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Assessment of ship structure under fatigue loading: FE benchmarking and extended performance analysis

Assessment of ship structure under fatigue loading: FE benchmarking and extended performance... Curved and Layer. Struct. 2022; 9:163–186 Research Article Aprianur Fajri, Aditya Rio Prabowo*, and Nurul Muhayat Assessment of ship structure under fatigue loading: FE benchmarking and extended performance analysis https://doi.org/10.1515/cls-2022-0014 commonly induce material failure in structures, and they Received Nov 16, 2021; accepted Feb 11, 2022 can be classified into two categories: static and dynamic loads. The most frequently encountered issues are typically Abstract: This paper presents a numerical procedure based related to the presence of dynamic loads, such as uninten- on the finite element (FE) method using ANSYS Workbench tional loads/impact loads originating from various sources software to analyse fatigue phenomena in ship structures. [1]. However, dynamic loads with a relatively small mag- Fatigue failure prediction is used as a stress–life approach, nitude (far below the yield point) might also cause failure when the stress is still in a linear area. This condition is if they continue indefinitely, which is referred as fatigue frequently referred as high-cycle fatigue. Five geometric failure [2]. shapes taken from midship points on the structure of a ship Although fatigue failure can occur in any structure, it are sampled. There are four types of materials: HSLA SAE is more prevalent in those subjected to cyclic loads or op- 950X, medium-carbon steel, SAE 316L, and SAE 304L. The erating in harsh environments. Ships comprise facilities types of loading imposed on each sample include three that are prone to fatigue due to working in corrosive condi- conditions: zero-based, zero mean, and ratio. Mesh conver- tions, being subjected to continuous loading by seawater gence analysis is conducted to determine the most effective waves, being impacted by changes in ambient tempera- mesh shape and size for analysing the structure. The results ture, and being subjected to other mechanical loads. Ships showed that the configuration of the geometric shapes, ma- are frequently constructed considering empirical loads (de- terials used, loading schemes, and mean stress theory affect sign loads), which reflect the most significant subjected the fatigue characteristics of the structure. static load. However, the causes and mechanisms of fatigue Keywords: Finite element method, fatigue phenomena, (induced by dynamic loads) remain unknown and under ship structure investigation. Ships are constructed from various highly complex structures and joints, responding differently to fatigue risk [3]. Fatigue failure can begin with cracks in lo- cations with a high-stress concentration. These cracks may 1 Introduction propagate in a specific direction and produce a fracture. The used materials, geometric shape, and type of loading Currently, technology advancement, particularly in engi- are factors to consider when examining the features of a neering structures, is accelerating. The complexity of the structure. The design must be economically viable and safe challenges and the obstacles encountered is also increas- to operate under various loading scenarios. Fatigue testing ing; one of the most frequent issues is material failure, should consider actual field scenarios, where testing and which is caused by various factors. Catastrophic material measurement should be performed with various parameter failures result in material losses, which frequently cause fa- adjustments. Understandably, if the standard experimental talities and damage to the environment. Operational loads procedures are used, the above will be extremely difficult, time-consuming, and prohibitively expensive. The finite element method (FEM) is one of the alternatives to this *Corresponding Author: Aditya Rio Prabowo: Department problem because it is highly effective in identifying and of Mechanical Engineering, Universitas Sebelas Maret, Ir. Su- visualising fatigue failure mechanisms. tami Street 36A, Surakarta, Central Java 57126, Indonesia; Email: This study presents some data related to fatigue assess- aditya@ft.uns.ac.id ment of the design of ship structures from different per- Aprianur Fajri, Nurul Muhayat: Department of Mechanical Engi- spectives. Previous research [1, 3–7] has identified several neering, Universitas Sebelas Maret, Ir. Sutami Street 36A, Surakarta, Central Java 57126, Indonesia Open Access. © 2022 A. Fajri et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License 164 | A. Fajri et al. potential issues that can be further investigated. The area in and the concept of the stress–cycle curve (S–N) curve and the middle of a ship (Figure 1) experiences the most extreme endurance limits are introduced. The linear damage hy- loading and has the highest risk of fatigue failure. These pothesis discovered in 1945 was still referenced when the problems should be further examined, using alternative stress-life approach was adopted to investigate the current methods and approaches to provide a complete explana- fatigue phenomenon. The 1979 loss of MV Kurdistan and tion of the phenomenon of weariness. This problem must the 1980 sinking of the Alexander L. Kielland platform due be discovered in advance and addressed entirely to avoid to fatigue failure [9] prompted academics to conduct addi- future disasters [8–10]. The purpose of this study is to de- tional research on this phenomenon, particularly in marine termine the effects of geometric shapes, material types, and structures. The growing importance of fatigue strength in loading types on the fatigue phenomenon occurring in ship maritime constructions has resulted in its study and design structures using the hot spot stress approach. This study recommendations. In the literature, there are numerous conducts fatigue analysis of numerous sample hot spots approaches for defining stress and implementing fatigue with material and applied load variations. This research assessment. The two most accepted methods for the stress is simply a follow-up that aims to fill in the gaps of prior analysis of the structure of a ship are the hot spot stress investigations. To the authors’ best knowledge, the FEM approach and the practical notch stress approach [5]. has not been tested by highly complex mesh convergence A study on the measurement of the fatigue of ship struc- investigations, which is critical for ensuring the accuracy tures was undertaken in [12] on a perpendicular joint con- of numerical simulation findings. sisting of a plate connection with a beam (shell–solid cou- pling). This study showed that finite element analysis may be used quite well to predict structural responses to fatigue loading, particularly in locations of high-stress concentra- tion. Because the metrics tested and compared in this study are displacement-related, other processes are required to determine fatigue life parameters, fatigue damage, and fa- tigue safety factor. Subsequently, in [5], a comparative study was conducted on various vessels using more advanced ap- proaches. The model under consideration is an integral part of the 4900 PCTC ship. The study established a method to determine the hot spot stress by examining global models. The areas most affected by a fatigue load were subsequently used to create a local model with mesh refinement in the crucial region. Loading scenarios were modelled in various ways, all of which involve using the same type of mate- rial. Based on the results of worldwide studies on models, there are other locations that may be exploited as research hot spots. In a study, the use of nonlinear time-domain Figure 1. Weakest Areas on Ship Structures [4] Figure 1: Weakest areas on ship structures [4] hydrodynamic models of container ships (DNV-class) [13] showed that the selected material affects the structural response under various loading schemes. The study com- pared HT32-grade steel with various materials. Different wave heights resulted in several different loading patterns. 2 Literature review The fatigue properties of the structures in response to this loading pattern were diversified; however, other hot spots 2.1 Pioneer works remain to be studied. The fatigue cracks propagation ap- proach can be used to analyse the fatigue characteristics Research on the phenomenon of fatigue has a very long in a shell structure, which is the magnitude of the crack history [3, 11]. The first paper on the fatigue phenomenon propagation caused by dynamic stresses on ships [14–16]. was written in 1837. A further development, the effect of This technique is predicated on the initial assumption of a stress concentration on the failure of axle trains, was in- crack in specimens derived from several possible sources. troduced in 1842. Systematic fatigue testing methods were This study found that variations in loading scenarios, such developed in 1860. This method was later modified in 1870, as the tangle force and he wave frequency, substantially af- Assessment of ship structure under fatigue loading | 165 fected the rate of fracture propagation. This method cannot procedure is called meshing. Each element contains var- describe fatigue prior to the onset of cracks. ious stress components, which can be determined using interpolation and extrapolation concepts. When conduct- ing fatigue analysis using the stress–life approach, each 2.2 Fundamental theory element must be searched for its corresponding stress value and subsequently compared to the fatigue data in the form Fatigue is the irreversible damage of items due to the stress– of an S–N curve. strain variations caused by external factors [17]. According Different types of stresses can be utilised to forecast fa- to [18], fatigue failure occurs in four stages: (1) nucleation tigue age, including axial stress (S or S ) and shear stress x y of cracks, (2) structurally dependent crack propagation, (3) (S ). Using the von Mises equation, these three types of xy crack propagation, and (4) failure. Numerous factors can stresses can be converted into normal or equivalent stress influence fatigue resistance including the type of applied (Eq. 3). This stress component is used in this study because load, material used, mechanical properties, manufacturing it encompasses all other stress components. Thus, for the techniques, surface roughness, operating temperature, en- simulation of fatigue due to cyclic loads, the maximum vironment, microstructure state, residual stress, corrosion, stress (S ) and the minimum stress (S ) must be ob- max min and crack initiation [19–22]. tained, and subsequently Eq. (4) is used to determine the Metals can be classified according to their uniaxial ratio. properties, which include engineering properties and ac- √︀ 2 2 2 .Seqv = Sx + Sy − SxSy + 3Sxy (3) tual characteristics. Engineering properties are types of characteristics used to compute the cross-sectional area min and the length of a sample in its original configuration. In R = (4) max comparison, stress–strain factors are calculated using the immediate space and size of a sample loading process. En- The fatigue data obtained from laboratory test pro- gineering stress (Eq. (1)) is fundamentally different from cesses shown in S–N curves become input variables. Typ- actual stress (Eq. (2)). ically, these data are collected at a mean of zero or R = −1 (Figure 2a). If the fatigue data are to be utilised to study an S = (1) issue under a zero-based loading condition (R = 0 or R = ∞) or with ratio R > 0 (see Figure 2b and Eq. (4)), then the mean stress must be corrected. Various theories can be em- σ = (2) A ployed, including the Goodman (England, 1899) (Eq. (5)), Soderberg (the USA, 1930) (Eq. (6)), Gerber (Germany, 1874) Above, P represents the axial tension stress, A denotes (Eq. (7)), and ASME elliptical (Eq. (8)) theories [23–26]. the initial cross-sectional area of the sample, and A rep- resents the instantaneous cross-sectional area of the sam- ple. When assessing a structure, the actual stress, which Alternating mean + = 1 (5) is affected by the cross-sectional variation, is employed. S S Endurance limit ultimate When materials are tested for strength in the laboratory, the shape of the specimen is highly simple, allowing di- Alternating S mean + = 1 (6) mensional changes to be easily observed and quantified S S Endurance limit yield directly. However, dimensional changes are exceedingly difficult to detect in complex structures, such as ship struc- tures. Each piece has its unique distribution of stress. Ex- pectedly, doing trials on a complete design will require a significant amount of resources. This is because the cost of specialised sensors for stress stamping is high, and the arrangement is