Fatigue reliability quantitative analysis of cement concrete for highway pavement under high stress ratio

In order to obtain the change law of the fatigue reliability of cement concrete for highway pavement under high stress ratios, first, the probability densities of monotonic random variables including concrete fatigue life are deduced. And then, the fatigue damage probability densities of the Miner and Chaboche-Zhao models are deduced. By virtue of laboratory fatigue test results, the fatigue damage probability density functions of the two models can be obtained, considering different stress ratios. Finally, substituting load cycles into them, the change law of cement concrete fatigue reliability about load cycles can be acquired. The results show that under the same stress ratio, with the increase in the load cycle, the fatigue reliability declines from almost 100% to 0% gradually. No matter under what stress ratio, during the initial stage of the load action, there is always a relatively stable phase for fatigue reliability. With the increase in the stress ratio, the stable phase gradually shortens and the load cycle corresponding to the reliability of 0% also decreases. In the descent phase of reliability, the higher the stress ratio is, the lower the concrete reliability is for the same load cycle. Besides, compared with the Chaboche-Zhao fatigue damage model, the Miner fatigue damage model is safer.

Fatigue Reliability Assessment of Correlated Welded Web-frame Joints

The objective of this work is to analyze the fatigue reliability of complex welded structures composed of multiple web-frame joints, accounting for correlation effects. A three-dimensional finite element model using the 20-node solid elements is generated. A linear elastic finite element analysis was performed, hotspot stresses in a web-frame joint were analyzed and fatigue damage was quantified employing the S-N approach. The statistical descriptors of the fatigue life of a non-correlated web-frame joint containing several critical hotspots were estimated. The fatigue reliability of a web-frame joint wasmodeled as a series system of correlated components using the Ditlevsen bounds. The fatigue reliability of the entire welded structure with multiple web-frame joints, modeled as a parallel system of non-correlated web-frame joints was also calculated.

Thermo-mechanical fatigue reliability optimization of PBGA solder joints based on ANN-PSO

Based on a method combined artificial neural network (ANN) with particle swarm optimization (PSO) algorithm, the thermo-mechanical fatigue reliability of plastic ball grid array (PBGA) solder joints was studied. The simulation experiments of accelerated thermal cycling test were performed by ANSYS software. Based on orthogonal array experiments, a back-propagation artificial neural network (BPNN) was used to establish the nonlinear multivariate relationship between thermo-mechanical fatigue reliability and control factors. Then, PSO was applied to obtaining the optimal levels of control factors by using the output of BPNN as the affinity measure. The results show that the control factors, such as print circuit board (PCB) size, PCB thickness, substrate size, substrate thickness, PCB coefficient of thermal expansion (CTE), substrate CTE, silicon die CTE, and solder joint CTE, have a great influence on thermo-mechanical fatigue reliability of PBGA solder joints. The ratio of signal to noise of ANN-PSO method is 51.77 dB and its error is 33.3% less than that of Taguchi method. Moreover, the running time of ANN-PSO method is only 2% of that of the BPNN. These conclusions are verified by the confirmative experiments.

Hybrid reliability model for fatigue reliability analysis of steel bridges

A kind of hybrid reliability model is presented to solve the fatigue reliability problems of steel bridges. The cumulative damage model is one kind of the models used in fatigue reliability analysis. The parameter characteristics of the model can be described as probabilistic and interval. The two-stage hybrid reliability model is given with a theoretical foundation and a solving algorithm to solve the hybrid reliability problems. The theoretical foundation is established by the consistency relationships of interval reliability model and probability reliability model with normally distributed variables in theory. The solving process is combined with the definition of interval reliability index and the probabilistic algorithm. With the consideration of the parameter characteristics of the S-N curve, the cumulative damage model with hybrid variables is given based on the standards from different countries. Lastly, a case of steel structure in the Neville Island Bridge is analyzed to verify the applicability of the hybrid reliability model in fatigue reliability analysis based on the AASHTO.

