Incorporating mesh-insensitive structural stress into the fatigue assessment procedure of common structural rules for bulk carriers

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1 csnak, 2015 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 pissn: , eissn: Incorporating mesh-insensitive structural stress into the atigue assessment procedure o common structural rules or bulk carriers Seong-Min Kim 1,2 and Myung-Hyun Kim 2 1 Industrial Application R&D Institute, Daewoo Shipbuilding & Marine Engineering Co., LTD., Geoje-si, Gyeongnam, Korea 2 Department o Naval Architecture and Ocean Engineering, Pusan National University, Busan, Korea ABSTRACT: This study introduces a atigue assessment procedure using mesh-insensitive structural stress method based on the Common Structural Rules or Bulk Carriers by considering important actors, such as mean stress and thickness eects. The atigue assessment result o mesh-insensitive structural stress method have been compared with CSR procedure based on equivalent notch stress at major hot spot points in the area near the ballast hold or a 180 K bulk carrier. The possibility o implementing mesh-insensitive structural stress method in the atigue assessment procedure or ship structures is discussed. KEY WORD: Mesh-insensitive structural stress; Common structural rules; Fatigue strength evaluation; Bulk carriers; Hot spot stress. INTRODUCTION It is well known that most atigue damages in bulk carriers occur mostly in the area near ballast holds because its structural members are subjected to high internal pressure due to ballast water. According to the International Association o Classiication Societies (IACS) damage record, atigue damages to members in the ballast hold o bulk carriers is 99.8% o the total damage cases or primary members. Thereore, the damages to cargo holds in bulk carriers other than ballast holds are less than 0.2%. Approximately 72% o atigue damages occurred at the connections between the inner bottom platings and the plates o lower stools or hopper tanks (IACS, 2010a). It is evident that atigue problem in bulk carriers is an on-going issue and a highly accurate atigue assessment method is needed to ensure saety o ship structures and prevent pollution as well as liesaver. Hot spot stress approach is commonly used or atigue lie assessment o ship structures (Lee et al., 2010; Park et al., 2011). Fatigue assessment procedure in Common Structural Rules (CSR) or Bulk Carriers also incorporates the equivalent notch stress range obtained by multiplying the equivalent hot spot stress range by a atigue notch actor. Finite element analysis using very ine mesh with a typical element size o the plate thickness is commonly employed or atigue assessment o the ballast hold, such as at the lower stool and the bilge hopper connections. The calculation o hot spot stress in the vicinity o the weld toe involves many diiculties and uncertainties. In addition, the design rule procedures sometimes provide inconsistent results Corresponding author: Myung-Hyun Kim, kimm@pusan.ac.kr This is an Open-Access article distributed under the terms o the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

2 2 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 depending on the calculation method or the hot spot stress with respect to stress extrapolation and element selection. Recently, a mesh-size insensitive structural stress deinition that provides a stress state at the weld toe using a relatively large mesh size was proposed (Dong, 2001). The structural stress deinition is based on elementary structural mechanics theory and provides an eective measure or the stress state in ront o the weld toe. The structural stress is expressed in the orm o membrane and bending stress components that satisy equilibrium conditions based on inite element analysis. In this method, balanced nodal orces are used to estimate the local stresses in the vicinity o the considered weld toe. The results, thereore, have less deviation than the stress obtained rom shape unctions inside the elements (Dong and Hong, 2003). The structural stress approach or atigue assessments has been widely investigated in various industrial ields. In the ield o shipbuilding, a comparative study has been perormed employing hot spot stress and structural stress approach to evaluate the atigue strength at the shell on the longitudinal side o a container vessel (Kim et al., 2009). While many studies on the application o structural stress approach or atigue assessment o structural details have been carried out (Dong, 2004; Healy, 2004; Hong and Dong, 2004; Dong, 2005), there is no attempt to employ the approach or atigue assessment o bulk carriers. In this study, a atigue assessment procedure that incorporates mesh-insensitive structural stress method based on CSR or Bulk Carriers is suggested and compared with the atigue evaluation result based on hot spot stress method commonly used in CSR. SUMMARY OF FATIGUE ASSESSMENT PROCEDURE IN CSR Fatigue assessment procedure in CSR or Bulk Carriers (IACS, 2010b) is adopted based on the equivalent notch stress range obtained by multiplying the equivalent hot spot stress range by a atigue notch actor. Extrapolation-based hot spot stress is employed to obtain stresses at geometric discontinuities using the mesh size that corresponds to the plate thickness as shown in Fig. 1. Fig. 1 Deinition o hot spot stress at an intersection o two plates. From the calculated hot spot stress range, σw, the equivalent notch stress range ( σ equiv ) can be calculated using Eq. (1). σ = σ (1) equiv mean W where mean is the correction actor or mean stress. The equivalent notch stress range is calculated with Eq. (2). σ = K σ (2) eq, j equiv where K indicates the atigue notch actor as deined in Table 1.

