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。     

随机载荷作用下疲劳寿命分布预测模型

为了研究构件在随机载荷下的疲劳寿命分布,建立疲劳寿命分布预测模型.应用雨流计数法,将随机载荷-时间历程处理成以载荷幅值和均值为随机变量的二维联合概率密度函数,得到构件的二维疲劳载荷谱.从Miner累积损伤的定义出发,分析了累积损伤分散性的来源.以此为基础,通过建立等幅疲劳中值Sa-Sm-N曲面,提出了基于二维载荷谱的疲劳寿命分布预测模型,当累积损伤的概率分布已知时,可以估算出构件的疲劳寿命分布,进而得到零件在任一时刻的可靠度.最后,给出了一个具体应用实例.结果表明所提出的疲劳寿命分布预测方法具有较好的工程实用价值.     

Quadratic damage rule in random loading case

The simple mathematical structure of the quadratic damage rule (QDR) enables mathematical expression of the failure condition in the case of random loading. Random loading after modified rainflow analysis is considered as a random marked point process. Moments of the damage distribution can be expressed by use of ensemble averages. A condition for validity of the first damage moment solution is formulated. The QDR damage first moment solution involves failure predictions for both stationary and non‐stationary loadings. In these cases, final fracture conditions suitable for practical use are derived. QDR predicts fatigue lives that are always shorter than the linear damage rule (LDR) in the case of stationary loading with short interval of statistical dependence of random variables. QDR appears to be a suitable additional engineering tool for random loading fatigue life predictions considering loading sequence and loading level interactions.     

Cumulative fatigue damage dynamic interference statistical model

After studying in depth the statistical characteristics of cumulative fatigue damage D(t) and its critical value D_c, a new dynamic interference statistical model for fatigue reliability analysis is presented in this paper. Because the non-linearity of fatigue damage accumulation has been taken into account, this model is able to predict the fatigue reliability for random spectrum loading. To verify the predicted results, two fatigue experiments were conducted in which the numbers of specimens were more than 100, using fighter spectrum loading (FALSTAFF spectrum) and constant-amplitude loading respectively. It is shown that the new model is reliable, practicable and better than existing models.     

Evaluation of fatigue life for titanium alloy TC4 under variable amplitude multiaxial loading

Fatigue tests under variable amplitude multiaxial loading were conducted on titanium alloy TC4 tubular specimens. A method to estimate the fatigue life under variable amplitude multiaxial loading has been proposed. Multiaxial fatigue parameter based on Wu–Hu–Song approach and rainflow cycle counting and Miner–Palmgren rule were applied in this method. The capability of fatigue life prediction for the proposed method was checked against the test data of TC4 alloy under variable amplitude multiaxial loading. The prediction results are all within a factor of two scatter band of the test results.     

Frequency based fatigue analysis and temperature effect

This paper proposes a temperature modified Dirlik method to estimate the high cycle fatigue damage for uniaxial loadings caused by random vibrations directly from a power spectral analysis. Besides, the methodology for combining the frequency based fatigue analysis with the temperature effect is represented. This approach is based on a new definition of loading as a random Gaussian process. The fatigue damage estimation of the high pressure die-cast aluminium alloy AlSi₉Cu₃ is investigated at elevated temperatures. Finally, numerical simulations on the known power spectral densities with different shapes at different temperatures are performed in order to establish proper dependence between the temperature modified Dirlik method, the rainflow cycle counting, the linear cumulative fatigue damage and the spectral bandwidth parameters. The proposed method enables computationally fast fatigue damage estimation for the random loadings and the temperature histories.     

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.     

Fatigue life estimation under random loading using the energy criterion

A procedure for estimating the useful life of a component for a given (admissable) probability of fatigue fracture origination under random loading is presented. The method uses material constants obtained from the S/N and cyclic stress/strain curves, standard deviation and probability density distribution of the loading process and a macroblock of harmonic cycles obtained by applying the rainflow cycle counting method to the random loading process. Theoretical and experimental lives are found to exhibit good agreement.     

