Weibull应力方法预测低合金钢的韧脆转化曲线

采用三参数的Weibull分布描述断裂韧度的统计规律。结合ASTM E1921-05标准,详细讨论了标准断裂试样韧脆转化曲线的建立过程;为了将标准断裂试样的测试结果用于低约束断裂试样,采用两参数的Weibull分布描述裂纹尖端局部区域的应力状态与失效概率之间的关系,并用Weibull应力将各种不同约束水平的裂纹尖端应力场联系起来,得到了预测低约束断裂试样韧脆转化曲线的公式。然后对两种A533B钢三点弯曲断裂试样进行了实例计算,进一步分析了Weibull应力的有限元计算结果,根据这些结果预测的韧脆转化曲线与试验数据相比非常吻合,证明了该文提出的方法是有效的。     

三参数威布尔分布参数估计及在可靠性分析中的应用

威布尔分布是可靠性中应用最广泛的分布之一。三参数威布尔分布尤其适用于在开始使用时有一时间段内不发生故障的情况。由于该分布的位置参数不等于0,在参数估计时不能采用简单的参数估计方法实现,限制了该分布形式在可靠性分析中的应用。根据三参数威布尔分布的特点提出了一种综合图解法和遗传算法的参数估计方法,应用该方法可以获得更精确的参数估计值。随后应用于某系列数控车床计算机数控系统的故障分析中,验证了本文提出的参数估计方法的可行性。     

两种国产涡轮盘材料疲劳寿命概率分布规律初探

基于两种国产发动机轮盘材料GH4133和1Cr11Ni2W2MoV低循环疲劳实验数据,选择三种常用的分布函数(对数正态分布、双参数Weibull分布和三参数Weibull分布),用概率图法和柯尔莫哥洛夫-斯米尔诺夫检验方法进行拟合优度检验,以考察分布函数的总体拟合效果.通过经验失效率的变化趋势来评估分布函数是否符合疲劳失效机制.结果表明:形状参数大于1的三参数Weibull分布函数是建立国产轮盘材料GH4133和1Cr11Ni2W2MoV疲劳寿命分布的理想数学模型.对数正态分布函数在本工作所研究的轮盘材料低循环疲劳寿命范围内是合理的.双参数Weibull分布函数用作国产轮盘材料疲劳寿命分布模型时必须进行假设检验.     

The effect of the threshold stress on the determination of the Weibull parameters in probabilistic failure analysis

In the analysis of brittle materials and components the probability of failure is commonly modelled using a two-parameter Weibull distribution. Occasionally, a three-parameter model is used when the material shows significant threshold behaviour. In this paper two methods for determining the three-parameter constants are discussed. Two theoretical two- and three-parameter distributions are then analysed to examine the number of samples needed to determine the parameters accurately. The two-parameter models are the best fits of the three-parameter models and their failure distributions are very similar to the three-parameter distributions. It is concluded that far more specimens need to be tested than is usually the case to be confident that the correct distribution has been found.     

基于GM-噪声SVR方法的矿山设备可靠性参数估计

为了有效估计小子样条件下矿山设备的三参数威布尔分布可靠性模型参数,提出基于GM-噪声SVR的参数估计方法。该方法以灰色估计法(GM)为基础估计模型的位置参数,采用基于训练样本数量和噪声参数寻优的ε - 带支持向量回归机(ε-SVR)估计尺度参数和形状参数,并通过拟合的三参数威布尔分布函数分析预测和解决设备的可靠性问题。算例结果表明,GM-噪声SVR方法可以很好地用于矿山设备可靠性模型参数估计,估计某带式输送机三参数威布尔分布可靠性模型的位置参数、尺度参数和形状参数依次为3.1525、188.3763、1.0476,平均无故障时间为188 h,标准均方根误差NRMSE为0.0519。这表明该方法的可行性和有效性。     

Reliability analysis for wind turbines with incomplete failure data collected from after the date of initial installation

Reliability has an impact on wind energy project costs and benefits. Both life test data and field failure data can be used for reliability analysis. In wind energy industry, wind farm operators have greater interest in recording wind turbine operating data. However, field failure data may be tainted or incomplete, and therefore it needs a more general mathematical model and algorithms to solve the model. The aim of this paper is to provide a solution to this problem. A three-parameter Weibull failure rate function is discussed for wind turbines and the parameters are estimated by maximum likelihood and least squares. Two populations of German and Danish wind turbines are analyzed. The traditional Weibull failure rate function is also employed for comparison. Analysis shows that the three-parameter Weibull function can obtain more accuracy on reliability growth of wind turbines. This work will be helpful in the understanding of the reliability growth of wind energy systems as wind energy technologies evolving. The proposed three-parameter Weibull function is also applicable to the life test of the components that have been used for a period of time, not only in wind energy but also in other industries.     

