估计三种常用应力 -寿命模型概率设计 S-N曲线的统一方法

提出了适于三参数、Langer和Basquin三种常用应力－寿命模型称为广义极大似然法的估计概率设计S－N曲线及其置信限的统一方法。方法将概率设计S－N曲线表示为对数疲劳寿命均值和均方差曲线的广义形式。与现有常规和经典极大似然法方法不同，考虑所有试验数据的统计特征，应用最小二乘法先估计出均值曲线中的材料常数，然后利用极大似然原理和数学规划法估计出均方差曲线中的材料常数。有效性采用拟合相关系数、拟合误差均方差值和置信限综合评价。对反应堆不锈钢管道焊接头虚拟应力幅－裂纹萌生寿命数据及45＃碳钢成组法和极大似然法疲劳试验应力－寿命数据的分析说明了方法的有效性。一般来说，三参数模型的拟合效果最好，Langer模型次之，Basquin模型最差。本文方法的拟合效果好于现有方法，并尽量避免了现有方法受试验数据局部统计特征影响而可能给出偏于非安全估计的缺陷。

Unified Approach for Estimating the Probabilistic Design S-N Curves of Three Commonly Used Fatigue Stress-Life Models

A unified approach,referred to as general maximum likelihood method,is presented for estimating probabilistic design S-N curves and their confidence bounds of the three commonly used fatigue stress-life models,namely three parameter,Langer and Basquin.The curves are described by a general form of mean and standard deviation S-N curves of the logarithm of fatigue life.Different from existent methods,i.e.,the conventional method and the classical maximum likelihood method,present approach considers the statistical characteristics of whole test data.The parameters of the mean curve is firstly estimated by least square method and then,the parameters of the standard deviation curve is evaluated by mathematical programming method to be agreement with the maximum likelihood principle.Fit effects of the curves are assessed by fitted relation coefficient,total fitted standard error and the confidence bounds.Application to the virtual stress amplitude-crack initiation life data of a nuclear engineering material,Chinese 1Cr18Ni9Ti stainless steel pipe-weld metal,has indicated the validity of the approach to the S-N data where both S and N show the character of random variable.Practices to the two stes of S-N data of Chinese 45＃ carbon steel notched specimens (k t=2.0) have indicated the validity of present approach to the test results obtained respectively from group fatigue test and from maximum likelihood fatigue test.At the practices,it was revealed that in general the fit is best for the three-parameter model,slightly inferior for the Langer relation and poor for the Basquin equation.Relative to the existent methods,present approach has better fit.In addition,the possible non-conservative predictions of the existent methods,which are resulted from the influence of local statistical characteristics of the data,are also overcome by present approach.