relatively intricate. Consequently, an alter- nate approach for analysing the strength of a structure is to employ an FEM-based software. The FEM is a numerical technique for solving mathematical problems that include specified boundary conditions. In principle, when used to solve a problem, a space model is separated into mul- Figure 2: Loading conditions: a. Zero-mean; b. Ratio Figure 2. Loading Conditions: a. Zero-Mean; b. Ratio tiple portions of the domain referred as up elements; this 166 | A. Fajri et al. (︂ )︂ Alternating mean + = 1 (7) S S Endurance limit ultimate (︂ )︂ (︂ )︂ 2 2 Alternating mean + = 1 (8) S S Endurance limit yield ∑︁ D = (9) i=1 The magnitude of fatigue life can be determined using the Palmgren–Miner linear damage hypothesis (Eq. (9)), where denotes the number of stress range cycles caused by various factual stressors S (1 ≤ i ≤ k) and N represents i i the number of cycles required to cause the failure of the alternating constant stress, S (S–N curve). Failure occurs when cumulative damage (D) exceeds one. 3 Preparation and methodology This research is conducted in several stages, and each stage Figure 3: Research scheme Figure 3. Research Scheme has its role. Literature studies are conducted to ensure that the used methods follow existing scientific rules. Prior re- ture study are inputted into the software manually. Sub- search is referred to define the input variables and the fun- sequently, the process of meshing divides a geometry into damental assumptions. Material properties are obtained several small domains called elements. The mesh size is from the results of laboratory tests with recognised stan- determined to achieve convergence of calculation value dards. Numerical methods are validated before use. One and time efficiency. Following this, the boundary condition approach involves benchmark analysis procedures. The is determined to set the placement of the pedestal and the shapes and magnitudes of the meshes for all geometries are loading location. Fatigue analysis is conducted using the different; therefore, convergence studies are conducted to fatigue tool in ANSYS Workbench. The parameters that can choose the most optimal mesh. These stages are discussed be varied are fatigue damage, fatigue life, safety factor, and in more detail sequentially in this section. biaxiality indication. The values of some output parame- ters are subsequently analysed and related for inference. The research scheme in this study is shown in Figure 3. 3.1 Assessment procedures A literature study is conducted to understand the phe- 3.2 Engineering three-dimensional models nomenon of fatigue in ship structures. It identifies several problems related to fatigue in the construction of ships and The studied samples are taken from several locations on the the methods and the approaches that can be used to in- structure of a ship that can represent the most prone parts vestigate fatigue. The method used is the FEM with CAE to fatigue failure. Furthermore, these samples are formed simulation software, and the technique used is the stress– into three-dimensional models, following a limit condition life approach, which is applied to the hot spot stress area. applied based on the loading conditions that occur in the Before use, this method is validated to replicate previous field. Areas with high-stress concentrations (hot spot stress) research, and subsequently the results are compared. If the typically have a short fatigue life. error is relatively small and meets certain criterion, then this method is valid and worth using. Geometric models are built using ANSYS Modeller, a CAD program integrated with ANSYS Workbench. Fur- thermore, the material properties obtained by the litera- Assessment of ship structure under fatigue loading | 167 Figure 4. Geometry Locations on Midship Section Model Figure 4: Geometry locations on midship section model [27] a. b. c. d. e. Figure 5. Geometry Model: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Joint [12]; c. Figure 5: Geometry model: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 5: Side-Stiffened Panel [28] d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] 168 | A. Fajri et al. a. b. c. d. e. Figure 6. Meshing and Boundary Conditions: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Figure 6: Meshing and boundary conditions: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry Perpendicular Joint [12]; c. Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 3: Stool joint [12]; d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] 5: Side-Stiffened Panel [28] 3.2.1 Geometry location 3.2.2 Sample models and boundary conditions Based on a literature study on the global models of ships, it Boundary conditions are applied to the built geometric is found that the hull and the midship (Figure 1) are the most models (Figure 5), as shown in Figure 6. Based on a litera- vulnerable areas to failure owing to stress concentration. ture study, the magnitude of the load, the position of the Therefore, v fi e types of sample models are taken in the support, and other configurations are adjusted to the actual above sections representing the hot spot areas on a ship needs. structure (Figure 4). One model is used to investigate the Some other parameters that are not set in this study are effects of the applied material, loading scheme, and mean left constant or follow the default settings of ANSYS soft- stress correction theory on the fatigue behaviour that occurs ware. Some basic assumptions that need to be highlighted in the structure. When one variable is examined, the other are that the approach used in this study is the stress–life variables are considered constant. approach and the stress is still in the linear area below Assessment of ship structure under fatigue loading | 169 the material yield point. The model is in perfect condition, there is no initial crack, and the smoothness of the surface HSLA SAE 950X 900 SAE 316L is considered uniform. Mesh convergence is conducted for Medium-Carbon SAE 304L each model using different mesh sizes. One method to de- termine the range of mesh sizes to be used is based on the 700 element length to thickness (ELT) ratio. According to [7], ELT values of 5–10 can analyse a complex structure. A small ELT ratio implies that the analysis result is close to the ac- tual value, and consequently the computing time is long. The meshing technique used is local meshing. Mesh in the area of interest is refined thrice smoother than the global mesh. The stress that appears subsequently represents the 100 hot spot stress, whose value is more significant than the 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 nominal stress. Fatigue Life (Cycles) Figure 7. S–N curves of HSLA SAE 950X [29], Medium-Carbon Steel [30], SAE 316L [31], and SAE 304L [32] Figure 7: S–N curves of HSLA SAE 950X [30], medium-carbon steel [31], SAE 316L [32], and SAE 304L [33] 4 Materials Four types of materials are used in this study: high-strength 5 Benchmark study on simple case low-alloy steel (HSLA) SAE 950X [30], medium-carbon steel [31], SAE 316L [32], and SAE 304L [33]. The material prop- Koksal [34] previously completed an FEM fatigue analysis erties used as input parameters are listed in Tables 1 and 2 on notched cantilever beams. The research material was a and shown in Figure 7. HSLAs are relatively new materi- structural steel, with the mechanical parameters listed in als and are still not as well-known as SAE 316L and 304L Table 3 and the S–N curve shown in Figure 8c. The dimen- for applications in marine structures. Although medium- sions of the geometric model are 1000 × 100 × 75 mm; on carbon steels have good mechanical properties, they are one side of the beam, a notch with a large angle of 90 and rarely used in marine structures with some consideration. a depth of 25 mm is created (Figure 8a). Cantilever beams Table 1: Chemical composition Type of material Material composition wt% C Cr Mo Si Mn S P Ni Cu Co N V Nb HSLA SAE 950X 0.23 0.9 1.35 0.05 0.04 0.15 0.04 Medium-carbon 0.44 0.04 0.02 0.23 0.57 0.16 0.24 0.002 SAE 316L 0.29 17.54 2.38 0.5 1.8 0.012 0.032 12.6 0.26 0.18 0.077 SAE 304L 0.02 18.5 0.049 1.78 0.011 0.014 9.78 Table 2: Mechanical properties Type of material Modulus of elasticity (MPa) Yield strength (MPa) Ultimate strength (MPa) HSLA SAE 950X 204700 437 485 Medium-carbon 210000 490 710 SAE 316L 200000 283 592 SAE 304L 190200 277 572 Table 3: Mechanical properties of structural steel (ANSYS) Modulus elasticity (GPa) Ultimate tensile strength (MPa) Poisson’s ratio Yield Strength (MPa) 200 460 0.3 250 Stress Amplitude (MPa) 170 | A. Fajri et al. Table 4: Verification results Value Previous test (33) Re-simulation result Error (%) Min fatigue life 90,700.00 89,948.00 0.83 Min safety factor 0.60824 0.60686 0.20 Maximum equivalent alternating stress 141.72 142.04 0.20 a. b. c. Structural Steel (ANSYS) -500 0 1 2 3 4 5 6 10 10 10 10 10 10 10 Fatigue Life (Cycle) Figure 8. a. Cantilever Beam Design [33]; b. Boundary Condition; c. S–N Curve of Structural Steel (ANSYS) Figure 8: a. Cantilever beam design [34]; b. Boundary condition; c. S–N curve of structural steel (ANSYS) 6 5 9x10 are intended for a minimum cycle life of 10 . Their one end is stationary, whereas the other end is loaded with a force 8x10 Present simulation 5 Previous test of 10 kN in the direction of the z-axis (Figure 8b). 7x10 Based on a convergence study, a 4-mm mesh produces 6x10 90,322 elements and a single processing step requires 20 5x10 s for computation. A tetrahedral mesh with Jacobian ratio 4x10 = 1 is chosen as the mesh shape. The applied loading is a 3x10 zero-based force of 10 kN. After applying a cyclical load, the 2x10 remaining settings are kept as default or constant. Table 4 1x10 lists and Figure 9 shows the verification findings. 0 15 30 45 60 75 90 105 120 135 150 Alternating Stress (MPa) Figure 9. Validation Results: Benchmarking with Previous Test [34] Figure 9: Validation results: benchmarking with previous test [35] Alternating Stress (MPa) Fatigue Life (Cycle) Assessment of ship structure under fatigue loading | 171 a. b. Figure 10. Mesh Convergence Tests: a. Nominal Stress; b. Hot Spot Stress Figure 10: Mesh convergence tests: a. Nominal stress; b. Hot spot stress a. b. Figure 11. Size 15-mm Mesh Quality: a. Aspect Ratio; b. Skewness Figure 11: Size 15-mm mesh quality: a. Aspect ratio; b. Skewness 172 | A. Fajri et al. 6 Mesh convergence study 7 Results and discussion The shape and size of a mesh significantly influence sim- The data that are successfully captured are processed and ulation results. Generally, a small mesh size implies that grouped based on the investigated variables. The informa- the analysis results are close to the actual condition [36]. tion displayed as contour images and graphs shows the Concurrently, a small mesh size implies numerous formed relationships among the variables. elements. Consequently, the computing time becomes long, and in some cases, the computer devices used cannot deal with these calculations [37, 38]. Thus, a mesh convergence 7.1 Effect of geometry shape study is needed to choose the most suitable shape and size of a mesh. When the simulation results meet the criteria and It can be observed from Figure 12a that Geometry 1 under the time required for one simulation is relatively short, the loading produces a maximum stress of 252.47 MPa, which mesh is considered appropriate. Simulation results are con- is still below the stress yield. Stress concentration occurs in sidered convergent if the changes in the mesh size do not the connection area and spreads to the plate area. A mini- affect the values of the tested parameters. ANSYS software mum stress of 1.2082 MPa occurs in the support area, which provides several forms of meshes, including hexahedron, experiences the slightest moment. Geometry 2 (Figure 12b) pyramid, prism, and tetrahedron. A hexahedron-shaped has a stress of 289.76 MPa, which is relatively larger than mesh is considered ideal because it produces relatively Geometry 1. Geometry 3 (Figure 12c) experiences almost the small elements and is the form most easily analysed by same stress as Geometry 2 because Geometries 2 and 3 have a program solver [39]. However, this mesh cannot adjust a similar adjacent ship structures and boundary conditions. shape well, particularly for a complex geometry. Although However, Geometry 3 can distribute the stress better than it produces relatively larger elements, a tetrahedron mesh Geometry 2. Geometry 4 (Figure 12d) experiences a very can be used for complex geometries. Therefore, this type of high stress, which amounts to 312.67 MPa in the neck area. mesh is chosen for this study. Geometry 5 (Figure 12e) is under a very small stress of 188.83 A convergence test is conducted on Geometry 2 by con- MPa. The received load is well