Most components or structures experience in service a variety of cyclic stresses. In the case of cyclic constant amplitude loading the fatigue crack growth depends only on the crack, the component geometry and the applied loading. In the case of variable amplitude loading it also depends on the preceding cyclic loading history. Various types of load sequence (overloads, under-loads, or combination of them) may induce different load-interaction effects which can cause either acceleration or reduction of the fatigue crack growth rate. The previously developed UniGrow fatigue crack growth model for constant amplitude loading histories which was based on the analysis of the local stress-strain material behaviour at the crack tip has been improved, modified and extended to such a level of sophistication that it can be used for fatigue crack growth analyses of cracked bodies subjected to arbitrary variable amplitude loading spectra. It was shown that the UniGrow model enables to correctly predict the effect of the applied compressive stress and tensile overloads by accounting for the existence of the internal (residual) stresses induced by the reversed cyclic plasticity around the crack tip. This idea together with additional structural memory effect model has been formalized mathematically and coded into computer program convenient for predicting fatigue crack growth under arbitrary variable amplitude loading spectra. The experimental verification of the proposed model was performed using 7075-T6, 2024-T3, 2324-T7, 7010-T7, 7050-T7 aluminium alloys, Ti-17 titanium alloy, and 350WT steel. The good agreement between theoretical and experimental data proved the ability of the UniGrow model to predict fatigue crack growth and fatigue crack propagation life under a wide variety of real variable amplitude loading spectra.

Most components or structures experience in service a variety of cyclic stresses. In the case of cyclic constant amplitude loading the fatigue crack growth depends only on the crack, the component geometry and the applied loading. In the case of variable amplitude loading it also depends on the preceding cyclic loading history. Various types of load sequence (overloads, under-loads, or combination of them) may induce different load-interaction effects which can cause either acceleration or reduction of the fatigue crack growth rate. The previously developed UniGrow fatigue crack growth model for constant amplitude loading histories which was based on the analysis of the local stress-strain material behaviour at the crack tip has been improved, modified and extended to such a level of sophistication that it can be used for fatigue crack growth analyses of cracked bodies subjected to arbitrary variable amplitude loading spectra. It was shown that the UniGrow model enables to correctly predict the effect of the applied compressive stress and tensile overloads by accounting for the existence of the internal (residual) stresses induced by the reversed cyclic plasticity around the crack tip. This idea together with additional structural memory effect model has been formalized mathematically and coded into computer program convenient for predicting fatigue crack growth under arbitrary variable amplitude loading spectra. The experimental verification of the proposed model was performed using 7075-T6, 2024-T3, 2324-T7, 7010-T7, 7050-T7 aluminium alloys, Ti-17 titanium alloy, and 350WT steel. The good agreement between theoretical and experimental data proved the ability of the UniGrow model to predict fatigue crack growth and fatigue crack propagation life under a wide variety of real variable amplitude loading spectra.

NiTi (also known as Nitinol) is an almost equiatomic alloy of nickel and titanium and has many applications in various industries, such as biomedical, automotive, and aerospace. NiTi shape memory alloys undergo martensitic phase transformations under both thermal and mechanical loading and exhibit unique properties, such as superelasticity (SE) and shape memory effects (SME). Modeling the fatigue behavior of this alloy is very challenging due to the unique mechanical response of the material. Moreover, there are very limited studies on the fatigue behavior of this alloy under more realistic loading conditions, such as variable amplitude loading and multiaxial loading. In this study, strain-controlled cyclic experiments have been conducted in different conditions to study the variable amplitude fatigue behavior of superelastic NiTi. Nonzero mean strain/stress behavior of superelastic NiTi is investigated, and it is demonstrated that the classical fatigue models for mean strain/stress correction do not appropriately model the nonzero mean strain/stress fatigue behavior of superelastic NiTi. It is shown that, despite common metals (e.g., steel, aluminum, and titanium alloys), mean strain also affects the fatigue behavior of superelastic NiTi, as the resulting mean stress does not fully relax under cyclic load. Two energy-based fatigue models have been proposed based on the results in this study and provide acceptable correlation with experimental observations. The models proposed in this research, account for the effects of mean strain/stress and variations in cyclic deformation. The variations in the cyclic deformation can be due to several factors, such as slight changes in chemical composition, heat treatment processes, texture, etc. The predicted fatigue lives using the proposed fatigue model fall within scatter bands of 1.5 times the experimental life for constant amplitude loading. Analyses also show that the proposed total fatigue toughness parameter, ΣWt, together with the Rainflow cycle counting technique can accurately predict the fatigue life under more realistic loading condition, such as two-step (i.e. high-low and low-high) and variable amplitude load-paths.

