Theoretical framework for estimating a product's reliability using a variable‐amplitude loading spectrum and a stress‐based approach

An innovative approach for predicting the reliability of a structure that is subject to a variable‐amplitude dynamic load is presented. In this approach, a Gassner durability curve with its scatter is modelled using a 2‐parametric Weibull's probability density function (PDF). The trend of the Gassner durability curve is modelled with a general hyperbola equation in a log‐log scale. The hyperbola equation is applied to represent the durability curve for the 63.2% probability of fatigue failure that describes the dependency of the Weibull's scale parameter on the loading spectrum's maximum stress. Equations are derived to link the parameters of the hyperbola curve to the material's S‐N curve and the loading spectrum. The Weibull's shape parameter is estimated from the scatter of the material's S‐N curve. The proposed Gassner‐curve model is applied to calculate the fatigue reliability from the PDF of the loading spectrum's maximum stress and the PDF of the durability‐curve's amplitude stress for the selected number of loading‐cycles‐to‐failure.     

Reliability Target Assessment Based on Integrated Factors Method (IFM): A Real Case Study of a Sintering Plant

The success of a company depends on customer’s satisfaction: quality, price, and service. These three goals depend in particular on R.A.M.S. characteristics: reliability, availability, maintainability, and safety. In the last few years, in order to guarantee high standards of reliability and maintainability, new methodologies and techniques have been developed to estimate the R.A.M.S. targets. In particular, the reliability target represents both the starting and the ending point of R.A.M.S. analysis. The design of the reliability target of a system is a crucial aspect of reliability analysis, as it affects the performance of the system and components. This paper aims to develop a new approach called “IFM Target,” to define the reliability target for complex systems through the integrated factors method, to combine the advantages of usually used approaches, and to overcome some criticalities highlighted in a careful literature analysis. The proposed method has been applied on a sintering system. The results show the effectiveness of the proposed approach.     

盘管复合填料型闭式冷却塔性能分析

本文介绍了闭式冷却塔的原理与分类,并归纳总结出简要数学模型。提供了一种测试方法,并用该方法测试分析填料冷却性能以及填料对闭式冷却塔性能的影响,用最小二乘法得到填料特性数N′=0.8λ0.9,并绘制出相关曲线,得出在闭式冷却塔中增加填料可以强化冷却性能。针对放置在不同位置的填料对闭式冷却塔性能影响进行了理论分析,得出闭式冷却塔中填料放置在盘管的上方比放置在盘管下方冷却性能更好。     

Durability analysis of carburized components using a local approach based on elastic stresses

The carburizing of non‐homogeneously stressed components is often used to improve the fatigue properties. In order to predict fatigue life curves the local behavior has to be analyzed. Therefore, cyclic material properties of the carburized surface layer and the core were investigated. In general it is challenging to obtain the input data necessary for a durability analysis of carburized components with the local strain approach. Therefore, a simple method is proposed to estimate the life curve of carburized components under proportional constant‐ and variable‐amplitude loading. With a S‐N curve for a similar component as input local elastic stresses can be back‐calculated. Experimental results show a strong influence of the highly stressed volume on the fatigue properties of the carburized surface layer. This effect can be taken into account with a size correction factor calculated on the basis of a weakest link model. Based on an appropriate local elastic stress‐life curve and regarding the size effect, durability analysis can be improved in an early stage of design. Fatigue tests on notched specimens and components of vehicle transmission cases were used to compare experimental and numerical results.     

Fatigue Test Analysis of Automotive Key Parts Based on Censored Data and Small Sample Setting

The study discusses how some challenges from a small sample fatigue test can be analysed statistically and resolved. In terms of data dispersion, fatigue data are initially processed by confidence, and then, the fatigue life curve is replaced by the parabolic reliability approximation. Fatigue data under various reliability levels are obtained. Instead of the traditional single S–N curve, the mean value curve and mean square deviation curve of the S–N curve are computed based on the processed fatigue data. The S–N curve with reliability is deduced by applying quantile theory. The S–N curve is improved by considering the effects of low‐amplitude load strengthening. The benefits of the modification are visible in the comparison of the fatigue life before and after low‐amplitude load strengthening. Copyright © 2016 John Wiley & Sons, Ltd.     

