Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

First Advisor

David Chelidze


Predicting fatigue life is still an unresolved challenge in engineering practice. One of the problems in developing an effective damage predictive model is that damage variables are hard to measure. In this dissertation, a reliable and practical methodology for estimating damage variables from easily measurable variables is presented and validated by simulations and experiments. The tracking method is based on the application of the smooth orthogonal decomposition and new characteristics of a dynamical system called Characteristic Lengths and Distances. These features which are derived from the Birkhoff Ergodic Theorem, are fast to calculate and do not require large data or computational resources.

The fatigue life prediction problem is further complicated by the nonlinear coupling between applied loads and fatigue life. Conventional fatigue damage models consider only basic load statistical quantities (e.g., mean, variance) which do not capture nonlinear behaviors. A new experimental system|coupling structural and crack growth dynamics|is used to show that fatigue damage accumulation is different under chaotic (i.e., deterministic) and stochastic (i.e., random) loading, even when both excitations possess the same spectral and statistical signatures. Furthermore, the conventional rain- ow counting method considerably overestimates damage in case of chaotic forcing. Important nonlinear loading characteristics, which can explain the observed discrepancies, are identified and suggested to be included as loading parameters in new macroscopic fatigue models.

An analytical approach to model fatigue damage accumulation is also considered. A coupled field dynamic model is derived using Hamilton's principle for a simply supported uniform Euler-Bernoulli beam containing a single-edge crack. In this model, the fatigue crack length is treated as a generalized coordinate of a mechanical system. The fatigue accumulation is a result of the interaction between the beam oscillations and the crack propagation dynamics. Nonlinear characteristics of the beam motion are introduced as loading parameters to the fatigue model to match experimentally observed dynamics. The method of averaging is utilized as an analytical and numerical tool to compare the accumulation of fatigue damage in the system predicted by our model with Paris' law and the experimental data.