Modification of Wirsching’s Model for Fatigue Reliability Analysis

First, Wirsching's model, which is widely employed in fatigue reliability anlysis of marine and offshore structures, is analysed systematically. It is found that the very important random variable A in Wirsching's model can not be directly determined from fatigue experiment because of the irreversibility of fatigue test, and in fact, what Wirsching studied from testing results is not A but a of the statistical Miner's rule. Second, by use of the statistical Miner's rule, a modified Wirsching's model is proposed. Thirdly and more importantly, based on the two-dimensional probabilistic Miner's rule, a new model is established for fatigue reliability analysis of structural components subjected to specified cyclic loading of variable amplitude or stochastic time history. In the end, an example is presented, from which it will be seen that this new model is very convenient to use and feasible to engineering practice.

Dynamic Fatigue Reliability Analysis of Transmission Gear Considering Failure Dependence

Multiple failuremodes and strength degradation are usually inherent in the gear transmission system,which brings new challenges for conducting fatigue reliability analysis and design.This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of theCopula function and Gamma process.Firstly,the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history.The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model.The marginal distribution functions of tooth contact fatigue and dedendumbending fatigue are calculated respectively based on the dynamic interferencemodel.Finally,the joint distribution of the two failure modes can be obtained by the t-Copula function to characterize the failure dependence,and so the dynamic fatigue reliability considering failure dependence can be estimated.The effectiveness of the proposed method is illustrated with examples.The results reveal the temporal law of reliability and the effects of failure dependence on dynamic fatigue reliability.

Application of response surface method for contact fatigue reliability analysis of spur gear with consideration of EHL

In order to consider the effects of elastohydrodynamic lubrication(EHL) on contact fatigue reliability of spur gear, an accurate and efficient method that combines with response surface method(RSM) and first order second moment method(FOSM) was developed for estimating the contact fatigue reliability of spur gear under EHL. The mechanical model of contact stress analysis of spur gear under EHL was established, in which the oil film pressure was mapped into hertz contact zone. Considering the randomness of EHL, material properties and fatigue strength correction factors, the proposed method was used to analyze the contact fatigue reliability of spur gear under EHL. Compared with the results of 1.5×105 by traditional Monte-Carlo, the difference between the two failure probability results calculated by the above mentioned methods is 2.2×10-4, the relative error of the failure probability results is 26.8%, and time-consuming only accounts for 0.14% of the traditional Monte-Carlo method(MCM). Sensitivity analysis results are in very good agreement with practical cognition. Analysis results show that the proposed method is precise and efficient, and could correctly reflect the influence of EHL on contact fatigue reliability of spur gear.

Fatigue reliability based on residual strength model with hybrid uncertain parameters

The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliability with randomness, the fatigue reliability with hybrid parameters can be obtained. The presented hybrid model can adequately consider all uncertainties affecting the fatigue reliability with hybrid uncertain parameters. A comparison among the presented hybrid model, non-probabilistic set-theoretic model and the conventional random model is made through two typical numerical examples. The results show that the presented hybrid model, which can ensure structural security, is effective and practical.

Fatigue Reliability of Blade Root of Turbocharger Turbine for Vehicle Application

The blade root fatigue is one of important failure modes of turbocharger turbine for vehicle application,and the reliability and life of turbine with blade root fatigue failure mode are studied.Firstly,the stress characteristics of turbine are analyzed,and based on the operating profile of turbocharger corresponding to the endurance test of engine,the stress spectrum of turbine with blade root fatigue failure mode is studied with the simulation method.Then,with the number of endurance test profile cycle as the life parameter,the reliability model and failure rate model of turbine with blade root fatigue failure mode are derived respectively. Finally,the rules that the reliability and failure rate of turbine with the blade root fatigue failure mode changes as life parameters are studied,and the life probabilistic characteristics of turbine are also studied.

Fatigue Reliability Analysis of Aircraft Turbine Disc under Random Loads

Due to bad working conditions and complicated structure,kinds of complicated cycle loads work on turbine disc, and it's difficult to determine the stress distribution of their equivalent load.Based on the traditional stress-strength interference model and conditional reliability,the reliability models of turbine disc without the stress distribution are established in this paper. In the range of fatigue limit, by improving fatigue life curve, the relationship between turbine disc's life probability distribution and material GH4133B's is got,and so is the relationship between life and stress.Then,on the basis of test data of smooth material test-piece from references,the fatigue life probability distribution of material testpiece is found out,and then the fatigue life probability distribution of turbine disc is confirmed. The fatigue life probability distribution of turbine disc is taken into reliability model and the reliability of turbine is analyzed disc under random loads. And this analysis result confirms the variation trend of engine's reliability.

