估计三种常用疲劳应力—寿命模型P—S—N曲线的统一经典极大似然法

拓展经典极大似然法到Langer模型，提出了估计三参数、Langer和Basquin三种常用疲劳应力-寿命模型P-S-N曲线及其置信限的统一方法。方法用于处理极大似然法疲劳试验得到的S-N数据，该试验在特别关注的参考载荷试验一组试样，其余试样在不同载荷下试验，以参考载荷试验数据的统计参量为基础，按照每个模型中材料常数协同处于相同概率水平原则，将曲线表示为对数疲劳寿命均值和均方差线的广义形式，至多4个材料常数，曲线中的材料常数按极大似然原理采用数学规划法求出。45#碳钢缺口试样（kt=20)对称循环加载试验数据的分析说明了方法的有效性，分析还揭示合理模型有必要通过比较拟合效果、预计误差和应用安全性来确定，三参数模型的拟合效果最好，Langer模型稍差，Basquin模型较差，从拟合效果、预计误差和应用安全性角度，Basquin模型不适于描述该套数据。此外，经典极大似然法估计结果可能因受局部统计参量影响而给出非安全估计，有必要发展改进的可以最大限度着小这种影响的方法。

A Unified Classical Maximum Likelihood Approach for Estimating P-S-N Curves of Three Commonly Used Fatigue Stress-Life Relations

A unified classical maximum likelihood approach for estimating P-S-N curves of the three commonly used fatigue stress-life relations, namely three parameter, Langer and Basquin, is presented by extrapolating the classical maximum likelihood method to the Langer relation. This approach is applied to deal with the S-N data obtained from a so-called maximum likelihood method-fatigue test. In the test, a group of specimens are tested at a so-called reference load, which is specially taken care of by practice, and residual specimens are individually fatigued at different loads. The approach takes a basis of the local statistical parameters of the logarithms of fatigue lives at the reference load. According to an assumption that the material constants in each relation are concurrently in same probabilistic level, the curves is described by a general form of mean and standard deviation curves of the logarithm of fatigue life, in which four material constants are at most contained. The constants in the curves are estimated by a mathematical programming method to be in agreement with the maximum likelihood principle. Availability of the approach has been indicated by an analysis of the S-N data of 45# carbon stell-notched specimens ( kt=2.0 ) subjected to fully reversed axial loads. The analysis reveals that an appropriate relation should be determined by comparing the fit, the fitted error and the safety in practice, of the three relations. The fit is best for three-parameter relation, slightly inferior for the Langer one and poor for the Basquin. Considering the fitted error and the safety in practice, the Basquinone is not an appropriate relation for the data. In addition, classical maximum likelihood method-based predictions might be affected by the local statistical characteristics of test data at the reference load to be non-conservatively. To avoid the affects, an improved method, which could reduce the affects to a minimum, should be worthily explored.