Evaluation of fatigue damage model predictions for fixed offshore wind turbine support structures

This work deals with the evaluation of the spectral fatigue damage prediction of a tripod offshore wind turbine support structure subjected to combined stochastic wave and wind – induced loads. The stochastic loadings are defined using the sea states based on a scatter diagram related to the North Atlantic. Further, the power spectral density of the hot spot stress is estimated accordingly. The prediction of fatigue damage is evaluated in several spectral fatigue damage models including the Rayleigh, Wirsching–Light, Tunna, α_0.75, Tovo and Benasciutti, Zhao–Baker, Rice and Dirlik models. Critical hot spot locations, which experience the most fatigue damage, are analysed based on the finite element method and the S–N fatigue damage approach. The time-domain solution based on the rainflow cycle counting method is assumed to be the “real” data and the model that best fits the fatigue damage of the wind turbine support structure is identified with the Akaike’s Information Criterion.     

Energy-based time derivative damage accumulation model under uniaxial and multiaxial random loadings

A new fatigue life prediction method using the energy-based approach under uniaxial and multiaxial random loadings is proposed. The uniqueness of the proposed model is based on a time-derivative damage accumulation unlike classical cycle-based damage accumulation models. Thus, damage under arbitrary random loading can be directly obtained using time-domain integration without cycle counting. First, a brief review of existing models is given focusing on their applicability to uniaxial/multiaxial, constant/random, and high cycle fatigue/low cycle fatigue loading regimes. Next, formulation of time-derivative damage model is discussed in detail under uniaxial random loadings. Then, an equivalent energy concept for general multiaxial loading conditions is used to convert the random multiaxial loading to an equivalent random uniaxial loading, where the time-derivative damage model can be used. Finally, the proposed model is validated with extensive experimental data from open literature and in-house testing under various constant and random spectrum loadings.     

基于应力概率密度和功率谱密度法的随机声疲劳寿命预估方法研究

针对航空发动机燃烧室火焰筒结构的声疲劳问题,研究了一种用于随机载荷下结构疲劳寿命预估的有效方法。首先,对薄壁结构在随机载荷作用下的Von Mises应力过程的概率分布作了研究,给出了应力峰值概率密度函数的表达式。基于Miner线性理论,提出了基于应力概率密度和功率谱密度法的随机声疲劳寿命预估方法,并建立了疲劳寿命预估模型。以某型航空发动机燃烧室火焰筒结构为例,在采用耦合的有限元和边界元方法计算出随机声疲劳应力基础上,应用所建立的模型进行了疲劳寿命估算,并对计算结果进行了宽带修正。结果表明,该方法对航空薄壁结构随机疲劳寿命分析具有实用性。     

Thermisch– mechanisches und isothermes Ermüdungsverhalten der Nickelbasis – Superlegierung IN 792 CC

Thermal-mechanical and isothermal fatigue behaviour of the nickel-base superalloy IN 792 CC Many components used in high temperature applications are exposed to complex thermal-mechanical loadings during operation. For this reason the effect of start-stop-cycles with thermalmechanical fatigue (TMF) as consequence was investigated by means of In-Phase(IP)and Out-of-Phase (OP) TMF tests. The fatigue life of the γ'hardend nickel-base cast superalloy IN 792 CC decreases with increasing maximum temperatures T_max of the TMF cycles, due to the increasing plastic deformations and the increasing mean stress (OP-TMF) or increasing intergranular; damage (IP-TMF), respectively. These relations can be satisfactorily described using the Manson-Coffin-relationship or the damage parameters of Smith-Watson-Topper and Ostergren. By contrast, the influence of different phase shifts between temperature and mechanical loading also cannot be approximately described with one consistant relation between damage parameters and fatigue life. The evaluation of TMF loadings based on results from isothermal LCF-tests with the same frequency and respective mechanical strain leads always to an overrating of the fatigue life, even if the temperature of the isothermal test is the maximum temperature of the TMF cycle. This applies when comparing mechanical loading values as well as when comparing damage parameters.     

