Procee~ngs of the Eleventh (2001) International Offshore and Polar Engineering Conference Stavanger, Norway, June 17-22, 2001 Copyright 2001 by The International Society of Offshore and Polar Engineers ISBN 1-880653-51-6 (Set); ISBN 1-880653-55-9 (VoL IV); ISSN 1098-6189 (Set)

Recommended Hot Spot Analysis Procedure for Structural Details of FPSOs and Ships Based on Round-Robin FE Analyses

Wolfgang Fricke Technical University Hamburg

Harburg, Germany

ABSTRACT

As part of the Joint Industry Project 'FPSO Fatigue and Frac- ture Capacity', a Special Task Group with nine participants per- formed investigations regarding finite element (FE) modelling and analysis of typical structural details in FPSO's (Floating Produc- tion, Storage and Offioading Units) as well as in ships. The purpose of this special effort was to develop recommendations on appropri- ate hot spot stress methods and S-N data for fatigue strength design. In total, five details with different characteristics, from both geometry and fatigue loading perspectives, were selected for which stress measurements and fatigue tests are available. Various finite element models were developed by participants, using different types and sizes of elements, modelling and stress evaluation tech- niques as well as FE programs. Comparisons between the analysis results and measured stresses near the weld toes allow conclusions to be drawn. Three different stress extrapolation techniques for predicting hot spot stresses at the weld toes were investigated. The resulting hot spot stresses, together with the estimated fatigue lives, are compared against the existing design S-N curves published by the International Institute of Welding (IIW). It was concluded that the hot spot stresses predicted using the three stress extrapolation techniques, where the element sizes and stress evaluation points are determined by the plate thickness, can be used with the current design S-N curves. Most significantly, one of the recommended methods requires no stress extrapolation, which is considered an attractive and practical alternative to the existing practices devel- oped by class societies. This method will provide significant saving on analysis efforts during design.

KEY WORDS: Stress analysis, hot spot stress, finite element method, fatigue, welded joint

INTRODUCTION

The hot spot stress approach for the fatigue strength assessment of welded joints is based on the assumption that the local stress increase at the weld toe can be subdivided into two parts, one governed by the structural (i. e. macro-geometrical) stress increase and the other created by the localized notch stress due to the weld toe itself which is restricted to a region of approx. 2 - 3 mm around the toe. Furthermore, it is assumed that the fatigue assessment can be based on the first part, i. e. the structural stress at the 'hot spot', together with an appropriate S-N

curve, which implicitly considers the effects of the localized notch and, furthermore, is valid for a certain class of weld shapes and materials. Regarding the hot spot stress, experimental and analytical procedures have been derived for its determination by extrapolating the structural stress outside the localized notch-affected zone to the weld toe. The approach was firstly applied in the 1970's to tubular joints of offshore structures, where the increase in structural stress can be very high due to local bending of the tubular shell close to the connection between brace and chord (Almar-N~ess, 1985).

The hot spot stress approach was later applied also to welded plate structures (Radaj, 1990)being typical for FPSO's (Floating Production, Storage and Offloading Units) and ships. Here, three different types of hot spots at weld toes can be identified which are exemplified in Fig. 1: a) b) c)

at the weld toe on the plate surface at an ending attachment at the weld toe around the plate edge of an ending attachment along the wdd of an attached plate (weld toes on both the plate and attachment surface).

Figure 1. Types of Hot Spots in Welded Structures

For weld toes on a plate or shell surface, i. e. types a) and c), the structural stress can be defined as the sum of the axial and bending part of the stress distribution in the thickness direction (Niemi, 1993). How- ever, a unique definition of the structural stress at plate edges (weld toe type b), which can be used for fatigue strength assessment, is not possi- ble. Therefore, extrapolation of edge stresses is currently regarded as the only practical way for the determination of hot spot stresses.

The hot spot stress approach has often been criticized. Especially the problem of defining appropriate reference points for the stress extrapolation created many debates. Several codes and guidelines in various industrial sectors recommend different procedures for the

89

determination of hot spot stresses and S-N curves. Even in the shipbuilding and offshore industry, the procedures established by the classification societies and other authorities are diverging. Uncertainties about the suitability of the hot spot stress approach have been raised by round-robin analyses such as ISSC (1997) showing large scatter and differences between analysis results and measured stresses.

