Fatigue assessment of welde aluminium ship details

Fatigue Assessment of Welded Aluminum Ship Details

Biird Wathne Tveitenl Torgeir Moan2 (M)

ABSTRACT

The main objective of this paper is to establish and verljj methoa!r for the assessment of the fatigue strength of welded aluminum ship details. A nominal stress range approach, a structural stress range approach, and a notch stress range approach using curves have been applied to numerous test SN-data obtained porn constant amplitude fatigue tests of ahzminum stlfenew’girder connections. i%e emphasis has been placed on review and verification of alrea~ published hot-spot stress extrapolation procedures for plate structures, and development and verl~cation of a new robust and general method for the structural stress extrapolation to be used together with a hot-spot design SN-curve. The proposed extrapolation method has been based on the asymptotic behavior of the stresses adjacent to an idealized notch (“singularity’?. On basis of the fatigue test SN-data obtained in this study, relevant SN-curves to be used together with the new extrapolation procedure proposed in this work and with the alrea~ published extrapolation methods have been suggested. The new fatigue analysis procedure based on a structural stress approach has shown to provide an accurate and robust tool for predicting the fatigue strength of as-welded and profile ground fillet welded aiuminum details.

INTRODUCTION

Aluminum high speed vessels are increasingly applied as

large fast ferries in service around the world and

catamarans of more than 120 meters length have already been built and operated for some time, Ships are subjected to significant cyclic loading and are therefore vulnerable to fatigue failure. Until recently fatigue has not been an explicit design consideration for aluminum ships. It has been claimed that the fatigue strength of aluminum ship structures is sufficient when certain “allowable” stresses given in the ship rules are complied with. However, with the increasing size of aluminum ships fatigue may become

an important structural design criterion. Heggelund,

Tveiten and Moan (1998) have shown that fatigue can

actually govern the design of stiffener/web frame

connections at the top and the bottom of large aluminum high-speed catamarans. A more rational approach would then be to have explicit fatigue requirements. There are currently no fatigue design codes which are specifically established for the use in design of aluminum ships but DNV (1997) has issued a preliminary fatigue design code for aluminum ship structures based on a notch stress range

approach and corresponding SN-curves. Existing

aluminum design codes primarily deal with the design of aeronautic, automotive and civil engineering structures and none of these design codes are specifically established for the use in design of aluminum ships.

The main objective of this paper is to establish and verify methods for the assessment of the fatigue strength

1 Norwegian University of Science and Technology, currently employed at Halliburton AS 2 Norwegian University of Science and Technology

of welded aluminum ship details. A nominal stress range approach, a structural stress range approach, and a notch stress range approach using SN-curves have been applied

to numerous test SN-data obtained from constant

amplitude fatigue tests of aluminum stiffener/girder

connections.

SN-CURVE APPROACH

The basis for current design practice for ships subjected to

variable amplitude loading is primarily SN-curves

combined with the hypothesis of linear cumulative

damage, Miner-Palmgren hypothesis (Miner 1945). The SN-curves are based on experimental measurement of the fatigue life in terms of cycles to failure, N, for different loading levels under different environments. For the SN-curve approach, the initial and final crack depth are not an explicit design consideration but all possible cracks are treated as inherent uncertainties and a safe fatigue life is

defined according to a lower level confidence limit

obtained from statistical regression analysis on relevant set of fatigue test data. For welded joints where large tensile residual stresses are an inherent feature caused by the welding and the assembly process, the fatigue life is assumed to be solely dependent on the stress range, S, the “stress-range philosophy”.

Adopting the SN-curve approach together with the

Miner-Palmgren hypothesis, the criterion for fatigue

failure can be expressed as:

D=z+~~

1

l?i .

Sire’

iVj”

(1)

(2) (3) where ni is the number of cycles in stress range block (i) and nj is the number of cycles in stress range block (j), Si is the stress range in stress range block (i) and Ni is the corresponding number of cycles to failure and Sj is the stress range in stress range block (j) and N. is the corresponding number of CyCkSto faihre, & iS the stress range at some reference fatigue life, Nk (usually taken as

the stress range at 5.106 cycles), and al and ml are

geometricalhnaterial parameters obtained from constant

amplitude SN-curve tests. D is the cumulative damage index and in a constant amplitude stress history, D = 1, at failure. A is the allowable damage,

The Miner-Palmgren summation may also be

expressed in terms of an equivalent stress range, Sw, as:

(4)

where N is the fatigue life given by the total number of cycles to failure. Equation (4) can be rewritten for cases where different (a,m) sets have been applied for different regimes of the stress range as:

s [

~ni.(si)”’’+(sk)’”’+. ~n..(p. _JJp :

=

eq _{Ni + Nj}

1

where (i) is associated with stress ranges with fatigue life less than 5.106 cycles (the “knee-point” of the SN-curve), Q) is ass~ciated with stress ranges with fatigue life more than 5.10 cycles, and skis the stress range 5.106 cycles.

Constant amplitude fatigue tests of welded aluminum details in corrosive environments have to very little extent been reported in the literature. DNV (1997) has suggested

a modification of the SN-curve in air for welded

aluminum joints in corrosive environments without any protection (e.g, cathodic protection or protective paint) by introducing a parallel shift of the SN-curve by 30$Z0 downwards and including no slope correction or cut-off

level. The SN-curves for welded aluminum joints in

corrosive environments are based on fatigue tests reported by Paauw et. al. (1985).

STRESS RAISING EFFECTS IN WELDED STRUCTURES

Introduction

The SN-curve approach may be based on different

representations of the stress distribution in the vicinity of fatigue vulnerable areas. It is crucial to clearly define the stress level used in the fatigue assessment procedure so

that the stress range used in the fatigue design is

consistent with the stress range which was applied in the derivation of the SN-curve. The fatigue strength of welded aluminum joints depends largely upon the weld quality

such as initial defects, as well as local and global

geometrical parameters causing stress concentrations. For welded structures there are two main stress raising effects:

the effect of the structural discontinuity (global

geometrical effects), and the effect of the local notch at the weld toe (local geometrical effects). The actual stress

causing the fatigue cracking can be categorized as:

nominal stress, Gn, structural stress, q, and notch stress, ah (Figure 1). The nominal stress can be calculated from frame models or coarse global finite element models, while structural stress and notch stress calculations require a local finite element model.

Bracket

Figure 1 Stress distribution across the plate thickness and along the surface in the vicinity of a welded attachment

Calculation of the Structural Stress

The notch effects caused by the local geometrical

discontinuities at the weld toe have to be excluded from the structural stress. This can be achieved by carrying out an extrapolation procedure of the structural stress from

outside the region close to the weld toe which is

influenced by the local notch. The extrapolation points

must be located such that thenonlinear stress peak caused

by the local notch effects at the weld toe is not included in the stress results. At the same time, the points should be sufficiently close to catch the trend in the stress caused by global geometrical effects, e.g. brackets. The stress at the

extrapolation points can be obtained by strain gage

measurement on actual structural components, or by

means of numerical stress analysis.

