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In this dissertation the work done in the projects KME-410/502 will be presented.The overall objective in these projects is to evaluate and develop tools for designingagainst fatigue in single-crystal nickel-base superalloys in gas turbines. Experimentshave been done on single-crystal nickel-base superalloy specimens in order toinvestigate the mechanical and fatigue behaviour of the material. The constitutivebehaviour has been modelled and veried by FE-simulations of the experiments.Furthermore, the microstructural degradation during long-time ageing has been investigatedwith respect to the material's yield limit. The eect has been includedin the constitutive model by lowering the resulting yield limit. Moreover, the fatiguecrack initiation of a component has been analysed and modelled by using acritical plane approach in combination with a critical distance method. Finally, asan application, the derived single-crystal model was applied to all the individualgrains in a coarse grained specimen to predict the dispersion in fatigue crack initiationlife depending on random grain distributions. This thesis is divided into three parts. In the rst part the theoretical framework,based upon continuum mechanics, crystal plasticity, the critical plane approachand the critical distance method, is derived. This framework is then used in thesecond part, which consists of six included papers. Finally, in the third part, detailsof the used numerical procedures are presented.

AA6061 Al alloys modified with addition of Mn, Cr and Cu were homogenized at temperatures between 350 ºC and 550 ºC after casting. STEM experiments revealed that the formation of α-Al(MnFeCr)Si dispersoids during homogenization were strongly affected by various factors such as heating rate, concentration of Mn, low temperature pre-nucleation treatment and homogenization temperature. Through analysis of the STEM results using an image software Image-Pro, the size distributions and number densities of the dispersoids formed during different annealing treatments were quantitatively measured. It was revealed that increasing the heating rate or homogenization temperature led to a reduction of the number density and an increase in size of the dispersoids. The number density of dispersoids could be markedly increased through a low temperature pre-nucleation treatment. A higher Mn level resulted in the larger number density, equivalent size and length/width ratio of the dispersoids in the alloy. Upsetting tests on two of these Mn and Cr-containing AA6061 (Al-Mg-Si-Cu) Al alloys with distinctive Mn contents were carried out at a speed of 15 mm s-1 under upsetting temperature of 450 ºC after casting and subsequent homogenization heat treatment using a 300-Tone hydraulic press. STEM experiments revealed that the finely distributed α-Al(MnFeCr)Si dispersoids formed during homogenization showed a strong pinning effect on dislocations and grain boundaries, which could effectively inhibit recovery and recrystallization during hot deformation in the two alloys. The fractions of recrystallization after hot deformation and following solution heat treatment were measured in the two alloys with EBSD. It was found that the recrystallization fractions of the two alloys were less than 30%. This implied that the finely distributed α-dispersoids were rather stable against coarsening and they stabilized the microstructure by inhibiting recovery and recrystallization by pinning dislocations during deformation and annealing at elevated temperatures. By increasing the content of Mn, the effect of retardation on recrystallization were further enhanced due to the formation of higher number density of the dispersoids. STEM and 3-D atom probe tomography experiments revealed that α-Al(MnFeCr)Si dispersoids were formed upon dissolution of lathe-shaped Q-AlMgSiCu phase during homogenization of the modified AA6061 Al alloy. It was, for the first time, observed that Mn segregated at the Q-phase/matrix interfaces in Mn-rich regions in the early stage of homogenization, triggering the transformation of Q-phase into strings of Mn-rich dispersoids afterwards. Meanwhile, in Mn-depleted regions the Q-phase remained unchanged without segregation of Mn at the Q-phase/matrix interfaces. Upon completion of α-phase transformation, the atomic ratio of Mn and Si was found to be 1:1 in the α-phase. The strengthening mechanisms in the alloy were also quantitatively interpreted, based on the measurements of chemical compositions, dispersoids density and size, alloy hardness and resistivity as a function of the annealing temperature. This study clarified the previous confusion about the formation mechanism of α-dispersoids in 6xxx series Al