Bridging S-N Method and Fracture Mechanics in Fatigue Evaluation of Fillet Welded T joints of an Oil Tanker

1.1. Background of study / Pozadina istraživanja

Ships, offshore platforms, and other marine constructions are subjected to complex loading histories due to the repeated nature of the ocean environment that leads to fatigue damage, which may fail marine structure if not treated properly [1,2]. For example, the occurrence of excessive stresses due to welding dramatically affects fatigue life through changes in effective stress ratio at the crack-tip during fatigue crack growth which can alter both crack-propagation path and rate [3,4]. It is also shown that local fatigue approaches that account for actual geometry and residual stresses can minimize variability in stress-life (S–N) curves, resulting in a much more dependable assessment of the fatigue [5,6].

The DNV guideline for fatigue analysis in ship structures aims to preserve structural integrity by assessing hotspot stress [7]. A major concern is the accurate evaluation of fatigue damage, which helps forecast the initiation of fatigue cracks in undercut areas of ship structures where stresses concentrate, such as weld toes [8,9]. However, it advocates for a structural hot-spot stress approach, which is preferable to the nominal stress approach when considering the complex geometries and high-stressed regions typical of welded connections [10]. The geometrical stress amplitude at the hot spot is calculated using finite element analysis (FEA) and then integrated with a unified S- N curve to estimate fatigue strength [8,11]. The incorporation of the International Institute of Welding (IIW) hotspot stress approach allows for a more precise method of calculating stress values, significantly improving the fatigue life prediction for fillet welded joints common in ship structures. Although the IIW hotspot stress method is highly efficient and provides a solid foundation for fatigue assessment, design codes such as Eurocode 3 offer a well standardized approach, particularly in fatigue classification and the implementation of the S- N curve [12]. The hotspot stress method exists in Eurocode 3, and it can be used to determine the most dangerous locations for fatigue failure, thus representing a better assessment than nominal stress methods [13].While the IIW emphasizes that only the geometrical stress amplitude at a hotspot needs to be accurately determined, Eurocode 3 retains this concept, acknowledging the importance of capturing the correct stress distribution in welded joints [14]. The combination of guidelines provided by Eurocode 3 and the IIW method takes weld size and load-carrying capacity into a more accurate evaluation of fatigue life [8,15]. Fracture mechanics provides a general methodology for the interaction between mechanical and geometric parameters in welded joints that may enhance reliability and safety prediction of ship structures [16]. This approach in conjunction with Paris's law results in a more stringent analysis of the endurance of joints concerning fatigue crack propagation [17]. The localized area of damage, which plays a crucial role in the growth of cracks, is effectively incorporated into this method [18]. Fatigue life predictions and maximum load carrying capacities will be estimated based on the integration of the Eurocode 3 guidelines with the IIW hotspot stress method and fracture mechanics principles. FRANC2D software will be used to perform and validate the crack propagation analyses against published experimental data, accomplishing the most needed connection of theoretical models to actual situations in marine structures. To overcome these shortcomings, the current study seeks to perform a full fatigue examination of a 2000 DWT oil tanker class approved fillet welded T-joints. The study will identify stress concentrations, which are recognized as hotspot regions by constructing a finite element (FE) model of cargo hold and static analysis for various loading circumstances according to GL rules.

2.1. Fatigue Assessment Framework: Eurocode 3 Compliance / Okvir za procjenu zamora: sukladnost s Eurokodom 3

Eurocode 3 (EN 1993), the European standard for the design of steel structures, establishes comprehensive protocols for ensuring structural integrity under cyclic loading. Its fatigue specific provisions (EN 1993-1-9) provide the foundational methodology for this study. The standard’s approach centers on stress range (Δσ) as the governing fatigue parameter.

Eurocode 3 (EN 1993) is the European standard that governs the structural design of steel components, ensuring safety, reliability, and serviceability throughout the intended service life of structures. Fatigue design is addressed specifically in Part 1-9 of the standard, which provides a detailed methodology for assessing the fatigue strength of steel structures subjected to cyclic loading. This is particularly relevant for welded joints in marine applications, where load variations from waves, cargo, and vessel motion are frequent and severe.

The fatigue provisions in Eurocode 3 are based on a nominal stress or hotspot stress approach, with structural details classified into predefined categories, each associated with a characteristic S–N curve derived from experimental data. These S–N curves relate the applied stress range to the number of cycles to failure and incorporate safety factors to account for uncertainties in material properties, geometry, and loading conditions. Additionally, the code employs cumulative damage assessment using Miner’s rule to evaluate the overall fatigue life under variable amplitude loading.

In the context of this study, Eurocode 3 serves as both a benchmark and a reference framework for fatigue life prediction. The fatigue resistance of fillet-welded T-joints is assessed using the hotspot stress method in accordance with the standard, enabling direct comparison of predicted fatigue life against code-specified endurance limits. The conservative nature of the standard is critically examined through fracture mechanics analysis, providing deeper insight into crack growth behavior and verifying whether the code’s assumptions hold under realistic marine loading scenarios.

