# 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 detail | FAT 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 |

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:

For welded joints m_{0} = 3. If N < 10^{7} the slope exponent m equals 3. At more than 10^{7} cycles the slope of the SN – curve changes with m = 5.

A different way to write this is:

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 m_{0} = 3 and N between 10,000 and 5·10^{8} are shown below.

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:

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.

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 Case | Applied cycles | Stress Range (MPa) | Cycles to failure | Damage |
---|---|---|---|---|

Tack | 50,000 | 175 | 191,067 | 0.261 |

Wave | 200,000 | 50 | 8,192,000 | 0.024 |

Total |
0.285 |

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.