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Fatigue damage assessment of corroded oil tanker details based on global and local stress approaches
International Journal of Fatigue 43 (2012) 197–206
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue damage assessment of corroded oil tanker details based on global and local stress approaches K. Tran Nguyen, Y. Garbatov, C. Guedes Soares ⇑ Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
a r t i c l e
i n f o
Article history: Received 16 October 2011 Received in revised form 20 March 2012 Accepted 2 April 2012 Available online 10 April 2012 Keywords: Fatigue Effective notch stress Corrosion Finite element analysis
a b s t r a c t Fatigue damage assessment of double hull oil tanker structural details is performed, based on global and local structural finite element models. The wave-induced vertical and horizontal bending moments, as well as local pressure loads are accounted for in the fatigue damage calculations. Local stress analyses are considered based on the notch stress approach. Time-dependent stresses as a function of corrosion deterioration are analyzed based on nonlinear corrosion wastage during the design life of ship. The effective notch stress approach is applied for analyzing the stress distributions and the fatigue damage of the welded joint at two hotspots. The hotspots are located between the flat bar stiffener of a transverse web frame and the flange of a longitudinal stiffener at the side shell of a tanker ship hull. The details under consideration are modeled separately in a fine mesh employing the sub model techniques. Finally the fatigue damage assessment accounting for corrosion deterioration of the considered hotspots is analyzed. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The complex ship hull structures contain numerous geometrical discontinuities and are subjected to complex loading conditions (external and internal pressures, global bending moments, etc.). As a consequence the stress levels have become higher and fatigue strength assessment has been an important criterion in the structural design of ships. Fatigue assessment has been gaining attention during the last decades and much effort has been spent to develop different methods for predicting the fatigue strength/life of welded joints structure. Fatigue assessment of welded components in ship structural details have been performed initially by using the nominal stress based S–N curves [1]. The nominal stress may be easily calculated directly from the beam theory or based on empirical formulae, as well from coarse finite element analysis. However, for obtaining an accurate assessment of the stress response of the hull structure, the hotspot stress approach is applied. It is based on refined finite element (FE) method. The hotspot stress approach for fatigue damage of structural details has been included for fatigue design in several Classification Societies. The hotspot stress is defined as local stress obtained by extrapolating stresses at certain distances away from a geometrically discontinuous area such as the weld toe. Fricke and Kahl [2] applied three different structural stress approaches to fatigue strength assessment of three different welded structural details. Fatigue lives were predicted using the design ⇑ Corresponding author. E-mail address: [email protected] (C. Guedes Soares). 0142-1123/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2012.04.004
S–N curves, recommended within the different approaches and compared with the results of fatigue tests evaluated for a corresponding probability of survival. Chakarov et al. [3,4] analyzed symmetrical and unsymmetrical longitudinally stiffened panels, determining the hotspot stress distribution and stress concentration factors, in view of thickness change misalignment, angular imperfections, rotation of transverse weld toes and residual deformations. Some of the limitations of the hotspot stress approach are that the notch stresses caused by weld beads and sharp notches are excluded from the calculated stresses. It is therefore necessary to use the effective notch stress approach for determining the nonlinear stress distribution of welded structures due to this presence. The notch stress approach for fatigue assessment of welded joints correlates the stress range in a fictitious rounding of the weld toes or roots to the fatigue life using the design S–N curves. Radaj [5] developed the effective notch stress approach by introducing fictitious effective notches of radius 1 mm to weld toes or weld roots in order to avoid the stress singularities in sharp notches. Fricke [6] presented a guideline for the notch modeling and stress analysis. The approach has been widely used, due to the increasing computational capacity as has been demonstrated by Pedersen et al. [7]. The approach is suitable for assessing all types of welded joints using a single S–N curve. However, it requires more modeling and analysis work than the nominal or hotspot stress approaches. Further studies have been performed by Park and Miki [8] for the large-size welded joints, and the effective notch stress approach has been included in the IIW (International Institute of Welding) fatigue design recommendations [9]. Saad et al. [10]
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analyzed the hotspot and effective notch stresses accounting for the effect of contact elements of two welded specimens (doubler plates and double lap joint) subjected to fatigue load. Based on the results of the FE models analyzed, polynomial regression equations assessing the stress concentration factors at the weld toe and weld root were derived. Fricke and Paetzold [11] performed the full-scale fatigue tests for two types of ship structures to validate the S–N approaches for fatigue strength assessment with the numerical analysis based on the structural hotspot stress as well as the effective notch stress approach have been applied. Recently, Tran Nguyen et al. [12] have used the effective notch stress approach for the fatigue damage assessment of a tanker structural detail based on a local FE model. Finite element stress analyses at the notch surface of weld toes have been also studied. Moreover, ship structures also operate in a complex environment with the high humidity and the aggressive marine atmosphere. The side shell of ship hulls is subjected to the effect of sea and ballast water, rich in high chloride content, oxygen and other corrosive minerals. Corrosion has a harmful consequence from the point of view of safety and lead to thickness reduction, fatigue cracks and unstable failure of ship structures. Hence the corrosion problems are considered to be the most important factors leading to age-related structural degradation of ship structures. A corrosion model was proposed by Guedes Soares and Garbatov [13] that described the growth of corrosion wastage by a nonlinear time dependent function. It allowed how to evaluate the expected thickness reduction of the structural details during the design life of ship on the corrosion deterioration over time. The study presented here performs the fatigue damage assessment of a welded joint of the structural details at the side shell of a tanker and deals with a finite element analysis based on the global and local stress approaches accounting for corrosion deterioration. The effective notch stress distributions are evaluated at the places of two hotspots round the weld toes. The effect on the time dependent notch stresses as a function of corrosion deterioration are analyzed here with the reference to nonlinear corrosion wastage model [13]. The FE models are composed by shell, solid elements and applying advanced sub-modeling techniques. This paper is organized in the following manner. The damage case with the fatigue cracks, which may occur at the critical hotspots of the structural details is considered in Section 2. The fatigue loads and the combined global and local stress range are described in Section 3. Finite element modeling procedure and FE stress analysis as well as the time dependent notch stress analysis are discussed in Sections 4 and 5, respectively. Finally, the fatigue damage assessment is presented in Section 6.
Fig. 1. Mid-ship section of the oil tanker.
Fig. 2. Structural plan of the connection detail.
principal particulars of the oil tanker and the mid-ship section properties are given in Table 1. To define the local stress distribution at the intersection between the longitudinal stiffeners and the transverse web frame, a finite element analysis based on global and local structural FE models employing the sub model techniques is performed here. The effective notch stress, ENS approach is applied for investigating the fatigue damage of the weld joint at the two hotspot positions.
2. Study case A suitable damage case with fatigue cracks may initiate at hotspot points of the weld toe and grow through the thickness of the plate such as the connection between the flat bar stiffener attached to a transverse web frame (web-stiffener) and the flange of a longitudinal stiffener at the side shell. Typical connections of longitudinal to transverse structural elements at double side of an oil tanker are considered (see Fig. 1). During the inspection, fatigue cracks may be detected by the surveyor at an earlier stage in ship structures, or they may be detected after penetrating the side shell. In the majority of cases, there are two hotspot points, one is at the toe of the web-stiffener (HS1), and the second is at the flange of the flat bar close to the cutout (HS2), as can be seen from Fig. 2. The oil tanker (VLCC – very large crude carrier) has already been designed, successfully built and spent some years in-service. The
Table 1 Vessel hull characteristics. Length overall, Loa Length between perpendiculars, Lbp Breadth molded, B Depth molded, D Design draft (state of fully loaded), Tf Ballast draft (state of ballast loaded), Tb Block coefficient, CB Maximum service speed, v Web frame spacing, ls Moment of inertia about the vertical axis, Iz Moment of inertia about the horizontal axis, Iy Height of neutral axis above base line, no Vertical wave hogging bending moment, M hWV Vertical wave sagging bending moment, M sWV Horizontal wave bending moment (fully loaded), MWH Horizontal wave bending moment (ballast loaded), MWH
332 m 320 m 58 m 31 m 20.8 m 14 m 0.815 16 kn 5.12 m 4207.925 m4 1479.421 m4 13.525 m 44,04,303 kN m 47,39,923 kN m 26,42,960 kN m 21,72,486 kN m
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The shell elements with 4 and 8 nodes are used in the FE analysis of cargo-tank and local models respectively, the solid element with 20 nodes is applied in solid sub models for the notch stress approaches by employing the commercial software ANSYS [14].