This incorporation of Eurocode 3 not only ensures that the analysis adheres to recognized engineering practices but also allows for the evaluation of its conservatism in predicting fatigue performance. The outcomes reinforce the relevance of the code in structural design while also supporting potential refinements or calibrations for specific applications in the marine industry.

2.2. Finite Element Analysis / Analiza konačnih elemenata

The 2000 dwt oil tanker analyzed in this investigation is a classification society, DNV-approved, and specifically designed coastal vessel subject to intensive safety and structural standards regulations. The tanker's principal dimensions are given below in Table 1.

Table 1 Principal particulars of the oil tanker

Tablica 1. Glavni podaci naftnog tankera

Typically, the finite element model includes the designated hold along with an additional half hold at each end, resulting in a model that spans ½ + 1 + ½ tanks or holds. This approach provides a more comprehensive understanding of structural behavior. In situations where the ship's structure and loads are symmetric, it is permissible to model only half the breadth of the vessel [7]. The hull structure is made of Grade A mild steel, with yield strength 235 MPa and ultimate tensile strength 400 MPa, providing resistance against mechanical and environmental stresses. The coordinate system and the global model are shown in Figure 2.

In ANSYS, the finite element model is built employing four-node shell elements. The mesh metrics have been checked to ensure all the parameters are within the range, as shown in Figure 3. The results from the mesh sensitivity study are provided in Figure. 4, which displays that an element size of 30 mm is ideal for achieving accurate outcomes, striking an effective balance between detail and computational demands.

Figure 2 Coordinate system and cargo hold model

Slika 2. Koordinatni sustav i model teretnog prostora

Figure 3 Mesh metric of the cargo hold model

Slika 3. Mrežna metrika modela teretnog prostora

Figure 4 Mesh convergence

Slika 4. Konvergencija mreže

2.3. Application of Load and Boundary Condition / Primjena opterećenja i granični uvjet

For simplified fatigue calculations, internal and exterior pressure loads are determined to be employed when global hull girder loads may be given as end moment. For this cargo hold analysis, the following loads are considered [19].

Global bending moments and shear forces are applied by creating a rigid element at the neutral axis. Shear pressures and bending moments are applied at both ends to maintain balance. At the free end section, tight constraints are applied on all nodes positioned on the longitudinal members, ensuring that the transverse section remains flat after deformation. The loads and specific boundary conditions applied are shown in Figure 5 and summarized in Table 2 below [20].

Table 2 Boundary condition

Tablica 2. Granični uvjet

Figure 5 Application of loads and bending moment

Slika 5. Primjena opterećenja i trenutka savijanja

After the static analysis few fillet welds had shown great susceptibility to crack formation as shown in Figure 6 which are;

Figure 6 Location of hotspots of global model; a) HS1: Joint between the margin plate and inner shell bracket; b) HS2: Joint between the inner shell longitudinal and inner shell plate and c) HS3: Joint between the inner shell plate and main deck bracket

Slika 6. Lokacija žarišnih točaka globalnog modela; a) HS1: spoj između rubne oplate i nosača unutarnje oplate, b) HS2: spoj između uzdužne i unutarnje oplate, c) HS3: spoj između unutarnje oplate i nosača glavne palube

2.4. Submodeling for Local Analysis / Podmodeliranje za analizu lokacije

The sub-modeling technique was used to construct local models of the identified hotspots to conduct a detailed analysis. Local models of the detected hotspots were developed using the sub-modeling technique to conduct a detailed examination of hotspots, as illustrated in Figure 7 and 8.

Figure 7 Local model of a) HS1, b) HS2, c) HS3

Slika 7. Model (prikaz) lokacije a) HS1, b) HS2, c) HS3

Figure 8 Submodeling.

Slika 8. Podmodeliranje

Boundary conditions allow to transfer external loads, like e.g., the global hull girder loads, to the local model. The proposed size of the local model has been selected based on a compromise in order to minimize the impact of boundaries on the structural detail being analyzed and to define boundary conditions in which a particular solution can be clearly defined [7]. According to the IIW recommendation, local models are developed with a finer mesh size as mentioned [21].

Figure 9 Stress contour of local models, a) HS1, b) HS2, c) HS3

Slika 9. Kontura naprezanja modela lokacije, a) HS1, b) HS2, c) HS3

2.5. Calculation of Hotspot Stress Using IIW Recommendations / Izračun žarišnog naprezanja korištenjem IIW preporukama

In simplified models, the welds are not simulated, except for circumstances when the results are affected by local bending due to an offset between plates or due to a limited distance between adjacent welds. Figure 10 illustrates the specific regions where stress extrapolation is performed in finite element models with a fine mesh. For fatigue-critical spots on the plate's surface, two reference points are placed at defined distances from the weld toe [21].

The structural hotspot stress is calculated using the following equation [21].

To establish a relationship between hotspot stresses and fatigue life, a fatigue category identified by a FAT number is used. The FAT curves shown in Figure 11, represents the maximum allowable stress range, measured in N/mm² or MPa, corresponding to fatigue life of up to 2 million cycles (2 × 10⁶ cycles). Based on the IIW standards, for the load-carrying two-sided fillet welded joints, it is recommended to use FAT 90.