一般尺度法的振动疲劳强化系数分析

在Dirlik模型的基础之上,结合一般尺度法（General scaling law）提出适用于平稳宽带随机过程的疲劳强化系数模型。一般尺度法认为结构在原始载荷和强化后载荷下的应力响应功率谱各阶谱矩成简单的线性关系;与Dirlik宽带疲劳损伤模型结合,便得到适用于平稳宽带随机过程的疲劳强化系数模型。为了验证模型的有效性,分别在原始加速度功率谱和经一般尺度法强化后的加速度功率谱载荷下;对悬臂梁采用雨流计数(Rainflow counting)和Miner损伤准则进行疲劳寿命预测,得到它们的疲劳强化系数,并与疲劳强化系数模型得到的疲劳强化系数进行对比。结果表明：提出的疲劳强化系数模型精度为99.7 %,由此可验证疲劳强化系数模型的有效性。     

Fatigue life prediction under variable loading based on a new damage model

To examine the performance of nonlinear models proposed in the estimation of fatigue damage and fatigue life of components under random loading, a batch of specimens made of 6082 T 6 aluminium alloy has been studied and some of the results are reported in the present paper. The paper describes an algorithm and suggests a fatigue cumulative damage model, especially when random loading is considered. This paper contains the results of mono-axial random load fatigue tests with different mean and amplitude values performed on 6082 T 6 aluminium alloy specimens. Cycles were counted with rainflow algorithm and damage was cumulated with a new model proposed in this paper and with the Palmgren–Miner model. The proposed model has been formulated to take into account the damage evolution at different load levels and it allows the effect of the loading sequence to be included by means of a recurrence formula derived for multilevel loading, considering complex load sequences. It is concluded that a ‘damaged stress interaction damage rule’ proposed here allows a better fatigue damage prediction than the widely used Palmgren–Miner rule, and a formula derived in random fatigue could be used to predict the fatigue damage and fatigue lifetime very easily. The results obtained by the model are compared with the experimental results and those calculated by the most fatigue damage model used in fatigue (Miner’s model). The comparison shows that the proposed model, presents a good estimation of the experimental results. Moreover, the error is minimized in comparison to the Miner’s model.     

Frequency-domain methods for a vibration-fatigue-life estimation – Application to real data

The characterization of vibration-fatigue strength is one of the key parts of mechanical design. It is closely related to structural dynamics, which is generally studied in the frequency domain, particularly when working with vibratory loads. A fatigue-life estimation in the frequency domain can therefore prove advantageous with respect to a time-domain estimation, especially when taking into consideration the significant performance gains it offers, regarding numerical computations. Several frequency-domain methods for a vibration-fatigue-life estimation have been developed based on numerically simulated signals. This research focuses on a comparison of different frequency-domain methods with respect to real experiments that are typical in structural dynamics and the automotive industry. The methods researched are: Wirsching–Light, the α_0.75 method, Gao–Moan, Dirlik, Zhao–Baker, Tovo–Benasciutti and Petrucci–Zuccarello. The experimental comparison researches the resistance to close-modes, to increased background noise, to the influence of spectral width, and multi-vibration-mode influences. Additionally, typical vibration profiles in the automotive industry are also researched. For the experiment an electro-dynamic shaker with a vibration controller was used. The reference-life estimation is the rainflow-counting method with the Palmgren–Miner summation rule. It was found that the Tovo–Benasciutti method gives the best estimate for the majority of experiments, the only exception being the typical automotive spectra, for which the enhanced Zhao–Baker method is best suited. This research shows that besides the Dirlik approach, the Tovo–Benasciutti and Zhao–Baker methods should be considered as the preferred methods for fatigue analysis in the frequency domain.     

A new frequency domain method for random fatigue life estimation in a wide‐band stationary Gaussian random process

A new frequency domain method for random fatigue life estimation in a wide‐band stationary Gaussian random process was proposed for application in fatigue analysis. Simulations of the power spectral densities of different types were firstly performed; the simulated results showed that the accuracy and applicability for the current frequency domain methods are not only related to the spectral type but also associated with the types of the analysed materials. Compared with the current methods, the proposed method, in which the rain‐flow amplitude obeys Nakagami distribution, has better universality and could significantly reduce the error for the random fatigue life estimation with simulated and actual spectra. Verified application in cast‐steel fatigue life analysis were performed between random fatigue life and constant amplitude fatigue life. It is shown that the fatigue life analysis under random load cannot be ignored and the proposed new method can serve as a recommended method.     

