Modeling of fatigue in RORO ships

M

A S TER T HES I S

2012-09-25

Modeling of fatigue in RORO ships

ES K I L AM U N D I N

eamundin@kth.se

Centre for Naval Architecture

A

BSTRACT

The largest modern Pure Car and Truck Carriers (PCTC’s) are typically 230 meters long and have 13 cargo decks. In order to facilitate rapid loading and unloading these ships have been subject to a development of reducing any obstructing structures in the cargo hold, meaning that the transversal shear preventing structures, i.e. the racking bulkheads, has been taken to a minimum. Previous studies have concluded that some points on the racking bulkheads, as a result of the stripped down design, are subject to high stresses resulting from wave induced accelerations of the ship.

In this M.Sc. Thesis the fatigue life of a corner of a transverse bulkhead opening in a 230 meter long PCTC with a capacity of 7200 cars is calculated with different methods.

• Fatigue life is calculated from recorded ship motion data with the notch stress method in conjunction with rain flow counting and the cumulative damage principal.

• Fatigue life is calculated according to (DNV CN. 30.7, 2010), based on a Lloyd’s Register FE model load case. • Actual findings on the ship are compared to the calculated results. Due to the lack of inspection data this

comparison is not very extensive and only more briefly discussed.

It is concluded that the fatigue life of the examined point, calculated from recorded motion data is 9.6 years and the fatigue life according to DNV is 8.0 years. It is also found that the fatigue damage is cumulated in almost discrete portions and thus the calculated fatigue life can be inaccurate when a short period of time is evaluated as is done in this thesis. A modification to the racking bulkhead with respect to fatigue life is also analyzed and it is concluded that the fatigue life in the examined point could be extended significantly by some simple modifications to the geometry.

C

ONTENTS

2.4. Rain flow counting algorithm ... 5

2.4.1. Counting ... 6

2.5. Cumulative damage principal ... 7

2.6. Weld effects on fatigue ... 8

2.7. Fatigue life assessment methods ... 9

2.7.1. Nominal stress method ... 9

2.7.2. Structural stress / hot spot method ... 10

2.7.3. Notch stress method ... 11

2.7.4. Fracture mechanics ... 11

2.7.5. Component testing ... 12

2.8. Range of application ... 12

3. Method of calculating fatigue from recorded motions ... 13

3.1. FE-models of the ship ... 13

3.1.1. Global FE-model ... 15

3.1.2. Intermediate FE-model ... 15

3.1.3. Local 3d solid FE-model... 15

3.2. Sampling of stresses ... 16

3.3. Equipment for recording motion data ... 20

3.4. Preparation of motion data and calculation of stress ... 20

3.5. Stress and fatigue calculations ... 23

3.6. Analyzed journey ... 24

4. Class rule method ... 25

5. Results and discussion ... 27

6. Design optimization ... 28

6.1. Analysis ... 28

7. Results and discussion of design optimization ... 29

8. General conclusion... 30 9. Acknowledgements ... 31 References Appendix I Appendix II Appendix III Appendix IV Appendix V Appendix VI Appendix VII

1.

I

Fatigue has been investigated and explored since the 19

utilized S-N curves to describe the fatigue life in metal structures evolve by building ships of steel and production increased was the WWII were US ship yards alone built 5777

79000 landing crafts (ibiblio). During this period the production rate was high, 14 474 tons were built by US ship yards in

tonnage of these produced Liberty ships reached 29 million (tons dwt) and a produced 1000 ships between 1972 and 2002

But the high production pace took its toll. D

significant brittle hull fractures and 19 ships broke in half (!)

Although the problems in the Liberty ships were not originating from development of the cracks. Cracks developed in stress concentrations, could then, due to the welding, run unobstructed

Fatigue problems have historically caused a mentioned, and the classification societies are w economics constantly call for better performance

the ships are pushed further and further towards the limit of wha from fatigue due to vertical bending moments but an

and Pure Car and Truck Carriers (PCTC). Due to their construction with many decks

increasing size and reduced amount of primary transversal structure these ships mostly suffer from fatigue due to global transversal shearing, i.e. racking.

As a result of the above mentioned development been called for by the ship operators and RORO ships and this was done as a M.Sc. Thesis

further progress in this field the aim of this thesis work is to develop and benchmark a fatigue life assessment method based on Söder’s previous work and compare it to classificati

The M/V Mignon is a Pure Car and Truck Carrier

It was built in Korea in 1999 by Daewoo Shipbuilding and Marine Engineering (DSME) meters by Hyundai Vinashin Shipyard in Vietnam.

openings in the racking bulkhead and this is a

verified) that the ship was inspected prior to elongation

been available (or done?) of the ship before it was elongated it is hard to evaluate how much damage was cumulated during the first 6 years of operation, but it is believed that it would be lower than if the ship was built as elongated from the beginning.Drawings of the studied racking bulkhead are shown

is marked in Figure 2.

More descriptive pictures of the investigated position and crack are 1

Fatigue has been investigated and explored since the 19th _{century and one of the pioneers was}

s to describe the fatigue life in metal structures. During this time the ship building industry started and production increased. One major point in the history of the

US ship yards alone built 5777 naval ships (Tassava, C., 2008), not including smaller boats such as t During this period the production rate was high, 2710 Liberty ships

in the years 1941 to 1945, and it took about 50 days ships reached 29 million (tons dwt) and as a comparison

2002 and a total ship tonnage of 80 million (tons dwt pace took its toll. Due to poor material and poor design, nearly 1500 of

and 19 ships broke in half (!) without warning (Naval Officers Club)

iberty ships were not originating from the welding itself this had a significant impact on the Cracks developed in stress concentrations, typically around sharp edged cargo

unobstructed from plate to plate (MatDL).

Fatigue problems have historically caused a number of catastrophic failures, some much more fatal than the above and the classification societies are working hard to find a balance between reliability and economy.

better performance fatigue life becomes a more and more important issue

the ships are pushed further and further towards the limit of what is possible. The majority of ship types suffer mostly vertical bending moments but an exception to this are the RORO ships, e.g

and Pure Car and Truck Carriers (PCTC). Due to their construction with many decks and an ongoing development of increasing size and reduced amount of primary transversal structure these ships mostly suffer from fatigue due to global As a result of the above mentioned development an increasing knowledge in the area of racking induced

and Wallenius Lines started this work by investigating racking induced stress in as a M.Sc. Thesis on the 230 m Wallenius Lines vessel PCTC Mignon

further progress in this field the aim of this thesis work is to develop and benchmark a fatigue life assessment method based on Söder’s previous work and compare it to classification rule calculations and actual ship

Mignon is a Pure Car and Truck Carrier (PCTC) operated by Wallenius Lines, Stockholm, Sweden

