Design Fatigue Factors Research Articles

Effect of environmental modelling and inspection strategy on the optimal design of floating wind turbines

In order to reduce design conservatism and consequently the cost of energy, appropriate and cost-optimal safety factors should be derived, in light of environmental load uncertainties and lifetime costs. In the present work, a linearized dynamic model has been used together with Monte Carlo simulations and a numerical design optimization procedure to evaluate the impact of the description of wind and wave loads on the fatigue reliability and optimal design of a 10 MW spar floating wind turbine. Trade-offs between design costs and inspection costs with different design fatigue factors (DFFs) have also been assessed. The analyses have been performed for a realistic wind park site, where an environmental model has been developed based on hindcast data. Considering stochastic turbulence intensity, wind-wave misalignment, wind directional distribution, and a two-peak wave spectrum reduced the long-term fatigue damage by approximately two-thirds along the fatigue-critical part of the support structure compared to the base model. Re-designing the tower and platform with the full environmental model resulted in 11% reduction in CAPEX. However, due to the applied design optimization procedure, consistent reliability levels were achieved along the tower length, which resulted in important system side effects for the total structural reliability. Trade-offs between CAPEX and OPEX were derived based on a probabilistic fracture mechanics model and reliability updating through inspections. The necessary inspection intervals to achieve the same accumulated reliability after 20 years of operation were identified with different DFFs, and cost-optimal safety factors were computed with different OPEX costs and interest rates.

Calibration of design fatigue factors for offshore structures based on fatigue test database

The concept of Design Fatigue Factors (DFFs) was introduced for providing desired level of safety in structural fatigue design in offshore structures, often associated with damage calculated from S-N curves. Calculation of fatigue damage from S-N curves can be affected by multiple factors, e.g. types of weld class, corrosion condition, loading conditions, stress concentration on different geometries etc. Each of them can be subject to different level of uncertainties. This study investigates probabilistic models of uncertainty of the fatigue strength in the S-N curves frequently used in offshore oil and gas, and the offshore wind industry based on a comprehensive fatigue test database. It then recalibrates the DFFs from a detailed reliability analysis. The results have shown that with the same target reliability while the DFFs for in air condition in T curve and D curve can remain the same as those from current standards, the DFFs for F curves are reduced especially for the corrosive environmental conditions which has the maximum reduction up to about three times.

Analysis of probabilistic fatigue damage of mooring system for offshore fish cage considering long-term stochastic wave conditions

ABSTRACT This study deals with the probability distribution of fatigue damage of the mooring system for offshore fish cage considering the uncertainty of long-term wave conditions. A set of numerical simulations for offshore fish cage are performed to predict the fatigue damage of the mooring system. Through a virtual stochastic process model, the probability density function of the long-term fatigue damage of the mooring system is achieved by the generalized probability density evolution method, and the failure probability of the mooring system is predicted. The results demonstrate that the generalized probability density evolution method can effectively provide the fatigue damage distribution from the stochastic point of view. And the calibration of the engineering-based fatigue design factor of the current regulation can be conducted through the fatigue reliability analysis considering the uncertainty of the long-term wave conditions. This study provides a new understanding of the long-term fatigue damage distribution.

Fatigue reliability of large monopiles for offshore wind turbines

Upscaling of traditional monopiles to support larger offshore wind turbines introduces fatigue-related design challenges. The design becomes mainly driven by wave-induced fatigue loads, and potential resonant responses can have significant contributions to fatigue. It is essential that these changes in load characteristics be reflected in the design codes. In this paper, fatigue reliability analysis of a wave sensitive, large monopile supporting a 10 MW offshore wind turbine is demonstrated. Reliability-based calibration of fatigue design factors is based on an extensive set of numerical simulations, where the statistical distribution of turbulence intensity and preservation of wave-induced resonant responses are considered. Results show that a minimum fatigue design factor, FDF⩾3 is recommended. The results and methodology presented in this study can assist with identifying the technical limitations and economic viability of upscaling monopiles.

