A simple surrogate model for the rainflow fatigue damage arising from processes with bimodal spectra

There are many applications, in particular offshore engineering, in which the load process comprises a high frequency and a low frequency component, and each component can be regarded as a narrowband process. Many researchers have proposed spectral methods for evaluating the rainflow fatigue damage for such bimodal processes, nevertheless the accuracies of these methods still have room for improvement. Recently, the author has developed an analytical approach that compares well with numerical simulation; unfortunately, the approach is intricate and difficult to implement. This paper presents a new formula that is accurate, and yet simple enough for adoption in standard spreadsheets and design codes. The formula is valid for a wide range of parameter values and yields the exact theoretical result under several limiting conditions. The formula is calibrated based on extensive numerical simulations, and the database of results are fully presented herein so that they may be used directly in design, or for further studies.     

基于谱分析LNG船典型热点疲劳可靠性分析

  目的  现代LNG运输船的营运寿命通常不少于40年,相比于平均营运20~25年的其他类型商船而言,其船体结构会承受更多的交变应力,因此,有必要对LNG运输船的疲劳强度进行分析。  方法  采用谱分析法对17万立方米级LNG运输船疲劳强度分析。针对均匀满载出港和正常压载出港2种装载工况以及营运于北大西洋海区疲劳环境条件40年设计寿命的要求,通过谱分析得到累计疲劳损伤和预估疲劳寿命,对一些不满足要求的关键区域进行优化。  结果  结果显示,经优化后该船型船体结构疲劳性能满足设计要求。  结论  本文给出了对提高结构疲劳性能在建造和营运阶段可采取的质量控制建议,可为大型LNG运输船疲劳强度的研究和对相关船体结构质量的控制提供参考。     

Study on the application of spectral fatigue analysis

1Introduction Fatiguefailurehaslongbeenanimportantissuefor shipsandoffshorestructures.Toensuresufficientfa tiguestrengthduringtheservicelife,afatiguestrength assessmentneedstobedoneatthedesignstage.Gen erally,methodsforassessingfatiguestrengthcanbe classi…     

基于谱分析法的FPSO剩余疲劳寿命研究

疲劳破坏是船舶与海洋工程结构破坏的主要模式之一。多年来,船舶结构的疲劳断裂问题一直是造船界广泛关注的问题[1]。对于由大型油船改装而成的FPSO而言,预测并延长其服役寿命是很关键的。本文通过谱分析法对船体疲劳损伤度进行计算,分别对油船和FPSO阶段进行计算从而得到FPSO剩余疲劳寿命。通过建立3D有限元模型,采用热点应力方法来确定评估处应力传递函数,分别计算各个短期海况损伤度并通过线性叠加来计算总的损伤度以及剩余疲劳寿命。根据疲劳评估结果,更加高效地实施船体结构的检测及维修。     

随机波浪载荷作用下导管架平台动力响应及疲劳可靠性分析

主要针对波浪载荷作用下导管架式海洋平台结构的疲劳可靠性进行研究.采用Airy线性波浪理论,将导管架结构离散成空间梁有限单元结构;在此基础上采用结构模态分析方法,编程计算了平台结构在随机波浪载荷作用下的位移、速度、加速度和应力随机响应及其概率统计量.导管架结构疲劳可靠性分析建立在频域响应的基础上,假设结构响应的应力范围服从Rayleigh分布,利用结构应力传递函数得到结构应力响应谱,然后利用Miner线性累积损伤准则推导出结构疲劳寿命的概率分布函数,并考虑结构疲劳强度影响系数的随机性,求得结构在随机应力谱下给定疲劳寿命时的疲劳可靠性指标.文中所建立方法可用于导管架式平台结构的疲劳安全评估.     

Multi-scale modeling of fatigue crack propagation applied to random sequence of clustered loading

Fatigue crack propagation in marine structures is obviously governed by mechanics of the considerably different four levels of multi-scale problems. Problems of structural response to environmental loads have length scale of several hundred meters, whereas possible detectable size of cracks from initial defects in a weld is of the order of millimeters. Once a fatigue crack initiates, crack tip plasticity is of the order of several grain sizes, while the resulting fatigue crack growth in each load cycle is of the order of nanometers. In our previous work, the first author and their associates have developed the so-called CP-System, which can treat the first two multi-level problems as an integrated system. Furthermore, we have incorporated the third level of mechanics by using the stress intensity range corresponding to the repeated tensile plastic deformation ahead of the crack tip. In the present paper, we shall discuss a more rational integral equation-based formulation in order to integrate the third and fourth levels of micro-mechanics to the first two levels of continuum mechanics.The method is then applied to fatigue crack propagation under the effects of random sequence of clustered loading. As an example of the random sequence of clustered load, we shall use the so-called “storm model”. In the crack propagation simulation, we have to take into account of the plastic wake on the crack surfaces, whose thicknesses are influenced by the material parameters involved in the crack growth model. These parameters are first identified by the fatigue tests under combined constant and random loading using a CT specimen. Then, fatigue crack growth is investigated by numerical simulation and fatigue tests for various random sequences of clustered loading. The experimental and numerical results agree quite well with each other, and fatigue crack propagation is found to be considerably retarded under random sequence loading, so that the conventional equivalent stress approach may provide rather conservative results to the real seaway loading.     