Este trabalho tem como objetivo a comparação dos resultados de ensaios de durabilidade em um suporte do eixo traseiro de um veículo leve de passeio, submetido a dois tipos distintos de testes: durabilidade em rodagem real e em simuladores de estradas. Após o término dos ensaios, o componente apresentou resultados diferentes: as trincas podem ser observadas na peça submetida à rodagem real, e os danos não ocorrem no eixo que foi testado em simulador. As discrepâncias citadas podem estar ligadas a possíveis erros, ocorridos durante a transferência dos dados pertinentes ao teste real para o simulador. / The aim of this research is comparing results from durability tests performed at a rear axle bracket of a small passenger car. The part was tested using two different kinds of tests: real (proving ground) durability and simulated (road simulator) durability. After that, the part showed different final results: several cracks can be observed at the part that was tested at the proving ground and no real damage was inflicted at the part that was test at the road simulator. These differences can be related to transferability problems that occurred during data analysis and transfer from real test to a simulated one.

Este trabalho tem como objetivo a comparação dos resultados de ensaios de durabilidade em um suporte do eixo traseiro de um veículo leve de passeio, submetido a dois tipos distintos de testes: durabilidade em rodagem real e em simuladores de estradas. Após o término dos ensaios, o componente apresentou resultados diferentes: as trincas podem ser observadas na peça submetida à rodagem real, e os danos não ocorrem no eixo que foi testado em simulador. As discrepâncias citadas podem estar ligadas a possíveis erros, ocorridos durante a transferência dos dados pertinentes ao teste real para o simulador. / The aim of this research is comparing results from durability tests performed at a rear axle bracket of a small passenger car. The part was tested using two different kinds of tests: real (proving ground) durability and simulated (road simulator) durability. After that, the part showed different final results: several cracks can be observed at the part that was tested at the proving ground and no real damage was inflicted at the part that was test at the road simulator. These differences can be related to transferability problems that occurred during data analysis and transfer from real test to a simulated one.

L'objectif de cette thèse est de démontrer comment faire une analyse théorique de fatigue et de mécanique de la rupture d'une structure éolienne à l'axe horizontal. La chaîne des calculs nécessaires pour atteindre cet objectif s'avère être particulièrement longue pour deux raisons : d'abord, la vitesse du vent varie aléatoirement avec le temps ; deuxièmement, l'amplitude de vibration du mât est amplifié en raison des ses fréquences naturelles de vibration. Un chapitre entier est consacré à la modélisation de la vitesse du vent dans l'espace et dans le temps. Ce même chapitre démontre comment synthétiser un signal aléatoire à partir d'une fonction de densité spectrale de puissance (DSP). La force axiale du rotor est le chargement le plus important sur une structure éolienne à l'axe horizontal. Cette force a un rapport non linéaire avec la vitesse du vent. Cela implique la nécessité de déterminer la DSP de la force axiale à partir de son signal, en se servant d'une technique d'estimation spectrale. La méthode Thomson Multitaper s'est avéré la plus satisfaisante pour cette application. La DSP des déplacements du mât est déterminée en associant la réceptance du système structurel avec la DSP de la force qui représente tous les chargements. Un signal de contrainte peut finalement être synthétisé à partir de sa DSP. La technique de comptage de cycles de chargement connue sous le nom de rainflow est abordée et appliquée. Le fait que le signal de contraintes a une amplitude variable implique la nécessité d'employer une technique plus avancée de simulation de propagation de fissures. La technique choisie pour cette thèse est connue sous le nom de strip-yield (bande d'écoulement). / The objective of this thesis is to demonstrate how to do theoretical analyses of fatigue and fracture mechanics in a structure for horizontal axis wind turbine. The chain of calculations required to reach this objective is particularly long for two reasons : firstly, the wind speed varies randomly with time , secondly, the vibration amplitude of the mast is amplified due to its natural frequencies of vibration. A whole chapter is dedicated to modeling the wind speed in space and time. The same chapter shows how to synthesize a random signal by employing a power spectral density function (PSD). The axial force of the rotor is the most important loading on a structure for horizontal axis wind turbine. This force has a non linear relation with the wind speed. This implies the need to determine the PSD of the axial force from its signal, by employing a spectral estimation method. The Thomson Multitaper method revealed to be the most satisfactory for this application. The PSD of displacement of the mast is determined by associating the receptance of the structural system and the PSD of the force representing all loadings. Finally, a signal of stress can be synthesized from its PSD. The fatigue cycle counting method known as rainflow is discussed and employed. The fact that the signal of stress has a variable amplitude implies the need of a more sophisticated method to simulate a crack propagation. The method chosen in this thesis is called strip-yield.