Figure 1. PCTC Mignon

It was built in Korea in 1999 by Daewoo Shipbuilding and Marine Engineering (DSME) and in 2005 it was elongated shin Shipyard in Vietnam. In 2006 inspections revealed a crack in the radius of one of the hatch

and this is a contributing factor to why this M. Sc. Thesis is done prior to elongation and that no damage was discovered at that

been available (or done?) of the ship before it was elongated it is hard to evaluate how much damage was cumulated during believed that it would be lower than if the ship was built as elongated from the ing bulkhead are shown in Figure 3 (right) and the lengthwise position in

vestigated position and crack are presented in Figure 27 to

ury and one of the pioneers was Wöhler (1819-1914) who During this time the ship building industry started to history of the ship building industry not including smaller boats such as the 2710 Liberty ships with a displacement of about 50 days to complete each ship. The s a comparison Hyundai Heavy Industries

wt).

nearly 1500 of the Liberty ships had (Naval Officers Club).

this had a significant impact on the sharp edged cargo hatches and number of catastrophic failures, some much more fatal than the above orking hard to find a balance between reliability and economy. Today as fatigue life becomes a more and more important issue as the design of majority of ship types suffer mostly are the RORO ships, e.g. Pure Car Carriers (PCC) and an ongoing development of increasing size and reduced amount of primary transversal structure these ships mostly suffer from fatigue due to global racking induced mechanics has started this work by investigating racking induced stress in vessel PCTC Mignon (Söder, 2008). To further progress in this field the aim of this thesis work is to develop and benchmark a fatigue life assessment method

ship fatigue failure findings. , Stockholm, Sweden, Figure 1.

and in 2005 it was elongated 28.8 In 2006 inspections revealed a crack in the radius of one of the hatch is done. It is believed (but not damage was discovered at that time. As no analysis has been available (or done?) of the ship before it was elongated it is hard to evaluate how much damage was cumulated during believed that it would be lower than if the ship was built as elongated from the (right) and the lengthwise position in the ship

2

The capacity of the ship is 7200 RT43 car units (1 RT43 unit equals 7.38975 m2_{) or 3700 car units and 600 trucks in case}

of mixed load. The ship is classified by Lloyd’s Register as +100A1, Vehicle carrier, movable decks, “deck no. 4, 6 and 8 strengthened for carriage of Roll on/Roll off Cargoes” and the main particulars and general arrangement of the ship are given in Table 1, Figure 2 and Figure 3 (left).

Table 1. Main particulars of PCTC Mignon

Length overall (LOA) 227.90 m

Length between perpendiculars 219.30 m

Breadth moulded 32.26 m

Depth moulded to upper deck 33.48 m

to freeboard deck 14 m

Draft moulded (design) 9.50 m

(scantling) 11.02 m

Service speed at design draft 20.5 kn

No of decks (incl. bridge deck) 14

Figure 2. General arrangement of PCTC Mignon. Note the elongated section marked in the middle. The arrow indicates the position of the racking bulkhead.

3

2.

F

In order to explain the fundamentals of fatigue theory here follows a brief introduction which has been written with influence mainly from (Schijve, 2004) and documents from IIW, the International Institute of Welding. Fatigue in this type of ship structures is generally induced by cyclic loads in the range of ~104 _{to ~10}9 _{cycles and elastic deformations, and}

hence that is the focus here.

2.1. I

Metals are crystalline materials and the process leading to failure is proceeding on different levels starting inside the grains of the material, in the initial phase of the fatigue life. As a result of the free unsupported surface side, the grains on the surface are more susceptible to deform, i.e. the yield stress is lower than that of the material in general. This is referred to as “the surface effect” and is the key factor to the origin of fatigue cracks. It should also be pointed out that when the material is affected by pure tension this is actually transformed into shear stress inside the grains. As the grains are positioned in various directions, and thus experience different shear stresses, this leads to the random behavior of fatigue crack initiation.

When the material is exposed to cyclic plastic deformation, with stresses below the yield stress of the material in general, this leads to a slip between layers inside the grain, forming a slip step.

As the slip step is created a thin oxide layer is formed on the surface making it hard to reverse the process. Also as stress concentrations build up in the slip step, strain hardening occurs and makes the material less flexible. This concentrates the stress even more and makes it more susceptible to further slipping, i.e. cyclic slip. For each cycle more slip steps are created and eventually this leads to the formation of a slip band (also referred to as crack nucleation) and as the size of the slip band increase it eventually develops into a microcrack as presented in Figure 4 and Figure 5.

Figure 4. Slip lines clearly visible. (Schijve, 2004)

Figure 5. Same as Figure 4, but plastically strained 5%. The visible microcrack is indicated by an arrow. (Schijve, 2004)

As the process of forming microcracks is slow the majority of the fatigue life is spent in this period as presented in Figure 6. Note the relative scale; the fatigue life when starting from a polished surface is not the same as when starting from a defect.

4

2.2. C

In the beginning the development of the crack is limited to a single grain where slip bands are forming as a result of the free surface effects. The crack growth phase is started as the development of the crack no longer depends on these free surface effects. As a microcrack is formed, Figure 7, there is normally a resistance to crack growth across the grain border and this leads to an uneven crack growth rate, and can even make it stop from growing completely. Eventually, if more and more grains are comprised in the crack, a more or less continuous crack growth rate occurs and a crack tip is formed into the material with the shape of a semi-elliptical line, Figure 8.

Figure 7. Cross section seen from the side of a crack proceeding through many grains. (Schijve, 2004)

Figure 8. Cross section seen from above of a crack proceeding through many grains. (Schijve, 2004)

This is referred to as a macrocrack and it grows normal to the largest principal stress with a propagation rate of approximately 10-6 _{to 10}-3 _{mm per cycle. The process driving the crack has now changed from being a surface}

phenomenon to being a process advancing into the material, and now depending on the crack growth resistance of the material. Final failure occurs when the remaining uncracked cross section no longer can carry the load. A summary of the process leading to final failure is presented in Figure 9.

Figure 9. The development of cracks from initiation to final failure (Schijve, 2004).

During the initiation period the governing factor is the stress concentration, which is based on the maximum and mean stress in the material, i.e. depending on the stress distribution. In the crack growth period the governing factor is the stress intensity, which is based on the nominal stress and the size of the crack. Finally fracture toughness, which is a material parameter, is governing the final failure.

2.3. T

S-N

Since the early work by Wöhler in the late 19th _{century many years of intense research has led to a set of curves which are}

calibrated to give the fatigue life for different stress levels, materials, specimen geometries and load spectrums. These curves are obtained from fatigue tests and based on the mean minus two standard deviations and thus associated with a 97.6 % probability of survival. By printing the number of cycles to failure and the stress range in a log-log diagram the life is represented by a straight line as shown in Figure 10 (or as presented here, a net of curves for different stress ranges). Note that different parts of the curve have different slope which is described below. Also note that parent material has a flatter slope from start. This is because parent material lacks the defects introduced by the welding process. The curve is described by the equation

10 10 10

m

Log N Log C m Log σ N C σ−

= − ⋅ ∆ → = ⋅ ∆ (1)

where N is the number of cycles to failure, C is the capacity, ∆σ is the stress range and -m is the slope of the curve, with a minus for negative slope. According to recent research the line changes slope, by shifting m from 3 to 5 (for welds), at 107

cycles to describe the long term behavior (Hobbacher, 2008).