Parametric method for the assessment of fatigue damage for marine shaft lines

An original parametric method is introduced for the assessment of the fatigue life of marine shaft lines. The particularity of the method lies in the fact it introduces a relevant load modelling around a limited number of parameters specific to marine shaft lines while depicting the loading complexity (multiaxiality, mean stress effect, non-proportionality of the loading path). The method is designed to allow for assessments, in both in-use and pre-design phase shafts, towards a particular fatigue damage mode. The observations made in this study show two damage modes. On one hand, a damage mode issued from multiaxial cycles and associated with ship maneuvers, corresponding to HCF regime. On the other hand, there is a damage mode in the VHCF regime resulting from bending stress cycles due to the structure rotary bending.     

基于改进谱分析法的船舶疲劳强度直接计算

针对目前船舶疲劳强度评估问题,频域谱分析法将应力范围服从Rayleigh窄带分布,造成结果偏保守.而时域法则计算时间过长,无法满足快速预估需求.本文以频域谱分析法为基础,提出一种适用于宽带随机过程的改进谱分析法,并以实船为算例进行计算分析.结果 表明,基于改进谱分析法的疲劳计算结果与精确解差距较小,可以提供一个相对可靠...     

A state-of-the-art review on fatigue life prediction methods for metal structures

 Metals are the most widely used materials in engineering structures, and one of the most common failure modes of metal structures is fatigue failure. Although metal fatigue has been studied for more than 160 years, many problems still remain unsolved. In this article, a state-of-the-art review of metal fatigue is carried out, with particular emphasis on the latest developments in fatigue life prediction methods. All factors which affect the fatigue life of metal structures are grouped into four categories: material, structure, loading, and environment. The effects of these factors on fatigue behavior are also addressed. Finally, potential problems to be resolved in the near future are pointed out. Received: January 7, 2002 / Accepted: March 25, 2002     

半潜平台波浪载荷不确定性及结构疲劳可靠性研究

在海洋平台结构疲劳强度分析的不确定因素中波浪载荷的不确定性对其影响较大,为了评估疲劳载荷计算过程中波浪载荷的不确定性文章建立了海浪谱型、波高、波浪载荷传递函数、平均跨零周期、海况发生概率和浪向等引起的波浪载荷不确定性的评估方法和公式.同时为了评估波浪载荷传递函数的不确定性进行了波浪载荷模型试验.重点对西北太平洋和中国南海的海况进行了分析计算,定量统计回归出西北太平洋的有义波高和平均跨零周期修正公式,以及中国南海不同季节海况和浪向分布规律对半潜平台波浪载荷和疲劳寿命的影响因子.最后根据波浪载荷不确定性以及结构疲劳分析中的其他不确定因素计算分析了半潜平台典型结构的疲劳可靠度.     

Hysteretic damping of soils for well conductor fatigue analysis

The fatigue assessment of a well conductor is a critical design task during offshore exploration and development of hydrocarbons. In recent years, major progress has been made towards the modelling of soil-conductor interaction. Upgraded soil-conductor interaction springs (i.e., p-y curves) and damping models are developed and are gaining acceptance by the industry. However, there is a general lack of simplified procedures to incorporate the soil damping into the time-domain structural analysis of a wellhead system. Thus, the motivation of this paper is to close this gap by proposing a simplified procedure for incorporating the soil damping in the well conductor time domain analysis. The procedure is generic and allows for convenient adoption of alterative p-y spring and damping models. Design charts for equivalent soil system damping ratio versus the lateral deflection of the conductor are developed through parametric analyses based on representative wellhead configurations with typical soil strength profiles in the Gulf of Mexico to facilitate practical design.     

