<div>An important challenge in predicting fatigue and creep crack growth is describing crack growth rates under transient conditions. Transient conditions occur when similitude is violated at the crack tip due to the applied loads or material behavior. Crack growth models like the Paris law, valid for homogeneous materials under constant-amplitude cyclic loading or sustained loading, no longer apply. Transient crack growth rates are strongly influenced by changes in plastic deformation at the crack tip. Activation of time-dependent damage and viscoplastic deformation at high temperatures further complicates the problem.</div><div><br></div><div>This thesis advances knowledge and predictive capabilities for transient creep and fatigue crack growth in metals, with specific applications to two technologically-relevant nickel-base superalloys. Finite element computations of crack growth following overloads and in multilayered materials are conducted. Crack extension is an outcome of the boundary value problem through an irreversible cohesive zone model and its interaction with plasticity and viscoplasticity in the bulk material.</div><div><br></div><div>First, fatigue crack growth in rate-independent materials is analyzed. The plasticity formulation considers both plastic strain and gradients of plastic strain, which produce hardening beyond that predicted by classical plasticity models. The computations demonstrate that hardening due to plastic strain gradients plays a significant role in transient fatigue crack growth following overloads. Fatigue crack growth transients associated with material inhomogeneity are studied through the case of a crack growing toward interfaces between plastically dissimilar materials. Interactions between the interface strength and the yield strength mismatch are found to govern crack growth rates near the interface. Hardening due to plastic strain gradients is important for finding the critical conditions associated with crack bifurcation at an interface and penetration through an interlayer.</div><div><br></div><div>Subsequently, crack growth in rate-dependent materials is analyzed. For materials characterized by power-law viscoplasticity, fatigue crack growth rates following overloads are found to depend strongly on the material rate sensitivity. The computations predict a transition from acceleration- to retardation-dominated post-overload crack growth as the rate sensitivity decreases. The predicted post-overload crack growth rates show good agreement with high-temperature experimentally-measured trends for Alloy 617, a solid solution strengthened nickel-base superalloy proposed for use in next-generation nuclear power plants. The results demonstrate why Alloy 617 behaves in a relatively brittle manner following overloads despite being characterized as a creep-ductile material. Crack growth is also studied in materials where rate dependence is captured through time-dependent damage and dislocation storage and dynamic recovery processes. This approach is relevant for high-strength creep-brittle materials, in which the viscoplastic zone grows with the advancing crack. The computations predict crack growth retardation for several loading waveforms containing overloads. The amount of retardation depends strongly on the overload ratio and subsequent unloading ahead of the crack tip. The predicted post-overload crack extension shows good agreement with high-temperature experimentally-measured trends for Alloy 718, a precipitation-hardened nickel-base superalloy used in turbine engines and power generation applications. The results demonstrate why Alloy 718 behaves in a ductile manner following overloads, despite being characterized as a creep-brittle material.</div>

This thesis investigates fatigue crack growth rate behavior in the threshold and near-threshold regimes for a Ti-6Al-4V (STOA) alloy using two proposed ASTM procedures- (1) load-shedding (LS) using a larger load-shed rate than the current ASTM Standard E647 load-reduction (LR) test procedure, and (2) compression pre-cracking constant-amplitude (CPCA) or load-increasing (CPLI) and load-shedding (CPLS). Tests were conducted at a low stress ratio (R = 0.1) on compact C(T) specimens of two different widths (W = 51 and 76 mm) and threshold fatigue crack growth rates were generated. These test data were compared to previous test data produced from the same batch of material using the current LR and the CPCA test procedure. While no test procedure provided an exact representation of the threshold value (?Kth), the compression pre-cracking (CP) procedures were the most promising. The LR, LS, and CPLS test procedures were influenced by prior loading-history and various crack-closure mechanisms, leading to higher ?Kth values and slower crack growths in the threshold regime. The LS tests (at shed-rates of -0.08,-0.32, and -0.95 mm-1) generated ?Kth values that were 15% to 32% higher than the estimated threshold stress-intensity factor range (?*Kth)R=0.1. The CP test procedures are a more accurate alternative for developing near-threshold and threshold fatigue crack growth rates. The CPLS test procedure produced a ?Kth value that was 10% higher than (?*Kth)R=0.1. LR and LS tests produced different ?Kth values as a function of the specimen width for the given load ratio. The CP test procedures produced consistent crack growth rates over the same range of ?K values examined, independent of the specimen width. Further research is required for developing test procedure(s) capable of providing a more definitive representation of the ?Kth value and closureree fatigue crack growth rates in the threshold regime.