Figure 10 Reference points for linear extrapolation of hotspot stress

Slika 10. Referentne točke za linearnu ekstrapolaciju žarišnog naprezanja

Number of cycles to failure is estimated using following calculation as per the guideline [22]:

Where:

Δσ = structural hotspot range

N = number of cycles

C = design value of “fatigue capacity” (= 2×10⁶ FAT^m)

m = 3 =slope of the upper part of the S-N curve

FAT = fatigue strength at 2×10⁶ cycles

Figure 11 S-N curve with different FAT class [22]

Slika 11. S-N krivulja s različitim klasama snage zamora (FAT klasama)

2.6. Assessment of Fillet Welded Joints in Steel Structures According to Eurocode 3 / Procjena kutno zavarenih spojeva u čeličnim konstrukcijama prema Eurokodu 3

In the context of oil tankers, adherence to Eurocode 3 ensures that the welded joints can withstand the operational loads they encounter during service. The assessment begins by applying tensile loads to the hotspot locations identified earlier – HS1, HS2, and HS3. These loads are determined based on the design resistance of the fillet welds, following the guidelines stipulated in Eurocode 3 [12].

According to Eurocode 3, the design resistance of a fillet weld is regarded sufficient if, at every point along its length, the cumulative impact of all forces per unit length transmitted by the weld satisfies the following requirement:

Where:

F_w, _Rd = design weld resistance

F_w, _Ed = design value of weld force

The design shear strength of the weld [TeX:] f_{v,wd}$f_{v,wd}$ is calculated using:

[TeX:] f_{v,wd} = \frac{\frac{f_{u}}{\sqrt{3}}}{\beta_{w}\gamma_{M2}}$f_{v,wd}=\frac{\frac{f_u}{\sqrt{3}}}{{\beta }_w{\gamma }_{M2}}$ (4)

Where, β_w= correlation factor = 0.8

γ_M2= Safety factor = 1.25

a = leg length of the weld

The design resistance per unit length of the weld is then:

With the maximum tensile loads applied to the hotspot regions, the fatigue life of the welded joints is reviewed. The HS1, HS2, and HS3 finite element models are modified to accommodate the maximum tensile loads obtained by eqn 5. The hotspot stresses [TeX:] \sigma_{\text{hs}}\ ${\sigma }_{\mathrm{\text{hs}}}$are recalculated using the refined models and the surface stress extrapolation method as given in equation (1) recommended by the International Institute of Welding (IIW). The stress contour after analysis is shown in Figure 12.

Figure 12 Analysis of the joints on the application of weld resistance as per Eurocode 3; a) HS1, b) HS2, c) HS3

Slika 12. Analiza spojeva primjenom otpornosti zavara prema Eurokodu 3;a) HS1, b) HS2, c) HS3

2.7. Crack Propagation Analysis Using Fracture Mechanics / Analiza propagacije pukotine korištenjem mehanikom loma

To estimate the fatigue life of a component accurately, it is necessary to simulate cracked growth once fracture initiation has occurred, as this has a large impact on the remaining life of the structure of interest. In this sense, the foundations of fracture mechanics give a good platform to examine crack progression behavior during the loading cycle.

In this investigation, cracks are introduced at the previously reported hotspot locations – HS1, HS2, and HS3 – within the fillet-welded T-joints of the oil tanker. Creating cracks makes it feasible to mimic the propagation of the precisely produced crack under cyclic tensile stress. Consequently, it gives a more thorough perspective of the fatigue process after the onset of failure.

Paris's Law provides a fundamental empirical relationship in fracture mechanics that describes the crack growth rate under cyclic loading conditions. It is particularly useful for predicting the progression of fatigue cracks in materials subjected to repetitive stress cycles. The law is expressed mathematically as:

Where [TeX:] \frac{\text{da}}{\text{dN}}\ $\frac{\mathrm{\text{da}}}{\mathrm{\text{dN}}}$represents the crack growth rate per cycle, C and m are material-specific constants obtained experimentally, and ΔK is the stress intensity factor range experienced during a loading cycle.

For this study C is considered as 2.60 × 10^-11 and m as 2.75. By integrating Paris's Law over the crack length from the initial size [TeX:] a_{i}$a_i$ to the critical size [TeX:] a_{c}\ $a_c$ the total number of cycles to failure [TeX:] N_{f}$N_f$ can be estimated:

The FRANC 2D (Fracture Analysis Code in Two Dimensions) software is used to simulate the crack propagation behavior and apply Paris's Law appropriately as shown in Figure 13, Figure 14 and Figure 15.

Figure 13 Stress concentration at the weld toe and crack initiation at the location of stress concentration

Slika 13. Koncentracija naprezanja na vrhu zavara i početak pukotine na mjestu naprezanja

Figure 14 Crack propagation

Slika 14. Propagacija pukotine

Figure 15 Deformed structure after crack propagation.

Slika 15. Deformirana struktura nakon propagacije pukotine