The work in this thesis is concerned with the mechanics of the initiation and growth of small fatigue cracks from notches under service load histories. Fatigue life estimates for components subjected to variable amplitude service loading are usually based on the same constant amplitude strain-life data used for constant amplitude fatigue life predictions. The resulting fatigue life estimates although they are accurate for constant amplitude fatigue, are always non conservative for variable amplitude load histories. Similarly fatigue life predictions based on small crack growth calculations for cracks growing from flaws in notches are non conservative when constant amplitude crack growth data are used. These non conservative predictions have, in both cases, been shown to be due to severe reductions in fatigue crack closure arising from large (overload or underload) cycles in a typical service load history. Smaller load cycles following a large near yield stress overload or underload cycle experience a much lower crack opening stress than that experienced by the same cycles in the reference constant amplitude fatigue tests used to produce design data. This reduced crack opening stress results in the crack remaining open for a larger fraction of the stress-strain cycle and thus an increase in the effective portion of the stress-strain cycle. The effective strain range is increased and the fatigue damage for the small cycles is greater than that calculated resulting in a non conservative fatigue life prediction. Previous work at Waterloo introduced parameters based on effective strain-life fatigue data and effective stress intensity versus crack growth rate data. Fatigue life calculations using these parameters combined with experimentally derived crack opening stress estimates give accurate fatigue life predictions for notched components subjected to variable amplitude service load histories. Information concerning steady state crack closure stresses, effective strain-life data, and effective stress intensity versus small crack growth rate data, are all obtained from relatively simple and inexpensive fatigue tests of smooth specimens in which periodic underloads are inserted into an otherwise constant amplitude load history. The data required to calibrate a variable amplitude fatigue crack closure model however, come from time consuming measurements of the return of crack closure levels for small cracks to a steady state level following an underload (large cracks for which crack closure measurements are easier to make cannot be used because at the high stress levels in notches under service loads a test specimen used would fracture). For low and moderately high hardness levels in metals crack growth and crack opening stress measurements have been made using a 900x optical microscope for the small crack length at which a test specimen can resist the high stress levels encountered when small cracks grow from notches. For very hard metals the crack sizes may be so small that the measurements must be made using a confocal scanning laser microscope. In this case the specimen must be removed from the test machine for each measurement and the time to acquire data is only practical for an extended research project. The parameters for the crack closure model relating to steady state crack closure levels vary with material cyclic deformation resistance which in turn increases with hardness. One previous investigation found that the steady state crack opening level was lower and the recovery to a steady state crack opening stress level after an underload was more rapid for a hard than for a soft metal. This observation can be explained by the dependence of the crack tip plastic zone size that determines crack tip deformation and closure level on metal hardness and yield strength. Further information regarding this hypothesis has been obtained in this thesis by testing three different steels of varying hardness levels (6 HRC, 35 HRC, and 60 HRC) including a very hard carburized steel having a hardness level (60 HRC) for which no crack opening stress data for small cracks had yet been obtained. This thesis introduced a new test procedure for obtaining data on the return of crack opening stress to a steady state level following an underload. Smooth specimens were tested under load histories with intermittent underload cycles. The frequency of occurrence of the underloads was varied and the changes in fatigue life observed. The changes in damage per block (the block consisted of an underload cycle followed by intermittent small cycles) were used to determine the value of the closure model parameter governing the recovery of the crack opening stress to its steady state level. Concurrent tests were carried out in which the crack opening stress recovery was measured directly on crack growth specimens using optical microscope measurements. These tests on metals ranging in hardness from soft to very hard were used to assess whether the new technique would produce good data for crack opening stress changes after underloads for all hardness levels. The results were also used to correlate crack closure model parameters with mechanical properties. This together with the steady state crack opening stress, effective strain-life data and the effective intensity versus crack growth rate data obtained from smooth specimen tests devised by previous researchers provided all the data required to calibrate the two models proposed in this investigation to perform strain-life and small crack growth fatigue analysis.