Increasing the capacity shifts the curve upwards to the right, describing bigger resistance to failure. The different level curves are named based on the stress level that results in failure at 2·106 _{cycles, i.e. the FAT value. As an example a}

5

Figure 10. Fatigue resistance S-N curves for steel at very high cycles

applications. Note the gentle slope after 1e7 cycles, compared to Figure 15

(Hobbacher, 2008).

2.4. R

This method was developed by Endo and Matsuishi in 1968 and is a way of counting the stress cycles when the stress is a spectrum of loads, e.g. as in Figure 11. S-N curves are developed from constant amplitude loadings of test specimens and in order to use them the rain flow counting algorithm can be utilized to calculate a set of constant amplitude equivalents. As only the stress range is of interest in fatigue life evaluation, the stress time series is first reduced to a sequence of peak and trough values which is then processed by the algorithm. The resulting sequence of stress ranges can then be evaluated by the cumulative damage principal (described below) in order to calculate the resulting fatigue life. The theory behind the rain flow algorithm is based on the stress-strain properties of linearly elastic materials. If a specimen is loaded over time as shown in Figure 11 the resulting stress-strain diagram is according to Figure 12. The rain flow algorithm treats every plastic deformation loop separately as if generated by separate cycles and here this results in 5 deformation loops.

Figure 11. Stress-time series Figure 12. Stress-strain diagram

with one main and four smaller plastic deformation loops.

6 2.4.1. COUNTING

By turning the stress-time series 90° clock wise and applying the rain flow algorithm the interpretation according to the “pagoda roof” style is according to Figure 13. An alternative interpretation of the algorithm is called “reservoir counting” and is presented in (Schijve, 2004). The rules of the “falling water” are, according to (Ariduru, 2004) (somewhat modified):

a) The drop will stop if it meets a peak or trough larger than that of departure. b) It stops if it meets the path traversed by another drop, previously determined. c) It will also stop if the time series ends.

d) The drop can fall on another roof and continue to slip according to rules a) and b). A stop means that the value at that point is evaluated.

Figure 13. Applying the rain flow algorithm in a "pagoda roof" style and the resulting stress range readings. Peak values from top to bottom:

[-15 13 10 15 -3 15 -12 -3 -13 2 -15] (rounded to nearest integer).

By reading the left and right hand side separately, a list of ½- cycles is achieved which by pairing up corresponding range pairs gives the resulting list of range cycles according to Table 2. Note that range pairs here refers to associated ranges together forming a cycle, not to be confused with range pairs of the range pair exceedance counting method.

Table 2. 1/2-cycles and resulting cycles from rain flow count.

Stress range Cycles (left side) Cycles (right side) Result (sum)

30 1/2 1/2 1

18 1/2 1/2 1

16 1/2 1/2 1

9 1/2 1/2 1

3 1/2 1/2 1

Comparing Table 2 with the plastic deformation loops of Figure 12 the compliance is shown in Figure 14.

7

2.5. C

This is a method developed by Palmgren and popularized by Miner to assess the fatigue life when a structure is exposed to a spectrum load. The basic hypothesis is that the varying stress levels can be divided in a finite number of stress levelsSi. Stress levels are calculated according to the methods above and for each stress level there is a maximum fatigue life, i.e. a number of cycles when failure will occur,N_i when exposed to the stress levelS_i. The amount of fatigue life consumed in each plastic deformation loop i, called damageD_i, is calculated as

i i i n D N = (2)

where niis the number of cycles the structure is exposed to at that level. In order to assess the total damage this is summed according to 1 m i i i n D N = =

_∑

where m are the number of levels the stress is divided into. Theoretically the sum reaches unity at failure, but in reality this is not the case. Also the method does not take into account the order in which loads are applied. These two major disadvantages are taken into account in the recommendations regarding variable amplitude loading given by the IIW (Hobbacher, 2008) and includes a modified S-N curve, Figure 15, along with the use of a reduced damage sum of 0.5, hereafter named DReduced .

Figure 15. Fatigue resistance S-N curves for steel at

variable amplitude loading. Note the steeper slope after

1e7 cycles, compared to Figure 10. (Hobbacher, 2008)

A simple example:

A structure is loaded in two different stress range levels, 36 MPa and 100 MPa at constant amplitude. From tests it has been determined that the fatigue behavior is described by the FAT36 curve and that the damage resulting in failure is 0.5, i.e. equal toDReduced. First the structure is loaded 5·105 times at 36 MPa. The resulting damage at this stress level according to the FAT36 curve in Figure 15 and equation (2) is

5 6 5 10 0.25 2 10 i i i n D N ⋅ = = = ⋅ (4)

The remaining damage is now 0.25. From the same curve at the 100 MPa level it can be read that the maximum number of cycles to failure is 90000. By manipulating equation (2) to D Ni⋅ i=nithe remaining number of cycles is calculated as 0.25·90000=22500 cycles.

8

2.6. W

When metal is welded together a lot of changes are introduced to the structure, e.g. notches, stress concentration, weld defects and residual stresses. All these defects affect the fatigue life in a negative way and the weld defects, e.g. cold laps, cracks and porosity, as shown in Figure 16 are actually equivalent to the kind of macro cracks resulting from the initiation period.

Figure 16. Different fatigue sensitive weld defects:

a) cold lap at weld toe (~0,2 mm)

b) crack at weld toe, undercut, (~0,2 mm)

c) root defect and initial crack

d) interbead crack

(Samuelsson, et al., 2010)

Further on, the notches, the stress concentrations and the residual stresses also reduce the initiation period and this also leads to a reduced fatigue life.

In the case of untreated material the process of forming macrocracks is slow, as it includes the initiation period, and the majority of the fatigue life is in this period. In the case of welded structures, e.g. structures found in ships, the initiation period is practically eliminated and the majority of the fatigue life is in the crack growth period. In Figure 17 a comparison between specimens with and without surface effects, i.e. the initiation period, is presented. It can be seen that there is a stress level dependency and as a ship is in the range around or below the knee of the S-N curve it is obvious that a weld can affect the fatigue life dramatically.

Figure 17. Results on fatigue life with and without surface effects. Note that scales are logarithmic. (Schijve, 2004)

9

2.7. F

A ship is a complex structure and it is a hard task to find areas where cracks will start to propagate.

Welds induces both stress concentrations and defects (due to the welding process) and is thereby one major factor in limiting the fatigue life, e.g. the presence of a weld roughly raises the stress by a factor 3. Today there are five main methods of assessing the fatigue life in welded components (Hobbacher, 2008).

Nominal stress method Hot spot stress method Notch stress method

Fracture mechanics methods. Component testing

Below follows a brief description of the different methods and in Table 3 the main characteristics of the different methods are presented. The different methods are presented in order of time consumption, with the least time consuming first. All methods except component testing normally use modeled stresses from FEM analysis.

2.7.1. NOMINAL STRESS METHOD

In this method the nominal stress in the structure is evaluated, i.e. the stress some distance away from the examined stress concentration. This means that the stress in the structure is evaluated with no respect to the geometry or weld. The fatigue life is then read in an S-N curve associated with the detail category, i.e. the specific geometry and weld type, according to Figure 18 and Figure 19. One disadvantage with this method is that there are only a limited number of listed geometries and this call for great experience and engineering skill in the assessment of the fatigue life.