Numerical simulation of fatigue crack propagation under biaxial tensile loadings with phase differences

Fatigue crack propagation under the biaxial tensile loading, which loading directions are normal and parallel to the initial crack position, is highlighted in this study. Most of in-service structures and vessels are subjected to many types of loading. Generally, these loadings have different axial components with different phases. However, the structural integrities of structures and vessels are evaluated according to design codes based on theoretical and experimental investigations under a uniaxial loading condition. Most of these codes are based on the S–N curves approach. An approach that does not use S–N curves has been favored by researchers, with the fracture mechanics approach preferred for evaluating the fatigue life of structures. An advanced fracture mechanics approach was developed based on the Re-tensile Plastic zone Generating (RPG) stress criterion for fatigue crack propagation. In this study, fatigue crack propagation tests under biaxial loading with six different phase and loading conditions are performed and the effect of the phase difference under biaxial loading is evaluated. A numerical simulation method of fatigue crack propagation based on the RPG stress criterion under different biaxial loading phase conditions is presented and compared to measured data.     

Fatigue life estimation of explosive cladded transition joints with the use of the spectral method for the case of a random sea state

The problem with fatigue lifetime estimation of explosive cladded transition joints under random loading conditions has been described. The paper presents the fatigue test results performed for the random state of tension-compression under a generated spectrum according to the Pierson-Moskowitz model. The obtained spectrum has a non-Gaussian characteristic. The tested material consists out of a transition joint clad with four layers of aluminium alloy A5083, A1050, Titanium Grade 1 and steel Grade D. The material has been tested for the existence of residual stresses after the welding process with the hole drilling method. The welding process has been also simulated with ANSYS and the residual stresses have been generated for the Goldak volumetric distribution. The obtained values of residual stresses comprise to the values of real tests performed for the hole drilling method. The information about the residual stress values have been taken into account in the process of fatigue lifetime estimation in the form of non-zero mean stresses compensation inside the clad. The fatigue life has been calculated with the use of the frequency domain method. The Goodman mean stress compensation model has been used in the process of residual stress compensation. The non-gaussianity has been compensated with the use of the Bracessi formula. The obtained fatigue life assessment results have been compared with stand test results. The calculated results are within the scatter area of 3, but individual scatter values have been calculated for calculated series.     

Experimental and finite element analysis of fatigue strength for 300 mm2 copper power conductor

The fatigue strength of a 300 mm² stranded copper conductor was investigated experimentally and by finite element (FE) analysis. An analytical model was also developed and validated. Wires taken from the outer layer of the conductor were fatigue tested in tension–tension loading and compared with similar data for wires taken from a 95 mm² conductor. The wire cross section was deformed due to the compacting process that was applied during fabrication. When corrected for stress concentrations due to the deformation the data for the two sets of wire fell within the same scatter-band. Full scale testing was carried out in a specially designed rig with constant tensile load and reversed displacement controlled bending with a fixed curvature variation. The loading is a simulation of the loading of a power cable hanging from a floating vessel through a bellmouth. Conductors were tested in two states; dry and lubricated. A finite element model was established for the copper conductor. The model was formulated by a combination of elastic beam and beam-contact elements that included the effects of friction. The effect of local bending due to contact forces was included in the model. Two contact conditions were investigated; the point (trellis) contact between adjacent layers of wire and the inline contact within each layer and between the first layer (centre wire) and the second layer. The FE model was validated by a calibration test of a full scale conductor, and by sensitivity studies varying the size and the number of elements of the model. Fatigue analysis of the conductor was carried out, based on the S–N curve for individual wires. Taking into account the effects of friction and local bending, agreement was obtained between predicted and experimental fatigue strength of the conductor, for the FE model as well as the analytical model.     

Numerical simulation of fatigue crack propagation under superimposed stress histories containing different frequency components with several mean stress conditions

Fatigue crack propagation behavior under superimposed stress histories containing different frequency components with several mean stress conditions was investigated. Numerical simulation of fatigue crack propagation based on an advanced fracture mechanics approach using the RPG (Re-tensile Plastic zone Generating) stress criterion for fatigue crack propagation was improved to extract the effective part from the applied stress history for fatigue crack propagation. The parameter, which is based on the plastic hysteresis energy consumed in the vicinity of a crack tip, was applied and implemented into the numerical simulation code of fatigue crack propagation. Fatigue crack propagation tests under various superimposed stress conditions with several mean stress conditions were performed and compared with the fatigue crack propagation histories obtained from the improved numerical simulations. These comparisons show the validity of the proposed procedure for extracting the effective stress history from the superimposed stress histories with different frequency components and mean stresses. Additionally, practical fatigue strength evaluations based on the linear cumulative fatigue damage parameter were conducted to investigate the tendency of the fatigue damage value under these stress conditions.     