To calculate the local stress distribution which

captures the stress raising effects due to the structural

discontinuities, a local finite element model with a

sufficient finite element mesh size to pick up the gross geometrical behavior of the joint has to be modeled. In contrast to the calculation of the nominal stresses where only frame models or coarse global finite element models

are sufficient, the calculation of the structural stress

requires more complex finite element models and

consequently higher computational efforts. The mesh

refinement of large, global finite element models at the hot-spot locations is not feasible. However the structural geometry at the hot-spot locations can be reanalyzed by means of the submodeling technique (also known as the

cut-boundary displacement method or the speeified

boundary displacement method). The displacements on the cut boundary of the global model are specified as boundary conditions for the local finite element model (the submodel).

The analyst has several possibilities for modeling the structural geometry at the hot-spot location, ranging from finite solid elements (three-dimensional elements), thick or thin finite shell elements, or a combination of these. Finite shell element models as well as coarse finite solid

element models (one finite element layer over the

thickness) are characterized by a linear stress distribution over the plate thickness. Therefore, both types of finite element modeling are suitable for the calculation of the structural stress since the nonlinear stress distribution due

to the presence of the weld toe in the thickness directions

is excluded. On the other hand, finite solid element

models with several finite element layers over the plate thickness attempt to show more or less accurately the nonlinear peak stress, depending on the element type (8 or

20 nodes), integration scheme, and number of finite

elements over the thickness. A thorough presentation of the finite element modeling technique is beyond the scope of this work. Niemi (1995) and Tveiten (1999) present comprehensive recommendations and studies concerning

the application of the finite element method for the

determination of stresses in structural details.

A comparative study of ship structural details

including test results and numerical stress analysis (Sumi

1997) has shown that the stresses close to the weld toe

obtained from shell finite element analysis were generally lower than the stresses obtained from finite solid element analysis. The difference was most likely due to different practice of including (or excluding) the weld stiffness in the finite shell element model. This may have a significant effect on the extrapolation of the structural stress since the

extrapolation is performed within the zone close to the weld leading to different results depending on whether a finite shell element model or a finite solid element model have been used in the stress analysis, or in particularly how the weld has been accounted for in the finite element

model. When finite solid elements are used in the

structural modeling, the structural geometry and the weld stiffness can be accurately represented in the local model. Only an idealized representation of the weld geometry is needed to reflect the overall stiffness of the detail. However, when using finite shell elements in the structural

modeling some problems arise since the finite shell

elements only provide a model for the mid-plane of the plates and thus the influence of the welds has to be included by some sort of model idealization (by e.g. rigid links, thicker elements at the weld area, or inclined shell elements.

Methods for Structural Stress Extrapolation

Traditionally, most extrapolation methods assume that the local notch effects (local geometrical effects) are localized within a small distance close to the weld toe expressed as a fraction of the main plate thickness (0.4.t to 0.5.t) and

that the structural stress can be obtained by an

extrapolation of stresses from outside this region. An other criterion suggested by Meneghetti and Tovo (1998) is to present the local stress field on a double logarithm form recognizing that the local stress field close to an idealized notch with zero radius becomes log-linear while

any other stress components become nonlinear. This

makes it possible to separate the two components and perform some sort of extrapolation of the stresses not influenced by the notch to obtain the structural stress.

Over the last years several extrapolation procedures for the determination of the local structural stress at the weld toe of welded joints have been suggested. Most research has been focused on tubular steel joints used in offshore structures and a general method, the European Convention for Structural Steelwork (ECCS) procedure

(Radenkovic 1981) has been well established and is

currently used in fatigue design of tubular joints. For

plated structures numerous procedures to obtain the

structural stress have been proposed, but there is still no universally accepted method.

Nierni (1994,1995) has suggested two extrapolation methods for obtaining the structural stress in the vicinity of single-sided edge gussets welded to a stressed member. The structural stress includes the effects of structural discontinuities, but the local geometrical effects of the notch at the weld toe are not included. In this case there is

no self-evident indication of the location of the

extrapolation points, such as plate thickness, which is normally taken as basis. Niemi (1994,1995) proposes two alternative methods:

1.

2.

Three extrapolation points at fixed distances at

the plate edge are defined and quadratic

extrapolation to the weld toe is performed to obtain the structural stress, c~.

Two extrapolation points at the plate edge are defined relative to the apparent size, t.PP, as:

o.15.t,pp and 0.30. t,PP. The apparent s:ze is

deterrmned as t. ~ = f

mm{ B,l.5.L,15.H} where B

is the height o the stressed member, L is the length of the attached gusset plate, and H is the height of the attached gusset plate.

The International Institute of Welding, IIW

(Hobacher 1996) has suggested both a linear and a

quadratic extrapolation method for the determination of the structural stress in welded plated and tubular joints

based on strain gage measurements or finite element

analysis. The two point (linear) extrapolation method is to be used in cases of mainly membrane stress, while the three point (quadratic) extrapolation is used in cases of shell bending caused by e.g. eccentric attachments in large diameter tubes or at plane plates. The distance to the leading extrapolation point should be 0.4,t, which stems

from the assumption that the local notch effects are

localized within that distance. Both extrapolation schemes can be used for numerical stress analysis by means of finite element analysis and electrical resistance strain gage measurements. It is noted, however, that the methods do not apply to edge attachments.

A proposed extrapolation method for obtaining the

Structural Stress

Common for existing extrapolation methods is firstly that they assume that the local notch effects (local geometrical effects) are localized within a small distance close to the weld toe and secondly that the global geometrical effects can be separated from the local notch effects by an

extrapolation of stresses from outside this region as a

function of some structural dimension (the main plate thickness for plated structures (Hobacher 1996) or the height of the member for attached plate gussets (Niemi

1994,1995)). The existing extrapolation methods have

traditionally been derived from experience and systematic

finite element analysis of specific welded joint

configurations. Instead of an extrapolation procedure

dependent on some structural dimension to separate the local and global stress, the separation of the global and local geometrical effects close to a weld toe (modeled as a singularity) can be based on the asymptotic behavior of stresses adjacent to an idealized notch (“singularity”).

traction free stiaces

Figure 2 Elastic stress field close to a singularity

The stress field close to a singularity in a continuous elastic medium has been shown to be proportional to the distance from the singularity powered to an exponent, ~(@ as a function of the vertex angle, et (Figure 2).

o(r)=

rfl(a)+

o(e)

where r and e are polar coordinates, Cl is a constant, f(t)) is a dimensionless function of tl, and 0(()) are higher order

terms of the stress field solution. P(u) is a negative exponent when the vertex angle, CX,is less than 180. As

r+ O, it is shown that the leading term of the series

expansion approaches infinity but other terms remain

finite or approach zero. Thus the stress near the

singularity varies with ?(”). The stress solution given in Equation (6) has been based on the soultion presented by Williams (1952) for a corner of a plate with traction free surfaces, in which the Airy stress function, 0, has been

expressed on the form as an eigenfunction series

expansion as@ = ra+lF(e;k).