Using computer techniques for vibration damage estimation under stochastic loading using the Monte Carlo Method for aerospace applications

The main focus of this article is a review of legacy methods for vibration damage estimation under stochastic loading and extending research made by Dirlik and Bendat using two combined methods: FEM and Monte Carlo simulation, for which we used Python programming for aerospace applications. For some aircraft, regulated by the RTCA international aviation standard DO-160G (Environmental Conditions and Test Procedures for Airborne Equipment), stochastic loading is defined as one of the requirements. This article will focus on the stochastic loading impact on the fatigue life assessment made on a dummy sample, and frequency and time domain damage estimation shall be considered in parallel to compare both results. Additionally, dummy PSD responses shall be defined in the frequency domain for signal statistical parameters research. The article introduces Rainflow Cycle Counting methods in the frequency domain for procedures used commercially in aerospace applications. The first method introduced and developed further is the Dirlik method of Rainflow Cycle Counting in the frequency domain, which is the most popular method in commercial use. The second technique introduced and developed further was established by Bendat — the Narrow Band Method. The new empirical equation presented in this paper is the modification of the Narrow Band Method fitted for general use (narrow band, wide band, and white noise signals). A new approach for the integration of spectral moments is introduced in this paper, allowing for an accurate evaluation of the signal statistic parameters in the frequency domain for use in the modified Dirlik and Narrow Band methods. Research results also revealed new phenomena not researched by Dirlik, such as high vibration damage variation from stochastic loading, which depends on the frequency resolution (the block size used in Inverse Fourier Transformation). This discovery will be the subject of further study. Research results presented in this paper will also be utilised to combine stochastic and deterministic loading scenarios for military helicopters, as well as fighter aircraft, and will be the subject of further research.     

A frequency domain approach for estimating multiaxial random fatigue life

This paper presents a probabilistic method for fatigue life estimation within the frequency domain for structural elements subjected to multiaxial random loadings. Multivariate Monte Carlo Simulation is used to account for the correlation between the stress components and their different probability of occurrence and, moreover, enables stochastics during damage analysis to be allowed for and, at the same time, uses any suitable, material dependent multiaxial fatigue criterion known from the time domain. Comparison of the evaluated fatigue damage with experimental results from vibration tests on a demonstrator, chosen from common application fields in the automobile industry, shows good correlation.     

Strain-life approach in thermo-mechanical fatigue evaluation of complex structures

This paper is a contribution to strain‐life approach evaluation of thermo‐mechanically loaded structures. It takes into consideration the uncoupling of stress and damage evaluation and has the option of importing non‐linear or linear stress results from finite element analysis (FEA). The multiaxiality is considered with the signed von Mises method. In the developed Damage Calculation Program (DCP) local temperature‐stress‐strain behaviour is modelled with an operator of the Prandtl type and damage is estimated by use of the strain‐life approach and Skelton's energy criterion. Material data were obtained from standard isothermal strain‐controlled low cycle fatigue (LCF) tests, with linear parameter interpolation or piecewise cubic Hermite interpolation being used to estimate values at unmeasured temperature points. The model is shown with examples of constant temperature loading and random force‐temperature history. Additional research was done regarding the temperature dependency of the K_p used in the Neuber approximate formula for stress‐strain estimation from linear FEA results. The proposed model enables computationally fast thermo‐mechanical fatigue (TMF) damage estimations for random load and temperature histories.     

A simple unified critical plane damage parameter for high-temperature LCF life prediction of a Ni-based DS superalloy

A simple unified critical plane damage parameter (i.e., the modified resolved shear strain range ?γ _mod) based on a slip mechanism-related critical plane concept was proposed in this paper, integrating life prediction of low cycle fatigue (LCF) behavior affected by anisotropy, load ratio and stress concentration into one framework, where the critical plane is determined as the slip plane on which the damage parameter is the maximum during the cycle. For notched specimens, this procedure was specially carried out at the fatigue initiation sites located on the notch surface, which were well predicted by the distribution of Von-Mises stress range ?σ _Mises. The applications of this damage parameter in a directionally solidified superalloy at high temperatures showed that the LCF lives resulting from complicated loading conditions (i.e., variable material orientation, temperature, loading ratio and notch feature) were well simulated consistently, and the predicted fatigue life is within a scatter band of ±3.     