The residual stresses from welding can be reduced over time as the ship is subjected to fatigue loading. Therefore, the total combined stress range for fatigue analysis is reduced by the mean stress correction factor for the considered region of the weld joints as [15]:
3. Fatigue loads
fm ¼
In order to evaluate the dynamic stress levels caused by the relative deflection in the fatigue assessment of longitudinal at a ship structure, fatigue damage is calculated for the variations in loading conditions that the hull structure may experience during the expected operation time. The simplified fatigue load cases for the oil tanker are expected to be 42.5% of its lifetime in each of the full and ballast load condition. The remaining time of 15% are assumed to be spent in harbor water (see Table 2). The fatigue loads are divided into two levels: global hull girder and local dynamic pressure loads. The global loads are composed of vertical and horizontal wave induced bending moment. The local dynamic pressure loads are to be considered as external and internal pressures acting on the hull and tank boundaries of ship in the two loaded conditions respectively. The static loads are also included to calculate the mean stress correction factor. The global wave bending moments, external and internal dynamic pressures, static pressures are calculated in compliance with the current rule of IACS [1]. The load cases at 104 probability level of the long-term Weibull distribution are applied to the finite element global and local models for estimation of the fatigue stress response analysis in the hull ship structure. For each loading condition, the global (Drg) and local (Drl) dynamic stress range components are considered as well as combined together. The combined global stress range response is taken from the vertical (Drv) and horizontal (Drh) wave induced hull girder bending stresses:
where rt ¼ maxf½rstatic þ Dr=2 [ 0g is the tension rc ¼ minf½rstatic Dr=2 [ 0g is the compression stress.
Dr g ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dr2v þ Dr2h þ 2qvh Drv Drh
ð1Þ
where qvh is the average correlation coefficient. The vertical and horizontal stress range is given as:
z Drv ¼ M hWV MsWV Iy
Drh ¼ 2MWH
ð2Þ
y Iz
ð3Þ
The combined local stress range response due to the external dynamic pressure (pe), which induce a stress amplitude (re) and the internal dynamic pressure (pi) inducing a stress amplitude (ri) is estimated by assuming an average long-term distribution at the local details between pressure loaded cases as [15]:
Dr l ¼ 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2e þ r2i þ 2qei re ri
ð4Þ
where qei is the average function of location correlation between the external and internal pressures of the detail considered. The combined total global and local stress range response (Dr) is defined as [15]:
Dr ¼ max ðDrg þ 0:6Drl Þ [ ð0:6Drg þ Drl Þ
ð5Þ
Table 2 Fraction of the total design life spent at sea. Loading condition
Fraction (pn)
Full load Ballast load
0.425 0.425
rt þ 0:7jrc j rt þ jrc j
ð6Þ stress,
4. Finite element modeling 4.1. Global and local models Due to the complexity of the ship structure, a finite element model is required for fatigue damage assessment. Several levels of FE analyses may be used by employing the sub modeling techniques to achieve a better accuracy. The flowchart of the FE models used here for fatigue analysis is shown in Fig. 3. All the FE models were created based on the same thickness scantlings and material properties complying with the rules [1]. The modulus of elasticity and the Poisson ratio are 206 GPa and 0.3 respectively. Sub-modeling [14] as used here is a finite element technique for refined analysis of a sub region, which contains singularities, geometry discontinuities, or corrosion induced material degradation areas based on global analysis results. The motivation for such a refined analysis is to achieve more accurate results, thereby providing detailed stress information in highly stressed areas. For the local region one can create a sub-model with fine mesh while keeping the global model with a coarse mesh. This methodology is also known as the cut boundary displacement method. Displacements calculated along the boundary of the global model are specified as boundary condition for the sub models. The advantage of using a sub model is that the analysis is carried out separately from the local model. The FE meshes of the global model and sub-model may be completely different, even using different element types. In this way, the FE analysis may be controlled step by step, ensuring maximum accuracy and less computing time. The objective of the FE global model is to represent the global stress distribution of the primary members in the hull. The cargo hold-tank model is modeled to covers ½ + 1 + ½ cargo tank length in the amid-ship region, which is sufficient to estimate the behavior of the oil tanker structure. The FE cargo hold model (global model) is built up according to the IACS [1] and the DNV [15]. In order to estimate stresses in accurate manner for fatigue assessment, the longitudinal stiffeners are included in this model (see Fig. 4). The 4-noded shell elements (SHELL63) are used for modeling the structural details in the global model with a mesh size of 900 mm, smaller than spacing between longitudinal stiffeners. The global model is analyzed using the load cases and boundary conditions as given in [15]. The full breadth cargo hold model is subjected to lateral pressures and it is connected by vertical springs using the COMBIN14 element in the vertical direction at the intersection of the transverse bulkheads with both side shells and the longitudinal bulkheads. The spring stiffness constant, K, is calculated as indicated in [1]. The local web frame sub model (local model) is modeled at the same location with respect to the global origin co-ordinate at the mid-ship region of oil tanker (see Fig. 4). The cut-boundary conditions interpolation is performed on the model. The higher order 8nodes elements (SHELL93) are used for local FE model with an element size of 250 mm creating a finer mesh than the global model one. Fig. 5 shows the local shell model (shell model) for the FE submodel analysis at the critical position on the side shell. It is
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Fig. 3. Flowchart of the sub-modeling technique.
Global model SHELL63
Local model SHELL93
Fig. 4. Global and local FE models (shell plating is not shown).
extended to 2 transverse web frame spacing and 4 longitudinal stiffener spacing. The flat bars are attached to the web frame and longitudinal stiffeners with the length equal to spacing between longitudinal stiffeners on the side and the inner side shell of the double hull. In addition, the shell model included cut-out at the intersections in web frame. The load cases and cut-boundary conditions are
Fig. 5. Shell model with flat bars attached to web frame and longitudinal stiffeners.
applied in the same way. The SHELL93 element is continued to be used for analyzing with fine meshes that the element size is 100 mm.
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1st sub-model
Solid model
HS2
HS1
Displacements interpolated from shell-to-solid model Fig. 6. Solid FE model and 1st sub-model.
2nd sub-model 1/2 52785 elements
3rd sub-model 1/2 113957 elements
gap of 0.1 mm
r = 1 mm 45o
Fig. 7. FE 2nd and 3rd sub-models for hotspots 1 and 2.
