Evaluation of fatigue aspects in ship structural design

Deift University of Technology

Ship Hydromechanics Laboratory

Library

Mekelweg 2, 2628 CD Deift

The Netherlands

Phone: +31 15 2786873 Fax: +31 15 2781836

"EVALUATION OF FATIGUE ASPECTS

IN SHIP STRUCTURAL DESIGN"

ir. J.H. Vink, prof. Ir. B. Boon1, ir. B.C. Buisman1 Deift University of Technology (DUT)

ABSTRACT

The pros and cons of the S-N approach and the fracture mechanics approach for prediction of the fatigue life of ship structures are discussed.

Instead of "Detail Classes" and a mixture of the nominal- plus hot spot- sress concept, it is proposed to use only one S-N líne

accor-ding to the notch stress concept, in combination with parametric formulae for the stress concentration due to the welds and geometric stress concentration factors which can either be based upon standard

cases or FEIl calculations.

In order to determine the total fatigue life of large constructions, including the crack growth stage up to a critical crack length, the fracture mechanics approach is an essential tool, which still re-quires large scale experiments for verification and calibration. The results of fatigue experiments on a large scale test piece of a ship structural detail are presented and discussed.

Keywords: fatigue strength, fatigue life, fracture mechanics, large scale experiments

NOTATION

in inverse slope of S-N line

A10 zero stress intercept on log N axis of mean line for i-th segment of

S-N curve (50% probability of survival), cycles

A k zero stress intercept on log N axis of (mean_k*lg8) line for i-th

segment of S-N curve, cycles

k survival index: number of standard deviations below mean line lg standard deviation of log N for S-N curve

lg0 standard deviation of log o for S-N curve

AO stress range

¿00 constant amplitude fatigue limit for stress range

A cut off limit for stress range

reference stress range value at the detail exceeded once out of N0 cycles

N0 total number of cycles associated with the stress range level

N number of stress cycles

NL number of stress cycles during lifetime of ship

N1 number of stress cycles to crack initiation

Ncr number of stress cycles from crack length a0 until aer

Nf number of stress cycles until fatigue failure acc. to S-N concept R stress ratio: R = o_/o =

D damage parameter used in conjunction with S-N concept and linear

damage accumulation hypothesis

D0 total damage due to variable amplitude stress spectrum

Díaur.

total damage at point of fatigue failure

d. damage contribution due to stress cycles in stress range i

n1 number of stress cycles in stress range i

h shape parameter of Weibull distribution q weibull scale parameter

International Maritiu Conference Indonesia '97

Íç,99-iB. Vink, B. Boon. B.C. Buisman

Q(X probability of exceedance of x stress intensity range

crack propagation exponent in Paris' equation C constant in Paris' equation

a(N) crack length as function of stress cycles

a0 initial crack length

critical crack length

y stress concentration factor

Y geometric stress concentration factor, excluding stress raising

ef-fects due to geometry of weld

stress concentration factor which accounts for weld geometry WCA actual midship section modulus at coaming, m2

w required midship section modulus at coaning, in2

EVALUATION OF FATIGUE ASPECTS IN SHIP STRUCTURAL DESIGN 3

i INTRODUCTION

Whereas fatigue is a standard design check in offshore industry already for more than two decades, explicit fatigue analysis has not been part of

standard ship design practice until recently.

Due to the increased use of high strength steels in structures of large tankers, bulkcarriers and containerships, in combination with more effort in optimised constructions and new details to further reduce steel weight and building cost, fatigue failure has gradually become a relevant design criterion, supplementary to the conventional yield strength and buckling criteria.

Also for medium sized merchant vessels there is a continuing trend of more extreme concepts in combination with usage of high strength steels, resul-ting in reduced margins against fatigue.

Fatigue failure is a very localised phenomenon, which depends exponentially on maximum stress levels at weld details and other stress raisers. For welded structures the fatigue strength is almost similar for high and normal yield strength steel, as it is mainly governed by imperfections at welds etc. Because of this, the fatigue life of high strength steel ship constructions is strongly decreased as the working stress levels are in-creased almost in proportion with the yield stress of the steel.

The following methods for evaluation of the fatige life will be diBcussed in view of the underlying principles, their possibilities and drawbacks:

* _{S-N concept, which is mostly applied until now for fatigue evaluation}

of ship structures. The S-N concept can be further subdivided as

fol--lows:

= Nominal Stress approach,

= Hot Spot or Structural Stress approach,

= Notch Stress approach,

* _{Fracture Mechanics Approach, using the Paris' law for subcritical}

fa-tigue crack-growth, and the Stress Intensity at the crack tip.

Based upon the principles of these methods, the need for large scale expe-riments is discussed.

Realizing the increased importance of fatigue as a criterion to evaluate the adequacy of ship structural details, a project was initiated with the main goal to evaluate and supplement the methods for prediction of the

fatigue life for welded ship structures, taking into account both the crack initiation and crack growth stage. After a short survey of recent fatigue damages on medium sized Dutch merchant vessels, a structural detail was selected for doing large scale experiments. The subject detail is a good example which shows that there is a need to increase the awareness on the fatigue aspect of ship structural components. In this respect it is of utmost importance that a ship structural engineer has good knowledge of the aspects which are related to fatigue, in order that he will be able to make sound and cheap details and has expertise to evaluate them.

First results of the experiments and comparisons with existing fatigue evaluation methods will be presented in this paper.

2 FATIGUE EVALUATION METHODS

2.1 General

In principle there are two methods of fatigue analysis:

i SN-concept; this is an accumulated damage analysis, which is indepen-dent of a visible crack. The damage parameter is normally defined as the ratio of number of stress cycles that have been experienced and number of stress cycles that can be sustained until failure, both using the same load spectrum.

2 _{Fracture mechanics approach; assessment of the propagation of a sharp}

initial crack as well as determination of the critical crack length.

Furthermore, for an explicit fatigue analysis the cumulative damage of an infinite number of possible load variations has to be considered for ship structural details. In order to evaluate the fatigue damage due to variable amplitude loading, usually a linear damage accumulation scheme is adopted according to the Palmgren-Miner rule.

2.2 SN-concept

2.2.1 S-N curve representations

Until now, this is the method mostly applied for fatigue evaluation of ship structures.

It uses results of constant amplitude loading on small specimen expressed as a load-life relationship in one of the following formats, see fig. 1:

- normal two segment SN-line with fatigue limit for constant amplitude

loading, equation (1):

t.o=Max[(

_A1

Nf>1

2

(1)

-

one segment SN-line for simplified damage calculation in case of vari-able amplitude loading, equation (2):

1 =

Al2

(2)

alternatively, the more frequently used format of equation (3):

log

N =

log A1 2-m.log oa (3)

- three segment SN-line, as regularly used for variable amplitude

loa-ding, equation (4):

Max [

Nf)

Nf

A1,2

i -i;;-;)

In the above formats for S-N lines, the constants m and A are based upon the results of constant amplitude tests. The design codes use "Detail Classes" for grouping detail geometries on a scale of fatigue vulnerabili-ty. Detail Classes are indicated with letters, B C D etc, or numbers, depending upon the code considered.

The stress range, cy, to be used in conjunction with the S-N approach is defined as the algebraic difference between the maximum and minimum stress

inacycle:

0.x0iiic

For welded details the inverse slope of the first segment of the S-N line usually has a value m1 = 3, and for the second segment m2 = 5.