channelled throughout the tinuously changing the mesh, following which the stress surface of the model. Thus, the structure is subsequently values in all changes are compared. Two meshing tech- strengthened by stiffeners. niques are applied: global and local meshing. Global mesh- First, the amount of stress in the structure is inversely ing is used to examine the nominal stress on one intact coupled with the predicted fatigue life. A large value of the structure. In comparison, local meshing is used to search stress implies a short fatigue life. It can be proven from for the stress hot spots in critical areas. The stress magni- Figure 13d that Geometry 4, which experiences the highest tudes of the stress hot spots are above the nominal stress stress, has a very short fatigue life. In contrast, Geometry 5 because the distribution investigated covers a more detailed (Figure 13e), which is under little stress, has a good fatigue scope. Based on the test results (Figures 10a and 10b), a life. The second point to note is the relation between the 15-mm mesh is determined as the best to solve this first case. stress concentration and the minimum fatigue life. Based In addition to no change occurring in the stress value, a on literature studies, fatigue failure typically begins with computing time of less than 4 s is the most relevant consid- an initial crack. Initially, Geometries 2 and 3 (Figures 13b eration. A mesh with a smaller size is not chosen because and 13c) seem safe, where the red contoured area is rela- it requires a longer computing time. Although a mesh with tively small. However, the stress exceeds the endurance a larger size tends to produce values far below the criteria limit, where based on calculations, the corresponding area or away from the actual conditions, the mesh quality test will fail in specific cycles. Failure typically begins with a shows that the inspection area has a good aspect ratio and fatigue crack. Although very small in size, such a crack is skewness. The aspect ratio (Figure 11a) is the most exten- very dangerous because it can propagate very rapidly. sive with the smallest mesh. The aspect ratio approaching Figure 14 shows the safety factor of each geometry. the value of 1 is better because the governing equation be- Please note that ships are structures designed with a high comes more superficial and makes it easier for solvers to level of security. Therefore, to ensure their ability to be qual- find the final result. The data are expected if the skewness is ified to withstand repeated loading, the fatigue safety factor in the range of −2–2. As shown in Figure 11b, the skewness is calculated based on a design life of 10 cycles. Areas with magnitude is still in the field of 0.059686–0.99432, which a fatigue safety factor of 1 are expected to survive when indicates that the mesh has a good quality. undergoing 1 billion cycles. Geometry 1 (Figure 14a) has a Assessment of ship structure under fatigue loading | 173 uniform minimum distribution of safety factors with values 3.3328 and 3.4809 mm, respectively. Both these forms un- below 1, i.e., the areas with red contours are predicted to dergo the most significant deformation among all condi- fail before they can undergo 1 billion cycles. As shown in tions. This indicates that both structures are deformable, Figure 14d, Geometry 4 has the structure with the lowest and the different geometries are rigid. However, the defor- level of security, whereas Geometry 5 has the safest form of mations have no significant effect on the phenomenon of the system. fatigue failure. When compared with Figure 13, it can be Total deformation (Figure 15) presents the deformation observed that the contours of the total deformation are distribution in the structure due to the loading process. different from the contours of the fatigue life. Areas that Geometries 2 and 3 (Figures 15b and 15c) are deformed by experience maximum deformation do not necessarily have a. b. c. d. e. Figure 12. Alternating Stress Results: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Figure 12: Alternating stress results: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; Joindt . [1 Geomet 2]; c.r yG4: eo Bottom-stiffened metry 3: Stoopl anel Join [28]; t [12 e.]; Geomet d. Geo rym 5: eSide-stiffened try 4: Bottop m anel -Sti[29] ffened Panel [27]; e. Geometry 5: Side- Stiffened Panel [28] 174 | A. Fajri et al. a. b. c. d. e. Figure 13. Fatigue Life Results: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Joint Figure 13: Fatigue life results: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; c. Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 5: Side-Stiffened [12]; d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] Panel [28] Assessment of ship structure under fatigue loading | 175 a. b. c. d. e. Figure 14. Safety Factor Results: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Joint Figure 14: Safety factor results: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] [12]; c. Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 5: Side-Stiffened Panel [28] 176 | A. Fajri et al. a. b. c. d. e. Figure 15. Total Deformation Results: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Figure 15: Total deformation results: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] Joint [12]; c. Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 5: Side- Stiffened Panel [28] Assessment of ship structure under fatigue loading | 177 Geometry 1 Geometry 2 Geometry 3 Geometry 4 Geometry 5 8 8 8 0,0 2,0x10 4,0x10 6,0x10 Fatigue Life (Cycle) Figure 16. Relationship Between Alternating Stress and Fatigue Life of Each Geometry Figure 16: Relationship between alternating stress and fatigue life of each geometry Figure 17. Fatigue Results: Maximum Deformation, Minimum Safety Factor, Maximum Damage, and Minimum Figure 17: Fatigue results: Maximum deformation, minimum safety factor, maximum damage, and minimum life Life a short fatigue life. The deformation is still in the elastic very short fatigue life, whereas Geometry 5 has good fatigue area, which is a condition that allows the structure to re- resistance. In Figure 17a, Geometries 4 and 1 show slight turn to its original shape after the load is removed. This is deformation, whereas Geometries 2 and 3 undergo the most supported by the evidence that the stress (Figure 12) is still extensive deformation. Figure 17b shows that all geometries below the material yield point. are still in critical areas, where the minimum safety factor Figure 16 compares the performance of all geometries is below 1. However, Geometry 5 is relatively safe because under fatigue loading. Each geometry presents a unique it has the highest safety factor. Figure 17c presents that a response. Geometry 4 has the weakest characteristic or a large damage occurrence implies a short fatigue life. Alternating Stress (MPa) 178 | A. Fajri et al. 7.2 Effect of material used 950X (Figure 18a) material has a minimum fatigue life of 2.2571e5 cycles, which is longer than those of the SAE 316L Geometry 2 is adopted as a sample to investigate the ef- and 304L materials. The used medium-carbon steel (Fig- fect of the type of material used on the fatigue force on the ure 18b) has the highest fatigue resistance of all types of structure. In addition to material variations, other variables considered materials. However, it should be noted that cor- that affect this property, such as the magnitude of loading, rosion can shorten the age of fatigue because it can trigger surface smoothness, stress corrosion factor, and loading the appearance of an initial crack. Of the four types of mate- scheme, are considered constant. SAE 316L and 304L ma- rials, only the carbon medium has no corrosion resistance terials are marine-grade steels, i.e., they meet standards properties. The medium-carbon and SAE 316L materials for forming marine structures. The HSLA 950X material is a have better stress distributions than HSLA 950X and SAE steel that is not yet commonly used in the marine structure 304L. industry. Despite its high toughness and corrosion resis- Based on the contours of the safety factor (Figure 19), tance, the HSLA is considered less effective owing to its rea- it is determined that the SAE 316L material has the low- sonably high production cost. Although a medium-carbon est security, followed by SAE 304L. The HSLA 950X and steel has good strength, it is not recommended for marine medium-carbon materials have a higher safety factor than structure applications. It can be observed that the HSLA the specified criteria limit. Thus, none of the four materials a. b. c. d. Figure 18. Fatigue Life: a. HSLA 950X; b. Medium-Carbon; c. SAE 316L; d. SAE 304L Figure 18: Fatigue life: a. HSLA 950X; b. Medium-carbon; c. SAE 316L; d. SAE 304L Assessment of ship structure under fatigue loading | 179 a. b. c. d. Figure 19: Safety factor: a. HSLA 950X; b. Medium-carbon; c. SAE 316L; d. SAE 304L Figure 19. Safety Factor: a. HSLA 950X; b. Medium-Carbon; c. SAE 316L; d. SAE 304L is entirely safe and will potentially fail in a given cycle. Fig- HSLA 950X ures 20 and 21 show that the sequence of materials with the MEDIUM-CARBON SAE 316L 250 highest to the lowest fatigue resistance is medium-carbon SAE 304L steel, HSLA 950X, SAE 304L, and SAE 316L. Other factors that must be considered are the working environment con- ditions. The medium-carbon material will be brittle at a low temperature. Under a relatively small impact, the load alone can destroy the structure in these conditions. HSLA 950X, SAE 316L, and 304L are laboratory-tested and proven to withstand low temperatures. More research on this phe- nomenon needs to be conducted in the future. 4 5 6 7 8 9 10 11 12 13 14 10 10 10 10 10 10 10 10 10 10 10 Fatigue Life (Cycle) Figure 20. Relationship Between Alternating Stress and Fatigue Life for Each Material Used Figure 20: Relationship between alternating stress and fatigue life for each material used Alternating Stress (MPa) 180 | A. Fajri et al. Figure 21. Fatigue Results: Maximum Deformation, Minimum Safety Factor, Maximum Damage, and Minimum Figure 21: Fatigue results: Maximum deformation, minimum safety factor, maximum damage, and minimum life for each material used Life for Each Material Used a. b. c. d. Fatigue Life (Cycle) Maximum Alternating Stress (MPa) 650,21 7x10 6,5984E6 6x10 5x10 4x10 3x10 2x10 289,76 1x10 8,7435 200 216,74 -1x10 Fully Reversed Zero-Based Ratio -2 Scale Factor 1 Load Type Figure 22: Alternating stress results: a. Fully reversed; b. Zero-based; c. Ratio; d. Relevance with fatigue life Figure 22. Alternating Stress Results: a. Fully Reversed; b. Zero-Based; c. Ratio; d. Relevance with Fatigue Life Fatigue Life (Cycle) Maximum Alternating Stress (MPa) Assessment of ship structure under fatigue loading | 181 7.3 Effect of load type safety factor values produce the safest conditions among all types of loading. Three types of loading are compared (Figure 22). At the same amount of load, varying stresses will be produced if the type of loading is different. As can be observed, the load- 7.4 Effect of mean stress correction theory ing ratio type only produces an alternating stress of 216.74 MPa. Similarly, when the exposure is changed to fully re- The data presented in the S–N curves were obtained from versed, the stress appears to be 289.76 MPa. When the geom- the results of the fatigue tests conducted in the laboratory. etry is subjected to the highest loading ratio, the generated Fatigue tests are commonly conducted on uniaxial testing stress increases several folds to 650.21 MPa. This loading machines with a fully reversed loading scheme. These data ratio type occurs when the bending and tensile forces have cannot be used as the basis for analysing fatigue phenom- different values. There are some materials whose tensile ena in structures that undergo non-fully reversed loading strengths are higher than the compressive strength and vice because the structural responses present different charac- versa. Thus, a material can be safe under a zero-based or teristics relative to the data shown in S–N curves. Therefore, fully reversed loading type, whereas it is fatal under the the stress that emerges under non-fully changed conditions loading ratio. Therefore, the selection of materials needs to must be corrected using a mean stress theory. Mean stress consider the type of loading that the structure may experi- theories have different effects. For example, in this study, ence. The fatigue life material will certainly be affected by the loading scheme is changed to zero-based loading to the type of loading. show differences. Figure 24 shows the maximum stress of The loading type does not affect the geometry defor- each mean stress theory used. Under the same conditions, mation (see Figure 23). The fully reversed, zero-based, and the