Problem Little research has taken place to investigate fretting fatigue under conditions of variable amplitude loading (VAL) and no research using a complex loading spectra representative of reality. The effect of cycles below the endurance limit has yet to be established for fretting fatigue within such a spectrum. These cycles are of particular concern owing to the large number of these cycles present in comparison to other cycles within the spectrum. Any effects of VAL on local conditions within the contact had also yet to be established. Solution This project attacked the problem of fretting fatigue under conditions of VAL on two fronts. Firstly a vigorous VAL testing program (reconstructed from in-service data) was employed to investigate the effect of VAL on life and damage in general. The relative importance of cycles within the spectrum, particularly those below the endurance limit, with regards to life was investigated. Secondly to establish the effect of VAL within the contact region finite element modelling (FEM) was performed. Single and three level loading histories were applied to the model in order to establish the effect of VAL locally within the contact and offer explanations to the experimental observations. A series of damage prediction parameters including Ruiz and strain life initiation parameters were assessed for their ability to predict such behaviour. A methodology for predicting fretting fatigue life and damage has also been developed during this project. Two contact geometries were tested: a cylindrical Hertzian contact and the rounded punch contact. Conclusions Cycles of amplitude below the constant amplitude fretting fatigue endurance limit are nondamaging within a VAL spectrum. This was primarily attributed to the cycles below the endurance limit having a unique location of damage that other cycles do not influence. More sites of crack initiation were observed in samples that had experienced VAL than those tested under conditions of constant amplitude loading (CAL). The multiple sites of initiation were attributed to the point of maximum damage changing location during VAL. The size of the slip region of a cycle was found to decrease post overload as was the magnitude of Ruiz predicted damage. Strain life parameters also predicted a beneficial effect of an overload on the predicted lives of following CAL cycles. Miner predictions of life were conservative due to the assumptions made by the parameter. Miner sums damage over the entire contact region, essentially attributing that damage to a single location. Miner therefore does not take into account the changing location of maximum damage and the effects of load order and interaction. An alternative methodology for predicting fretting fatigue life during VAL has been presented that has been shown to be more accurate than traditional Miner and can account for unique features within the VAL spectrum e.g. training flights. Both Miner and the VAL methodology have shown that it is the small amplitude cycles within a spectrum that are the most damaging.

A new set of numerical methods for predictive modelling of quasistatic and dynamic crack propagation in brittle materials for aerospace applications based upon the Symmetric Interior Penalty Galerkin Method (SIPG) and the Nonsymmetric Interior Penalty Galerkin Method (NIPG) is proposed. This new approach to solving problems in Computational Fracture Mechanics belongs to the family of Discontinuous Galerkin Finite Element Meth- ods (DGFEMs) and draws on the qualities of both the classical Finite Element Methods (FEMs) and Finite Volume Methods (FVMs) in order to overcome the shortcomings and limitations which both methods exhibit when trying to address the transition from contin- uum to discontinuum during material fracture. This thesis focuses mainly on the numerical linear algebra aspects associated with the two above DGFEM methods when applied to crack propagation problems. A new precondi- tioning technique for the iterative solution of linear systems of equations is introduced and its qualities are presented by means of numerical examples. A coupling technique with pre- conditioners for conforming approximations is also introduced. Several improvements and extensions to the original technique are presented to make crack propagation simulations with the SIPG viable. Results for both quasistatic and dynamic fracture propagation are presented. Practical aspects ofthe implementation are also discussed, revealing the important issues that still have to be addressed and that constitute paths for further research.

This study aims to understand the mechanism of elastomer abrasion using Finite Element Analysis (FEA) techniques. A blade abrasion device is used to create the abrasion patterns. The initiation of the abrasion patterns is investigated by observing how the cracks develop on the moulded flat elastomer surface. At first, cracks initiate at the location of the maximum tensile stress, yielding a crack growth angle of between 30o~50° with the elastomer surface. The angle being greater as the normal load applied on the blade is increased. The crack growth angle reduces as the crack increases in length. It passes through several steps, each with a reduced crack growth angle and eventually reaches a much smaller angle generally observed at the steady state of abrasion. This initial crack growth process is predicted well by the FEA simulation. Both the experimental and the computed results suggest that the initial cracks in elastomer abrasion originate from micro-vibrations generated during the slip phase of stick-slip motion. This stick-slip motion is regularly encountered during the frictional contact between a soft elastomer and hard abrader. The propagation of the abrasion patterns after reaching steady state is also investigated using a blade abrasion device. The second part of this investigation examines the effect of the normal and frictional forces on the rate and direction of crack growth during the abrasion process. Comparison is drawn between the rates of material loss as measured experimentally under a range of test conditions and the predictions calculated using a fracture mechanics based FEA. For the first time here it is shown that an explicit dynamic FEA model can be used to reliably predict the stored energy release rate in a complicated large strain contact model. A series of different finite element models were developed to investigate the tearing processes at a specific asperity under each revolution or pass of the abrasion blade. These models predict for SBR materials the rate of the resulting tearing processes well.