The log-linear property of the stress field close to a singularity provides a means for separating the global and local geometrical effects and thus the extent of the local notch effects. On the basis of the asymptotic behavior of stresses adjacent to a singularity, the following structural stress extrapolation procedure has been proposed (Figure 3):

1. To separate the stress rising effects by means of a

double logarithm plot of the stress field obtained by means of a detailed finite element analysis (weld modeled with no radius and a weld toe angle, @ = 450), and to recognize that the local stress field close

to an idealized notch with zero radius (stress

singularity) becomes log-linear while any other stress components become nonlinear in a logarithm plot. The stress results used in the analysis should be evaluated at the finite element Gauss points. For the case of, $ = 45°, the exponent ~(ct) = -0.326.

2. To fit a curve to the stress field influenced by the

structural geometry by means of a polynomial of second order (quadratic) and extrapolate to the weld toe location. The field influenced by the structural geometry is defined as the distance from the end of the influencing zone of the singularity to the point where the structural stress and the nominal stress coincide (Figure 3).

The weld toe angle, $ = 45°, was assumed to represent an average value of the maximum weld toe

angle found in practice for as-welded aluminum

structures. In a series of measurements on aluminum butt

welds and fillet welds produced at five different

Norwegian yards, an average value of the maximum weld toe angle of 48.4° has been found to be a representative value for as-welded aluminum welds (Paauw et. al 1985).

The calculation of the local stress field by means of a finite element analysis requires a rather detailed finite element model with a very tine element mesh at and close to the notch in order to ensure that the stress singularity is accounted for. Preferably, 20-node finite solid elements should be used, however, 8-node finite shell elements (or membrane elements) can in manv cases be used for some

simple detail configurations. “

The curve fitting of the structural stress field by means of a polynomial of second order is easily done with

the method of least squares. Even if higher order

polynomial seems to provide an excellent fit of the curve

within the data points, an extrapolation of the curve

outside the data points may give rather poor results due to the highly oscillatory behavior towards the ends of the interpolation interval. To obtain a robust extrapolation method the extrapolation should be performed by means of a polynomial with an order not higher than of second degree. The extrapolation method depends on a relatively accurate determination of the nominal stress to determine the region which is solely influenced by the structural

Stressdistributionon a log-logscale Region influenced by the loeat notch Region NominalStlWSS influenced region by the structural Quadraticextrapolation by meansof themethod of leastsquares — —-b Stressedmember

Figure 3 Proposed extrapolation method based on a “singularity check”

geometry. However, the proposed extrapolation method

eludes the weakness of the extrapolation methods

suggested by e.g. Niemi (1994,1995) and Hobacher

(1996) in that the extrapolation method is independent of

any structural dimension to determine the region

influenced solely by the structural geometry and thus the location of the extrapolation points. The proposed method is instead dependent on a numerical stress singularity,

which is possible to reproduce in all structural

components normally found in ship structures independent of the actual geometrical dimensions of the detail. A drawback with the proposed extrapolation method is that

it requires a rather detailed (time consuming) finite

element analysis to ensure that the local singularity at the

notch (weld toe) has been properly accounted for.

However, it maybe possible on basis of systematic studies

using the presented method to come up with simple

guidance for extrapolation points or simplified parametric equations for structural stress concentration factors of different welded joint configurations.

NUMERICAL STRESS ANALYSIS

Introduction

The general-purpose finite element program system SESAM (Super Element Structural Analysis Modules) was used in the numerical stress analysis. The computer

program is documented in SESAM Technical Description (1996). The purpose of the finite element analysis was to calculate the stress distribution close to the weld toe to obtain the structural stress concentration factor, Kg, and the notch stress concentration factor, Kh, using both

8-node finite shell elements and 20-node finite solid

elements. The structural stress concentration factor in this study was determined by means of the extrapolation methods suggested by Niemi (1994, 1995), IIW (Hobacher 1996) and the proposed extrapolation procedure based on a separation of the structural and the local stress field by means of a “singularity check”. The finite element types used in the numerical stress analyses were 8-node finite shell elements and 20-node finite solid elements. The notch stress concentration factor was calculated by means of a 20-node finite solid element model with an accurate modeling of the weld geometry at the hot-spot locations according to the measured weld toe characteristics (Table

1). The calculated notch stress was consistent with the

definition of the notch stress given in the fatigue design recommendations for steel and aluminum ship structures suggested by the DNV (1996,1997). Two different load cases have been analyzed:

1. Applied longitudinal membrane tensile stress

2. Concentrated load applied at web frame

Geometrical properties of test specimens

A total of 44 as-welded test specimens were included in the test program, 22 flat badbracket connections (Figure 4) and 22 bulb stiffener/bracket connections (Figure 5). The flat bar, the brackets, and the transverse plate were

made of aluminum alloy 5083-Grade F, while the

extruded longitudinal stiffener with plate flange (shaded area at Figure 5) was made of aluminum alloy 6082.

Soo

_J

1

F-1

Figure 4 Geometrical dimensions of flat badbracket

connection

A plastic cast which was sectioned and photographed through a microscope replicated the weld geometry at the hot-spot locations for all test specimens. For the as-welded flat badbracket connections and the longitudinal bulb stiffener/bracket connections (named detail A and B) the weld toe radius, p, and the weld toe angle, & were measured for each casting at one saw cut section. This two-parameter description of the weld toe has been shown to provide an accurate description of the local conditions

at the weld toe location (Engesvik 1981). The

characteristic values of the weld geometry of the flat

badbracket connection and the bulb stiffener/bracket

connection are given in Table 1.

.

..1

ill

SectionA-A

_Ill

‘ii;{i,,

rAlll /

(}

Figure 5 Geometrical dimensions, bulb stiffener/bracket connection

Table 1 Weld toe characteristics for test specimens

F/atbar/bracketconnectionp[m] $

Smallest value 0.1 10°

Largest value 12.0 85°

Mean value 1.2 55°

Standard deviation 1.84 16.6°

Bulb stiffener/bracket connection (detail A)

Smallest value 3.5 17°

Largest value 14.6 65°

Mean value 8.2 41°

Standard deviation 3.1 16°

Bulb st~~ener/bracket connection (detail B)

Smallest value 6.0 15°

Largest value 13.5 55°

Mean value 8.9 33°

Standard deviation 2.1 11°

Nominal Stresses according to elastic beam theory

For the flat badbracket connection subjected to tensile

loading, the nominal stress was simply calculated as the applied force divided by the cross section area of the flat

bar, F/A. For the longitudinal bulb stiffener/bracket

connection subjected to bending, the local nominal

stresses were calculated by means of elastic beam theory for unsymmetrical cross sections. The effect of shear lag was accounted for by a constant effective breadth, b.ff = 0.54.b where b is the breadth of the test specimen.