Goodman, Soderberg, Gerber, and ASME elliptic theo- ratio type loading produce the same total deformation of ries correct the maximum stress to 206.6 MPa, 216.74 MPa, 3.3328 mm. The loading ratio of 2 with a scale factor of 1 does 159.08 MPa, and 153.57 MPa, respectively. First, it is notice- the most damage. A large damage implies a short fatigue able that the Goodman and Soderberg theories produce life. When a geometry is subject to zero-based loading, the almost the same stress values, whereas the Gerber theory Figure 23. Fatigue Results: Maximum Deformation, Minimum Safety Factor, Maximum Damage, and Minimum Figure 23: Fatigue results: Maximum deformation, minimum safety factor, maximum damage, and minimum life for each loading type Life for Each Loading Type 182 | A. Fajri et al. a. b. c. d. Figure 24: Alternating stress using different mean stress correction theories: a. Goodman; b. Soderberg; c. Gerber; d. ASME elliptic values are close to the results of the correction by the ASME than the Gerber and ASME elliptic theories. When used Figure 24. Alternating Stress using Different Mean Stress Correction Theories: a. Goodman; b. Soderberg; c. elliptic theory. Based on literature studies, the Goodman to predict the age of fatigue, the Goodman and Soderberg Gerber; d. ASME Elliptic and Soderberg theories are very suitable for analysing brit- theories result in a minor period of fatigue. tle materials, whereas the stress on ductile materials can The mean stress correction theory used does not af- be suitably corrected using the Gerber and ASME elliptic fect the deformation value in the geometry (Figure 27). The theories. Soderberg theory produces the most damage and a very The stress distribution and the safety factor distribu- short fatigue life. The ASME elliptic theory causes a slight tion (Figure 25) for each criterion have the same contours damage and leads to excellent fatigue life. Specifically, dif- but different values when reviewed. Figure 26 shows that ferent means stress theories introduce different character- the Goodman and Soderberg theories are very conservative, istics into a geometric structure. Each theory has its advan- with which the limit of failure is set far below the results of tages and disadvantages, and each depends on the material the lab experiments. The Gerber and ASME elliptic theories used. set higher failure limits than the other methods, approach- ing the data shown on the S–N curves. The Goodman and Soderberg theories result in smaller safety factor values Assessment of ship structure under fatigue loading | 183 a. b. c. d. Figure 25: Safety factor using different mean stress correction theories: a. Goodman; b. Soderberg; c. Gerber; d. ASME elliptic Figure 25. Safety Factor using Different Mean Stress Correction Theories: a. Goodman; b. Soderberg; c. Gerber; d. ASME Elliptic Goodman Soderberg Gerber ASME Elliptic 8 8 8 8 9 0,0 2,0x10 4,0x10 6,0x10 8,0x10 1,0x10 Fatigue Life (Cycle) Figure 26. Relationship Between Alternating Stress and Fatigue Life using Different Mean Stress Correction Figure 26: Relationship between alternating stress and fatigue life using different mean stress correction theories Theories Alternating Stress (MPa) 184 | A. Fajri et al. Figure 27. Fatigue Results: Maximum Deformation, Minimum Safety Factor, Maximum Damage, and Minimum Figure 27: Fatigue results: Maximum deformation, minimum safety factor, maximum damage, and minimum life for each mean stress theory Life for Each Mean Stress Theory Used used shorter fatigue life, they have good corrosion resistance. 8 Conclusion These materials are designed according to marine-grade steel standards. In this paper, the research results on the effects of geomet- Further research on the fatigue behaviour in low-cycle ric shapes, material types, loading types, and mean stress fatigue needs to be conducted considering other factors correction theories were presented. The research methods such as corrosion resistance and environmental tempera- were validated by comparison with previous research. A ture. Compared to fully reversed loading, zero-based load- difference in the results of <5% indicates that the technique ing produces relatively low stresses; therefore, a structure used in this study is valid and can be accounted. Differ- will have a safe fatigue life in this condition. The same nom- ences in the geometric shapes and locations of the struc- inal weighting ratio type leads to higher stresses, resulting ture affect the fatigue behaviour. The above study results in short-life fatigue. The mean stress theory used does not prove that the bottom-stiffened panel has the highest fa- have a significant difference when the loading type with- tigue risk, whereas the side-stiffened panel has the lowest. stood by the structure is the same as in the lab experiment The medium-carbon steel material has a high resistance results (fully reversed). The Goodman theory corrects the to high-cycle fatigue, which is the loading of fatigue with stress far below the safe limit when the loading scheme is an intensity below the yield strength of the material. Fa- changed to zero-based and ratio. The Goodman and Gerber tigue characteristics against low-cycle fatigue need to be theories are relatively more conservative than the Soder- studied further. However, this material cannot be used for berg and ASME elliptic theories. ship structure applications because of its low corrosion re- sistance. Corrosion can decrease strength because this will Acknowledgement: The authors are grateful to the Indone- trigger the onset of a fatigue crack. The medium-carbon sia Endowment Fund for Education (LPDP), Ministry of steel is also brittle; therefore, when a rupture occurs, the Finance, Republic of Indonesia for the financial support propagation is expected to have a high speed. Although provided for this research. the HSLA, SAE 316L, and 304L materials have relatively Assessment of ship structure under fatigue loading | 185 Author contributions: All authors have accepted responsi- [17] Bishara M, Horst P, Madhusoodanan H, Brod M, Daum B, Rolfes R. A structural design concept for a multi-shell blended wing body bility for the entire content of this manuscript and approved with laminar flow control. Energies. 2018;11(2):1–21. its submission. [18] Hansen PF, Winterstein SR. Fatigue damage in the side shells of ships. Mar Structures. 1995;8(6):631–55. Conflict of interest: The authors state no conflict of inter- [19] Boardman B. Fatigue resistance of steels. In: ASM Handbook est. Volume 1: Properties and Selection: Irons, Steels, and High- Performance Alloys. ASM International; 1987. p. 77–81. [20] Gaidai O, Storhaug G, Naess A, Ye R, Cheng Y, Xu X. Eflcient fatigue assessment of ship structural details. Ships Offshore Struct. 2020;15(5):503–10. References [21] Ślęzak T. Fatigue examination of HSLA steel with yield strength of 960 MPa and its welded joints under strain mode. Metals (Basel). [1] Li Z, Ringsberg JW, Storhaug G. Time-domain fatigue assessment 2020;10(2):1–14. of ship side-shell structures. Int J Fatigue. 2013;55:276–90. [22] Vaara J, Kunnari A, Frondelius T. Literature review of fatigue [2] Xiu R, Spiryagin M, Wu Q, Yang S, Liu Y. Fatigue life assess- assessment methods in residual stressed state. Eng Fail Anal. ment methods for railway vehicle bogie frames. Eng Fail Anal. 2020;110:104379. 2020;116:104725. [23] Venkatasudhahar M, Dilipraja N, Mathiyalagan P, Subba SV, [3] Fajri A, Prabowo AR, Muhayat N, Smaradhana DF, Bahatmaka A. Sathyaseelan P, Logesh K. Finite element analysis of fatigue life Fatigue analysis of engineering structures: State of development of spot welded joint and the influence of sheet thickness and and achievement. Procedia Struct Integr. 2021;33:19–26. spot diameter. Int J Mech Mechatron Eng. 2014;14(06):76–82. [4] Ringsberg JW, Li Z, Tesanovic A, Knifsund C. Linear and nonlin- [24] Pastorcic D, Vukelic G, Bozic Z. Coil spring failure and fatigue ear FE analyses of a container vessel in harsh sea state. Ships analysis. Eng Fail Anal. 2019;99:310–8. Offshore Struct. 2014;10(1):20–30. [25] Raymond L. Browell PE, Hancq A. Predicting fatigue life with AN- [5] Tasdemir A, Nohut S. Fatigue analysis of ship structures with SYS workbench: How to design products that meet their intended hinged deck design by finite element method. A case study: fa- design life requirements. 2006 International ANSYS Conference. tigue analysis of the primary supporting members of 4900 PCTC. 2006 May 2-4. Mar Structures. 2012;25(1):1–12. [26] Lotsberg I, Sigurdsson G. Hot spot stress S-N curve for fa- [6] Prabowo AR, Bae DM, Sohn JM, Zakki AF, Cao B, Cho JH. Effects of tigue analysis of plated structures. J Offshore Mech Arctic Eng. the rebounding of a striking ship on structural crashworthiness 2006;128(4):330–6. during ship-ship collision. Thin-Walled Struct. 2017;115:225–39. [27] Glen IF, Dinovitzer A, Paterson RB, Luznik L, Bayley C. Fatigue [7] Prabowo AR, Putranto T, Sohn JM. Simulation of the behavior of Resistant Detail Design Guide For Ship Structures (No. SR-1386). a ship hull under grounding: effect of applied element size on Ship Structure Committee; 1999. structural crashworthiness. J Mar Sci Eng. 2019;7(8):270. [28] He W, Liu J, Xie D. Numerical study on fatigue crack growth at a [8] Vukelić G, Vizentin G. Common Case Studies of Marine Structural web-stiffener of ship structural details by an objected-oriented Failures. Failure Analysis and Prevention. InTech; 2017. pp. 135– approach in conjunction with ABAQUS. Mar Struct. 2014;35:45– [9] France EJ. The Alexander L. Kielland Disaster Revisited: A Review [29] Okawa T, Sumi Y, Mohri M. Simulation-based fatigue crack man- by an Experienced Welding Engineer of the Catastrophic North agement of ship structural details applied to longitudinal and Sea Platform Collapse. J Fail Anal Prev. 2019;19(4):875–81. transverse connections. Mar Struct. 2007;19(4):217–40. [10] Sedmak A. Computational fracture mechanics: an overview from [30] Dindinger P. HSLA 345X (SAE950X) Fatigue Test Report. F.D.E early efforts to recent achievements. Fatigue Fract Eng Mater Committee. Ontario, Canada; 2014. Struct. 2018;41(12):2438–74. [31] Li C, Dai W, Duan F, Zhang Y, He D. Fatigue life estimation of [11] Schütz W. A history of fatigue. Eng Fract Mech. 1996;54(2):263– medium-carbon steel with different surface roughness. Appl Sci (Basel). 2017;7(4):1–11. [12] Osawa N, Hashimoto K, Sawamura J, Nakai T, Suzuki S. Study on [32] Jacquelin B. FHAP. SAE 316L Fatigue Test Report. Ontario, Canada; shell-solid coupling FE analysis for fatigue assessment of ship structure. Mar Structures. 2007;20(3):143–63. [33] Nachtigall AJ. SAE 304L Fatigue Test Report. Ontario, Canada: [13] Li Z, Ringsberg JW, Storhaug G. Time-domain fatigue assessment F.D.E. Committee. Ontario, Canada; 2012. of ship side-shell structures. Int J Fatigue. 2013;55:276–90. [34] Köksal NS, Kayapunar A, Çevik M. Fatigue analysis of a notched [14] Alshoaibi AM, Fageehi YA. 2D finite element simulation of mixed cantilever beam using ANSYS workbench. Proceedings of the mode fatigue crack propagation for CTS specimen. Integr Med Fourth International Conference on Mathematical and Compu- Res. 2020;9(4):7850–61. tational Applications. 2013 Jun 11-13; Manisa, Turkey. 2013. p. [15] Božić Ž, Schmauder S, Wolf H. The effect of residual stresses on 111–8. fatigue crack propagation in welded stiffened panels. Eng Fail [35] Fajri A, Prabowo AR, Surojo E, Imaduddin F, Sohn JM, Adiputra Anal. 2018;84:346–57. R. Validation and Verification of Fatigue Assessment using FE [16] Zhang Y, Huang X, Wang F. Fatigue crack propagation prediction Analysis: A Study Case on the Notched Cantilever Beam. Procedia for marine structures based on a spectral method. Ocean Eng. Struct Integr. 2021;33:11–8. 2018;163:706–17. [36] Prabowo AR, Ridwan R, Muhayat N, Putranto T, Sohn JM. Tensile analysis and assessment of carbon and alloy steels using fe 186 | A. Fajri et al. approach as an idealization of material fractures under collision [39] Prabowo AR, Sohn JM, Putranto T. Crashworthiness perfor- and grounding. Curved Layer Struct. 2020;7(1):188–98. mance of stiffened bottom tank structure subjected to impact [37] Prabowo AR, Sohn JM. Nonlinear dynamic behaviors of outer loading conditions: ship-rock interaction. Curved Layer Struct. shell and upper deck structures subjected to impact loading in 2019;6(1):245–58. maritime environment. Curved Layer Struct. 2019;6(1):146–60. [38] Prabowo AR, Laksono FB, Sohn JM. Investigation of structural performance subjected to impact loading using finite element approach: case of ship-container collision. Curved Layer Struct. 2020;7(1):17–28. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Curved and Layered Structures de Gruyter

Assessment of ship structure under fatigue loading: FE benchmarking and extended performance analysis