The industry, however, considers the hot spot stress approach as a very practical approach, offering a better alternative compared to the traditional nominal stress approach for the assessment of individual joint geometries in ships and FPSO's, which vary from detail to detail due to different scantlings and geometrical configurations. As large differences in fatigue assessment procedures as well as under-predicted fatigue lives cannot be tolerated, much effort has been spent into further investigations of the hot spot stress approach within the Joint Industry Project (JIP) "FPSO Fatigue Capacity" with 18 partners, coordinated by Det Norske Veritas. Within this project, a special task group performed investigations to answer the following questions: 1. Which ways of modelling yield hot spot stresses with sufficient

accuracy for typical structural details? 2. How correlate certain types of stress extrapolation with S-N curves

available? It was intended to perform round-robin stress analyses on a number

of typical details where local strain measurements and fatigue test data are available, allowing comparison with stress and life calculations. In total, nine partners have participated in the work, offering a wide range of modelling and evaluation techniques as well as finite element analysis programs. As certain procedures and ideas about stress determination and evaluation exist, it was decided to include all of them in the analysis rather than systematically varying certain modelling parameters. Insofar, the round-robin stress analysis reflects current techniques from which recommendations for appropriate procedures can be derived. Further questions arising from the analysis are intended to be investigated in Phase II of the project.

It should be noted that the investigation is focussed on the fatigue assessment of weld toes only and not on possible cracks originating from the root of welds with incomplete penetration which are usually assessed on the basis of the nominal stresses in the weld throat. Also the assessment of stress peaks at rounded plate edges are outside the scope of this paper.

SELECTION OF STRUCTURAL DETAILS

The structural details were selected considering the following criteria: all three types of hot spots shown in Fig. 1 should be included plate bending caused by the attachment should be included, which

is quite typical for details in ships and FPSO's strain measurements and fatigue tests should be available; models

tested within the JIP are preferred because detailed or additional information is available

Five details have been selected for the round-robin hot spot stress analysis, which are shortly described in the following:

Detail l: ISSC Model The first detail, the model for the study of ISSC (1997) already

mentioned and further described by lwahashi et al. (1998), is the con- nection of a buckling stiffener 100x12 to the flange of a T-shaped lon- gitudinal (web 350x12, flange 150x20). This model being typical for FPSO and tanker structures was tested experimentally in the Japanese research project SR 219 so that local strain measurements are available, however no fatigue test data, as turned out later. The finite element model shown in Fig. 4 gives an impression of the structure. The longi- tudinal is subjected to bending and shear, creating an increased hot spot stress at the welded connection with the buckling stiffener. It should be noted that the fillet weld has an increased leg length of 13 mm to avoid root failure. The hot spot belongs to type a) in Fig. 1.

Detail 2: Gussets on Plate Edge The second model, gussets on plate edges shown in Fig. 2a, has been

taken from tests performed by HHI in the IIP (Kim, 1999). Two 150 mm long and I0 mm thick gussets, representing face bars with tapered ends, are fillet-welded to the edges of a plate strip 60 x 10 ram, which is subjected to tensile stresses. The critical weld toe belongs to type b) in Fig. 1.

Detail 3" Doubling Plate The third detail is the doubling plate shown in Fig. 2b, where the

critical weld toe on the plate surface belongs to type c) in Fig. 1. The model considered here was investigated in the Japanese research project SR 202 (Yagi et al., 1991), so that strain measurements and fatigue tests are available. When the parent plate is subjected to tension, the one- sided doubling plate causes secondary bending. This has to be consid- ered in the analysis, creating some modelling problems in connection with shell elements.

In the course of the analysis, relatively large differences between the Japanese measurements and the analytical results were found. These are most likely caused by angular distortion during the welding of the doubling plate on the plate strip. As pronounced stress magnification due to misalignment shall be considered in the applied stress rather than in the design S-N curve, a stress magnification factor Km= 1.2 and a certain stress gradient were estimated for the local stress on the basis of additional tests and calculations performed.

Detail 4: Hopper Corner Model The fourth detail is the hopper comer shown in Fig. 2c which was

also tested in the JIP. The critical weld is located at the transition from the 10 mm thick flange to the sloped hopper plate. The structure is subjected to a vertical force, producing bending and shear in the beam. The stress increase will be referred to the nominal bending stress at the knuckle under the assumption of full effective breadth. The weld toe belongs to type c) in Fig. 1.