The zero stress intercept of segment i of an S-N line, A, is based upon statistical evaluation of results of constant amplitude loading for the relevant details. As these results show scatter the codes work with "mean"

lines and "mean minus k*(standard deviation of log N)" lines. Mean lines (k = O) represent S-N curves with a 50% probability of survival and mean minus 2*standard deviation lines (k = 2) represent S-N lines with a 97.7%

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EVALUATION OF FATIGUE ASPECTS NSHIP STRUCTURAL DESIGN 5

bility of survival. Most codes publish their design S-N curves for k = 2 only. In case the value of lg is indicated too, S-N curves for any pro-bability of survival can be constructed using data for the standard normal distribution in combination with equation (5):

log Alk

=

log A10-k*1g

(5)

The choice between a one-, two or three segment S-N representation is nor-mally dictated by the code, based upon constant or variable amplitude loading and environmental conditions. Sometimes there is an option to choose for simplicity a one segment line instead of three segment line in order to make damage predictions easier in case of variable amplitude loading.

Some codes clearly show a cut off limit whereas others don't, thus giving some doubt about how to handle.

From the above formats it is clear that the S-N approach can take into account the effect of a fatigue limit: no fatigue damage is caused in case the stress range is less than the fatigue limit, equation (1), or a cut off ilmit, equation (4).

2.2.2 Fatigue life prediction

Two cases have to be distinguished for a fatigue life prediction based upon the S-N approach:

* For constant amplitude loading the fatigue life N can be determined by reading off the appropriate S-N line for the given stress range AO.

* _{In case of variable}

amplitude

loading, the procedure is slightly more involved, as a damage accumulation hypothesis has to be used.

From the practical point of view, Palingren [1] and Miner [2] introduced a linear damage accumulation rule, stating that the damage caused by n load cycles at load range o1 is equal to the ratio of the applied number of load cycles, n, and the fatigue resistance of the detail at the same load range, as represented by equation (6):

The total damage due to cycles at different load levels can then be evaluated with equation (7):

D0

₌

E d1

Dajj

(7)

i=i i

This damage accumulation concept implicitly uses a damage scaling where

D0 = O

means no damage and

D0 =

means detail failure, where

normally

Df_iuro =

1.

For variable amplitude loading following steps have to be carried out to complete a fatigue analysis:

a. a stress range histogram has to be constructed. In shipbuilding

practice, it is usual to work with a long term probability of excee-dance of stress levels according to the Weibull distribution, fig. 2

[3] and equation (8):

exp[(-)']

(8)

The Weibull scale parameter, q, is defined in equation (9): International Maritii Conference Indonesia '97

aa0

q

- (in N0)h/h

The Weibull shape parameter, h, is related with ship type, ship dimensions, location of structural component which is considered etc. Parametric formulae for the Weibull shape parameter, h, are pu-blished by classification societies, e.g. [4] [5).

Equation (10) represents the stress range density distribution func-tion which belongs to the Weibull distribufunc-tion:

=

aa3{1 -

0:12)1/h

(10)

Using the long-term stress range distribution according to the Wei-bull distribution in combination with a one aeqment S-N line, and

assuming the linear damage accumulation rule to be applicable (7), the total damage, due to the entire stress range histogram (10), is represented by equation (11):

'

_ni

1

(0)mi

N0.

=

i

A

Alk

r(1-)

the fatigue life can be calculated with help of equation (12) in terms of the number of stress cycles until failure, assuming that the stress range histogram is applicable for the full lifetime of the ship (N0 = NL):

Nf =

Ei

-D0

D0

Instead of using the damage parameter, D, as calculated from (11), the ratio of the allowable and applied reference stress range value of the Weibull distribution can be calculated with equation (13):

(l)1/i1

D0

2.2.3 Types of S-N approach

The methods to calculate fatigue strength according to the SN-concept can be further subdivided into following three types:

Nominal stress approach:

The stress range used in this case is to be based upon simple beam theory. The stress concentration associated with structural geometry and weld toe

is allowed for by selection of the relevant S-N curve, see fig. 3 [6], from a set of Detail Classes for different details, see fig. 4 [3].

A number of drawbacks associated with this method are:

- in many cases the detail in question cannot easily be classified in the system of "Detail Classes" as they represent only a very limited number of basic configurations,

- it is not possible to account for the essential difference between de-tails A and B as shown in fig. 5. Both these aspects result in a

rela-tively large scatter in fatigue strength, which has to be covered by the design S-N line used in the code

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EVALUATION OF FATIGUE ASPECTS IN SHIP STPJJCTURAL DESIGN 7

-

the nominal stress cannot be easily defined in many cases, for example where the joint is situated in a region of stress concentration resul-ting from the gross shape of the structure which is not covered by one of the Detail Classes, see fig. 6 [4]. In these situations the stress in way of the weld has to be calculated instead of using a standard de-tail category. An other example is the stress concentration due to fa-brication aspects like excentricities etc. In fact this means that the Nominal stress concept is to be replaced by the Hot Spot stress appro-ach in such cases.

Geometric or Hot Spot stress approach:

In this approach, the stress range for reading off in the S-N curve has to include the stress concentration associated with the structural geometry, but not due to the weld detail itself. This concept is generally applied for fatigue evaluation of welded structures and for tubular joints in offshore structures. In principle a single design fatigue curve is

appli-cable for all welded details when this approach is adopted.

In order to exclude the influence of details of the weld geometry as much as possible, the hot spot or geometric stress in way of the weld toe is extrapolated from FEM-results in two points near to the weld, see fig. 7

[4]. However, there is no uniform advice on aspects as:

- element type to be used: 3-D solids or 2-D plates, with or without

inidside nodes,

- ratio of element size and plate thickness,

- stress averaging technique: nodal stresses or element stresses

- position of points of which FEM stress is used for the extrapolation, - extrapolation method (linear or quadratic)

- S-N line to be used for this method

Notch stress or local stress/strain approach:

This method still goes one step further by also including the effect of stress concentration of the local notch in addition to the general stress concentration due to structural geometry. This approach is mainly used for

unwelded geometry with stress concentration. In case it is applied for welded details, the stress concentration due to the weld geometry has to be included. As many factors are important in view of this (weld dimensions, weld shape, curvature at the weld toe, undercut etc) it is normal practice to apply stress concentration factors which are based upon parametric

formula and other empirical corrections which account for these aspects. In case the stress concentration at the toe of the weld is to be calculated by FE-method, a very fine mesh is required, see Fig. 8 [7].

2.2.4 Evaluation of the three S-N approaches

The relationships between the S-N lines of these three approaches is clear-ly indicated in Fig. 9 [8]: in all cases where the geometric or global stress concentration has been calculated, the nominal stress approach can be replaced by the hot spot stress approach, and in case the stress concen-tration due to the weld geometry has been evaluated or prescribed, see e.g.

[4] [5], the notch stress approach can be used.

The nominal stress approach is very simple to use, but it has little preci-sion due to problems related with the need that an infinite range of de-tails has to be classified with a limited nwnber of detail categories. As a result the nominal stress method will in average be over-conservative as the design S-N curves account for the large scatter in fatigue results. Furthermore, the selection of the proper S-N curve is critical because of influence of geometry on the fatigue behaviour.

The advantage of the hot spot stress approach is that the joint classifi-. cation has been replaced by using the hot spot or structural stress range, which can be calculated in principle for any geometry, no matter its com-plexity. As finite element calculations become more and more standard practice in ship structural design, the use of slightly more accurate models for the evaluation of geometric stresses at details is a logical

8 LH. Vink, B. Boon. B.C. Buisman

step further. Uniform guidance for finite element models and extrapolation methods to determine the hot spot stress are essential, see [4] [6] [9].

