Tato disertační práce vychází z výzkumu v rámci francouzsko-českého programu doktorátu pod dvojím vedením na pracovišti Institut français de mécanique avancée v Clermont-Ferrand a na Ústavu fyziky materiálu AV v Brně. Úvodní výzkumný úkol na brněnském pracovišti se zabýval numerickou analýzou pole napětí v okolí čela trhliny v tenké kovové fólii. Zvláštní pozornost byla zaměřena na vliv speciálního typu singularity v průsečíku čela trhliny s volným povrchem. Těžiště disertační práce spočívá v numerickém modelování a stochastické analýze problémů šíření trhlin se složitou geometrií v dvojrozměrném prostoru. Při analýze těchto problémů se dříve zřídka používaly numerické metody, a to z důvodu vysoké náročnosti na výpočtový čas. V této disertaci je ukázáno, že aplikací moderních metod numerické mechaniky a vhodných technik v analýze spolehlivosti lze tyto problémy řešit s pomocí numerických metod i na PC. Ve spolehlivostní analýze byla využita lineární aproximační metoda FORM. Pro rychlost šíření trhlin se vycházelo z Parisova-Erdoganova vztahu. Pro parametry tohoto vztahu byl použit dvourozměrný statistický model, který postihuje vysokou citlivost na korelaci obou parametrů. Mechanická odezva byla počítána rozšířenou metodou konečných prvků (XFEM), která eliminuje výpočetní náročnost a numerický šum související se změnou sítě v klasické metodě konečných prvků. Prostřednictvím přímé diferenciace bylo odvozeno několik vztahů pro derivace funkce odezvy, čímž se dosáhlo lepší numerické stability a konvergence spolehlivostní analýzy a výrazného zkrácení doby výpočtu. Problém zatížení s proměnou amplitudou byl řešen aplikací transformace zatížení metodou PREFFAS. Využití distribuce výpočtů v síti PC umožnilo další zrychlení analýzy.

Tato disertační práce vychází z výzkumu v rámci francouzsko-českého programu doktorátu pod dvojím vedením na pracovišti Institut français de mécanique avancée v Clermont-Ferrand a na Ústavu fyziky materiálu AV v Brně. Úvodní výzkumný úkol na brněnském pracovišti se zabýval numerickou analýzou pole napětí v okolí čela trhliny v tenké kovové fólii. Zvláštní pozornost byla zaměřena na vliv speciálního typu singularity v průsečíku čela trhliny s volným povrchem. Těžiště disertační práce spočívá v numerickém modelování a stochastické analýze problémů šíření trhlin se složitou geometrií v dvojrozměrném prostoru. Při analýze těchto problémů se dříve zřídka používaly numerické metody, a to z důvodu vysoké náročnosti na výpočtový čas. V této disertaci je ukázáno, že aplikací moderních metod numerické mechaniky a vhodných technik v analýze spolehlivosti lze tyto problémy řešit s pomocí numerických metod i na PC. Ve spolehlivostní analýze byla využita lineární aproximační metoda FORM. Pro rychlost šíření trhlin se vycházelo z Parisova-Erdoganova vztahu. Pro parametry tohoto vztahu byl použit dvourozměrný statistický model, který postihuje vysokou citlivost na korelaci obou parametrů. Mechanická odezva byla počítána rozšířenou metodou konečných prvků (XFEM), která eliminuje výpočetní náročnost a numerický šum související se změnou sítě v klasické metodě konečných prvků. Prostřednictvím přímé diferenciace bylo odvozeno několik vztahů pro derivace funkce odezvy, čímž se dosáhlo lepší numerické stability a konvergence spolehlivostní analýzy a výrazného zkrácení doby výpočtu. Problém zatížení s proměnou amplitudou byl řešen aplikací transformace zatížení metodou PREFFAS. Využití distribuce výpočtů v síti PC umožnilo další zrychlení analýzy.