alloys. Four-point bend fatigue tests on two modified AA6061 Al alloys with different Si contents (0.80 and 1.24 wt%, respectively) were carried out at room temperature, f = 20 Hz, R = 0.1, and in ambient air. The stress-number of cycles to failure (S-N) curves of the two alloys were characterized. The alloys were solution heat treated, quenched in water, and peak aged. Optical microscopy and scanning electron microscopy were employed to capture a detailed view of the fatigue crack initiation behaviors of the alloys. Fatigue limits of the two alloys with the Si contents of 0.80 and 1.24 wt% were measured to be approximately 224 and 283.5 MPa, respectively. The number of cracks found on surface was very small (1~3) and barely increased with the applied stress, when the applied stress was below the yield strength. However, it was increased sharply with increase of the applied stress to approximately the ultimate tensile strength. Fatigue crack initiation was predominantly associated with the micro-pores in the alloys. SEM examination of the fracture surfaces of the fatigued samples showed that the crack initiation pores were always aspheric in shape with the larger dimension in depth from the sample surface. These tunnel-shaped pores might be formed along grain boundaries during solidification or due to overheating of the Si-containing particles during homogenization. A quantitative model, which took into account the 3-D effects of pores on the local stress/strain fields in surface, was applied to quantification of the fatigue crack population in a modified AA6061 Al alloy under cyclic loading. The pores used in the model were spherical in shape, for simplicity, with the same size of 7 μm in diameter. The total volume fraction of the pores in the model were same as the area fraction of the pores measured experimentally in the alloy. The stress and strain fields around each pore near the randomly selected surface in a reconstructed digital pore structure of the alloy were quantified as a function of pore position in depth from the surface using a 3-D finite element model under different stress levels. A micro-scale Manson-Coffin equation was used to estimate the fatigue crack incubation life at each of the pores in the surface and subsurface. The population of fatigue cracks initiated at an applied cyclic loading could be subsequently quantified. The simulated results were consistent with those experimentally measured, when the applied maximum cyclic stress was below the yield strength, but the model could not capture the sudden increase in crack population at UTS, as observed in the alloy. This discrepancy in crack population was likely to be due to the use of the spherical pores in the model, as these simplified pores could not show the effects of pore shape and their orientations on crack initiation at the pores near surface. Although it is presently very time-consuming to calculate the crack population as a function of pore size and shape in the alloy with the current model, it would still be desirable to incorporate the effects of shape and orientation of the tunnel-shaped pores into the model, in the future, in order to simulate the fatigue crack initiation more accurately in the alloy.

The main goal of this diploma thesis is the examination of the influence of structure directionality on fatigue properties of formed aluminium alloy 6082/T6. The main attention is focused on the study of the influence of structure directionality on kinetics of short fatigue cracks growth. The measurement of short fatigue cracks growth was performed on cylindrical samples. The samples were made in two different directions; one parallel with the forming direction and second perpendicular to the forming direction. Servo hydraulic machine MTS 880 was used for the cyclic loading. The samples were cycled at two different constant stress amplitudes. Cyclic loading was systematically interrupted in order to measure the length of short cracks by a light microscope. Tensile tests, measuring of cycling hardening-softening curves, observation of microstructure, observation of surface relief, measuring of microhardness and fractographical analysis of fracture surfaces were used for further examination of the influence of the structure directionality. Some of these measured characteristics did not show any influence of the structure directionality (microhardness, fatigue life curve, Young modulus). In other cases is this influence measurable, however insignificant (yield stress, ultimate stress, cyclic hardening-softening curves and kinetics of short fatigue cracks growth). It can be summarised that the material, though the directionality of its microstructure is apparent, shows relatively isotropic mechanical behaviour.