Design evaluation of the fractured main landing gear of a BAE Jetstream SX-SKY aircraft

Purpose– The purpose of this paper is to study the main landing gear (MLG) mechanism configuration.Design/methodology/approach– Mechanism kinematics and dynamics, stress analysis and sizing of the MLG structural members, and fatigue issues related with the mechanism operation. Spreadsheet solutions were incorporated to this survey to analyze the most conceivable loading situations, and important factors of the mechanism design for an initial evaluation of safety implications.Findings– MLG design approach along with conservative fatigue design factors lies in the area of accepted limits in commercial aircraft industry.Research limitations/implications– MLG loading associated with landing as well as those associated with ground maneuvers (steering, braking and taxiing) contribute significantly to fatigue damage, along with the stresses induced by manufacturing processes and assembly. The application of FEA methods for the design of the landing gear does not always guarantee a successful approach to the problem solution, if precise analytical solutions are not available in advance.Practical implications– From the investigation of this incident of fractured struts of the MLG it is confirmed that the reduction in Pintle Housing diameter on the upper part has contributed to the avoidance of damaging the fuel tank above the MLG that would lead to a catastrophic event. On the other hand, the airframe of the SKY-Jet was proved efficient for a belly landing with minor damages to the passengers and heavier damages for the aircraft.Social implications– On-line vibration monitoring sensors hooked up to the landing gear strut and Pintle House would greatly enhance safety, without relying in optical surveys in hard to access and inspect areas of the landing gears mechanisms housings.Originality/value– Analytic methods were adopted and spreadsheet solutions were developed for the MLG main loading situations, along with design issues concerning mechanism kinematics and dynamics, stress analysis and sizing of the MLG structural members, as well as fatigue issues related with the mechanism operation. Spreadsheet solutions were incorporated to this survey to analyze the most conceivable loading situations, and important factors of the mechanism design for an initial evaluation of safety implications.

Fatigue reliability and calibration of fatigue design factors of wave energy converters

Target reliability levels, which are chosen dependent on the consequences in case of structural collapse, are used in this paper to calibrate partial safety factors for structural details of wave energy converters (WECs). The consequences in case of structural failure are similar for WECs and offshore wind turbines (no fatalities, low environmental pollution). Therefore, it can be assumed that the target reliability levels for WEC applications can be overtaken from offshore wind turbine studies. The partial safety factors cannot be directly overtaken from offshore wind turbines because the load characteristics are different. WECs mainly focus on wave loads where for offshore wind turbine the wind loads are most dominating. Fatigue failure is an important failure mode for offshore structures. The scope of this paper is to present appropriate Fatigue Design Factors (FDF), which are also called Design Fatigue Factors (DFF), for steel substructures of WECs. A reliability-based approach is used and a probabilistic model including design and limit state equation is established. For modelling fatigue, the SN-curve approach as well as fracture mechanics are used. Furthermore, the influence of inspections is considered in order to extend and maintain a certain target safety level. This paper uses the Wavestar prototype located at Hanstholm (DK) as case study in order to calibrate FDFs for welded and bolted details in steel structures of an offshore bottom-fixed WEC with hydraulic floaters.

Correction: Márquez-Domínguez, S.; Sørensen, J.D. Fatigue Reliability and Calibration of Fatigue Design Factors for Offshore Wind Turbines. Energies 2012, 5, 1816–1834

The authors wish to make the following correction to this paper [1]. [...]

Fatigue Reliability and Calibration of Fatigue Design Factors for Offshore Wind Turbines

Consequences of failure of offshore wind turbines (OWTs) is in general lower than consequences of failure of, e.g., oil & gas platforms. It is reasonable that lower fatigue design factors can be applied for fatigue design of OWTs when compared to other fixed offshore structures. Calibration of appropriate partial safety factors/Fatigue Design Factors (FDF) for steel substructures for OWTs is the scope of this paper. A reliability-based approach is used and a probabilistic model has been developed, where design and limit state equations are established for fatigue failure. The strength and load uncertainties are described by stochastic variables. SN and fracture mechanics approaches are considered for to model the fatigue life. Further, both linear and bi-linear SN-curves are formulated and various approximations are investigated. The acceptable reliability level for fatigue failure of OWTs is discussed and results are presented for calibrated optimal fatigue design factors. Further, the influence of inspections is considered in order to extend and maintain a given target safety level.

Fatigue design factors for ECAPed materials

Equal channel angular pressing (ECAP) was successfully performed on commercial pure aluminum, aluminum 6061 alloy and commercial pure copper by route B C. Tensile and fatigue (under constant stress) tests shows a significant enhancement in mechanical properties consisting of hardness, yield strength, ultimate tensile strength and endurance limit, but the ductility of the alloys reduced with employing this process. Two fatigue design factors K l and K h has been suggested to co-related fatigue data from coarse grained (CG) to ultra-fine grained (UFG) materials.