3 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 3 Table 1 Fatigue notch actor K. Subject Without weld grinding With weld grinding Butt welded joint Fillet welded joint Non-welded locations The equivalent notch stress range is corrected with the ollowing ormula. σ = σ (3) E, j coat material thick eq where: coat : Correction actor or corrosive environment, = 1.05 or water ballast tanks and uel oil tank = 1.03 or dry bulk cargo holds and void space material : Correction actor or the material, 1200 = ReH thick : Correction actor or plate thickness, which is 1.0 or hatch corners, lat bar or bulb stieners, or : 0.25 t thick = or t 22 mm 22 = 1.0 or t < 22 mm thick R eh : Minimum yield stress, in 2 N mm, o material, Possible atigue cracks considered in this study are those occurring between the insert plates o lower stool and the inner bottom connections. They should be accounted or in the thickness eect i the plate thickness is more than 22 mm. Other correction actors, coat = 1.05 or ballast hold and ReH = 235 MPa or mild steel, are assumed or equivalent notch stress calculation. The cumulative probability density unction o the long-term distribution o combined notch stress ranges is taken as a twoparameter Weibull distribution: x x F( x) = 1 exp ( ln N R ) σ E (4) where: x : Weibull shape parameter, equivalent to N : Number o cycles, equivalent to 10 R The elementary atigue damage or each loading condition is calculated using the ollowing ormula: αnl Dσ 4 3 ξ 7 D = Γ + 1, v + v γ + 1, v K ξ ξ 4 E 4 ξ R ( ln N ) (5) where: K : S-N curve parameter, equivalent to

4 4 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 α : Coeicient depending on loading condition N L : Total number o cycles or the designated ship s lie, N L 0.85TL = 4log L T L : Design lie, in seconds, corresponding to 25 years o ship s lie, equivalent to Γ : Type 1 incomplete gamma unction γ : Type 2 incomplete gamma unction v = ln N σ E ξ R A FATIGUE LIFE ASSESSMENT PROCEDURE INCORPORATING MESH-INSENSITIVE STRUCTURAL STRESS Mesh-insensitive structural stress The stress gradient, which occurs at the weld toe through the plate thickness, is shown in Fig. 2(a). This stress gradient is categorized into a linear component generated due to structural discontinuity and a non-linear notch component generated by the notch eect at the weld beads, as illustrated in Fig. 2(b). Here, the ormer, which is explained by a mechanically equilibrium condition or the imposed load, can be deined as a structural stress ( σ s ). The deined structural stress can be expressed as a sum o the membrane stress ( σ m ) and bending stress ( σ b ). The non-linear notch component is obtained by considering the notch eect or the imposed load mode and is inally used to estimate the atigue lie. ESS SS Structural stress (SS) = + + σ m σ b Sel-equilibrating stress (Notch eect) Equivalent Structural stress (ESS) (a) Stress at weld toe. Fig. 2 Deinition o the structural stress. (b) Stress decomposition. Using the nodal orces ( Fy 1, F y2), the orce per unit length, that is line orces ( y1, y2) which are distributed along the weld line deined between the nodes can be calculated. This means that, or a shell element with our node points as shown in Fig. 3, the line orce can be calculated using Eq. (8), which should satisy Eq. (6), which is an equilibrium condition between F F and the line orces ( 1, 2). At this time, the line moments ( mx 1, mx2) can be calculated using M, M obtained in Eq. (7). the nodal orces ( 1, 2) the same method as stated in Eq. (9) using the balanced nodal moments ( ) 1 0 ( ) x1 x2 F x dx =0 (6) yi y

