| Summary: | 博士 === 國立臺灣大學 === 機械工程學研究所 === 90 === Abstract of Dissertation Presented to the Graduate School
of National Taiwan University in Partial fulfillment of the
Requirements for the Degree of Doctor of Philosophy
STUDY OF STOCHASTIC FATIGUE CRACK GROWTH MODELS
AND THEIR EXPERIMENTAL VERIFICATION
BY
CHIH-CHUNG NI
JULY 2002
Advisor: Dr. Wen-Fan Wu
Major Department: Mechanical Engineering
To capture the statistical nature of fatigue crack growth, many stochastic models have been proposed in the literatures. Many of the proposed models are either lack of experimental verification or just verified by only one data set. Therefore, the adequacies of these stochastic models need to be investigated further by other available data sets. In the present study, a second order polynomial stochastic fatigue crack growth equation is proposed and its two extreme cases, the random variable case and random white noise case, are investigated. Besides, the analytically close-form solutions of the stochastic equation are also derived. A correlation parameter, correlation time, is involved in the process of Monte Carlo simulation and its effect on the results of the stochastic equation is also investigated. Experimental work is conducted under both constant amplitude loading and random loading to obtain the fatigue crack growth data of a batch of 2024-T351 aluminum alloy specimens and some statistical analysis of these data are studied. The experimental data are then applied to the proposed second-order polynomial stochastic equation as well as some other equations proposed by other researchers to verify their adequacy. These equations include the Paris-Erdogan law, modified Paris-Erdogan law, randomized Paris-Erdogan law, randomized Forman law, and randomized power law. Different approximate methods including Monte Carlo simulation, first-order second-moment method, and Yang and Manning’s method are utilized to evaluate those stochastic equations. The comparison of crack growth curves, median crack growth curve, distribution function of the random time to reach a specified crack size, and probability of crack exceedance among different equations and those of the experimental data are made. The results show that the proposed second-order polynomial stochastic equation can fit all three groups of experimental data very well while other equations can fit only one group of data. Therefore, the proposed stochastic equation can be used for the fatigue reliability prediction of structures or components made of the tested material.
KEYWORDS: Fatigue crack growth, stochastic analysis, random process, random variable, Monte Carlo simulation.
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