Frequency based fatigue analysis and temperature effect

Risers and umbilicals are exposed to dynamic loading from waves and floater motions. These structures are known to have a pronounced non-linear response characteristic. Non-linear time-domain finite element analyses is in general required to give an adequate description of the non-linearities involved. Analyses of a large number of short-term environmental conditions considering stochastic wave loading are required to give a representative description of the long-term fatigue loading on the structure. Short term fatigue damage is established by means of rain-flow cycle (RFC) counting in each stationary short-term condition. It is has been experienced that significant statistical uncertainties can be present in the short-term fatigue damage estimates. This is because the accumulated fatigue damage in a stationary condition normally has significant contribution from the largest stress cycles in the realisation. Selection of proper simulation length is hence essential to obtain reliable fatigue life estimates. Applicable codes and standards for risers and umbilicals provide Design Fatigue Factors (DFF) to secure adequate safety against failure due to wave induced fatigue. The total uncertainty in the calculated fatigue damage comes from various sources and the DFFs in e.g. DNV-OS-F201 “Dynamic Risers” and API-RP-2RD corresponds to a certain uncertainty level in the fatigue damage estimate. A recommended target value for the statistical uncertainty of the fatigue damage estimates is given with basis in these design codes. The objective of this paper is to give a description of a methodology recommended for time domain fatigue assessment. Special focus will be on the importance of adequate simulation time for predicting the short-term fatigue damage and selection of the short-term seastates in the scatter diagram. Statistical uncertainty is one source that the analyst actually can influence by selecting proper analysis methodology. A statistical uncertainty meassure can be used to evaluate the robustness in the estimated fatigue life. Assessment of statistical uncertainty in fatigue damage estimate is demonstrated by case studies. The fatigue assessment methodology discussed in this paper, will be described in an update of DNV-RP-F204 “Riser Fatigue” 2010.