Fatigue reliability analysis of kiln welded shell

This paper presents a probabilistic reliability method for the welded shell during crack growth. The crack growth model incorporated with a failure assessment diagram（FAD） , which can provides a better estimation of the critical crack length, is developed to describe fatigue failure. All variables for particular welded joints of the shell are studied. Among them, the stress variables are based on the calculated stress by using the finite element （FE） code ANSYS. Fatigue reliability analysis of the welded shell is performed by using the Monte Carlo simulation method. The failure probability curve of the example kiln is significantly useful to determine the repair schedule of shell cracks.

Fatigue reliability for LNG carrier

The procedure of reliability-based fatigue analysis of liquefied natural gas(LNG) carrier of membrane type under wave loads is presented. The stress responses of the hotspots in regular waves with different wave heading angles and wave lengths are evaluated by global ship finite element method(FEM) . Based on the probabilistic distribution function of hotspots' short-term stress-range using spectral-based analysis,Weibull distribution is adopted and discussed for fitting the long-term probabilistic distribution of stress-range. Based on linear cumulative damage theory,fatigue damage is characterized by an S-N relationship,and limit state function is established. Structural fatigue damage behavior of several typical hotspots of LNG middle ship section is clarified and reliability analysis is performed. It is believed that the presented results and conclusions can be of use in calibration for practical design and initial fatigue safety evaluation for membrane type LNG carrier.

FATIGUE RELIABILITY CALCULATION MODEL FOR COMPONENT UNDER RANDOM LOADING

in reliability design of fatigue under random loading, the influence of loading se-quence must be considered. In order to avoid the uneertain hypothesis in the Miner's rule, ie. thatthe sum of damage equals one represents failure, this paper proposes the probabilistic relativeMine's rule. This paper also presents a new method for calculating reliability, ie. the syntheticmethod of Miner's rule and interference model. This model considers not only the influence ofstress concentration, dimension and surface, but also the influence of stress amplitude and se-quence.

FATIGUE RELIABILITY DESIGN AND ESTIMATION METHOD FOR VARIABLE LOADING

A method is presented for estimating fatigue reliability under variable loading, which isbased on load cycles-fatigue life interference theory as well as cumulative fatigue damageanalysis. The basic opinion is that for variable loading the increment of failure probability pro-duced by each load cycle is determined by the stress level as well as the damage state at whichthis load cycle applies Contrast to 'conditional reliability-equivalent life methodology'. this meth-od calculates the equivalent cycle numbers between different stress levels according to cumulativefatigue damage rule but not equivalent failure probability.

Fatigue reliability assessment for bridge welded details using long-term monitoring data

A reliability assessment method of fatigue life based on the long-term monitoring data is developed for welded details in steel box girder,and the application research is presented with examples of welded rib-to-deck details in Runyang Bridges. Firstly the fatigue damage limit-state function is established based on S-N curves and Miner's rule,and the probability distribution characteristics of the coefficients in the function are discussed in detail. The uncertainties in fatigue loading effects are mainly studied based on long-term monitoring data. In the traditional studies,only the uncertainty of equivalent stress range is considered in fatigue reliability assessment. However,stress cycle number is also treated as a random variable in this paper because we know traffic flow every day differs in a thousand ways. Then the optimization method is employed to calculate the fatigue reliability. After studying the changing law of the reliability indices with time and the effect of the randomness of stress cycle number on reliability,the effect of the traffic growth on the reliability is studied. This study shows that the uncertainty in the fatigue life of the welded details can be well studied based on structural health monitoring,so it is necessary to carry out long-term strain monitoring of the welded details for accurate fatigue reliability assessment during the whole service period.

Design optimization of a wind turbine gear transmission based on fatigue reliability sensitivity

Fatigue failure of gear transmission is one of the key factors that restrict the performance and service life of wind turbines.One of the major concerns in gear transmission under random loading conditions is the disregard of dynamic fatigue reliability in conventional design methods.Various issues,such as overweight structure or insufficient fatigue reliability,require continuous improvements in the reliability-based design optimization(RBDO)methodology.In this work,a novel gear transmission optimization model based on dynamic fatigue reliability sensitivity is developed to predict the optimal structural parameters of a wind turbine gear transmission.In the model,the dynamic fatigue reliability of the gear transmission is evaluated based on stress–strength interference theory.Design variables are determined based on the reliability sensitivity and correlation coefficient of the initial design parameters.The optimal structural parameters with the minimum volume are identified using the genetic algorithm in consideration of the dynamic fatigue reliability constraints.Comparison of the initial and optimized structures shows that the volume decreases by 3.58%while ensuring fatigue reliability.This work provides new insights into the RBDO of transmission systems from the perspective of reliability sensitivity.