Fatigue and crack-growth tests were conducted on 7050-T7451 aluminum alloy under a wide range of loading conditions. Crack-growth tests were conducted on compact, C(T), specimens under constant-amplitude loading, single-spike overloads, and a simulated aircraft spectrum loading. Fatigue tests were also conducted on single-edge-notch bend, SEN(B), specimens under constant-amplitude loading and three aircraft load spectra. The FASTRAN, life-prediction code, was used to make crack-growth predictions on the C(T) specimens; and to make fatigue-life calculations using a 12-micrometer initial flaw size at the center of the edge-notch on the SEN(B) specimens. The predictions agreed fairly well with most of the tests, except the model was unconservative on the single-spike overload tests and the severe spectrum Mini-TWIST+ Level 1 tests. The discrepancy was suspected to be caused by a low constraint factor and/or crack paths meandering around overload plastic zones. A roughness- and plasticity-induced crack-closure model would be needed to improve the model.

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Fatigue in concrete is a complex phenomenon involving formation of microcracks, their coalescence into major crack and simultaneous formation of the fracture process zone ahead of the crack tip. Complex phenomena are best dealt through an energy approach and hence it is reasonable to use the theory of thermodynamics. Fracture mechanics and damage mechanics are two theories that are based on physically sound principles and are used to describe failure processes in materials. The former deals with the study of macroscopic cracks, whereas the latter defines the state of microcracking. In this study, the concepts from these theories are utilized to improve our understanding and modeling of fatigue process in concrete. In this thesis, a closed form expression for the thermodynamic function entropy is proposed and examined for its size independency and its use as a material property to characterize failure of concrete under fatigue. In the thermodynamic formalism, dissipative phenomena are described by a dissipation potential or its dual, from which evolution laws for internal variables could be defined. In this work, closed form expressions for dual of dissipation potential are derived using concepts of dimensional analysis and self-similarity within the framework of fracture mechanics and damage mechanics. Consequently, a fatigue crack propagation law and a fatigue damage evolution law are proposed respectively. A method is proposed in this study to correlate fracture mechanics and damage mechanics theories by equating the potentials obtained in each theory. Through this equivalence, a crack could be transformed into an equivalent damage zone and vice versa. Also, damage state corresponding to a given crack in a member can be quantified in terms of a damage index. An analytical way of computing size independent S-N curves is proposed, using a nonlocal damage theory by including aggregate size and specimen size in the formulation. It is realized from this study that fracture mechanics and damage mechanics theories should be used in a unified manner in order to accurately model the process of fatigue in concrete. Furthermore, based on the models developed in this study, several damage indicators for fatigue of concrete are proposed. The advantages and limitations of each of these indices are presented such that, the relevant damage index could be used, based on available parameters. Additionally, deterministic sensitivity studies are carried out to determine the most important parameters influencing fatigue life of a concrete member.

A austenita retida está sempre presente na microestrutura de camada cementada de aços, em maior ou menor quantidade. Como é uma fase dúctil comparada à martensita, sua presença tem sido alvo de muita controvérsia. Este trabalho apresenta um estudo sobre a influência da austenita retida na propagação de trincas curtas por fadiga em camada cementada de aço SAE 8620. Foram feitos ensaios de fadiga por flexão em quatro pontos, a temperatura ambiente, em corpos de prova sem entalhe com três níveis de amplitude de tensão e razão de tensões de 0,1. Através de diferentes ciclos de cementação e tratamentos térmicos, foram obtidas camadas cementadas com quatro níveis de austenita retida na microestrutura. O teor de austenita retida foi medido através da técnica de difração de Raios-X. Trincas superficiais foram monitoradas por meio da técnica de réplicas de acetato. Como resultados foram obtidos tamanho de trinca em função do número de ciclos e taxa de crescimento de trincas curtas. Corpos de prova com maiores níveis de austenita retida apresentaram maior vida em fadiga. / The retained austenite is always present in case carburized steel microstructure in small or high percentages. Since it is a ductile phase, its presence has long been a controversial subject. The influence of retained austenite on short fatigue crack propagation in case carburized SAE 8620 steel was studied in this work. Four-point-bend fatigue tests were carried out at room temperature in specimens without notch using three levels of stress range and a stress ratio of 0.1. Four different amount of retained austenite in the case carburized microstructure were obtained through different cycles of carburizing and heat treating. The retained austenite content was measured by X-ray technique, and the surface short crack growth was monitored by means of acetate replication technique. Crack length versus number of cycles and crack growth rate versus mean crack length were obtained as results. Specimens with higher levels of retained austenite in the carburized case showed longer fatigue life.