Fatigue crack growth (FCG) is a major cause of failure in many engineering components and structures that are subjected to dynamic loading conditions. Several models have been proposed for estimating crack growth rate da/dN under various conditions. The majority of work reported has focused on constant amplitude (CA) loading and some for variable amplitude (VA) loading. The estimation of da/dN under VA loading is complex due to effects of several factors such as plasticity, crack tip blunting, residual stresses, crack tip closure and crack tip branching which are associated with different levels of loading. These factors which cause acceleration or deceleration of the crack growth are known as interaction effects. Crack closure has been identified to be one of the main interaction factors, and finite element (FE) models have been developed to quantify it in terms of crack opening stresses. There are however still a number of issues regarding the modelling parameters such as mesh size, element type, number of loading increments and material hardening models that should be used and on whether crack closure represents the interaction effects sufficiently. Also modelling long crack lengths has been perceived to be too computationally intensive and therefore studies focus on short crack lengths only.

Fatigue is one of the main failure mechanisms in engineering. Mechanical surface treatments are being widely used to reduce the incidence of fatigue failures. A new surface treatment, laser shock peening, or laser peening (LP) is being widely studied especialJy in the aerospace industry. LP-induced beneficial residual stresses (RS) act against structural loads leading to an increase in fatigue resistance. Therefore, one of the main parameters determining the fatigue life improvement after LP is the RS fields. Hence, it is crucial that the RS measurement and optimization is carried to obtain the most prolonged fatigue life after LP. RS after LP were obtained by incremental hole drilling, surface X-ray diffraction, synchrotron X-ray diffraction and neutron diffraction. The contour method of stress measurement was developed for thin samples and near-surface measurements in thick samples. Near-surface RS as well as RS in thin plates after LP, which are very challenging to obtain in a reliable manner due to geometrical and material constraints, were measured by at least two different methods to increase the confidence in the results. The possibility of application of LP to thin sections was investigated in this dissertation. After examining different LP parameters and systems, a beneficial RS field after LP was obtained. RS measurements and fatigue tests by Cranfield University, UK, suggest that LP can be applied to thin plates to have a significant increase in fatigue resistance as long as LP parameters are chosen appropriately. RS measurements were also conducted for thick samples after LP. RS results with fatigue tests conducted by EADS lW, Germany, confirm the increase in fatigue performance. Increase in surface roughness and geometrical distortion after LP were also observed for both thin and thick aluminium alloy samples after LP.

This thesis concerns primarily the residual stress characterisation in fastener holes cold worked by a novel StressWave process, and the prediction of the fatigue crack growth under the influence of such residual stress. Aerospace 2024-T351 aluminium alloy plate of 6.35mm thickness containing a nominal 06.35mm hole was used. Using neutron and laboratory X-ray diffraction measurements, a large compressive residual stress was found in StressWave and split-sleeve cold-worked holes. Detailed stress mapping indicates that a StressWave hole contains a highly symmetric residual stress field with a wider compression region. Conversely, the spht-sleeve technique generates a complex asymmetric stress variation through the specimen thickness and around the hole. Independently, a comprehensive finite element study was conducted to reveal the residual stess development associated with two distinct cold-working techniques at various stages. Favourable agreement was achieved between the experiment and simulations. The deformation mechanism associated with the cold-working process is decisive to the behaviour of the residual stress field created. The symmetric crack growth behaviour observed-in StressWave specimens permits a through-thickness crack geometry to be considered. Accordingly, Green's functions for a single crack and two symmetric cracks originating from the edge of a circular hole were developed. These solutions were verified using weight function and finite element analysis and are therefore appropriate for subsequent study of fatigue crack growth. A theoretical framework was proposed to explicate the interaction of residual stress with the superimposed loading at the crack tip, which was mathematically expounded as a function of stress intensity factor and stress ratio. This analytical framework provides a reasonable correlation between the mean stress and crack closure criteria.