4.2. 3D solid sub-models Finite element solid sub-models were created in order to calculate the stress distribution and deformations in more accurate manner for fatigue damage assessment of the structural details. FE analysis accuracy of welded joints based on the effective notch stress approach depends very much on the element types and mesh density. Shell-to-solid sub-modeling techniques were used for achieving accuracy in the computation of the local stress at the critical hotspots in front weld toes of flat bar attached to flange plate (see Fig. 6). As shown in Figs. 6 and 7, three levels of solid sub-models were necessary for transferring nodal displacements as the boundary conditions from the solid model to local sub-models. The solid
elements can provide a better stress distribution because they may model precisely the shapes of the weld connections. The 3D solid element (SOLID95) is used for the FE solid models. The SOLID95 element is a higher order element with 20 nodes, three degrees of freedom per node and translation in x, y and z directions. This type of element may tolerate irregular shapes without loss of accuracy. It is used to comply with the recommendation presented in [6,16]. The SOLID95 element has been also applied as for examples in [3,10,12,17,18] for studying welded structural details. For this study, the sub-models are analyzed by using the tetrahedral-shaped solid elements. The weld shapes for the connection between the flange plate and the flat bar plate is modeled with a leg length, l = 4.5 mm, as well as a gap of 0.1 mm by introducing a clearance in the FE solid and the sub models. The fictitious effective notch radius of 1 mm is
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Fig. 8. Global displacements – external dynamic pressures in full load condition.
Global model Local model Shell model Solid model SHELL63 SHELL93 SHELL93 SOLID95 Fig. 9. Number of elements along the longitudinal stiffener in FE models.
included around the welded toes as recommended by IIW [6,16]. Relatively fine meshes are set up with an element size of 0.2 mm along the circumference of effective notch in the third sub-models (see Fig. 7).
5. Finite element stress analysis 5.1. Global and local stress analysis The deformation and normal stresses of the structural primary members in the mid-ship area are obtained by FE analysis of the global model. The global displacements are transferred to the local models by a sub-modeling technique. Fig. 8 shows one case of the displacements for global model for the external pressure under full load condition. The FE stresses depend on the mesh size and the element type that is used. In order to obtain more precisely the normal bending stress caused by lateral load cases on the stiffeners, the change of mesh division and element types are applied for each sub-model case as shown in Fig. 9. It is found, from the FE results based on the net scantling, that the mesh size and element type have a significant influence on the stress distributions for the longitudinal stiffeners, as shown in Figs. 10 and 11. It should be noted that the location of peak stresses at the intersection of longitudinal stiffener and transverse web frame is converged better for FE local model using SHELL93 element with finer mesh than the FE global model using SHELL63. As can be seen in Fig. 10, the distributions of principal normal stress subjected to external pressures are nearly the same in full and ballast condition. Remarkable in Fig. 11 is the relatively high increase of the stresses for the ballast load compared to the full load condition. The effect of internal pressures on the stress distributions for full load condition is not significant in both FE models.
Fig. 10. Normal stress due to external pressures in full, ballast load conditions, FE global and local models.
Figs. 12 and 13 also show the stress distributions on the flange of longitudinal stiffener of FE shell and solid models for the net scantling in full and ballast loading condition caused by external and internal pressure respectively. It can be observed that the distributions of normal stresses are almost similar in the two loading cases for both FE models using the SHELL93 and SOLID95 element. It should be also noted that the flat bar appearance combined with the weld bead shape induced an influence on the stress distributions in FE solid models. The stresses increased significantly at the two critical hotspots of the welded toes. Similar to the FE global and local models, the effect of internal pressure in full loading condition are not remarkable for the FE shell and solid models. 5.2. Effective notch stress approach The maximum principal stresses are used for the fatigue damage assessment of welded joints. The stress distributions in front of and around the weld toes are analyzed for a typical load case with the net thickness scantlings (see Fig. 14). The effective notch stress distribution for different cross sections along the weld toe line at HS1 and HS2 for external pressure in full and ballast loading condition can be seen in Fig. 15a and b. In general the stress distributions are the same in two loading cases. It is found, from the FE analysis, that the absolute values of stresses decrease from the section (a–a) to the section (e–e). It can be also observed that the stresses increase from the first points to midpoints and then fall down rapidly to the end points at the sections (a–a to c–c). The stress distribution is almost uniform at the sections (d–d) and (e–e). The maximum principal stresses on the effective notch surfaces at HS1 are always less than HS2 from the section (a–a) to the section (c–c) in the two loading cases as can be seen in Fig. 16. It should be noted that the stresses are nearly equal at the sections (d–d) and (e–e) for HS1 and HS2 in both loading conditions. It is also shown that the effective notch stress distribution decreases from the section (a–a) to (e–e) along the weld toe line with the coordinate TL. Similar analysis for the effective notch stresses distribution of different cross-sections along the weld toe line at two critical hotspots had also been performed for internal pressure and global bending moments in full and ballast loading condition. Tables 3 and 4 list the result of the effective notch stresses at two critical hotspot points for the two loading conditions due to lateral pressures and global loads respectively. It can be found from the FE analysis that the critical weld joints at structural details
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Fig. 11. Normal stress due to internal pressures in full, ballast load conditions, FE global and local models.
Fig. 14. Effective notch radius along the weld toe line co-ordinate TR and TL.
5.3. Time-dependent notch stress analysis
Fig. 12. Normal stress due to external pressures in full, ballast load conditions, FE shell and solid models.
Corrosion is recognized to be the most important phenomena leading to degradation of strength and fatigue life of ship structures as well as many other steel structures. The conventional models of corrosion wastage assume a constant corrosion rate, leading to a linear relationship between the material lost and time. General corrosion, which is the most common form of corrosion, takes place over the entire surface of the metal and is the one addressed here. At the ship design stage, corrosion addition (tk) is used to increase the required net thickness of structural hull members to compensate for the expected thickness reduction during the design life of ship as recommendation of the Rules [1]. However, no any procedure of rules covers all possible growth of corrosion wastage for structural details over time. Guedes Soares and Garbatov [13] proposed one model that describes the time-dependent growth of corrosion wastage:
( dðtÞ ¼
Fig. 13. Normal stress due to internal pressures in full, ballast load conditions, FE shell and solid models.
have high increase of effective notch stress subjected to external dynamic sea pressures. The static stress is analyzed in the same manner as the dynamic stress, using static loads for calculating the mean stress correction factor.
d1 ½1 eðtsc Þ=st t > sc 0
t 6 sc
ð7Þ
This model is based on the solution of a differential equation of corrosion wastage and governed by several parameters that represent the long-term non-linear description of corrosion deterioration under average environmental conditions, where d(t) is the corrosion depth at time t, d1 is the long-term thickness of the corrosion wastage, sc is the good corrosion protection time and st is the transition time. Based on the analysis of Garbatov et al. [19] for fitting the sets of corrosion data of tankers provided by ABS [20,21], the defined mathematical descriptors of Eq. (7) are given as d1 = 2 mm, sc = 10.5 years and st = 17 years (see Fig. 17). The aim of the stress analysis accounting for corrosion deterioration is to evaluate the effective notch stress at the weld toes with respect to the thickness reduction of the structural details in corrosion environment during the service life. FE analyses are performed with the different thicknesses of structural details. The Classification Societies [1] define the mean corrosion depth within their fatigue assessment rules for the expected design ship life of 25 years is about 1.5 mm (7.5% mean thickness of details) at side shell of tanker. Fig. 18 plotted the time-dependent combined total global and local notch stress range for the two loading condition in a corrosion
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(a) Full loading
(b) Ballast loading.
Fig. 15. Stress distribution at two hotspots – external pressure.
6. Fatigue damage assessment The fatigue damage accounting for corrosion is a process, which is the outcome of synergistic interactions among the environment, material microstructure, and cyclic loads over the time. Since the mechanisms of stress corrosion-fatigue are specific to a particular time-dependent by material–environment–dynamic load, it is not surprising that quantitative modeling of this complex process is still in its infancy. In general, the design of ship structural details for the fatigue life assessment is based on the S–N approach. The design S–N curve is represented by [1,16]:
log N ¼ log K m log Dro
Fig. 16. Effective notch stress distributions, HS1 and HS2 – external pressure.