10

Figure 19. S-N curves for different fatigue classes FAT36-FAT160,

normal steel and standard applications. Not the flat curve after 1e7

cycles. (Hobbacher, 2008)

2.7.2. STRUCTURAL STRESS / HOT SPOT METHOD

This is the most used method as of today and it is recommended in many Classification Society design codes. In the structural stress method the fatigue life is evaluated by assessing the stress in the point where a crack is most likely to occur, commonly denoted the “hot spot”. This is usually done by sampling stress values some distance away from the point of interest and then linearly extrapolating the hot spot stress, also denoted as “geometrical stress” as presented in Figure 20. As the hot spot stress does not take the weld in to account this is taken care of in the S-N curve used to determine the fatigue life. Usually this method calls for a FE-analysis in order to model the stresses in the structure.

Figure 20. Definition of hot spot (or geometric) stress (a) and measuring points for stress extrapolation (b). (Hobbacher, 2008).

11 2.7.3. NOTCH STRESS METHOD

This is the method used in this thesis to evaluate the fatigue life. By evaluating stresses in a special FE-model and assuming linear elastic material behavior, a direct reading from one S-N curve can be done. The characteristics of the FE-model used in this type of analysis are that the discontinuities, e.g. the transition between base material and/or welds, the “notch”, or a weld root crack tip, is modeled to have a specific fictitious radius as presented in Figure 21.

.

Figure 21. Fictitious effective radius of 1 mm in a FEM-model (Hobbacher, 2008).

Earlier this method was used only for material thicknesses > 5 mm in conjunction with the FAT 225 S-N curve but recently valid results for material thicknesses < 5 mm has been achieved by a 0.05 mm radius in conjunction with the FAT 630 S-N curve. These FAT classes refer to the maximum principal stress but if von Mises equivalent stress is used it is recommended to make a reduction by at least one FAT class (this subject is currently undergoing investigation (Fricke, 2010)). This modeling technique requires a fine mesh model and sometimes also one or more sub models. In order to resolve stresses in a correct way it is recommended to use < 0.25 mm elements in the radiuses, i.e. > 3 elements per 45 degrees, as presented in Figure 22 and Figure 23.

Figure 22. Fictitious notch radius, 3 elements per 45 degrees (Fricke, 2010).

Figure 23. Fictitious root crack radius, 3 elements per 45 degrees (Fricke, 2010).

2.7.4. FRACTURE MECHANICS

This method is commonly based on linear elastic fracture mechanics (LEFM), i.e. Paris law (Paris, Ergodan, 1963), and the assumption of an initial crack. Mathematically this is described as

(

)

where da dN is the crack growth per cycle, K∆ is the stress intensity factor range and C0 and m are crack growth

parameters (depending on material and testing conditions, and also determined experimentally). Although LEFM is one of the most time consuming methods it may be the method of choice in a number of situations, such as stated by (HSE, 2001)

• To assess the fitness-for-purpose of a joint known to contain flaws

• To assess whether post-weld heat treatment is required during fabrication or after weld repair • When the effects of variations in geometrical or stress parameters for a given detail are being studied

• When the joint detail under consideration is not adequately represented by one of the simple joint classifications • To determine the frequency of in-service inspection

• To assess the remaining fatigue life of a joint in which fatigue cracks already exist • To assess the structural integrity of castings.

12 2.7.5. COMPONENT TESTING

The most direct method of assessing the fatigue life of a structure is to put it in a testing machine and expose it to the load it is designed for. As ships are large, complex structures, built in small series, this approach is normally neither cost-effective nor practically doable. Regardless of this research is done and Figure 24 gives an example of this.

Figure 24. Test specimen and rig for component testing of a corner connecting the web frames of a ship’s side and deck. Note the measurements in mm, i.e. not for the small test lab! (Fricke, 2010)

2.8. R

Different methods require different amounts of work and produce different results. Table 3 lists the methods described above and some key features (Samuelsson, et al., 2010).

Table 3. Range of application and some pros and cons for different fatigue life assessment methods.

Method Toe

failure

Root failure

Time Negative notes Positive notes

Nominal stress
- 1 Difficult to find nominal stress

Many S-N curves

Simple to use

Structural stress
- 2 Requires an experienced analyst Mainly two S-N curves

Effective notch

3 May require big FE-models One S-N curve

LEFM

5 Time consuming, hard to find

stress intensity factor

Describes reality best Can follow crack growth Component

testing

13

3.

M

In this M. Sc. Thesis a mathematical model is used to evaluate fatigue damage from recorded motion data. This model can be summarized in four parts:

1 A FE-model is done and unit accelerations are applied to six different sections of the ship, resulting in coefficients of influence.

2 Motion data is used to calculate accelerations and resulting stresses. 3 Rain flow counting is used to assess stress ranges.

4 Cumulative damage method is used to calculate the resulting fatigue life.

3.1. FE-

In order to describe the ship a local coordinate system is defined in CoG according to Figure 25 and ship motions in six degrees of freedom, defined according to Figure 26 and Table 4.

Figure 25. Local coordinate system, defined from CoG (Söder, 2008).

Figure 26. Degrees of freedom, defined from CoG (Söder, 2008).

Table 4. Degrees of freedom and their directions.

DoF Positive direction η1 surge Forward

η2 sway To port

η3 heave Upwards

η4 roll Starboard side down

η5 pitch Bow down

η6 yaw Bow to port

To model stresses the ship is modeled in three different levels of detail in a global, an intermediate and a local 3D solid model. The global model is a shell element model, according to Figure 27, which describes the global deflections of the whole ship. Note that the hoistable decks 5, 7 and 9 are not modeled as they don’t contribute to the ships racking stiffness. These decks are considered to be hoisted and the weights of these decks are added to the total mass of the ship as increased density to the fixed decks above. The intermediate model is a shell model of the examined bulkhead and the adjacent parts of decks 6 and 8, according to Figure 28. The movable decks are treated as described for the global model. These two FE-models were done earlier as part of a master thesis by (Söder, 2008). Finally the local 3D solid model describes the area just around the point of interest, including finer geometrical properties such as weld geometry, Figure 29. This model is done according to the latest IIW recommendations (Fricke, 2010). Figure 30 show a picture of the analyzed structure and in Appendix I a more covering picture is presented. In Figure 31 a close-up picture of the discovered crack is also presented. As a reference the thickness of the cracked steel plate is 30 mm.

Figure 27. Global FE-model of PCTC Mignon

structures highlighted. The analyzed bulkhead is indicated by an arrow. (Söder, 2008)

Figure 29. Local 3D solid model of the analyzed structure viewed from aft.

Figure 31. Close-up photo of the analyzed structure viewed from by arrows (Photo by Mignon crew).

0.000

14

model of PCTC Mignon with racking constraining structures highlighted. The analyzed bulkhead is indicated by an arrow.