The results of finite element models have still to be corrected with empi-rical factors to include stress raising due to eccentricity, angular mis-match etc.

The hot Spot stress approach does not explicitly account for the stress raising effect due to weld geometry etc. Because of this, additional empi-rical corrections have to be included, which means that there is not a single design S-N line which has to be used in conjunction with this con-cept.

Apart from the nominal dimensions of the weld, the notch stress approach requires detailed information about the geometry of weld shape, undercut etc, and a much more detailed finite element model to evaluate the stress distribition in way of the weld. As these parameters can show strong scat-ter in practice, it is questionable which values have to be used for direct calculations. Instead of spending the additional effort to do these calcu-lation it is becoming more a tendency now to use parametric design formulae for the additional stress concentration factor due to the weld, which take account of global weld dimensions and empirical correction factors for other aspects as e.g. weld type, weld finishing, weld improvement methods

etc.

Because of the large variety of structural details in ships and the need for a relatively simple and practical procedure, the notch stress approach seems relevant for fatigue evaluation of ship structures, where the geome-tric stress concentration as based upon finite element calculations is com-bined with an extensive set of parametric formulae for stress concentration factors to evaluate the stress concentration due to the weld geometry. If

this method is well balanced, it is possible that only one design S-N curve will suffice for all welded connections.

The linear damage accumulation rule, as described above, is quite an over-simplification of reality for variable amplitude loading, where loading sequence effects play a role. Still it is almost the only practical method for use in combination with the S-N approach. Also the introduction of 3 segment S-N curves instead of the normal 2 segment one for use in

combi-nation with variable amplitude loading is intended to arrive at better predictions.

Further aspects which deserve more study in combination with the S-N ap-proach are:

- effect of mean stress level due to still water loading,

- thickness effect,

- effect of corrosion and cathodic protection,

- effect of residual stresses,

For most of these aspects more or less empirical corrections are in use, but they are not rigorously accounted for. Nevertheless, this rather

prac-tical approch makes the S-N approach simple and suitable for a design tool.

2.2.5 Definition of "failure"

The failure criteriuin as normally used in conjunction with the S-N appro-ach, D0 = 1, is based upon tests with constant amplitude loading on rela-tively small specimen of standard geometry, see Fig. 10 [10], where the definition of "failure" is not really uniform. The number of cycles to failure, N, at stress level i, as used in literature can be either based upon:

- a "visible crack" or a "through thickness crack" has developed (11)

- loss of strength of the specimen [11] and complete fracture of the

spe-cimen [12]

- crack initiation defined as 20% drop of tensile load [13].

On the other hand, this failure criteriuin for small specimen is not capable to predict the total fatigue life of large structures as it does not

re-flect the residual fatigue life during the crack growth stage. In ship

EVALUATION OF FATIGUE ASPECTS IN SHIP SIRUCTURAL DESIGN 9

structures rather long cracks may be acceptable, depending upon stress range level, the actual place of the crack and the configuration (redistri-bution of stresses due to redundant nature of constructions, structures with intersecting plates etc.), which means that a significant fraction of the total fatigue life will remain after the formation of a through the thickness crack.

2.3 The fracture mechanics approach

2.3.1 Fields of application for fracture mechanics

The fracture mechanics approach assumes a sharp initial crack of any length.

Its main usefullness is in its ability to:

- predict the number of cycles required to propagate from an initial small crack to a final crack size; subcritical fatigue crack growth.

- calculate the critical crack size; instable crack growth or brittle

fracture. Brittle fracture prediction is based upon the toughness

para-meter kÇ. . A typical situation leading to brittle fracture would be a fatigue crack which is subjected to a severe stress intensity at low temperature, during a bad storm or collision, which takes it beyond the arresting capacity of the material.

- set defect acceptance standards, using fitness for purpose criteria,

which include:

* _{a "failure" criterium based upon aspects as:}

+ critical crack size,

+ a criterium for oil spill in relation with environmental

accep-tance levels,

+ a criterium for leakage of seawater in relation with the type of

compartment,

+ functionality of the system,

+ psychological acceptance level.

* _{likely crack growth between inspections,}

* maximum crack length which may be left undetected during inspection,

using an inspection period and a critical length,

2.3.2 Crack growth prediction using fracture mechanics approach:

The relation between the crack growth rate and the loading for normal steel is indicated in Fig. 11.

The most well known model for crack growth is the Paris-Erdogan law for subcritical (ductile) fatigue crack growth, region B in Fig. 11. This linear log-log relation is represented in equation (14):

-= :

Region B

(14)

Here, K = K.- K., is the loading parameter (stress intensity factor ran-ge), while C and m are crack propagation constants of the material. For steel qualities as normally used in ships, these constants are:

m= 3

C = 3*1 in air and 2.3*10'3 in marine environments (units in N and

Iran)

These values for C are safe upperbounds.

In the near threshold range, region A in Fig. 11, the influence of the threshold value for the stress intensity, K+ = min value of stress inten-sity for growth of crack, can be incorporated by extending the crack growth relation according to equation (15):

-= c( (K)m'- (AKth)m")

Region A plus B

(15)

For welded steel structures following threshold value is recommended:

10 J.H. Vink,B. Boon, B.C. Buisman

= (170 à 214)*R, but not less than 63 N/mm3"2, where R is the stress

ratio: R = o/o = [14]

In the upswing region of the crack growth curve, region C in Fig. 11, the influence of the critical value of the stress intensity factor, K ,

combi-ned with the influence of the stress ratio, can also be incorporated in the crack growth relation according to [15), see equation (16) of Forman:

da

C. ((K)m'CKth)m')

dl'J

(1-R)K-LK

RegionA, .BplusC

(16)

The value of the fracture toughness, K, is strongly related with the mate-rial quality (Grade) of the steel used.

Starting with the Paris-Erdogan law for crack growth in region B, equation (14), the number of cycles for growth of a crack from an initial length, a0, until a final length, a1, follows from equation (17):

N

N=fdn=1

da

(17)

Based upon the result for a center cracked plate, the stress intensity for any cracked configuration can be represented with equation (18), where Y(a) is a correction coefficient which takes account of the geometry and crack length:

(18)

After some reordering this results in equation (19), which shows the

cha-racteristic form of an S-N curve, see equation (2):

(.{) (19)

where:

a1

da

Y(a) (t.a)m1/'2

From the above analogy it appears that the inverse slope of the S-N line,

m, and the exponent, m, of the Paris' equation are closely related, which makes it logical that both have the same value: ni = m = 3.

The above summarised equations for the crack growth rate use an implicit assumption that the crack growth rate is independent of the prehistory of crack growth and/or loading spectrum. This means that the fracture mecha-nics approach as explained sofar does not cater for loading sequence

ef-fects either.

In general a fatigue crack can propagate in three modes, depending on the relative orientation of loading near the crack tip, see Fig. 12. In view of this, three different stress interisitiy factors, K1 K20 and K002 , are

in-troduced. Apart from the prediction the crack growth rate, for mixed mode loading also the direction of crack growth is important, which makes crack growth prediction for these cases much more complicated.

For prediction of the direction for crack growth under mixed mode loading several criteria can be used according to Suini [16], as:

- direction with maximum opening mode stress intensity, K1.

EVALUATION OF FATIGUE ASPECTS IN SHIP STRUCTURAL DESIGN 11

-

direction where the shearing mode stress intensity, K11, vanishes, known

as the local symmetry criterion.

- direction normal to maximum hoop stress.

- direction which gives maximum elastic energy release rate.

- direction of minimum strain energy density.

No uniform opinion exists until now which of the above criteria is the best one to be used.

