and ‘i2’ of loading condition (j) ,belonging to the two principal hot spot stress range directions, pX and pY, is calculated by the following formula based on hot spot stress components as defined in Ch 9, Sec 5, [3.1.2], Ch 9, Sec 5, [3.3.2] and Ch 9, Sec 5, [4.2.3]:

θ : Angle between the direction x of the element coordinate system and the principal direction pX of the principal hot spot stress range coordinate system (Ch 9, Sec 5, [3.1.2], Ch 9, Sec 5, [4.2.3]). The direction x of the element coordinate system is defined as the normal to the weld toe.

The one of the two mean stresses σ_{mean, i(j),pX} and σ_{mean, i(j),pY} which has a principal stress direction with an absolute value less than 45° is defined as σ_{mean1, i(j)}, belonging to Δσ_{HS1, i(j)}. The other mean stress is defined as σ_{mean2, i(j)} belonging to Δσ_{HS2, i(j)}.

3.3 Thickness effect

3.3.1

Plate thickness primarily influences the fatigue strength of welded joints through the effect of geometry, and through-thickness stress distribution. The correction factor, f_thick, for plate thickness effect is taken as:

For t_n50 ≤ 22 mm, f_thick = 1.0.
For t_n50 > 22 mm, f_thick = (t_n50 /22)ⁿ

where:

t_n50 : Net thickness of the considered member in way of the hot spot for welded joints or base material free edge, in mm.

For simplified stress analysis, the net thickness to be considered for stiffeners is as follows:
- Flat bar and Bulb profile: no correction,
- Angle bar and T-bar: flange net thickness.
For FE analysis, the net thickness to be considered is the net thickness of the member where the crack is likely to initiate and propagate.

For 90° attachments, i.e. cruciform welded joints, transverse T-joints and plates with transverse attachment, the net thickness to be considered is to be taken as:

n : Thickness exponent provided in Table 1 and Table 4 respectively for welded and non-welded joints. n is to be selected according to the considered stress direction. For this selection, Δσ_HS1 and Δσ_HS2 are considered perpendicular and parallel to the weld respectively.

d : Toe distance, in mm, as shown in Figure 2, taken as:

d = t_2n50 + 2ℓ_leg

t_1n50 : Net thickness, in mm, of the continuous plate as shown in Figure 2.

t_2n50 : Net thickness, in mm, of the transverse attach plate where the hot spot is assessed, as shown in Figure 2.

ℓleg : Fillet weld leg length, in mm.

When post-weld treatment methods are applied to improve the fatigue life of considered welded joint, the thickness exponent is provided in [6].

Figure 2 : Toe distance for cruciform welded joints, transverse T-joints and plates with transverse attachment