Structural Stress Concentration Factors obtained

from Finite Element Analysis

The shell element formulation provided a model for the mid-plane of the plates, and the actual material thickness was given as an element property. Due to this

two-dimensionality of the shell element formulation the

unsymmetrical bulb section had to be modeled with an equivalent built-up flange section which could produce approximately the same local nominal stress field as in the

actual bulb section. The equivalent bulb section

(S-tiffener) used in the finite shell element analysis

consisted of an equivalent web thickness of 4.5mm, an

equivalent web height of 62.Omrn, an equivalent flange thickness of 13.Omm, and an equivalent flange width of 15.5mm.

In this study, the effect of the fillet welds in the shell

finite element model of the flat badbracket connection

was introduced by means of inclined shell elements at the end of the brackets with the same thickness as the flat bar

(Figure 6). For the bulb stiffener/bracket connection,

longitudinal inclined shell elements along the bracket in the longitudinal direction, and at the bracket ends with

thickness twice the bracket thickness were used for

modeling the weld stiffness. The weld which was included in the finite solid element model was modeled with an idealized weld profile with no radius and a weld toe angle, @= 45°.

Figure 6 Inclined shell element model of the bulb stiffener/bracket connection

For the flat badbracket connection, comparison of

finite shell element results and finite solid element results showed no significant difference between the stress results (Figure 7).

Figure 7 Comparison between stress results obtained from finite shell element analysis and finite solid element analysis, flat badbracket connection

For the longitudinal bulb stiffener/bracket connection, the inclined finite shell element solutions used in thk 6

study seems to give a good representation of the weld stiffness (Figure 8). Similar promising results were also

reported by Fricke and Petershagen (1992) on a

longitudinal stiffener/bracket connection (T-stiffener)

using inclined finite shell elements to model the weld

stiffness. The stress distributions for the bulb

stiffener/bracket connection shown in Figure 8 clearly

demonstrate that the stress results obtained by the finite solid element model include the local notch stress caused by the weld toe, whereas the finite shell element model is not able to resolve the actual nonlinear peak stress. However, the finite element stress results show good

correspondence in the region influenced solely by the

structural ~eometry. This confurns that shell element does account fo; the ov&ill stiffness of the weld.

I

2.9I _{

o 20 40 60 80 100

Distance fmm weld toe. hml

sided gusset was used. Therefore, the plate strip breadth, B, was taken as half the breadth of the flat bar, B = 35mm. With respect to the finite element analysis from which the

extrapolation methods were derived from, this was

interpreted to be the most appropriate choice for the particular detail tested in this study. Niemi (1994,1995) claims that any” size effect” is automatically accounted for by the quadratic extrapolation procedure since the shape variation of the stress distribution in the crack plane due to changes in the dimensions is accounted for in the local structural stress. While for the second method the “size effect” has to be considered by multiplying the hot-spot

fatigue stren th by a

?’ conventional size factor,

f(t)= (~&,P)02 where ~~ = 25mm. Including the “size

effect” in the structural stress concentration factor, Kg, instead of in the fatigue strength curve, the structural stress concentration factor obtained from the extrapolation method 2 can be written as, Kg,.O~= K.Jf(t). Note that the plate strip breadth, B, in this study was taken as half the breadth of the flat bar, B = 35mm, and thus giving an apparent size of, t,PP= 35mm and a size factor of, f(t) = 0.92.

Figure 8 Comparison between stress results obtained from fi~ite shell ele-ment analysis and finite solid element analysis, bulb stiffener/bracket connection (detail A)

The stress results obtained from finite shell element models are highly dependent on the anrdyst’s skills and previous experience. Thus, other models of the weld toe area (e.g. by means of rigid elements) could have given better agreement with those obtained from the finite solid element model. It is in the authors’ opinion that finite solid element models preferably should be used in the calculation of the structural stress, at least in cases where little or no previous experience on the use of finite shell element models are available, to calibrate the finite shell element models.

For the flat badbracket connection used in this study there was no clue as to the location of the extrapolation points, e.g. relative to the size of as the plate thickness, which is taken as the basis for the extrapolation procedure suggested by the IIW (Hobacher 1996). However, Niemi (1994, 1995) has suggested two extrapolation methods for obtaining the structural stress in the vicinity of single-sided edge gussets welded to a stressed member. Niemi (1994,1995) does not present any element type or element

size requirements but the extrapolation methods were

originally derived on basis of a very fine mesh (element size from 0.02 mm to 0.1 mm) at the hot-spot location using parabolic plane stress elements. This implies the use of mesh refinement that ensure convergence for practical purposes. For the finite solid element model the same

mesh refinement was used in the calculation of the

structural stress and the notch stress. The extrapolation

methods proposed by Niemi (1994,1995) were originally derived for single-sided gussets but in this study a

two-1

Dbtenco from weld too, [m

1

Figure 9 Stress distribution of the flat badbracket connection presented on a log-log scale

For the longitudinal bulb stiffener/bracket connection

presented in this study, the stress extrapolation was

performed by means of the extrapolation methods

suggested by the IIW (Hobacher 1996). When applying the finite element method together with the extrapolation method suggested by HW (Hobacher 1996) to obtain the structural stress at the hot-spot location, the refinement of the mesh is recommended to be so fine that any further refinement does not result in any significant change of the

stress distribution inside the area between the

extrapolation points. The extrapolation points were related to the equivalent thickness of the upper flange, & = 13mm, used in the finite shell element model, and the extrapolation was performed to the weld toe. It is also recommended that the weld should be included in the finite element model. In the case of finite shell element models the weld can be modeled by means of e.g. rigid elements or inclined shell elements. The latter was used in this study. The refinement of the element mesh using 8-node shell elements resulted in an element size of 0.0460& at and close to the extrapolation points. For the 20-node finite solid element model with a weld of zero radius, the mesh refinement was identical to the one used in the calculation of the notch stress. The quadratic extrapolation

was performed by means of the least squares method with a polynomial of second order using the three specified extrapolation points given by the IIW (Hobacher 1996).