Wind turbine blades are the most critical components of wind turbines. Full-scale blade fatigue testing is required to verify that the blades possess the strength and service life specified in the design. Unfortunately, the test must be run for a long time period. This problem led the blade testing laboratories to accelerate fatigue testing time. To achieve the objective, this thesis proposes two novel methods called STFT- and WT-based fatigue damage part extracting methods which are based on short-time Fourier transform (STFT) and wavelet transform (WT), respectively. For WT, different wavelet functions which are Morl, Meyr, Dmey, Mexh and DB30 are studied.
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\nAn aerodynamic computer code, HAWTsimulator, based on blade element momentum theory has been developed. This code is used to generate the sets of aerodynamic loads acting along the span of a ‘SERI-8 wind turbine blade’ in the range of wind speed from cut-in to cut-out. SERI-8 blades are installed on 65 kW wind turbines. Each set of aerodynamic loads is applied on the finite element model of the SERI-8 blade in structural software (ANSYS) to generate a plot of von Mises stress at the critical point on the blade versus wind speed. By relating this relationship to the wind speed data, the stress-time history at the critical point on the SERI-8 blade can be generated. It has the same sampling rate and length as the wind speed data.
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\nA concept of applying accumulative power spectral density (AccPSD) distribution with time to identify fatigue damage events contained in the stress-time history has been introduced in this thesis. For STFT, AccPSD is the sum of power spectral density (PSD) of each frequency band at each time interval in the spectrogram. For WT, AccPSD is the sum of PSD of wavelet coefficients of each scale at each time interval in the scalogram. It has been found that the locations of AccPSD spikes imply where the fatigue damage events are. Based on an appropriate AccPSD level called a cutoff level, the fatigue damage events can be identified at time location of the stress-time history.
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\nA fatigue computer code, HAWTfatigue, based on stress-life approach and Miner’s linear cumulative damage rule has been developed. Basically, the code is used for evaluating the fatigue damage and service lifetime of horizontal axis wind turbine blade. In addition, the author has implemented STFT- and WT-based fatigue damage part extracting methods into the code. Fatigue damage parts are extracted from the stress time history and they are concatenated to form the edited stress-time history. The effectiveness of STFT- and WTbased algorithms is performed by comparing the reduction in length and the difference in fatigue damage per repetition of the edited stress-time histories generated by STFT and WT to those of the edited stress-time history generated by an existing method, Time Correlated Fatigue Damage (TCFD) used by commercial software.
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\nThe findings of this research project are as follows:
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\n1. The comparison of the reduction in length of the edited stress-time histories generated by TCFD, STFT and WT indicates that WT with the Mexh wavelet has the maximum reduction of 20.77% in length with respect to the original length, followed by Meyr (20.24%), Dmey (19.70%), Morl (19.66%), DB30 (19.19%), STFT (15.38%), and TCFD (10.18%), respectively.
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\n2. The comparison of the retained fatigue damage per repetition in the edited stress-time histories generated by TCFD, STFT and WT indicates that TCFD has the retained fatigue damage per repetition less than the original fatigue damage per repetition by 0.076%, followed by Mexh (0.068%), DB30 (0.063%), STFT (0.045%), Meyr (0.032%), Dmey (0.014%), and Morl (0.013%), respectively.
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\n3. Both comparison of reduction in length and comparison in the retained fatigue damage per repetition of the edited stress-time histories suggest that WT is the best method for extracting fatigue damage parts from the given stress-time history. It has also been indicated that not only do STFT and WT improve accuracy of fatigue damage per repetition retained in the edited stress-time histories, but also they provide the length of the edited stress-time histories shorter than TCFD does. Thus, STFT and WT are useful methods for performing accelerated fatigue tests.
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\n4. It has been found that STFT is controlled by two main factors which are window size and cutoff level. Also, WT is controlled by three main factors which are wavelet decomposition level, cutoff level and wavelet type.
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\nTo conclude, the edited stress-time history can be used by blade testing laboratories to accelerate fatigue testing time. STFT- and WT-based fatigue damage part extracting methods proposed in this thesis are suggested as alternative methods in accelerating fatigue testing time, especially for the field of wind turbine engineering.

In this work, a computational framework is proposed for fatigue damage estimation in structural systems by integrating operational experimental measurements in a high-fidelity, large-scale finite element model. The proposed method is applied in a linear steel substructure of a lignite grinder assembly at a Public Power Corporation power plant. A finite element model of the steel base is developed and updated to match the dynamic characteristics measured in real operating conditions. This is achieved through coupled use of numerical and experimental methods for identifying, updating, and optimizing a high-fidelity finite element model. The full stress time histories of the complex mechanical assembly are estimated, at critical locations, by imposing operational vibration measurements from a limited number of sensors in the updated finite element model. Fatigue damage and remaining lifetime is subsequently estimated via commonly adopted engineering approaches, such as Palmgren–Miner damage rule, S–N curves, and rainflow cycle counting. Incorporation of a numerical model of the structure in the response estimation procedure permits stress estimation at unmeasured locations, thereby enabling the drawing of a complete and substantially dense fatigue map consistent with the vibration measurements. Fatigue predictions via the proposed framework are highly correlated to experimental fatigue results, proving the efficiency and applicability of the framework.

