Effect of residual stresses on the fatigue behaviour of welded joints depending on loading conditions and weld geometry

The structural durability of welded structures is determined by the interaction of different influencing parameters such as loading mode, spectrum shape, residual stresses and weld geometry among others. Examples from plant, offshore, transportation and automotive engineering show how these parameters influence the fatigue life and to what extent they are considered in design codes. Especially, under spectrum loading, the stress decreasing effect of tensile residual stresses is not as high as under constant amplitude loading; this knowledge benefits light weight design. The overloads harmed only the low strength joints under pulsating bending. In all other cases investigated, with low, medium and high-strength steels, a significant decrease of fatigue life was not observed; on the contrary, significant improvement of fatigue life could even be observed. However, a systematic interaction with material strength, loading mode and residual stresses was not apparent.     

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.     

An improved fatigue life model for mechanical components considering load strengthening characteristics

The small load has fuzziness on the strengthening and damage of the component under the action of random fatigue load. This paper introduces the two-dimensional membership function in fuzzy mathematics to characterize the relationship between stress amplitude, mean value, and damage below the fatigue limit. An exponential function is used to describe the strengthening effect. Under the two-dimensional load spectrum, the influence of various levels on the component's life is comprehensively considered, and the fatigue life prediction model under random load is proposed. Through the small sample experiment of the car swing support rod, the relevant parameters of the model are obtained. The difference between the modified two-dimensional and the two-dimensional load spectrum is compared in fatigue life prediction results. The rules of membership function selection and parameter setting are summarized, and it makes the estimation of component load spectrum life more reasonable.     

基于机车车轮的动态疲劳可靠性研究

 随着火车速度的不断提高,对火车走行部件的疲劳可靠性要求也越来越高．根据疲劳寿命预测理论,建立了某机车车轮受力危险点在不同路况下的疲劳寿命曲线．以实测数据和有限元分析所得数据为基本参数,采用线性累积损伤法则和Monte-Carlo模拟,对车轮在等幅载荷和随机载荷谱共同作用下进行疲劳寿命预测,得到了车轮在不同路况下可靠度随路程变化的关系曲线．为火车的安全性维护提供了理论依据,对火车的安全运行有重大的实际应用价值．     

考虑车桥耦合效应的大跨悬索桥钢-混组合梁疲劳损伤评估

为了研究不同疲劳车辆荷载作用下大跨度悬索桥钢-混组合梁的疲劳寿命,以及在考虑车桥耦合效应变化时运营期内钢-混组合梁疲劳损伤累积变化规律,以某主跨720 m的悬索桥为例进行了分析。基于局部梁段有限元模型静力分析确定了疲劳细节关注点,得出相应的应力集中系数;利用P-M及CDM两种评估模型对疲劳荷载模型Ⅲ、AASHTO规范标准疲劳车及河北省疲劳荷载谱三类疲劳车辆荷载作用下的疲劳损伤度及疲劳寿命进行了评估;考虑车桥耦合动力效应分析了车辆载重量、行车速度、桥面铺装恶化及未来交通量增长对结构运营期内的疲劳损伤累积的影响。结果表明,该类钢-混组合梁悬索桥疲劳状态评估最不利梁段为1/8跨处,易发生疲劳破坏的节点为靠近吊点位置的主梁顶板与腹板连接处。疲劳荷载模型Ⅲ与当地疲劳荷载谱作用下的疲劳损伤量比较接近,AASHTO疲劳车作用下的损伤累积量明显低于另外两类。不同部位疲劳细节关注点的累积损伤量变化趋势与速度的关系不太明确,行车载重量、交通量增长以及桥面铺装恶化均加速疲劳损伤累积的增长。     

Prediction and evaluation of fatigue life for mechanical components considering anelasticity‐based load spectrum

To accurately predict the degraded fatigue life of components under random loads, anelasticity effect of metal on life estimation needs to be explored. Weighting coefficient and dynamic elastic modulus are introduced to modify the calculation process of the model. By establishing an equal‐amplitude fatigue median surface and applying Miner linear fatigue cumulative damage theory, a fatigue life prediction model of the component under random loads is proposed. The model can be used to calculate the degraded fatigue life of components, which provides a theoretical basis for life estimation under random load spectrum. The two‐dimensional load spectrum is compared with the unprocessed two‐dimensional load spectrum and the one‐dimensional program spectrum in life prediction results. With the comparison of the target life and simulation life and the data calculated by the model of the automobile front stabilizer bar, it is concluded that the data obtained by the modified model are more reasonable and accurate.     

复合材料疲劳可靠性研究

将复合材料疲劳可靠性研究领域划分为载荷／环境谱的编制、疲劳性能、疲劳寿命估算及疲劳可靠性分析与设计四个方面,并分别简述了各自方面的研究进展。     

A hybrid frequency–time domain method for predicting multiaxial fatigue life of 7075‐T6 aluminium alloy under random loading

A hybrid frequency–time domain method for predicting multiaxial fatigue life under random loading is developed on the basis of combination of the frequency domain and time domain analysis. The critical damage point of the structure is determined by the frequency domain equivalent stress method. Then, the fatigue life prediction is made in time domain by generating random load‐time histories from the power spectral density of the critical point. The method is validated with the random vibration fatigue test of 7075‐T6 aluminium alloy. It has been shown that the results of fatigue life calculated by hybrid method are well correlated with the experiment.     

