Fatigue, or failure of material due to repeated cyclic loading, is one of the most common causes of mechanical failures. The risk of fatigue in a load carrying component is often lowered by adding material, thereby reducing stresses. This increases the component weight, reducing the performance of the component and increasing its manufacturing cost. There is thus a need to design components to be as light as possible, while keeping the risk of fatigue at a low enough level, i.e. there is a need for optimization of the component subject to fatigue constraints.  This thesis deals with design against fatigue using topology optimization, which is a form of structural optimization where an optimal design is sought by using mathematical programming to decide which parts of a design domain should be filled with material, and which should not.  To predict fatigue, accurate representation of the geometry and accurate stress computation are of utmost importance. In this thesis, methods for imposing constraints such as minimum inner radii and minimum member sizes in the form of four new density filters are proposed. The filters are able to generate a very sharp representation of the structural boundary. A method for improving the accuracy of stress results at the structural boundary is also proposed, based on extrapolation of results from the interior of the structure. The method gives more accurate stresses, which affects the resulting structures when solving optimization problems.  A formulation for fatigue constraints in topology optimization is proposed, based on the weakest link integral. The formulation avoids the problem of choosing between accurate but costly local constraints, and efficient but approximate aggregated constraints, and gives a theoretical motivation for using expressions similar to the p-norm of stresses.  For verifying calculations of the fatigue probability of an optimized structure, critical plane criteria are commonly used. A new method for evaluating such criteria using optimization methods is proposed, and is proved to give results within a user given error tolerance. It is shown that compared to existing brute force methods, the proposed method evaluates significantly fewer planes in the search of the critical one. / <p>QC 20150504</p>

High cycle fatigue tests were carried out on a medium strength continuous casting AA 5754 Al alloy, and new generation high strength AA 2026 and AA 2099 Al alloys. The effect of texture on fatigue properties and short crack behavior were studied. The strengthening mechanisms were also thoroughly investigated for the two high strength alloys.Texture played an important role in the anisotropy of fatigue strength for the AA 5754 Al alloy. Being a solution strengthened alloy, it had a fatigue strength of 120% σy. High strength Al alloys had a strong tendency for planar slip due to the high density of coherent and shearable precipitates in the alloys. Texture was a key factor controlling the crack initiation and propagation. The crack path and the possible minimum twist angles were measured using EBSD and calculated theoretically by a crystallographic model. Based on the micro-texture measured by EBSD, the crack paths were predicted for the AA 2099 alloy and confirmed by the observed values.The excellent balance of superior fatigue properties and high tensile strength of AA 2026 and AA 2099 was attributed to the reduced population of Fe-containing particles, homogeneously distributed precipitates and dislocations. The addition of Zr coupled with the optimized thermo-mechanical treatment strongly restrained the recrystallization, refined the grain structure and promoted the homogenization of the precipitates. Moreover, the retainment of the deformation texture developed during the hot extrusion provided significant orientation strengthening in the high strength Al alloys.Fatigue cracks tended to initiate at coarse second phase particles on sample surfaces and the crack population varied markedly with the applied stresses in the high strength Al alloys. The relationship between of the crack population and the applied stress level was studied and quantified by a Weibull distribution function. Since the measured cracknumbers were associated with the crack initiate sites (i.e., the weakest links) in an alloy, the fatigue weakest-link density, which is defined as the crack population per unit area when stress close to the ultimate tensile stress, and the weakest-link strength distribution can all be calculated and regarded as a property of the studied materials.

This dissertation consists of three essays on theoretical analysis of economic agents' decision making and incentives. Chapter 1 gives an outline of the subjects to be examined in the subsequent chapters and shows their conclusions in brief. Chapter 2 explores the decision problem of a superordinate (a principal) regarding whether to delegate its authority or right to make a decision to a subordinate (an agent) in an organization. We first study the optimal contracting problem of the superordinate that specifies the allocation of the authority and wage in a principal-agent setting with asymmetric information, focusing on two motives for delegation, "informative" and "effort-incentive-giving" delegation. Further, we suggest delegating to multiple agents as a way of addressing the asymmetric information problem within an organization, focusing on another motive for delegation, "strategic" delegation. Chapter 3 analyzes the behavior of players in a particular type of contest, called "the weakest-link contest". Unlike a usual contest in which the winning probability of a group in a contest depends on the sum of the efforts of all the players in the group, the weakest-link contest follows a different rule: the winning probability of a group is determined by the lowest effort of the players in the group. We first investigate the effort incentives of the players in the weakest-link contest, and then check whether the hungriest player in each group, who has the largest willingness to exert effort, has an incentive to incentivize the other players in his group in order to make them exert more effort. Chapter 4 examines the decision making of software programmers in the software industry between an open source software project and a commercial software project. Incorporating both intrinsic and extrinsic motivation on open source project participation into a stylized economic model based on utility theory, we study the decision problem of the programmers in the software industry and provide the rationale for open source project participation more clearly. Specifically, we examine the question of how the programmers' intrinsic motivation, extrinsic motivation, and abilities affect their project choices between an open source project and a commercial project, and effort incentives. / Ph. D.