Welded Joint Fatigue Reliability Analysis on Bogie Frame of High-Speed Electric Multiple Unit

A new method for welded joint fatigue reliability analysis on bogie frame of high-speed electric multiple unit(EMU) is proposed according to the International Union of Railways(UIC) standard, the Britain Standard Institute(BSI) standard and the Miner rule. Firstly, the fatigue calculation condition is loaded according to the UIC standard. The welded joint damage ratio is calculated by the BSI standard. Fatigue reliability analysis is conducted for a typical welded joint based on probabilistic design system(PDS) module in software ANSYS 14.0.In the system, the automatic program is prepared by ANSYS parametric design language(APDL) to calculate the welded joint fatigue damage ratio. Meantime, the relationship between the input variables and the output response is fitted by the response surface(RS) method. Then, the RS method is improved by the orthogonal design.Specifically, the selecting process optimization for the RS method based on the orthogonal design is conducted to improve the fitting efficiency of the RS method. Finally, a program of the automatic analysis documents is generated by Microsoft foundation class(MFC) technique. Through the self-defined interface, the researchers can easily import the automatic generation of the orthogonal table into the PDS module and analyze the fatigue reliability. Results show that the improved RS method can better fit the RS which covers the sample area, and the distribution law agrees well with the actual situation. At the same time, the improved RS method reduces the calculation time.

Research on Nonlinear Dynamic Simulation and Fatigue Reliability Life Prediction for Synthesis Transmission System of Self-Propelled Gun

Aiming to the puzzle that the inner load of nonlinear synthesis transmission system is difficult to obtain,a new kind of virtual prototype establishment and simulation method is put forward. The influence on nonlinear vibration with flexible rotor, bearing backlash is analyzed based on a virtual prototype. To validate the virtual prototype of nonlinear gear transmission system, the corresponding test platform is established. The consistency between simulation results and test results proves that the simulation results of the virtual prototype can be used to calculate the fatigue reliability life of key components. A new kind of fatigue reliability life prediction method of gear system considering multi-random parameter distribution is put forward based on the fatiguestatistic theory. Considering the periodicity of gear meshing, linear interpolation method is adopted to obtain the stress-time course of random load spectrum based on the gear's complicated torque provided by virtual prototype.The gear's P-Sa-Sm-N curved cluster can be simulated based on material's P-S-N curve. The simulation process considers the parameter distributions of stress concentration coefficients, dimension coefficients and surface quality treatment coefficients, and settles the puzzle that traditional test methods cannot acquire the gear's fatigue life of all reliability levels. This method can provide the distribution function and the interval of fatigue reliability life of gear's danger region, and has a guide meaning for the gear maintenance periods determination and reliability evaluation.

γ-p-S_a-S_m-N SURFACE THEORY AND TWO-DIMENSIONAL RELIABILITY MINER RULE FOR FATIGUE RELIABILITY-BASED DESIGN

First of all, the concept of γ_p_S a_S m_N (confidence level_reliability_stress amplitude_stress mean_fatigue life) surface is presented. Then the formulas of p_S a_S m_N surface and γ_p_S a_S m_N surface are derived. In addition, fatigue strength distribution function and two_dimensional reliability Miner rule are obtained. At last, an example is given.

CALCULATION OF FUZZY RELIABILITY IN THE CASE OF RANDOM STRESS AND FUZZY FATIGUE STRENGTH

The fuzzy sets theory is introduced into the fatigue reliability analysis. The concepts of maximizing set and minimizing set are developed to decide the ordering value of each fuzzy number, and these values can be used to determine the order of the fuzzy numbers. On the basis of the works mentioned above, the membership function defining the fuzzy safety event can be calculated, and then the fuzzy reliability in the case of stress and fuzzy fatigue strength is deduced. An example is given to illustrate the method.