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Curved and Layer. Struct. 2022; 9:163–186 Research Article Aprianur Fajri, Aditya Rio Prabowo*, and Nurul Muhayat Assessment of ship structure under fatigue loading: FE benchmarking and extended performance analysis https://doi.org/10.1515/cls-2022-0014 commonly induce material failure in structures, and they Received Nov 16, 2021; accepted Feb 11, 2022 can be classified into two categories: static and dynamic loads. The most frequently encountered issues are typically Abstract: This paper presents a numerical procedure based related to the presence of dynamic loads, such as uninten- on the finite element (FE) method using ANSYS Workbench tional loads/impact loads originating from various sources software to analyse fatigue phenomena in ship structures. [1]. However, dynamic loads with a relatively small mag- Fatigue failure prediction is used as a stress–life approach, nitude (far below the yield point) might also cause failure when the stress is still in a linear area. This condition is if they continue indefinitely, which is referred as fatigue frequently referred as high-cycle fatigue. Five geometric failure [2]. shapes taken from midship points on the structure of a ship Although fatigue failure can occur in any structure, it are sampled. There are four types of materials: HSLA SAE is more prevalent in those subjected to cyclic loads or op- 950X, medium-carbon steel, SAE 316L, and SAE 304L. The erating in harsh environments. Ships comprise facilities types of loading imposed on each sample include three that are prone to fatigue due to working in corrosive condi- conditions: zero-based, zero mean, and ratio. Mesh conver- tions, being subjected to continuous loading by seawater gence analysis is conducted to determine the most effective waves, being impacted by changes in ambient tempera- mesh shape and size for analysing the structure. The results ture, and being subjected to other mechanical loads. Ships showed that the configuration of the geometric shapes, ma- are frequently constructed considering empirical loads (de- terials used, loading schemes, and mean stress theory affect sign loads), which reflect the most significant subjected the fatigue characteristics of the structure. static load. However, the causes and mechanisms of fatigue Keywords: Finite element method, fatigue phenomena, (induced by dynamic loads) remain unknown and under ship structure investigation. Ships are constructed from various highly complex structures and joints, responding differently to fatigue risk [3]. Fatigue failure can begin with cracks in lo- cations with a high-stress concentration. These cracks may 1 Introduction propagate in a specific direction and produce a fracture. The used materials, geometric shape, and type of loading Currently, technology advancement, particularly in engi- are factors to consider when examining the features of a neering structures, is accelerating. The complexity of the structure. The design must be economically viable and safe challenges and the obstacles encountered is also increas- to operate under various loading scenarios. Fatigue testing ing; one of the most frequent issues is material failure, should consider actual field scenarios, where testing and which is caused by various factors. Catastrophic material measurement should be performed with various parameter failures result in material losses, which frequently cause fa- adjustments. Understandably, if the standard experimental talities and damage to the environment. Operational loads procedures are used, the above will be extremely difficult, time-consuming, and prohibitively expensive. The finite element method (FEM) is one of the alternatives to this *Corresponding Author: Aditya Rio Prabowo: Department problem because it is highly effective in identifying and of Mechanical Engineering, Universitas Sebelas Maret, Ir. Su- visualising fatigue failure mechanisms. tami Street 36A, Surakarta, Central Java 57126, Indonesia; Email: This study presents some data related to fatigue assess- aditya@ft.uns.ac.id ment of the design of ship structures from different per- Aprianur Fajri, Nurul Muhayat: Department of Mechanical Engi- spectives. Previous research [1, 3–7] has identified several neering, Universitas Sebelas Maret, Ir. Sutami Street 36A, Surakarta, Central Java 57126, Indonesia Open Access. © 2022 A. Fajri et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License 164 | A. Fajri et al. potential issues that can be further investigated. The area in and the concept of the stress–cycle curve (S–N) curve and the middle of a ship (Figure 1) experiences the most extreme endurance limits are introduced. The linear damage hy- loading and has the highest risk of fatigue failure. These pothesis discovered in 1945 was still referenced when the problems should be further examined, using alternative stress-life approach was adopted to investigate the current methods and approaches to provide a complete explana- fatigue phenomenon. The 1979 loss of MV Kurdistan and tion of the phenomenon of weariness. This problem must the 1980 sinking of the Alexander L. Kielland platform due be discovered in advance and addressed entirely to avoid to fatigue failure [9] prompted academics to conduct addi- future disasters [8–10]. The purpose of this study is to de- tional research on this phenomenon, particularly in marine termine the effects of geometric shapes, material types, and structures. The growing importance of fatigue strength in loading types on the fatigue phenomenon occurring in ship maritime constructions has resulted in its study and design structures using the hot spot stress approach. This study recommendations. In the literature, there are numerous conducts fatigue analysis of numerous sample hot spots approaches for defining stress and implementing fatigue with material and applied load variations. This research assessment. The two most accepted methods for the stress is simply a follow-up that aims to fill in the gaps of prior analysis of the structure of a ship are the hot spot stress investigations. To the authors’ best knowledge, the FEM approach and the practical notch stress approach [5]. has not been tested by highly complex mesh convergence A study on the measurement of the fatigue of ship struc- investigations, which is critical for ensuring the accuracy tures was undertaken in [12] on a perpendicular joint con- of numerical simulation findings. sisting of a plate connection with a beam (shell–solid cou- pling). This study showed that finite element analysis may be used quite well to predict structural responses to fatigue loading, particularly in locations of high-stress concentra- tion. Because the metrics tested and compared in this study are displacement-related, other processes are required to determine fatigue life parameters, fatigue damage, and fa- tigue safety factor. Subsequently, in [5], a comparative study was conducted on various vessels using more advanced ap- proaches. The model under consideration is an integral part of the 4900 PCTC ship. The study established a method to determine the hot spot stress by examining global models. The areas most affected by a fatigue load were subsequently used to create a local model with mesh refinement in the crucial region. Loading scenarios were modelled in various ways, all of which involve using the same type of mate- rial. Based on the results of worldwide studies on models, there are other locations that may be exploited as research hot spots. In a study, the use of nonlinear time-domain Figure 1. Weakest Areas on Ship Structures [4] Figure 1: Weakest areas on ship structures [4] hydrodynamic models of container ships (DNV-class) [13] showed that the selected material affects the structural response under various loading schemes. The study com- pared HT32-grade steel with various materials. Different wave heights resulted in several different loading patterns. 2 Literature review The fatigue properties of the structures in response to this loading pattern were diversified; however, other hot spots 2.1 Pioneer works remain to be studied. The fatigue cracks propagation ap- proach can be used to analyse the fatigue characteristics Research on the phenomenon of fatigue has a very long in a shell structure, which is the magnitude of the crack history [3, 11]. The first paper on the fatigue phenomenon propagation caused by dynamic stresses on ships [14–16]. was written in 1837. A further development, the effect of This technique is predicated on the initial assumption of a stress concentration on the failure of axle trains, was in- crack in specimens derived from several possible sources. troduced in 1842. Systematic fatigue testing methods were This study found that variations in loading scenarios, such developed in 1860. This method was later modified in 1870, as the tangle force and he wave frequency, substantially af- Assessment of ship structure under fatigue loading | 165 fected the rate of fracture propagation. This method cannot procedure is called meshing. Each element contains var- describe fatigue prior to the onset of cracks. ious stress components, which can be determined using interpolation and extrapolation concepts. When conduct- ing fatigue analysis using the stress–life approach, each 2.2 Fundamental theory element must be searched for its corresponding stress value and subsequently compared to the fatigue data in the form Fatigue is the irreversible damage of items due to the stress– of an S–N curve. strain variations caused by external factors [17]. According Different types of stresses can be utilised to forecast fa- to [18], fatigue failure occurs in four stages: (1) nucleation tigue age, including axial stress (S or S ) and shear stress x y of cracks, (2) structurally dependent crack propagation, (3) (S ). Using the von Mises equation, these three types of xy crack propagation, and (4) failure. Numerous factors can stresses can be converted into normal or equivalent stress influence fatigue resistance including the type of applied (Eq. 3). This stress component is used in this study because load, material used, mechanical properties, manufacturing it encompasses all other stress components. Thus, for the techniques, surface roughness, operating temperature, en- simulation of fatigue due to cyclic loads, the maximum vironment, microstructure state, residual stress, corrosion, stress (S ) and the minimum stress (S ) must be ob- max min and crack initiation [19–22]. tained, and subsequently Eq. (4) is used to determine the Metals can be classified according to their uniaxial ratio. properties, which include engineering properties and ac- √︀ 2 2 2 .Seqv = Sx + Sy − SxSy + 3Sxy (3) tual characteristics. Engineering properties are types of characteristics used to compute the cross-sectional area min and the length of a sample in its original configuration. In R = (4) max comparison, stress–strain factors are calculated using the immediate space and size of a sample loading process. En- The fatigue data obtained from laboratory test pro- gineering stress (Eq. (1)) is fundamentally different from cesses shown in S–N curves become input variables. Typ- actual stress (Eq. (2)). ically, these data are collected at a mean of zero or R = −1 (Figure 2a). If the fatigue data are to be utilised to study an S = (1) issue under a zero-based loading condition (R = 0 or R = ∞) or with ratio R > 0 (see Figure 2b and Eq. (4)), then the mean stress must be corrected. Various theories can be em- σ = (2) A ployed, including the Goodman (England, 1899) (Eq. (5)), Soderberg (the USA, 1930) (Eq. (6)), Gerber (Germany, 1874) Above, P represents the axial tension stress, A denotes (Eq. (7)), and ASME elliptical (Eq. (8)) theories [23–26]. the initial cross-sectional area of the sample, and A rep- resents the instantaneous cross-sectional area of the sam- ple. When assessing a structure, the actual stress, which Alternating mean + = 1 (5) is affected by the cross-sectional variation, is employed. S S Endurance limit ultimate When materials are tested for strength in the laboratory, the shape of the specimen is highly simple, allowing di- Alternating S mean + = 1 (6) mensional changes to be easily observed and quantified S S Endurance limit yield directly. However, dimensional changes are exceedingly difficult to detect in complex structures, such as ship struc- tures. Each piece has its unique distribution of stress. Ex- pectedly, doing trials on a complete design will require a significant amount of resources. This is because the cost of specialised sensors for stress stamping is high, and the arrangement is relatively intricate. Consequently, an alter- nate approach for analysing the strength of a structure is to employ an FEM-based software. The FEM is a numerical technique for solving mathematical problems