Il été prouvée dans plusieurs études de la littérature que la taille d'un composant affecte sa tenue en fatigue et cette tendance est plus prononcée dans le régime de fatigue à grand nombre de cycles. Plus précisément, une baisse de la limite de fatigue est observée et est souvent expliquée par l’augmentation, avec l’augmentation du volume sollicité, de la probabilité de trouver un défaut critique ou une zone plus faible dans le matériau. Le présent mémoire fait partie d'un projet de recherche français (QUAUSI) regroupant plusieurs partenaires industriels et académiques qui vise à contrôler la qualité d'usinage des composants structuraux d'avions. Un des défis consiste à définir un critère approprié d'acceptabilité de défauts pour la conception en FGNC. Le critère doit être capable de prendre en compte une large gamme de défauts de surface et de composants de tailles et de géométries différentes. L'objectif principal étant de mieux comprendre l'impact des états de surface périodiques (caractéristique du type d'usinage utilisé) sur la limite de fatigue, Il a fallu d'abord vérifier si un effet de taille peut être observé quand un nombre croissant de défauts de surface simples sont introduits à la surface d'échantillons polis. Le matériau d’étude est l’alliage d'aluminium 7050 (Al Zn6CuMgZr). Une grande campagne d'essais de fatigue sous charge de flexion plane à R=-1 est effectuée sur des éprouvettes présentant des défauts hémisphériques, de différents tailles et nombres, et des états de surface usinés. Les résultats des essais ont permis de caractériser à la fois l'effet Kitagawa et l'effet d'échelle sur la tenue fatigue. Une approche probabiliste basée sur le concept du maillon le plus faible associé à un critère d'amorçage de fissure de fatigue approprié est utilisée pour prendre en compte la répartition des contraintes et la taille du volume fortement sollicité. Les prédictions utilisant des simulations EF montrent un bon accord avec les résultats expérimentaux et illustrent l'importance de prendre en compte l'effet d'échelle lors de la conception de composants contenant différents types de défauts de surface ou de motifs de rugosité.Mots-clés : Défaut de surface, fatigue à grand nombre de cycles, diagramme de Kitagawa-Takahashi, Le plus faible concept de lien, alliage AA7050 / The size of a component has been proved in several studies of the literature to affect the fatigue strength and this trend is known to be more pronounced in the High Cycle Fatigue regime. More exactly a drop of the fatigue limit is observed and this evolution is very often explained by the probability to find a critical defect or a weakest zone in the material as the stressed volume rises. The present manuscript is part of a French research project gathering several industrial and academic partners that aims to control the machining quality of aircraft structural components. For one part of the project the challenge is to define a proper defect acceptability criterion for HCF design purpose. It must be able to account for a large range of surface defects and of component sizes and geometries. Even though the primary objective was to better understand the impact of periodic surface micro-geometry patterns (characteristic of the type of machining used) on the fatigue limit, we thought that it was first necessary to check if a size effect can be observed when an increasing number of artificial simplified surface defects are introduced at the surface of smooth specimens. The aeronautical material under investigation is a 7050 Aluminum alloy (Al Zn6CuMgZr). A large fatigue testing campaign under fully reversed plane bending loading is undertaken on specimens with artificial surface hemispherical defects. Defect number varies from 1 to 44 per specimen whereas their size ranges from 60 µm to 800 µm. Testing results allow the characterization of both Kitagawa effect and scale effect on the fatigue response. A probabilistic approach based on the weakest link concept together with a proper fatigue crack initiation criterion is used to account for the stress distribution and the size of the highly stressed volume. Predictions using FE simulations show a good agreement with experimental results and illustrate the importance of taking the scale effect into account while designing components containing different types of surface defects or roughness patterns.Keywords : Surface defect, HCF, Kitagawa-Takahashi diagram, Weakest link concept, AA7050 alloy.

An extensive review of probabilistic techniques in fatigue analysis indicates that there is a need for new microstructure-sensitive methods in describing the effects of notches on the fatigue life reduction in cyclically loaded components. Of special interest are notched components made from polycrystalline nickel-base superalloys, which are used for high temperature applications in aircraft gas turbine engine disks. Microstructure-sensitive computational crystal plasticity is combined with novel probabilistic techniques to determine the probability of failure of notched components based on the distribution of slip within the notch root region and small crack initiation processes. The key microstructure features of two Ni-base superalloys, a fine and coarse grain IN100, are reviewed and the method in which these alloys are computationally modeled is presented. Next, the geometric model of the notched specimens and method of finite element polycrystalline reconstruction is demonstrated. Shear-based fatigue indicator parameters are used to characterize the shear-based, mode I formation and propagation of fatigue cracks. Finally, two different probabilistic approaches are described in this work including a grain-scale approach, which describes the probability of forming a crack on the order of grain size, and a transition crack length approach, which describes the probability of forming and propagating a crack to the transition crack length. These approaches are used to construct cumulative distribution functions for the probability of failure as a function of various notch root sizes and strain load amplitudes.