Detail 5: Load Carrying Fillet Welds The last detail is again a model tested in the JIP, i. e. the fillet-

welded connection between a vertical I-beam and a vertical plate, which represents a stiffener connection being subjected to shear and bending, see Fig. 2d. Reference stress is again the nominal bending stress at the upper edge of the vertical plate. The weld toe at the hot spot belongs to type b) in Fig. 1.

c) Detail 4 d)Oetail 5

/

Figure 2. Details 2 - 5 selected for Round Robin Analysis (Detail 1 is shown in Fig. 4)

90

FINITE ELEMENT MODELLING AND STRESS EVALUATION

In order to find appropriate techniques for modelling welded struc- tures as well as evaluating the hot spot stress increase due to structural effects, a great variety of models and ways of evaluation was taken into consideration. In principle, the different types of modelling can be divided into two groups, illustrated in Fig. 3: * using plate or shell dements without weld representation; the

elements are located in the mid-plane of the associated plate; in

In most cases, the element length and breadths close to the weld toe were chosen as t x t (t = plate thickness). Fig. 4 exemplifies the model- ling by Detail 1. Smaller element dimensions (typically t/2 or t/4) were selected for meshes indicated by 2Solid2Ow(f) and 4Solid8w. Additional remarks on specific modelling aspects are given in the following.

Shell elements t welds) F /4 = 98 kN , - - -

.o0e,

i i i?i

w = attachment width w

Symmetry

Figure 3. Typical Finite Element Models for the Welded Joint

Shell Model

some cases the weld is included in a simplified way using solid elements with the possibility to model the fillet welds Detail 1

t f /

\ I \1 \ |

Shown in Fig. 1 Support

Variations are seen in different element types offered by the finite element programs as well as element sizes chosen by the analyst. The following dement types were considered in the investigation, using special short names as mentioned below:

1Solid20w and 2Solid20w 20-noded isoparametric solid element, used with either one or two

element layers over full or half plate thickness modelled (prefix 1 and 2, respectively). The welds are generally included (suffix w), in some models very simply disregarding the root gap (see Fig. 3).

4Solid8w 8-noded solid element, normally used with four layers over the plate

thickness. The welds are included in the models (suffix w).

Solidpw Higher-order solid elements (geometric p-elements) with refined

mesh and optimised shape function in the critical area. The welds are included in the models (suffix w).

Shell& Shell8r and Shell8p 8-noded shell element without weld representation. In case of off-

sets, either rigid links (suffix r) or a plate connection between the mid- planes of the plates (suffix p) are arranged.

Shell4, Shell4r and Shell4p Same as above, but with 4-noded shell elements, partly having con-

stant stress state (css) and partly improved in-plane bending behaviour.

Shell8w 8-noded shell model with simplified weld representation by arrang-

ing a reinforced plate strip at the foot of the attached plate, having the thickness increased by one leg length and extending to the actual weld toe position. The endings are sloped, meeting the weld toe position on the parent plate.

Figure 4. Typical Finite Element Modelling

In Detail 1 (ISSC-Model), the reinforced fillet weld attracts addi- tional stresses which is considered in one shell model containing the weld in a simplified way (ShellSw). In almost all shell models of Detail 2 (Gusset on Plate Edge) the gussets were arranged directly at the edge of the longitudinal plate edge except for one model where the shell elements were arranged in the mid-plane of the gusset and connected by a reinforced plate strip with sloped ends (Shell8w). Detail 3 (One-Sided Doubling Plate) was generally modelled taking the offset into account. In case of shell elements, either rigid links or vertical plate elements were arranged, see Fig. 5a.

a) Doubl ing F' "

rigid links or p la te elements

b) Hopper Corner

Figure 5. Modelling of Offsets in Shell Models

91

One specific problem of Detail 4 (Hopper Corner Model) is the off- set between the intersecting horizontal, vertical and sloped plate at the critical point. This is automatically accounted for in solid models, while it is considered only in part of the shell models by a plate connection between the two intersection points, see Fig. 5b. These models are denoted by Shell8p and Shell4p. An additional study showed that this offset reduces the stresses in the actual structure by up to 10 % in the vicinity of the hot spot. For Detail 5 (Load Carrying Fillet Welds), again one shell model contains the weld in simplified form (Shell8w).