Figure 9 shows the stress distribution for the flat

baribracket connection obtained from the finite solid

element model with no radius and a weld toe angle, $ =

45°, presented on a double logarithm form. The plot

clearly shows that the stress distribution close to the notch

(the weld toe) is log-linear while the other stress

components are non-linear. It is seen from Figure 9 that the notch effects were localized within a shows that the local notch effects are localized within a distance of

approximately 3. 15mm. For the longitudinal bulb

stiffener/bracket connections, a double logarithm plot of the stress field showed that the notch effects were localized within a distance of 8. 10mm (bending) and 5.85 (tensile) for detail A, and 5.70mm (bending) and 4.70mm (tensile) for detail B. In this study the stress gradient in the region which was assumed to be solely governed by the structural stress field (extending to 27mm for the flat badbracket connection and to 70mrn to 75mm for detail A and B, respectly) was fitted by means of least squares

method with a polynomial of second order and

extrapolated to the weld toe. The structural stress

concentration factors obtained from the finite element

analysis are presented in Tables 2, 3, and 4.

Table 2 Structural stress concentration factors, ~, for the

flat ba.dbracket connection &

Extrapolation method suggested by Niemi (199?, 1995) e.mm Quadratic extrapolation, method 1

Shell element analysis 1.38

Solid element analysis 1.43

Linear extrapolation, method 2

Shell element analysis 1.26 1.37

Solid element analysis 1.28 1.39

Proposed extrapolation method

Shell element analysis 1.35

Solid element analysis 1.34

Table 3 Structural stress concentration factors, KS,for bulb stiffener/bracket connection (detail A)

Kg,binding & axi~ Kg,K ~tii.~

e.Ulal

Extrapolation method suggested by IIW (Hobacher 1996)

Finite shell element analysis

Linear extrapolation 1.694 1.592 1.064

Quadratic 1.767 1.667 1.066

extrapolation

Finite solid element analysis

Linear extrapolation 1.708 1.558 1.096

Quadratic 1.791 1.622 1.104

extrapolation

Proposed extrapolation method

Shell element 1.558 1.523 1.043

analysis

Solid element 1.505 1.464 1.028

Table 4 Structural stress concentration factors, & for bulb stiffener/bracket connection (detail B)

Kg, ~nding Kg,~id *SJ

c.axial Extrapolation method suggested by

IIW (Hobacher 1996) Finite shell element analysis

Linear extrapolation 1.571 1.578 0.996

Quadratic 1.636 1.635 1.001

extrapolation

Finite solid element analysis

Linear extrapolation 1.568 1.493 1.050

Quadratic 1.634 1.549 1!051

extrapolation

Proposed extrapolation method

Shell element 1.488 1.522 0.978

analysis

Solid element 1.442 1.407 1.025

analysis

The accuracy of the structural stress obtained from the extrapolation methods will clearly dependent on the location of the extrapolation points. In this study it is seen that for the extrapolation methods suggested by Niemi

(1994,1995), all the extrapolation points are located

outside the region affected by the local notch (singularity)

and well inside the region solely influenced by the

structural geometry. This explains the good

correspondence between the structural stress

concentrations obtained from the proposed extrapolation method and the stress concentration factors obtained from

the extrapolation methods suggested by Niemi

(1994,1995).

In lieu of the results presented in Tables 2, 3 and 4 it is noticed that the structural stress concentration factors obtained from the linear and the quadratic extrapolation procedure suggested by the IIW (Hobacher 1996) were generally higher than the structural stress concentration factors obtained from the proposed extrapolation method based on a “singularity” check (by 5% to 19%). Both the

proposed extrapolation method and the quadratic

extrapolation method suggested by the IIW (Hobacher 1996) were performed by means of the method of least squares and the higher structural stress concentration factor obtained from the quadratic extrapolation method suggested by the IIW (Hobacher 1996) could be explained

by the fact that the quadratic extrapolation was only

performed in the leading part of the stress field influenced by the structural geometry and thus in a region with an overall steeper stress gradient. The leading extrapolation point used in the linear and the quadratic extrapolation (Hobacher 1996) applied on the stress results obtained from the finite solid element analysis of detail A was within the region influenced by the singularity (notch) and

this could explain the relatively higher stress

concentration factor (19.OYO)compared to the proposed extrapolation method .

Notch Stress Concentration factor obtained from

Finite Element Analysis

To obtain the notch stress concentration factor, KM,

the weld geometry was modeled according to the

measured weld geometry. Characteristic weld geometry data is presented in Table 1. 20-node finite solid element

models were used in the derivation of the notch stress, The notch stress concentration factor, Kh, was defined as

the calculated principal notch stress at the weld toe

location divided by the nominal at the weld toe location. The characteristic values of the notch stress concentration factors are presented in Tables 5, 6, and 7. The finite solid element models of the flat bar/bracket connection and the bulb stiffener/bracket connection are presented in Figures

10andll.

Table 5 Characteristic values of the notch stress concentration factors, Kk, flat brdbracket connection

Maximum value 5.17

Minimum value 2.35

Mean value 3.14

Standard deviation 0.71

Table 6 Characteristic values of the notch stress concentration factors, KM,bulb stiffenedbracket connection (detail A)

& bcnting &t, benting ~ IWldmsf kL&ll

Maximum value 2.41 2.14 1.126

Minimum value 1.99 1.80 1.103

Mean value 2.14 1.92

Standard deviation 0.12 0.10

Table 7 Characteristic values of the notch stress concentration factors, KM,bulb stiffener/bracket connection (detail B)

Kk4bending &t, bending

Maximum value 1.95 1.83 1.060

Minimum value 1.70 1.63 1.048

Mean value 1.80 1.72

Standard deviation 0.08 0.07

6TFC. s.,.,, Sm. 5W69S I

Elcmmt siz al weld tIM lncatinm

0.054[mm]X0.059[mm]X0.052[mm]

Figure 10 Finite solid element of flat badbracket connection

Tabulated Notch Stress Concentration factor.

The DNV (1997) has suggested two sets of notch stress

concentration factors, KM = Kg..KW, for supporting

members welded to stiffener flanges to be used together with their design SN-curves III and IV. The set with the highest values is to be used for built-up stiffener/bracket connections while the other with the lowest values is to be used for extruded stiffeners/bracket connections.

It is important to note that the difference in the notch stress concentration factors between built-up members and extruded members is not due to geometry but rather due to the difference in the fatigue strength observed for small-scale built-up and extruded members. The difference in the fatigue strength has been based on small-scale fatigue tests (ECCS 1992) which have shown a tendency for a lower fatigue strength for built-up beam test specimens than for extruded beam test specimens due to different levels of long-range residual stresses. Higher residual stresses are experienced in the built-up beam due to the

fabrication process (the welding and the assembly

process). However, in a real ship structure it is most likely that the levels of long-range residual stresses are of the same order for built-up and extruded beams caused by the assembly process of the whole structure. In the author’s

opinion there are not enough experimental evidence

obtained from residual stress measurement on real

aluminum ship structures that may justify the use of a lower stress concentration factor for extruded beams in complex ship structures and at this point no extra benefit

should be given for joints made of extruded beams

compared to built-up beams.

