The work reported in this thesis investigates the effect of chaos and other types of non-linear motion on the fatigue life prediction of mechanical components in a number of physical systems. Three different dynamic systems were investigated. A rotor system with a radial clearance, a boiler-tube type system and a vibration absorber type system with a small Two-Mass System.  Mathematical models are presented for each system and experimental test rigs are constructed.  Numerical simulations of the rotor system are presented and show good correlation between theoretical and experimental results. Displacement data from the experimental test rigs was scaled to represent stresses within the mechanical components of the test rigs in two different ways.  Firstly, the data was scaled uniformly across each range of tests for each system.  A second method was utilised to scale the data so that each set of data had the same RMS response amplitude, to reduce the effect that relative magnitude of motion has on fatigue life predictions.  Both types of scaled data were then processed using commercially available fatigue analysis software to provide fatigue lives for specific test runs. The Rainflow cycle counting method with the Goodman mean stress hypothesis and the Haibach fatigue damage criterion was used for the fatigue life calculations throughout this work. Relative comparisons between the fatigue lives at different operating conditions were made for all three systems, and conclusions were drawn using the most relevant data. These conclusions show that motion containing side bands in the frequency domain, indicating a modulating effect in the time domain, have a significantly more damaging effect on the fatigue life than simple harmonic motion.  High order super-harmonic content in the response also ahs a more damaging effect. Conclusions regarding the effects of chaotic motion are less clear.  Both more damaging and less damaging situations were found.  No conclusive evidence was found that chaos is generally good or generally bad for the fatigue life of dynamic system components, however evidence that side bands, sub-harmonic and super-harmonic motion is generally damaging is presented. The use of one-dimensional mappings was also investigated to provide a theoretical source of chaotic motion in a response that is similar to that of simple dynamic systems.  Again, no strong conclusive evidence was found to conclude that chaos was ‘good’ or ‘bad’ for the fatigue life of dynamic system components.

Fracture failure in piping systems is a common problem in the process industries, and the thesis describes the research that  has been undertaken by the author in modelling and analysing a particular example of such a system, namely an expansion loop subjected to pressure and temperature loading.  The work has been used to investigate the difficulties that arise in linking non-linear fracture mechanics analysis with reliability computations. The thesis includes a critical review of both linear and non-linear fracture mechanics and a separate review of advanced structural reliability methods. An improved response surface method has been proposed in this research to conduct a reliability assessment where the structural behaviour is modelled and the <i>J</i>-integral is computed using finite element software.  Of particular interest has been the development of a methodology that is able to handle the non-linearities inherent in the material stress strain curve.  Although it was possible to develop a response surface to achieve a good fit in the region of FROM/SORM design point, it led to instability in the FORM/SORM implementation.  The research then focussed on the use of directional simulation as a solution technique for this class of problems. The material used in the construction of the expansion loop was AISI-321 stainless steel and to model this correctly in the reliability-based assessment the full range stress-strain behaviour was required in FE analysis.  The material was tested in the laboratory and a new piecewise continuous stress-strain model has been developed which involves a linear-elastic part and two subsequent non-linear parts both of the Ramsberg-Osgood type.  For the purposes of reliability assessment a new stochastic stress-strain model has been developed taking into account uncertainties in yield strength and in operating temperatures, together with the associated yield strength – temperature dependency. An integral part of the research has  been a study of the <i>J</i>-integral profile along the crack front using 3-D FE analysis, for a number of CT (Compact Tension), beam and CCT (Central Crack Tension) specimens, with a range of thickness.  This has brought new findings which are of importance in both deterministic and probabilistic assessment.

Structural Health and Usage Monitoring has gained considerable interest throughout the engineering technologies. Especially for the aircraft industry, where damage can lead to catastrophic and expensive failures, and the vehicles involved undergo regular cost intensive inspections, a Health and Usage Monitoring System (HUMS) has one of the highest payoffs. Furthermore, HUMS allow new design principles for the realisation of lightweight aircraft structures. Different approaches towards a HUMS can be found in the literature. A system based on load monitoring and damage detection could provide highest potential for implementation in future aircrafts. This thesis investigates the use of multifunctional fibre Bragg grating (FBG) sensors for structural health and usage monitoring. It is shown, how FBG sensors can be used simultaneously for both, a strain sensing based load monitoring system and a Lamb wave based damage detection system. Several fundamental areas are addressed analytically and experimentally. This work adds new approaches towards the implementation of large area FBG sensor networks using fibre optical rosettes and temperature compensated strain sensors. A miniaturised build-up technique for a FBG temperature sensor is demonstrated which allows multiplexing of several strain and temperature sensors within a single fibre network. The use of a backing patch for FBG sensors is studied numerically and experimentally. In this thesis, surface mounted and structural integrated FBG sensors are used to detect Lamb waves. The theoretical approach that leads to the development of an appropriate ultrasonic interrogation system for FBG sensors is introduced. Numerical simulations on the influence of the grating dimensions on its ability to detect ultrasonic strain fields and their experimental validation are presented. Three different tasks of damage identification based on Lamb waves are considered: detection of damage, localisation of damage and severity of damage. Experimental results on all three tasks show that FBG sensors can compete with existing technologies. As part of the experimental work, a reliable, temperature independent damage index is introduced and a novel detection scheme using fibre grating rosettes and Genetic Algorithms for the localisation of damage is developed. The results of a simple fatigue test experiment on which the same FBG sensors were used to measure the load parameters and the crack size agree very well with the results using standard technologies.