System‐level reliability sensitivity analysis by using weighted average simulation method

In addition to reliability analysis, investigation of the uncertainties' effect on the safety of structures can be regarded as one of the great concerns in engineering fields. The present study provides an efficient perturbation‐based reliability sensitivity analysis approach based on weighted average simulation method (WASM) to attain uncertainties effects on the structures safety. Without asking additional samplings and/or requiring to function derivation (that is necessary in score function method), the proposed approach simultaneously uses the finite difference and weight flexibility feature of WASM to estimate the parameter sensitivities of a reliability problem. The proposed method has also been successfully applied to the improved version of WASM to obtain reliability based sensitivity results with very few samples. The accuracy and efficiency of the proposed method is examined by solving five analytical and engineering examples with highly nonlinear performance functions and system‐level reliability problems. For each example, results are compared with those obtained by Monte Carlo simulation and common reliability methods. It is shown that the method is capable of solving real world system‐level engineering problems efficiently and accurately.     

基于矩方法的特高压输电塔抗风可靠度分析

该文研究特高压输电塔抗风可靠度。基于等效随机静风荷载模型,引入矩方法分析特高压输电塔的抗风体系可靠度。该方法基于等价极值事件,利用统计矩点估计法求解得到等价极值变量前四阶统计矩信息后,即可方便地获得特高压输电塔体系可靠度指标及相应失效概率。1000kV级特高压SZT2钢管塔的数值算例分析表明:1) 矩方法简单、高效,将其运用于特高压输电塔抗风可靠度分析切实可行,具有重要的理论意义和工程实用价值;2) 在采用点估计法进行等价极值变量统计矩估计时,所取估计点数目应依据失效概率收敛情况而定,并非任意选取或取得越多越好。     

向心关节轴承铰节点的试验研究

某电视塔螺旋上升的外筒柱与楼面钢梁之间的连接采用了一种基于向心关节轴承的万向球铰节点,该节点由向心关节轴承、销轴、嵌固板和耳板等部件组成,构造复杂,为此进行了节点轴向和径向同步加载试验。通过跟踪测试,得到了节点各部件的应变和位移;并发现了关节轴承完好,而突缘与耳板的连接螺纹脱开等现象。利用ABAQUS进行了基于接触单元的节点弹塑性有限元分析,得到了节点各部件的力学性态,并据此给出了节点设计的改进建议。     

Thermography in high cycle fatigue short‐term evaluation procedures applied to a medium carbon steel

This paper focuses on the fatigue life calculation for an unalloyed medium carbon steel SAE1045 (German DIN‐standard: C45E), by applying an energy dissipation‐based approach quantified through thermographic measurements. The purpose of this approach is to establish an intrinsic dissipation model and to predict characteristics derived from the cyclic deformation behavior of stress‐controlled fatigue tests, eg, the fatigue limit and the S‐N data by using simplified (zero‐dimensional, 0D) thermodynamic equations. In order to investigate the possibilities for a rapid evaluation while simultaneously reducing the experimental effort, one load increase test (LIT) and two constant amplitude tests (CATs) were carried out. The S‐N data evaluated on such a basis is competitive to conventionally determined S‐N data as will be shown.     

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).     

Evaluation of fatigue life of aluminium alloy wheels under bending loads

This paper presents the details of S–N curve for aluminium alloy (Al) A356.2‐T6 and fatigue life of alloy wheels under bending load of cornering fatigue test (CFT). Development of S–N curve has been carried out by conducting rotary bending fatigue test at different stress levels as per Standards IS 5075. The rotary bending fatigue test has been performed under constant amplitude fatigue loading. The CFT of the wheel in normal driving mode has been carried out as per the procedure given in Japanese Industrial Standard Disc Wheels (JIS D_4103). It has been observed from the test that the cracks are initiated at the spoke and hub joining area closer to spanner hole on the front face of the wheel. Fatigue life of the alloy wheel has been predicted by finite element analysis (FEA), simulating the realistic test conditions. From finite element analysis, it has been observed that the maximum stress occurs at the mounting face of the wheel. Further, it has been observed that there is significant difference between the computed fatigue life and experimental value. Parametric study has been carried out for reliable fatigue life estimation and proposed an appropriate safety factor for fatigue life estimation under rotary bending test.     