Figure 28. FE-model of the evaluated bulkhead viewed from fore

indicates the position of the local 3D solid model pictured in Figure

model of the analyzed Figure 30. Photo of the analyzed structure viewed from aft

(Photo by Mignon crew).

up photo of the analyzed structure viewed from aft. The discovered crack is indicated

0.000 0.025 0.050 0.075 0.100

model of the evaluated viewed from fore. The arrow e position of the local 3D solid

Figure 29.

. Photo of the analyzed structure viewed from aft.

aft. The discovered crack is indicated 0.100 [m]

15 3.1.1. GLOBAL FE-MODEL

After preparation of the model in Design Modeler it is imported into Simulation (the simulation module of Ansys), where meshing is performed. Mainly rectangular shaped elements of about 1 meter are used and totally this model consists of 151 000 elements and 122 000 nodes. The global model is loaded in Ansys according to (Söder, 2008). In short this means that a unit load of 1 m/s2 _{in the y-direction (coordinate system according to Figure 25) affecting section k is applied and}

balanced with force distributions according to Figure 32 and Figure 33. It is hard to achieve perfect balance and in order to avoid rigid body motion the model is locked in a point P. The reaction force in this point is small and the position is far away from the point of interest and is thus considered not to affect the solution. From this state nodal displacements are recorded and saved to a file, i.e. one file for each of the load cases k [1,6].

Figure 32. Front view of the ship with vertical division into sections and unit acceleration (here affecting section 3 of the ship), (Söder,

2008) with some modifications.

Figure 33. Force distributions balancing the ship when subjected to acceleration in the y-direction (Söder, et al.,

2011).

3.1.2. INTERMEDIATE FE-MODEL

The intermediate model of the bulkhead is meshed and run in Ansys and the nodal displacements from the global model are applied as boundary conditions to the model. This imposes strain into the model which in turn results in stresses in the material. Nodal displacements are again recorded and saved to a file.

As in the global model shell elements of mainly rectangular shape are used but in this case the size is smaller, mainly 0.05 meters, and in the area of the local 3D solid model 0.03 meter elements are used. Totally this model consists of 595 000 elements and about the same number of nodes.

3.1.3. LOCAL 3D SOLID FE-MODEL

In the final sub model special care is taken to apply nodal displacements from the shell model to the 3D solid model in a correct way, and here the built-in Shell-to-solid cut boundary interpolation command CBDOF is used. In this model brick and tetrahedron elements of varying size are used as presented in Figure 29 and Figure 34. The elements around the fictitious radiuses are sized in order to achieve a sufficient number of elements as presented in chapter 2.7.3. In the weld notch 0.25 mm tetrahedron elements were used and in the weld root 0.5 mm tetrahedron elements were used. As the recommended number of elements refer to brick elements and the above element sizes refer to the length of the base of the tetrahedron the elements are thought to give sufficient resolution. This submodel consists of 360 000 elements and 594 000 nodes.

16

Figure 34. Local 3D solid model showing the weld (zoomed in view of Figure 29).

In Figure 35 the root side of the weld is presented. It should be noted that the penetration is modeled to be -1 mm (penetration defined according to Figure 36). This is done by mistake and makes the analysis conservative regarding stresses in the weld root (stresses are exaggerated). Nevertheless this did not affect the analysis as no value in the root exceeded any value in the weld toe (which is in line with theory).

Figure 35. 3D solid model (viewed from the back side) showing the root side of the weld. Note the fictious

radius on both the weld toe and root.

Figure 36. Definition of penetration (Samuelsson, et al., 2010).

3.2. S

The local 3D solid model is divided into different regions in order to find the relevant maximum stress. This is due to the fact that there are some errors in the boundaries that are introduced by the software and by disregarding them it is easier to find the relevant maximum stress. The division is visible in Figure 29, Figure 34 and Figure 35 where different regions have different color.

In order to find the maximum von Mises stress special care is taken to evaluate the stresses in both the root and notch on both sides of the bulkhead. Unit accelerations are applied to 6 different sections of the ship and the maximum stress is sampled, resulting in 12 different “stress samples”.

In 9 cases the maximum stress is found in two specific points, referred to as “Point 1” and “Point 2” and as presented in Figure 37 and Figure 38. Reference is made to Appendix II for more exact positions of these points.

iPositive

penetration

iNegative

17

Figure 37. Evaluation point 1 on the fore side, referred to as “Point 1”.

Figure 38. Evaluation point 2 on the aft side, referred to as “Point 2”.

The objective is to find the point where the stresses give the shortest fatigue life. In this case it is believed that this is true for the point referred to as “Point 1” as it is subjected to the highest stresses in five cases out of six and that the stresses in the remaining section 5 is small enough to have little impact on the fatigue life. The values sampled in “Point 1” are thus used as input to the calculation of the coefficients of influence as presented in chapter 3.5. Detailed presentations of the stresses in “Point 1” and “Point 2” are given in Appendix III .

Table 5. Measured stresses in “Point 1” and “Point 2” resulting from unit accelerations [MPa , von Mises stress]. Bold figures represent stresses that are maximum and found in “Point 1”.

Section of applied unit acceleration 1 2 3 4 5 6

Stress in “Point 1” (fore side) 7.7551 41.056 38.865 29.869 0.5393 1 _2.7972

Stress in “Point 2” (aft side) 5.9668 31.224 29.29 23.056 1.1447 2 _1.7711 3 1 _{Max stress in the geometry is 5.773 MPa.} 2 _{Max stress in the geometry is 6.0943 MPa.} 3 _{Max stress in the geometry is 1.9098 MPa.}

An example of the stress distribution resulting from a unit load affecting section 1 (according to subdivision presented in Figure 32) is also presented in Figure 39, Figure 40 and Figure 41.

Figure 39. Stress distribution of the whole intermediate FE-model, resulting from lateral unit acceleration

of 1 m/s2 applied to section 1, viewed from fore. Note the difference in the stress of 2.5241 MPa (sampled

18

Figure 40. Stress distribution in relevant regions of the local 3D solid FE-model, where the maximum

stress is sampled. Stress is resulting from a lateral unit acceleration of 1 m/s2 applied to section 1, viewed

from fore.

Figure 41. Close-up view of Figure 40. Stress is resulting from a lateral unit acceleration of 1 m/s2 applied to

19

As can be seen in Figure 39 the whole racking bulkhead is bending and shearing from the applied forces (acting mainly in the –y-direction). This result in stresses in the rounded corners of the bulkhead openings which is what could be expected. In Figure 42 to Figure 45 the stresses resulting from lateral acceleration of ±1 m/s2 _{applied to section 1 and 5 is presented.}

Note that the stress distributions presented in Figure 42 and Figure 43 are qualitatively representative for sections 1-4 and 6 as well. Also note that due to limitations in Ansys the displacements are scaled differently.

Figure 42. Stress distribution resulting from a lateral

acceleration of 1 m/s2 applied to section 1 in the

–y-direction. Displacement exaggerated 3900 times.

Figure 43. Stress distribution resulting from a lateral

acceleration of –1 m/s2 applied to section 1 in the

–y-direction. Displacement exaggerated 3700 times.