The stresses were evaluated with two objectives, (a) to compare the computed stresses with measured values in the area close to the hot spot and (b) to extrapolate the stresses to the hot spot using common tech- niques, from which the following three were selected: 1. Linear extrapolation over reference points 0.5 and 1.5 x plate

thickness t away from the hot spot (technique preferred by most classification societies)

2. Linear extrapolation over reference points 0.4 and 1.0 x plate thickness t away from the hot spot (technique recommended by the International Institute of Welding, see Hobbacher, 1996)

3. No extrapolation, but considering the stress value at 0.5 x plate thickness t as the relevant hot spot stress

Typical stress evaluation paths are indicated in Fig. 3. First compari- son of the analysis results showed that a better agreement between the results from the different models and from the measurements is achieved if the distance of the read-out-points (ROP's) is measured to the hot spot as modelled, i. e. to the weld toe if the weld is modelled or, else, to the structural intersection point, if the weld is not modelled. The same applies to the point where the stress is extrapolated to. The justifi- cation for this procedure, which affects the results for sheU models without weld representation, is that the stress at the fictitious weld toe position is in many cases too low due to the reduced stiffness compared to the real structure. This means on the other hand, that the proposed extrapolation to the structural intersection point may yield conservative results - a tribute to simple modelling.

A great variability exists in selecting the type of stress and in evalu- ating the stresses at the desired locations. The selected details do not show significant differences between principal and directional stress (perpendicular to the weld toe) so that the type of stress does not affect the results here. Either nodal stresses or element stresses are evaluated, the latter normally extrapolated linearly from the integration points to the plate surface or edge and in some cases averaged to obtain a mid- side stress. Particularly for 4-noded shell elements, different results were obtained depending on the shape function and the consideration of

in-plane stress components. By comparing all results, conclusions are drawn with respect to appropriate ways of determining hot spot stresses.

PRESENTATION AND DISCUSSION OF THE RESULTS

The evaluated stresses are summarized in Figs. 6 - 10, where also the measured stresses are shown. The nominal stress has been set to unity for details 2 - 5, so that the results are actually hot spot stress concentration factors (SCF's). It should be kept in mind that also the measured stresses contain some uncertainties which was revealed in the tests by scattering strains obtained from different comparable locations and test models. The right part of the figures shows the stresses at read- out-points (ROP's) selected by the participants. These ROP's are located at certain distances from the hot spot modelled (i. e. weld toe or structural intersection point, if the weld is not modelled, see previous chapter) and can be identified as nodal or element stresses (at mid-side or integration points) in those cases where the element length equals the plate thickness t (exceptions are finer meshes denoted by 2Solid2Ow, 4Solid8w and Solidpw). The left part gives the stresses extrapolated to the hot spot according to the three methods mentioned above. The stresses at the reference points were interpolated by the participants by curve fitting.

In order to facilitate the interpretation of the results, different types of symbols were chosen for the results from solid and shell models. The symbols have been connected by straight dotted lines with smaller dots for shell models. These straight lines appear to increase the scatter, however, relevant are only the symbols. The measurement results are plotted using continuous lines. They have not been extrapolated. Fine mesh solid models with higher-order elements, which play a special role, can be recognized by: * open squares (p-elements Solidpw) full squares (2Solid20w(39) In the following, the results are discussed in detail tbr the different models.

Detail I (ISSC-Model), Fig. 6 The measurement shows a stress of approx. 140 MPa at a distance

10 mm away from the hot spot (ISSC, 1997). Only one coarse solid model is included (1Solid2Ow), yielding slightly higher stresses. Here, the results are somewhat affected by the singularity at the hot spot, although the stress was averaged over the attachment width (buckling stiffener plus welds) by arranging relatively wide solid elements. On the contrary, the very fine solid mesh (2Solid2Ow(f)) shows smaller stresses with a steep stress increase to the hot spot.

220 , 220

200 200

~180 ~180

~160 - r 16o

~140 ~ E14c

~100 ~ 10

80 - 8C

Re~ P~. (t=2Omm)

i i T i r r

0 10 20 30

~Exper iment

,,-I-- ,Shell4

"~- .Shell8

- .0- .Shell8w

- ~- .Shell8

- -I-- .Shell4

- "~- .Shell8

- ,o- .Shell4(css)

- -('-- .SheU4 1Solid20w

~2So l id2Ow( f l

:

40 50 60

distance ROP's to hot spot [mm]

Figure 6. Stress Results for Detail 1 (ISSC-Model)

92

The results of the shell models are fairly scattered. Looking again at the location 10 mm away from the hot spot, three results are relatively close to the measured ones, while four others are remarkably lower. The reason for this could not be clarified as the stress evaluation points and methods are quite different (at nodes, at element centres, and extrapo- lated from integration points to the element edge).