[pt] O grande potencial exploratório em águas profundas motiva a busca de um conhecimento tecnológico necessário para viabilizar a exploração e produção em alto mar. Paralelamente à busca de novas tecnologias de exploração e produção, a diminuição do risco de falha estrutural em unidades de exploração do tipo offshore tornou-se uma preocupação constante do setor, uma vez que falhas estruturais podem significar elevados custos decorrentes da utilização parcial de equipamentos, manutenção extemporânea, parada de produção, perdas materiais e, principalmente, perdas humanas e danos ao ecossistema. Este trabalho apresenta um estudo sobre a influência da quantidade de martensita revenida sobre a cinética de propagação da trinca de fadiga em aço estrutural do tipo grau R4, largamente utilizado em componentes estruturais para sistemas de ancoragem de unidades flutuantes do tipo offshore, sendo fabricados por meio de soldagem por centelhamento. Corpos de prova do tipo CT foram usinados a partir do material de base e do material de solda e submetidos a tratamentos térmicos de têmpera em diferentes temperaturas de austenitização, sendo submetidos a tratamentos de revenido em temperatura única. A fim de promover uma comparação com a condição microestrutural industrial, corpos de prova também foram usinados de elos de amarras após procedimentos industriais de soldagem por centelhamento, têmpera e revenido. Posteriormente, num total de cinco condições microestruturais, os corpos de prova foram ensaiados sob condições cíclicas de carregamento, objetivando a determinação das curvas de crescimento de trinca (a versus N and da/dN versus DK curves). Os resultados do desempenho em fadiga do material demonstram que a diminuição da quantidade de martensita revenida resultou no aumento da vida útil em fadiga do material, que a condição industrial está associada com a menor resistência à fadiga observada e que a vida em fadiga do material depende da posição de retirada do corpo de prova. / [en] The great explor atory potential in deep waters has led companies in the oil sector to search for the necessary technological improvement to make the offshore exploration and production feasible. In parallel to searching for new technologies, the reduction in risks of structural failure has become the sector s constant practice, considering that such failures mean high costs due to partial use of equipments, extemporary maintenance, production stops, material losses and, mainly, damage to the ecosystem and loss of lives. A study has been made concerning the influence of the fraction of tempered martensite on the kinetics of fatigue crack growth in a grade R4 structural steel, largely used for fabricating offshore mooring chains by means of flash welding. CT specimens were machined from the base material as well as the welded joints and subjected to quenching from different austenizing temperatures and tempering at a given temperature. Aiming at the comparison with the material in industrial condition, CT specimens were also machined from chain links after flash welding, quenching and tempering under industrial conditions. After that, in a total of five microstructural conditions, the specimens were cyclically loaded in order to obtain the fatigue crack growth curves (a versus N and da/dN versus DK curves). The results show that the fatigue life of the material has increased when decreasing the fraction of tempered martensite, the industrial condition is associated with the smallest fatigue resistance and the fatigue life depends on the position where the fatigue specimens were taken form the chain like.

Despite the phenomena of fracture and fatigue having been the focus of academic research for more than 150 years, it remains in effect an empirical science lacking a complete and comprehensive set of predictive solutions. In this regard, the focus of the research in this thesis is on the development of new cohesive-zone models for fracture and fatigue that are afforded an ability to capture strain-rate effects. For the case of monotonic fracture in ductile material, different combinations of material response are examined with rate effects appearing either in the bulk material or localised to the cohesive-zone or in both. The development of a new rate-dependent CZM required first an analysis of two existing methods for incorporating rate dependency, i.e.either via a temporal critical stress or a temporal critical separation. The analysis revealed unrealistic crack behaviour at high loading rates. The new rate-dependent cohesive model introduced in the thesis couples the temporal responses of critical stress and critical separation and is shown to provide a stable and realistic solution to dynamic fracture. For the case of fatigue, a new frequency-dependent cohesive-zone model (FDCZM) has been developed for the simulation of both high and low-cycle fatigue-crack growth in elasto-plastic material. The developed model provides an alternative approach that delivers the accuracy of the loading-unloading hysteresis damage model along with the computational efficiency of the equally well-established envelope load-damage model by incorporating a fast-track feature. With the fast-track procedure, a particular damage state for one loading cycle is 'frozen in' over a predefined number of cycles. Stress and strain states are subsequently updated followed by an update on the damage state in the representative loading cycle which again is 'frozen in' and applied over the same number of cycles. The process is repeated up to failure. The technique is shown to be highly efficient in terms of time and cost and is particularly effective when a large number of frozen cycles can be applied without significant loss of accuracy. To demonstrate the practical worth of the approach, the effect that the frequency has on fatigue crack growth in austenitic stainless-steel 304 is analysed. It is found that the crack growth rate (da/dN) decreases with increasing frequency up to a frequency of 5 Hz after which it levels off. The behaviour, which can be linked to martensitic phase transformation, is shown to be accurately captured by the new FDCZM.