This work deals with fatigue properties and stability of microstructure of ultrafine-grained (UFG) copper prepared by severe plastic deformation by means of equal channel angular pressing (ECAP) method. The effect of different fatigue loading regimes and thermal exposition on microstructural changes was investigated and the fatigue lifetime curves were experimentally determined. The research attention was focussed on localization of cyclic plastic deformation and fatigue crack initiation in UFG structure. Experimental results indicate that after stress-controlled fatigue loading (both symmetrical and asymmetrical) the microstructure remains ultrafine; no grain coarsening was observed. Contrary to this, strain-controlled fatigue loading results in formation of bimodal structure. Grain coarsening was observed also after thermal exposition at 250 °C for 30 minutes. Annealing at lower temperatures does not result in grain coarsening or development of bimodal structure. Fatigue loading results in development of surface relief in form of cyclic slip markings. Their density, distribution and shape differ for particular fatigue loading regimes. Differences in crack initiation mechanism in low- and high-cycle fatigue region were found. Nevertheless, the characteristic feature for all loading regimes was stability of UFG microstructure in the region of cyclic slip bands and fatigue cracks.

[pt] A grande maioria das estruturas que trabalham sob cargas alternadas precisa ser dimensionada para evitar a iniciação de trincas por fadiga, o principal mecanismo de dano mecânico nesses casos. Os vários parâmetros dos modelos de previsão de dano à fadiga usados nesses projetos devem ser preferencialmente medidos a partir do ajuste otimizado de suas equações a dados experimentais medidos de forma adequada. Na realidade, a precisão das previsões baseadas nesses modelos depende diretamente da qualidade dos ajustes utilizados para obtenção desses parâmetros. Sendo assim, o objetivo principal deste trabalho é estudar a melhor maneira de se obter os parâmetros dos principais modelos de previsão da iniciação de trincas por fadiga através de ajustes de dados experimentais baseados no algoritmo de LevenbergMarquardt. Primeiro, foram realizados diversos ensaios εN em uma liga de alumínio 6351-T6 para averiguar o desempenho do ajuste proposto para asequações de Coffin-Manson e de Ramberg-Osgood. Em seguida, foram usados dados da literatura de outros oito materiais para ajustar modelos deformaçãovida clássicos, assim como com o expoente de Walker, para assim avaliar o efeito de cargas médias não-nulas em testes εN. Por fim, foi estudado o ajuste de um modelo SN com expoente de Walker que considera limites de fadiga e efeitos de carga média. Esse estudo também inclui considerações estatísticas para quantificar o fator de confiabilidade a partir de diferentes hipóteses de funções densidade de probabilidade, baseadas em dez conjuntos de dados da literatura. / [en] Most structures working under alternate loadings must be dimensioned to prevent fatigue crack initiation, the main mechanism of mechanical damage in these cases. The various parameters from the fatigue damage prediction models used in these projects should preferably be measured by optimally fitting their equations to well-measured experimental data. In fact, the accuracy of the predictions based on these models depends directly on the quality of the adjustments used to obtain these parameters. As a result, the main purpose of this work is to study the best way to obtain the parameters of the leading prediction models of fatigue crack initiation through experimental data fittings based on the Levenberg-Marquardt algorithm. First, several εN tests were performed on a 6351-T6 aluminum alloy to verify the performance of the proposed fit for the Coffin-Manson and Ramberg-Osgood equations. Then, data from the literature of eight other materials were used to fit classic strainlife models, as well as models based on the Walker exponent, to evaluate the effect of non-zero mean loads in εN tests. Finally, the fitting of an SN model including the Walker exponent was studied, which considers fatigue limits and mean load effects. This study includes as well statistical considerations to quantify the reliability factor from different probability density function assumptions, based on ten data sets from the literature.