The general trend, that solid elements overestimate and shell ele- ments underestimate the stresses, has been observed also in other stud- ies (e. g. ISSC, 2000). Poutiainen and Niemi (2000) showed that this happens in those cases where a web is arranged below the plate with a longitudinal attachment. In order to limit the under-estimation of stresses, the in-plane bending behaviour of plates should be improved (the 4-noded elements showing the lowest results have only constant stress state (css)) and the element width might have to be restricted. Niemi (1995) proposed the 'attachment width' (thickness of attachment plus twice weld leg length) for the breadth over the two elements in front of the weld. Furthermore, the consideration of the relatively thick

When looking at the hot spot stresses extrapolated over 0.5t/1.5t, the scatter is moderate within 10 % (152 MPa 15 MPa). It increases if the extrapolation is performed over 0.4t/1.0t. This is obviously a result of the relatively coarse meshes, matching better the first extrapolation technique.

Detail 2 (Gussets on Plate Edge), Fig. 7 The measurement shows a mean structural stress increase by 1.7 at a

location 5 mm away from the hot spot, however with a large scatter. If the two smallest stresses resulting from the fine meshes with

higher-order solid elements (2Solid2Ow(j') and Solidpw) and one from the 4-noded shell elements with constant stress state (css) are excluded, the results are fairly close together. This can also be seen in the hot spot stresses extrapolated over 0.St/1.5t, which are between [.85 and 2.08, i. e. _+6 %. The different idealisations of the root gap and stress evalua- tions in solid models (averaged over thickness or taken at comer) have little effect on the results. Again, the scatter is much higher if the stress is extrapolated over 0.4t/1.0t, which is due to the steep stress increase in

weld slightly increases the stress (by approx. 2 %).

3.2

3.0

2.8

~, 2 .6

2.4

~ 2.2

~2.0

-~1.8

~ 1.4

1.2

1.(1

0.8

, , 3.2

3.0

2.8

(n 2'6

~2.4

02.2

~2.0

1.4

1.2

1.0

0.8

Ref. Pts. (t=10mm)

front of the hot spot.

' !~Exper iment 1Solid20w

--]- - S olidpw : 4Solid8w 0 4Solid8w

~a~.- 2Solid20w --Jk.-- 2Solid20w

= 2Solid2Ow(f) - .0- .Shell8w - .-t..- .Shell4

I I - -I--,Shell4

. :

10 5 20 25 30

d is tance ROP 's to hot spot [mm]

Figure 7. Stress Results for Detail 2 (Gussets on Plate E~dge)

2,2 . , 2.2

2.0 I 2.0

~1.8 ~)1.8 '-- I::lZ

1.2 1.2

1.0 -- 1.0

Ref. Ots. (t= 1gram)

I J--O'--Experiment I I i - - ,so, 2ow j

I --E~-- Solidpw I

i~ I - -e" 1Slid20w

~ -)

Detail 3 (One-Sided Doubling Plate), Fig. 8 The results are fairly close together at the hot spot and match the

measured values containing the stress magnification factor Km explained earlier. The scatter in the results is mainly due to the problem of correctly modelling the offset in the shell element models. Most of the results originating from shell models with connections by plates or rigid links are slightly above the other ones.

The remaining results for the coarse solid models are very close together, also when looking at the extrapolated stresses.

Detail 4 (Hopper Corner Model), Fig. 9 At a first glance, the results appear rather scattered. Only the mean

value from the measurement, which also showed a large scatter, has been plotted.

Five models, where the misalignment illustrated in Fig. 5b has not been considered (Shell4 and Shell8) show the highest results at 5 mm distance from the hot spot. If these results as well as those from the

models with higher-order solid elements (2SoIid2Ow09 and Solidpw) are excluded, the scatter is fairly small, resulting in a hot spot stress increase between 1.96 and 2.16 if extrapolated over 0.5t/1.5t i. e. +5% from the mean.

Detail 5 (Load Carrying Fillet Welds), Fig. 10 Also for this model, the results reveal a high scatter. As for detail 2,

the stress singularity plays a part, increasing additionally the stress -values close to the hot spot. It is unclear why the measurements show rather small values.

The scatter is much reduced, if the results for the fine meshes with higher-order solid elements (2Solid2Ow(D and Solidpw) as well as the lowest results for the 4-noded shell elements with constant stress state (css) are again excluded. Then the hot spot stress increase varies between 1.64 and 2.18 (_+10%) if extrapolated over 0.5t/1.5t, where the lowest result refers to a model with simplified weld representation (ShellSw).