Figure 44. Stress distribution resulting from a lateral

acceleration of 1 m/s2 _{applied to section 5 in the}

–y-direction. Displacement exaggerated 4600 times.

Figure 45. Stress distribution resulting from a lateral

acceleration of –1 m/s2 _{applied to section 5 in the}

–y-direction. Displacement exaggerated 3500 times.

As presented above the stress distributions are very similar for stresses resulting from unit loads to sections 1-4 and 6, and the main deformation mode is bending. This is judged from visual inspection of Figure 42 and Figure 43.

Stresses resulting from a unit load to section 5 are behaving somewhat different, and the main mode of deformation is shearing. This is judged from visual inspection of Figure 44 and Figure 45.

In theory close to CoG the main forces should come only from the sway motion and as the distance to CoG increases more and more forces resulting from roll motion should be added. For any load acting close to but not in CoG this should then result in shear forces and this explain the different behavior resulting from the unit load to section 5.

In the above figures it is also visible that steel plates of different thicknesses are used in the racking bulkhead, resulting in discontinuities and rectangular patterns in the stress distributions.

20

3.3. E

Ship motions in six degrees of freedom, defined according to Figure 26 and Table 4, are recorded by the SeaWare EnRoute Live system (Seaware AB, ), equipped with a Seatex MRU H high accuracy motion sensor, at a sampling rate of 10 Hz. The coordinates of the motion sensor, defined from the center of gravity (according to Figure 25) is given in Table 6.

Table 6. Coordinates of the Seatex MRU H high accuracy motion sensor.

X Seaware 57 m

Y Seaware 2,2 m

Z Seaware 27,5 m

3.4. P

As the recorded motion signal has a lot of high frequency noise the signal is filtered in MatLab using a low-pass FFT-filter with a cut-off frequency of 0.06 Hz. This cut off frequency was determined by visual inspection of spectrum plots from the unfiltered and filtered signal. In order to have data volumes that the available computer can handle (2*2.26 GHz, 4 GB RAM, Vista), a batch of files of approximately 106 _{data points each, equal to about 28 hours of recorded motion data, is}

saved. The sway motion has some discontinuities that seem to be a result of the recording software (presented in Appendix IV ) and this is also corrected during the batch save process.

The total length of the period when recording took place is 175 days and the total time of the recorded data during the period is 159.7 days. Due to the Gibbs phenomenon the filtered signal has to be cut off in the beginning and end of each time series (totally 1.2 % is cut off), resulting in a reduced recorded time of 157.8 days. In Figure 46 a plot of a filtered versus an unfiltered signal is presented and from visual inspection it is determined that 600 seconds should be cut off in the beginning and the end of every time series.

Figure 46. Errors in the end (discontinuity) of a time series due to FFT filtering, ie. the Gibbs phenomenon.

Sample plots of time signals from recorded motions, resulting accelerations, and the resulting stress (in “Point 1”, according to chapter 3.2) are shown in Figure 47. The resulting stress is based on all accelerations acc1-6 and plots of these

accelerations versus time are presented in Figure 48 (showing Acc1-6) and Figure 49 (showing only acc1+6 for better

visibility). 0 100 200 300 400 500 600 700 800 -20 -10 0 10 20 30 40 50 60 70 time [s] p o s it io n [ m ] Sway motion Filtered signal Unfiltered signal

21

Figure 47. Sway, roll, accelerations and the resulting stress in “Point 1” (as presented in chapter 3.2) .

Figure 48. Variations in the accelerations acc1-6 plotted versus time. Reference is made to

Table 4 in section 3.1 for directions of accelerations.

Figure 49. Variations in the accelerations acc1 and acc6 plotted versus time.

1 2 3 4 5 6 7 8 9 10 60 65 70 Time [min] [m ]

Sway, Roll, acceleration and stress

Sway, η₂ 1 2 3 4 5 6 7 8 9 10 -5 0 5 Time [min] [d e g ] Roll, η₄ 1 2 3 4 5 6 7 8 9 10 -0.50 0.5 Time [min] [m /s 2 ] ACC 1 1 2 3 4 5 6 7 8 9 10 -0.50 0.5 Time [min] [m /s 2 ] ACC 6 1 2 3 4 5 6 7 8 9 10 -1000 100 200 Time [min] [M P a ] Stress, σ 0 1 2 3 4 5 6 7 8 9 10 -0.5 0 0.5 Time [min] A c c [ m /s 2 ] acc₁ acc₂ acc 3 acc 4 acc₅ acc₆ 0 1 2 3 4 5 6 7 8 9 10 -0.5 0 0.5 Time [min] A c c [ m /s 2 ] acc₁ acc₆

22

Judging from Figure 47 it is indicated that ACC1 and ACC6 are mainly differing in amplitude. This is more pronounced for

greater amplitudes and in Figure 48 and Figure 49 the similarity of the different signals are clearly visible. This is due to the differences in magnitude of the contributing parts to the total acceleration. In Figure 50 and Figure 51 these acceleration parts are presented for accelerations in “Point 1” resulting from a unit load to section 1 and 6 (plots of all acceleration parts are appended in Appendix V ). In Table 7 relative values for the magnitude of the different contributions are presented.

Table 7. Relative magnitude of accelerations.

Section ACCGravitation ACCSway ACCRoll

1 1 0.336 0.16

6 1 0.336 0.046

The acceleration due to the roll motion is much smaller than the others an as this is the only part in the total acceleration that is changing for the different sections this is the reason for the small differences seen in Figure 48 and Figure 49. This is also in line with results produced by (Söder, 2008).

Figure 50. Comparison of different contributions to the total stress, resulting from a unit load to section 1.

Figure 51. Comparison of different contributions to the total stress, resulting from a unit load to section 6.

0 1 2 3 4 5 6 7 8 9 10

-0.50 0.5 1

Comparison of different contributions to transversal acceleration affecting section 1.

Time [min] A c c [ m /s 2]

Acc. from gravitation

0 1 2 3 4 5 6 7 8 9 10 -0.2 0 0.2 Time [min] A c c [ m /s 2]

Acc. from sway

0 1 2 3 4 5 6 7 8 9 10 -0.1 0 0.1 Time [min] A c c [ m /s 2]

Acc. from roll

0 1 2 3 4 5 6 7 8 9 10 -0.5 0 0.5 Time [min] A c c [ m /s 2] Total acceleration 0 1 2 3 4 5 6 7 8 9 10 -0.50 0.5 1

Comparison of different contributions to transversal acceleration affecting section 6.