that include specified boundary conditions. In principle, when used to solve a problem, a space model is separated into mul- Figure 2: Loading conditions: a. Zero-mean; b. Ratio Figure 2. Loading Conditions: a. Zero-Mean; b. Ratio tiple portions of the domain referred as up elements; this 166 | A. Fajri et al. (︂ )︂ Alternating mean + = 1 (7) S S Endurance limit ultimate (︂ )︂ (︂ )︂ 2 2 Alternating mean + = 1 (8) S S Endurance limit yield ∑︁ D = (9) i=1 The magnitude of fatigue life can be determined using the Palmgren–Miner linear damage hypothesis (Eq. (9)), where denotes the number of stress range cycles caused by various factual stressors S (1 ≤ i ≤ k) and N represents i i the number of cycles required to cause the failure of the alternating constant stress, S (S–N curve). Failure occurs when cumulative damage (D) exceeds one. 3 Preparation and methodology This research is conducted in several stages, and each stage Figure 3: Research scheme Figure 3. Research Scheme has its role. Literature studies are conducted to ensure that the used methods follow existing scientific rules. Prior re- ture study are inputted into the software manually. Sub- search is referred to define the input variables and the fun- sequently, the process of meshing divides a geometry into damental assumptions. Material properties are obtained several small domains called elements. The mesh size is from the results of laboratory tests with recognised stan- determined to achieve convergence of calculation value dards. Numerical methods are validated before use. One and time efficiency. Following this, the boundary condition approach involves benchmark analysis procedures. The is determined to set the placement of the pedestal and the shapes and magnitudes of the meshes for all geometries are loading location. Fatigue analysis is conducted using the different; therefore, convergence studies are conducted to fatigue tool in ANSYS Workbench. The parameters that can choose the most optimal mesh. These stages are discussed be varied are fatigue damage, fatigue life, safety factor, and in more detail sequentially in this section. biaxiality indication. The values of some output parame- ters are subsequently analysed and related for inference. The research scheme in this study is shown in Figure 3. 3.1 Assessment procedures A literature study is conducted to understand the phe- 3.2 Engineering three-dimensional models nomenon of fatigue in ship structures. It identifies several problems related to fatigue in the construction of ships and The studied samples are taken from several locations on the the methods and the approaches that can be used to in- structure of a ship that can represent the most prone parts vestigate fatigue. The method used is the FEM with CAE to fatigue failure. Furthermore, these samples are formed simulation software, and the technique used is the stress– into three-dimensional models, following a limit condition life approach, which is applied to the hot spot stress area. applied based on the loading conditions that occur in the Before use, this method is validated to replicate previous field. Areas with high-stress concentrations (hot spot stress) research, and subsequently the results are compared. If the typically have a short fatigue life. error is relatively small and meets certain criterion, then this method is valid and worth using. Geometric models are built using ANSYS Modeller, a CAD program integrated with ANSYS Workbench. Fur- thermore, the material properties obtained by the litera- Assessment of ship structure under fatigue loading | 167 Figure 4. Geometry Locations on Midship Section Model Figure 4: Geometry locations on midship section model [27] a. b. c. d. e. Figure 5. Geometry Model: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Joint [12]; c. Figure 5: Geometry model: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 5: Side-Stiffened Panel [28] d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] 168 | A. Fajri et al. a. b. c. d. e. Figure 6. Meshing and Boundary Conditions: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Figure 6: Meshing and boundary conditions: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry Perpendicular Joint [12]; c. Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 3: Stool joint [12]; d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] 5: Side-Stiffened Panel [28] 3.2.1 Geometry location 3.2.2 Sample models and boundary conditions Based on a literature study on the global models of ships, it Boundary conditions are applied to the built geometric is found that the hull and the midship (Figure 1) are the most models (Figure 5), as shown in Figure 6. Based on a litera- vulnerable areas to failure owing to stress concentration. ture study, the magnitude of the load, the position of the Therefore, v fi e types of sample models are taken in the support, and other configurations are adjusted to the actual above sections representing the hot spot areas on a ship needs. structure (Figure 4). One model is used to investigate the Some other parameters that are not set in this study are effects of the applied material, loading scheme, and mean left constant or follow the default settings of ANSYS soft- stress correction theory on the fatigue behaviour that occurs ware. Some basic assumptions that need to be highlighted in the structure. When one variable is examined, the other are that the approach used in this study is the stress–life variables are considered constant. approach and the stress is still in the linear area below Assessment of ship structure under fatigue loading | 169 the material yield point. The model is in perfect condition, there is no initial crack, and the smoothness of the surface HSLA SAE 950X 900 SAE 316L is considered uniform. Mesh convergence is conducted for Medium-Carbon SAE 304L each model using different mesh sizes. One method to de- termine the range of mesh sizes to be used is based on the 700 element length to thickness (ELT) ratio. According to [7], ELT values of 5–10 can analyse a complex structure. A small ELT ratio implies that the analysis result is close to the ac- tual value, and consequently the computing time is long. The meshing technique used is local meshing. Mesh in the area of interest is refined thrice smoother than the global mesh. The stress that appears subsequently represents the 100 hot spot stress, whose value is more significant than the 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 nominal stress. Fatigue Life (Cycles) Figure 7. S–N curves of HSLA SAE 950X [29], Medium-Carbon Steel [30], SAE 316L [31], and SAE 304L [32] Figure 7: S–N curves of HSLA SAE 950X [30], medium-carbon steel [31], SAE 316L [32], and SAE 304L [33] 4 Materials Four types of materials are used in this study: high-strength 5 Benchmark study on simple case low-alloy steel (HSLA) SAE 950X [30], medium-carbon steel [31], SAE 316L [32], and SAE 304L [33]. The material prop- Koksal [34] previously completed an FEM fatigue analysis erties used as input parameters are listed in Tables 1 and 2 on notched cantilever beams. The research material was a and shown in Figure 7. HSLAs are relatively new materi- structural steel, with the mechanical parameters listed in als and are still not as well-known as SAE 316L and 304L Table 3 and the S–N curve shown in Figure 8c. The dimen- for applications in marine structures. Although medium- sions of the geometric model are 1000 × 100 × 75 mm; on carbon steels have good mechanical properties, they are one side of the beam, a notch with a large angle of 90 and rarely used in marine structures with some consideration. a depth of 25 mm is created (Figure 8a). Cantilever beams Table 1: Chemical composition Type of material Material composition wt% C Cr Mo Si Mn S P Ni Cu Co N V Nb HSLA SAE 950X 0.23 0.9 1.35 0.05 0.04 0.15 0.04 Medium-carbon 0.44 0.04 0.02 0.23 0.57 0.16 0.24 0.002 SAE 316L 0.29 17.54 2.38 0.5 1.8 0.012 0.032 12.6 0.26 0.18 0.077 SAE 304L 0.02 18.5 0.049 1.78 0.011 0.014 9.78 Table 2: Mechanical properties Type of material Modulus of elasticity (MPa) Yield strength (MPa) Ultimate strength (MPa) HSLA SAE 950X 204700 437 485 Medium-carbon 210000 490 710 SAE 316L 200000 283 592 SAE 304L 190200 277 572 Table 3: Mechanical properties of structural steel (ANSYS) Modulus elasticity (GPa) Ultimate tensile strength (MPa) Poisson’s ratio Yield Strength (MPa) 200 460 0.3 250 Stress Amplitude (MPa) 170 | A. Fajri et al. Table 4: Verification results Value Previous test (33) Re-simulation result Error (%) Min fatigue life 90,700.00 89,948.00 0.83 Min safety factor 0.60824 0.60686 0.20 Maximum equivalent alternating stress 141.72 142.04 0.20 a. b. c. Structural Steel (ANSYS) -500 0 1 2 3 4 5 6 10 10 10 10 10 10 10 Fatigue Life (Cycle) Figure 8. a. Cantilever Beam Design [33]; b. Boundary Condition; c. S–N Curve of Structural Steel (ANSYS) Figure 8: a. Cantilever beam design [34]; b. Boundary condition; c. S–N curve of structural steel (ANSYS) 6 5 9x10 are intended for a minimum cycle life of 10 . Their one end is stationary, whereas the other end is loaded with a force 8x10 Present simulation 5 Previous test of 10 kN in the direction of the z-axis (Figure 8b). 7x10 Based on a convergence study, a 4-mm mesh produces 6x10 90,322 elements and a single processing step requires 20 5x10 s for computation. A tetrahedral mesh with Jacobian ratio 4x10 = 1 is chosen as the mesh shape. The applied loading is a 3x10 zero-based force of 10 kN. After applying a cyclical load, the 2x10 remaining settings are kept as default or constant. Table 4 1x10 lists and Figure 9 shows the verification findings. 0 15 30 45 60 75 90 105 120 135 150 Alternating Stress (MPa) Figure 9. Validation Results: Benchmarking with Previous Test [34] Figure 9: Validation results: benchmarking with previous test [35] Alternating Stress (MPa) Fatigue Life (Cycle) Assessment of ship structure under fatigue loading | 171 a. b. Figure 10. Mesh Convergence Tests: a. Nominal Stress; b. Hot Spot Stress Figure 10: Mesh convergence tests: a. Nominal stress; b. Hot spot stress a. b. Figure 11. Size 15-mm Mesh Quality: a. Aspect Ratio; b. Skewness Figure 11: Size 15-mm mesh quality: a. Aspect ratio; b. Skewness 172 | A. Fajri et al. 6 Mesh convergence study 7 Results and discussion The shape and size of a mesh significantly influence sim- The data that are successfully captured are processed and ulation results. Generally, a small mesh size implies that grouped based on the investigated variables. The informa- the analysis results are close to the actual condition [36]. tion displayed as contour images and graphs shows the Concurrently, a small mesh size implies numerous formed relationships among the variables. elements. Consequently, the computing time becomes long, and in some cases, the computer devices used cannot deal with these calculations [37, 38]. Thus, a mesh convergence 7.1 Effect of geometry shape study is needed to choose the most suitable shape and size of a mesh. When the simulation results meet the criteria and It can be observed from Figure 12a that Geometry 1 under the time required for one simulation is relatively short, the loading produces a maximum stress of 252.47 MPa, which mesh is considered appropriate. Simulation results are con- is still below the stress yield. Stress concentration occurs in sidered convergent if the changes in the mesh size do not the connection area and spreads to the plate area. A mini- affect the values of the tested parameters. ANSYS software mum stress of 1.2082 MPa occurs in the support area, which provides several forms of meshes, including hexahedron, experiences the slightest moment. Geometry 2 (Figure 12b) pyramid, prism, and tetrahedron. A hexahedron-shaped has a stress of 289.76 MPa, which is relatively larger than mesh is considered ideal because it produces relatively Geometry 1. Geometry 3 (Figure 12c) experiences almost the small elements and is the form most easily analysed by same stress as Geometry 2 because Geometries 2 and 3 have a program solver [39]. However, this mesh cannot adjust a similar adjacent ship structures and boundary conditions. shape well, particularly for a complex geometry. Although However, Geometry 3 can distribute the stress better than it produces relatively larger elements, a tetrahedron mesh Geometry 2. Geometry 4 (Figure 12d) experiences a very can be used for complex geometries. Therefore, this type of high stress, which amounts to 312.67 MPa in the neck area. mesh is chosen for this study. Geometry 5 (Figure 12e) is under a very small stress of 188.83 A convergence test is conducted on Geometry 2 by con- MPa. The received load is well channelled throughout the tinuously changing the mesh, following which the stress surface of the model. Thus, the structure is subsequently values in all changes are compared. Two meshing tech- strengthened