Damage accumulation modeling under uniaxial low cycle fatigue at elevated temperatures

The paper presents a fatigue damage accumulation model, which allows us to predict fatigue life under low cycle uniaxial loadings at elevated temperatures. The structure of the model has been based on the stress–strain curves obtained during the experimental study. The model has been verified experimentally by applying experimental studies carried out on ENAW-2024T3 aluminum alloy and 2Cr–2WVTa steel. Moreover, a comparison between the results of fatigue life prediction using the proposed damage accumulation model was done with the results obtained on the basis of various generally applied models, based on the Manson–Coffin dependency. Furthermore this paper presents the results of experimental studies carried out on the aluminum alloy ENAW 2024 T3 under uniaxial low cycle fatigue loadings in the conditions of elevated temperatures. In the course of the study, material constants and the parameters of the stress–strain curve in the range of low cycle fatigue for four levels of temperatures (20, 100, 200 and 300 °C) were set.     

Wiener chaos expansions for estimating rain-flow fatigue damage in randomly vibrating structures with uncertain parameters

The problem of estimating the fatigue damage in randomly vibrating structures with uncertain parameters is considered. The loadings are assumed to be stationary and Gaussian. The corresponding accumulated fatigue damage is described through the rain-flow cycle counting algorithm. For stationary and ergodic loads, the accumulated rain-flow fatigue damage can be estimated if the system and the load spectrum are known. However, these estimates would be erroneous if the structure properties and/or the spectrum parameters of the loading are significantly uncertain. Corrections to account for the parameter uncertainties is usually obtained using the Gauss error propagation formula, and is accurate for small parameter variations. An alternative approach based on Wiener chaos expansions is employed to estimate the rain-flow fatigue damage in linear/nonlinear structural systems with parameter uncertainties. The performance of the proposed approach is compared with the Gauss error propagation formula. The proposed method is illustrated through fatigue damage estimation of three simplified examples involving a moving vehicle on a rough road, Morison’s force due to random sea waves and the blade of a wind turbine.     

热声激励下金属薄壁结构的随机疲劳寿命估算

金属薄壁结构在热声载荷作用下会发生复杂的大挠度非线性响应,结构内部快速变化的复杂应力严重降低了结构的疲劳寿命。在结构热声激振非线性响应分析基础上,采用雨流循环计数法对应力响应时间历程进行疲劳循环计数,通过Morrow TFS,SWT平均应力模型将疲劳循环进行零均值等效处理,结合Miner线性损伤累积理论,计算结构的热声疲劳寿命。以2024-T3型铝合金薄板为研究对象,计算得到了屈曲前后四种温度条件有限带宽高斯白噪声载荷作用下的非线性动态响应,并估算了疲劳寿命。分析结果表明,屈曲前结构的疲劳寿命随着温度升高下降,屈曲后结构持续跳变时的疲劳寿命持续下降直至最低,结构进入间歇跳变区域后疲劳寿命上升,结构热声疲劳寿命与非线性响应特征具有特定的对应关系。     

About the creep-fatigue interaction on the fatigue behaviour of off-axis woven-ply thermoplastic laminates at temperatures higher than Tg

The influence of plasticity and viscous effects on the fatigue behaviour of off-axis C/PPS laminates was investigated at temperatures higher than glass transition temperature. The obtained results clearly show that creep and fatigue are mutually influencing phenomena. Compared to the reference fatigue behaviour (with no prior loading), the fatigue life can be significantly extended with prior creep depending on loading conditions. Indeed, the strain accumulation seems to slow down after a long time creep preload, as if the time-dependent mechanisms were “evacuated” during this preload. The same conclusion can be drawn for the damage accumulation when the prior creep stresses are higher than the damage threshold or when the hold time is long enough, inducing significant plastic deformations. In angle-ply laminates, such deformations are associated with the reorientation of fibres. They contribute to the reduction of stress intensities, which results in increasing both fatigue life and maximum strain ɛ_max at failure during fatigue loadings.     

