Quantitative review of probabilistic approaches to fatigue design in the medium cycle fatigue regime中周疲劳状态下疲劳设计概率方法的研究综述
![]()
Kufoin E, Susmel L, 2024. Quantitative review of probabilistic approaches to fatigue design in the medium cycle fatigue regime. Probabilistic Engineering Mechanics, 75: 103589.DOI: 10.1016/j.probengmech.2024.103589
摘要 | Abstract
为量化材料疲劳行为，需使用 Wöhler 图。现有技术表明，多年来已提出并通过大量疲劳数据集验证了多种适用于确定 Wöhler 曲线的方法。试验疲劳数据的变化导致了统计分析和设计的需求。本文重点关注中周疲劳范围 (即 103 至 107 周期内失效)，综述了相关统计方法，特别是美国材料试验学会 (American Society for Testing Materials, ASTM) 和国际焊接学会 (International Institute of Welding, IIW) 建议的方法以及所谓的线性回归法 (linear regression method, LRM)。通过虚拟数据集 (这些数据集满足特定统计要求) 以及文献中的试验疲劳数据集，对这些方法的响应进行了评估。虽然在两倍或更小范围内的散布带对所有方法都很相似，但美国材料试验学会方法是最保守的。关键词: 中周疲劳, 散布带, 生存概率, 回归分析, 应力水平, 疲劳设计To quantify the fatigue behaviour of materials, a Wöhler diagram is required. The state of the art shows that, over the years, numerous approaches suitable for determining Wöhler curves have been devised and validated through large fatigue data sets. The variation in experimental fatigue data elicits the use of statistics for analysis and design purposes. By focusing on the medium-cycle fatigue regime (i.e., failures in the range 103÷107 cycles to failure), this paper reviews relevant statistical approaches, particularly the methods suggested by the American Society for Testing Materials (ASTM) as well as the International Institute of Welding (IIW) and the so-called Linear Regression Method (LRM). Their responses were assessed on virtual data sets tailored to satisfy specific statistical requirements as well as experimental fatigue data sets from the literature. While the scatter bands at two times or less of the spread are similar for all approaches, the ASTM approach is seen to be the most conservative.Keywords: Medium cycle fatigue; Scatter band; Probability of survival; Regression analyses; Stress levels; Fatigue design创新点 | Highlights
- Statistical approaches to estimate fatigue design curves are reviewed
- The problem of estimating mean fatigue curves is analysed
- Strategies recommended to be used to determine scatter bands are reviewed
- Standard approaches are assessed based on virtual data sets
![]()
Fig. 1. S-N curve profile for the various fatigue regimes
图 2: 平均 S-N 曲线显示的散布因子性质、生存概率的参考应力水平与散布带的定义Fig. 2. Mean S-N curve showing the nature of the scatter factor K_D, the reference stress levels σ_{0,P%} at a probability of survival P, and the definition of the scatter band
图 3: 双曲线显示的平均曲线置信区间与相关数据点Fig. 3. Hyperbolic curves showing the confidence interval of the mean curve and the associated data points
图 4: 随反斜率值增加的理论数据在 95% 生存概率下平均曲线与设计应力水平下设计曲线: (a) 反斜率 3.6; (b) 反斜率 10; (c) 反斜率 15.1; (d) 反斜率 28.3Fig. 4. Mean curves, design curves with the design stress levels for increasing inverse slopes values at a probability of survival of 95% for the data in Tab. 4: (a) Inverse slope 3.6; (b) Inverse slope 10; (c) Inverse slope 15.1; (d) Inverse slope 28.3
Fig. 5. Change in scatter bands with increasing inverse slope
图 6: 随方差增加生成的理论数据: (a) 第 1 组数据的平均曲线与设计曲线; (b) 第 2 组数据的平均曲线与设计曲线; (c) 第 3 组数据的平均曲线与设计曲线; (d) 第 4 组数据的平均曲线与设计曲线Fig. 6. Graphs representing data from Tab. 5: (a) Mean and design curve for data 1; (b) Mean curve and design curve for data 2; (c) Mean curve and design curve for data 3; (d) Mean curve and design curve for data 4
Fig. 7. Change of scatter band with increasing variance
Fig. 8. Change in the size of scatter band with percentage replication
图 9: 具有恒定方差、样本集、反斜率与带宽的理论疲劳数据不同重复水平: (a) 20%; (b) 35%; (c) 55%; (d) 75%Fig. 9. Variated replication level of theoretical fatigue data with constant variance, sample set and inverse slope and spread: (a) 20%; (b) 35%; (c) 55%; (d) 75%
图 10: 不同样本集数量的散布带与设计应力: (a) 6 个; (b) 8 个; (c) 12 个Fig. 10. Scatter bands and design stresses for varied magnitude of sample set: (a) n = 6; (b) n = 8; (c) n = 12
图 11: 文献中选定疲劳数据集的散布带随反斜率增加的变化Fig. 11. Trends in scatter band with increasing inverse slope of selected fatigue datasets from literature
图 12: 改变方差、反斜率与样本集下文献中疲劳数据集散布带的美国材料试验学会法、国际焊接学会法与线性回归法对比Fig. 12. Comparing scatter bands of ASTM, IIW and LRM of fatigue data sets from literature with changing variance, inverse slope and sample set
作者信息 | Authors
Elvis Kufoin
英国谢菲尔德大学 (University of Sheffield) 土木与结构工程系
Luca Susmel, 通讯作者 (Corresp.) 英国谢菲尔德大学 (University of Sheffield) 土木与结构工程系Email: l.susmel@sheffield.ac.uk
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