5 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~ yi i 0 y ( ) F x x xdx =0 (7) 2 2 y1 ( 2 Fy 1 Fy2), y2 ( 2Fy2 Fy 1) l l (8) 2 2 m x1 ( 2 Mx 1 Mx2), mx2 ( 2Mx2 Mx 1) l l (9) where 1 = element size along the weld F y1 Element y F y2 l y2 M x1 Element y M x2 y1 1 x Weld line 2 m x1 l m x2 1 x Weld line 2 Fig. 3 Local line orce and the line moment rom nodal orces and moments or a our-node shell element. A membrane stress and a bending stress are calculated with Eq. (10) using the line orce and the line moment obtained previously. Thereater, the structural stress, which is expressed as a sum o membrane and bending stresses can be calculated. y 6mx s = sm + sb = + (10) 2 t t where σ s is the structural stress and is the line orce towards y direction, and y The equivalent structural stress ( S eq ) σ m, σ b are the membrane and bending stresses, respectively. t is the plate thickness, m x is the line moment towards x-axis. which is estimated by considering the thickness eect and loading mode o the previously obtained structural stress, can be deined with Equations (2-15) (Battelle, 2004). S = eq t s s 2 m 1 2m m ( ) I r (11) where bending ratio ( ) 2m σ s is the stress range obtained as a structural stress and t r, which indicates corrections or various loading modes and can be divided into a load- and displacementcontrolled conditions. In this study, the loading mode eects, semi-elliptical crack, respectively. 2 m is the term or the thickness. I( r ) is the unction o I( r ) 1 m is employed as in Eqs. (12) and (13) or edge crack and ( ) m I r = r r r r r (12) ( ) m I r = r r r r r r (13) Since the thickness correction, loading mode eects and geometrical discontinuities are already included in Eq. (11), any type o weld joints or loading modes can be evaluated consistently with the equivalent structural stress. Based on Eq. (11), over

6 6 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~ results o existing atigue tests or both various weld joints and loading modes are itted in Fig. 4, and a master S-N curve was determined by Dong et al. (2002). Based on Fig. 4, the required parameters or S-N relationship can be obtained using Eq. (14) and Eq. (15). Correction actor and standard deviation o the itted curve in Fig 4 is and respectively. Here, mean minus two standard deviation curve is selected or design master S-N curve. For the mean master 0S-N curve, C = , m ' = 3.08 log N = log S (14) eq For the design master S-N curve, C = , m ' = 3.08 log N = log S (15) eq Fig. 4 The master S-N curve by using equivalent structural stress parameter. Mesh-insensitive structural stress procedure based on CSR or bulk carriers A atigue assessment o bulk carriers that incorporates mesh-insensitive structural stress approach based on CSR or Bulk Carriers procedure can be summarized as shown in Fig. 5. Fig. 5 Comparison o procedure or equivalent notch stress range and equivalent structural stress range.