Fitting fatigue data with a bi‐conditional model

The formulation of a probability‐stress‐life (P‐S‐N) curve is a necessary step beyond the basic S‐N relation when dealing with reliability. This paper presents a model, relevant to materials that exhibits a fatigue limit, which considers the number of cycles to failure and the occurrence of the failure itself as statistically independent events, described with different distributions and/or different degree of scatter. Combining these two as a parallel system leads to the proposed model. In the case where the S‐N relation is a Basquin's law, the formulations of the probability density function, cumulative distribution function, quantiles, parameter and quantile confidence interval are presented in a procedure that allows practically any testing strategy. The result is a flexible model combined with the tools that deliver a wide range of information needed in the design phase. Finally, an extension to include static strength and applicability to fatigue crack growth and defects‐based fatigue approach are presented.     

Fatigue tests of notched specimens made from butt joints at steel

The weld toe as well as the weld root of joints acts as a geometrical notch, which decreases the fatigue strength of welded components. Local approaches used for fatigue assessment account for the local stress concentration when referring to the notch stress as a fatigue parameter. This applies also to the approaches based on the notch stress intensity factor like, for example, the averaged strain energy density, neglecting the actual notch radius and considering a sharp notch as a simplification. A uniform S‐N curve valid for different types of welded joints and failure locations was derived from re‐analyses of fatigue test results as documented in literature. The fatigue tests described in this paper aimed at validating that energy‐based S‐N curve by dedicated tests on artificially notched specimens. At first, four parameters were investigated in order to estimate their influence on the fatigue strength and to select appropriate notch geometries for the final step of the test campaign. The advantages of these tests are that both the exact notch geometry and the local stress range at the notch, including misalignment effects, were identified and considered in experimental data analysis. This paper presents the results of the rather comprehensive testing activities and comparisons with the design‐S‐N curve mentioned, yielding unexpected fatigue behaviour. This can be explained by the short crack propagation life.     

基础模拟方式对泰州大桥地震响应的影响

建立了3种基础-土相互作用模拟方式,分别为考虑一定桩身柔性的固结独塔模型,基于“m”法的线性独塔模型,以及采用“p-y”曲线法的非线性独塔模型。采用El-Centro和Kobe两种地震波分别对3个模型进行计算分析,结果发现,基于“m”法的线性独塔沉井模型与“p-y”曲线法的非线性独塔沉井模型相比响应偏大,而基于“m”法的线性独塔群桩基础模型则与“p-y”曲线法的非线性独塔群桩基础模型有较好的吻合。     

Investigation the effect of tightening torque on the fatigue strength of double lap simple bolted and hybrid (bolted–bonded) joints using volumetric method

In this research, the effect of the tightening torque on the fatigue strength of 2024-T3 double lap simple bolted and hybrid (bolted–bonded) joints have been investigated experimentally by conducting fatigue tests and numerically by implementing finite element analysis. To do so, three sets of specimens were prepared and each of them subjected to tightening torque of 1, 2.5 and 5 Nm and then fatigue tests were carried out under different cyclic longitudinal load levels. In the numerical method, the effect of the tightening torque on the fatigue strength of the considered joints has been studied by means of volumetric method. To obtain stress distribution around the notch (bolt hole) which is required for the volumetric method, nonlinear finite element simulations were carried out. In order to estimate the fatigue life, the available smooth S–N curve of Al2024-T3 and the fatigue notch factors obtained from the volumetric method were used. The estimated fatigue life was compared with the available experimental test results. The investigation shows that there is a good agreement between the life predicted by the volumetric method and the experimental results for different specimens with a various amount of tightening torques. The results obtained from the experimental analysis showed that the hybrid joints have a better fatigue strength compared to the simple bolted joints. In addition, the volumetric method and experimental results revealed that the fatigue life of both kinds of the joints were improved by increasing the clamping force resulting from the torque tightening due to compressive stresses which appeared around the bolt hole.     

Residual Lifetime Assessment of an Ancient Riveted Steel Road Bridge

Abstract: The present paper reports research work carried out to characterise the fatigue behaviour of the Portuguese Pinhão riveted road bridge, built in 1903 over the Douro river. The present traffic conditions are completely different from those foreseen by the bridge designer, rising new concerns, with respect to the bridge integrity, namely its fatigue behaviour. An experimental programme was performed using original material removed from the bridge. The chemical composition and microstructures of the removed materials were characterised. Also, the notch toughness, at room temperature, was evaluated using both notch impact and Crack Opening Displacement (COD) tests. Fatigue crack growth tests were also used to evaluate the fatigue crack growth behaviour. Finally, fatigue tests of riveted joints were conducted in order to define an appropriate S‐N curve. The experimental results were used to evaluate the residual fatigue strength of the bridge, adopting both S‐N and Fracture Mechanics approaches. The analysis revealed a good tolerance to fatigue cracking, even in the presence of small fatigue cracks, detected in the joints.     

