陈龙, 黄天立, 周浩. 基于比例型Paris公式和逆高斯过程的金属疲劳裂纹扩展随机模型[J]. 工程力学, 2021, 38(10): 238-247. DOI: 10.6052/j.issn.1000-4750.2020.09.0671
引用本文: 陈龙, 黄天立, 周浩. 基于比例型Paris公式和逆高斯过程的金属疲劳裂纹扩展随机模型[J]. 工程力学, 2021, 38(10): 238-247. DOI: 10.6052/j.issn.1000-4750.2020.09.0671
CHEN Long, HUANG Tian-li, ZHOU Hao. STOCHASTIC MODELLING OF METAL FATIGUE CRACK GROWTH USING PROPORTIONAL PARIS LAW AND INVERSE GAUSSIAN PROCESS[J]. Engineering Mechanics, 2021, 38(10): 238-247. DOI: 10.6052/j.issn.1000-4750.2020.09.0671
Citation: CHEN Long, HUANG Tian-li, ZHOU Hao. STOCHASTIC MODELLING OF METAL FATIGUE CRACK GROWTH USING PROPORTIONAL PARIS LAW AND INVERSE GAUSSIAN PROCESS[J]. Engineering Mechanics, 2021, 38(10): 238-247. DOI: 10.6052/j.issn.1000-4750.2020.09.0671

基于比例型Paris公式和逆高斯过程的金属疲劳裂纹扩展随机模型

STOCHASTIC MODELLING OF METAL FATIGUE CRACK GROWTH USING PROPORTIONAL PARIS LAW AND INVERSE GAUSSIAN PROCESS

  • 摘要: 疲劳失效是金属构件的主要失效方式之一,该文针对金属疲劳裂纹扩展过程中的不确定性,以“首次达到给定裂纹长度a的时间t(a)”为随机描述量,采用比例型Paris公式描述裂纹的平均扩展路径,建立基于逆高斯过程的单样本疲劳裂纹扩展随机模型和考虑样本异质性的裂纹扩展随机效应模型,分别采用最大似然估计法(MLE)和最大期望算法(EM)推导了单样本模型和随机效应模型的参数估计公式。最后,利用提出的裂纹扩展随机模型拟合了68个铝合金板的疲劳裂纹数据,对结果进行了拟合优度分析。结果表明:该文提出的疲劳裂纹扩展随机模型能够有效地分析和解释金属疲劳裂纹扩展过程中的不确定性。

     

    Abstract: Fatigue failure is one of the main failure modes of metal components. In order to describe the uncertainty associated with metal fatigue crack growth, a stochastic description based on the “time t(a) to first reach a predefined crack length a” allows for the process mean in each specimen to equal to a proportional Paris law. Then, a simple model and a random effect model based on the inverse Gaussian process (IGP) are established, which are used to describe the variability across a single specimen and specimens, respectively. Then the model parameters for the simple model and the random effect model are estimated by using the maximum likelihood estimate (MLE) method and the expectation maximization algorithm (EM), respectively. Finally, the proposed models are used to fit the 68 Virkler fatigue datasets and the good-of-fit test is analyzed. The results show that the proposed models are effective candidates for description and interpretation of the uncertainty of metal fatigue crack growth.

     

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