Fretting fatigue is a damage process that may arise in engineering applications where small cyclic relative displacements develop inside contacts leading to detrimental effects on the material fatigue properties. Fretting is located in regions not easily accessible, which makes it a dangerous phenomenon. It is therefore important to be able to make reliable predictions of the fretting fatigue lives. The work presented in this thesis has its focus on different aspects related to fretting fatigue in the titanium alloy Ti-17. A fretting experiment was developed which allowed for separate control of the three main fretting loads. Initially, the evolution of the coefficient of friction inside the slip region was investigated experimentally and analytically. Subsequently, 28 fretting tests were performed in which large fatigue cracks developed. The fretting tests were firstly evaluated with respect to fatigue crack initiation through five multiaxial fatigue criteria. The criteria predicted a too high fretting fatigue limit. A possible clue to the discrepancy was found in the fretting induced surface roughness with the asperity-pit interactions. The fatigue growth of the large fretting cracks was numerically modelled through a parametric crack growth procedure. The predicted lives were compared to the experimental outcome. The numerical simulations showed that linear elastic fracture mechanics was an appropriate tool for the prediction of fretting fatigue propagation lives in the long crack regime. Fatigue cracks spend most of their propagation life in the small crack regime. The possibility of modelling the small crack behaviour is therefore very important from the engineering point of view. The fatigue growth of through thickness short cracks was studied experimentally and numerically in the four-point bend configuration. It was found that linear elastic fracture mechanics and closure-free material growth data furnished conservative estimates for cracks longer than 50 μm. One method to improve fretting fatigue life is to shot peen the contact surfaces. Experimental results on fretting life with or without shot peening were simulated. The fatigue life enhancement in shot peened specimens could be explained by slower crack growth in the surface material layer with residual compressive stresses. / QC 20100827

L’amélioration des performances spécifiques des alliages métalliques de l’aéronautique est une démarche constante. Les alliages de titane sont des matériaux privilégiés par les constructeurs aéronautiques car ils allient hautes propriétés mécaniques et faible densité.Parmi ces matériaux, les alliages β-métastables qui ont pour particularité de retenir jusqu’à 40% de phase β connaissent un fort regain d’intérêt pour les motoristes (Ti-17) comme pour des applications de structure type trains d’atterrissage (Ti-5553 et Ti-10-2-3). Ce travail a pour but d’analyser le comportement mécanique et la durabilité de ces alliages soumis à des sollicitations monotones et cycliques en lien avec les microstructures.Des essais mécaniques ont pour cela été développés à partir de différentes microstructures métallurgiques qu’elles soient issues d’un traitement industriel ou spécifique visant à simplifier ces dernières. Les mécanismes de déformation (systèmes de glissement) et d’endommagement (amorçage de fissures) ont été identifiés et analysés à différentes échelles par microcopie optique et électronique à balayage en intégrant les notions d’orientation cristallographique (EBSD). Le recours à des essais réalisés in situ sous microscope (optique et MEB) et à une métrologie adaptée aux échelles pertinentes a permis d’identifier les éléments micro-structuraux clés et les cinétiques de développement de ces processus. Un des faits marquants est le rôle majeur de l’anisotropie de propriétés mécaniques de la phase β qui a également fait l’objet de simulations numériques. / The improvement of specific performances of metallic materials used for aerospaceapplications needs continuous researches and developments. Titanium alloys are materials ofchoice for aerospace companies thanks to their high mechanical properties and low density.Among them, the β-metastable alloys that retain up to 40% of β phase are more and moreintroduced in aircraft engines (Ti-17) and for structural parts (e.g. landing gears in Ti-5553and Ti-10-2-3).This work aims to analyse the mechanical behaviour and durability of these alloyssubmitted to monotonic or cyclic loadings. Mechanical tests have been developed on differentindustrial microstructures as on academic simplified ones produced by specific thermaltreatments. Deformation mechanisms (slip systems) and damage processes (cracks initiation)were identified and analyzed at different scales using microscopes (optical and SEM) andcrystallographic features were studied by EBSD. Specific in situ tests performed undermicroscopes (optical and SEM) and digital images correlation techniques at scales of interesthave permitted to identify and to quantify the key microstructural parameters and the kineticsof these processes. One major result concerns the influence of the anisotropy of mechanicalproperties associated to the β phase.