The work in this thesis is concerned with the mechanics of the initiation and growth of small fatigue cracks from notches under service load histories. Fatigue life estimates for components subjected to variable amplitude service loading are usually based on the same constant amplitude strain-life data used for constant amplitude fatigue life predictions. The resulting fatigue life estimates although they are accurate for constant amplitude fatigue, are always non conservative for variable amplitude load histories. Similarly fatigue life predictions based on small crack growth calculations for cracks growing from flaws in notches are non conservative when constant amplitude crack growth data are used. These non conservative predictions have, in both cases, been shown to be due to severe reductions in fatigue crack closure arising from large (overload or underload) cycles in a typical service load history. Smaller load cycles following a large near yield stress overload or underload cycle experience a much lower crack opening stress than that experienced by the same cycles in the reference constant amplitude fatigue tests used to produce design data. This reduced crack opening stress results in the crack remaining open for a larger fraction of the stress-strain cycle and thus an increase in the effective portion of the stress-strain cycle. The effective strain range is increased and the fatigue damage for the small cycles is greater than that calculated resulting in a non conservative fatigue life prediction. Previous work at Waterloo introduced parameters based on effective strain-life fatigue data and effective stress intensity versus crack growth rate data. Fatigue life calculations using these parameters combined with experimentally derived crack opening stress estimates give accurate fatigue life predictions for notched components subjected to variable amplitude service load histories. Information concerning steady state crack closure stresses, effective strain-life data, and effective stress intensity versus small crack growth rate data, are all obtained from relatively simple and inexpensive fatigue tests of smooth specimens in which periodic underloads are inserted into an otherwise constant amplitude load history. The data required to calibrate a variable amplitude fatigue crack closure model however, come from time consuming measurements of the return of crack closure levels for small cracks to a steady state level following an underload (large cracks for which crack closure measurements are easier to make cannot be used because at the high stress levels in notches under service loads a test specimen used would fracture). For low and moderately high hardness levels in metals crack growth and crack opening stress measurements have been made using a 900x optical microscope for the small crack length at which a test specimen can resist the high stress levels encountered when small cracks grow from notches. For very hard metals the crack sizes may be so small that the measurements must be made using a confocal scanning laser microscope. In this case the specimen must be removed from the test machine for each measurement and the time to acquire data is only practical for an extended research project. The parameters for the crack closure model relating to steady state crack closure levels vary with material cyclic deformation resistance which in turn increases with hardness. One previous investigation found that the steady state crack opening level was lower and the recovery to a steady state crack opening stress level after an underload was more rapid for a hard than for a soft metal. This observation can be explained by the dependence of the crack tip plastic zone size that determines crack tip deformation and closure level on metal hardness and yield strength. Further information regarding this hypothesis has been obtained in this thesis by testing three different steels of varying hardness levels (6 HRC, 35 HRC, and 60 HRC) including a very hard carburized steel having a hardness level (60 HRC) for which no crack opening stress data for small cracks had yet been obtained. This thesis introduced a new test procedure for obtaining data on the return of crack opening stress to a steady state level following an underload. Smooth specimens were tested under load histories with intermittent underload cycles. The frequency of occurrence of the underloads was varied and the changes in fatigue life observed. The changes in damage per block (the block consisted of an underload cycle followed by intermittent small cycles) were used to determine the value of the closure model parameter governing the recovery of the crack opening stress to its steady state level. Concurrent tests were carried out in which the crack opening stress recovery was measured directly on crack growth specimens using optical microscope measurements. These tests on metals ranging in hardness from soft to very hard were used to assess whether the new technique would produce good data for crack opening stress changes after underloads for all hardness levels. The results were also used to correlate crack closure model parameters with mechanical properties. This together with the steady state crack opening stress, effective strain-life data and the effective intensity versus crack growth rate data obtained from smooth specimen tests devised by previous researchers provided all the data required to calibrate the two models proposed in this investigation to perform strain-life and small crack growth fatigue analysis.