Table 3 Effective local notch stress components. HS
Stresses due to lateral pressures (N/mm2) External (re)
Full loading 1 2
Internal (ri)
Static (rs)
484.33 585.49
28.70 1.20
259.82 585.44
Ballast loading 1 346.12 2 413.94
152.52 230.52
780.74 1251.0
environment for hotspot 1 and 2. It is found that the effective notch stress range increased over the time. The peak values of the local notch stress range, corresponding to the initiation interval of failure of the corrosion protection system at t = 10.5 years, have an increase for hotspots 1 and 2 in full loading conditions. The maximum notch stresses are located at time of 25th year in full and ballast loading conditions for both hotspots.
ð8Þ
where N is predicted number of cycles to failure for a given reference stress range, Dro, m is the negative inverse slope of the S–N curve, K is the constant depending on material property, weld joint and log K is the intercept of log N-axis of the S–N curve. In this study, the effective notch stress approach is applied according to the IIW recommendation [9]. The single FAT225 S-N curve is used for the approach and for plate thickness P5 mm with the curve slope m = 3 and log K = 13.36. For ocean structures, the probability density function of longterm notch stress range is represented by the two-parameter Weibull distribution, and the fatigue damage ratio based on Palmgren–Miner approach may be calculated as [22] for hotspot j:
Dnj ¼
voTd K
Dr m o;nj ½Lnðno Þ
C 1þ m=an
m
an
;
n ¼ 1; 2
ð9Þ
where the index n is a number of the considered loading conditions with n = 1 for the full loading and n = 2 for the ballast loading respectively. The long-term average response zero-crossing frequency is taken as mo = 0.1 Hz, Td is the intervals of ship design life, C is the Gamma function, and an is the Weibull stress range shape for the nth loading condition. The long-term effective notch stress range, Dro,nj, over the time may be calculated as:
Dro;nj ¼ fe fm Drnj
ð10Þ
where fe = 0.8 is the environmental wave climate correction factor [15] and the effect of mean stress correction factor fm is defined by Eq. (6).
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K. Tran Nguyen et al. / International Journal of Fatigue 43 (2012) 197–206 Table 4 Effective global notch stress components. Stresses due to global loads (N/mm2)
HS
Vertical wave BM (rwv)
Horizontal wave BM (rwh)
Stillwater BM (rsw)
19.79 23.11
79.53 96.79
22.22 27.09
19.79 23.11
65.45 79.52
22.22 27.09
Sagging
Hogging
Full loading 1 2
21.24 24.84
Ballast loading 1 2
21.24 24.84
1.6
Corrosion depth
Corrosion depth, d(t) [mm]
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0
3
6
9
12
15
18
21
24
27
30
33
Time, t [year] Fig. 17. Time-dependent reference corrosion model.
Fig. 19. Fatigue damage of hotspots 1 and 2.
1450
HS1_Full
HS1_Ballast
HS2_Full
HS2_Ballast
Notch stress range [N/mm 2 ]
1300
1150
1000
850
700
550 10.5
13.5
16.5
19.5
22.5
25.5
Fig. 20. Time-dependent total cumulative fatigue damage of hotspots 1, 2 over the thickness reduction of structural details.
Time, t [years] Fig. 18. Time-dependent notch stress range of hotspots 1 and 2.
Finally, the total cumulative fatigue damage under corrosionfatigue conditions can be determined by a linear accumulative damage in non-corrosive and corrosive environment for any hotspot j such as:
Dj ¼
2 X pn Dnj n¼1
!
2 X þ pn Dnj coated
n¼1
! ð11Þ stresscorrosion
where pn is a part of the lifetime spent in each of loading condition n (see Table 2). The second term on the right hand side is obtained by the sustained dynamic load case acting on the hull girder with the thickness reduction of structural details over time. The overall fatigue damage of welded joint for the two critical hotspot points 1 and 2 due as a result of different loading is shown in Fig. 19. It can be seen from Fig. 20 that, in general, the cumulative fatigue damage over time obtained from the effective notch stress approach is lower for the hotspot 1 than the hotspot 2. It should be also noted that the fatigue damage is limited in the interval
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without corrosion which corresponds of the good corrosion protection coating.
grateful to Dr George Wang for his initiative to promote this scholarship.
7. Conclusion
References
Fatigue strength assessment of a side-longitudinal stiffener considering the two most probable crack initiation points in a double hull oil tanker has been done here based on global and local structural finite element models. The analyses are performed for two basic loading conditions accounting for the expected operation time in each of the considered conditions. The finite element models are composed by shell and solid elements using ANSYS software and applying advanced sub-modeling techniques. The effective notch stress approach cannot be directly used for complex structures without sub-model techniques, which require additional modeling and computational effort. It does, however, allow the effects of a local weld shape and radius at weld toe to be considered. The global finite element model of the amid-ship region of a tanker was subjected to two different dynamic loads, one is due to the global bending moment and another one is due to the lateral pressures in the full and ballast loading conditions respectively. A local detailed finite element analysis was performed to obtain the overall stress distributions at the notch surface of weld toes at the two critical hotspot points. Based on the evaluation of the global, local and effective notch stress for FE models, it was found that the higher order elements and mesh sizes have a significant effect on the assured convergence of results. The time-dependent notch stresses as a result of corrosion degradation were analyzed based on the reference nonlinear corrosion wastage model. As a result of the performed analysis, the total cumulative corrosion-fatigue damage at two hotspot points is rather high in all the loading cases after the initiation of failure of the corrosion protection system. It has been found that the fatigue damage at point 2 is higher than the one at point 1. The hotspot 2 location is the weakest point of the welded joint from the fatigue damage point of view. The fatigue damage assessment was based on the effective notch stress approach, being one of the most practical methods in combination with detailed finite element analysis. It has been recognized that the calculated local notch stress around the singularities of welded joints of the structural details depends very much on the structural idealization, the thickness scantling, the element types and the mesh subdivision. Acknowledgements The work of the first author has been financed by a Ph.D. scholarship from ABS, the American Bureau of Shipping. The authors are
[1] IACS. Common structural rules for double hull oil tankers. In: International association of classification societies; 2010. [2] Fricke W, Kahl A. Comparison of different structural stress approaches for fatigue assessment of welded ship structures. Mar Struct 2005;18:473–88. [3] Chakarov K, Garbatov Y, Guedes Soares C. Fatigue analysis of ship deck structures accounting for imperfections. Int J Fatigue 2008;30:1881–97. [4] Chakarov K, Garbatov Y, Guedes Soares C. Comparative stress concentration factor analysis of an imperfect welded deck structure. Int Shipbuild Prog 2008;55:47–62. [5] Radaj D. Design and analysis of fatigue resistant welded structures. Cambridge: Woodhead Publishing Ltd.; 1990. [6] Fricke W. Guideline for fatigue assessment by notch stress analysis for welded structures. In: IIW Doc; 2008. [7] Pedersen M, Mouritsen O, Hansen M, Andersen J, Wenderby J. Re-analysis of fatigue data for welded joints using the notch stress approach. Int J Fatigue 2010;32:1620–6. [8] Park W, Miki C. Fatigue assessment of large-size welded joints based on the effective notch stress approach. Int J Fatigue 2008;30:1556–68. [9] Hobbacher A. Recommendations for fatigue design of welded joints and components, IIW doc.1823-07. Welding Research Council Bulletin 520. International Institute of Welding, New York; 2009. [10] Saad S, Tran Nguyen K, Garbatov Y, Guedes Soares C. Fatigue stress assessment accounting for contact effect. In: Proceeding of the 10th international conference on marine science and technology. Union of Scientists of Varna, Bulgaria; 2010. p. 23–33. [11] Fricke W, Paetzold H. Full-scale fatigue tests of ship structures to validate the S–N approaches for fatigue strength assessment. Mar Struct 2010;23:115–30. [12] Tran Nguyen K, Garbatov Y, Guedes Soares C. Fatigue damage assessment of a tanker structural detail based on the effective notch stress approach. In: Guedes Soares C, Santos N, Garbatov Y, Sutulo S, editors. Maritime technology and engineering. London, UK: Taylor & Francis Group; 2012. [13] Guedes Soares C, Garbatov Y. Reliability of maintained, corrosion protected plates subjected to non-linear corrosion and compressive loads. Mar Struct 1999;12:425–45. [14] ANSYSÒ. Online manuals. In: United States of America: ANSYS Inc.; 2007. [15] DNV. Fatigue assessment of ship structures. In: Det Norske Veritas; 2010. [16] Hobbacher A. Recommendations for fatigue design of welded joints and components. In: IIW Doc; 2007. [17] Feltz O, Fricke W. Experimental and numerical fatigue analysis of partial-load and full-load carrying fillet welds at doubler plates and lap joints. In: Guedes Soares C, Das PK, editors. Analysis and design of marine structures. London, UK: Taylor and Francis Group; 2009. p. 247–53. [18] Gaspar B, Garbatov Y, Guedes Soares C. Effect of uncertain weld shape on the structural hot spot stress distribution. In: Guedes Soares C, Das PK, editors. Analysis and design of marine structures. London, UK: Taylor and Francis Group; 2009. p. 267–78. [19] Garbatov Y, Guedes Soares C, Wang G. Non-linear time dependent corrosion wastage of deck plates of ballast and cargo tanks of tankers. J Offshore Mech Arct Eng 2007;129:48–55. [20] ABS. ABS database of corrosion wastage for oil tankers. In: American Bureau of Shipping; 2002–07. [21] Wang G, Spencer J, Elsayed T, Estimation of corrosion rates of oil tankers. In: Proceeding of the 22nd international conference on offshore mechanics and arctic engineering, Cancun, Mexico. OMAE2003-37361; 2003. [22] Nolte K, Hansford J. Closed-form expressions for determining the fatigue damage of structures due to ocean waves. In: Proceeding of offshore technology conference, Houston Texas, USA; 1976. p. 861–70.