Time [min] A c c [ m /s 2]

Acc. from gravitation

0 1 2 3 4 5 6 7 8 9 10 -0.2 0 0.2 Time [min] A c c [ m /s 2]

Acc. from sway

0 1 2 3 4 5 6 7 8 9 10 -0.04 -0.020 0.02 0.04 Time [min] A c c [ m /s 2]

Acc. from roll

0 1 2 3 4 5 6 7 8 9 10 -0.5 0 0.5 Time [min] A c c [ m /s 2] Total acceleration

23

3.5. S

The stressσ_i in location ,i due to any momentary acceleration distribution a_{y k,} to section k is given by

, ,

i k y k i k k

m a C

σ =

_∑

[ ]

where mkis the total mass (

0 arg

k k c o

m =m +m ) and Ci k, is the coefficient of influence, according to equation (10). In order

to calculate accelerations ay k, from recorded motions, motion data are differentiated twice numerically according to

(

)

( )

(

)

( )

where ηi is the recorded motion, t is the time and t∆ is the sampling period. As shown by (Söder, 2008) only sway and roll motions contribute significantly to the stress in the racking bulkhead and hence only the accelerations ηɺɺ and 2 ηɺɺ are 4

of interest in this analysis. The measured value at the position of the measuring system ηɺɺ2,Seaware is transformed toηɺɺ2,CoG

according to

2,CoG 2,Seaware 4,Seaware ZSeaware

ηɺɺ =ηɺɺ −ηɺɺ ⋅ (8)

Angular measurements are not affected by position and hence ηɺɺ4,CoG =ηɺɺ4,Seaware. The gravitational force contribute by the sine component of the roll angle and finally the acceleration in the y-direction for an arbitrary Z-position of the racking bulkhead is given by

, , 2, 4, sin 4,

y k CoG CoG CoG k CoG

a = −ηɺɺ +ηɺɺ Z −g η (9)

In order to calculate stresses and resulting fatigue life the theory of unit loads, coefficients of influence and linear superpositioning is used. With FEM software the constant coefficients of influence, Ci k, , in a specific position ,i resulting

from mass and momentary acceleration distribution in section ,k can be derived as

0 , , 0 0 , i k i k k y k C m a σ = ⋅ (10) where 0 , i k σ is the stress, 0 k

m is the mass of the ships structure and 0 ,

y k

a is a unit acceleration of 2

1m s , according to (Söder, et al., 2011). The resulting coefficients of influence for the investigated position are given in Table 8.

Table 8. Coefficients of influence for the investigated point, resulting from accelerations in sections k [1,6], rounded to six significant digits.

k 1 2 3 4 5 6

[

]

k

C unitless 3.15248e-5 2.86904e-5 2.56196e-5 1.69134e-5 2.44359e-7 4.23818e-7

As presented in Table 9 the coefficients 1-4 are fairly evenly proportional to the distance to the CoG (in this case the calculations are done with the average of the occurring CoG values of the analyzed period, i.e. no regard to time traveled with each CoG value). The small differences in these sections are believed to be due to the hatches in the bulkhead that introduce lower shear holding capabilities.

Coefficients 5 and 6 are also evenly proportional to the distance to the CoG but are significantly smaller. This is believed to be due to that the lower part of the ship, i.e. deck 6 and downwards is significantly stiffer than the rest of the ship. This is also shown by (Söder, 2008) where an analysis of a ship clamped from deck 6 and downwards show very small differences regarding maximum stress in the bulkhead, compared to a ship balanced by sea pressures.

Table 9. Positions of sections relative to the CoG (rounded to one decimal) and coefficients of influence divided by the distance to CoG (normalized by the smallest value and rounded to two decimals).

Section 1 2 3 4 5 6

Position [m] 25.7 20.1 15.0 9.7 3.8 -6.3

[

]

k

24

Stress ranges are determined by the rain flow counting method and from these ranges the cumulative damage is calculated according to equation (3) and the fatigue life is then calculated from the cumulative damage as

Re Measured FatigueLife duced T T D D = (11)

where TMeasuredis the length of the measured time series in seconds, D is the cumulative damage and DReducedis the reduced damage sum equal to 0.5 as described in chapter 2.5.

3.6. A

Due to logistic problems with sending the recorded motion data it was not possible to use data from Mignon and instead motion data from her sister ship PCTC Undine was used. As these two ships are in the same series they are considered to be equal. Recorded motion data during approximately 6 months of world trade was used in the analysis and the traveled route is according to Table 10.

A little simplified the main parts of the traveled route are one turn around the globe and two return trips from Europe to USA. This means the Atlantic is crossed five times.

Table 10. Ports of the traveled route by M/S Undine 2010-09-05 to 2011-02-26.

Start Interim ports → End

1/4 of JP-Suez BE → SE1 → DE → SE2 → BE → → GB

GB → CA → US1→ US2 → US3 → DE → BE → GB

GB → CA → US1 → US2 → US4 → MX1 → → MX2

MX2 → CO → US2→ US3 → US5 → DE → BE → GB

GB → CA → US1 → US2 → US4 → VE → Pan → JP

JP → 2/5 of JP-Suez End of recording

Note that End and next Start point is the same port.

Legend: BE=Zeebrugge, Belgium; CA=Halifax, Canada; CO=Cartagena, Colombia; DE=Bremerhaven, Germany; GB=Southampton, Great Britain; JP=Nagoya, Japan; MX=Mexico (1=Veracruz, 2=Manzanillo); Pan=Panama channel; SE=Sweden (1=Malmoe, 2=Gothenburg); Suez=Suez channel; US=USA (1=New York, 2=Brunswick, 3=Charleston, 4=Galveston, 5=Baltimore); VE=Maracaibo, Venezuela.

25

4.

C

Fatigue life is calculated according to DNV Classification Notes no. 30.7 (DNV CN. 30.7, 2010) except for the FE-model. It is a calculation based on a Weibull distributed stress range for the maximum hot spot stress. The stresses are sampled at 0.5·t and 1.5·t according to Figure 52 and Figure 53, as recommended by (DNV CN. 30.7, 2010). This is due to the fact that in a shell element FE-model the weld is not modeled and thus the position of the “true” hot spot (as presented in Figure 52) is not defined.

The stress used here is obtained from a FE-model analysis done by (Söder, 2008). In that analysis a Lloyds Register (LR) load case comprising a 30 degree heel and a fully loaded ship is used in conjunction with a balanced DNV boundary condition. This is an extreme load case where the stress is estimated to be exceeded once out of 108 _{cycles, i.e. a}

probability level of 10-8_.

The reason for using this load case is that no DNV load case was available in Söder’s work and it is believed that the output from the FE-analysis should produce a similar stress value as a DNV load case.

It can be argued if this combination of load and boundary condition is valid and the results presented in this section should thus be evaluated with caution. Comparison of different classification societies have been done (W.Fricke, 2001), showing similar stress values for analyses done according to DNV and Lloyd’s Register. It should be noted though that in this study a detail in the upper longitudinal structure on a Panamax container vessel was evaluated (in order to reduce uncertainties). As a comparison direct calculation using a spectral method and long term wave statistics was also evaluated, showing values in the higher range compared to the classification societies.

The study show a difference in the resulting stresses sampled in the FE models from DNV and Lloyd’s Register of about 10 %.

Figure 52. Hot spot sampling points. Hot spot

26

Figure 53. Stress extrapolation in a three-dimensional shell FE model to the weld toe. Note that neither the weld nor the thickness of the material is regarded in this extrapolation. (DNV CN. 30.7, 2010).