Thermoelastic Stress Analysis (TSA) is a well established technique for studying stress fields around a crack tip. Recent work utilised the observation that individual isopachics (contours of constant stress) around a crack tip appeared to take the form of a cardioid. Various computational approaches were successfully used to estimate stress intensity factors using the first order Westergaard equations. Whilst this worked well for mode I cracks, there was less success when applying the equation to mixed mode situations; it appeared as though a pure cardioid form was not an appropriate description of the isopachics for mixed mode cracks. The work carried out in this thesis concentrates on (i) developing an algorithm that is able to accurately estimate crack tip parameters from thermoelastic data using the Williams expansion and (ii) evaluating the effectiveness of the approach using simulated fields. In the first part of the study it is shown that the higher order terms in the Williams expansion are responsible for creating the rotation of the isopachics noted in previous work. One of the higher order terms in the expansion is the T-stress which is thought to be responsible for controlling the stability of crack growth. A differential evolution is used to estimate the parameters of the Williams expansion and fit the parameters to thermoelastic data. This would allow the calculation of the stress intensity factors and T-stress for the crack, as well as estimate the crack tip position. Both mode I and mixed mode plates are used in an effort to accurately calculate the crack tip parameters. It is shown from both experimental results and simulations that using DE to fit the Williams expansion directly to thermoelastic data is technique that requires further work and investigations. Although the crack tip can be accurately located, the stress intensity factors and T-stress estimations are consistently inaccurate. It is also shown that the results of the parameters are dependent upon the size of the data array used. The T-stress is never accurately estimated and the results for the stress intensity factors are inconsistent. However, the shortcomings of the DE algorithm are highlighted, and possibilities to remedy the problems are suggested.

This thesis describes an approach to fracture analysis combining composition measurements, fractographic observations and geometrical model predictions for a ferritic model material.

The present study is devoted to solution of the 3-D elastodynamic problem of a cracked material with the focus on the effect of the cracks’ closure. The detailed procedure for deriving the system of boundary integral equations for displacements and tractions is presented. Full expressions of the integral kernels evaluated by the consecutive differentiation of the Green’s displacement tensor are given in the current work. Due to the contact that takes place between the opposite faces of the crack under the applied harmonic loading, the resulting process is not a harmonic, but a steady-state periodic one. As a result, components of the stress-strain state are expanded into exponential Fourier series. The system of boundary integral equations is solved numerically with the use of an iterative procedure. The solution is refined during the iteration process until the distribution of physical values satisfies the contact constraints. The hyper-singular integrals are treated in the sense of the Hadamard finite part. The distributions of the contact forces and displacement discontinuities at the cracks’ surface are investigated. The stress intensity factors are obtained and analyzed for different values of the wave frequency and crack configuration. Influence of the material properties and numerical parameters on the solution is studied and the possible relations are found. The significance of taking the effect of the cracks’ closure into account was shown. The difference between the results obtained for the case of accounting for cracks’ closure and neglecting it is not only qualitative but also quantitative and can reach more than 100% for two closely located in-plane cracks. Finally, the main results are summarised. It is shown that accounting for the crack closure is vital for the correct assessment of the stress strain state in the vicinity of the crack front. Moreover, a set of recommendations regarding future work are given.

Fatigue resistance by crack bridging in pre-cracked Ti-6Al-4V/SCS-6 composites has been investigated experimentally using in-situ synchrotron X-ray microtomography and diffraction strain mapping techniques. Measurements were performed at room temperature and, in the ter case, at elevated temperatures. This was carried out using qualitative observation of the crack growth morphology and quantitative measurements of the ply-by-ply fibre and matrix strain distributions in the vicinity of the crack, both as a function of crack growth and distance from the crack plane. Qualitative tomographic observations showed that the crack front bowed out between fibres and eventually reconnected further downstream. This led to some matrix bridging the crack even when the crack front was some way past a given fibre and to a more tortuous non-planar crack path, both of which could increase the fatigue resistance. The rate of crack growth slowed somewhat near the fibres, but the magnitude of crack opening displacements was relatively insensitive to the actual locations of the fibres. This was associated with the crack bridging traction being applied by each fibre extending over a large interfacial sliding distance of the order of 0.8-1 mm from the crack plane. The effectiveness of crack bridging was demonstrated through the reduction of more than 70% of the nominally applied stress intensity factor at the crack tip.