<p>There has been a long-standing need in the marketplace for the economic production of small lots of components that have complex geometry. A potential solution is additive manufacturing (AM). AM is a manufacturing process that adds material bottom-up. It has the distinct advantages of low preparation cost and high geometric creation capability. Components fabricated via AM are now being selectively used for less-demanding applications in motor vehicles, consumer products, medical products, aerospace devices, and even some military projects.</p><p><br></p> <p>For engineering applications, high value-added components require consistency in the fatigue properties. However, components fabricated by AM have large variation in the fatigue properties compared to those by conventional manufacturing processes. To alleviate unpredictable catastrophic failures of components, it is essential to study and predict fatigue life. Previous study reported that fatigue crack initiation process accounts for a large portion of fatigue life, especially for low loading amplitude and high cycle fatigue. However, this major portion of fatigue life prediction is mostly ignored by main stream researchers working on fatigue modeling. For industrial applications, engineers often specify a lower stress condition to obtain a higher safety factor. Under these circumstances, fatigue crack initiation becomes even more important, so it is essential to further study of crack initiation.</p><p><br></p> <p>The objective of this research is to develop a fatigue crack initiation model for metal components produced by AM. To improve life prediction accuracy, the model must incorporate the effect of different microstructures, which are typically produced by AM due to a large number of repetitive cycles of re-heating and re-cooling processes. To fulfill this objective, the tasks are separated into three studies: (1) developing a temperature model to simulate temperature history, (2) modeling the component’s microstructure for the potential crack initiation zone, and (3) developing a fatigue crack initiation model for life estimation. A summary of each task is provided in the following.</p> <p>First, the role of temperature model is to understand the mechanism that leads to the variation of microstructures. The existing temperature models are computationally expensive to obtain an accurate prediction of the temperature history due to repetitive heating and cooling. The main reason is that these models considered entire boundary conditions of all the material points. In this section, we proposed and employed the concept of effective computation zone, which can save the computational time significantly for AM process. </p><p><br></p> <p>Second, it is critical to include the effect of microstructure in the fatigue life model since the microstructure variation at different locations within the real AM component is large. The grain size variation is modeled by using representative volume element, which is defined as a volume of heterogeneous material that is sufficiently large to be statistically representative of the real component’s microstructure. Regarding phase transformation, a continuous cooling transformation (CCT) diagram is a useful tool that can be used with a thermal model for microstructure design and manufacturing process control. However, traditional CCT diagrams are developed based on slow and monotonic cooling processes such as furnace cooling and air cooling, which are greatly different from the repetitive heating and cooling processes in AM. In this study, a new general methodology is presented to create CCT diagrams for materials fabricated by AM. We showed that the effect of the segmented duration within the critical temperature range, which induced precipitate formation, could be cumulative. </p><p><br></p> <p>Third, the existing fatigue crack initiation life model has poor accuracy. One of the reasons for the poor accuracy is the coefficients change due to the variation in microstructure is not accounted for. In this section, a semi-empirical fatigue crack initiation model is presented. The important coefficients include maximum persistent slipband width, energy efficiency coefficient, resolved shear stress and plastic slip rate per cycle. These coefficients are modeled and determined as a function of microstructure, which can improve the accuracy of life estimation.</p><p><br></p> <p>The contribution of this study is to provide a new engineering tool for designing the melting AM process based on scientific research. With this tool, the fundamental mechanism contributing to a large variation of the fatigue life of the metal components made by AM process can be understood, attributed, predicted and improved. The seemly ‘stochastic’ nature of fatigue life of the AM components can be changed to be more deterministic and predictable. This approach represents a major advance in fatigue research on AM materials. The model developed is considered as a tool for research, design, and control for laser-based AM process applications. </p>