When simulating the growth of fatigue cracks, the values of the stress intensity factors, K1

(i

= I, II and III), have to be evaluated for each new position of the crack tip in order to make sufficiently accurate pre-dictions for direction and speed of crack growth during the next interval. For basic geometries, the stress intensity factor can be found in hand-books, see e.g. [17] [18) [19]. For these cases the stress intensity is expressed as: K Y.O.V(1.a), where:

- a is characteristic (half) length of the crack,

- o is the far field stress level (nominal stress value).

- Y is a correction coefficient depending upon the actual geometry of the

crack and detail; Y = i for a plate with an infinitely small crack of length 2a and loaded with a uniaxial stress o perpendicular to the crack.

In case of arbitrary geometries, the stress intensity factors have to be evaluated with help of finite element calculations. In view of this, sever-al numericsever-al methods are described in literature:

- direct method, based upon interpolation of the displacements of nodes near the crack tip [20). In order that an accurate description of the singular stress field near the crack tip can be made, this method re-quires a ring of triangular quarterpoint elements near the crack tip, see Fig. 13. Furthermore the elements near the crack tip have to be very small, which will increase the computer time. Fig. 14 gives a com-parison between results of this method and exact values for a strip with a center crack of variable length. See Fig. 15 for the element mesh of the strip.

- indirect methods, based upon energy principles. These methods differ in

the way to calculate the change of energy when the crack is virtually extended. The main advantage of these methods is that they do not re-quire quarterpoint elements neither a very fine mesh near the crack

tip, which reduces computing time. The difficulty of these methods is

to find the correct relation between the calculated parameter(s) and stress intensitiy factors K1

(i

= I II and III), while the results also show some dependency upon the path or region which is used for inte-gration. Following methods belong to this category:

+ J integral method, see [21] [22) [23] [24] [18],

+ Modified Crack Closure Integral, [25], + Stiffness Derivative method, [26] [27],

+ Equivalent Domain Integral method, [28]

As these methods are still in development, experiments, preferably on large

scale components, are still necessary for calibration purposes and to get better insight in the factors involved in crack growth in real structural configurations.

2.3.3 Evaluation of the advantages of fracture mechanics approach:

The main advantages of the crack growth calculation above the SN-concept

are:

- the stress intensity concept can be used to predict crack growth for any geometry,

- relatively high precision in fatigue failure prediction,

- the residual fatigue life after the formation of a through thickness crack can be accounted for,

- the load redistribution and load shedding effects in redundant large scale structures due to the presence of a crack of any length can be accounted for in the finite element model which is used for evaluation of the stress intensity factor.

12 J.H. Vink, B. Boon, B.C. Buisman

Some disadvantages of this method are:

- for crack growth prediction, the stress intensity factor has to be

calculated for each step during the simulation process, which requires a considerable computing effort,

- the crack initiation period and size of an initial crack can not be de-termined with this approach.

Furthermore, the fracture mechanics approach as described so far does not cater for a number of aspects which are more or less the same as mentioned with the S-N approach:

- influence of variations in mean stress level (stress ratio R) due to

still water loading,

- loading sequence or spectrum effect, - effect of residual stresses,

- heat affected zone (HAZ),

- the influence of corrosion due to seawater and cathodic protection,

- etc,

As the influence of these effects on crack initiation and crack growth is not sufficiently understood until now, experimental verification is impor-tant, especially on large scale structural components instead of small test specimen.

From research it appears that a proper crack closure model can take account of the dynamic behaviour of the crack during variable amplitude loading, inclusive of the effect of mean stress level and tensile or compressive overload, resulting in an effective stress intensity range, AK, which has to be used in the crack growth equations instead of K, [29]. The methods that cater for the crack closure effect can be classified on a scale from mainly empirical to fundamental. The empirical ones require only little additional computation time whereas the fundamental ones take much more computing effort for more reliable crack growth predictions. A very simple improvement for crack growth predictions can be realised by use of an effective stress range which is based upon the tensile part of the stress cycles only, as the compressive part will not contribute to growth of the

crack.

The third mentioned aspect can be included in the fracture mechanics ap-proach in principle too by use of built in strains when evaluating the stress intensity factor.

2.3.4 Crack initiation simulation methods:

In order that a prediction of the total fatigue life of a component loaded in fatigue can be based upon the fracture mechanics approach, the crack initiation period for the development of a small initial crack, length a0, is an important parameter. In literature, three methods are mentioned to account for the intiation period:

- an S-N based approach: As the standard S-N curves are based upon small

specimen, they predict total fatigue lives which are close to the ini-tiation period for a small (0.25 inch) or a through thickness crack. - fracture mechanics approach based upon a (very) small initial crack. This method is applicable for constructions with stress raisers as discontinuities or welds. It assumes the existence of small imperfecti-ons (pre-existing microscopic cracks, notches at the surface, weld de-fects etc.) where cracks initiate due to localized plastic deformation from the very beginning. The crack propagation model is applied for an initial crack length in the range of 0.04 and 0.5 nun, basad upon expe-rience [30) [31] [3] [27]. For the crack initiation stage, with small crack lengths up to the plate thickness, the stress intensity range has to be based upon the complete stress cycle, as there may exist high local residual tensile stresses due to welding.

- local strain approach. This method uses a strain life relationship for

the most highly stressed area, based upon the Coffin-l4anson equation for plastic strain with a correction for the elastic strain according to Basquin, see [27]. This approach is mainly applicable for non welded details, and requires a summation of the strain history of each element ahead of the crack path.

EVALUATION OF FATIGUE ASPECTS IN SHIP StRUCTURAL DESIGN 13

3 LARGE SCALE TESTS

3.1 Arquments for larqe scale fatigue tests

Among the above indicated arguments for experiments to verify fatigue life predictions, there are a number of phenomena that require experiments on

large scale testpieces instead of small specimen as used for S-N curves: - influence of actual structural detail

- details of the stress pattern near the crack tip for actual plate thickness, inclusive of HAZ, weld defects etc.,

- load redistribution in the structure during the crack growth stage for the actual structural geometry.

- residual welding stresses may be different for large scale structures as compared with small specimen.

- fracture resistance of intersecting plate sructures,

- initial deflections of plate panels and misalignment or building

tole-rances, which may introduce repeated buckling stresses.

In order to get better insight into the degree of correlation between pre-sent fatigue prediction methods and actual fatigue damage experienced on ships in service, fatigue exeriments on a large scale ship structure compo-nent were done in the Ship Structures Laboratory of the Deift University of Technology.

3.2 Selection of detail to be tested

The detail for doing large scale tests was chosen because of fatigue pro-blems that appeared on a number of medium sized open type container and multy purpose ships of length L = 100 à 120 m, with 2 holds of approx. 30 à 35 m length each.

Each hatchopening is closed with two pairs of single folding hatch covers, which are split approximately at half length of the hatchway. One pair of covers is folding together to a vertical position in way of the aftmost end coasting of the hatchway, and the other pair to the foremost one, see Fig.

16 132).

