基于不确定微分方程的疲劳可靠性建模  

Reliability modelling for fatigue based on uncertain differential equation

作　　者：李晓阳[1,2] 陶昭 张慰[1,2] LI Xiaoyang;TAO Zhao;ZHANG Wei(School of Reliability and Systems Engineering,Beihang University,Beijing 100083,China;Science and Technology on Reliability and Environmental Engineering Laboratory,Beihang University,Beijing 100083,China)

机构地区：[1]北京航空航天大学可靠性与系统工程学院,北京100083 [2]北京航空航天大学可靠性与环境工程技术国防重点实验室,北京100083

出　　处：《航空学报》2022年第8期475-491,共17页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(51775020,51875019);科学挑战计划(TZ2018007);中央高校基本科研业务费专项资金(YWF-21-BJ-J-515)。

摘　　要：为了合理量化疲劳裂纹扩展过程中时间维度的不确定性的动态变化特征,从小时间尺度(即宏观上相对较小的时间单位)出发,介绍了不确定理论中的不确定微分方程来刻画不确定性的动态变化特征。具体地,在不确定理论的框架下,针对考虑裂纹闭合和高载迟滞效应的裂纹扩展过程,考虑时间维度的不确定性的动态变化特征以及物理属性、外界载荷和裂纹阈值的不确定性的静态特征并分别进行量化描述,进而给出小时间尺度下基于不确定微分方程的疲劳裂纹扩展模型;以裂纹长度为性能参数,构建出裕量方程,并推导出确信可靠度函数,完成疲劳可靠性建模。通过开展疲劳裂纹扩展实验,对建立的模型进行应用,给出了确信可靠度评估结果和裂纹扩展预测结果。此外,通过模型的讨论分析,表明了小时间尺度下进行疲劳裂纹扩展建模以及对不确定性进行细致分类和科学量化的重要意义。To quantify the dynamic characteristic of uncertainty in the fatigue crack growth process in the time dimension,the uncertain differential equation of uncertainty theory is introduced to describe the dynamic characteristic of uncertainty from a small time scale(i.e.,smaller time unit macroscopically).Specifically,for the crack growth process considering the crack closure and the retardation effect caused by overloads,the dynamic characteristic of the uncertainty in the time dimension and the static characteristic of the uncertainties in the physical properties,the external load and the crack threshold are considered and quantified in the framework of uncertainty theory.A fatigue crack growth model based on the uncertain differential equation is built from the small time scale.The margin equation is constructed regarding the crack length as the performance parameter,and the reliability function is deduced for the fatigue reliability modelling.The proposed model is applied to a case of fatigue crack growth experiment,and the reliability evaluation and the prediction of crack growth are obtained.The discussion and analysis of the proposed model shows that the modelling of fatigue crack growth from the small time scale and the careful classification and scientific quantification of the uncertainties are significant.

关 键 词：疲劳裂纹扩展 不确定性 动态变化 小时间尺度 不确定微分方程 可靠性 

分 类 号：V215.55[航空宇航科学与技术—航空宇航推进理论与工程] TB114.3[理学—概率论与数理统计]