Fatigue of Maritime Structures – A Wider View Volker Bertram, ENSIETA, Brest/France, volker.bertram@ensieta.fr

Fatigue is increasingly important in the structural design of maritime structures and associated rules. New paradigms in “design for fatigue” pose problems for traditional cost estimates. Current efforts towards “design for production” will also benefit fatigue life, as forming of non-developable plates imposes internal stresses and reduces fatigue life. 1. Introduction Maritime structures were traditionally designed for static maximum loads (design loads). However, ship and offshore structures are very much subject to dynamic loads, coming from, Fig.1: - propellers and diesel engines excite elastic vibrations in local structures. The number of load cy-

cles is usually much higher than for those due to seaways. - Seaways excite local changing pressures. Typical frequencies are 0.1 Hz leading to load cycle

number of 107 to 108 over the life span of ships. In addition, sudden impacts in seaways (slam-ming) can trigger ship vibrations called “whipping”.

- Changing loading conditions (cargo and ballast cycles) yield few load cycles with high stress am-plitudes

In extreme cases, fatigue failure can lead to total loss of offshore structures or ships, Fig.2.

source: Germanischer Lloyd

Fig.1: Various sources excite vibrations causing eventually fatigue problems Structural failure due to dynamic loads differs from failure due to static loads: - Failure due to static loads may be due to plastic deformation, buckling and brittle fractures. The

failure appears after a single load. - Failure due to dynamic loads is characterized as follows: During crack initiation, microscopic cracks appear due to accumulated plastic deformations at

microscopic scale. Single micro-cracks may grow individually or combine with other cracks to macro-cracks. During crack propagation, the macro-crack growths orthogonal to the direction of maximum main stress. The crack propagation speed is typically 10-8…10-3 mm per load cycle. There is no spontaneous failure (“stable crack growth”), but cracks may still be unacceptable e.g.

due to leakages. If a critical crack length is reached, the structure fails rapidly having insufficient residual strength.

Fig.2: Spectacular maritime disaster linked to fatigue of structures: “Alexander L. Kielland”

Fig.3: Fatigue testing at TU Hamburg-Harburg

Several factors have contributed to the increasing importance of fatigue strength: - structures are increasingly sophisticated. Finite-element analyses are used as standard tools to mini-

mize the structural material reducing thus also margins for fatigue strength. - High-tensile steels are increasingly used. These increase static strength, but have the same features

as mild steel for corrosion and fatigue. - As the power-to-weight ratio of ships increased, so did problems with vibrations. 2. Investigation approaches for fatigue The increasing importance of fatigue strength for maritime structures has resulted corresponding re-search activities and recommendations for design, fabrication and operation of maritime structures to counter the increased risks described above. These worldwide research efforts, for more than three decades now, have produced an amount of publications that it is impossible to give a comprehensive overview. The best starting point for at least extensive literature surveys remains the proceedings of the ISSC (International Ship Structure Conference). In reality, fatigue problems appear after a certain number of load cycles, often only after months or even years of operation. The feedback for design is then often slow. Experiments allow to accelerate the time scale in applying realistic loads at a much higher frequency and observing then fatigue problems (after the same number of load cycles) in much shorter time, namely hours or days. As fatigue concerns microscopic structures failure, at a level where the material can no longer be con-sidered as a homogeneous substance, neither scaled down models (one cannot easily scale down ap-propriately the grain size of the investigated material) nor classical structural analysis (based on con-tinuous mechanics) were suitable tools for investigations of mechanisms. This left initially mainly full-scale model testing with then necessarily small specimens. Eventually, a few large testing facilities appeared worldwide which allow to test at least some structural details composed of complex 3-d structural elements, such as stiffeners, brackets, flanges etc. These allowed investigation of real(istic) ship details particularly prone to fatigue problems. Fig.3 shows the large testing facility in Hamburg with such a structural detail. 3-d complex assembled structures have a different fatigue behavior than simple plane material specimen or even single welds which are frequently tested in smaller testing fa-

cilities. ENSIETA in Brest is in the process of installing one of the larger such testing facilities which will add to France’s capabilities (and competence) in the field of maritime fatigue.

Fig.4: Excerpt from classification rules showing catalogue of structural details and stress concentra-tion factor corrections

Fig.5: Structural design: conventional (left) and designed for fatigue strength (right)

Over several decades, test data were accumulated for many typical ship structures and these data have been used by classification societies (along with feedback from fatigue damages on actual ships) to compile catalogues of stress increasing factors, Fig.4. These catalogues allow a simple, pragmatic ap-proach to structural design. The structural designer can compute macroscopic nominal stress using long established and widely available standard tools for structural analysis. The catalogues then give a correction for the influence of a discontinuity (like a weld or a corner) allowing to transform fatigue strength into a changed upper limit for the static stresses. The approach is pragmatic, but not applica-ble to structures which are not (yet) found in the catalogues. This poses problems each time new struc-tural details or new materials are used. The collective experience of model tests, advanced structural analysis and feedback from ship opera-tions has also resulted in recommendations how to design certain, frequent structural designs in ships, but “design for fatigue” is rarely taught in universities. (Theory of fatigue is widely taught and pub-lished, practical design not, as it requires typically industry experience and knowledge less widely dis-seminated.) Fig.5 shows one example, namely how to conventional holes for weld intersections are of-ten designed (using the simple circle segments dating from pre-CAD eras) and how they can be de-signed for improved fatigue strength.