When closing, first one pair of covers is lowered, with the wheels at the front corners rolling over the rails. When both panels of the pair are almost unfolded and level, the wheels roll downward along a short sloping part of the rail, in order that the covers are lowered onto their seals for watertightness. Then, the other pair of covers can be lowered in the same way

This principle of automatic realization of watertightness when closing the covers as realised with interrupted rails, see fig. 17, originates from smaller ships and ships without continuous longitudinal coainings. Once this had become more or less a standard solution, it was also applied at ships of greater lengths and/or continuous hatch coamings, even in cases where high strength steel was used in the longitudinal strength members, thus creating a major discontinuety in way of the mo8t highly stressed extreme fibre of the hull. This was exactly the situation when the fatigue problems emerged. On the ships visited, after being in service for about 4 years, fatigue cracks had developed in the horizontal coaming plates, originating from the weld in way of the end of the interrupted rails, see fig. 18. When looking to the detail adopted, an experienced structural engineer can draw simply a number of alternatives which meet both the requirements:

clo-sing of the covers and also lower the stress concentration for a good deal. The lesson to be learned is that awareness of potential fatigue problems in

the design stage will help to prevent a lot of trouble with fatigue cracks later [33] [34] [12].

After all, it is a good example, which demonstrates a number of aspects:

- fatigue awareness is also relevant for structural engineers which are

working on medium sized ships

- details which have been used previously need not be acceptable for new ships with diffetent length, type, arrangement, material etc.

14 1H. Vink, B. Boon, B.C. Buisman

- try to remove stress raisers as much as possible: by choosing better details a lot of (fatigue) problems can be avoided

- also the certifying authorities were not sufficiently fatigue aware in

these cases and missed the chance to correct it beforehand.

3.3 Testpiece

The testpiece as used for the fatigue and crack growth experiments, see Fig. 19, consists of two longitudinal hatch coamings which are rotated 90° about a

longitudinal

axis. Each coaliLing is fitted with interrupted hatch

cover rails. The dimensions of the cross section and rail of the testpiece are chosen as much as possible equal to the dimensions on board of the ships, see Fig. 20. Both the coaming and rail are made of ordinary mild steel, o = 245 N/mm2.

The advantage of this arrangement is that 4 identical discontinuities can be tested at one time, provided that the lengths of cracks are kept suf

fi-ciently small that no mutual influence exists. This means that the first cracks have to be stopped or repaired at a certain length, and only the last one can grow until collapse of the testpiece.

3.4 Fatigue loading for the testpiece

During the fatigue tests, the testpiece was loaded by a parallel movement at one end while the load range is kept constant.

The loadrange used, F = 1080 kN resulting in = 43.6 N/mm2 over the net section without rail, is based upon a minimum expected number of

cy-cles, N,, = 0.44*106 (97.7% probability of exceedance), and a maximum

expected number of cycles, NL.,, = 2.80*106 (2.3% probability of exceedance), while the mean line gives = 1.11*106 cycles. As S-N line the DNV notch stress concept line I for air or cathodic protection [4], was used in combination with the default value Y,, = 1.5 for the stress concentration due to the weld. The geometric stress concentration factor, Yg = 3.51, was determined from linear extrapolation of the strain gauge measurements during the static tests for two sets of strain gauges in line with the corners of an interrupted rail, see Fig. 21, where the leg length of the weld is +/-12 mm.

During the full length of the fatigue test program the loading was fixed at FL., = 1180 kN and F = 100 kN.

4 TEST RESULTS AND EVALUATION

4.1 Crack initiation

Initial defects in welded constructions, like microcracks, weld defects, notches etc, have sizes that can range from very small up to the order of a millimeter. Depending upon their size it will take a shorter or longer

period before they have grown so much that the change in stresses can be measured with strain gauges near the weld toe.

In Fig. 22 the output of the straingauges located 6 mm away from the weld toe for the rail end at location BA, see Fig. 19, is plotted over the cy-cles. This graph shows that crack initiation was already measurable at N = 0.1 à 0.2*106 cycles at the bottom corner of the rail end. The crack at this location was visibly detected only at N = 0.49*106 cycles when it had a length of 55 mm (sum of cracks at bottom and top corner of the rail). Fig. 23 shows the growth of the total cracklength at the outer and inner side of the plate for the same location BA. A linear extrapolation of the measured cracklength at the outerside results in zero cracklength at N = 0.15*106, which very well matches with the first decrease of strain gauge output.

For the rail ends located at CA and 3V the picture is analogue, except that the moment of crack initiation is later, see Fig. 24. At location CV crack initiation did not appear at all up to N = 3.4*106 cycles.

From Fig. 25 it can be concluded that the moment of crack initiation is not influenced by asymmetrical loading of the testpiece, and it is remarkable

that:

- crack

initiation

at the back side, position BA and CA, was earlier than at the front side, while the measured strains are lower at the back

EVALUATION OF FATIGUE ASPECTS IN SF11? STRUCTURAL DESIGN 15

side of the testpiece.

- crack

initiation

did not start at all up to

N =

3.4*106 cycles at loca-tion CV, which showed the highest strains.

From this it can be deducted that the crack initiation period is not only determined by the stress level but also strongly depends upon other factors as micro cracks, weld defects, weld finishing and residual stresses due to welding.

A visual check of the welds in advance did however not give rise to strong suspection of the welds at locations BA and CA, nor were the welds at location BV and CV qualified as significantly better.

4.2 Throuqh thickness cracks

The development of a through thickness crack will be used as failure crite-rium for the presentation of the results for this large scale test speci-men. This choice is made because it is the best equivalence with the

defi-nition of failure for small specimen, see Fig. 10, where the crack growth life is very limited after a through thickness crack has developed.

In Fig. 26 the moment of failure for the discontinuities of the testpiece are compared with the predicted scatterband of the notch stress S-N line I of DNV [4], at the notch stress level

0b

= 230 N/mm2, as follows from the applied load range of 1080 kN in combination with the stress concentration

factors Y .Y_ 3.51*1.5

Whereas die three cracks that developed fall within the expected range of mean +1- 2*standard deviations, the forth crack even did not initiate at mean + 2*standard deviations.

4.3 Crack qrowth

The first two cracks that developed, location BA and CA, had to be stopped in a rather early stage, in order to exclude mutual influence.

Fig. 27 shows the growth of crack length at the outer side of the plate for the crack at location BA: see Fig. 28 for an explanation of the dimensions Ab, Ao, Bb and Ro.

Two individual cracks started, one at each corner of the rail end, who coalesced at N = 0.7*106. From thereon, the crack grew further until it was

stopped at N = 1.11*106 cycles.

The growth of cracklength for the third crack at location BV is shown in Fig. 29. Again 2 individual cracks started at the corners of the rail, which coalesced at N = 2.3*106 cycles. At N = 2.4*106 a through thickness crack had developed, and at about N = 2.6*10' a crack of 80 umi length had

developed in the edge strip 125* 14. As still no noticeable changes in the

strain gauge readings at location CV were found at that moment, it was decided that the fourth crack might not initiate at all and crack 3 was allowed to grow further. Fig. 30 shows that the growth of the crack in the strip 125* 14 at location BV gradually slowed down when the crack tip ap-proached the free edge of the strip, until it finally collapsed at N = 2.85*106. As no sudden increase of the crack growth speed of the side plate is found at that moment, see Fig. 29, this supports the impression that the decreasing crack growth speed in the strip is caused by an unloading due to a secondary bending effect. Crack growth simulations have to clarify this assumption in a later stage.

At N = 3.2*106 the speed of crack growth in the side plate, Fig. 29, rather abrubtly increased as in a short period the crack at location BA again had grown to considerable length, thus additionally weakening this cross sec-tion of the test piece.

Final collapse took place at N = 3.4*10', due to ductile fracture when the tips of the cracks at BV and BA had left a distance of only 25 cm in the bottomplate.