Contents lists available at SciVerse ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue damage assessment of corroded oil tanker details based on global and local stress approaches K. Tran Nguyen, Y. Garbatov, C. Guedes Soares ⇑ Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
a r t i c l e
i n f o
Article history: Received 16 October 2011 Received in revised form 20 March 2012 Accepted 2 April 2012 Available online 10 April 2012 Keywords: Fatigue Effective notch stress Corrosion Finite element analysis
a b s t r a c t Fatigue damage assessment of double hull oil tanker structural details is performed, based on global and local structural finite element models. The wave-induced vertical and horizontal bending moments, as well as local pressure loads are accounted for in the fatigue damage calculations. Local stress analyses are considered based on the notch stress approach. Time-dependent stresses as a function of corrosion deterioration are analyzed based on nonlinear corrosion wastage during the design life of ship. The effective notch stress approach is applied for analyzing the stress distributions and the fatigue damage of the welded joint at two hotspots. The hotspots are located between the flat bar stiffener of a transverse web frame and the flange of a longitudinal stiffener at the side shell of a tanker ship hull. The details under consideration are modeled separately in a fine mesh employing the sub model techniques. Finally the fatigue damage assessment accounting for corrosion deterioration of the considered hotspots is analyzed. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The complex ship hull structures contain numerous geometrical discontinuities and are subjected to complex loading conditions (external and internal pressures, global bending moments, etc.). As a consequence the stress levels have become higher and fatigue strength assessment has been an important criterion in the structural design of ships. Fatigue assessment has been gaining attention during the last decades and much effort has been spent to develop different methods for predicting the fatigue strength/life of welded joints structure. Fatigue assessment of welded components in ship structural details have been performed initially by using the nominal stress based S–N curves [1]. The nominal stress may be easily calculated directly from the beam theory or based on empirical formulae, as well from coarse finite element analysis. However, for obtaining an accurate assessment of the stress response of the hull structure, the hotspot stress approach is applied. It is based on refined finite element (FE) method. The hotspot stress approach for fatigue damage of structural details has been included for fatigue design in several Classification Societies. The hotspot stress is defined as local stress obtained by extrapolating stresses at certain distances away from a geometrically discontinuous area such as the weld toe. Fricke and Kahl [2] applied three different structural stress approaches to fatigue strength assessment of three different welded structural details. Fatigue lives were predicted using the design ⇑ Corresponding author. E-mail address: [email protected] (C. Guedes Soares). 0142-1123/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2012.04.004
S–N curves, recommended within the different approaches and compared with the results of fatigue tests evaluated for a corresponding probability of survival. Chakarov et al. [3,4] analyzed symmetrical and unsymmetrical longitudinally stiffened panels, determining the hotspot stress distribution and stress concentration factors, in view of thickness change misalignment, angular imperfections, rotation of transverse weld toes and residual deformations. Some of the limitations of the hotspot stress approach are that the notch stresses caused by weld beads and sharp notches are excluded from the calculated stresses. It is therefore necessary to use the effective notch stress approach for determining the nonlinear stress distribution of welded structures due to this presence. The notch stress approach for fatigue assessment of welded joints correlates the stress range in a fictitious rounding of the weld toes or roots to the fatigue life using the design S–N curves. Radaj [5] developed the effective notch stress approach by introducing fictitious effective notches of radius 1 mm to weld toes or weld roots in order to avoid the stress singularities in sharp notches. Fricke [6] presented a guideline for the notch modeling and stress analysis. The approach has been widely used, due to the increasing computational capacity as has been demonstrated by Pedersen et al. [7]. The approach is suitable for assessing all types of welded joints using a single S–N curve. However, it requires more modeling and analysis work than the nominal or hotspot stress approaches. Further studies have been performed by Park and Miki [8] for the large-size welded joints, and the effective notch stress approach has been included in the IIW (International Institute of Welding) fatigue design recommendations [9]. Saad et al. [10]
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analyzed the hotspot and effective notch stresses accounting for the effect of contact elements of two welded specimens (doubler plates and double lap joint) subjected to fatigue load. Based on the results of the FE models analyzed, polynomial regression equations assessing the stress concentration factors at the weld toe and weld root were derived. Fricke and Paetzold [11] performed the full-scale fatigue tests for two types of ship structures to validate the S–N approaches for fatigue strength assessment with the numerical analysis based on the structural hotspot stress as well as the effective notch stress approach have been applied. Recently, Tran Nguyen et al. [12] have used the effective notch stress approach for the fatigue damage assessment of a tanker structural detail based on a local FE model. Finite element stress analyses at the notch surface of weld toes have been also studied. Moreover, ship structures also operate in a complex environment with the high humidity and the aggressive marine atmosphere. The side shell of ship hulls is subjected to the effect of sea and ballast water, rich in high chloride content, oxygen and other corrosive minerals. Corrosion has a harmful consequence from the point of view of safety and lead to thickness reduction, fatigue cracks and unstable failure of ship structures. Hence the corrosion problems are considered to be the most important factors leading to age-related structural degradation of ship structures. A corrosion model was proposed by Guedes Soares and Garbatov [13] that described the growth of corrosion wastage by a nonlinear time dependent function. It allowed how to evaluate the expected thickness reduction of the structural details during the design life of ship on the corrosion deterioration over time. The study presented here performs the fatigue damage assessment of a welded joint of the structural details at the side shell of a tanker and deals with a finite element analysis based on the global and local stress approaches accounting for corrosion deterioration. The effective notch stress distributions are evaluated at the places of two hotspots round the weld toes. The effect on the time dependent notch stresses as a function of corrosion deterioration are analyzed here with the reference to nonlinear corrosion wastage model [13]. The FE models are composed by shell, solid elements and applying advanced sub-modeling techniques. This paper is organized in the following manner. The damage case with the fatigue cracks, which may occur at the critical hotspots of the structural details is considered in Section 2. The fatigue loads and the combined global and local stress range are described in Section 3. Finite element modeling procedure and FE stress analysis as well as the time dependent notch stress analysis are discussed in Sections 4 and 5, respectively. Finally, the fatigue damage assessment is presented in Section 6.