ST .,-0! .

Figure 11 Finite element model of bulb stiffener/bracket connection (detail A)

In this study the notch concentration factors for built-up beams were used since the constant amplitude fatigue testing was performed on a high R-ratio (R = 0.44) and it was therefore assumed that any positive effects on the fatigue life due to a possible low residual stress level in the test specimen could be ruled out. The tabulated notch stress concentration factors are presented in Table 8.

Table 8 Tabulated notch stress concentration factors according to DNV (1997)

Tabulated Kb

Flat brdbracket connection 2.50

Detail A 2.50

Detail B 1.93

FATIGUE TEST PROGRAM Fatigue test rig arrangement

Two different test rig arrangements were used in the fatigue test program. The flat badbracket connection was

tested in tensile loading (Figure 12), while the

longitudinal bulb stiffener/bracket connection was tested under three point bending (Figure 13).

steel6’auw

E

Witblmddl

Test spmimm 31 Hydraulic SAPS 42

Figure 12 Test rig arrangement, tensile loading

The test rig used for the flat badbracket connection was arranged in order to simulate the effect of global hull

beam loads acting on longitudinal stiffener/transverse

girder web connections. The axial loading was provided by a servo hydraulic actuator capable of producing a maximum dynamic load of* 500kN. The fatigue loading was applied in load control. The actuator was mounted in a steel frame and the test specimens were locked by hydraulic clamps. The testing was performed in laboratory air at ambient temperature with a loading frequency of 10 HZ for the constant amplitude tests and with an average loading frequency of 17.48 HZ for the variable amplitude tests. The variable amplitude loading was applied by means of Wave Action Standard History (WASH(W)), a

time history simulating a non-stationary wide band

loading. A more detailed description of the load spectrum is given in Hartt (1986) and in TSC (1989). Fitting a

Weibull distribution to the cumulative stress ranges

obtained by Rainflow counting of the WASH(W) by means of the linear least squares regression method, the Weibull shape parameter, h, was found to be 1.19 and the Weibull scale parameter, q was found to be 22.69. In a

study by Heggelund, Tveiten, and Moan (1998), the

Weibull shape parameter for the stress distribution due to global wave loading in a midship stiffener/web frame connection of a high speed large aluminum catamaran was

found to be in the range of 0.8- 1.1 depending on the

location of the fatigue cracking and on the operational limitations.

The test rig used for the longitudinal bulb

stiffener/bracket connection was arranged in order to

simulate the effect of lateral load transferred from

longitudinal stiffeners into transverse girder web. To

maintain a well-controlled testing environment a pinned boundary solution for the test specimen was employed. At each model end a 14mm flat aluminum plate was attached and equipped with a fixed shaft. One of the end pIates also had an additional ball bearing which eliminated all friction at the support and secured an ideal, pinned end support. The loading was provided by a servo hydraulic actuator capable of producing a maximum dynamic load of +25kN.

The fatigue loading was amlied in tension with load

control. ‘me testin~ was pe~formed in laboratory air

ambient temperature with a loading frequency

approximately 4.5 HZ.

A.

LaJ

---K

4

\

F&l SIM +A Meld Skal ‘lbt

IAm@YFbJ’

‘A

\

Figure 13 Test rig arrangement, three-point bending

Constant amplitude fatigue test results for flat

barlbracket connections

The data were analyzed assuming a linear SN-curve on a log-log scale, using statistical regression analysis. Due to the rather limited number of as-welded

test specimens (12 test specimens) the slope of the

regression line, m, was fixed according to the slope of the appropriate design curve. The details tested in this study

had four possible locations of fatigue crack failure

subjected to the same nominal stress state and

environment. The fatigue failure was defined as a

complete loss of the load bearing capacity of the cross sectional area and no repair of the fatigue cracks was performed during the fatigue test program. Consequently, the SN-data derived from the fatigue tests in this study will be at the lower end of the scatter band since the fatigue life has been taken as the fatigue failure at the “weakest link” location.

The test SN-data together with their mean regression curves using a nominal stress range and a structural stress range obtained from the proposed extrapolation method are presented in Figures 14 and 15.

In order to consider the present fatigue test results

with regard to design implications, a factor of

conservatism of design, ~, was defined as the stress

obtained at the approximated parallel 95 Yo lower limit

confidence regression line at a reference fatigue life,

N,.~=2.106, obtained by test results, divided by the

characteristic design stress range given by fatigue design codes and recommendations at the same reference fatigue life. Thus a ~ > 1.0 would indicate a safe fatigue life prediction by means of the design SN-curve of the codes and a ~ c 1.0 would indicate a possibility of an unsafe

fatigue life prediction of the codes. The factor of

conservatism of design of the as-welded flat badbracket connection obtained from the different design codes using a local nominal stress approach is presented in Table 9.

Strain gage measurements and finite element analysis

showed that the influence of secondary bending effects were negligible and they were not included in the nominal stress range.

Table 9 shows that all the design codes based on a

local nominal stress range provided safe fatigue life

calculations for the as-welded flat bar/bracket connection failing from the weld toe location. All the aluminum

fatigue design codes were overly conservative when

predicting the fatigue strength of the as-welded test

specimen used in this study.

The nominal design codes refer to as-welded details of standard quality and geometrical identical details with a more favorable weld toe geometry (a possible larger weld toe radius or a possible smaller weld toe angle) would consequently have an higher fatigue strength. In lieu of the test results obtained in this study it could therefore be suspected that the rather conservative fatigue test results in this study were caused by a rather smooth weld toe geometry and thus low stress concentrations at the weld

toe location. However, the weld toe geometry

measurements of the test specimens in this study (Table 1) showed weld toe characteristics which were equivalent to what are normally found for as-welded details (e.g. Paauw et. al. 1985). Thus the weld toe geometries of the test specimens were representative for as-welded aluminum details found in practice.

It has been shown that small-scale fatigue test

specimens may be of insufficient size to retain the full

amount of residual stresses experienced in full-scale

structures (Aab@ et. al. 1985), implying longer fatigue lives for small-scale fatigue test specimens, particularly in the long life region. It has, however, been reported that the

lack of residual stresses in laboratory fatigue test

specimens can be eliminated by testing the specimens on a high R-ratio (Aab@ 1985). Residual stress measurements on an unbroken test specimen selected randomly from the whole test sample gave a surface residual stress level of 118MPa (error margin 19MPa) at a distance 2mrn from the weld toe. This was approximately 77% of the yield strength of the base material. The residual stress level was suspected to be even higher closer to the weld toe due to the high residual stress gradients normally found close to the weld toe for welded aluminum structures (Mazzolani 1995). Note also that the yield strength close to the weld toe (in the heat-affected zone, HAZ) was assumed to be somewhat reduced compared to the yield strength of the base material caused by the heat input during the welding process. The rather high residual stress level found in the

test specimen confined that the fatigue test specimens in

this study were able to retain high residual stresses in the

magnitude of the yield stress (in the HAZ). Additionally, the constant amplitude fatigue testing was performed on a high R-ratio (R= 0.44) and it was therefore assumed that any positive effects on the fatigue life due to a possible lack of residual stresses in the test specimen could be ruled out.