Non-destructive fatigue damage characterization of laminated thermosetting fibrous composites

The fatigue behaviour of the laminated thermosetting Fiberdux 6376-HTA composite material is studied experimentally for both constant and variable amplitude stress reversal loading. The fatigue-induced material degradation is correlated to non-destructive evaluation data obtained from C-scan graphs through the concept of the damage severity factor ( DSF ). The DSF is able to account for the varying severity of damage at the different specimen locations and is used to quantify the fatigue-induced damage. The concept of the DSF , introduced earlier by the authors for constant amplitude fatigue loading of thermoplastic fibrous composites, is applied to characterize fatigue damage of thermosetting fibrous composites and is extended to account for variable amplitude loading. Constant amplitude fatigue tests at various stress levels were performed to correlate fatigue damage to the change of mechanical properties, such as axial stiffness, residual tensile strength and interlaminar shear strength, and to develop expressions to relate DSF to the degradation of the mechanical properties with increasing fatigue damage. Correlation between DSF evolution and consumed fatigue life is made and fatigue damage functions involving stress amplitude dependency are formulated. These expressions together with a modified rainflow method are then used to assess fatigue life under variable amplitude fatigue loading; computed fatigue lives are compared against experimental results.     

A stochastic theory of cumulative fatigue damage

A Stochastic theory for the cumulative fatigue damage of structural component with random fatigue strength under random loading is proposed on the basis of the Stratonovich-Khasminskii theorem. The analytical solutions for the probability densities of the cumulative fatigue damage and fatigue life and for the reliability function are given for steel and reinforced concrete components, with constant fatigue strength subject to narrow band stationary Gaussian stress process with zero mean. The results agree very well with those of digital simulation. It is noted that the theory can be applied, in principle, to metallic and some nonmetallic materials, to both narrow band and wide band stress process, and can be adapted to a sequence of n stationary stress process or quasi-stationary stress process. The scatter and degradation of fatigue strength can also be incorporated into the theory.     

Fatigue of welded steel joints under wideband loadings

Fatigue tests were conducted on high-strength welded steel cruciform-shaped specimens subjected to random loadings to investigate the effects of loading intensity, nonnormality and frequency bandwidth on the rate of fatigue damage accumulation. The test result are compared with predictions made using the Rayleigh approximation and rainflow analysis in terms of cycles and times to failure. Results indicate that nonnormality can significantly increase the rate of fatigue damage accumulation and result in nonconservative fatigue life estimates if it is effect is not accounted for properly. Likewise, frequency content was also found to influence the rate of fatigue damage accumulation, but to a lesser extent than nonnormality.     

A critical investigation of techniques for stress determination and equivalent static analysis in fatigue life estimation

This study entails the fatigue analysis of a complex plate-like structure subjected to random loading. The stress and fatigue life assessment is performed by means of experimental strain gauge measurements, finite element analysis and a quasi-static fatigue assessment procedure known as the fatigue equivalent static load (FESL) methodology. Firstly, the integrity of shell elements for accurately capturing the stiffness properties and stress distribution in the vicinity of welds is investigated. Furthermore, the stress response of the structure to random dynamic loading is investigated and validated in terms of its suitability for assessment by the FESL methodology. Nominal stress and hot-spot stress fatigue life predictions are made, based on measurements as well as the FESL procedure. The viability and integrity of the FESL methodology is critically assessed after which the actual fatigue life of the structure under particular loading conditions is determined for comparison.     

Fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading

The paper contains a new algorithm for estimation of fatigue life in HCF regime under multiaxial random loading using spectral methods. Loading of Gaussian distribution and narrow‐ and broad‐band frequency spectra were assumed. Various characteristic states of multiaxial loading were considered. The equivalent stress history was determined with use of the failure criteria of multiaxial fatigue based on the critical plane. For determination of the critical plane position, the method of variance was applied. During simulation, the authors compared the results obtained by a spectral method in the frequency domain with those from the rain‐flow algorithm in the time domain. The paper also contains the results of fatigue tests for 18G2A structural steel subjected to bending and combined bending with torsion. The tests were performed in order to verify the proposed algorithms for determination of fatigue life. It has been shown that under multiaxial random loading results of fatigue life calculated according to the considered algorithms in frequency and time domains are well correlated with the results of experiments.     

Influence of correlations between stresses on calculated fatigue life of machine elements

The correlation between components of the random stress tensor and its influence on the calculated fatigue life of machine elements were analysed. Three covariance matrices of components of biaxial stress state were considered. They were determined from measurements of strains in an element of a vibrating screen for aggregate, in the back wall of a bus, and in a welded element of excavator fittings. Calculations were made according to four criteria of multiaxial random fatigue. Cycles were counted with the rainflow method, and damage was cumulated with the Palmgren-Miner hypothesis. It was found that convariances of random stress state components strongly influence the calculated fatigue life.     