A Goodness-of-Fit Test for the Two Parameter vs. Three Parameter Weibull; Confidence Bounds for ThreshoId

An investigation is described herein of modifications of the two-parameter Weibullgoodness-of-fit test of Mann, Scheuer and Fertig (1973). It is assumed that the sole alternative of interest is any three-parameter Weibull distribution. The power of candidate test statistics is investigated, therefore, only under various three-parameter Weibull alternative hypotheses.

It is found that for a fixed selection of gaps (differences of adjacent order statistics) used in the numerator and in the denominator of the approximately F dist ributed test statistic, nothing is gained by weighting the gaps in order to minimize the variances and thus to maximize the numbers of degrees of freedom.

A test statistic which is a modified version of that of Mann, Scheuer and Fertig is shown to have higher power under three-parameter Weibull alternatives, and a simple method for approximating critical values of the test statistic is described. The test statistic is shown to be a monotone function of an unknown threshold (location) parameter for the three-parameter Weibull model. Hence, the methodology described for testing for a zero threshold parameter can be used to obtiain a confidence interval for this parameter. Methods for combining life-test data for application to progressively censored samples are also described.     

Reliability analysis of wind turbine subassemblies based on the 3-P Weibull model via an ergodic artificial bee colony algorithm

The Weibull distribution is the most widely used model for the reliability evaluation of wind turbine subassemblies. Considering the important role of the location parameter in the three-parameter (3-P) Weibull model and its rare application in wind turbines, this study conducted a reliability analysis of wind turbine subassemblies based on field data that obeyed the 3-P Weibull distribution model via maximum likelihood estimation (MLE). An improved ergodic artificial bee colony algorithm (ErgoABC) was proposed by introducing the chaos search theory, global best solution, and Lévy flights strategy into the classical artificial bee colony (ABC) algorithm to determine the maximum likelihood estimates of the Weibull distribution parameters. This was validated against simulation calculations and proved to be efficient for high-dimensional function optimization and parameter estimation of the 3-P Weibull distribution. Finally, reliability analyses of the wind turbine subassemblies based on different types of field failure data were conducted using ErgoABC. The results show that the 3-P Weibull model can reasonably evaluate the lifetime distribution of critical wind turbine subassemblies, such as generator slip rings and main shafts, on which the location parameter has a significant effect.     

Fatigue lifetime of glass fabric/epoxy composites

Monotonic and fatigue tests were carried out in four-point bending on a glass fabric/epoxy composite, using two different stress ratios. Ultimate failure both in monotonic tests and in fatigue was precipitated by microbuckling phenomena happening at the compression side of the specimens. The experimental results were evaluated adopting a fatigue model statistically implemented, based on the hypothesis of a two-parameter Weibull distribution of the monotonic strength, previously assessed for random glass fibre reinforced plastics failed in tension. The fatigue model was able to account for the effect of the stress ratio on the fatigue life, accurately predicting the classical S–N curve. By the model, the virgin strength for each specimen failed in fatigue was evaluated, and the distributions of the measured and calculated monotonic strength were compared. Some discrepancies between the two distributions, resulting in poor agreement in the tail portions of the curves, were noted. It is shown that the inconsistencies found are probably attributable to the inadequancy of a two-parameter Weibull curve to describe the actual material trend. Better results were obtained by using a three-parameter Weibull distribution.     

Three-parameter vs. two-parameter Weibull distribution for pultruded composite material properties

The three-parameter and two-parameter Weibull distributions are compared using 26 mechanical property data sets of fiber-reinforced polymeric (FRP) composite materials manufactured by the pultrusion process. Both strength and stiffness properties were examined. The probability distributions were compared on the basis of goodness of fit, nominal design values, and allowable load to achieve uniform reliability. It is recommended that the two-parameter Weibull distribution be used to characterize FRP composite material properties. The primary basis for this recommendation is small differences in nominal design values and small differences in allowable loads between the two-parameter and three-parameter Weibull distributions. Other supporting reasons for the recommendation are similar observed significance levels in distribution fitting, computational efficiency, and the fact that the location parameter of the three-parameter Weibull distribution is near the first order statistic.     