Engineering structures often experience non-Gaussian random vibrations, yet the propagation of non-Gaussianity through linear systems and its impact on fatigue are not fully understood. By numerical simulations, this study employs the moment-based Hermite translation model to generate non-Gaussian excitation and stress response time series. Time-domain fatigue damage analyses using the generated stress time series reveal that non-Gaussianity notably affects fatigue damage estimates: kurtosis [Formula: see text] 3 exacerbates fatigue damage, while kurtosis [Formula: see text] 3 mitigates it; skewness exerts a weaker impact but necessitates mean stress correction; and the fatigue-strength exponent in the S–N curve determines the extent of non-Gaussian effects. The non-Gaussian response of linear single-degree-of-freedom systems under non-Gaussian excitation is investigated through vibration analyses. The results demonstrate that damping ratio and excitation power spectral density (PSD) govern the non-Gaussianity transmission. For slowly varying PSDs encompassing the natural frequency, kurtosis transmissibility correlates with the ratio of the system’s bandwidth to PSD bandwidth and can be predicted by the proposed empirical model. PSDs offset from the natural frequency enhance kurtosis transfer. When both skewness and kurtosis are present, input skewness markedly modulates kurtosis transmissibility, indicating a need to account for skewness–kurtosis coupling. Overall, both skewness and kurtosis weaken during transmission. These findings underscore the complexity of fatigue analysis under non-Gaussian loads and highlight the importance of incorporating non-Gaussianity in random vibration fatigue assessments.

Fatigue life prediction considering temperature effect for carbon fibre reinforced composites under variable amplitude loading

The present study intends to investigate the effect of temperature on cumulative fatigue damage of laminated fibre-reinforced polymer (FRP) composites. The effect of temperature on fatigue damage is formulated based on a previously proposed residual stiffness fatigue damage model. The fatigue strength of FRP composite laminates is also formulated to have temperature dependent parameters. The research work is divided into three main parts; the first part reviews the fatigue damage mechanism is fibre-reinforced composites based on stiffness degradation. The recent residual stiffness of Varvani-Shirazi was used as the backbone structure of damage analysis in this thesis. This model is capable of damage assessment while the effects of maximum stress, stress ratio and fibre orientation of FRP composites were recognized. The Varvani-Shirazi damage model was further developed to assess fatigue damage of FRP composites at various temperatures (T). Inputs of the damage model are temperature dependent parameters including Young's modulus (E), ultimate tensile strength(ðult) and fatigue life (Nf). As the next part of the proposed analysis, the temperature dependency of each parameter is formulated, and the relations of E-T and ðult-T are substituted in the Varvani-Shirazi fatigue model. Finally, all terms and equations are evaluated with the experimental data available in the literature. Six sets fatigue data were used in this thesis to evaluate fatigue of FRP specimens. The predicted results were found to be in good agreement with the experimentally obtained data. The proposed fatigue damage model was found promising to predict the fatigue damage of unidirectional (UD) and women FRP composites at different temperatures. Temperature dependant parameters of Young's modulus, ultimate tensile strength, and S-N diagram were also found to be responsive when used of UD, cross-ply, and quasi-isotropic FRP laminates.

Effects of heat treatment on the thermal properties of AZ91D magnesium alloys in different casting processes

Fatigue damage in randomly vibrating jack-up platforms under non-Gaussian loads

This study investigates the relationship between inflow properties of offshore wind turbines and fatigue damage accumulation in key machine components, specifically focusing on blade root and blade bearing fatigue. It showcases how LiDAR measurements can be used with a simulation model to provide fatigue damage estimations for a deployed turbine based on field data. By updating standardized wind field models with LiDAR measurements, the sensitivity of fatigue damage accumulation to variations in turbulence intensity and wind shear profiles is analyzed, and potential under- or over-predictions of fatigue damages are discussed. This approach offers valuable insights into more accurate lifetime predictions for turbine components and explores the possible benefits of LiDAR measurements and digital twin frameworks for fatigue damage estimation.