疲劳寿命计退火特性及电阻变化推算载荷谱的研究

对三种交变应变量循环后的疲劳寿命计在不同温度下进行退火实验,由它们在低于再结晶温度退火后电阻去除量的不同,得出疲劳寿命计在交变应变作用下电阻累积的主要机理。根据疲劳寿命计的标定特性曲线和在载荷谱下的响应特性,由三个不同方向粘贴的疲劳寿命计电阻变化推算载荷谱,该方法扩大了疲劳寿命计的使用范围。     

Fatigue crack growth simulation of aluminium alloy under spectrum loadings

Fatigue crack growth in structure components, which is subjected to variable amplitude loading, is a very complex subject. Studying of fatigue crack growth rate and fatigue life calculation under spectrum loading is vital in life prediction of engineering structures at higher reliability. The main aim of this paper is to address how to characterize the load sequence effects in fatigue crack propagation under variable amplitude loading. Thus, a fatigue life under various load spectra, which was predicted, based on the Austen, Forman and NASGRO models. The findings were then compared to the similar results using FASTRAN and AFGROW codes. These models are validated with the literature-based fatigue crack growth test data in 2024-T3 Aluminium alloys under various overload, underload, and spectrum loadings. With the consideration of the load cycle interactions, finally, the results show a good agreement in the behaviour with small differences in fatigue life compare to the test data.     

Safe-life analysis accounting for the loading spectra variability

The scatter of the variable load spectra is considered separately from the scatter of the aircraft structure to assess the safe-life of a fleet. Suppose the fatigue life under the specified load spectrum follows the log-normal distribution with a constant coefficient of variation, and the load spectra damage follows the log-normal distribution with a constant standard deviation, the theoretical distribution function of fatigue life of the fleet that accounts for the variability of the structure and the load spectrum is derived with the conditional probability model. Monte-Carlo simulation shows that the distribution of the fleet fatigue life can be described approximately by a log-normal distribution function, and the log expectation is the log mean life under variable load spectra and the variation equals the sum of the structural variation and the load spectra variation. The scatter factor method is then adopted to assess the safe-life. The scatter factor of the individual aircraft with definite load spectrum, as well as the scatter factor of the in-service fleet that takes the actual load scatter into consideration are listed.     

随机荷载作用下参数不确定结构的疲劳损伤估计

基于改进区间分析和频域疲劳计算方法,对参数不确定结构在平稳高斯荷载作用下的疲劳损伤进行研究,提出完全混合和简化计算两种方法。采用区间变量模型定义结构的不确定参数,功率谱密度描述外荷载的随机性;利用有理级数显式表示结构区间频响函数及在平稳高斯荷载作用下不确定结构的应力响应区间。通过数值方法验证疲劳损伤期望率关于不确定参数的单调性后,将应力响应中不确定参数的界限完全组合提出完全混合方法,准确估计参数不确定结构的疲劳损伤期望率区间;简化计算方法则将不确定参数的界限适当组合,由显式表达式近似计算结构的疲劳损伤期望率区间。算例表明,两种方法均具有较高计算精度,且大幅减少计算量。     

Verbesserung der Lebensdauerabschätzung durch Berücksichtigung des Lebensdauervielfachen

Fatigue life assessments of parts are frequently undertaken using the nominal stress concept. The main element in the process is the linear damage accumulation concept according Palmgren and Miner. Statistical analyses show the calculated fatigue life to commonly be on the unsafe side and the accuracy to be low. A higher accuracy would be advantageous, as the present use of effective damage sums is only an adaption. Improvements of the original Palmgren‐Miner rule made use of in practical calculations have mainly been achieved by taking into account amplitudes below the fatigue limit as further damage. The method described in the following utilises a different approach. The influence of the spectrum shape and the inclination of the S‐N curve under constant amplitude loading on the progression of the S‐N curve under variable amplitude loading, easily made visible in statistical comparisons of calculated and experimental fatigue lives, shall be included in a new correction function. The verification of the improvement of the fatigue life estimation can be undertaken using existing experimental data of steel specimens. Furthermore calculations are carried out to find optimized parameters of two Palmgren‐Miner modifications (Haibach, Liu/Zenner).     

Spectrum fatigue of composite bolted joints

The new Swedish fighter JAS39 Gripen has a large number of primary structures made of composites. On those structures a large number of bolted joints are used which during the aircraft's service life will be subjected to spectrum fatigue loading. Consequently it is important to study the spectrum fatigue life of bolted joints. Specimens with a double-lap configuration and six bolts have been fatigue loaded at the load ratios R=−0.2 and R=−5. Specimens were also fatigue loaded with a vertical fin spectrum which had different amounts of elimination of load cycles. A linear damage rule, Miner's rule, was used to predict the spectrum fatigue life. The experimental results show that the shortest fatigue life occurs for specimens loaded at R=−1 followed by specimens loaded at R=−0.2. The longest fatigue life occurred for specimens loaded at R=−5. It was found that 50% elimination of load cycles in the spectrum can be used without affecting the fatigue life. The Miner's rule predictions appeared to overestimate the spectrum fatigue life. From bolt failure it was found that the first bolt row transfers the largest amount of load in the specimens.     