Table 9 Factor of conservatism for the flat badbracket connection

Design code Nm~ti N,.~.-u _c

Nominal stress range approach

BS8118 17 28.84 1.70

ECCS 18 30.31 1.68

IIW 16 28.84 1.80

Eurocode 9 18 29.73 1.65

Structural stress range approach, extrapolation Niemi (1994,1995)

Quadratic extrapolation, method 1

Shell element 25/40 39.80 1.58/0.99

model

Solid element 25/40 41.24 1.68/1 .03

model

Linear extrapolation, method 2

Shell element 25/40 39.51 1.59/0.99

model

Solid element 25/40 40.09 1.60/1.00

model

~;:dral stress range approach, proposed extrapolation

Shell element 25/40 38,93 1.55/0.97

model

Solid element 25/40 38.64 1.54/0.97

model

Notch stress range:~proach, DN6~ ~~97)

Tabulated KM 1.69

Calculated KM 45 60:63 1.38

The joint classification of structural details found in nominal fatigue design codes based on nominal stress implies that joints with different mean values and standard deviations are included in the same detail class and this

will increase the scatter of the joint category. The

logarithm of the standard deviation of the test specimen sample in this study using a fixed slope exponent was

approximately, STDV]O~N= 0.090, which indicates a much

smaller scatter and thus a much higher lower bound

fatigue strength than generally seen for same detail

configurations in design codes.

In the design codes based on a nominal stress range approach, the stress raisers due to local weld geometry and structural discontinuities are implicitly included in the

fatigue strength curves. Moreover, the design codes

normally assume an average leg length of about 10mrn. The test specimens tested in this study had an average leg length of about 20mm. The rather large leg lengths seen for the test specimens have moved the weld toe location to a region of a lower structural stress. This resulted in a smaller implicit structural stress concentration factor in the test SN-curves than assumed in the design SN-curves found in design codes. It was therefore assumed that the rather large leg lengths of the test specimens could partly

explain the rather high fatigue strength of the flat

badbracket connection tested in this study.

In lieu of the discussion above it can be concluded that fatigue classes 16 to 18 together with the local nominal stress can safely be used to predict the fatigue life of an aluminum brackethlat bar connection subjected to

axial loading. The rather conservative fatigue lives

obtained in this study compared to the design codes using

the local nominal stress range approach could be

explained by a rather narrow scatter of the test results and thus a higher lower bound fatigue strength compared to

design SN-curves, and by the exceptionally long leg

lengths of the test specimens which have moved the weld toe to a region of lower structural stress.

In this study the structural stress concentration factor was found by two extrapolation methods suggested by Niemi (1994,1995) and a proposed extrapolation method based on a “singularity” check. At the present time no recommendations on a suitable hot-spot design SN-curve are available for the fatigue design of aluminum structures by using a structural stress range approach. Since the effect of the local weld geometry are included in the design hot-spot SN-curve, it is necessary that the local conditions at the weld toe of the details are reflected in the

SN-curve. That means that different hot-spot SN-curves

should be used for e.g. as-welded, profile ground welds,

or toe ground welds.

The results obtained from the numerical stress

analyses were used together with the design SN-curve 25 and 40 taken from the IIW fatigue design recommendation (Hobacher 1996). The design SN-curve 25 of the IIW fatigue design recommendation is the design curve which is commonly assigned to a transversely loaded butt weld with a weld toe angle >50°, The design SN-curve 25 was

chosen on basis of the measured weld geometry

characteristics presented in Table 1 where an average value of the weld toe angle can be found to be more than 55°. The fatigue class 40 was chosen since that design curve had been suggested by Nierni (1996) to be used safely together with structural stress concentration factors for aluminum butt and fillet welds failing from the weld toe. The design SN-curve 40 of the IIW fatigue design recommendation is the design curve which is commonly assigned to a transversely loaded butt weld made in shop in flat position with a weld toe angle <30° and inspected by NDT (non destructive testing). Note, however, that the hot-spot design SN-curve 40 was originally suggested for butt and fillet welded aluminum joints of relatively thin plates and extrusion (up to 6mm) failing from the weld toe location.

It is important to note that when a fatigue class of e.g. a butt weld is taken as a design hot-spot SN-curve, angular and axial misalignments of varying magnitude have been present in the axially loaded specimens behind the design

SN-curves. Therefore, the design hot-spot SN-curves

include to some extent an unknown allowance for

secondary bending stresses. Numerical stress analysis and strain gage measurements in this inverstigation showed that the stress state at the hot-spot locations during the fatigue tests could be assumed for the most part to comprise of tensile loading and it could therefore be expected that the fatigue strength of the test specimens would be somewhat higher than the fatigue strength of the design hot-spot SN-curve.

Table 9 shows that the design hot-spot SN-curves together with the extrapolation procedures to obtain the structural stress concentration factor, KS provide safe life predictions for the bracketi flat bar connection tested in

this study. The results in this study seemed to correspond well with the findings of Niemi (1996) with respect to the appropriate hot-spot SN-curve. However, considering that fatigue class 40 was originally suggested for butt and fillet welded aluminum joints of relatively thin plates and extrusion (up to 6mm), the rather narrow scatter of the fatigue test results, and the fact that no misalignment effects were present in the test results, fatigue class 25 was assumed to be a more suitable choice in the fatigue design of the as-welded flat bar/bracket.

In this study the local notch stress was obtained from tabulated stress concentration values, and by finite solid element analysis modeling of the actual weld geometry. The tabulated stress concentration factor caused by the local weld geometry and the structural geometry was found in the DNV draft fatigue recommendation (1997). The SN-curve was taken to be the DNV design SN-curve

III for joints in non-corrosive environments which is

identical to ECCS (1992) design SN-curve 45 for full penetration butt welds on extruded beams.

