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Cracking up? The art of keeping a yacht keel in one piece

In recent years the performance of monohull racing yachts has dramatically increased, partly due to the introduction of canting keels. This new technology brings challenges for engineers to ensure the keels are designed safely, using available tools and codes of practices. As we have seen as recent as 2013 keels still fail. This is despite the use of high strength materials in their designs. The truth is that their strength, so trustworthy under static loads, is no indicator of fatigue life under repeated, smaller loads. Managing keel fatigue in monohull racing yachts is complex, however with the right fatigue analysis, fatigue failures can be prevented.

This issue has recently been addressed in the GL Guidelines for Racing Yachts over 24 m which now include an Annexe outlining the fatigue assessment of keels. The aim of this article is to give some background information about fatigue and explain the analysis method.

Feeling fatigued?

Cracks begin at small flaws in the keel – a scratch, a bad weld, a corrosion pit or a kerb may start the process. In polished steel the cracks initiate at crystal boundaries. Cyclic loads far below the strength of the material can cause irreversible slips along metal grain boundaries. This eventually results in microscopic cracks that can dangerously grow under repeated strain. Eventually the cross section area that remains is too small to carry the loads and the keel becomes a monument on the bottom of the sea.

There is a long history of fatigue problems in engineering. In the 19th century, boilers and locomotives were known to fail under cyclic loading. In 1842 a French train derailed and burst into flames as a result of a broken axle. This disaster catalysed the first systematic research into metal fatigue.

In aviation, three aircraft broke up in mid-flight in the 1950s. These jetliners – De Havilland Comets – were the first to fly with pressurised cabins and square windows. The accidents were traced back to stress concentrations and metal fatigue at the corners of the windows. Since then aircraft use windows with rounded corners.

In the maritime area one of the worst disasters was the capsize of the Alexander L. Kielland oil platform in the North Sea in 1980, killing 123 people. The disaster was due to fatigue in a 6 mm fillet weld which held a sonar device to a structural cross brace.

In yachting, any component that is subject to repeated cyclic loading may have problems with fatigue. These could be rigging components, keel fins or hull structures. It is worthwhile understanding the basics of fatigue so that informed design decisions can be made to prevent failure.

Analysing Fatigue

Codes

Because fatigue is relatively well understood in numerous industries there are several standards available which outline fatigue analysis. I recommend:

  • GL Rules for Classification and Construction, I Ship Technology, 3 Special Craft, 7 Guidelines for the Structural Design of Racing Yachts ≥ 24 m, Annex A Keel Fatigue Assessment
  • EN 1993-1-9: Eurocode 3: Design of steel structures – Part 1-9: Fatigue
  • BS7608: 1993 Code of practice for fatigue design and assessment of steel structures

I have used methods from the GL Rules in this article, however the approach in the other standards is principally the same.

Analysis Procedure

  • Calculate the stress range and the number of times this load is applied to the structure
  • Determine the FAT Class of the design detail being analysed by selecting from the examples in the selected code
  • Calculate the number of cycles to failure for the detail class and given stress range in accordance with the code
  • Calculate the safety factor: divide the cycles to failure by the actually applied cycles

The stress range is the difference between the maximum and minimum stress during one load cycle. The stress level is irrelevant. A load cycle between -50 MPa and +50 MPa is the same as a load cycle between 100 MPa and 200 MPa. Both have a stress range of 100 MPa.

FAT Classes

The FAT Class is determined by the type of connection detail. In the GL Rules the FAT Class denotes the stress range that can be applied for 2,000,000 cycles with a probability of survival of 97.5%. The table below lists some examples for steel.

 

Connection detailFAT Class
(MPa)
Flat plate with smooth edges 160
Transverse butt weld, ground flush on both sides, 100% NDT 112
Longitudinal butt weld, ground flush, NDT, with weld start / stops 90
Full cross section transverse splices in plates or flats, regular weld, NDT 80
Transverse butt welds made from one side only (partial penetration possible), no NDT 36

Table 1: Detail Class Examples

It is immediately clear that it is best to completely eliminate connections and welds in high stress regions. In this case a stress range of 160 MPa can be applied for 2,000,000 cycles. If transverse welds are required it is crucial that a high quality full penetration weld is used. This is so that a stress range of at least 80 MPa can be assumed. If the weld is only accessible from one side and no NDT is carried out to verify that the weld achieved full penetration, a stress range of only 36 MPa has to be assumed.