by stiffeners. niques are applied: global and local meshing. Global mesh- First, the amount of stress in the structure is inversely ing is used to examine the nominal stress on one intact coupled with the predicted fatigue life. A large value of the structure. In comparison, local meshing is used to search stress implies a short fatigue life. It can be proven from for the stress hot spots in critical areas. The stress magni- Figure 13d that Geometry 4, which experiences the highest tudes of the stress hot spots are above the nominal stress stress, has a very short fatigue life. In contrast, Geometry 5 because the distribution investigated covers a more detailed (Figure 13e), which is under little stress, has a good fatigue scope. Based on the test results (Figures 10a and 10b), a life. The second point to note is the relation between the 15-mm mesh is determined as the best to solve this first case. stress concentration and the minimum fatigue life. Based In addition to no change occurring in the stress value, a on literature studies, fatigue failure typically begins with computing time of less than 4 s is the most relevant consid- an initial crack. Initially, Geometries 2 and 3 (Figures 13b eration. A mesh with a smaller size is not chosen because and 13c) seem safe, where the red contoured area is rela- it requires a longer computing time. Although a mesh with tively small. However, the stress exceeds the endurance a larger size tends to produce values far below the criteria limit, where based on calculations, the corresponding area or away from the actual conditions, the mesh quality test will fail in specific cycles. Failure typically begins with a shows that the inspection area has a good aspect ratio and fatigue crack. Although very small in size, such a crack is skewness. The aspect ratio (Figure 11a) is the most exten- very dangerous because it can propagate very rapidly. sive with the smallest mesh. The aspect ratio approaching Figure 14 shows the safety factor of each geometry. the value of 1 is better because the governing equation be- Please note that ships are structures designed with a high comes more superficial and makes it easier for solvers to level of security. Therefore, to ensure their ability to be qual- find the final result. The data are expected if the skewness is ified to withstand repeated loading, the fatigue safety factor in the range of −2–2. As shown in Figure 11b, the skewness is calculated based on a design life of 10 cycles. Areas with magnitude is still in the field of 0.059686–0.99432, which a fatigue safety factor of 1 are expected to survive when indicates that the mesh has a good quality. undergoing 1 billion cycles. Geometry 1 (Figure 14a) has a Assessment of ship structure under fatigue loading | 173 uniform minimum distribution of safety factors with values 3.3328 and 3.4809 mm, respectively. Both these forms un- below 1, i.e., the areas with red contours are predicted to dergo the most significant deformation among all condi- fail before they can undergo 1 billion cycles. As shown in tions. This indicates that both structures are deformable, Figure 14d, Geometry 4 has the structure with the lowest and the different geometries are rigid. However, the defor- level of security, whereas Geometry 5 has the safest form of mations have no significant effect on the phenomenon of the system. fatigue failure. When compared with Figure 13, it can be Total deformation (Figure 15) presents the deformation observed that the contours of the total deformation are distribution in the structure due to the loading process. different from the contours of the fatigue life. Areas that Geometries 2 and 3 (Figures 15b and 15c) are deformed by experience maximum deformation do not necessarily have a. b. c. d. e. Figure 12. Alternating Stress Results: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Figure 12: Alternating stress results: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; Joindt . [1 Geomet 2]; c.r yG4: eo Bottom-stiffened metry 3: Stoopl anel Join [28]; t [12 e.]; Geomet d. Geo rym 5: eSide-stiffened try 4: Bottop m anel -Sti[29] ffened Panel [27]; e. Geometry 5: Side- Stiffened Panel [28] 174 | A. Fajri et al. a. b. c. d. e. Figure 13. Fatigue Life Results: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Joint Figure 13: Fatigue life results: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; c. Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 5: Side-Stiffened [12]; d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] Panel [28] Assessment of ship structure under fatigue loading | 175 a. b. c. d. e. Figure 14. Safety Factor Results: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Joint Figure 14: Safety factor results: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] [12]; c. Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 5: Side-Stiffened Panel [28] 176 | A. Fajri et al. a. b. c. d. e. Figure 15. Total Deformation Results: a. Geometry 1: Hatch Coaming Model [16]; b. Geometry 2: Perpendicular Figure 15: Total deformation results: a. Geometry 1: Hatch coaming model [16]; b. Geometry 2: Perpendicular joint [12]; c. Geometry 3: Stool joint [12]; d. Geometry 4: Bottom-stiffened panel [28]; e. Geometry 5: Side-stiffened panel [29] Joint [12]; c. Geometry 3: Stool Joint [12]; d. Geometry 4: Bottom-Stiffened Panel [27]; e. Geometry 5: Side- Stiffened Panel [28] Assessment of ship structure under fatigue loading | 177 Geometry 1 Geometry 2 Geometry 3 Geometry 4 Geometry 5 8 8 8 0,0 2,0x10 4,0x10 6,0x10 Fatigue Life (Cycle) Figure 16. Relationship Between Alternating Stress and Fatigue Life of Each Geometry Figure 16: Relationship between alternating stress and fatigue life of each geometry Figure 17. Fatigue Results: Maximum Deformation, Minimum Safety Factor, Maximum Damage, and Minimum Figure 17: Fatigue results: Maximum deformation, minimum safety factor, maximum damage, and minimum life Life a short fatigue life. The deformation is still in the elastic very short fatigue life, whereas Geometry 5 has good fatigue area, which is a condition that allows the structure to re- resistance. In Figure 17a, Geometries 4 and 1 show slight turn to its original shape after the load is removed. This is deformation, whereas Geometries 2 and 3 undergo the most supported by the evidence that the stress (Figure 12) is still extensive deformation. Figure 17b shows that all geometries below the material yield point. are still in critical areas, where the minimum safety factor Figure 16 compares the performance of all geometries is below 1. However, Geometry 5 is relatively safe because under fatigue loading. Each geometry presents a unique it has the highest safety factor. Figure 17c presents that a response. Geometry 4 has the weakest characteristic or a large damage occurrence implies a short fatigue life. Alternating Stress (MPa) 178 | A. Fajri et al. 7.2 Effect of material used 950X (Figure 18a) material has a minimum fatigue life of 2.2571e5 cycles, which is longer than those of the SAE 316L Geometry 2 is adopted as a sample to investigate the ef- and 304L materials. The used medium-carbon steel (Fig- fect of the type of material used on the fatigue force on the ure 18b) has the highest fatigue resistance of all types of structure. In addition to material variations, other variables considered materials. However, it should be noted that cor- that affect this property, such as the magnitude of loading, rosion can shorten the age of fatigue because it can trigger surface smoothness, stress corrosion factor, and loading the appearance of an initial crack. Of the four types of mate- scheme, are considered constant. SAE 316L and 304L ma- rials, only the carbon medium has no corrosion resistance terials are marine-grade steels, i.e., they meet standards properties. The medium-carbon and SAE 316L materials for forming marine structures. The HSLA 950X material is a have better stress distributions than HSLA 950X and SAE steel that is not yet commonly used in the marine structure 304L. industry. Despite its high toughness and corrosion resis- Based on the contours of the safety factor (Figure 19), tance, the HSLA is considered less effective owing to its rea- it is determined that the SAE 316L material has the low- sonably high production cost. Although a medium-carbon est security, followed by SAE 304L. The HSLA 950X and steel has good strength, it is not recommended for marine medium-carbon materials have a higher safety factor than structure applications. It can be observed that the HSLA the specified criteria limit. Thus, none of the four materials a. b. c. d. Figure 18. Fatigue Life: a. HSLA 950X; b. Medium-Carbon; c. SAE 316L; d. SAE 304L Figure 18: Fatigue life: a. HSLA 950X; b. Medium-carbon; c. SAE 316L; d. SAE 304L Assessment of ship structure under fatigue loading | 179 a. b. c. d. Figure 19: Safety factor: a. HSLA 950X; b. Medium-carbon; c. SAE 316L; d. SAE 304L Figure 19. Safety Factor: a. HSLA 950X; b. Medium-Carbon; c. SAE 316L; d. SAE 304L is entirely safe and will potentially fail in a given cycle. Fig- HSLA 950X ures 20 and 21 show that the sequence of materials with the MEDIUM-CARBON SAE 316L 250 highest to the lowest fatigue resistance is medium-carbon SAE 304L steel, HSLA 950X, SAE 304L, and SAE 316L. Other factors that must be considered are the working environment con- ditions. The medium-carbon material will be brittle at a low temperature. Under a relatively small impact, the load alone can destroy the structure in these conditions. HSLA 950X, SAE 316L, and 304L are laboratory-tested and proven to withstand low temperatures. More research on this phe- nomenon needs to be conducted in the future. 4 5 6 7 8 9 10 11 12 13 14 10 10 10 10 10 10 10 10 10 10 10 Fatigue Life (Cycle) Figure 20. Relationship Between Alternating Stress and Fatigue Life for Each Material Used Figure 20: Relationship between alternating stress and fatigue life for each material used Alternating Stress (MPa) 180 | A. Fajri et al. Figure 21. Fatigue Results: Maximum Deformation, Minimum Safety Factor, Maximum Damage, and Minimum Figure 21: Fatigue results: Maximum deformation, minimum safety factor, maximum damage, and minimum life for each material used Life for Each Material Used a. b. c. d. Fatigue Life (Cycle) Maximum Alternating Stress (MPa) 650,21 7x10 6,5984E6 6x10 5x10 4x10 3x10 2x10 289,76 1x10 8,7435 200 216,74 -1x10 Fully Reversed Zero-Based Ratio -2 Scale Factor 1 Load Type Figure 22: Alternating stress results: a. Fully reversed; b. Zero-based; c. Ratio; d. Relevance with fatigue life Figure 22. Alternating Stress Results: a. Fully Reversed; b. Zero-Based; c. Ratio; d. Relevance with Fatigue Life Fatigue Life (Cycle) Maximum Alternating Stress (MPa) Assessment of ship structure under fatigue loading | 181 7.3 Effect of load type safety factor values produce the safest conditions among all types of loading. Three types of loading are compared (Figure 22). At the same amount of load, varying stresses will be produced if the type of loading is different. As can be observed, the load- 7.4 Effect of mean stress correction theory ing ratio type only produces an alternating stress of 216.74 MPa. Similarly, when the exposure is changed to fully re- The data presented in the S–N curves were obtained from versed, the stress appears to be 289.76 MPa. When the geom- the results of the fatigue tests conducted in the laboratory. etry is subjected to the highest loading ratio, the generated Fatigue tests are commonly conducted on uniaxial testing stress increases several folds to 650.21 MPa. This loading machines with a fully reversed loading scheme. These data ratio type occurs when the bending and tensile forces have cannot be used as the basis for analysing fatigue phenom- different values. There are some materials whose tensile ena in structures that undergo non-fully reversed loading strengths are higher than the compressive strength and vice because the structural responses present different charac- versa. Thus, a material can be safe under a zero-based or teristics relative to the data shown in S–N curves. Therefore, fully reversed loading type, whereas it is fatal under the the stress that emerges under non-fully changed conditions loading ratio. Therefore, the selection of materials needs to must be corrected using a mean stress theory. Mean stress consider the type of loading that the structure may experi- theories have different effects. For example, in this study, ence. The fatigue life material will certainly be affected by the loading scheme is changed to zero-based loading to the type of loading. show differences. Figure 24 shows the maximum stress of The loading type does not affect the geometry defor- each mean stress theory used. Under the same conditions, mation (see Figure 23). The fully reversed, zero-based, and the