Recent developments in frequency domain multi-axial fatigue analysis

The purpose of this paper is to discuss the recent developments in multi-axial spectral methods, used for estimating fatigue damage of multi-axial random loadings from Power Spectral Density (PSD) data. The difference between time domain and frequency domain approaches in multi-axial fatigue is first addressed, the main advantages of frequency domain approach being pointed out. The paper then critically reviews some categories of multi-axial spectral methods: approaches based on uniaxial equivalent stress (strength criteria, “equivalent von Mises stress”, multi-axial rainflow counting), critical plane criteria (Matake, Carpinteri-Spagnoli, criterion based on resolved shear stress on critical plane), stress-invariants based criteria (Crossland, Sines, “Projection-by-Projection”). The “maximum variance” method and the Minimum Circumscribed Circle/Ellipse formulations defined in the frequency domain are also discussed. The paper critically analyses also non-proportional multi-axial loadings and the role of material fatigue parameters (e.g. S/N curves for bending/torsion) in relation to specific methods. The paper concludes with general comments on advantages and possible limitations in the use of multi-axial spectral methods, with special focus on the assumption of stationarity and Gaussianity in modelling multi-axial random loadings.     

Shape of the power spectral density matrix components: Influence on fatigue damage

The damage estimation for a structure under random loading is a challenge in fatigue assessment, especially when the loading is multiaxial. The comparison of the effect of different spectra on fatigue damage is essential when the structure can be subjected to different types of loadings. Therefore, in the present paper, the expected fatigue damage produced on metallic structures by combined bending and torsion stationary proportional and nonproportional loading is evaluated varying the shape of spectra of the normal and shear stress tensor components.     

Cumulative damage model based on equivalent fatigue under multiaxial thermomechanical random loading

A new creep–fatigue damage cumulative model is proposed under multiaxial thermomechanical random loading, in which the damage at high temperature can be divided into the pure fatigue damage and the equivalent fatigue damage from creep. During the damage accumulation process, the elementary percentage of the equivalent fatigue damage increment is proportional to that of the creep damage increment, and the creep damage is converted to the equivalent fatigue damage. Moreover, combined with a multiaxial cyclic counting method, a life prediction method is developed based on the proposed creep–fatigue damage cumulative model. In the developed life prediction method, the effects of nonproportional hardening on the fatigue and creep damages are considered, and the influence of mean stress on damage is also taken into account. The thermomechanical fatigue experimental data for thin‐walled tubular specimen of superalloy GH4169 under multiaxial constant amplitude and variable amplitude loadings were used to verify the proposed model. The results showed that the proposed method can obtain satisfactory life prediction results.     

Analogies between spectral methods and multiaxial criteria in fatigue damage evaluation

This work aims to emphasize some analogies existing between multiaxial fatigue criteria and spectral methods in the context of fatigue damage assessment for uniaxial stochastic loadings in the frequency domain. Among multiaxial criteria available in literature, attention is focused on the so-called “Projection-by-Projection” (PbP) approach, in which fatigue damage of a multiaxial process is computed by using a non-linear summation rule of single damage contributions of uncorrelated projected loadings. In this work the theoretical framework of PbP method will be used to provide a possible mathematical interpretation of the so-called “single moment” (SM) approach, a spectral method for estimating fatigue damage in uniaxial stochastic loadings that was elaborated in 1990 on a purely “empirical” basis. The idea here formalized is to split the spectrum of a uniaxial process into an infinite set of narrow-band spectral contributions, so to define a set of mutually uncorrelated uniaxial narrow-band stochastic processes. The analogy between the damage of a multiaxial process and that of a uniaxial process split into infinitesimal spectral components is shown. Once the formal analogy between uniaxial and multiaxial spectral methods is established, numerical simulations are used to evaluate the accuracy of SM method with reference to different types of stochastic processes with bimodal spectral density.