7 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 7 The equivalent notch stress range and equivalent structural stress range are used as local stresses to determine the atigue lie o bulk carriers using CSR atigue assessment procedure and the structural stress approach, respectively. Stress concentration due to geometric discontinuities in the vicinity o weld toe is included in the hot spot stress range and structural stress range. The mean stress eect, atigue notch actor, coating eect, material strength eect and thickness eect are taken into account explicitly in CSR procedure or bulk carriers. The structural stress approach is also able to consider those eects, except or the coating eect due to corrosive environment. The equivalent structural stress approach is has already been investigated or the material strength eect. The terms ( 1 R) 1 m represent the mean stress eect, ( ) 1 m t 2 m 2m I r represent the atigue notch eect and represent the thickness eect. Only the coating eect is considered with the same coeicient o 1.05 or corrosive environment. This means that all eects aecting the atigue lie o bulk carriers in CSR, except or corrosion, are explicitly considered in the structural stress procedure. The dierences between the two procedures are seen in the S-N curves, local stresses due to geometric discontinuities and coeicients or several eects. The eect o any mean stress that inluences the atigue strengths can be evaluated by summing any residual stresses and the structural mean stress. The correction actor or mean stress in CSR atigue procedure can be calculated using Eq. (16). σ = σ (16) equiv, j mean, j w, j Whereas, i structural stress is used or atigue lie assessment, the mean stress eect can be calculated using Eq. (17) or positive R ratio shown in Fig. 6(a) or Eq. (18) or negative R ratio shown in Fig. 6(b) (Battelle, 2004). S = s S = s s 1 1 m ( 1 ) m ( ) R I r t ( 1 ) m ( ) s s s 2 1 m R I r t 2 m 2m 2 m 2m (17) (18) (a) σ min 0. (b) σ min < 0. Fig. 6 Stress range and stress ratio deinition in cyclic loading. The correction actor or plate thickness, thick, is 1.0 or hatch corners, lat bar or bulb stieners, Otherwise it is; thick t = or t 22 mm = thick 1.0 or t < 22 mm where t is the net thickness in mm

8 8 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 The thickness eect, which is an eect o atigue lie reduction by plate thickness, was introduced by Gurney (1981) and a quantitative assessment method was proposed. Since then, the thickness exponent proposed by Gurney is generally used or plate thickness eect on atigue strength estimation. International Institute o Welding (Hobbacher, 2009) recommended that the use o thickness exponent should depend on the joint type, such as butt, cruciorm, T-joint and tubular joints, based on the atigue results rom various researches (Yagi et al. 1991; Orjaster, 1995; Gurney, 1995). ( 2 m) 2m The thickness eect in the structural stress method is implemented through t in Eqs. (17) and (18). The thickness correction or equivalent structural stress was validated (Battelle, 2004) using the atigue test results or various joint types and thicknesses (Yagi et al., 1991). The thickness exponent employed in CSR or Bulk carriers is not able to consider the thickness eect i the reerence thickness is less than 22 mm, as shown in Fig. 7. Also, Fig. 7 shows that atigue lie reduces linearly with plate thickness using the thickness exponent method depending on the thickness exponent, while atigue lie reduces with consideration o thickness ( 2 m) 2m eect or plates thicker than 1 mm using the term t in the structural stress method. However, Gurney (1995) has mentioned that the plate thickness below 22 mm may be considered. Fig. 7 Example o thickness eect between hot spot stress and structural stress. FATIGUE ASSESSMENT OF 180 K BULK Target vessel In this study, the inite element model or three cargo holds o 180 K bulk carrier was used or the atigue assessment as shown in Fig. 8. The principal dimension o the target vessel is listed in Table 2. Fig. 8 The FE model o the target vessel.

9 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 9 Table 2 Principal dimension o the target vessel. L.O.A. L.B.P. Breadth (moulded) Depth (moulded) Design drat (moulded) Abt m m m m m The typical three locations or possible atigue crack points were assumed in the vicinity o the intersection o lower stool, inner bottom plating, bilge hopper plate and inner bottom plating as listed below: IB-LS (sloping): the connection between inner bottom plating and sloping plate o lower stool IB-LS (vertical): the connection between inner bottom plating and vertical plate o lower stool IB-BH (sloping): the connection between inner bottom plating and sloping plate o bilge hopper Fig. 9 Three hot spot points on 180 K bulk carrier. These three locations are considered as atigue vulnerable locations in bulk carriers. The connection between the inner bottom plating and the lower stool is normally stiened by a thick insert plate as illustrated in Fig. 10. Fig. 10 Plate thickness in the vicinity o insert plate at LS-IB connection (sloping).