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The desire for energy and resource savings brings magnesium alloys as lightweight materials with high specific strength more and more into the focus. Most structural components are subjected to cyclic loading. In the course of computer aided product development, a numerical prediction of the fatigue life under these conditions must be provided. For this reason, the mechanical properties of the considered material must be examined in detail. Wrought magnesium semifinished products, e.g. magnesium sheet metals, typically reveal strong basal textures and thus, the mechanical behavior considerably differs from that of the well-established magnesium die castings. Magnesium sheet metals reveal a distinct difference in the tensile and compressive yield stress, leading to non-symmetric sigmoidal hysteresis loops within the elasto-plastic load range. These unusual hysteresis shapes are caused by cyclic twinning and detwinning. Furthermore, wrought magnesium alloys reveal pseudoelastic behavior, leading to nonlinear unloading curves. Another interesting effect is the formation of local twin bands during compressive loading. Nevertheless, only little information can be found on the numerical fatigue analysis of wrought magnesium alloys up to now. The aim of this thesis is the investigation of the mechanical properties of wrought magnesium alloys and the development of an appropriate fatigue model. For this purpose, twin roll cast AM50 as well as AZ31B sheet metals and extruded ME21 sheet metals were used. Mechanical tests were carried out to present a comprehensive overview of the quasi-static and cyclic material behavior. The microstructure was captured on sheet metals before and after loading to evaluate the correlation between the microstructure, the texture, and the mechanical properties. Stress- and strain-controlled loading ratios and strain-controlled experiments with variable amplitudes were performed. Tests were carried out along and transverse to the manufacturing direction to consider the influence of the anisotropy. Special focus was given to sigmoidal hysteresis loops and their influence on the fatigue life. A detailed numerical description of hysteresis loops is necessary for numerical fatigue analyses. For this, a one-dimensional phenomenological model was developed for elasto-plastic strain-controlled constant and variable amplitude loading. This model consists of a three-component equation, which considers elastic, plastic, and pseudoelastic strain components. Considering different magnesium alloys, good correlation is reached between numerically and experimentally determined hysteresis loops by means of different constant and variable amplitude load-time functions. For a numerical fatigue life analysis, an energy based fatigue parameter has been developed. It is denoted by “combined strain energy density per cycle” and consists of a summation of the plastic strain energy density per cycle and the 25 % weighted tensile elastic strain energy density per cycle. The weighting represents the material specific mean stress sensitivity. Applying the energy based fatigue parameter on modeled hysteresis loops, the fatigue life is predicted adequately for constant and variable amplitude loading including mean strain and mean stress effects. The combined strain energy density per cycle achieves significantly better results in comparison to conventional fatigue models such as the Smith-Watson-Topper model. The developed phenomenological model in combination with the combined strain energy density per cycle is able to carry out numerical fatigue life analyses on magnesium sheet metals.

Este trabalho discutiu o estudo da inferência de carregamento e a reconstrução fratográfica da taxa de propagação da trinca por fadiga em histórias de vôos simulados do tipo Twist, mini-Twist, Falstaff e mini-Falstaff. O material estudado foi uma liga de alumínio de grau aeronáutico SAE-AMS 7475 T7351 na qual foram obtidas as propriedades mecânicas a partir dos ensaios de tração e dureza, análise química, metalográfica. Foram realizados ensaios de amplitude constante de carregamento em corpos de prova com geometria tipo C(T) extraídos de um bloco e ensaios de amplitude variável em corpos de prova com geometria tipo M(T) extraídos de uma placa. Corpos de prova do tipo C(T) foram extraídos da orientação L-T e T-L, à temperatura ambiente com diferentes espessuras para a realização de ensaios de propagação de trinca por fadiga (da/dN vs. &#916K) com distintos valores de razão de carregamento,R (0,1;0,3; 0,5; 0,7 e 0,8) de acordo com a norma ASTM-E647 (1993). Foram realizados dois tipos de ensaios de fadiga com amplitude constante de carregamento. Primeiro, o ensaio com &#916P constante para obtenção dos dados dos estágios II e III das curvas da/dN vs. &#916K para distintos valores de R e, posteriormente, o ensaio com &#916K constante e R crescente para ser utilizado no estudo da inferência de carregamento de amplitude constante a partir da relação entre a morfologia da estria, H/s e a razão de carregamento R. Adicionalmente foram realizados ensaios de tenacidade à fratura, nas direções L-T e T-L, conforme a norma ASTME1820 (1999). As taxas de propagação macroscópica e microscópica foram comparadas e boas correlações foram obtidas para um intervalo entre 0,1 a 1,0 &#956m/ciclo, mesmo com distintos R. Através da técnica proposta por Berkovitz (1995), o espectro de carregamento foi estimado para distintos valores de R, através da técnica de parametrização do fator K e os resultados foram comparados ao espectro de carregamento real imposto pela máquina de ensaio. Após os ensaios de amplitude constante de carregamento foram realizados ensaios de amplitude variável com a aplicação em corpos de prova M(T) de espectros de vôos simulados padronizados