Dunlop Aerospace Braking Systems Plc. (DABS) is an international leading aircraft wheel and brake manufacturer. DABS had two wheel units, which were causing qualification problems in terms of fatigue cracking. Loughborough University (LU) proposed a novel robust non-contact, and non-destructive optical Shearographic Sensor System (SSS) for measuring and studying aircraft wheel deformation and behaviour when subjected to large static structural loading, with the aim to: i) Develop a novel robust optical sensor system for routine industrial use. ii) Demonstrate the novel and routine implementation for large scale structural loading/testing. iii) Identify high deformation concentration areas on aircraft wheel structures. iv) Provide routine quantitative data to DABS. v) Develop the novel understanding of error propagation, resolution and repeatability of the interferometer design. A series of laboratory experiments were conducted to demonstrate the functionality, repeatability, and reliability of the instrument to produce valid deformation data in a controlled environment in the optical metrology laboratory at LU. The SSS produced valid high quality deformation data using a Square Clamped Plate (SCP). The data was calibrated and correlated using a Linear Variable Differential Transducer (LVDT) system. The repeatability and reliability tests showed a high repeatability range of the SSS in the controlled environment of (5.95x10-8m) in the case of 10mm Horizontal lateral shear with Collimated laser illumination (10HC) and (1.22x10-7m) in the case of 10mm Vertical lateral shear with Collimated laser illumination (10VC). This accelerated the transfer of the SSS into the industrial environment at DABS, where heavy testing machineries operate routinely, which generated additional error and variation sources to the data produced by the SSS. A series of deflation/ inflation pressure and static structural load tests were completed on Boeing757 and BAe 146 wheel. The results showed that the data quality was sufficiently good to allow DABS to validate the FE model of the wheel, in spite of the surrounding uncontrolled and disturbing environment. Further repeatability and reliability tests were completed on the BAel46 wheel. This was to identify and discuss the engineering reality of the repeatability, reproducibility, and accuracy of the SSS, The results showed that the SSS achieved a better repeatability range in the laboratory in comparison to the industrial workplace at DABS, whichwas (1.60xl0-5m) and (1.08xl0-5m) forthe same shearing directions. As a result, DABS was provided with large amount of numerical data from the Boeing757 and the BAe142 wheels, in partial derivative and displacement format, ready for FE model validation. Commercial exploitation of the SSS into other industrial sectors and for various applications was completed via Laser Optical Engineering Ltd.

