This thesis has two parts. In the first part, we use the results of new fatigue experiments conducted with variable load levels as well as variable stress ratios to critically assess three (two old and one relatively new) cumulative fatigue damage models. These models are deterministic. Such models are usually tested using multiple blocks of periodic loading with differing amplitudes. However, available data pertains to zero-mean loading, and does not investigate the role of variable stress ratio (Smin/Smax). Here, we present experimental results for variable stress ratios. Two specimen geometries and two materials (Al 2014and Al 2024)are tested. Manson’s double linear damage rule (DLDR)gives the highest accuracy in predicting the experimental outcome, even in the presence of variable stress ratios, whereas predictions of the newer model (“A constructive empirical theory for metal fatigue under block cyclic loading,” Proceedings of the Royal Society A, 464 (2008), 1161-1179) are slightly inferior. The widely used Miner’s rule is least accurate in terms of prediction. The merits and drawbacks of these models, in light of the experimental results, are as follows. The DLDR, though accurate, has minor scientific inconsistencies and no clear generalization. The constructive model has possible generalizability and more appealing scientific consistency, but presently has poorer accuracy. Miner’s rule, least accurate, lies within the constructive approach for special parameter values. The DLDR can guide the new (constructive)approach through new parameter fitting criteria. In the second part of this thesis, we consider the scatter in fatigue life and use the Weibull distribution to describe ‘S-N-P’ curves. We first assume homoscedasticity (load-independent or constant variance) and present a way to draw a p-percentile line on a log-log load-life plot. Then heteroscedasticity (load-dependent variance) in fatigue life is incorporated and a simple statistical model is proposed, to obtain a straight line percentile plot at a pre-specified probability of survival ps. The proposed method is illustrated for Al 2014-T6 and Al 2024-T4 data sets (extracted manually) from MMPDS-01 (a data handbook).

The reliability of modern gas turbine engines is largely due to careful damage tolerant design a method of structural design based on the assumption that flaws (cracks) exist in any structure and will continue to grow with usage. With proper monitoring, largely in the form of periodic inspections at conservative intervals reliability and safety is maintained. These methods while reliable can lead to the early retirement of some components and unforeseen failure if design assumptions fail to reflect reality. With improvements to sensor and computing technology there is a growing interest in a system that could continuously monitor the health of structural aircraft as well as forecast future damage accumulation in real-time. Through the use of two-dimensional and three-dimensional numerical modeling the initial goals and findings for this continued work include: (a) establishing measurable parameters directly linked to the health of the blade and (b) the feasibility of detecting accumulated damage to the structural material and thermal barrier coating as well as the onset of damage causing structural failure.

The reliability of modern gas turbine engines is largely due to careful damage tolerant design a method of structural design based on the assumption that flaws (cracks) exist in any structure and will continue to grow with usage. With proper monitoring, largely in the form of periodic inspections at conservative intervals reliability and safety is maintained. These methods while reliable can lead to the early retirement of some components and unforeseen failure if design assumptions fail to reflect reality. With improvements to sensor and computing technology there is a growing interest in a system that could continuously monitor the health of structural aircraft as well as forecast future damage accumulation in real-time. Through the use of two-dimensional and three-dimensional numerical modeling the initial goals and findings for this continued work include: (a) establishing measurable parameters directly linked to the health of the blade and (b) the feasibility of detecting accumulated damage to the structural material and thermal barrier coating as well as the onset of damage causing structural failure.

This thesis is about using structural-dynamics based methods to address the existing challenges in the field of Structural Health Monitoring (SHM). Particularly, new structural-dynamics based methods are presented, to model areas of damage, to do damage diagnosis and to estimate and predict the sensitivity of structural vibration properties like natural frequencies to the presence of damage. Towards these objectives, a general analytical procedure, which yields nth-order expressions governing mode shapes and natural frequencies and for damaged elastic structures such as rods, beams, plates and shells of any shape is presented. Features of the procedure include the following: 1. Rather than modeling the damage as a fictitious elastic element or localized or global change in constitutive properties, it is modeled in a mathematically rigorous manner as a geometric discontinuity. 2. The inertia effect (kinetic energy), which, unlike the stiffness effect (strain energy), of the damage has been neglected by researchers, is included in it. 3. The framework is generic and is applicable to wide variety of engineering structures of different shapes with arbitrary boundary conditions which constitute self adjoint systems and also to a wide variety of damage profiles and even multiple areas of damage. To illustrate the ability of the procedure to effectively model the damage, it is applied to beams using Euler-Bernoulli and Timoshenko theories and to plates using Kirchhoff's theory, supported on different types of boundary conditions. Analytical results are compared with experiments using piezoelectric actuators and non-contact Laser-Doppler Vibrometer sensors. Next, the step of damage diagnosis is approached. Damage diagnosis is done using two methodologies. One, the modes and natural frequencies that are determined are used to formulate analytical expressions for a strain energy based damage index. Two, a new damage detection parameter are identified. Assuming the damaged structure to be a linear system, the response is expressed as the summation of the responses of the corresponding undamaged structure and the response (negative response) of the damage alone. If the second part of the response is isolated, it forms what can be regarded as the damage signature. The damage signature gives a clear indication of the damage. In this thesis, the existence of the damage signature is investigated when the damaged structure is excited at one of its natural frequencies and therefore it is called ``partial mode contribution". The second damage detection method is based on this new physical parameter as determined using the partial mode contribution. The physical reasoning is verified analytically, thereupon it is verified using finite element models and experiments. The limits of damage size that can be determined using the method are also investigated. There is no requirement of having a baseline data with this damage detection method. Since the partial mode contribution is a local parameter, it is thus very sensitive to the presence of damage. The parameter is also shown to be not affected by noise in the detection ambience.

The reliability of modern gas turbine engines is largely due to careful damage tolerant design a method of structural design based on the assumption that flaws (cracks) exist in any structure and will continue to grow with usage. With proper monitoring, largely in the form of periodic inspections at conservative intervals reliability and safety is maintained. These methods while reliable can lead to the early retirement of some components and unforeseen failure if design assumptions fail to reflect reality. With improvements to sensor and computing technology there is a growing interest in a system that could continuously monitor the health of structural aircraft as well as forecast future damage accumulation in real-time. Through the use of two-dimensional and three-dimensional numerical modeling the initial goals and findings for this continued work include: (a) establishing measurable parameters directly linked to the health of the blade and (b) the feasibility of detecting accumulated damage to the structural material and thermal barrier coating as well as the onset of damage causing structural failure.

The reliability of modern gas turbine engines is largely due to careful damage tolerant design a method of structural design based on the assumption that flaws (cracks) exist in any structure and will continue to grow with usage. With proper monitoring, largely in the form of periodic inspections at conservative intervals reliability and safety is maintained. These methods while reliable can lead to the early retirement of some components and unforeseen failure if design assumptions fail to reflect reality. With improvements to sensor and computing technology there is a growing interest in a system that could continuously monitor the health of structural aircraft as well as forecast future damage accumulation in real-time. Through the use of two-dimensional and three-dimensional numerical modeling the initial goals and findings for this continued work include: (a) establishing measurable parameters directly linked to the health of the blade and (b) the feasibility of detecting accumulated damage to the structural material and thermal barrier coating as well as the onset of damage causing structural failure.

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