Investigation of closed-form solutions to estimate fatigue damage on a building

Industry advances continue to enable pursuit of more challenging drilling targets with complex well bore trajectories. Many of these targets are in costly deepwater and/or remote operating areas. Demand for a practical, field-proven drill pipe fatigue management system has grown as drill string failures due to fatigue contribute to a significant amount of non-productive time and cost. The response to this demand has been the development of an engineered approach that combines pipe section positioning and inspection scheduling based on estimated fatigue damage rather than rotating hours or footage drilled. Successful real-time field implementation with ongoing drilling programs demonstrates that the cumulative fatigue damage technique is a valuable and proven tool for risk mitigation and cost reduction. The cumulative fatigue damage technique and its implementation have been introduced in previous literature [1,3,8,10]. This method of monitoring fatigue damage due to rotary operations allows the pipe to be evaluated under real-time operating conditions along a specific section or the entire length of the drill pipe. Monitoring begins at spud and is performed on each joint of drill pipe as it traverses along the well path to total depth (TD). This not only allows a quantitative measure of the relative fatigue damage accumulated joint by joint for the drill pipe, but also provides the opportunity to manage logistics, forecast pipe inspections and position pipe sections to minimize cumulative drill string fatigue damage. The cumulative fatigue damage technique has been successfully applied in the field[1,10]. Hind casting, pre-drill planning and real-time analyses have been utilized for assessing drill string design as well as pipe management. The current case study further demonstrates the methodology introduced in the previous literature and illustrates the modeling and management of fatigue damage over a three well project. The subject operator originally anticipated that pipe inspection may be required before each well to mitigate costly historical drill pipe failures. However, the cost and logistical challenges of mid-program pipe inspection in remote operations could not be ignored. Described is the pipe management strategy employed to complete the drilling program without drill pipe failures and without the need for any mid-program inspections. In addition, the inspection results post TD of the third programmed well have been evaluated and correlated back to expected pipe damage, making this an excellent case study for the further deployment of this technology.

High temperature coke drums in refining enterprises are subjected to a harsh working environment that undergoes periodic changes under various factors such as temperature, pressure, and load for a long time. Fatigue damage is one of the main ways to cause coke drum failure. The stress and strain fields of coke drums are axisymmetric. The stress and strain at each point are in a complex three-dimensional state and cannot be simply treated as one-dimensional problems. This article studies the construction of an online fatigue damage monitoring system for the coke drum, which obtains real-time strain monitoring data. The multi-axis complex strain spectrum is transformed into an equivalent strain spectrum. Combined with the developed dual parameter four peak valley rain flow fast counting algorithm program, the Miner linear cumulative fatigue damage model is used to calculate the cumulative damage caused. Finally, the remaining life of the high-risk, crack-prone area of the coke drum is predicted. This article is based on the method of predicting the multiaxial fatigue life of coke drums using equivalent strain spectra. The results from the multiaxial fatigue life prediction method based on equivalent strain spectra are more accurate than those derived from one-dimensional uniaxial strain calculations. This approach partially resolves the challenges of applying multiaxial fatigue theory in engineering practice. The online monitoring and residual life prediction analysis system for fatigue damage of the coke drum has been applied on site in petrochemical enterprises and has achieved good results, providing a technical foundation for enterprises to carry out reliability-centered maintenance.

Influence of temperature on concrete beams strengthened in flexure with CFRP

Although acceleration and cumulative absolute velocity (CAV) are used as seismic indexes, their relationship with the damage mechanism is not yet understood. In this paper, a simplified evaluation method for seismic fatigue damage, which can be used as a seismic index for screening, is derived from the stress amplitude obtained from CAV for one cycle in accordance with the velocity criterion in ASME Operation and Maintenance of Nuclear Power Plants 2012, and the linear cumulative damage due to fatigue can be obtained from the linear cumulative damage rule. To verify the performance of the method, the vibration response of a cantilever pipe is calculated for four earthquake waves, and the cumulative fatigue damage is evaluated using the rain flow method. The result is in good agreement with the value obtained by the method based on the relative response. When the response spectrum obtained by the evaluation method is considered, the value obtained by the evaluation method has a peak at the peak frequency of the ground motion, and the value decreases with increasing natural frequency above the peak frequency. A higher peak frequency of the base leads to a higher value obtained by the evaluation method.

Assessment of fatigue damage induced by Non-Gaussian bimodal processes with emphasis on spectral methods