A probabilistic static fatigue model for transverse cracking in CFRP cross-ply laminates

This paper presents a delayed-fracture model for transverse cracking in CFRP cross-ply laminates under static fatigue loading. First, a delayed-fracture model for a crack in a brittle material was established on the basis of the slow crack growth (SCG) concept in conjunction with a probabilistic fracture model using the three-parameter Weibull distribution. Second, the above probabilistic SCG model was applied to transverse cracking in cross-ply laminates under static fatigue loading. The stress and the length of the unit element in the transverse layers were calculated with the aid of a shear-lag analysis, taking the residual stress into account. The transverse crack density was expressed as a function of applied stress and time with the parameters in the Paris law and the Weibull distribution function specified, in addition to the mechanical and geometrical properties. Unknown parameters were determined from experiment data gathered in static tensile and static fatigue tests. The reproduced transverse crack density at various applied loads agreed well with the experiment results.     

经编用钼丝纤维强力的概率分布分析

钼丝是用于制造空间可展开网状天线反射体的关键材料之一,具有高强度、低伸长、低热膨胀系数等特性。对钼丝纤维分别在3种不同拉伸隔距下进行强力测试与统计分析,发现钼丝纤维强力符合二参数和三参数的Weibull分布规律,并且更适合采用三参数Weibull分布来描述;随着拉伸隔距的增加,钼丝纤维的强度下降,强度分散性减小,表现出明显的尺寸效应。     

BFRP筋温度损伤后的疲劳性能研究

开展温度损伤后的玄武岩纤维增强复合材料(BFRP)疲劳性能研究,对其在高温环境中的合理使用具有重要意义。提出改进单点-成组法,借助灰色理论GM(1,1)模型结合极值原理对疲劳S-N曲线三参数表达式进行回归分析,推导随应力水平变化的三参数Weibull概率密度函数,根据极大似然估计原理确定分布参数。通过非线性拟合方法建立综合考虑温度和可靠度影响的Weibull概率疲劳T-P-S-N模型。通过温度损伤后的BFRP筋疲劳性能试验研究温度损伤对其疲劳性能的影响,并验证理论模型。结果表明:BFRP筋疲劳寿命随温度和可靠度的升高疲劳寿命呈下降趋势,与实际相符;建议模型能较好描述BFRP筋疲劳性能随温度和可靠度的变化趋势。     

Static fatigue of rubbery polymers: statistical approach to the failure process

A phenomenological theory of a stochastic process was applied to the study of the failure mechanism of static fatigue of rubbery polymers. Static fatigue, namely, creep and stress relaxation experiments, were made on two specimens, pure vulcanizate and carbon-reinforced vulcanizate of acrylonitrile-butadiene rubber (NBR). The distributions of the lifetime were analysed by means of the function in the form of the Weibull distribution, which is an improvement of the stochastic theory proposed by Kawabataet al. The experiments proved the validity of the theory. Furthermore, the experimental results suggest that, in pure vulcanizate, a critical crack initiates and propagates unstably (random process at Weibull modulus of unity), and that, in carbon-reinforced vulcanizate, multi-cracks initiate and propagate stably due to the presence of carbon black particles (wear-out process at Weibull modulus of 1 to 3). The scattering in the lifetime of pure vulcanizate seems to reflect the inherent characteristics of the polymer.     

A probabilistic fatigue model based on the initial distribution to consider frequency effect in plain and fiber reinforced concrete

The objective of this work is twofold. First, we aim to develop a new fatigue model valid for quasi-brittle materials like concrete, which properties have considerably larger standard deviation than metals. Having this in mind, we fit the measured strength data with a three-parameter Weibull cumulative distribution function and in turn take it as the initial distribution for an asymptotic fatigue model in concrete. Second, we endeavor to take into account the observed influence of frequency and stress ratio on the fatigue life in concrete, both plain and reinforced with fibers. The developed model is validated against fatigue tests in compression on cubic specimens for different stress ratios and loading frequencies. All the parameters have found physical meaning in the extensive experimental tests performed for two plain high strength concretes and two concretes reinforced with fibers. The secondary strain rate is found to be correlational with the number of cycles to failure. Finally, a reduced test procedure is proposed for fatigue strength characterization.     