Built on the recent successes in understanding the crystallographic mechanism for short fatigue crack (SFC) growth across a grain boundary (GB) and developing an experimental method to quantify the GB resistance against short crack growth, a microstructure-based model was developed in this study to simulate the growth behaviors of SFCs in 3-D, by taking into account both the driving force and resistance along at each point along the crack front in an alloy. It was found that the GB resistance was a Weibull function of the minimum twist angle of crack deflection at the boundary in AA2024-T3 Al alloys. In the digital microstructure used in the model, the resistance at each GB that the short crack interacted with could be calculated, as long as the orientations of grains and the crack were known. In the model, an influence function accounting for the overlapping effect of the resistance from the neighboring grain boundaries was proposed, allowing for calculation of the total resistance distribution along the crack front. In order to overcome the time consuming problem for the existing equations to derive the distribution of stress intensity factor along the crack front under cyclic loading, an analytical equation was proposed to quantify the stress intensity factor distribution along an irregular shape planar crack. By introducing two shape-dependent factors, the fractured area and the perimeter of the crack front, the newly proposed equation could readily and accurately derive the stress intensity factor distribution along the crack front that had large curvatures and singularities. Finally, a microscopic-scale Paris’ equation was proposed that took into account both the driving force, i.e., stress intensity factor range, and the total resistance to calculate the growth rate at each point along crack front. The model developed in this work was able to incorporate microstructure, such as grain size and shape, and texture into simulation of SFC growth in 3-D. It was capable of simulating all the anomalous growth behaviors of SFCs, such as the marked scatters in growth rate measurement, retardation and arrest at grain boundaries, and crack plane deflection at grain boundaries, etc. The model was used to simulate the growth behaviors of SFCs initiated from prefractured constituent particles in order to interpret the multi-site fatigue crack initiation observed in AA2024-T351 Al alloys. Three types of SFCs were observed initiating from these particles, namely, type-I non-propagating cracks; type-II cracks which were arrested soon after propagating into the matrix; and type-III propagating cracks. To quantitatively study the 3-D effects of particle geometry and micro-texture on the growth behaviors of micro-cracks in these particles, rectangular micro-notches with different dimensions were fabricated using focused ion beam in the selected grains on the T-S planes in AA2024-T351 Al alloys, to mimic the pre-fractured particles in these alloys. Knowing the notch dimensions or particle shape, grain orientation and GB geometry, the simulated crack growth behaviors were consistent with the experimental observations, and the model was able to verify that the three types of cracks evolved from these particles were mainly associated with the thickness and width of the pre-fractured particles, though the particle geometry and grain orientation could also affect the behaviors of fatigue crack initiation at the particles. When the widths of the particles were less than 15 μm, like in most high strength Al alloys, the simulated results confirmed that the crack type was only associated with the particle thickness, consistent with the experimental results in AA2024-T351 alloys with a strong rolling texture. The lives for the SFCs to reach 0.5 mm in length were quantified with the model in the AA2024 alloy, revealing that there was a bimodal distribution in the life spectrum calculated, with the longer life peak being related to larger twist angles of crack deflection at the first GB the cracks encountered and the shorter life peak being associated with small twist angles (< 5°) at the first GB. The model further demonstrated the influence of grain structure on SFC growth by considering two different grain structures with the same initial short crack, namely, a layered grain structure with only the primary GBs perpendicular to the surface and the layered grains with both primary and secondary GBs. Depending on their positions and geometry, the secondary GBs could still exert a strong retarding effect on SFC growth on surface. The model was validated by matching to the growth rate measured on surface of a SFC in an AA8090 Al-Li alloy. Good consistency was achieved between the simulated and experimentally measured growth rates when both the primary and secondary GBs were considered in the model. The model developed in this study exhibits its potential applications to optimizing the microstructure and texture in alloys to enhance their fatigue resistance against fatigue crack growth, and to satisfactory life prediction of engineering alloys.