10 10 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 Insert plates are widely used or lower stool and inner bottom connections to enhance atigue strength. Speciic net thicknesses o insert plates used in this study are listed in Table 3. Table 3 Plate thickness in the vicinity o insert plate. Location LS/IB plating Insert plate LS-IB (sloping), LS mm mm LS-IB (sloping), IB mm mm LS-IB (vertical), LS mm mm LS-IB (vertical), IB mm mm The hot spot locations and the corresponding atigue cracks or each model considered in this study are illustrated in Fig. 11. (a) Lower stool-inner bottom connection (sloping). (b) Lower stool-inner bottom connection (vertical). (c) Bilge hopper-inner bottom connection (w/o insert plate). Fig. 11 Considered atigue cracks. Fatigue assessment result A total o 32 load cases were subjected to the model with respect to load cases and loading conditions given in Tables 4 and 5. The hot spot stress results o all 32 load cases were given in Tables 6 to 8.

11 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 11 Table 4 Hot spot stress result or IB-LS (sloping) connection. Equivalent design waves H F R P Load case H1 H2 F1 F2 R1 R2 P1 P2 Heading Head sea Follow sea Eect Max. bending moment Max. bending moment Beam (Port : weather side) Max. roll Beam (Port: weather side) Max. external pressure Sag. Hog. Sag. Hog. (+) (-) (+) (-) Table 5 Hot spot stress result or IB-LS (sloping) connection. No. Description Loading Pattern At Mid Fore Load Case (Design Wave) 1 Full Load 2 Alternate H1 F1 R1 P1 H2 F2 R2 P2 H1 F1 R1 P1 H2 F2 R2 P2 3 4 Normal ballast Heavy ballast H1 F1 R1 P1 H2 F2 R2 P2 H1 F1 R1 P1 H2 F2 R2 P2 Table 6 Hot spot stress result or IB-LS (sloping) connection. Load cases Head sea Following sea Roll Max. Pressure Max. H1 H2 F1 F2 R1 R2 P1 P2 Homogeneous Loading conditions Alternate Normal ballast Heavy ballast Table 7 Hot spot stress result or IB-LS (vertical) connection Load cases Head sea Following sea Roll Max. Pressure Max. H1 H2 F1 F2 R1 R2 P1 P2 Homogeneous Loading conditions Alternate Normal ballast Heavy ballast

12 12 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 Table 8 Hot spot stress result or IB-BH (sloping) connection. Load cases Head sea Following sea Roll Max. Pressure Max. H1 H2 F1 F2 R1 R2 P1 P2 Homogeneous Loading conditions Alternate Normal ballast Heavy ballast The results o structural stress or the three hot spot points are given in Tables 9 to 11. From our loading conditions, the structural stress o predominant load cases was calculated or both tension and compression sides to ind the stress ratio or the mean stress eect consideration. Table 9 Structural stress values at IB-LS (sloping) connection. Predominant load case (+) Predominant load case (-) Homo. Alter. N.B. H.B. σ m (MPa) σ b (MPa) σ s (MPa) Bending ratio σ m (MPa) σ b (MPa) σ s (MPa) Bending ratio Stress ratio Δσ s (MPa) Table 10 Structural stress values at IB-LS (vertical) connection. Predominant load case (+) Predominant load case (-) Homo. Alter. N.B. H.B. σ m (MPa) σ b (MPa) σ s (MPa) Bending ratio σ m (MPa) σ b (MPa) σ s (MPa) Bending ratio Stress ratio Δσ s (MPa)