The FAT Class does not depend on the material. The GL Rules can be applied to all structural steels and stainless steels. It is assumed that the yield strength is less than 390 MPa. If higher strength steels are used and higher fatigue stress ranges are used in the analysis, supporting test data has to be supplied. Therefore it does not make sense to use high strength steels for structures which experience reverse bending and are fatigue critical. Fins made from high strength steel will have an enormous safety factor under static loads but will still fail at the same fatigue load as a keel made from regular mild steel.

The situation is different for rigging components where a high constant load with superimposed cyclic loads may be experienced.

Another implication of this is that there are only two ways one can improve fatigue performance. The designer can either improve the connection detail by eliminating welds, grinding welds smooth and ensuring full penetration or reduce the stress range by increasing the cross section. On keel fins an increased cross section will require an increased root thickness which leads to higher drag.

SN – Curve

In the GL Rules the stress range of the FAT Class is for 2,000,000 load cycles and a probability of survival of 97.5%. What if the actual stress range is larger or smaller? How can the cycles to failure be calculated? The number of cycles to failure can be calculated using the following formula:

S-N Curve

For welded joints m0 = 3. If N < 107 the slope exponent m equals 3. At more than 107 cycles the slope of the SN – curve changes with m = 5.

A different way to write this is:

S-N Curve simple

Other standards assume that the steel structure will last forever if the stress range is low enough. This leads to horizontal curves past the cut off limit. The resulting graphs of the FAT Class examples of Table 1 with m0 = 3 and N between 10,000 and 5·108 are shown below.

S-N Curve Example

Example:

A forged keel experiences a stress range of 160 MPa. According to the detail category, it will survive 2,000,000 cycles with a probability of 97.5%. If the design is changed to a fabricated keel with a full penetration butt weld at the root, the category drops to 80 MPa. As a result the keel will only withstand:

Calculating N example

The introduction of the weld has reduced fatigue life to 1/8 of the original keel. To achieve the same fatigue life as the forged keel, the root thickness would have to be increased to reduce the stress range from 160 MPa to 80 MPa.

Big and little waves- dealing with non-constant amplitude loading

All the above is applicable to constant amplitude loading. This means every stress application is the same. Unfortunately this is not the case for most structures. Therefore a way has to be found to determine the fatigue life of structures which experience variable amplitude loading.

On yacht keels, events like tacks, gusts, waves, vertical accelerations and pitching cause stresses on the keel with various amplitudes. The amplitudes are also dependent on the external conditions like wave profile and wind strength.

The GL Rules give formula to calculate the design life based on theoretical wave encounters, probabilities for sea conditions and the resulting dynamic response of the yacht. For example fully reversed loads due to tacks and jibes are assumed to occur 30 times per day.

A better method would be to collect stress or acceleration measurements on similar keels on similar boats in similar conditions. Such measurements will be more accurate than theoretical data since measurements would take the complex interactions between a particular type of boat and the environment into account. For example a long and narrow yacht like Wild Oats XI will behave differently in the same weather conditions than a wide Open 60.

A so called ‘rainflow counting algorithm’ can be used to extract the stress ranges and the number of cycles from the measured data. The output would be a table containing the stress ranges and the number of times this stress range was applied.

Miner’s rule

The Miner’s rule is one of the accepted methods for adding damage caused by different stress ranges. Basically for every stress range the number of cycles to failure is divided by the actual number of cycles and the fractions are added up. The sum of the fractions is the damage D and has to be smaller than 1.

Miners Rule

Example:

Let’s consider a fixed keel yacht and calculate the damage caused by tacks and waves. It is assumed that the heel angle changes from -30° to +30° during a tack and that a wave causes a stress range of 50 MPa. The keel is fabricated using full penetration welds (FAT Class 80). During the design life of the keel the yacht tacks 50,000 times and is hit 200,000 times by that particular size wave.

In this example it is assumed that the keel is made from a material with a yield strength of 350 MPa and that a factor of safety for static strength of 2 is applied when the boat is heeled 90 degrees. The stress range during a tack is therefore exactly half the yield strength not taking buoyancy of the keel into account.

Load CaseApplied cyclesStress Range
(MPa)
Cycles to failureDamage
Tack 50,000 175 191,067 0.261
Wave 200,000 50 8,192,000 0.024
      Total 0.285

Table 2: Variable amplitude example

As can be seen these two load cases would consume about 29% of the fatigue life of the keel. All other load cases due to different size waves, gusts, and pitching would have to be added. It is also clear that in this particular example tacks are responsible for almost all fatigue damage because of the large stress range.