5 EVALUATION

5.1 Fatique life prediction for interrupted rail on board

The experiments have shown that the moment of fatigue failure of the inter-rupted rails during constant amplitude loading can be predicted

16 JR Vink, B. Boon, B.C. Buisman

ly accurate with S-N line I of DNV [4] according to the notch stress con-cept, in combination with stress concentration factors YgY_ = 3.51*1.5 Using a realistic long term load distribution for seagoing service, a prediction of the fatigue life on board of a ship can be made, based upon the linear damage accumulation hypothesis.

Assuming that the actual section modulus at coaming, W, of the ship is equal to the minimum required midship section modules, W,, the maximum wave bending stress range, hogging - sagging, is:

= 208 N/mm2 nominal stress, for a realistic block coefficient. Tis leads to a notch stress range:

= 208*3.51*1.5 = 1095 N/mm2

In case this stress range is being exceeded once out of NL = 10' cycles (20 year service) and using a Weibull distribution with shape factor h =1, the accumulated damage for the interrupted rail will not exceed D = 27.7 with a probability of 97.7%, see Fig. 31. This means that the detail of the inter-rupted rail will show no through thickness cracks within 20/27.7 = 0.72 years of service.

For comparison purposes, the prediction has also been made for a standard detail, being a cruciform joint, see Fig. 32 [4) with the default value

Y6.Y = 1.8

Calculations for this joint indicate that the accumulated damage will not exceed D = 0.82 with a probability of 97.7%, see Fig. 33.

The cruciform joint appears to be safe during the life time of a ship, whereas the interrupted rail is very fatigue prone due to its extremely high geometric stress concentration.

The predicted fatigue life of at least 0.72 years is considerably less than what was found on board, but this difference can be partly explained as follows:

- the actual section modulus of the ship was in excess of the rule

modu-lus by 11.3%, thus leading to a 38% longer fatigue life (1.113)

- there is difference in opinion whether and how the stress range has to be corrected for welded constructions in case the mean stress level of the cycle is low. Assuming that the still water bending moment on ave-rage over all voyages will be zero, a correction factor of 0.9 [4] [35] à 0.8 [3) [5] for the stress range is realistic, which results in an extension of the fatigue life prediction by 37% (1/0.9) up to 95%

(1/0.8).

- The actual ship may on average have sailed in less severe conditions

than assumed in the long term load distribution which has been used.

5.2 Crack growth stage

The measurements on the testpiece show that the crack propagation phase for

the third crack started at N = 2.4*106 cycles and lasted until rupture at N = 3.4*106 cycles, thus covering about 1.0*106 cycles.

If it is assumed that the crack propagation period would have been about of the same length in case the first crack had been tested until collapse, the fatigue life would have had following subdivision:

- 0.15*106 cycles until initiation,

- 0.49*10' cycles until visible crack (55 imu = sum of 2 cracks),

- 0.76*106 cycles until failure = through thickness crack, - 1.76*106 cycles until collapse.

From this it follows that the crack propagation phase takes a considerable percentage of the total fatigue life.

The above picture is, however, an oversimplification in some ways:

- the crack growth stage of crack BV has been shortened because at N = 3.2*106 the crack growth speed abrubtly increased due to the fact that crack BA additionally weakened the net section.

- during the experiments the loadrange has been kept constant, with a consequence that the increase in stress over the net section is stron-ger than would have been on board of a ship for a crack of the same length.

- the above used period of crack growth does not yet account for the

critical length in view of brittle fracture under an extreme load peak.

EVALUATION OF FATIGUE ASPECT S IN SHIP STRUCTURAL DESIGN 17

5.3 Comparison of S-N lines

The "Detail Classes" introduced in combination with sets of S-N lines, see e.g. Fig. 3 and 4, are only intended to distinguish between details with different stress concentration factors, thus introducing a rather inflexi-ble system.

As discussed, it is proposed to use only one basic S-N line (for welded constructions) according to the notch stress concept, in combination with appropriate parametric formulae for stress concentration due to the weld, Y, and hot spot or geometric stresses based upon FEM calculations.

For this purpose, in Fig. 34 it is indicated that S-N line I of DNV [4], notch stress concept, after being corrected with Y, = 1.5, is equivalent with S-N line D, nominal stress concept, [6], which is in principle appli-cable for continuous welds parallel or transverse to the direction of the applied stress.

In the saine way, Fig. 35 shows that the interrupted rail, with a geometric stress concentration Yg = 3.51, is much more severe than detail category G see Fig. 3 and 4. This means that the interrupted rail cannot be classified in the system of the nominal stress concept. Instead it requires an evalu-ation of the geometric stress according to the notch stress concept.

6 CONCLUSIONS

- crack initiation can be detected in a very early stage with help of

strain gauges,

- the crack initiation period for welded constructions shows a conside-rable scatter, but in the worst case crack initiation starts almost at the beginning,

- cracks initiate a long time before they become visible (10 à 25 mm) on a clean and well accessible position,

- cracks in ship structures on board, in tanks with dust, rust, coating and located at badly accessible positions, can have considerable length before they are detected by visual inspection,

- a proper definition of, and more data on the crack initiation period is important, and will be very helpfull in view of fatigue life prediction with help of the fracture mechanics approach,

- fatigue failure according to the S-N approach is almost equivalent with a through thickness crack, thus not accounting for the crack growth stage,

- instead of "Detail Classes" in combination with series of S-N lines, it

is proposed to work with one S-N line and appropriate stress

concentra-tion factors which, in order to avoid the limited scope of the detail cl&ss regime, in many cases will have to be based upon FE11

calculati-ons,

- the failure criteriu.m of S-N curves is not applicable for the total

fatigue life of large scale structures, where a through thickness crack is not decisive for failure,

- in order to evaluate the total fatigue life of large scale structures,

the crack growth stage has to be accounted for with help of the frac-ture mechanics approach,

- in view of improvement of crack growth and crack path predictions with help of the fracture mechanics approach, experimental verification is important, especially on large scale structural components,

- fatigue prone details can be removed already in the design stage if the

structural engineer is sufficiently fatigue aware.

REFERENCES

Palingren, A.: DIE LEBENSDAUER VON KUGELLAGERN, Zeitschrift des Ve-reins Deutscher Ingenieure, Band 68, No 14, 1924, p339-341

Miner, M.A.: CUMULATIVE DAMAGE IN FATIGUE, Journal of Applied Me-chanics, Vol 12, no 31, 1945, p 159-164

DNV: FATIGUE STRENGTH ANALYSIS FOR MOBILE OFFSHORE UNITS, Class Note 30.3, 1984

DNV: FATIGUE ASSESSMENT OF SHIP STRUCTURES, Technical Report 93-0432, Oslo, 1995

BV: FATIGUE STRENGTH OF WELDED SHIP STRUCTURES, Report NI 393 DSM ROOE, Paris, 1995

ABS: GUIDE FOR DYNAMIC BASED DESIGN AND EVALUATION OF CONTAINER CARRIER STRUCTURES, 1996

Petershagen, H., Fricke, W., Paetzold, H,: BETRIEBSFESTIGKEIT SCHIFFBAIJLICHER KONSTRUKTIONEN, Handbuch der Werften, band XXII,

1994

Fricke, W.: RULES AND PROCEDURES OF GERMANISCHER LLOYD FOR FATIGUE ASSESSMENT, Hamburg 1995

Niemi, E.: STRESS DETERMINATION FOR FATIGUE ANALYSIS OF WELDED COM-PONENTS, 115/11W-1221-93, Cambridge, 1995

ChaLmers, D.W.: DESIGN OF SHIPS' STRUCTURES, Chapter 13, London

1993

Report of Committee V.1: APPLIED DESIGN - STRENGTH LIMIT STATES FORMULATIONS, 12 th ISSC, Vol 2, 1995