2.8 ~ ,

2.6

2 .4

~ 2.2 ~ 2.0 ~.1.6

~ 1.4

~ 1.2

1.0

0.8

Ref . Pts . ( t= lOmm)

4,

0 5

- - (>-Exper iment - -I-- ,Shell4 - -I-- ,Shell4 - "~.- ,ShellSp - SK- ,Shell8 - -X- .Shell4p - -&- .ShellSp . .o. ,Shell4(css) - .-P- ,Shell4

1Solid20w r " , .--El-. Solidpw

" ' . 4SolidSw ~k- - 2 Solid20w

" '~: ]~1~ ~- . _ : " " " ~ . . ---=--2Solid2Ow(f)

~ i I i i I i I i,,

0 15 20 25 30

distance ROP's to hot spot [mm]

Figure 9. Stress Results for Detail 4 (Hopper Comer Model)

3.2

2.8

2.6

1.0

0.8 u2. ~. m.

Ref. Pts. (t=lOmm)

\\~ \ \,1

~',~L ~ %

~-xper lmen l

- -+- ,SheU4

- -I-- ,Shell4

- ~- .Shell8

- -~-,Shell8

- .o. ,Shell4(css)

, , , " , , ~

5

|

- N.-,, 'Shell4

- " .Shell8w ~ ISo l id20w

'--0--" S olidpw

- -A- -2Sol id20w

--@=- 4 SolidSw

~4So l id8w

- '=" - 2 S olid2Ow(t)

t:- = k

i i / i i i i

10 15 20 25 30

distance ROP's to hot spot [mm]

Figure 10. Stress Results for Detail 5 (Load-Carrying Fillet Welds)

94

DESIGN S-N CURVES

Available fatigue test data, i. e. fatigue lives obtained for given load levels, can be used to verify if the computed hot spot stresses correlate with standard S-N curves. Fatigue test data are available for details 2, 4 and 5 (Kim, 1999) and also for detail 3 (Yagi et al., 1991). In addition, models similar to details 1 and 3 have been analysed and tested by HHI, which are included in the present analysis as Model 1 (Longitudinal Gussets) and Model 3 (Two-Sided Doubling Plates). It should be noted that only tests with high R-ratio are taken from the data by Kim (1999).

The verification is performed on the basis of lower-bound hot spot SCF's from the analysis. In this way the comparison with standard S-N curves is conservative. As discussed before, the results from the fine meshes with higher-order solid elements as well as those from the 4- noded shells with constant in-plane stress state have been excluded which means that S-N curves derived are associated to analyses with certain modelling and extrapolation techniques.

The lowest SCF-values are mostly determined by solid models using 8-noded elements with dimensions t/4 x t/4 x t/4. The additional models 1 and 3 were also analysed by this technique and also by shell elements.

It is interesting to note that the results from the very fine solid mod- els (2Solid2Ow(f)), extrapolated over 0.4t and 1.0t, fit quite well with the other values extrapolated over 0.5t/1.5t. However, the results obtained from the p-elements are below these values.

The S-N plot in Fig. 11 shows the fatigue lives in relation to the hot spot stress range for the first extrapolation technique, i.e. nominal stress range multiplied by the lowest calculated hot spot SCF's extrapo- lated over 0.5t/1.5t. The details 4 and 5 show generally higher lives which are assumed to be due to beneficial residual stresses found in detail 5 and to a failure criterion defined by a relatively long crack. Furthermore, the results for model 1 and details 2 - 3 are closer to the lower bound due to the fact that only the worst of four competing hot spots in the models are represented.

In addition, the S-N curve FAT 100, characterized by a slope expo- nent m = 3 and a reference value of 100 MPa at 2 million cycles, is plotted in the figure, representing the lower bound of all results. The same evaluation for the other extrapolation techniques, which are omit- ted here, shows also FAT 100 as lower bound for the results extrapo- lated over 0.4t/1.0t, while FAT 90 is the lower bound for the results at 0.5t. It should be noted that all test data used here is related to joints with plate thickness ranging from 10 to 15 mm.

RECOMMENDATIONS FOR HOT SPOT STRESS ANALYSIS

Based on the results of the round-robin finite element analysis described above, the following recommendations can be given.

Hot spot stresses are calculated assuming linear material behaviour using an idealised structural model with no fabrication-related mis- lOOO

I00.

10

alignment. The latter have to be considered in certain joints where their pronounced misalignment effects are possible, such as plate butt welds, cruciform joints and transverse fillet welds on free plates, .by appropri- ate Kin-factors defined e. g. by Hobbacher (1996). The extent of the. local finite element model has to be chosen such that effects on the structural detail considered are sufficiently small and reasonable bound- ary conditions can be formulated.

In plate structures, three types of weld toes can be identified, which are exemplified in Fig. I. The relevant hot spot stress is the principal stress on the surface or at the edge of the plate acting approximately perpendicular to the weld toe (45 to 90).