Difference between fixed keels and canting keels

On canting keel yachts the keel is more horizontal when sailing to increase the righting moment. Therefore the keel fin experiences different loadings compared to a fixed keel yacht.

Tacks produce a much larger stress range because the keel moves through a larger angle. Based on the example in Table 2 this might quickly lead to fatigue failure since doubling of the stress range would increase the damage 8 fold.

Gusts and increases in heel angle due to wave action cause less damage because the righting moment produced by the keel increases not much if the keel is already almost horizontal.

A canting keel will experience higher stress ranges due to vertical accelerations. Vertical accelerations will produce high stresses at the root of a canting keel which even may reverse when hydrodynamic forces on the almost horizontal fin support the mass of the hull. The Volvo 65 Class for example is designed so that the keel produces dynamic lift to reduce the displacement of the hull. Potentially vertical accelerations could cause stress ranges with a magnitude similar to tacks.

Pitching of the yacht will cause high torques in a canting keel strut due to the high inertia of the keel bulb. If the pitch angle of the hull changes due to wave interaction torque in the keel strut will have to rotate the mass of the keel bulb.

Conclusion

Properly designed and manufactured fixed keels are likely to have sufficient fatigue life if they meet static load requirements. This coincidence is most likely the cause why fatigue in fixed keels has not been a major issue in the past. It is still possible for fixed keels to fail due to fatigue as the Excalibur capsize off the Australian coast with four deaths highlighted.

Canting keels experience much higher stress ranges during tacks, vertical accelerations and pitching motions. It is likely that a canting keel will require detailed fatigue analysis even if it meets static load requirements.

Fatigue performance cannot be improved by the selection of a higher strength material. Increasing the required static safety factor and allowing materials with high yield strength is also not a suitable approach for solving fatigue issues. Instead a reasonable static load case and separate fatigue load cases, preferably based on measured data, have to be used to ensure keels do not fail at sea.

With modern data logging systems it is relatively easy to record the load history of the keel. Therefore it is possible to monitor the actual stresses against the stresses assumed during fatigue analysis and replace the keel before it fails.

 

Composite construction background

Generally I would advise to use either a full carbon sandwich construction for a custom yacht or glass sandwich with carbon reinforcements. I would not recommend polyester resin because epoxy is much easier to work with and is by far the more superior material. Overall the material costs are only a relatively small fraction of the overall cost of the boat. It does not make sense to cut corners in this area especially on a one off custom designed yacht.

Why sandwich?

A sandwich core adds thickness to the laminate without adding much weight. Increasing thickness has a large effect on the bending stiffness of the structure. Doubling the thickness increases bending stiffness by a factor of 4.

A large laminate bending stiffness allows increased distances between stringers and frames. This makes construction easier and cheaper since less stringers and frames have to be build. It also gives greater flexibility in the interior design because there is less of a chance that required structural elements interfere with furniture.

Since sandwich core materials are light weight they are also excellent thermal insulators. This keeps the inside of the boat cooler in summer and warmer in winter.

In the past sandwich construction was only used above the waterline. The reason for this is that water ingress into the core would damage the hull and require extremely expensive repair.

With modern materials this is not an issue any more. Epoxy resin is a much less permeable to water than polyester resin. A properly build epoxy hull will not let water into the core. The water issue only exists with open celled cores like balsa wood which soak up moisture like a sponge. Most foams and honeycomb cores have a closed celled structure. Even if water leaks into the core it can’t spread throughout the hull. If epoxy resins and closed celled cores are used there are no reasons why sandwich construction can’t be used below the water line.

Epoxy or Polyester?

Epoxy resin slowly finds its way into boat construction. Epoxy has two big advantages over polyester. One is that it is a much better glue and the other is that it is less brittle.

The job of the resin is to bond neighbouring reinforcement fibres to each other to create a rigid part. Good bonding strength is therefore essential. If the loads exceed the bonding strength microscopic cracks appear in the laminate where the resin debonds from the fibre. The overall structure still holds together but it is irreversibly damaged. Over time the accumulation of micro cracks compromises strength and stiffness. This is the reason why older boats that have been used heavily are generally softer than new boats.