Deterministic Processing of Complex Multiaxial Fatigue Load Data on a Tubular Specimen with Hole

A study of the use of deterministic fatigue life prediction methods for a set of multiaxial experimental data on broad‐band random loading applied to a tubular specimen with a hole is presented. There is a discussion of the applicability of stress‐based predictions and strain‐based predictions based on the linear cumulative rule under current conditions. The only feasible criteria finally chosen for the application are strain‐based methods for analysing the fatigue life until fatigue crack initiation. Several methods differing in the damage parameter and application of the mean stress effect (MSE) are evaluated. The MSE is optimised so that a comparison of the predicted and experimental data have the least scatter and similar mean values. The results are presented, and the most promising method (by Erdogan and Roberts) has been selected. The positive properties of Walker mean stress correction and the failure of SWT and Landgraf methods are commented on.     

Random fatigue life prediction of carbon fibre-reinforced composite laminate based on hybrid time-frequency domain method

To evaluate fatigue life of composite laminate with hole under random loading, a random fatigue life prediction model is established by hybrid time-frequency domain method in this paper. Firstly, dynamic response of composite laminate is obtained from FE model in frequency domain. Secondly, root mean square of stress of six stress components of critical damage point in frequency domain are transferred to stresses in time domain. At last, 3D Tsai–Hill static failure criterion is adopted to convert the multiaxial stress into the uniaxial equivalent stress. Fatigue life is predicted by equivalent stress fatigue life code. The method is validated with the random vibration fatigue test of carbon fibre-reinforced composite laminate. Numerical results are compared with random fatigue experiments which show good agreement with numerical results.     

An improved method of calculating the peak stress distribution for a broad‐band random process

An improved method of fast fatigue life prediction under broad‐band random loading is proposed, which is based on the power spectral density of stress in the critical points of structures and the peak stress distribution of a stationary Gaussian random process. The improved method has higher precision than other existing approximate methods that are based on the peak stress distribution.     

Fatigue lifetime of welded joints under random loading: rainflow cycle vs. cycle sequence method

The evaluation of fatigue lifetime is a complex problem due to the loading cycle sequence effect influencing the fatigue damage process. In the literature two different approaches are usually adopted to solve the fatigue crack growth under time varying loading: the rainflow cycle (RFC) and the cycle sequence (CSQ) model. In this paper the performance of the recently proposed stochastic version of these methods is compared and applied to the evaluation of the fatigue lifetime of the welded cruciform tested in the literature. Non-Gaussianity and bandwidth effect are correctly captured by both methods but only the CSQ model enables us to examine the influence of the load sequence effect on the fatigue lifetime. Numerical results show that the retardation effect can be neglected for Gaussian and non-Gaussian loading as the bandwidth increases. Finally, this work shows the greater performance and flexibility of the CSQ model compared to the RFC model.     

The effects of load sequencing on the fatigue life of 2024-T3 aluminum alloy

Current fatigue life analysis of metallic rotorcraft dynamic components are based on a linear cumulative damage concept known as Miner's rule. This type of analysis assumes that there is no load sequence effect that occurs during the fatigue loading history. Past studies have shown that linear cumulative damage analysis of fatigue tests has produced life predictions that have been conservative as well as unconservative. Some of this uncertainty has been attributed to the fact that load sequence effects do exist in most fatigue load spectra. As a first phase the study reported herein was done to evaluate the load sequencing effects that could exist in commercial fixed-wing fatigue load spectra. To evaluate these effects a typical commercial wing spectra was reordered using a scheme that had previously been shown in fatigue block loading to produce the shortest fatigue lives. This scheme starts with the smallest load range in a load sequence and proceeds in ascending order until the largest load range is reached. Tests on open hole test specimens made of 2024-T3 aluminum alloy were conducted on the normal sequence of loads as well as the reordered scheme called lo–hi. Test results showed no significant differences between the fatigue lives of the normal load sequence and the reordered load sequence. A computer program called FASTRAN which calculates total fatigue life using only crack growth data was shown to predict the fatigue life of the spectrum tests with acceptable accuracy.     

Fatigue life prediction based on natural frequency changes for spot welds under random loading

Fatigue tests were carried out on tensile-shear spot-welded specimens under random loading; at the same time, natural frequencies at different life stages were measured. Test results were compared with that under constant amplitude loading. The relationship between damage and natural frequency change ratio established under constant amplitude loading is here modified. The nonlinear damage evolution equation was established using the damage represented by frequency change for spot welds. The fatigue life of spot welds under random loading was predicted with this damage evolution relationship using the rainflow counting method results, as well as other life prediction methods with different counting methods. Comparison of life prediction results showed that the method using changes of natural frequency can be an on-line approach and the predicted lives have a good agreement with the experimental data.