Models with thin plate or shell elements or alternatively with solid elements may be used. It should be noted that on the one hand the arrangement and type of elements have to allow for steep stress gradi- ents as well as for the formation of plate bending, and on the other hand, only the linear stress distribution in the plate thickness direction needs to be evaluated with respect to the definition of structural stress. The following methods of modelling are recommended, see also Fig. 3:

Plate and Shell Models. A simple modelling is offered by thin plate and shell elements which

have to be arranged in the mid-plane of the structural components. 8- noded elements are recommended particularly in case of steep stress gradients. Care should be given to possible stress underestimation especially at type b) weld toes in connection with 4-noded elements, which should contain at least improved in-plane bending modes.

The welds are usually not modelled except for special cases where the results are affected by high local bending, e. g. due to an offset between plates or due to a small free plate length between adjacent welds. Here, the weld may be included by vertical or inclined plate elements having appropriate stiffness or by introducing constrained equations to couple the node displacements. Particularly for weld toes of types b) and c), a simple alternative for weld modelling is offered by the arrangement of a reinforced plate strip at the foot of the attachment, having a thickness increased by one leg length and sloped ends, extending to the actual weld toe positions.

Solid Element Models: An alternative particularly for complex cases is offered by solid ele-

ments which need to have a displacement function allowing steep stress gradients as well as plate bending with linear stress distribution in the plate thickness direction. This is offered, e. g., by isoparametric 20-node elements (with mid-side nodes at the edges) which means that only one element in plate thickness direction needs to be arranged. An easy evaluation of the membrane and bending stress components is then possible if a reduced integration order with only two integration points in the thickness direction is chosen. Modelling of the welds is generally recommended and easily possible as shown in Fig. 3.

1.0E+04 1.0E+05 1.0E+06 1.0E+07

N (cycles)

Figure 11. Fatigue test results vs. hot spot stress range based on lowest calculated SCF's extrapolated over 0.5t/1.5t

95

Element Sizes: For both types of modelling, the dimensions of the first two or three

elements in front of the weld toe should be chosen as follows: Weld toes of types a) and c): The dement length should correspond

to the plate thickness. In the transverse direction, the plate thickness may be chosen again for the breadth of the plate elements. However, the breadth over the first two elements should not exceed the 'attachment width', i. e. the thickness of the attached plate plus 2 x the weld leg length (in case of type c: the thickness of the web plate behind plus 2 x weld leg length). This attachment width may also be taken for the width of solid elements in front of the weld toe, see Fig. 3. Still open is the question how the element size has to be defined e. g. for bulb profiles. Furthermore it should be noted that a much finer mesh is needed in case of 8-node solid elements.

Weld toes of type b): For weld toes at the plate edge, the plate thick- ness is principally not a suitable parameter to determine the element size and stress extrapolation points. A further study (Fricke and Bog- dan, 2001) shows that fixed values can better be used to describe the stress increase at in-plane notches. From this study and from details 2 and 5 of the current study it can be concluded that higher-order ele- ments with element lengths of 10 x 10 mm together with a linear extra- polation over the mid-side points yield conservative results. Therefore, it is recommended to use element dimensions fixed to these dimensions.

Stress Evaluation: The structural stress components on the plate surface should be

evaluated along the paths shown in Fig. 3 and extrapolated to the hot spot. Recommended are stress evaluation points located at distances 0,5 t and 1.5 t away from the hot spot modelled, where t is the plate thickness at the weld toe. If the weld is not modelled, the hot spot is the structural intersection point modelled. In case of type b) weld toes, fixed distances of 5 mm and 15 mm are recommended.

If a relatively coarse mesh with the element sizes mentioned above is chosen, the stresses may be evaluated as follows: * In case of plate or shell elements the surface stress may be evalu-

ated at the corresponding mid-side points (i. e. taking the mean value of the element stresses at the adjacent corners). At weld toes of type c) the stress may be averaged over the width of the attach- ment behind by taking the surface stress in the element centres as also shown in Fig. 3.

* In case of solid elements the stress may be extrapolated linearly to the surface centre (usually after averaging the stress components at each of the the two layers of integration points)

At weld toes of type b), only part of plate bending obviously needs to be considered. Further investigations are considered to be neces- sary as such cases are outside the scope of the present analysis.

Fatigue Assessment: If the hot spot stress is evaluated by linear extrapolation in the way

described, the fatigue strength may be assessed with a usual design S-N curve based on hot-spot stresses (e. g. Hobbacher, 1996).