The factor of conservatism of design for the DNV

draft recommendation (1997) using a calculated notch

stress concentration factor is 1.38 which indicates a safe fatigue life prediction. However, as a rule, the scatter of the fatigue life data plotted against a suitable stress range parameter should be as small as possible. Regression analysis of test SN-data using calculated notch stress gave a large scatter with a standard deviation of the test results, STDVION which was 3.7 times larger than the STDVIO@ of the test SN-data using the local nominal stress range and thus indicating that the calculated notch stress may not be well suited for fatigue design. The local geometry at weld toes for as-welded details tends to give large stress concentrations which may result in local exceeding of the yield stress for even moderate nominal stresses. With a nominal stress of 107.2Mpa and 67.7Mpa at the high stress region and the low stress region respectively, local

yielding at the weld toe was experienced in the test

specimens. It has been argued that this localized, rather small plastic zone will invalidate the elastic notch stress concentration factor as a relevant parameter for the fatigue strength assessment (Niemi 1995). For this reason an

effective fatigue notch stress factor, Kf, has been

introduced (Radaj 1996). It has been argued that the

increase of the notch stress concentration factor does not reflect the reduction of the fatigue life of the constant amplitude fatigue test data. Thus the fatigue strength reducing effect is not as strong as the increase of the notch stress would indicate. It is therefore suggested that the notch stress approach adopted by the DNV (1997) using calculated notch stress concentration factors should not be used for the fatigue design of as-welded components that are subjected to relatively large loads. Note however, that

in fluctuating loading, the behavior is assumed

predominantly elastic if the notch stress range remains below the 2 times yield stress due to shake down effects.

For large high speed aluminum catamarans, which are typically designed for 108 cycles (20 years), it has been shown that the low stress data will contribute most to the accumulated fatigue damage (Heggelund, Tveiten and Moan 1998) and the notch stress approach suggested by the DNV (1997) using calculated notch stress range might be considered as a suitable choice since the local peak

stresses at the weld toe are relatively moderate in

magnitude. But this still needs to be verified.

The factor of conservatism of design for the DNV

draft recommendation (1997) using a tabulated notch

stress concentration factor is 1.68, which is somewhat

higher than the factor of conservatism obtained using the calculated notch stress. Since the tabulated values are equal for all details, the standard deviation of the fatigue test data is equal to the standard deviation obtained by using nominal and structural stress ranges. The tabulated notch stress concentration factor (Table 8) is less than the mean minus 1 standard deviation value of the calculated

notch stress concentration factor (Table 5). This is

somewhat peculiar since the DNV draft recommendation

(1997) allows the use of calculated notch stress

concentration factors by means of detailed finite solid element analysis modeling of the weld toe geometry using the local weld toe geometry, and the use of tabulated notch stress concentration factors without any preferences with respect to the method and thus it should have been expected that the value should have been representative for upper bound values for notch stress concentration factors of as-welded details. Since the tabulated value is a lower bound value, it may either be representative for details with more favorable weld toe geometry (that is a larger weld toe radius and a smaller weld toe angle) or an

implicitly material dependent modification has been

introduced to account for the non-linear material behavior at the weld toe (an effective notch stress). In the authors’ opinion this illustrates a possible ambiguity in the DNV

draft fatigue recommendation (1997) in how the notch

stress should be defined, either as a notch (theoretical) stress range, Aoh, or as an effective notch stress range, Ao~. The ratio between the design fatigue class 45 (the ECCS (1992) design SN-curve 45 for full penetration butt welds on extruded beams) and the design fatigue class 18 (commonly assigned for this joint according to the ECCS (1992)) is 2.5. This fact indicates that the tabulated notch stress concentration factor suggested by the DNV (1997) is rather an effective fatigue notch factor, Kf, than a notch stress concentration factor, Kb.

Constant amplitude fatigue test results for

longitudinal bulb stiffener/bracket connection

The data were analyzed assuming a linear SN-curve on a log-log scale, using statistical regression analysis (Figures 14 and 15). Due to the rather limited number of as-welded test specimens (11 test specimens of detail A and 10 test specimens of detail B) the slope of the regression line, m, was fixed according to the slope of the appropriate design curve. All the welds had been profile ground at the yard before the delivery, that is the entire weld face has been machined and given a favorable shape to reduce the stress concentration factor. The welds had not been fully profile ground, that is toe ground to a depth of 0.5 mm below the bottom of any visible undercut (DoE 1990) to remove possible harmful defects at the weld toe had not been performed. It was expected that the constant amplitude fatigue test results of the longitudinal bulb

stiffener/web frame connection would show a larger

variability in that the production and the shipment of the fatigue test specimens had been subjected to a larger extent of unknown and uncontrolled parameters. This was confirmed by the regression analysis where the logarithm

of the standard deviation of the longitudinal bulb

stiffener/web frame connection was approximately 2 times

the logarithm of the standard deviation of the flat

barfbracket connection.

Table 10 Factor of conservatism for bulb stiffener/bracket connection, detail A

Design code N~f.~,. N,.f.~ _c

Nominal stress range approach

BS8118 20-- 21.17 1.06

ECCS 23 22.59 0.98

IIW 21.17 1.18

Eurocode 9 ;! 22.00 0.88

Structural stress range approach, extrapolation IIW (1996) Quadratic extrapolation Shell element 32(40 35.87 1. model Solid element 32/40 36.16 1. model Linear extrapolation Shell element 32/40 37.41 1. model 3/0.90 6/0.90 8/0.94 Solid element 32/40 37,92 1.190.95 model

Structural stress range approach, proposed extrapolation method

Shell element 32/40 32.99 1.03/0.82

model

Solid element 32/40 31.87 1.00/0.80

model

Notch stress range ;~proach, D:; ~:97)

Tabulated K~ 1.25

Calculated & 45 48.96 1.09

Tables 10 and 11 show that the BS8118 (1991) and IIW (Hobacher 1996) design recommendations provided safe fatigue life calculations for detail A failing from the weld toe location. On the other hand the ECCS (1992) and Eurocode 9 (1996) provide unsafe fatigue life predictions compared to the test SN-data. The fatigue class suggested by the Eurocode 9 (1996) refers to welded joints with a weld toe radius larger than 10mm, which was not true in this study (average p = 8.20mm) which can explain the unsafe fatigue life prediction. Eurocode 9 (1996) suggests fatigue class 18 for as-welded details which would have provided a safe life prediction for detail A. The fatigue class 23 suggested by the ECCS fatigue recommendation (1992) refers to as-welded details of any length attached by fillet welds on the flange of an extruded beam in the direction parallel to the stress. The fillet welds are assumed to be of standard quality of as-welded details and it is therefore disturbing that the ECCS fatigue design

recommendation (1992) provided an unsafe factor of

conservatism for the profile ground test specimens tested in this study. The fatigue class for the same detail configuration using a built-up beam instead of an extruded beam is fatigue class 18 which will result in a safe fatigue life prediction. This fact indicates that all or some of the positive effects of the extrusion process on the fatigue life obtained for extruded beam fatigue test specimens are not maintained for extruded beams used in a more complex structural component as discussed above.

Detail B is different from detail A in that the inclined bracket has been given a curvature to reduce the structural stress concentration factor, Kg. Tables 10 and 11 show

that the BS8 118 (1991), IIW (Hobacher 1996), and