Ageing of low alloy steel in nuclear applications commonly takes the form as a hardening and an embrittlement of the material. This is due to the evolution of the microstructure during irradiation and at purely thermal conditions, as a combination or separate. Irradiation introduces evenly distributed solute clusters, while thermal ageing has been shown to yield a more inhomogeneous distribution. These clusters affect the dislocation motion within the material and results in a hardening and in more severe cases of ageing, also a decreased work hardening slope due to plastic strain localization into bands/channels. Embrittlement corresponds to decreased fracture toughness due to microstructural changes resulting from ageing. The thesis presents a possible framework for modeling of ageing effects in low alloy steels.In Paper I, a strain gradient plasticity framework is applied in order to capture length scale effects. The constitutive length scale is assumed to be related to the dislocation mean free path and the changes this undergoes during plastic deformation. Several evolution laws for the length scale were developed and implemented in a FEM-code considering 2D plane strain. This was used to solve a test problem of pure bending in order to investigate the effects of the length scale evolution. As all length scale evolution laws considered in this study results in a decreasing length scale; this leads to a loss of non-locality which causes an overall softening at cases where the strain gradient is dominating the solution. The results are in tentative agreement with phenomena of strain localization that is occurring in highly irradiated materials.In Paper II, the scalar stress measure for cleavage fracture is developed and generalized, here called the effective normal stress measure. This is used in a non-local weakest link model which is applied to two datasets from the literature in order to study the effects of the effective normal stress measure, as well as new experiments considering four-point bending of specimens containing a semi-elliptical surface crack. The model is shown to reproduce the failure probability of all considered datasets, i.e. well capable of transferring toughness information between different geometries. / Åldring av låglegerade stål i kärntekniska användningsområden framträder typiskt som ett hårdnande och en försprödning av materialet. Detta på grund av utvecklingen av mikrostrukturen under bestrålning och under rent termiska förhållanden. Bestrålning introducerar jämt fördelade kluster av legeringsämnen. Termisk åldring har däremot visats ge upphov till en mer ojämn fördelning. Klustren hämmar dislokationsrörelsen i materialet och ger därigenom upphov till en ökning av materialets sträckgräns, vid en mer påtaglig åldring det även leda till ett sänkt arbetshårdnande på grund av lokalisering av plastisk töjning i s.k. kanaler/band. Försprödning är en sänkning av materialets brottseghet som en följd av de mikrostrukturella förändringar som sker vid åldring. Arbetet som presenteras i den här avhandlingen har gjorts i syfte till att ta fram ett möjligt ramverk för modellering av låglegerade stål.I Artikel I, används en töjningsgradientbaserad plasticitetsteori för att kunna fånga längdskalebeteenden. Längdskalan i teorin antas vara relaterad till dislokationernas medelfria väg och den förändring den genomgår vid plastisk deformation. Flera utvecklingslagar för längdskalan har analyserats och implementerats i en finita element kod för 2D plan deformation. Denna implementering har använts för att lösa ett testproblem bestående av ren böjning med syfte att undersöka effekterna av utvecklingen hos längdskalan. Alla de utvecklingslagar som presenteras i artikeln ger en minskande längdskala, vilket leder till vad som valt att kallas förlust av icke-lokalitet. Fenomenet leder till ett övergripande mjuknande vid fall där den plastiska töjningsgradienten har stor inverkan på lösningen. Resultaten är i preliminär överenstämmelse med de typer av lokalisering av plastisk töjning som observerats i starkt bestrålade material.I Artikel II utvecklas ett generaliserat spänningsmått i syfte att beskriva klyvbrott, här benämnt effektivt normalspänningsmått. Detta har använts i samband med en icke-lokal svagaste länk modell, som har applicerats på två experimentella studier från den öppna litteraturen i syfte att studera effekterna av det effektiva normalspänningsmåttet. Utöver detta presenteras även nya experiment på ytspruckna provstavar under fyrpunktsböj. I artikeln visas att modellen återskapar sannolikheten för brott för alla undersökta experimentuppställningar, d.v.s. modellen visas vara väl duglig för att överföra brottseghet mellan geometrier. / <p>QC 20190312</p>

This thesis compares Weibull weakest link theory with inclusion of one and all three principal stresses. Principal stresses needed for this theory were calculated with finite element method. The informational research is in the introduction of this thesis. It includes ceramic materials, Weibull weakest link theory, Gaussian quadrature over spherical surface and ceramic head of hip joint endoprothesis. Theoretical part is used for next calculations of probability of failure. The probability of failure of ceramic rod loaded by four-point bending is calculated in first calculations. This task is solved as contact in the next step. Next part of this thesis is about selection of suitable method of numerical integration. This method will be used in the calculation with all three principal stresses. The results of calculation with all three principal stresses are compared with the results of the calculation which includes only first principal stress. Firstly, this is done for cylindrical body and then used on head of hip joint endoprothesis. In the last part of this thesis, probability of fracture of head hip joint endoprothesis with shape deviation of nominal conicity is calculated.