A unified fatigue life prediction method for marine structures

Marine structures such as ships and offshore platforms are mostly designed with damage tolerance and this design philosophy requires accurate prediction of fatigue crack propagation process. Now more and more people have realized that only a fatigue life prediction method based on fatigue crack propagation (FCP) theory has the potential to satisfy the accuracy requirement and to explain various fatigue phenomena observed. In the past several years, the authors’ group has made some efforts in developing a unified fatigue life prediction (UFLP) method for marine structures. The key issue for this development is to establish a “correct” crack growth rate relation. In this paper the improvement of the crack growth rate model is dealt with first. A new crack growth rate model based on the concept of partial crack closure is presented. The capability of the model is demonstrated. Secondly, studies on the engineering approaches to determine the parameters in the new crack growth rate model are carried out and validated by comparing with the experimental results on a wide range of alloys. Thirdly, the preliminary studies on some significant problems such as load sequence effect are presented. Finally, further studies for the application of the UFLP method to the fatigue strength assessment of marine structures are pointed out.     

一种基于累积损伤理论和裂纹尖端弹塑性应力场的裂纹扩展预测方法

文章提出了一种预测疲劳寿命的应力循环叠加和损伤循环叠加的双重叠加方法。该方法依据累积损伤理论,通过分析变幅载荷下裂纹尖端的应力场,采用应力循环叠加的方法反映残余应力的影响;同时利用SWT应力应变和寿命的关系,循环叠加裂尖损伤。该方法能够很好地反映过载时裂纹扩展的迟滞效应,适合变幅载荷下疲劳寿命的评估分析。     

Time domain analysis procedures for fatigue assessment of a semi-submersible wind turbine

Long term time domain analysis of the nominal stress for fatigue assessment of the tower and platform members of a three-column semi-submersible was performed by fully coupled time domain analyses in Simo-Riflex-AeroDyn. By combining the nominal stress ranges with stress concentration factors, hot spot stresses for fatigue damage calculation can be obtained. The aim of the study was to investigate the necessary simulation duration, number of random realisations and bin sizes for the discretisation of the joint wind and wave distribution. A total of 2316 3-h time domain simulations, were performed.In mild sea states with wind speeds between 7 and 9 m/s, the tower and pontoon experienced high fatigue damage due to resonance in the first bending frequency of the tower from the tower wake blade passing frequency (3P).Important fatigue effects seemed to be captured by 1 h simulations, and the sensitivity to number of random realisations was low when running simulations of more than 1 h. Fatigue damage for the tower base converged faster with simulation duration and number of random realisations than it did for the platform members.Bin sizes of 2 m/s for wind, 1 s for wave periods and 1 m for wave heights seemed to give acceptable estimates of total fatigue damage. It is, however, important that wind speeds that give coinciding 3P and tower resonance are included and that wave periods that give the largest pitch motion are included in the analysis.     

A computational approach for fatigue crack propagation in ship structures under random sequence of clustered loading

The authors have developed a simulation program, CP-System, for multiple cracks propagating in a three-dimensional stiffened panel structure, where through-the-thickness crack propagation is formulated as a two-dimensional in-plane problem, and the crack propagation behavior is simulated by step-by-step finite element analyses. In order to evaluate the fatigue lives of marine structures accurately, it is necessary to take into account the load histories induced by sea waves, which may be composed of a random sequence of certain clustered loads with variable stress range. In the proposed crack growth model, the crack opening and closure behavior is simulated by using the modified strip yielding model, and the effective tensile plastic stress intensity range, ΔK _RP, is calculated by considering the contact of plastic wake along the crack surfaces. The adequacy of the proposed crack growth model is examined by comparison with fatigue tests under non-constant-amplitude loading. The usefulness of the developed method is demonstrated for a ship structural detail under certain simulated load sequences. It is shown that the fatigue crack growth of a ship structure is significantly retarded due to the load interaction effects, so that the conventional method for fatigue life assessment may predict a relatively conservative fatigue life of a structure.     

在随机载荷作用下用断裂力学法估算潜艇耐压壳体的疲劳寿命和裂纹尺寸

潜艇在上浮下潜的过程中承受着反复作用的由外部水压力所产生的随机载荷,耐压壳体面临着疲劳破坏。本文引入了潜艇的疲劳载荷谱,模拟了潜艇随机载荷历程,并对一次载荷历程估算了疲劳寿命;同时模拟了100次载荷历程,分别对疲劳寿命和裂纹尺寸进行了统计,结果表明裂纹的疲劳寿命符合威布尔分布,裂纹扩展尺寸服从对数正态分布。该结论与目前疲劳可靠性分析中使用的对数正态分布模型和威布尔分布模型相一致。