Fig. 1. Mid-ship section of the oil tanker.
Fig. 2. Structural plan of the connection detail.
principal particulars of the oil tanker and the mid-ship section properties are given in Table 1. To define the local stress distribution at the intersection between the longitudinal stiffeners and the transverse web frame, a finite element analysis based on global and local structural FE models employing the sub model techniques is performed here. The effective notch stress, ENS approach is applied for investigating the fatigue damage of the weld joint at the two hotspot positions.
2. Study case A suitable damage case with fatigue cracks may initiate at hotspot points of the weld toe and grow through the thickness of the plate such as the connection between the flat bar stiffener attached to a transverse web frame (web-stiffener) and the flange of a longitudinal stiffener at the side shell. Typical connections of longitudinal to transverse structural elements at double side of an oil tanker are considered (see Fig. 1). During the inspection, fatigue cracks may be detected by the surveyor at an earlier stage in ship structures, or they may be detected after penetrating the side shell. In the majority of cases, there are two hotspot points, one is at the toe of the web-stiffener (HS1), and the second is at the flange of the flat bar close to the cutout (HS2), as can be seen from Fig. 2. The oil tanker (VLCC – very large crude carrier) has already been designed, successfully built and spent some years in-service. The
Table 1 Vessel hull characteristics. Length overall, Loa Length between perpendiculars, Lbp Breadth molded, B Depth molded, D Design draft (state of fully loaded), Tf Ballast draft (state of ballast loaded), Tb Block coefficient, CB Maximum service speed, v Web frame spacing, ls Moment of inertia about the vertical axis, Iz Moment of inertia about the horizontal axis, Iy Height of neutral axis above base line, no Vertical wave hogging bending moment, M hWV Vertical wave sagging bending moment, M sWV Horizontal wave bending moment (fully loaded), MWH Horizontal wave bending moment (ballast loaded), MWH
332 m 320 m 58 m 31 m 20.8 m 14 m 0.815 16 kn 5.12 m 4207.925 m4 1479.421 m4 13.525 m 44,04,303 kN m 47,39,923 kN m 26,42,960 kN m 21,72,486 kN m
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The shell elements with 4 and 8 nodes are used in the FE analysis of cargo-tank and local models respectively, the solid element with 20 nodes is applied in solid sub models for the notch stress approaches by employing the commercial software ANSYS [14].
The residual stresses from welding can be reduced over time as the ship is subjected to fatigue loading. Therefore, the total combined stress range for fatigue analysis is reduced by the mean stress correction factor for the considered region of the weld joints as [15]:
3. Fatigue loads
fm ¼
In order to evaluate the dynamic stress levels caused by the relative deflection in the fatigue assessment of longitudinal at a ship structure, fatigue damage is calculated for the variations in loading conditions that the hull structure may experience during the expected operation time. The simplified fatigue load cases for the oil tanker are expected to be 42.5% of its lifetime in each of the full and ballast load condition. The remaining time of 15% are assumed to be spent in harbor water (see Table 2). The fatigue loads are divided into two levels: global hull girder and local dynamic pressure loads. The global loads are composed of vertical and horizontal wave induced bending moment. The local dynamic pressure loads are to be considered as external and internal pressures acting on the hull and tank boundaries of ship in the two loaded conditions respectively. The static loads are also included to calculate the mean stress correction factor. The global wave bending moments, external and internal dynamic pressures, static pressures are calculated in compliance with the current rule of IACS [1]. The load cases at 104 probability level of the long-term Weibull distribution are applied to the finite element global and local models for estimation of the fatigue stress response analysis in the hull ship structure. For each loading condition, the global (Drg) and local (Drl) dynamic stress range components are considered as well as combined together. The combined global stress range response is taken from the vertical (Drv) and horizontal (Drh) wave induced hull girder bending stresses:
where rt ¼ maxf½rstatic þ Dr=2 [ 0g is the tension rc ¼ minf½rstatic Dr=2 [ 0g is the compression stress.
Dr g ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dr2v þ Dr2h þ 2qvh Drv Drh
ð1Þ
where qvh is the average correlation coefficient. The vertical and horizontal stress range is given as:
z Drv ¼ M hWV MsWV Iy
Drh ¼ 2MWH
ð2Þ
y Iz
ð3Þ
The combined local stress range response due to the external dynamic pressure (pe), which induce a stress amplitude (re) and the internal dynamic pressure (pi) inducing a stress amplitude (ri) is estimated by assuming an average long-term distribution at the local details between pressure loaded cases as [15]:
Dr l ¼ 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2e þ r2i þ 2qei re ri
ð4Þ
where qei is the average function of location correlation between the external and internal pressures of the detail considered. The combined total global and local stress range response (Dr) is defined as [15]:
Dr ¼ max ðDrg þ 0:6Drl Þ [ ð0:6Drg þ Drl Þ
ð5Þ
Table 2 Fraction of the total design life spent at sea. Loading condition
Fraction (pn)
Full load Ballast load
0.425 0.425
rt þ 0:7jrc j rt þ jrc j
ð6Þ stress,
4. Finite element modeling 4.1. Global and local models Due to the complexity of the ship structure, a finite element model is required for fatigue damage assessment. Several levels of FE analyses may be used by employing the sub modeling techniques to achieve a better accuracy. The flowchart of the FE models used here for fatigue analysis is shown in Fig. 3. All the FE models were created based on the same thickness scantlings and material properties complying with the rules [1]. The modulus of elasticity and the Poisson ratio are 206 GPa and 0.3 respectively. Sub-modeling [14] as used here is a finite element technique for refined analysis of a sub region, which contains singularities, geometry discontinuities, or corrosion induced material degradation areas based on global analysis results. The motivation for such a refined analysis is to achieve more accurate results, thereby providing detailed stress information in highly stressed areas. For the local region one can create a sub-model with fine mesh while keeping the global model with a coarse mesh. This methodology is also known as the cut boundary displacement method. Displacements calculated along the boundary of the global model are specified as boundary condition for the sub models. The advantage of using a sub model is that the analysis is carried out separately from the local model. The FE meshes of the global model and sub-model may be completely different, even using different element types. In this way, the FE analysis may be controlled step by step, ensuring maximum accuracy and less computing time. The objective of the FE global model is to represent the global stress distribution of the primary members in the hull. The cargo hold-tank model is modeled to covers ½ + 1 + ½ cargo tank length in the amid-ship region, which is sufficient to estimate the behavior of the oil tanker structure. The FE cargo hold model (global model) is built up according to the IACS [1] and the DNV [15]. In order to estimate stresses in accurate manner for fatigue assessment, the longitudinal stiffeners are included in this model (see Fig. 4). The 4-noded shell elements (SHELL63) are used for modeling the structural details in the global model with a mesh size of 900 mm, smaller than spacing between longitudinal stiffeners. The global model is analyzed using the load cases and boundary conditions as given in [15]. The full breadth cargo hold model is subjected to lateral pressures and it is connected by vertical springs using the COMBIN14 element in the vertical direction at the intersection of the transverse bulkheads with both side shells and the longitudinal bulkheads. The spring stiffness constant, K, is calculated as indicated in [1]. The local web frame sub model (local model) is modeled at the same location with respect to the global origin co-ordinate at the mid-ship region of oil tanker (see Fig. 4). The cut-boundary conditions interpolation is performed on the model. The higher order 8nodes elements (SHELL93) are used for local FE model with an element size of 250 mm creating a finer mesh than the global model one. Fig. 5 shows the local shell model (shell model) for the FE submodel analysis at the critical position on the side shell. It is
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Fig. 3. Flowchart of the sub-modeling technique.
