Application of Extreme Value Theory in Material Defects Characterization and Fatigue Design
Doctoral thesis
Permanent lenke
http://hdl.handle.net/11250/241913Utgivelsesdato
2013Metadata
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Sammendrag
In this thesis, statistical and probabilistic fatigue assessment methods are developed and presented. The thesis consists of an introductory overview and four research papers.
The primary objective was to derive physically based and mathematically consistent methods. In that regard, material defects are adopted as the physical foundation and the starting point for further fatigue modeling. However, material defects are merely considered at a conceptual level for mathematical modeling purposes.
The statistical characterization of material defects is a central theme, where the relevance of extreme value theory is discussed and established. The shortcomings of the popular practice of utilizing asymptotic extreme value theory (and the corresponding distribution functions) in material defect characterization are demonstrated.
The general extreme value theory is considered and alternative distribution functions tailored for specific purposes are derived; \emph{sub-asymptotic} and \emph{special} extreme value distributions. The most noteworthy is the log-normal based special extreme value distribution.
The latter is the exact distribution function of extreme values arising from a log-normally distributed underlying variable. This distribution function is utilized to characterize the largest defects expected to occur in a component, when the material defects are assumed to be log-normally distributed. This distribution function is also adopted as the basis for the modeling of the other aspects of fatigue.
Material defects are divided into two classes; \emph{internal} and \emph{surface} defects. Internal defects refer to defects occurring in the volume of a component, while surface defects refer to internal defects intersecting a free surface. Thus, surface defects are treated as a transformed sub-set of the internal defects.
Due to the thorough modeling of material defects, statistical and probabilistic modeling of any aspect of fatigue is reduced to a mathematical mapping, through existing or new models, between defects and the aspect of interest. In this thesis, the fatigue limit is modeled in detail (where the $\sqrt{area}$ model according to Murakami is adopted), while the finite fatigue life is very briefly visited.
The primary result is a statistical and probabilistic fatigue limit assessment method. The method is based on material defects and includes the effect of surface defects as an integral part of the method through an original approach. The method evaluates the stress field of an arbitrary component and predicts the fatigue limit. Thus, it can be used in conjunction with finite element analysis software as a post-processor.
This thesis introduces and discusses new and alternative applications of extreme value theory in fatigue modeling. Furthermore, the significance and the value of exploring alternative approaches is demonstrated.