Assessment of fatigue load spectrum from fracture surface topography

The possibility of deducing load spectrum parameters from fatigue failure surfaces is explored by applying innovative, three-dimensional topographic characterization and analysis techniques to failure surfaces in aluminum sheet. Precise, high-resolution elevation maps of fracture surfaces were obtained using confocal optics scanning laser microscopy. Elevation power spectral density curves resulting from a fast Fourier transform of the elevation data appear sensitive to stress intensity range and environment. A conjugate fracture surface matching procedure, FRASTA, can detect and may provide a way to quantify overloads.     

Fatigue life evaluation of tension‐compression asymmetric material using local stress–strain method

In this paper, the low‐cycle fatigue characteristics of cold‐drawn steel were investigated under strain‐controlled uniaxial fatigue load. Cyclic softening was observed throughout fatigue life except for the initial relatively short period which exhibited cyclic hardening. Positive mean stress was found under fully reversed strain loading, indicating that there was a significant cyclic asymmetry. A modified local stress–strain method was proposed to estimate fatigue life of notched tension‐compression asymmetric material. In order to verify this method, fatigue experiments on two kinds of notched specimens with different notch radius were carried out under constant and block load spectrum. It was found that the modified local stress–strain method was more accurate than the traditional ones, the maximum relative error between predicted and experimental fatigue life was less than 6%.     

Probabilistic and testing analysis for the variability of load spectrum damage in a fleet

Scatter of fatigue life of a fleet is mainly caused by the variability in structures and load spectra. To ensure the safety in service, the probabilistic characterization of load spectrum variability should be researched in durability analysis and testing work. This paper investigates the variability of load damage rate of a fleet. Based on the flight historical parameters measured by individual aircraft tracking (IAT) from hundreds of aircrafts for a certain type of fighter in China, SWT formula and linear damage rule are used to evaluate the load damage, and then, one average and four other individual load spectra are selected corresponding to different damage severities. Fatigue tests are conducted with the Aluminum alloy 7B04-T74 specimens under five spectra and the Titanium alloy TA15M specimens under three of them. The engineering crack initiation lives are measured and the mean lives are estimated assuming the fatigue life following a log-normal distribution. An obvious difference of at least 2.4 times in the load damage rates is found in the fleet. The fatigue lives of a fleet of aircrafts are calculated by Neuber’s approach, and the probabilities refer to damage severities of those 5 load spectra in a fleet are evaluated. The statistical analysis of the fatigue lives and the probabilities shows that a lognormal distribution can be used to describe the variability of load damage rate of a fleet. The variation of the load damage rate is in the same order of magnitude with that in structural properties.     

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.     

The fatigue crack growth of a ship steel in seawater under spectrum loading

Fatigue crack growth of ABS EH36 steel under spectrum loading intended to simulate sea loading of offshore structures in the North Sea was studied using fracture mechanics. A digital simulation technique was used to generate samples of load/time histories from a power spectrum characteristic of the North Sea environment. In constant load-amplitude tests, the effects of specimen orientation and stress ratio on fatigue crack growth rates were found to be negligible in the range 2 × 10^?5 to 10^?3 mm/cycle. Fatigue crack growth rates in a 3.5% NaCl solution were two to five times faster than those observed in air in the stress intensity range 25 to 60 MPa √m. The average fatigue crack growth rates under spectrum loading and constant-amplitude loading were in excellent agreement when the fatigue crack growth rate was plotted as a function of the appropriately defined equivalent stress intensity range. This procedure is equivalent to applying Miner's summation rule in fatigue life calculations.     

Influence of spectrum loading sequences on fatigue life in a high-temperature environment

This paper discusses the fatigue life behaviour of aluminium alloy AA6061-T6 under spectrum loadings. Load sequences in spectrum loadings can have significant effects on fatigue life at room temperature and within the elevated temperature range. The main objective of this paper is to investigate the influences of load sequences effect on fatigue life at elevated temperature. Fatigue strain signal was obtained from the engine mount bracket of an automobile under normal driving conditions. Constant amplitude loading, high-to-low, and low-to-high loading sequences were then derived from the original fatigue strain signal to observe the fatigue behaviour at both room and elevated temperatures. The fatigue test was performed on AA6061-T6 specimen according to the ASTM E466 standard using a 100 kN servo-hydraulic fatigue testing machine within the temperature range of 27–250 °C. The elevated temperature range was chosen based on the maximum temperature of the engine mount bracket and the extreme temperature of the cylinder head that can be reached in service. After the test, fatigue fracture surfaces were sectioned and inspected using a high-magnification microscope. Results show that fatigue life behaviour at room temperature was significantly influenced by the load sequences in spectrum loadings. On the other hand, the effect of load sequences at a higher temperature was reduced.