Optimization research on S‐N curve of ring welding structure based on structural stress method

In engineering, △F‐N curves are usually used to predict the fatigue life of ring welding, which is time‐consuming, laborious, and not universal. To improve the above inadequacies, an S‐N curve for evaluating the fatigue life of the ring welded specimen is proposed. The fatigue life of ring welded specimens with different materials, plate thicknesses, and hole diameters is obtained by tensile and shear fatigue tests. Shell elements, CBar beam elements (a kind of beam element in Nastran that can simulate bending), and rigid elements are used to establish the finite element model of ring welding. The stress of the ring welding structure under tensile shear load is calculated according to the structural stress method. The stress range △ σs of the welding core is taken as the longitudinal coordinate and the experimental life N as the horizontal coordinate, using two‐parameter log‐log model and the least square method of the fatigue data for linear fitting to obtain the S‐N curve equation of fatigue life evaluation. Most of the data are located within five times of the life span, which proves that the predicted life is close to the actual life of the test, and it can provide a certain reference for design and life prediction of the ring welding structures.     

Fatigue assessment of a marine structural steel and comparison with Thermographic Method and Static Thermographic Method

Fatigue properties are of fundamental importance and extremely time consuming to be assessed. The aim of this research activity is to apply the Thermographic Method (TM) and the Static Thermographic Method (STM) during fatigue and tensile tests to correlate the temperature trend to the fatigue properties of an S355 steel. The material was retrieved from an in‐service port crane. Traditional fatigue tests were performed in order to evaluate the S‐N curve with a scatter band. Step load tests were carried out deriving the fatigue limit and the Energy Parameter of the material. Static tensile tests were performed to obtain the stress at which the temperature trend deviates from the thermoelastic behavior. The fatigue properties obtained by means of the energetic methods were compared to the traditional ones showing a good agreement.     

Second‐order reliability method‐based inverse reliability analysis using Hessian update for accurate and efficient reliability‐based design optimization

First‐order reliability method (FORM) has been mostly utilized for solving reliability‐based design optimization (RBDO) problems efficiently. However, second‐order reliability method (SORM) is required in order to estimate a probability of failure accurately in highly nonlinear performance functions. Despite accuracy of SORM, its application to RBDO is quite challenging due to unaffordable numerical burden incurred by a Hessian calculation. For reducing the numerical efforts, a quasi‐Newton approach to approximate the Hessian is introduced in this study instead of calculating the true Hessian. The proposed SORM with the approximated Hessian requires computations only used in FORM, leading to very efficient and accurate reliability analysis. The proposed SORM also utilizes a generalized chi‐squared distribution in order to achieve better accuracy. Furthermore, SORM‐based inverse reliability method is proposed in this study. An accurate reliability index corresponding to a target probability of failure is updated using the proposed SORM. Two approaches in terms of finding an accurate most probable point using the updated reliability index are proposed. The proposed SORM‐based inverse analysis is then extended to RBDO in order to obtain a reliability‐based optimum design satisfying probabilistic constraints more accurately even for a highly nonlinear system. The numerical study results show that the proposed reliability analysis and RBDO achieve efficiency of FORM and accuracy of SORM at the same time. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation of fatigue life of aluminum alloy wheels under radial loads

This paper is concerned with generation of S–N curve for aluminum alloy (Al) A356.2-T6 and estimation of fatigue life under radial fatigue load. The S–N curve is developed by conducting tests at different stress levels under constant amplitude loading. Tests are conducted on alloy wheels for fatigue life evaluation under radial loads. Finite element analysis (FEA) is carried out by simulating the test conditions to analyze stress distribution and fatigue life of the alloy wheels. It is observed from analysis that the prediction of fatigue life using FEA is found to be in close agreement with the corresponding experimental observations. An attempt has been made by conducting parametric study to suggest a suitable safety factor for reliable fatigue life prediction.