LZ50钢断裂韧度的合理统计模型

试验研究了LZ50车轴钢的断裂韧度的合理统计模型。结果表明,LZ50钢是一种偏脆性的材料,应当严格控制铁道车辆车轴的制造表面质量。同时证实了现有正态分布模型不能合理描述试验数据。为此,通过比较三参数Weibull、两参数Weibull、正态、对数正态、极小值和极大值6种常用统计分布对试验数据的拟合优度、数理一致性和尾部安全性,说明了极小值分布是良好统计模型。建立了断裂韧度的极小值概率测定方法,测定了典型存活概率和置信度下的材料断裂韧度值。     

Three-dimensional stress analysis and Weibull statistics based strength prediction in open hole composites

The critical failure volume (CFV) method is proposed. CFV is defined as a finite subvolume in a material with general nonuniform stress distribution, which has the highest probability of failure, i.e. loss of load carrying capacity. The evaluation of the probability of failure of the subvolumes is performed based on the lowest stress and thus provides an estimate of the lower bound of the probability of local failure. An algorithm for identifying this region, based on isostress surface parameterization is proposed. It is shown that in the case of material with strength following Weibull weak link statistics such a volume exists and its location and size are defined both by the stress distribution and the scatter of strength. Moreover the probability of failure predicted by using the CFV method was found to be close to that predicted by using traditional Weibull integral method and coincide with it in the case of uniform stress fields and in the limit of zero scatter of strength. Experiments performed on homogeneous epoxy resin plaques with and without holes showed that the predictions bound the experimentally measured open hole strength. The Weibull parameters used for prediction were obtained from testing only unnotched specimens of different dimensions. The effect of the hole size on tensile strength of heterogeneous materials such as quasi-isotropic carbon–epoxy composite laminates was considered next. Fiber failure was the only failure mechanism taken into account and a strain-based failure criterion was used in the form of a two parameter Weibull distribution. The stacking sequence was selected to minimize the effect of stress redistribution due to subcritical damage. Not unexpectedly an up to 30% underprediction of the strength of the laminates with small (2.54 mm diameter) holes was observed by using classical Weibull integral method as well as Weibull based CFV method. It was explained by examining the size of the CFV, which appeared to be below Rosen’s ineffective length estimate. The CFV method was modified to account for the presence of a limit scaling size of six ineffective lengths, consistent with recent Monte-Carlo simulations by Landis et al. [Landis CM, Beyerlin IJ, McMeeking RM. Micromechanical simulation of the failure of fiber reinforced composites. Mech Phys Solids 2000;48:621–48] and was able to describe the experimentally observed magnitude of the hole size effect on composite tensile strength in the examined range of 2.54–15.24 mm hole diameters.     

A STATISTICAL INVESTIGATION OF THE FATIGUE LIVES OF Q235 STEEL-WELDED JOINTS

An investigation into the fitting of six assumed distributions (three-parameter Weibull, two-parameter Weibull, extreme minimum value, extreme maximum value, normal and lognormal distributions) of 23 groups of fatigue life data for Q235 steel-welded joints is performed in terms of linear regression analyses. The results reveal that the fatigue life distribution shapes mostly tend to be positively skewed. Therefore, the extreme minimum value and normal distributions are not the most appropriate distributions to assume for a fatigue life evaluation. The three-parameter Weibull distribution may give misleading results in fatigue reliability analyses because the shape parameter is often lesss than 1. This means that the hazard rate decreases with fatigue cycling. This is contrary to the general understanding of the behaviour of welded joints. Reliability analyses may also be affected by slightly non-conservative evaluations in tail regions of the three-parameter Weibull distribution. The two-parameter Weibull distribution does not give as good a fit as either the extreme maximum value distribution or the lognormal distribution. On the other hand, the extreme maximum value and lognormal distributions can be safely assumed in reliability analyses due to the good total fit effects and the conservative evaluations in tail regions. In addition, the extreme maximum value distribution is in good agreement with the general physical understanding of the structural behaviour of welded joints.     

Reliability analysis using exponentiated Weibull distribution and inverse power law

Today in reliability analysis, the most used distribution to describe the behavior of devices is the Weibull distribution. Nonetheless, the Weibull distribution does not provide an excellent fit to lifetime datasets that exhibit bathtub shaped or upside‐down bathtub shaped (unimodal) failure rates, which are often encountered in the performance of products such as electronic devices (ED). In this paper, a reliability model based on the exponentiated Weibull distribution and the inverse power law model is proposed, this new model provides a better approach to model the performance and fit of the lifetimes of electronic devices. A case study based on the lifetime of a surface‐mounted electrolytic capacitor is presented in this paper. Besides, it was found that the estimation of the proposed model differs from the Weibull classical model and that affects the mean time to failure (MTTF) of the capacitor under analysis.