pela NLR do tipo Twist e Falstaff e seus vôos reduzidos, mini-Twist e mini- Falstaff, em uma máquina servohidráulica de ensaios dinâmicos. A partir destes ensaios notou-se que suprimir os vôos com os carregamentos menos severos influencia muito a vida da propagação da trinca de fadiga, quando vôos simulados do tipo Twist e mini-Twist, fato este não observado para o Falstaff e mini-Falstaff. Foi possível observar também o efeito da aceleração e desaceleração da trinca por fadiga observando os gráficos de d2a/dvôo vs. a obtidos dos ensaios de amplitude variável. Foi realizado um estudo da superfície de fratura do CP05 por meio da técnica fractográfica do reconhecimento de blocos marcadores sendo possível mostrar uma satisfatória reconstituição da taxa de propagação da trinca por fadiga de vôo simulado do tipo Falstaff por meio de medidas das marcações na superfície de fratura dos vôos mais severos, realizadas em imagens obtidas por MEV. / The loading inference and the fractographic reconstruction of fatigue crack propagation rate in simulated flight stories, as Twist, mini-Twist, Falstaff and mini-Falstaff were investigated in this work. The studied material was an aluminum alloy SAE-AMS 7475 T7351. Tensile and hardness tests were carried out in order to determine mechanical properties, as well as chemical and microstructure analysis of the material. C(T) specimens were extracted from a block of material for constant amplitude load testing and M(T) specimens were extracted from a plate and were tested in variable amplitude loading. The curves (da/dN vs. &#916K) for constant-amplitude loading were obtained from fatigue crack propagation tests performed in L-T and T-L directions in C(T) specimens for R (0.1; 0.3; 0.5; 0.7 and 0.8), at room temperature, according to ASTM-E647 (1993). Two different constant loading fatigue tests were performed. At constant &#916P and distinct values of R for obtaining data of stages II and III of da/dN - &#916K curves; and at constant &#916K and increasing the R ratio to be used in the inference of constant amplitude loading in the relation of H/s striation morphology (obtained from fractographic images) and the loading ratio, R. Additionally, fracture toughness tests were executed in T-L and L-T directions, according to ASTM-E1820 (1999). The macroscopic and microscopic fatigue crack propagations were compared and good correlation was obtained for the range 0.1-1.0 &#956m/cycle, for all R values. By using the K factor parametrization method, Berkovitz (1995), the loading spectrum was estimated for the distinct R-values and the results were compared to the actual spectrum imposed by the test machine. Variable amplitude tests were performed in M(T) specimens by applying simulating flight spectra normalized by NLR, as Twist, mini-Twist, Falstaff and mini-Falstaff, in a servohydraulic test machine MTS, in which a Flextest GT controller was coupled. The suppression of less severe loading flights showed a great influence in fatigue crack propagation life, in simulated flight tests Twist and mini-Twist, but not in Falstaff and mini-Falstaff. The acceleration and slowing down of fatigue crack were observed in the d2a/dflight - a curve obtained from variable loading tests. The fractured surfaces of some samples were examined by the fractographic technique of blocking marks recognition. A good reconstitution of fatigue crack propagation rate of a simulated flight like Falstaff was obtained by the measurements of marks in the fracture surfaces of the more severe flights, in MEV images.

One of the most prominent factors affecting the performance and longevity of risers is vortex induced vibration (VIV), which can cause severe fatigue damage, especially in risers used in deep waters. The available approaches for analyzing VIV induced fatigue in risers mainly focus on the VIV aspect of the problem; indeed less attention has been paid on the effect of VIV on a riser’s fatigue life and in prediction of fatigue life using various models. This dissertation first demonstrates how one can characterize fatigue of pipes and risers using an equivalent plate specimen as opposed to using a pipe specimen, thereby simplifying the task, yet obtaining good accuracy. Actual variable amplitude loadings (VAL) are used to study the fatigue crack growth in risers’ material with a focus on the various influencing parameters. Extensive experimental investigations are performed, followed by analytical and computational nonlinear finite element analyses. It is shown that the higher harmonics do cause significant fatigue damage, thus their influence should not be ignored. The influence of load interaction effects is also investigated, focusing on the fatigue crack growth retardation effects due to tension overloads, as well as the acceleration effects due to compression underloads. The crack closure concept is then used to explore into both the fatigue retardation and acceleration effects within a VAL scenario. An effective method for calculation of the stress intensity factor is proposed, which considers only the tensile portion of the stress range, while proposing another effective approach for accounting for the influence of compressive stress cycles. Moreover, a two-parameter approach is used in this dissertation, relating the fatigue crack growth rate (FCGR) to the crack tip opening displacement (CTOD). It is shown that the CTOD provides adequate information for calculating the FCGR under VAL, and it can be effectively used to account for the influence of the compressive stress cycles. The experimental investigation also considers the retardation effect resulting from the applied peak tensile overload cycles (TOLC) and the influence of various so-called “clipping” levels, demonstrating the significant influence of the TOLC on crack growth retardation in VAL.