The research project presents a fundamental understanding of the fatigue crack growth mechanisms of AISI 420 martensitic stainless steel, based on the comparison analysis between the theoretical and numerical modelling, incorporating research findings under isothermal fatigue loading for solid cylindrical specimen and the theoretical modelling with the numerical simulation for tubular specimen when subjected to cyclic mechanical loading superimposed by cyclic thermal shock. The experimental part of this research programme studied the fatigue stress-life data for three types of surface conditions specimen and the isothermal stress-controlled fatigue testing at 300 °C - 600 °C temperature range. It is observed that the highest strength is obtained for the polished specimen, while the machined specimen shows lower strength, and the lowest strength is the notched specimen due to the high effect of the stress concentration. The material behaviour at room and high temperatures shows an initial hardening, followed by slow extension until fully plastic saturation then followed by crack initiation and growth eventually reaching the failure of the specimen, resulting from the dynamic strain ageing occurred from the transformation of austenitic microstructure to martensite and also, the nucleation of precipitation at grain boundaries and the incremental temperature increase the fatigue crack growth rate with stress intensity factor however, the crack growth rate at 600 °C test temperature is less than 500 &deg;C because of the creep-fatigue taking place. The theoretical modelling presents the crack growth analysis and stress and strain intensity factor approaches analysed in two case studies based on the addition of thermo-elastic-plastic stresses to the experimental fatigue applied loading. Case study one estimates the thermal stresses superimposed sinusoidal cyclic mechanical stress results in solid cylinder under isothermal fatigue simulation. Case study two estimates the transient thermal stresses superimposed on cyclic mechanical loading results in hollow cylinder under thermal shock in heating case and down shock cooling case. The combination of stress and strain intensity factor theoretical calculations with the experimental output recorded data shows a similar behaviour with increasing temperature, and there is a fair correlation between the profiles at the beginning and then divergence with increasing the crack length. The transient influence of high temperature in case two, giving a very high thermal shock stress as a heating or cooling effects, shifting up the combined stress, when applied a cyclic mechanical load in fraction of seconds, and the reputations of these shocks, causing a fast failure under high thermal shock stress superimposed with mechanical loading. Finally, the numerical modelling analyses three cases studied were solved due to the types of loading and types of specimen geometry by using finite element models constructed through the ANSYS Workbench version 13.0. The first case is a low cyclic fatigue case for a solid cylinder specimen simulated by applying a cyclic mechanical loading. The second is an isothermal fatigue case for solid cylinder specimen simulated by supplying different constant temperatures on the outer surface with cyclic mechanical loading, where the two cases are similar to the experimental tests and the third case, is a thermo-mechanical fatigue for a hollow cylinder model by simulating a thermal up-shock generated due to transient heating on the outer surface of the model or down shock cooling on the inner surface with the cyclic mechanical loading. The results show a good agreement with the experimental data in terms of alternative stress and life in the first case. In case two results show the strain intensity factor is increases with increasing temperature similar to the theoretical solution due to the influence of the modulus of elasticity and the difference in life estimation with the experimental output record is related to the input data made of theoretical physical properties and the experimental stress-life data.

The goal of structural reliability is to assure that a structure adequately performs its intended function when operating under specified environmental conditions. The major source of unreliability is the variability that characterizes engineering structures subjected to inherent randomness in material properties, loading and geometrical parameters. A sensible approach to structural reliability must be able to evaluate and control the effects of this variability, quantifying the uncertainties in the design variables and measuring their impact on the strength of the final product. The objective of this research is to assess the role that uncertainties in material microstructure, in particular concerning the presence of defects such as pores, inclusions and through-thickness cracks, have in the failure of engineering structures. For this purpose, a computational procedure, based on the coupled use of Finite Element Analysis and Monte Carlo simulation, is proposed to evaluate the failure probability of complex mechanical components containing random flaws. The proposed methodology is particularly suited for the structural design of ceramic components, whose strength properties are significantly affected by the presence of microstructural defects. Material flaws are modelled by a population of volume-embedded micro-cracks characterized by different geometrical features and size distributions. For each population the number of flaws is assumed to follow a homogenous Poisson process and flaws are sampled with a uniform spatial distribution and a random orientation. The interaction of a crack with the stress field produced in the component by the applied load is determined through a mixed-mode fracture criterion. Several solutions have been compared in this respect. The study conducted clearly shows how the application of a traditional deterministic approach may lead to incorrect conclusions. Due to the stochastic nature of the flaw distribution, failure of a component may not be initiated at the point of highest nominal stress. The whole component volume contributes to the total probability of failure and therefore the entire stress field must be considered. Moreover, the sensitivity analysis carried out indicates that the parameters controlling the failure process are strictly dependent on loading conditions. In particular, a significant difference in behaviour between uniform and non-uniform stress states was identified. A new failure criterion for brittle materials is also proposed. The criterion is based on the maximum admissible individual probability of failure and is applicable to biaxial stress conditions.