Alternatively a simplified approach without any stress extrapolation seems to be reasonable where the stress is taken at the location 0.5 t (resp. 5 mm for weld toes of type b) away from the hot spot modelled and assessed with a design S-N curve reduced by one fatigue class.

If the hot spot stress is evaluated from strain measurements or from refined models with improved finite elements, a stress extrapolation over reference points at distances 0.4 and 1.0 x plate thickness or a quadratic extrapolation is recommended in line with Hobbacher (1996).

CONCLUDING REMARKS

The present study has been used in the JIP together with other data to derive a design hot spot S-N curve (Maddox, 2001). Here, a lower S-N curve was found, which might be due to additional test data and in particular to the inclusion of larger plate thickness (up to 25 ram).

The present study shows that further investigations are required to clarify especially the following items: Modelling and stress evaluation for very thick components, such as

bulbs of profiles Extent of plate bending to be considered at type b) weld toes Type of stress and evaluation in case of complex stress fields

Finally it should be noted that root cracking at fillet welds is not covered by the hot spot stress analysis procedure. Appropriate and practical procedures for the analysis of the relevant stresses in complex structures and their fatigue assessment are still to be developed.

ACKNOWLEDGEMENTS

The JIP has been supported by 19 participants under coordination of Det Norske Veritas. An overview over the project is given by Lotsberg (2001). The present study has been managed by Germanischer Lloyd. Hyundai Heavy Industries, as a participant of the JIP, performed the fatigue tests with small scale specimens of typical fillet welded joints in ship structures, which was one of the main tasks in the JIP forming the basis of the investigations described in the paper.

Nine participants contributed with great enthusiasm to the round- robin analyses: Weimin Chen (Umoe Technology), Ben Feron (Blue- water), W.S. Kim (Hyundai Heavy Industries), Helena Polezhaeva (Lloyd's Register of Shipping), Philippe Rucho (Bureau Veritas), Armin S~ibel (Germanischer Lloyd), Tore Ulldand (Aker Maritime), Richard Yee (American Bureau of Shipping) and also Y.-S. Choo (National University of Singapore). The author wishes to thank all of them for their work and all participants of the JIP for their valuable comments and permission to publish the results.

REFERENCES

Almar-N~ss, A. (1985). "Fatigue Handbook - Offshore Structures." Tapir Publishers, Trondheim.

Fricke, W. and Bogdan, R. (2001). "Determination of Hot Spot Stress in Structural Members with In-Plane Notches Using a Coarse Mesh." IIW-Doc. XIII- 1870-01, International Institute of Welding.

Hobbacher, A. (1996). "Fatigue Design of Welded Joints and Compo- nents." Abington Publishing, Cambridge (UK).

ISSC (1997). "Report of Committee ILl - Quasi-Static Response." Proc. of 13 th Int. Ship and Offshore Structures Congress (Ed. T. Moan and S. Berge), Elsevier Science.

ISSC (2000). "Report of Committee II.1 - Quasi-Static Response." Proc. of 14 th Int. Ship and Offshore Structures Congress (Ed. H. Ohtsubo and Y. Sumi), Elsevier Science.

Iwahashi, Y. et al. (1998). "Finite Element Comparative Study of Ship Structural Detail." Marine Structures 11, pp. 127 - 139.

Kim, W. S (1999): Fatigue Tests of Typical Welded Joints. Hyundai Heavy Industries Co., Ltd. Ulsan (unpublished).

Lotsberg, I. (2001). "Overview of the FPSO - Fatigue Capacity JIP." Proc. of OMAE'01, ASME, Rio de Janeiro.

Maddox, S. (2001). "Recommended Design S-N Curves for Fatigue Assessment of FPSOs. ISOPE' 2001, Stavanger.

Niemi, E. (1993). "Recommendations Concerning Stress Determination for Fatigue Analysis of Welded Components". IIS-IIW-1221-93, Abington Publishing, Cambridge (UK).

Poutiainen, I. and Niemi, E. (2000). The Determination of Hot Spot Stress in Gusset Structures Using a Coarse Element Mesh. IIW-Doc. XIII- 1820-2000, International Institute of Welding.

Radaj, D. (1990). Design and Analysis of Fatigue Resistant Structures. Abington Publishing, Cambridge (UK).

Yagi, J.; Machida, S.; Tomita, Y.; Matoba, M.; Kawasaki, T. (1991). "Definition of Hot Spot Stresses in Welded Plate Type Structure for Fatigue Assessment." IIW-Document IIW-XIII-1414-91, Interna- tional Institute of Welding.

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