Este trabalho discutiu o estudo da inferência de carregamento e a reconstrução fratográfica da taxa de propagação da trinca por fadiga em histórias de vôos simulados do tipo Twist, mini-Twist, Falstaff e mini-Falstaff. O material estudado foi uma liga de alumínio de grau aeronáutico SAE-AMS 7475 T7351 na qual foram obtidas as propriedades mecânicas a partir dos ensaios de tração e dureza, análise química, metalográfica. Foram realizados ensaios de amplitude constante de carregamento em corpos de prova com geometria tipo C(T) extraídos de um bloco e ensaios de amplitude variável em corpos de prova com geometria tipo M(T) extraídos de uma placa. Corpos de prova do tipo C(T) foram extraídos da orientação L-T e T-L, à temperatura ambiente com diferentes espessuras para a realização de ensaios de propagação de trinca por fadiga (da/dN vs. &#916K) com distintos valores de razão de carregamento,R (0,1;0,3; 0,5; 0,7 e 0,8) de acordo com a norma ASTM-E647 (1993). Foram realizados dois tipos de ensaios de fadiga com amplitude constante de carregamento. Primeiro, o ensaio com &#916P constante para obtenção dos dados dos estágios II e III das curvas da/dN vs. &#916K para distintos valores de R e, posteriormente, o ensaio com &#916K constante e R crescente para ser utilizado no estudo da inferência de carregamento de amplitude constante a partir da relação entre a morfologia da estria, H/s e a razão de carregamento R. Adicionalmente foram realizados ensaios de tenacidade à fratura, nas direções L-T e T-L, conforme a norma ASTME1820 (1999). As taxas de propagação macroscópica e microscópica foram comparadas e boas correlações foram obtidas para um intervalo entre 0,1 a 1,0 &#956m/ciclo, mesmo com distintos R. Através da técnica proposta por Berkovitz (1995), o espectro de carregamento foi estimado para distintos valores de R, através da técnica de parametrização do fator K e os resultados foram comparados ao espectro de carregamento real imposto pela máquina de ensaio. Após os ensaios de amplitude constante de carregamento foram realizados ensaios de amplitude variável com a aplicação em corpos de prova M(T) de espectros de vôos simulados padronizados pela NLR do tipo Twist e Falstaff e seus vôos reduzidos, mini-Twist e mini- Falstaff, em uma máquina servohidráulica de ensaios dinâmicos. A partir destes ensaios notou-se que suprimir os vôos com os carregamentos menos severos influencia muito a vida da propagação da trinca de fadiga, quando vôos simulados do tipo Twist e mini-Twist, fato este não observado para o Falstaff e mini-Falstaff. Foi possível observar também o efeito da aceleração e desaceleração da trinca por fadiga observando os gráficos de d2a/dvôo vs. a obtidos dos ensaios de amplitude variável. Foi realizado um estudo da superfície de fratura do CP05 por meio da técnica fractográfica do reconhecimento de blocos marcadores sendo possível mostrar uma satisfatória reconstituição da taxa de propagação da trinca por fadiga de vôo simulado do tipo Falstaff por meio de medidas das marcações na superfície de fratura dos vôos mais severos, realizadas em imagens obtidas por MEV. / The loading inference and the fractographic reconstruction of fatigue crack propagation rate in simulated flight stories, as Twist, mini-Twist, Falstaff and mini-Falstaff were investigated in this work. The studied material was an aluminum alloy SAE-AMS 7475 T7351. Tensile and hardness tests were carried out in order to determine mechanical properties, as well as chemical and microstructure analysis of the material. C(T) specimens were extracted from a block of material for constant amplitude load testing and M(T) specimens were extracted from a plate and were tested in variable amplitude loading. The curves (da/dN vs. &#916K) for constant-amplitude loading were obtained from fatigue crack propagation tests performed in L-T and T-L directions in C(T) specimens for R (0.1; 0.3; 0.5; 0.7 and 0.8), at room temperature, according to ASTM-E647 (1993). Two different constant loading fatigue tests were performed. At constant &#916P and distinct values of R for obtaining data of stages II and III of da/dN - &#916K curves; and at constant &#916K and increasing the R ratio to be used in the inference of constant amplitude loading in the relation of H/s striation morphology (obtained from fractographic images) and the loading ratio, R. Additionally, fracture toughness tests were executed in T-L and L-T directions, according to ASTM-E1820 (1999). The macroscopic and microscopic fatigue crack propagations were compared and good correlation was obtained for the range 0.1-1.0 &#956m/cycle, for all R values. By using the K factor parametrization method, Berkovitz (1995), the loading spectrum was estimated for the distinct R-values and the results were compared to the actual spectrum imposed by the test machine. Variable amplitude tests were performed in M(T) specimens by applying simulating flight spectra normalized by NLR, as Twist, mini-Twist, Falstaff and mini-Falstaff, in a servohydraulic test machine MTS, in which a Flextest GT controller was coupled. The suppression of less severe loading flights showed a great influence in fatigue crack propagation life, in simulated flight tests Twist and mini-Twist, but not in Falstaff and mini-Falstaff. The acceleration and slowing down of fatigue crack were observed in the d2a/dflight - a curve obtained from variable loading tests. The fractured surfaces of some samples were examined by the fractographic technique of blocking marks recognition. A good reconstitution of fatigue crack propagation rate of a simulated flight like Falstaff was obtained by the measurements of marks in the fracture surfaces of the more severe flights, in MEV images.

The desire for energy and resource savings brings magnesium alloys as lightweight materials with high specific strength more and more into the focus. Most structural components are subjected to cyclic loading. In the course of computer aided product development, a numerical prediction of the fatigue life under these conditions must be provided. For this reason, the mechanical properties of the considered material must be examined in detail. Wrought magnesium semifinished products, e.g. magnesium sheet metals, typically reveal strong basal textures and thus, the mechanical behavior considerably differs from that of the well-established magnesium die castings. Magnesium sheet metals reveal a distinct difference in the tensile and compressive yield stress, leading to non-symmetric sigmoidal hysteresis loops within the elasto-plastic load range. These unusual hysteresis shapes are caused by cyclic twinning and detwinning. Furthermore, wrought magnesium alloys reveal pseudoelastic behavior, leading to nonlinear unloading curves. Another interesting effect is the formation of local twin bands during compressive loading. Nevertheless, only little information can be found on the numerical fatigue analysis of wrought magnesium alloys up to now. The aim of this thesis is the investigation of the mechanical properties of wrought magnesium alloys and the development of an appropriate fatigue model. For this purpose, twin roll cast AM50 as well as AZ31B sheet metals and extruded ME21 sheet metals were used. Mechanical tests were carried out to present a comprehensive overview of the quasi-static and cyclic material behavior. The microstructure was captured on sheet metals before and after loading to evaluate the correlation between the microstructure, the texture, and the mechanical properties. Stress- and strain-controlled loading ratios and strain-controlled experiments with variable amplitudes were performed. Tests were carried out along and transverse to the manufacturing direction to consider the influence of the anisotropy. Special focus was given to sigmoidal hysteresis loops and their influence on the fatigue life. A detailed numerical description of hysteresis loops is necessary for numerical fatigue analyses. For this, a one-dimensional phenomenological model was developed for elasto-plastic strain-controlled constant and variable amplitude loading. This model consists of a three-component equation, which considers elastic, plastic, and pseudoelastic strain components. Considering different magnesium alloys, good correlation is reached between numerically and experimentally determined hysteresis loops by means of different constant and variable amplitude load-time functions. For a numerical fatigue life analysis, an energy based fatigue parameter has been developed. It is denoted by “combined strain energy density per cycle” and consists of a summation of the plastic strain energy density per cycle and the 25 % weighted tensile elastic strain energy density per cycle. The weighting represents the material specific mean stress sensitivity. Applying the energy based fatigue parameter on modeled hysteresis loops, the fatigue life is predicted adequately for constant and variable amplitude loading including mean strain and mean stress effects. The combined strain energy density per cycle achieves significantly better results in comparison to conventional fatigue models such as the Smith-Watson-Topper model. The developed phenomenological model in combination with the combined strain energy density per cycle is able to carry out numerical fatigue life analyses on magnesium sheet metals.