This thesis presents numerical and experimental research concerned with developing laboratory test specimens containing well-characterised residual stress fields. These specimens were then used to examine how residual stresses influenced fracture conditions. Three different materials were used in this work; an A508 ferritic steel, and two aluminium alloys, 2650 and 2024. Residual stresses were generated using a technique called local compression on both uncracked plates and cracked compact tension, C(T), specimens. Residual stresses introduced by single punching tools on the uncracked specimens were examined theoretically and numerically to benchmark further developments. Also residual stresses were measured using three techniques, deep-hole drilling (DHD), centre-hole drilling (ICHD) and synchrotron diffraction (HEXRD) and excellent agreement between measurement methods was obtained. A parametric study was carried out to determine the features of the residual stress field generated in cracked specimens. The position of single and double pairs of punching tools relative to the crack tip as well as the size of the punches were examined systematically. The numerical analyses revealed that positioning a single punching tool tangentially to the crack tip resulted in the generation of a tensile residual stress field ahead of a crack. Furthermore, double pairs of punching tools were shown to generate either tensile or compressive residual stresses normal to the crack plane depending on the relative position of the tools to the crack tip. The numerical findings were confirmed experimentally through HEXRD measurements and fracture tests. Local compression and prior overloading were applied to C(T) specimens to generate a residual stress field, either independently or in combination. It was found that tensile residual stresses reduced the apparent fracture toughness and that compressive residual stresses resulted in increased the fracture toughness. The shift in the apparent fracture toughness depended on the magnitude of the residual stresses and material, with the aluminium alloys being more susceptible to the presence of tensile residual stresses. A local approach based on the Beremin model was used to predict failure in the presence of residual stress fields in terms of fracture toughness for cleavage fracture in steel specimens. The overall trends from predictions were similar to the experiments, but there remain limitations in the model. For aluminium specimens, a method based on the William's series was employed to predict the stress intensity corresponding to a residual stress field (Kres). The measured changes in initiation toughness matched the predicted values of K1es.

The thesis reviews and studies current evaluation mechanisms, techniques and machines for testing rolling contact fatigue failure resistance and load capacity of coated components. The thesis investigates both normal and accelerated rolling contact fatigue evaluation test mechanisms and their models, and evaluation test technique principles suitable to the appraisal of coated bearing components. A major contribution of the thesis is the design and development of a new rolling contact fatigue evaluation test machine for coated components. Tests of the rolling contact fatigue of coated bearing raceways under the oil lubricant, grease lubricant and no lubricant conditions, applying the new rolling contact fatigue evaluation mechanisms, evaluation technique principles and the new test machine, have been performed. The accelerated rolling contact fatigue tests of the coated bearing raceways use SiC powder in the oil lubricant. The new rolling contact fatigue test machine has been found suitable for evaluating the rolling contact fatigue resistance of components with superhard coatings. The accelerated rolling contact fatigue test method has been shown to give comparable rolling contact fatigue test results to those obtained in a normal rolling contact fatigue test, while being much faster. In the fatigue test, the cyclic maximum shear stress produces an initial fatigue crack near the substrate surface of the test bearing raceways. The observed phenomena are consistent with theory, although the location of the initial crack is much closer to the surface than would be predicted by a 'static' Hertzian analysis. Insufficient traction forces on the contact surface between the rolling elements of a test coated bearing makes gross skidding occur, leading to rapid wear, over-heating and final failure of the test coated bearing. The LSO fatigue life of the test coated bearing raceway tends to decrease with increase of the coating thickness and coating hardness of the test coated bearing raceway.

Margins in defect assessment procedures such as BS 7910 and R6/4 have been examined for cleavage and ductile tearing from complex and re-characterised defects. A range of crack profiles with re-entrant sectors developed from two co-planar surface breaking defects by fatigue has been examined experimentally and numerically. Both studies show enhanced crack driving forces in the re-entrant sector combined with a loss of crack tip constraint. Cleavage failures from complex and re-characterised defects demonstrated that the re-characterisation procedure is not conservative when cleavage occurs at small fractions of the limit load. Failures close to the limit load benefit from constraint loss which counteract the amplified crack driving forces in re-entrant sectors and cause re-characterised defects to be more detrimental than the original complex defects. Benefit may be taken from statistical size effects, which are strongly dependent on the crack geometry. Experimental fatigue and ductile tearing studies show similar development of complex cracks towards the re-characterised shape and re-characterisation procedures, such as those given in BS 7910 and R6/4, are conservative for fatigue and ductile tearing. A procedure has been developed to quantify enhanced temperature margins due to constraint loss by comparing the self similar stress fields at a critical local fracture stress (the Ritchie-Knott-Rice approach) and through the Weibull stress. Agreement with the experimental data has been demonstrated and the temperature dependence of the material parameters has been discussed. Following Li (1997) and Karstensen (1996), a toughness mapping technique was discussed that allows mode I toughness to be translated into mixed-mode I+II toughness for stress controlled fracture. In support of the arguments, toughness of Mode I and mixed-mode I+II configurations was measured on a mild steel. The experimental data clearly show increased cleavage toughness for unconstrained mode I and mixed-mode fields and the correlation with the predictions from the numerical models was demonstrated.

Orientador : Francisco Carlos Serbena / Co-orientador : Carlos Maurício Lepienski / Dissertaçao (mestrado) - Universidade Federal do Paraná