13 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 13 Table 11 Structural stress values at IB-BH (sloping) connection. Predominant load case (+) Predominant load case (-) Homo. Alter. N.B. H.B. σ m (MPa) σ b (MPa) σ s (MPa) Bending ratio σ m (MPa) σ b (MPa) σ s (MPa) Bending ratio Stress ratio Δσ s (MPa) The equivalent notch stress, which was calculated based on the atigue assessment procedure o CSR or Bulk Carriers, and the equivalent structural stress based on the proposed procedure are given in Table 12. In order to calculate both the equivalent notch stress and the equivalent structural stress, the mean stress eect, thickness eect, coating and material strength eects were taken into account. Fatigue damage and atigue lie were calculated rom the equivalent notch stress and equivalent structural stress using the B-curve or CSR or Bulk Carriers and the master S-N curve or the structural stress procedure, respectively. Table 12 Results o equivalent notch stress and equivalent structural stress. IB-LS (sloping) IB-LS (vertical) IB-BH (sloping) ENS ESS ENS ESS ENS ESS Full Alter N.B H.B *Note: ENS; Equivalent Notch Stress range, ESS; Equivalent Structural Stress range Table 13 Fatigue damage results or CSR and the proposed structural stress procedure. Homo. Alter. N.B. H.B Sum IB-LS (sloping) IB-LS (vertical) IB-BH (sloping) CSR procedure Proposed SS procedure CSR procedure Proposed SS procedure CSR procedure Proposed SS procedure In terms o atigue damage at the considered hot spot points shown in Table 13, the structural stress procedure results show dierent but not signiicant atigue lie compared to the equivalent notch stress procedure in CSR or bulk carriers.

14 14 Int. J. Nav. Archit. Ocean Eng. (2015) 7:10~24 However, the dierence might be due to the usage o dierent slopes or the S-N curve as shown in Fig. 12. At high stress level, such as or IB-LS (vertical) case, there was not much dierence between the two S-N curves. However, at low stress level, which was less than 10 7 cycles, such as or IB-LS (sloping) case, the two S-N curves provided dierent atigue lie. Another reason or the dierence is the structural stress method is not able to relect the corrosion induced environment and atigue improvement methods considered in CSR. Fig. 12 Two S-N curves used in this study. Concluding remarks Fatigue assessment or lower stool and bilge hopper connections in a 180 K bulk carrier was carried out using CSR or Bulk Carriers based on the equivalent notch stress, and the mesh-insensitive structural stress approaches. The main indings o this study are summarized as ollows: In this study, a atigue lie evaluation procedure using mesh-insensitive structural stress based on CSR or bulk carriers has been proposed and compared with the present CSR atigue assessment procedure. Signiicant actors aecting atigue lie evaluation in CSR or bulk carrier are mean stress, plate thickness, corrosive environment, material strength and atigue notch eect. Mesh-insensitive structural stress approach was able to explicitly consider these eects to evaluate atigue lie, except or the corrosive environment actor. According to the analysis o the results, it was demonstrated that the extrapolation-based hot spot stress and structural stress provided similar geometric stress values within 20% dierence. The equivalent notch stress range and equivalent structural stress range also exhibited similar tendency. The calculated atigue damage at the structural locations considered in this study showed dierent results. It was assumed that dierent slopes o the S-N curves and the coeicients o several actors used in the two procedures contributed to the dierence. While the atigue procedure o CSR or Bulk Carriers is a classiication society rule available mainly or shipbuilding, the mesh-insensitive structural stress approach is a atigue assessment procedure or a general welded structure. In this regard, urther research and investigation are required to consider the structural stress approach as a viable atigue assessment procedure or ships and oshore structures. ACKNOWLEDGEMENTS This work was supported by the National Research Foundation o Korea (NRF) grant unded by the Korea government (MSIP) through GCRC-SOP (No ). Also, this work was supported by the National Research Foundation o Korea (NRF) grant unded by the Korea government (MEST) (No ).

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