Goodman, Soderberg, Gerber, and ASME elliptic theo- ratio type loading produce the same total deformation of ries correct the maximum stress to 206.6 MPa, 216.74 MPa, 3.3328 mm. The loading ratio of 2 with a scale factor of 1 does 159.08 MPa, and 153.57 MPa, respectively. First, it is notice- the most damage. A large damage implies a short fatigue able that the Goodman and Soderberg theories produce life. When a geometry is subject to zero-based loading, the almost the same stress values, whereas the Gerber theory Figure 23. Fatigue Results: Maximum Deformation, Minimum Safety Factor, Maximum Damage, and Minimum Figure 23: Fatigue results: Maximum deformation, minimum safety factor, maximum damage, and minimum life for each loading type Life for Each Loading Type 182 | A. Fajri et al. a. b. c. d. Figure 24: Alternating stress using different mean stress correction theories: a. Goodman; b. Soderberg; c. Gerber; d. ASME elliptic values are close to the results of the correction by the ASME than the Gerber and ASME elliptic theories. When used Figure 24. Alternating Stress using Different Mean Stress Correction Theories: a. Goodman; b. Soderberg; c. elliptic theory. Based on literature studies, the Goodman to predict the age of fatigue, the Goodman and Soderberg Gerber; d. ASME Elliptic and Soderberg theories are very suitable for analysing brit- theories result in a minor period of fatigue. tle materials, whereas the stress on ductile materials can The mean stress correction theory used does not af- be suitably corrected using the Gerber and ASME elliptic fect the deformation value in the geometry (Figure 27). The theories. Soderberg theory produces the most damage and a very The stress distribution and the safety factor distribu- short fatigue life. The ASME elliptic theory causes a slight tion (Figure 25) for each criterion have the same contours damage and leads to excellent fatigue life. Specifically, dif- but different values when reviewed. Figure 26 shows that ferent means stress theories introduce different character- the Goodman and Soderberg theories are very conservative, istics into a geometric structure. Each theory has its advan- with which the limit of failure is set far below the results of tages and disadvantages, and each depends on the material the lab experiments. The Gerber and ASME elliptic theories used. set higher failure limits than the other methods, approach- ing the data shown on the S–N curves. The Goodman and Soderberg theories result in smaller safety factor values Assessment of ship structure under fatigue loading | 183 a. b. c. d. Figure 25: Safety factor using different mean stress correction theories: a. Goodman; b. Soderberg; c. Gerber; d. ASME elliptic Figure 25. Safety Factor using Different Mean Stress Correction Theories: a. Goodman; b. Soderberg; c. Gerber; d. ASME Elliptic Goodman Soderberg Gerber ASME Elliptic 8 8 8 8 9 0,0 2,0x10 4,0x10 6,0x10 8,0x10 1,0x10 Fatigue Life (Cycle) Figure 26. Relationship Between Alternating Stress and Fatigue Life using Different Mean Stress Correction Figure 26: Relationship between alternating stress and fatigue life using different mean stress correction theories Theories Alternating Stress (MPa) 184 | A. Fajri et al. Figure 27. Fatigue Results: Maximum Deformation, Minimum Safety Factor, Maximum Damage, and Minimum Figure 27: Fatigue results: Maximum deformation, minimum safety factor, maximum damage, and minimum life for each mean stress theory Life for Each Mean Stress Theory Used used shorter fatigue life, they have good corrosion resistance. 8 Conclusion These materials are designed according to marine-grade steel standards. In this paper, the research results on the effects of geomet- Further research on the fatigue behaviour in low-cycle ric shapes, material types, loading types, and mean stress fatigue needs to be conducted considering other factors correction theories were presented. The research methods such as corrosion resistance and environmental tempera- were validated by comparison with previous research. A ture. Compared to fully reversed loading, zero-based load- difference in the results of <5% indicates that the technique ing produces relatively low stresses; therefore, a structure used in this study is valid and can be accounted. Differ- will have a safe fatigue life in this condition. The same nom- ences in the geometric shapes and locations of the struc- inal weighting ratio type leads to higher stresses, resulting ture affect the fatigue behaviour. The above study results in short-life fatigue. The mean stress theory used does not prove that the bottom-stiffened panel has the highest fa- have a significant difference when the loading type with- tigue risk, whereas the side-stiffened panel has the lowest. stood by the structure is the same as in the lab experiment The medium-carbon steel material has a high resistance results (fully reversed). The Goodman theory corrects the to high-cycle fatigue, which is the loading of fatigue with stress far below the safe limit when the loading scheme is an intensity below the yield strength of the material. Fa- changed to zero-based and ratio. The Goodman and Gerber tigue characteristics against low-cycle fatigue need to be theories are relatively more conservative than the Soder- studied further. However, this material cannot be used for berg and ASME elliptic theories. ship structure applications because of its low corrosion re- sistance. Corrosion can decrease strength because this will Acknowledgement: The authors are grateful to the Indone- trigger the onset of a fatigue crack. The medium-carbon sia Endowment Fund for Education (LPDP), Ministry of steel is also brittle; therefore, when a rupture occurs, the Finance, Republic of Indonesia for the financial support propagation is expected to have a high speed. Although provided for this research. the HSLA, SAE 316L, and 304L materials have relatively Assessment of ship structure under fatigue loading | 185 Author contributions: All authors have accepted responsi- [17] Bishara M, Horst P, Madhusoodanan H, Brod M, Daum B, Rolfes R. A structural design concept for a multi-shell blended wing body bility for the entire content of this manuscript and approved with laminar flow control. Energies. 2018;11(2):1–21. its submission. [18] Hansen PF, Winterstein SR. Fatigue damage in the side shells of ships. Mar Structures. 1995;8(6):631–55. Conflict of interest: The authors state no conflict of inter- [19] Boardman B. Fatigue resistance of steels. In: ASM Handbook est. Volume 1: Properties and Selection: Irons, Steels, and High- Performance Alloys. ASM International; 1987. p. 77–81. [20] Gaidai O, Storhaug G, Naess A, Ye R, Cheng Y, Xu X. Eflcient fatigue assessment of ship structural details. Ships Offshore Struct. 2020;15(5):503–10. References [21] Ślęzak T. Fatigue examination of HSLA steel with yield strength of 960 MPa and its welded joints under strain mode. Metals (Basel). [1] Li Z, Ringsberg JW, Storhaug G. Time-domain fatigue assessment 2020;10(2):1–14. of ship side-shell structures. Int J Fatigue. 2013;55:276–90. [22] Vaara J, Kunnari A, Frondelius T. Literature review of fatigue [2] Xiu R, Spiryagin M, Wu Q, Yang S, Liu Y. Fatigue life assess- assessment methods in residual stressed state. Eng Fail Anal. ment methods for railway vehicle bogie frames. Eng Fail Anal. 2020;110:104379. 2020;116:104725. [23] Venkatasudhahar M, Dilipraja N, Mathiyalagan P, Subba SV, [3] Fajri A, Prabowo AR, Muhayat N, Smaradhana DF, Bahatmaka A. Sathyaseelan P, Logesh K. Finite element analysis of fatigue life Fatigue analysis of engineering structures: State of development of spot welded joint and the influence of sheet thickness and and achievement. Procedia Struct Integr. 2021;33:19–26. spot diameter. Int J Mech Mechatron Eng. 2014;14(06):76–82. [4] Ringsberg JW, Li Z, Tesanovic A, Knifsund C. Linear and nonlin- [24] Pastorcic D, Vukelic G, Bozic Z. Coil spring failure and fatigue ear FE analyses of a container vessel in harsh sea state. Ships analysis. Eng Fail Anal. 2019;99:310–8. Offshore Struct. 2014;10(1):20–30. [25] Raymond L. Browell PE, Hancq A. Predicting fatigue life with AN- [5] Tasdemir A, Nohut S. Fatigue analysis of ship structures with SYS workbench: How to design products that meet their intended hinged deck design by finite element method. A case study: fa- design life requirements. 2006 International ANSYS Conference. tigue analysis of the primary supporting members of 4900 PCTC. 2006 May 2-4. Mar Structures. 2012;25(1):1–12. [26] Lotsberg I, Sigurdsson G. Hot spot stress S-N curve for fa- [6] Prabowo AR, Bae DM, Sohn JM, Zakki AF, Cao B, Cho JH. Effects of tigue analysis of plated structures. J Offshore Mech Arctic Eng. the rebounding of a striking ship on structural crashworthiness 2006;128(4):330–6. during ship-ship collision. Thin-Walled Struct. 2017;115:225–39. [27] Glen IF, Dinovitzer A, Paterson RB, Luznik L, Bayley C. Fatigue [7] Prabowo AR, Putranto T, Sohn JM. Simulation of the behavior of Resistant Detail Design Guide For Ship Structures (No. SR-1386). a ship hull under grounding: effect of applied element size on Ship Structure Committee; 1999. structural crashworthiness. J Mar Sci Eng. 2019;7(8):270. [28] He W, Liu J, Xie D. Numerical study on fatigue crack growth at a [8] Vukelić G, Vizentin G. Common Case Studies of Marine Structural web-stiffener of ship structural details by an objected-oriented Failures. Failure Analysis and Prevention. InTech; 2017. pp. 135– approach in conjunction with ABAQUS. Mar Struct. 2014;35:45– [9] France EJ. The Alexander L. Kielland Disaster Revisited: A Review [29] Okawa T, Sumi Y, Mohri M. Simulation-based fatigue crack man- by an Experienced Welding Engineer of the Catastrophic North agement of ship structural details applied to longitudinal and Sea Platform Collapse. J Fail Anal Prev. 2019;19(4):875–81. transverse connections. Mar Struct. 2007;19(4):217–40. [10] Sedmak A. Computational fracture mechanics: an overview from [30] Dindinger P. HSLA 345X (SAE950X) Fatigue Test Report. F.D.E early efforts to recent achievements. Fatigue Fract Eng Mater Committee. Ontario, Canada; 2014. Struct. 2018;41(12):2438–74. [31] Li C, Dai W, Duan F, Zhang Y, He D. Fatigue life estimation of [11] Schütz W. A history of fatigue. Eng Fract Mech. 1996;54(2):263– medium-carbon steel with different surface roughness. Appl Sci (Basel). 2017;7(4):1–11. [12] Osawa N, Hashimoto K, Sawamura J, Nakai T, Suzuki S. Study on [32] Jacquelin B. FHAP. SAE 316L Fatigue Test Report. Ontario, Canada; shell-solid coupling FE analysis for fatigue assessment of ship structure. Mar Structures. 2007;20(3):143–63. [33] Nachtigall AJ. SAE 304L Fatigue Test Report. Ontario, Canada: [13] Li Z, Ringsberg JW, Storhaug G. Time-domain fatigue assessment F.D.E. Committee. Ontario, Canada; 2012. of ship side-shell structures. Int J Fatigue. 2013;55:276–90. [34] Köksal NS, Kayapunar A, Çevik M. Fatigue analysis of a notched [14] Alshoaibi AM, Fageehi YA. 2D finite element simulation of mixed cantilever beam using ANSYS workbench. Proceedings of the mode fatigue crack propagation for CTS specimen. Integr Med Fourth International Conference on Mathematical and Compu- Res. 2020;9(4):7850–61. tational Applications. 2013 Jun 11-13; Manisa, Turkey. 2013. p. [15] Božić Ž, Schmauder S, Wolf H. The effect of residual stresses on 111–8. fatigue crack propagation in welded stiffened panels. Eng Fail [35] Fajri A, Prabowo AR, Surojo E, Imaduddin F, Sohn JM, Adiputra Anal. 2018;84:346–57. R. Validation and Verification of Fatigue Assessment using FE [16] Zhang Y, Huang X, Wang F. Fatigue crack propagation prediction Analysis: A Study Case on the Notched Cantilever Beam. Procedia for marine structures based on a spectral method. Ocean Eng. Struct Integr. 2021;33:11–8. 2018;163:706–17. [36] Prabowo AR, Ridwan R, Muhayat N, Putranto T, Sohn JM. Tensile analysis and assessment of carbon and alloy steels using fe 186 | A. Fajri et al. approach as an idealization of material fractures under collision [39] Prabowo AR, Sohn JM, Putranto T. Crashworthiness perfor- and grounding. Curved Layer Struct. 2020;7(1):188–98. mance of stiffened bottom tank structure subjected to impact [37] Prabowo AR, Sohn JM. Nonlinear dynamic behaviors of outer loading conditions: ship-rock interaction. Curved Layer Struct. shell and upper deck structures subjected to impact loading in 2019;6(1):245–58. maritime environment. Curved Layer Struct. 2019;6(1):146–60. [38] Prabowo AR, Laksono FB, Sohn JM. Investigation of structural performance subjected to impact loading using finite element approach: case of ship-container collision. Curved Layer Struct. 2020;7(1):17–28.

Journal

Curved and Layered Structures – de Gruyter

Published: Jan 1, 2022

Keywords: Finite element method; fatigue phenomena; ship structure

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