The obtained stress is multiplied by factors regarding the trade of the ship, mean stress effect and stress concentration due to the weld geometry. For ballast condition half the maximum stress is used. The stress range is obtained by multiplying the stress by two.

The roll period of the ship is 14.4 and 22 seconds for an empty and a heavily loaded ship respectively, according to LoadMaster (Kockum Sonics AB). Due to this the Weibull shape parameter ha is set to zero, giving h equal to

2.21 - 0.54 · log10(L), i.e. 0.93682 (rounded to five significant digits).

Damage is calculated by utilizing a bi-linear S-N curve with a shift in slope at 107 _{cycles associated with a 97.6 %}

probability of survival. This curve is referred to as S-N curve I “welded joint” by DNV and the FAT90 curve in the modified S-N curves for steel at variable amplitude loading by the IIW, Figure 54.

Figure 54. Fatigue resistance S-N curves for steel at

variable amplitude loading. (Hobbacher, 2008)

27

5.

R

The fatigue life calculated from 157.8 days of motion data is 9.6 years (rounded to two significant digits). It should be noted that the damage is cumulated in distinctive portions where the Atlantic and the east coast of the US is the dominating area of operation for those peaks, Figure 55.

It can also be noted that one large amount of damage was cumulated during a period including a crossing of the Atlantic in days 29 to 35. The damage cumulated during this period was 0.0106 (rounded to three significant digits) equal to 2.1 % of the total fatigue damage (based on the damage sum 0.5).

As a comparison the DNV analysis based on LR loads result in a fatigue life of 8.02 years.

Figure 55. Cumulated damage per day during the investigated period.

As the damage is cumulated in almost discrete portions the reliability in the fatigue life calculated based on this limited 158 days data set is low. This is shown in Table 11, where one crossing of the Atlantic (same as days 29-35 in Figure 55) is added or subtracted to the original fatigue life calculation.

Table 11. Influence of ± one crossing of the Atlantic.

Resulting fatigue life [years]

Original 9.6

One crossing added 6.5

One crossing subtracted 18.5

This is a rather coarse display but it highlights the fact that the fatigue life calculated from this short time is not to be taken too seriously. On the other hand the cumulated damage is not associated to this, and a more correct way to use fatigue information could be to use the relative damage as an indicator in order to judge the condition of the ship. One more possibility could be to use the damage plot in order to alter the route in order to avoid any unnecessary accumulation of damage to the ship.

0 20 40 60 80 100 120 140 160 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 10

-3 _{Cumulated damage per day}

Time [Days] D a m a g e I n d ia n O c e a n ← Ind ia n O c e a n M e d it e rr a n e a n G B C A U S ( N Y ) G B C A US ( N Y -B R S W K -G L S ) G B C A G L S P A N + 3 d a y s At S e a J P CA = Halifax, Canada

GB = Southampton, Great Britain JP = Nagoya, Japan

Pan = Panama channel US = USA

NY = New York BRSWK = Brunswick GLS = Galveston CA = Halifax, Canada

GB = Southampton, Great Britain JP = Nagoya, Japan

Pan = Panama channel US = USA

NY = New York BRSWK = Brunswick GLS = Galveston

6.

D

In the previous fatigue life analysis it is con openings in the racking bulkhead. Here it the edge of the radius, affects the fatigue life.

The bridge on the fore side of the bulkhead is only designed to carry walking crew and thus stopping the weld e.g. 100 mm from the bulkhead radius would not affect the function at all.

On the aft side of the bulkhead the welded

comparison to the radius on the opposite side of the same bulkhead opening which does not have any stiffener

not suffer from any buckling problems. Alternatively the bracket could be moved to the other side of the stiffener and thus not protrude towards the bulkhead opening radius.

In Appendix I a descriptive picture of the examined radius and its vicinity is appended.

6.1. A

In order to examine the result from moving the welds from the highly stressed areas version of the local 3D solid model according to

original local 3D solid model.

It should be noted that the geometry is not changed in the intermediate FE

would affect the results. This is true, but it is believed that the response in the intermediate

significantly if the welds are moved and thus the nodal displacements in the boundary to the local 3D solid model will be almost the same as well.

Nodal displacements resulting from unit loads to sections Mises stress on the radius is sampled according to

order to simplify the stress sampling, the maximum values are used except for stress resulting from a unit load to section 5. In this case an estimated representative stress for the examined area is used. By utilizing this sampling method the results are regarded as conservative. In Figure 56

nodal displacements applied from the shell model to the bounda away from the point of interest it is disregarded.

Pictures of all the resulting stress distributions are appended in

Figure 56. Modified geometry of the local 3D solid model. In this case the stress response is due to a

stress in the bottom tip, which is an error due to the applied displacements to th

28

analysis it is concluded that high stress occur in welds in the

Here it is investigated how a change in the geometry, i.e. moving the welds away from the edge of the radius, affects the fatigue life.

The bridge on the fore side of the bulkhead is only designed to carry walking crew and thus stopping the weld e.g. 100 uld not affect the function at all.

welded bracket could probably be removed completely. This is argued from a comparison to the radius on the opposite side of the same bulkhead opening which does not have any stiffener

Alternatively the bracket could be moved to the other side of the stiffener and thus not protrude towards the bulkhead opening radius.

descriptive picture of the examined radius and its vicinity is appended.

the result from moving the welds from the highly stressed areas, an analysis is done on

according to Figure 56. This model was done by deleting the welded parts of the not changed in the intermediate FE-model and thus it could be argued that this This is true, but it is believed that the response in the intermediate FE

significantly if the welds are moved and thus the nodal displacements in the boundary to the local 3D solid model will be from unit loads to sections k [1,6] are applied to the boundaries and the

according to Figure 56. As the maximum stress values occur in a small area, and in the maximum values are used except for stress resulting from a unit load to section 5. In this case an estimated representative stress for the examined area is used. By utilizing this sampling method the results

some stress is visible in the bottom tip of the model. This nodal displacements applied from the shell model to the boundary of the local 3D solid model but a away from the point of interest it is disregarded.

Pictures of all the resulting stress distributions are appended in Appendix VII .

. Modified geometry of the local 3D solid model. In this particular case the stress response is due to a unit load applied to section 1. Note the

stress in the bottom tip, which is an error due to the applied nodal displacements to the boundary.

in the radius of one of the hatch the geometry, i.e. moving the welds away from The bridge on the fore side of the bulkhead is only designed to carry walking crew and thus stopping the weld e.g. 100-200 bracket could probably be removed completely. This is argued from a comparison to the radius on the opposite side of the same bulkhead opening which does not have any stiffeners and does Alternatively the bracket could be moved to the other side of the stiffener and

analysis is done on a modified This model was done by deleting the welded parts of the model and thus it could be argued that this FE-model will not be changed significantly if the welds are moved and thus the nodal displacements in the boundary to the local 3D solid model will be are applied to the boundaries and the maximum von As the maximum stress values occur in a small area, and in the maximum values are used except for stress resulting from a unit load to section 5. In this case an estimated representative stress for the examined area is used. By utilizing this sampling method the results he bottom tip of the model. This is an error due to the solid model but as this is some distance