Recommended Design Fatigue Factors for Reassessment of Piles Subjected to Dynamic Actions From Driving

Calculated probabilities of fatigue failure depend on the analysis procedure used for design. Calculated probabilities of a fatigue failure also depend on long term stress ranges due to loading and uncertainties associated with this. In order to ensure the consistent safety level for assessment of fatigue failure, the design fatigue factors (DFFs) to be used for fatigue design should be dependent on the analysis procedure and premises used. In the present paper, an assessment of appropriate DFFs for piles subjected to dynamic actions from pile driving has been performed by probabilistic analysis based on: uncertainty with respect to dynamic cyclic stress during pile driving, and fatigue capacity of circumferential welds in piles. Accumulated probabilities of fatigue failures in pile butt welds are presented. An assessment of uncertainties involved in calculation of stress ranges during pile driving has been performed. It is shown that the uncertainty in loading when driving records are known is lower than that estimated on the basis of soil data. Thus, in order to obtain consistent safety levels, different DFFs should be used when calculated stress ranges are derived based on soil data only, as compared with the actual stress ranges and number of blows determined from driving records. The results from probabilistic analyses together with recommended design fatigue factors are presented in this paper.

Fatigue design of steel containment cylinders for CNG ship application

A reliable methodology is required for fatigue design of steel cylinders for Compressed Natural Gas (CNG) carriers in order to meet target safety level at an acceptable cost. This includes description of physical models that represents actual long term fatigue capacity of the Cargo Containment cylinders. The design methodology includes length of welds, fabrication tolerances, fabrication methodology and non destructive testing. It also involves definition of characteristic values for loading and capacity in addition to recommended Design Fatigue Factors. Three alternative fatigue design procedures requiring different Design Fatigue Factors to achieve a system target safety level of annual probability of failure less or equal to 10 −5 are presented.

New Appoaches to Inspection Planning of Fatigue Damaged Offshore Platforms

The present paper summarizes the results of research and development efforts over the last approximately five years to develop simplified and practically applicable approaches for reliability and risk based inspection planning. These efforts have led to the development of a generic inspection planning approach. Following the approach the fatigue sensitive details are categorized and described generically according to standard design parameters such as the Fatigue Design Factor (FDF) and the SN curve. When a measure of the structural consequences of fatigue failure e.g. the RSR and the corresponding probability of structural collapse given fatigue failure of the considered detail are known, generic inspection plans may derived as a function of the generic parameters together with the relative cost of inspections, repairs and failures. Due to the simplicity of the format of the developed inspection plans, the proposed approach has a high potential to be used in codes for the design and maintenance of steel structures. The validity of the proposed approach is illustrated through a study regarding inspection planning of a tri-pod offshore structure where generic inspection plans are obtained using two approximations, namely assuming equidistant inspection intervals and using constant thresholds for the annual probability of failure.

Codified Risk-Based Inspection Planning

Simplified methods are described for reliability- and risk-based inspection planning of steel structures. The methods simplify the practical aspects of identifying inspection plans complying both with specific requirements to the maximum acceptable annual probability of structural collapse and member failure and at the same time minimizing overall total service life costs. Generic inspections plans can then be established for representative fatigue sensitive details in terms of characteristics such as FDF (Fatigue Design Factor), detail type, RSR (Reserve Strength Ratio) given fatigue failure and inspection/repair techniques. Generic inspection plans can be used for design of new structures as well as for requalification of existing structures. In this paper it is described how generic inspection plans can be used for codification purposes in connection with inspection planning of steel structures.

Effects of Moisture Absorption and Test Method on the Properties of E-glass/Polyester Hull Laminates

Effects of moisture absorption on the tensile, compressive, shear, bending and bending fatigue properties of an iso-polyester/E-glass hull laminate were studied. Fickian diffusion constants were found that closely modeled moisture absorption. Comparisons were made of standard moisture experiments using boiling water versus long-term exposure. Results indicated that the boiling water test yielded significantly conservative values. Fatigue endurance limits were found to be near 25% of static load, indicating a fatigue design factor of four is required for infinite service with this material. Coupon results were used with finite element analysis (FEA) to predict panel deformations and strains. Good correlation was achieved.

A probabilistic damage tolerance concept for welded joints Part 2: a supplement to the rule based S– N approach

The first part of this paper presented the required statistics and stochastic models for reliability analysis of the fatigue fracture of welded plate joints. This present Part 2 suggests a probabilistic damage tolerance supplement to the design S– N curves for welded joints. The goal is to provide the practising engineer with simple tools that predict the reliability against fatigue fracture during service life. The impact of the chosen fatigue design factors (FDF) and the uncertainty in the applied stresses is revealed. The effect of an in-service inspection programme is also predicted. The results are presented as dimensionless matrices and suggested for use in support of decision-making at the design stage, without any advanced fracture mechanics modelling and stochastic simulation. One important advantage of this format is that the probability levels are presented regardless of actual weld class and target service life (TSL). This is obtained by introducing the FDF as a key parameter to the results. This parameter is defined as the ratio of predicted fatigue life over TSL. FDF is always calculated in the S– N approach which is mandatory in fatigue life prediction. Various welded details (classes) will have the same reliability level for the same FDF. This is true at the end of TSL and at earlier stages, i.e. fractions of TSL. The absolute value of TSL is immaterial for a given FDF. In the case of in-service inspection, the inspection interval is also given without dimensions as a fraction of TSL. Only the influence of future scheduled inspections is treated. Updating based on actual inspection results is not included as the scope of work is inspection planning at the design stage. Results for some frequent cases occurring in practice are readily derived and presented.