Lloyds Register: FATIGUE DESIGN ASSESSMENT PROCEDURE, LR-Ship Right, London 1996

Petinov, S., Yerinolaeva, N.: LOAD-HISTORY SENSITIVE CYCLIC CURVE CONCEPT IN RANDOM LOAD FATIGUE LIFE PREDICTIONS, Schiffatechnik, Band 40, p 107, 1993

Dijkstra, O.D., Snijder, H.H.: FATIGUE CRACK GROWTH MODELS AND THEIR CONSTANTS, IBBC-TNO, 1988

Ewalds, H.L., Wanhill, R.J.H.: FRACTURE MECHANICS, Delft

Universi-tary Press, ISBN 90.6562.0249, 1989

Suini, Y.,Chen Yang, Hayashi, S.: MORPHOLOGICAL ASPECTS OF FATIGUE CRACK PROPAGATION, Part I: Computational Procedure, To be published, Yokohama 1995

Murakam.i, Y., et.al.: STRESS INTENSITY FACTORS HANDBOOK, VOL I + II, Perga.mon Press, 1987

MurakailLi, Y., et.al.: STRESS INTENSITY FACTORS HANDBOOK, Vol III,

Pergamon Press, 1992

Tada, H., Paris, P.C., Irwin, G.H.: THE STRESS ANALYSIS OF CRACKS HANDBOOK, Del Research Corp. 1985

In ernationa Mari ioe Con erence In.onesia

EVALUATION OF FATIGUE ASPECTS IN SHIP STRUCTURAL DESIGN 19

FRACTURE MECHANICS, ANSYS-manual, Release 5.1, 1992

Anderson, T.L.: FRACTURE MECHANICS, FUNDAMENTALS AND APPLICATIONS, CRC Press, USA, 1991

Shreurs, P.: FRACTURE MECHANICS, PATO Course, Techn. Univ. Eindho-ven, 1994

Cherepanov, G.P.: MECHANICS OF BRITTLE FRACTURE, McGraw-Hill, 1979

Messner, T.W., Meda, G., Sinclair, G.B., SOLECKI, J.S.: J AND H IN-TEGRALS FOR THREE DIMENSIONAL FRACTURE MECHANICS WITH ANSYS, Pro-ceedings of ANSYS Conference, 1996

Rybicki, E.F., Karininen, M.F.: A FINITE ELEMENT CALCULATION OF STRESS INTENSITY FACTORS BY A MODIFIED CRACK CLOSURE INTEGRAL, En-gineering Fracture Mechanics, Vol 9, p 931-938, 1977

Parks, D.M.: A STIFFNESS DERIVATIVE FINITE ELEMENT TECHNIQUE FOR DETERMINATION OF CRACK TIP STRESS INTENSITY FACTORS, International Journal of Fracture, Vol 10, p 487-502, 1974

deLorenzi, H.G.: ON THE ENERGY RELEASE RATE AND THE J INTEGRAL FOR 3 D CRACK CONFIGURATIONS, International Journal of Fracture, Vol 19, p

183-193, 1982

Nikishkov, G.P., Atluri, S.N.: CALCULATION OF FRACTURE MECHANICS PARAMETERS FOR AN ARBITRARY THREE DIMENSIONAL CRACK BY THE 'EQUIVA-LENT DOMAIN INTEGRAL' METHOD, International Journal of Numerical Methods, Vol 24, p 1801-1821, 1987

Peeker, E.: EXTENDED NUMERICAL MODELLING OF FATIGUE BEHAVIOUR, The-sis no 1617, Ecole Polytechnique Federale Lausanne, 1997

Stensen, A.: CRACKS AND STRUCTURAL REDUNDANCY, Marine Technology, Vol 33, p 290-298, 1996

Suini, Y.: FATIGUE CRACK PROPAGATION AND REMAINING LIFE ASSESSSMENT OF SHIP STRUCTURES, To be published, Yokohama, 1997

Buxton, I.L., Daggitt, R.P., King, J.: CARGO ACCESS EQUIPMENT FOR MERCHANT SHIPS, London 1978

Gavin, A.G.: DETAIL DESIGN, KIVI Vermoeiingsdag, 1995

NN: GUIDELINES FOR THE INSPECTION AND MAINTENANCE OF DOUBLE HULL TANKER STRUCTURES, Tanker Structures Cooperative Forum, London, 1995

Fricke, W.: FATIGUE CONTROL IN STRUCTURAL DESIGN OF DIFFERENT SHIP TYPES, IMAM'93, yama, 1993

JE Vink. B. Boon, B.C. Buisman n.0 '4 E E

-S--z

b log N (oyais.)

Fig. 1: S-N curves with 1, 2 and 3 segments

s

q Q

Fig. 2: Weibull distribution [3]

loo IO

-flSaaa..fla...0aaaa...

iiini

11111 W

IIflhIIIIIIIlIllhIIIIìi

uIuuuuuu..uuu..up,.

IHI1UuiUiiBuiiuiUiiIH

______UUiiiUUiiHIiiiiiuplI

Io' I. (cy.

Fig. 3: Basic design S-N curves [6]

International Maritim Conference Indonesia '97

r

TYPE 4 WELDED ATTACHMENTS ON THE SURFACE OR EDGE OF A STRESSED MEMBER

4otes on potential modes of fitiurs

When trie welO s parallel to the direction 01 the applied stress iatsgue cracks normally Initiate at the weld anos. but when it is transvon. to p,.

direction of stressing ritmi usually mutue at the weld toe; for attachment! involving a sIngle, as opposed to. double. w.ld crac.s may also initiale at true wald root In. CrackS then propagate into tite stressed ,nembef. When the welds ar, on or adac.nt to th, edge. of tIre stressedmarnb the

stress concentration is increased and the fatigue strength s reduced, this s the reason f or speciFying an edge distance' in sorne of these omm

se also not. on edge distance n oint Type 2)

4.1 Parent metal (of the stressed member)

adjacent to toes or anos of bevel-butt

or filler welded attachments, regardless

of the orientation of the weld to the

direction of applied stress, arid whether or not the welds are continuous round

the attachment

(e) With attachment iength (parallel to tite

the direction 0f the applied stress)

I S0mni and with edge distance IOn,rrt

lb1 With attachment length (parallel to

tite dm,ection of trie applied stress)

>150mm end wuth edge diStance r I Otitis

Fig. 5:

EVALUATION OF FATIGUE ASPECTS IN SHIP SI RUCTURAL DESIGN 21

B

4.2 Parent metal pf the stressed member)

at the toes or the ends of butt or fillet

welded attachments on or within 10mm

of Trie edges or corners of a stressed member, and regardless of the shape

of the ertacrinrient

G Noie that the classification applies to

alf sizes of ittachment. lt would trieqef ore include, for esamp)e, the unction of two lIstiges at right angles. la such situations a low fatigue class.f cation can often be vOided by th, use of a transition piare Iseo also yo,nt Type3.3)

Butt welded oint! should be made with

an additional reinforcing fillet so as to

prosude a similar toe profile to that

which wouf e.st n a fillet welded

oint

Th, decrease in fatigue strength with

inc,aaslng attachment length is because

rho., load is uanferr,d into tite longer gusset giving an Incerase n stress

concentration

F2

;,'

/

Difference in details not accounted for in detail classification

Ac

1111111 111111111

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Typ. number. description and

flotes on nipa, of failure Class Esplanatory comments Examples, including failure moda.