Polyester structures typically micro crack when they are stretched by 0.x% whereas a good laminating epoxy micro cracks at 0.x%. Under normal loading one would aim to never exceed the micro cracking strain. If all other parameters are equal a polyester boat would need X% more fibre in the laminate simply because the resin does not stick as well to the fibre as epoxy. An epoxy boat can be deformed much more before damage occurs. An epoxy hull is therefore much less sensitive to occasional high loads under extreme conditions or during collisions with objects. A well designed and build epoxy hull will have a very long life and degenerate much less over time.

Epoxy also can’t create osmosis because the chemical reaction between the resin and water simply can’t happen. Epoxy is sometimes used to protect polyester resin from water.

Fibres

Glass fibres are by far the most commonly used reinforcements in yachts. They have good strength properties and are very cost effective. The main disadvantage of glass fibres is their relatively low stiffness and the density is more than twice that of carbon fibre. Compared to a carbon yacht glass fibre boats are therefore generally more flexible and heavier. To increase stiffness a lot of fibreglass is required which also increases resin and labour costs. In some areas the cost advantage of fibreglass over carbon therefore diminishes due to increased labour and resin costs. For these reasons the most economical way to build boats can be the use of glass fibre for the majority of the components and unidirectional carbon fibre for reinforcements on frames, stringers and bulkheads. This approach requires very careful engineering since the much higher stiffness of the carbon attracts most of the loads. The surrounding glass structure does not contribute significantly to the strength. If not enough carbon is added the carbon fibres will break first followed by the glass fibres which will lead to a complete collapse of the structure.

Fibres should be as long as possible and therefore woven, unidirectional or stitched fabrics are much preferred over chopped strand mat. With short fibres the loads have to be constantly transferred from one fibre to the other via the resin which reduces strength and stiffness. There is no reason to use chopped strand matt if epoxy resin is used. Polyester boats require layers of chopped strand mat between roving reinforcements to ensure adequate bonding between fibre layers. Since epoxy is a much better glue these layers are not required when using epoxy.

Cores

An ideal core is light weight and has great strength and flexibility. Closed cells are also important to limit resin take up and prevent water ingress.

There are quite a few suitable foam cores with different weights and strengths available. In the slamming area high ductility is important. Brittle cores are not suitable for this application because they would break under repeated impacts.

Honey comb cores have very high strength and very low weight. Unfortunately they are also very expensive and difficult to work with. They require an expert boat builder who has experience with this sort of material if it is used on curved surfaces.

A relatively cheap option is to use aluminium honey comb instead of the regular nomex paper honeycomb. Aluminium honeycomb has very high strength but in combination with water corrosion issues can arise. If the aluminium comes into contact with carbon electrolytic corrosion is also an issue. For this reason aluminium honeycombs are mainly used for high performance racing yachts which only have to last a few seasons. It would be possible to use aluminium honeycomb for interior components where good protection from the environment can be assured.

We would not recommend balsa cores for a custom boat. The main advantage of balsa is that it is cheap. Compared to foams balsa is quite heavy and brittle. Additionally properties can vary wildly because it is a natural product. The open cell structure of balsa leads to a lot of resin uptake during construction and moisture can spread through the core. Excessive moisture will lead to rot in the core and require very costly core replacement.

 

Design Process

The goal of the design process is to develop a boat which meets as far as possible the owner’s requirements whilst staying within the limits of good engineering practice.

The project kicks off with an extensive consultation phase to find out what the boat is going to be used for and what the owner’s preferences are. The outputs of this phase are the general dimensions of the boat, displacement estimate and first styling ideas.

Once the requirements are defined first 3D sketches are developed. With modern software it is quite easy to produce 3D surfaces to represent the boat. With 3D models it is easy to measure the displacement, headroom and other important dimensions. After this phase the hull and deck geometry is defined and the main structural members like bulkheads and stringers are put into place. Construction of the hull tooling and deck tooling can commence.

The next phase is to develop the interior and deck lay out. This is again done in close collaboration with the owner. Usually ideas are discussed over the phone and the 3D model is updated showing the proposals. The model is updated until it meets the owner’s requirements. During this phase clearances and dimensions are checked to ensure everything works as intended. This is where a detailed 3D model becomes invaluable. Once the design of an area of the boat has been finalised the structure is analysed to the relevant codes and production drawings are created from the 3D model.

The construction drawings can be sent electronically in full size and therefore it is easy to feed the data into computer controlled cutting machines or large size printers anywhere in the world. The result of this approach is that parts are built to very small tolerances and fit 100% first time. It is also possible to create photorealistic renderings of the design so that the owner has a good idea of what the finished product will look like.