The actual service loading histories of most engineering components are characterized by variable amplitudes and are sometimes rather complicated. The goal of this study was to estimate the fatigue life of nickel-chromium-molybdenum 30CrNiMo8HH steel alloy under axial and pure torsion variable amplitude loading (VAL) conditions. The investigation was directed at two primary factors that are believed to have an influence on fatigue life under such loading conditions: load sequence and mean stress. The experimental work for this research included two-step loading, non-zero mean strain loading, and VAL tests, the results of which were added to previously determined fully reversed strain-controlled fatigue data. The effect of load sequence on fatigue life was examined through the application of the commonly used linear damage accumulation rule along with the Manson and Marco–Starkey damage accumulation methods, the latter of which takes load sequence into account. Based on the two-step experimental results, both the Manson and Marco–Starkey methods were modified in order to eliminate the empirically determined constants normally required for these two methods. The effect of mean stress on fatigue life was investigated with the use of three life prediction models: Smith–Watson–Topper (SWT), Fatemi–Socie (FS), and Jahed–Varvani (JV). The cycles from the VAL histories were counted using a rainflow counting procedure that maintains the applied strain sequence, and a novel method was developed for the estimation of the total energy density required for the JV model. For two-step loading and for all three fatigue models employed, the modified damage accumulation methods provided superior fatigue life predictions. However, regardless of the damage accumulation method applied, the most satisfactory fatigue life correlation for VAL was obtained using the energy-based JV model.

The actual service loading histories of most engineering components are characterized by variable amplitudes and are sometimes rather complicated. The goal of this study was to estimate the fatigue life of nickel-chromium-molybdenum 30CrNiMo8HH steel alloy under axial and pure torsion variable amplitude loading (VAL) conditions. The investigation was directed at two primary factors that are believed to have an influence on fatigue life under such loading conditions: load sequence and mean stress. The experimental work for this research included two-step loading, non-zero mean strain loading, and VAL tests, the results of which were added to previously determined fully reversed strain-controlled fatigue data. The effect of load sequence on fatigue life was examined through the application of the commonly used linear damage accumulation rule along with the Manson and Marco–Starkey damage accumulation methods, the latter of which takes load sequence into account. Based on the two-step experimental results, both the Manson and Marco–Starkey methods were modified in order to eliminate the empirically determined constants normally required for these two methods. The effect of mean stress on fatigue life was investigated with the use of three life prediction models: Smith–Watson–Topper (SWT), Fatemi–Socie (FS), and Jahed–Varvani (JV). The cycles from the VAL histories were counted using a rainflow counting procedure that maintains the applied strain sequence, and a novel method was developed for the estimation of the total energy density required for the JV model. For two-step loading and for all three fatigue models employed, the modified damage accumulation methods provided superior fatigue life predictions. However, regardless of the damage accumulation method applied, the most satisfactory fatigue life correlation for VAL was obtained using the energy-based JV model.