Fig. 4:

Detail classification [3]

'tif e

Fig. 6:

Gross shape stress raising [4]

Fig. 7: Linear extrapolation for geometric stress at toe of weld [4]

Fig. 8: Model for notch stress [7]

H

A flomin (log) Sc1 (24O N/mm2 A r '! b V 2 B

n erna xon

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Design S-N Curve (Ps = 97,7%) based on: Notch Stress Hot-Spot Stress Nominal Stress o 2 106 N (log)

Fig. 9: Design SN curves of the three different approaches [8]

22 J.FI. Vink, B. Boon, B.0 Buisman

a

EVALUATION OF FATIGUE ASPECTS IN SHIP STRUCTURAL DESIGN 23

Fig. 10: Class F fatigue specimen

[10]

Fig. 11: Crack growth rate curve

Fig. 12: Crack propagation

mode s 0 20 0.10 000 0 02 04 0.6 0.8 alW-ratio

Fig. 14: Stress intensity factor for center cracked strip calculated with the displacement extrapolation method

,g

Fig. 13: Cracktip mesh for calcula-tion of stress intensity by displacement extrapola-tion method

Comparison of FEM and exact results

Center cracked plate HIW = 3

0 50

0.40

LU

± 0 30_o

Intermatìonal Maritiie Conference Indonesia '97

Mode I Mode U Mode fil

24 J.H. Vink, B. Boon, B.0 Buisman

HHIII

'HI"

_'Il'

'III"

I'll"

II"

I'll"

'III

"Il

u y

Fig. 15: Mesh for first quadrant of center crac-ked strip: H/W = 3

r

Fig. 17:

Interrupted rails for hatch cover wheels

Fig. 16: Single folding hatch covers [30]

In erna iona

Marl i Con erence In.onesia

Fig. 18: Crack in coaming-plate at end of rail

r

Fig. 19:

Testpiece: length of parallel part is

6*700 mm

32.O

Fig. 20:

Cross section of test-piece

EVALUATION OF FATIGUE ASPECTS IN SHIP SRUCURAL DESIGN 25

International Maritj. Conference Indonesia '97

Fig. 21:

Strain gauges at end of one rail

26 LIt Vink, B. Boon, ac. Buisman 200 150 100 co 50 Amplitude volts 09 -00 0.0 100 200 300 400 500 600 700 0 600 N

Fig. 22: Straingauge signal for location BA

Chan, nr.

Chan, nr. E23 : OTT(t-1 CLIIÑ.

Amp'itude 12 voltS 090.6 -O 100000 300000 500000 700000 900000 1100000 1300000 N

Fig. 23: Extrapolation of measured crack length at po-sition BA

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0.3

-100 200 300 400 500 600 700 20 900

N icxìocyc,es

0.6

-EVALUATION OF FATIGUE ASPECTS IN SHIP StRUCTURAL DESIGN 27

Fig. 24: Stages of crack development

Fig. 25: Constant level strain gauge readings: N = O 0.1*106 cycles

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Crack number 1 2 3 4

Position BA CA BV CV

Decrease in

straingauge reading

N1, = top corner 0.15*106 c. 0.15*106 c. 0.70*106 c. 3.40*106 c. bott. corner 0.30*106 c. 0.35*106 C. 1.60*106 c. no decrease Extrapoplation to a = O N0= 0.15*106 c. 0.25*106 c. Visible detection N = 0.49*106 c. 0.49*106 c. 1.27*106 c. L,. = 55 mm 25 mm 5 mm Through thickness crack = 0.76*106 c. 1.06*106 o. 2.40*106 c. L = 41 mm 60 sim 40 mm Crack stopped or repaired Nr = 1.11*106 C. 1.23*106 c. 3.40*106 c.

L =

150 mm 400 sim 1200 min

stopped repaired collapse

Section B Section C Average

Back side BA 0.650 CA 0.660 Back side 0.665 Front side BV 0.705 CV 0.710 Front side 0.707 Average Section B 0.6775 Section C 0.6750 Average of all 0.676

-20 -60 -100 -140 -180 -220 -260 -300 -340 -380 -420 -460 450000 -1- z-J 'J Q

z

Natcb, as

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Fig. 26: Comparison of measured cycles at failure and predictions

600000 750000 900000 1050000 1200000

Ab--Ao

Bb- Bo

Fig. 27: Crack growth development at location BA

1000 800 600 CU 500 <E 400

z

300 200 O) d L 100 80 Lfl Q., L 50 +

cl

40 30 20 10

28 J.H. Vink, B. Boon. B.C. Buisman

2

34568106

2 3456 810v

Nr o

cycles

-20 -60 -100 -140 -180 -220 -260 -300 -340 -380 -420 -460 1000000

EVALUATION OF FATIGUE ASPECTS IN SHIP STRUCI1JRAL DESIGN

D Lo=Ak-Ao Lkj=B-Bo LtotL+Lb crackpos Fig. 28: Definition of cracktip positions 1500000 2000000 2500000 3C)00000 3500000

----Ab.Ao- Bb

-Bo

Fig. 29: Crack growth development at location BV

3G J.H. Vink, B. Boon, B.C. Buisman

140

120

loo

80

o)

C

J

40

20

- 0 --

--

O

2400000 2500000 2600000 2700000 2800000 2900000

N

Fig. 30: Crack growth development in strip 125*14 at location BV

120 100 > 80 C a)

° 60

_a) a) 40 E (Q

0 20

EVAlUATION OF FATIGUE ASPECTS IN SHIP STRUCTURAL DESiGN 31

o

Loading and SN line

0 200 400 600 800 1000 1200

Stress range N/mm"2

Totafdaiiage: 2.76966 %

Numbe of cf asses: 100

Arage di age denty: 27.70 %

Fig. 31: cumulative damage calculation for interrupted rail

International Maritiie Conference Indonesia '97

12

Q) D) C

Z8

C/) (Q

o

6

II C c,)

o2-

C)

o

o o

200

400

600

800

1000

1200

Stress range N/mm"2

- Iog(N-f,i) -

log (n-i)

32 II-L Vink,B. Boon, B.0 Buisman

Fig.

32:

K-factors for cruciform joints [4]

International Mariti Conference Indonesia 97

7.6.b t3 eo Kg =1.0

ç>

t,

(

_> K = 0.90 +o.90(ta.ne)"4

Default value: K

= 1.8 t t-,

e=-+e0---L t1

t2

e0 0.3r1

K, from 7.6.a

e

K

ta

=1.0

7.6.c Kg = 1.0 K = 0.90 +0.90(tanO

>

Default value: K

1.8 f; I

K,=l.0

K,

=1.0

C)

-

o2-EVALUATION OF FATICHJE ASPECTS IN SHIP SIRUCFURAL DESIGN 33

o

0

100

200

300

400

Stress range N/mm"2

Iog(N-f,i)Iog(n-i)

Damage distribution

Loading and SN line

I I

Totadamage: 846 Number of classes: ioo

Arage damage denclty: o.e %

Fig. 33: Cumulative damage calculation for cruciform joint

International Mantle Conference Indonesia '97

o 100 200 300 400

1E4

1E2

lEi

1E3

lEi

lEO

t t

International Maritim Conference Indonesia '97

J.H. Vink, B. Boon, B.C. Buisman

3

4

5

6

7

8

9

log N

-v-line D [6]

--linel [4], corr

1.50

Fig. 34: Comparison of line I [4] after correction for Y, = 1.50, with line D, Fig. 3

3

4

5

6

7

8

9

logN

-a--line D[6}

line I [4] , corr =

5.265

Fig. 35: Comparison of line I, [4] after correction for YvYg 5.265, with line D, Fig. 3