Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

Committee Chair

Ganesh Subbarayan

Committee Co-Chair

Anil Bajaj

Committee Member 1

Stuart Bolton

Committee Member 2

Patricia Davies

Committee Member 3

Xiao Wang


The idea of a quantity D, which tracks the damage state of a material from 0 (virgin) to 1 (failed) is a well-established concept. In fatigue tests, where a given load cycle is repeated until failure, it is common to define damage D per cycle as the fraction of total life consumed per cycle, or 1/Nf. We begin by using Maximum Entropy method to develop a curve to model the life vs. load cycle relationship for a wrought aluminum alloy 2024-T351 in the low cycle fatigue range. The approach is novel in that the loading is described in terms in inelastic dissipation, rather than stress or strain. It is argued that inelastic dissipation provides a closer connection to the underlying physical damage processes. The resulting model is shown to fit the data set better than the Coffin-Manson equation, the Weibull distribution function, and other alternative functions. In wrought defect-free alloys such as 2024-T351, low cycle fatigue life is mainly determined by the number of cycles required for a persistent slip band (PSB) to form a propagating crack. Literature suggests that the process of crack formation in PSBs can be modeled as a Poisson process, for a constant amplitude test. This implies that once PSBs are established, typically in the first 10% of life, crack formation is equally likely on any cycle. Once the crack forms, the final 10% of life is occupied with crack growth. The premise that formation of cracks is a Poisson process provides a starting point for building a statistical model of the fatigue process. If the loading cycles are more severe, then the probability of crack initiation on each cycle is higher. It can be shown that the Coffin-Manson relationship and the Palmgren-Miner linear damage law can both be deduced from this model. Finally, it is shown that the scatter in lives at a given loading condition should follow the Erlang distribution, with a given positive shift. This is significant because the Erlang distribution has substantially the same left skewed shape as the Weibull and Log-normal distributions which are frequently used to model the scatter in fatigue lives. The second half of this work is concerned with the fatigue process of cast aluminum alloy AS7GU, which has many intrinsic defects from which fatigue cracks tend to initiate. Intermediate and high cycle fatigue life is dominated by crack growth rather than time for crack initiation. A different measure of D is developed, based on a non-linear stress-strain relationship and applicable to the elastic-dominated high cycle fatigue regime. It is based on a general constitutive law of an elastic material, which is shown to reduce to a quadratic stress strain relationship for a uniaxial test. Like the measure proposed in previous literature, this measure associates damage with the difference between the apparent stiffness of the specimen in tension vs. compression. However, unlike previously described measures, it connects the tension/compression asymmetry to a general nonlinear material model. The measure is applied to a sequence of axial fatigue tests and a rapid increase in the measured damage late in the life of the specimens is observed. Finally, the damage curves from the axial tests previously mentioned are interpreted in terms of a small crack growth law. The sizes of the cracks growing within the specimens during the tests are inferred from the measured D. A finite element model of the specimen was created to determine the relation between damage (as indicated by increase in compliance) and the size of a modeled crack. The finite element-determined relation is used to infer the size of the cracks in the specimens previously mentioned. A small crack growth law is fit to these inferred crack growth traces with good success.