Global model SHELL63
Local model SHELL93
Fig. 4. Global and local FE models (shell plating is not shown).
extended to 2 transverse web frame spacing and 4 longitudinal stiffener spacing. The flat bars are attached to the web frame and longitudinal stiffeners with the length equal to spacing between longitudinal stiffeners on the side and the inner side shell of the double hull. In addition, the shell model included cut-out at the intersections in web frame. The load cases and cut-boundary conditions are
Fig. 5. Shell model with flat bars attached to web frame and longitudinal stiffeners.
applied in the same way. The SHELL93 element is continued to be used for analyzing with fine meshes that the element size is 100 mm.
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1st sub-model
Solid model
HS2
HS1
Displacements interpolated from shell-to-solid model Fig. 6. Solid FE model and 1st sub-model.
2nd sub-model 1/2 52785 elements
3rd sub-model 1/2 113957 elements
gap of 0.1 mm
r = 1 mm 45o
Fig. 7. FE 2nd and 3rd sub-models for hotspots 1 and 2.
4.2. 3D solid sub-models Finite element solid sub-models were created in order to calculate the stress distribution and deformations in more accurate manner for fatigue damage assessment of the structural details. FE analysis accuracy of welded joints based on the effective notch stress approach depends very much on the element types and mesh density. Shell-to-solid sub-modeling techniques were used for achieving accuracy in the computation of the local stress at the critical hotspots in front weld toes of flat bar attached to flange plate (see Fig. 6). As shown in Figs. 6 and 7, three levels of solid sub-models were necessary for transferring nodal displacements as the boundary conditions from the solid model to local sub-models. The solid
elements can provide a better stress distribution because they may model precisely the shapes of the weld connections. The 3D solid element (SOLID95) is used for the FE solid models. The SOLID95 element is a higher order element with 20 nodes, three degrees of freedom per node and translation in x, y and z directions. This type of element may tolerate irregular shapes without loss of accuracy. It is used to comply with the recommendation presented in [6,16]. The SOLID95 element has been also applied as for examples in [3,10,12,17,18] for studying welded structural details. For this study, the sub-models are analyzed by using the tetrahedral-shaped solid elements. The weld shapes for the connection between the flange plate and the flat bar plate is modeled with a leg length, l = 4.5 mm, as well as a gap of 0.1 mm by introducing a clearance in the FE solid and the sub models. The fictitious effective notch radius of 1 mm is
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Fig. 8. Global displacements – external dynamic pressures in full load condition.
Global model Local model Shell model Solid model SHELL63 SHELL93 SHELL93 SOLID95 Fig. 9. Number of elements along the longitudinal stiffener in FE models.
included around the welded toes as recommended by IIW [6,16]. Relatively fine meshes are set up with an element size of 0.2 mm along the circumference of effective notch in the third sub-models (see Fig. 7).
5. Finite element stress analysis 5.1. Global and local stress analysis The deformation and normal stresses of the structural primary members in the mid-ship area are obtained by FE analysis of the global model. The global displacements are transferred to the local models by a sub-modeling technique. Fig. 8 shows one case of the displacements for global model for the external pressure under full load condition. The FE stresses depend on the mesh size and the element type that is used. In order to obtain more precisely the normal bending stress caused by lateral load cases on the stiffeners, the change of mesh division and element types are applied for each sub-model case as shown in Fig. 9. It is found, from the FE results based on the net scantling, that the mesh size and element type have a significant influence on the stress distributions for the longitudinal stiffeners, as shown in Figs. 10 and 11. It should be noted that the location of peak stresses at the intersection of longitudinal stiffener and transverse web frame is converged better for FE local model using SHELL93 element with finer mesh than the FE global model using SHELL63. As can be seen in Fig. 10, the distributions of principal normal stress subjected to external pressures are nearly the same in full and ballast condition. Remarkable in Fig. 11 is the relatively high increase of the stresses for the ballast load compared to the full load condition. The effect of internal pressures on the stress distributions for full load condition is not significant in both FE models.
Fig. 10. Normal stress due to external pressures in full, ballast load conditions, FE global and local models.
Figs. 12 and 13 also show the stress distributions on the flange of longitudinal stiffener of FE shell and solid models for the net scantling in full and ballast loading condition caused by external and internal pressure respectively. It can be observed that the distributions of normal stresses are almost similar in the two loading cases for both FE models using the SHELL93 and SOLID95 element. It should be also noted that the flat bar appearance combined with the weld bead shape induced an influence on the stress distributions in FE solid models. The stresses increased significantly at the two critical hotspots of the welded toes. Similar to the FE global and local models, the effect of internal pressure in full loading condition are not remarkable for the FE shell and solid models. 5.2. Effective notch stress approach The maximum principal stresses are used for the fatigue damage assessment of welded joints. The stress distributions in front of and around the weld toes are analyzed for a typical load case with the net thickness scantlings (see Fig. 14). The effective notch stress distribution for different cross sections along the weld toe line at HS1 and HS2 for external pressure in full and ballast loading condition can be seen in Fig. 15a and b. In general the stress distributions are the same in two loading cases. It is found, from the FE analysis, that the absolute values of stresses decrease from the section (a–a) to the section (e–e). It can be also observed that the stresses increase from the first points to midpoints and then fall down rapidly to the end points at the sections (a–a to c–c). The stress distribution is almost uniform at the sections (d–d) and (e–e). The maximum principal stresses on the effective notch surfaces at HS1 are always less than HS2 from the section (a–a) to the section (c–c) in the two loading cases as can be seen in Fig. 16. It should be noted that the stresses are nearly equal at the sections (d–d) and (e–e) for HS1 and HS2 in both loading conditions. It is also shown that the effective notch stress distribution decreases from the section (a–a) to (e–e) along the weld toe line with the coordinate TL. Similar analysis for the effective notch stresses distribution of different cross-sections along the weld toe line at two critical hotspots had also been performed for internal pressure and global bending moments in full and ballast loading condition. Tables 3 and 4 list the result of the effective notch stresses at two critical hotspot points for the two loading conditions due to lateral pressures and global loads respectively. It can be found from the FE analysis that the critical weld joints at structural details
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Fig. 11. Normal stress due to internal pressures in full, ballast load conditions, FE global and local models.
Fig. 14. Effective notch radius along the weld toe line co-ordinate TR and TL.
5.3. Time-dependent notch stress analysis
Fig. 12. Normal stress due to external pressures in full, ballast load conditions, FE shell and solid models.
Corrosion is recognized to be the most important phenomena leading to degradation of strength and fatigue life of ship structures as well as many other steel structures. The conventional models of corrosion wastage assume a constant corrosion rate, leading to a linear relationship between the material lost and time. General corrosion, which is the most common form of corrosion, takes place over the entire surface of the metal and is the one addressed here. At the ship design stage, corrosion addition (tk) is used to increase the required net thickness of structural hull members to compensate for the expected thickness reduction during the design life of ship as recommendation of the Rules [1]. However, no any procedure of rules covers all possible growth of corrosion wastage for structural details over time. Guedes Soares and Garbatov [13] proposed one model that describes the time-dependent growth of corrosion wastage:
( dðtÞ ¼
Fig. 13. Normal stress due to internal pressures in full, ballast load conditions, FE shell and solid models.
have high increase of effective notch stress subjected to external dynamic sea pressures. The static stress is analyzed in the same manner as the dynamic stress, using static loads for calculating the mean stress correction factor.
d1 ½1 eðtsc Þ=st t > sc 0
t 6 sc
ð7Þ
This model is based on the solution of a differential equation of corrosion wastage and governed by several parameters that represent the long-term non-linear description of corrosion deterioration under average environmental conditions, where d(t) is the corrosion depth at time t, d1 is the long-term thickness of the corrosion wastage, sc is the good corrosion protection time and st is the transition time. Based on the analysis of Garbatov et al. [19] for fitting the sets of corrosion data of tankers provided by ABS [20,21], the defined mathematical descriptors of Eq. (7) are given as d1 = 2 mm, sc = 10.5 years and st = 17 years (see Fig. 17). The aim of the stress analysis accounting for corrosion deterioration is to evaluate the effective notch stress at the weld toes with respect to the thickness reduction of the structural details in corrosion environment during the service life. FE analyses are performed with the different thicknesses of structural details. The Classification Societies [1] define the mean corrosion depth within their fatigue assessment rules for the expected design ship life of 25 years is about 1.5 mm (7.5% mean thickness of details) at side shell of tanker. Fig. 18 plotted the time-dependent combined total global and local notch stress range for the two loading condition in a corrosion
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(a) Full loading
(b) Ballast loading.