Fatigue Prediction Verification of Fiberglass Hulls

The growing use of marine composite materials has led to many technical challenges and one is predicting lifetime durability. This analysis step has a large uncertainty due to the lack of data from in-service composite vessels. Analytical models based on classical lamination theory, finite-element analysis, ship motions, probability and wind and wave mechanicswere used in this project to predict hull laminate strains, and fatigue tests were used to determine S-N residual stiffness properties of coupons. These predictions and test data were compared against two cored fiberglass sisterships having significantly different fatigue histories and undamaged laminates representing a new vessel. Strains were measured while underway and good correlation was achieved between predictions and measurements. Fatigue damage indicators were identified which could be used in vessel inspection procedures. Endurance limits were found to be near 25% of static failure load, indicating that a fatigue design factor of four is required for infinite service with this material. Standard moisture experiments using boiling water were compared with long-term exposure. Results indicated the boiling water test yielded significantly conservative values and was not a reliable means of predicting long-term effects. Panel tests were compared with a combined coupon and finite-element procedure. Results indicated the proposed procedure was a viable substitute, at least for the materials studied. A rational explanation for using thicker outer skin laminates in marine composites was identified through single-sided moisture flex tests. These showed that the reduced strength and stiffness due to moisture of the outer hull skin laminate could be compensated by increased thickness. Although the resulting unbalanced laminate is not ideal from a warping standpoint, the approach leads to consistent tensile failure of the inner skin when subjected to normal loads. Permeability considerations make this desirable for hull laminates.

Fatigue reliability: a review of recent advances

Fatigue is generally considered the most important failure mode in mechanical and structural systems. Reliability methods are appropriate for managing the large uncertainties that exist in fatigue design factors. In this paper, methods of fatigue reliability analysis are reviewed with emphasis on recent work, for which time variant reliability methods are used to model fatigue-weakened structures.

鋼構造柱梁仕口における梁端溶接部の疲労強度

For the purpose of designing against wind induced fatigue of high rise steel buildings, a series of fatigue tests on welded beam ends at the beam-to-column connections were carried out. Specimens were composed of welded built-up box section steel columns and built-up wide-flange steel beams using 490N/mm^2 class grade of steel. Three types of fabricating methods for beam end joint were examined ; i.e. a field welding type with bolted web and welded flanges , a shop welding type with conventional scallops and another shop welding type without scallop (Non scallop type). Seventeen specimens were prepared for high cycle fatigue tests , low cycle fatigue tests and varying amplitude fatigue tests . S-N diagrams for fatigue design and cumulative damage factors based on Miner's law were obtained and discussed, comparing with the JSSC design recommendation.

Optimal economic strategies with considerations of reliability of fatigue-sensitive structural systems

The integrity of structural systems relative to fatigue and fracture can be ensured by a rational program which coordinates a design, inspection, and repair process to minimize life-cycle costs in the context of a reliability analysis which treats uncertainties in fatigue design factors and inspection performance. The features of the process are summarized, and a simple illustration is provided. Research needs relative to this problem, delineated herein, are principally those of developing reliability models of material behavior, obtaining the data to compute parameter values, and developing efficient computational methods for fatigue reliability and maintainability analysis of “large”-scale series and redundant structures.

Considerations of probability-based fatigue design for marine structures

Fatigue is a major failure modelin marine structures which respond dynamically to random wave and wind loading. Oscillatory stresses produce fatigue at points of stress concentration, typically the welded joints. Because all fatigue design factors are subject to significant uncertainty, a reliability approach to management of such uncertainty seems appropriate. This article summarizes some studies in fatigue reliability research and demonstrates how reliability methods can be effectively utilized by designers to avoid fatigue in marine structural components. Included are (1) a description of fatigue damage under variable amplitude stresses employing the characteristics S-N and fracture mechanics models, (2) models for reliability assessment relative to fatigue and the use of these models to derive design criteria, and (3) an elementary application of system fatigue reliability analysis to establish component design criteria.