Fig.6: Increasingly fine finite-element models are used in fatigue and fracture analysis, Fricke ??? Traditional dimensioning of ship structures followed simple semi-empirical formulae giving directly the thickness of plates of stiffeners or a required section modulus. Fatigue strength, however, requires a more detailed stress analysis, Fig.6. Complex ship structures are increasingly analyzed using 3D fi-nite elements models. These models allow a realistic distribution of loads and capture the interaction between the main structures. Usually the whole ship hull with its main structures is modeled using plate elements. Secondary structures like stiffeners are modeled simplified using truss elements. The

analysis gives global nominal stress distributions for coarse grids. For fine grids, effects of effective width and geometry of the structure are also captured. Local finite-element models serve to determine the stress increase due to geometry of the structure. Usually plain-strain plate elements suffice to determine the notch stress at plate edges of holes. For hot-spot stress at weld toes and plate structures, either plate elements of volume elements are em-ployed. Volume elements require more effort, but consider the stiffness and load distributing effect of the weld better. The definition of the hot-spot stress requires the evaluation of the linear stress compo-nent over the plate thickness. This is automatically given for plate elements. For volume elements, an elegant solution is arranging only one element over the plate thickness. Then intermediate nodes are necessary at the element edges to capture the bending properly. Using only 2 integration points over the thickness yields directly the linear stress component. This can then be extrapolated to the plate edge to give the hot-spot stress. The loads for the local finite-element models come either from pre-scribed external stresses or deformations. These are taken either from a defined initial state or from a global analysis.

The notch stress at the weld toe respectively the notch factor is usually determined in a 2D model with very fine grids. Such models employ plain-strain plate elements. Linear-elastic analyses can employ boundary element methods reducing the effort for the model considerably. Both finite-element and boundary-element methods require a grid refinement near regions with high stress gradients.

3. Wider implications of fatigue strength Despite the considerable progress in understanding fatigue mechanisms and transforming this under-standing into design and manufacturing procedures, there is no shortage of open questions around fa-tigue of maritime structures: 1. Maritime structures (ships and offshore platforms) are among the largest man-made structures in

the world. Since scaled-down model tests are not possible, only relatively small structural details can be tested. Both machine size and energy consumption become exhibitively expensive as we try to move to larger test specimen. Therefore, test machines are increasingly used to validate nu-merical procedures for specimen of limited size and complexity, and larger structural details can only be investigated by (hopefully) validated numerical approaches. Both scope of validation and numerical performance (efficiency of algorithms and available hardware) show potential for im-provement.

2. Maritime structures are usually subject to multi-frequency, multi-amplitude excitation, e.g. broad-band ‘random’ excitation from the seaway superimposed on narrow-band frequency excitation from engines and propellers. While fatigue life is easily determined for single-frequency, single-amplitude excitation, the order in which different frequencies in a spectrum appear in the excita-tion history appears to influence the fatigue life of a specimen. This poses then questions on how (in what tile order) to apply loads in tests to derive appropriate predictions.

3. One of the excitation sources for load cycles in maritime structures is the seaway which can only be described in a stochastic manner. In addition, current numerical methods to analyze maritime structures in seaways are typically validated only for some global motion. Extensive validation of numerical tools for local loads is expected to be a major research goal for the global research com-munity for the next decade. First tentative steps, Bertram (1997), Iwashita et al. (2000), show already that methods yielding good global results (for heave and pitch motion) may well show large errors for local pressures (and thus probably also for stresses).

4. Fatigue tests for maritime structures usually accelerate time by using a higher frequency of load-cycles than in reality. The inherent assumption is that the structure as such does not change during the simulated test time. This is acceptable for cases where fatigue damage occurs within hours to weeks, typically induced by high-frequency propeller or engine excitation. However, if fatigue failure occurs after several years of operation in a corrosive environment (like ships and offshore platforms), interaction of corrosion and fatigue becomes important. Corrosion will certainly influ-ence fatigue as specimens will be reduced in strength to start with. However, fatigue and associ-ated micro-cracks may also influence progress of corrosion. At present, we see no possibility to

accelerate appropriately (and in a controlled fashion) the corrosion as well as the load-cycles. In-teraction of corrosion and fatigue for high-frequency load-cycles (where the corrosion state is con-sidered as steady during the investigated period) will be subject to investigations at ENSIETA in the near future.