Fig. 15. Stress distribution at two hotspots – external pressure.
6. Fatigue damage assessment The fatigue damage accounting for corrosion is a process, which is the outcome of synergistic interactions among the environment, material microstructure, and cyclic loads over the time. Since the mechanisms of stress corrosion-fatigue are specific to a particular time-dependent by material–environment–dynamic load, it is not surprising that quantitative modeling of this complex process is still in its infancy. In general, the design of ship structural details for the fatigue life assessment is based on the S–N approach. The design S–N curve is represented by [1,16]:
log N ¼ log K m log Dro
Fig. 16. Effective notch stress distributions, HS1 and HS2 – external pressure.
Table 3 Effective local notch stress components. HS
Stresses due to lateral pressures (N/mm2) External (re)
Full loading 1 2
Internal (ri)
Static (rs)
484.33 585.49
28.70 1.20
259.82 585.44
Ballast loading 1 346.12 2 413.94
152.52 230.52
780.74 1251.0
environment for hotspot 1 and 2. It is found that the effective notch stress range increased over the time. The peak values of the local notch stress range, corresponding to the initiation interval of failure of the corrosion protection system at t = 10.5 years, have an increase for hotspots 1 and 2 in full loading conditions. The maximum notch stresses are located at time of 25th year in full and ballast loading conditions for both hotspots.
ð8Þ
where N is predicted number of cycles to failure for a given reference stress range, Dro, m is the negative inverse slope of the S–N curve, K is the constant depending on material property, weld joint and log K is the intercept of log N-axis of the S–N curve. In this study, the effective notch stress approach is applied according to the IIW recommendation [9]. The single FAT225 S-N curve is used for the approach and for plate thickness P5 mm with the curve slope m = 3 and log K = 13.36. For ocean structures, the probability density function of longterm notch stress range is represented by the two-parameter Weibull distribution, and the fatigue damage ratio based on Palmgren–Miner approach may be calculated as [22] for hotspot j:
Dnj ¼
voTd K
Dr m o;nj ½Lnðno Þ
C 1þ m=an
m
an
;
n ¼ 1; 2
ð9Þ
where the index n is a number of the considered loading conditions with n = 1 for the full loading and n = 2 for the ballast loading respectively. The long-term average response zero-crossing frequency is taken as mo = 0.1 Hz, Td is the intervals of ship design life, C is the Gamma function, and an is the Weibull stress range shape for the nth loading condition. The long-term effective notch stress range, Dro,nj, over the time may be calculated as:
Dro;nj ¼ fe fm Drnj
ð10Þ
where fe = 0.8 is the environmental wave climate correction factor [15] and the effect of mean stress correction factor fm is defined by Eq. (6).
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K. Tran Nguyen et al. / International Journal of Fatigue 43 (2012) 197–206 Table 4 Effective global notch stress components. Stresses due to global loads (N/mm2)
HS
Vertical wave BM (rwv)
Horizontal wave BM (rwh)
Stillwater BM (rsw)
19.79 23.11
79.53 96.79
22.22 27.09
19.79 23.11
65.45 79.52
22.22 27.09
Sagging
Hogging
Full loading 1 2
21.24 24.84
Ballast loading 1 2
21.24 24.84
1.6
Corrosion depth
Corrosion depth, d(t) [mm]
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0
3
6
9
12
15
18
21
24
27
30
33
Time, t [year] Fig. 17. Time-dependent reference corrosion model.
Fig. 19. Fatigue damage of hotspots 1 and 2.
1450
HS1_Full
HS1_Ballast
HS2_Full
HS2_Ballast
Notch stress range [N/mm 2 ]
1300
1150
1000
850
700
550 10.5
13.5
16.5
19.5
22.5
25.5
Fig. 20. Time-dependent total cumulative fatigue damage of hotspots 1, 2 over the thickness reduction of structural details.
Time, t [years] Fig. 18. Time-dependent notch stress range of hotspots 1 and 2.
Finally, the total cumulative fatigue damage under corrosionfatigue conditions can be determined by a linear accumulative damage in non-corrosive and corrosive environment for any hotspot j such as:
Dj ¼
2 X pn Dnj n¼1
!
2 X þ pn Dnj coated
n¼1
! ð11Þ stresscorrosion
where pn is a part of the lifetime spent in each of loading condition n (see Table 2). The second term on the right hand side is obtained by the sustained dynamic load case acting on the hull girder with the thickness reduction of structural details over time. The overall fatigue damage of welded joint for the two critical hotspot points 1 and 2 due as a result of different loading is shown in Fig. 19. It can be seen from Fig. 20 that, in general, the cumulative fatigue damage over time obtained from the effective notch stress approach is lower for the hotspot 1 than the hotspot 2. It should be also noted that the fatigue damage is limited in the interval
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K. Tran Nguyen et al. / International Journal of Fatigue 43 (2012) 197–206
without corrosion which corresponds of the good corrosion protection coating.
grateful to Dr George Wang for his initiative to promote this scholarship.
7. Conclusion
References
Fatigue strength assessment of a side-longitudinal stiffener considering the two most probable crack initiation points in a double hull oil tanker has been done here based on global and local structural finite element models. The analyses are performed for two basic loading conditions accounting for the expected operation time in each of the considered conditions. The finite element models are composed by shell and solid elements using ANSYS software and applying advanced sub-modeling techniques. The effective notch stress approach cannot be directly used for complex structures without sub-model techniques, which require additional modeling and computational effort. It does, however, allow the effects of a local weld shape and radius at weld toe to be considered. The global finite element model of the amid-ship region of a tanker was subjected to two different dynamic loads, one is due to the global bending moment and another one is due to the lateral pressures in the full and ballast loading conditions respectively. A local detailed finite element analysis was performed to obtain the overall stress distributions at the notch surface of weld toes at the two critical hotspot points. Based on the evaluation of the global, local and effective notch stress for FE models, it was found that the higher order elements and mesh sizes have a significant effect on the assured convergence of results. The time-dependent notch stresses as a result of corrosion degradation were analyzed based on the reference nonlinear corrosion wastage model. As a result of the performed analysis, the total cumulative corrosion-fatigue damage at two hotspot points is rather high in all the loading cases after the initiation of failure of the corrosion protection system. It has been found that the fatigue damage at point 2 is higher than the one at point 1. The hotspot 2 location is the weakest point of the welded joint from the fatigue damage point of view. The fatigue damage assessment was based on the effective notch stress approach, being one of the most practical methods in combination with detailed finite element analysis. It has been recognized that the calculated local notch stress around the singularities of welded joints of the structural details depends very much on the structural idealization, the thickness scantling, the element types and the mesh subdivision. Acknowledgements The work of the first author has been financed by a Ph.D. scholarship from ABS, the American Bureau of Shipping. The authors are
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