5. Fatigue failures are usually detected in inspections of classification societies. While fatigue prob-lems are frequent, catastrophes due to fatigue are quite rare, because micro-cracks take usually a long time (sometimes months to years) before progressing to structure failure. They are then typi-cally detected and rectified at an early stage. The inspection requires surveyors (representatives of the classification society inspecting on-board) to look at the structures up close. This poses prob-lems in narrow spaces. The quest for more ships safety has already made double-hull constructions mandatory for tankers and double-hull constructions are under debate for bulk carriers (the second largest segment of the world fleet in terms of tonnage). The space between the inner and outer hull is quite narrow and difficult to access for humans. Here, robotics combined with machine vision is seen as one future solution to detect fatigue problems early in these new ship constructions, Fig.7, Weiss et al.(2004).

Fig.7: Narrow passage in double-hull tanker (left), inspection robot (right)

Fig.8: Aspects of plate forming are transformed into a producibility index which reflects at the same

time internal stresses which are bad for fatigue life 6. Ship hull forms are traditionally designed following hydrodynamics aspects. Only recently, as-

pects of ship productions are considered in some shipyards already when designing the ship hull, Bertram and El Moctar (2002). Ship hulls contain many plates that require forming, either using heat (thermal forming) or hydraulic pressure (cold forming). Both processes induce internal stresses in the formed parts which are increased by degree of curvature and twist, as well as mis-fits in assembly which are corrected by brute force and corrective welding with increased thermal energy input inducing further internal stresses. This traditional approach leads to both increased building cost and reduced fatigue life. Maximizing the amount of developable plates and accurate

manufacturing in turn reduces both production cost and fatigue problems. Methods to integrate approaches to evaluate (and maximize) the producibility in current CAD for ship structures are subject to ongoing research at ENSIETA in the framework of the Intership project, Fig.8, Potoudis (2004).

7. Estimating the production cost is a fundamental part of ship design. Traditionally, shipyards em-ploy empirical methods to estimate the cost of a new ship, as ships typically are one-of-a-kind products and orders are won based on early bids, i.e. naval architects must estimate costs a priori and within relatively short time (order of several days). Most of these traditional cost estimate ap-proaches are related to the ship weight, which in turn is estimated based on ship type and main dimensions as well as installed power and equipment and outfit, Schneekluth and Bertram (1998). Design for fatigue leads to much more elaborate structural design and assembly procedures, re-quiring e.g. polishing welds to reduce notch stresses. The structural weight is virtually unaffected, but the construction costs are naturally significantly higher. Thus a cost estimate following the tra-ditional approach with traditional empirical coefficients based on yesterday’s practice underesti-mates costs. New approaches to cost estimates need to be developed to reflect modern design-for-fatigue, design-for-production approaches in ship building. Such approaches are pursued world-wide at a few places and also subject to a research and development project involving ENSIETA, Bertram et al. (2004). The general idea is to decompose the production process into small ele-ments and add costs for each elementary step in a structural design or simulation phase.

4. Conclusion Fatigue for maritime structures has far more implications and aspects than ‘just’ the experimental and numerical aspects of mechanical investigations. Ultimately, engineering research is expected to yield better products and better procedures to support these products (from design to operation). A wider view shows many facets that need to be addressed. In my personal view, we will only succeed if we address the topic with a wider view, without reducing the importance of focused or even fundamental research. References BERTRAM, V. (1997), Vergleich verschiedener 3D-Verfahren zur Berechnung des Seeverhaltens von Schiffen (Comparison of various 3-d methods to compute the seakeeping behaviour of ships), Jahrbuch der Schiffbautechnischen Gesellschaft, Springer BERTRAM, V.; EL MOCTAR, O.M. (2002), Design for production in ship hull design, 37th WEGEMT School, Madrid BERTRAM, V., MAISONNEUVE, J.J.; CAPRACE, J.D.; RIGO, P. (2004), Cost assessment in ship production, paper prepared for submission to ‘The Naval Architect’ IWASHITA, H., NECHITA, M., COLAGROSSI, A., LANDRINI, M., BERTRAM, V. (2000), A critical assessment of potential flow models for ship seakeeping, 4th Osaka Colloquium on Seakeeping Performance of Ships, Osaka POTOUDIS, D. (2004), Etude de la fabricabilité des coques de navires (Study of the producibility of ship hulls), Final year project (PFE) report, ENSIETA SCHNEEKLUTH, H.; BERTRAM, V. (1998), Ship design for efficiency and economy, Butterworth+Heinemann, Oxford

WEISS, P. ; ANDRITSOS, F. ; SCHOM, F. ; FIDANI, A. (2004), Innovative robotic solutions for the survey and certification of ships and mobile offshore units, 3rd Conf. Computer and IT Applica-tions in the Maritime Industries (Eds. Armada and Bertram), Siguenza, pp.140-147