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.

Fatigue crack growth behavior of AA7050 T7451 aluminum alloy under mode II loading condition in two orientations was investigated. Compact shear specimens were prepared in TL and LT directions. A loading frame for mode II type of loading was manufactured. Using the loading frame and the specimen, KIIC values and mode II fatigue crack growth rates were calculated. Fractographic analysis of the fracture surfaces of both mode II fracture toughness test specimens and mode II fatigue crack growth test specimens were done to examine the effects of mode II load. KIIC values were measured between 1.3 and 1.5 times the KIC values for this alloy. As for mode II fatigue crack growth rates, TL orientation shows the highest mode II fatigue crack growth resistance.

The effect of different aging treatments on fatigue crack growth behavior of AA6013 aluminum alloy was investigated. C(T) (Compact Tension) specimens were prepared in L-T and T-L direction for fatigue crack growth tests. Samples were in T651 as received, T42 which is solution heat treated at 538 &ordm / C for 90 minutes, water quenched and aged in room temperature for 96 hours, and one group of samples were overaged at 245 &ordm / C for 12 hours after T42 condition was achieved. Hardness and conductivity measurements were achieved for all conditions after the heat treatments. Fatigue crack growth tests were performed at as received condition T651, T42 and 245 &ordm / C aged samples in laboratory air with sinusoidal loading of stress ratio R=0.1 and at a frequency of 1 Hz. The highest fatigue crack growth resistance is observed for T651 T-L and 245 &ordm / C overaged L-T condition.

Turbine engine blades are subjected to extreme conditions characterized by significant and simultaneous excursions in both stress and temperature. These conditions promote thermo-mechanical fatigue (TMF) crack growth which can significantly reduce component design life beyond that which would be predicted from isothermal/constant load amplitude results. A thorough understanding of the thermo-mechanical fatigue crack behavior in single crystal superalloys is crucial to accurately evaluate component life to ensure reliable operations without blade fracture through the use of "retirement for cause" (RFC). This research was conducted on PWA1484, a single crystal superalloy used by Pratt & Whitney for turbine blades. Initially, an isothermal constant amplitude fatigue crack growth rate database was developed, filling a void that currently exists in published literature. Through additional experimental testing, fractography, and modeling, the effects of temperature interactions, load interactions, oxidation and secondary crystallographic orientation on the fatigue crack growth rate and the underlying mechanisms responsible were determined. As is typical in published literature, an R Ratio of 0.7 displays faster crack growth when compared to R = 0.1. The effect of temperature on crack growth rate becomes more pronounced as the crack driving force increases. In addition secondary orientation and R Ratio effects on crack growth rate were shown to increase with increasing temperature. Temperature interaction testing between 649°C and 982°C showed that for both R = 0.1 and 0.7, retardation is present at larger alternating cycle blocks and acceleration is present at smaller alternating cycle blocks. This transition from acceleration to retardation occurs between 10 and 20 alternating cycles for R = 0.1 and around 20 alternating cycles for R = 0.7. Load interaction testing showed that when the crack driving force is near KIC the overload size greatly influences whether acceleration or retardation will occur at 982°C. Semi-realistic spectrum testing demonstrated the extreme sensitivity that relative loading levels play on fatigue crack growth life while also calling into question the importance of dwell times. A crack trajectory modeling approach using blade primary and secondary orientations was used to determine whether crack propagation will occur on crystallographic planes or normal to the applied load. Crack plane determination using a scanning electron microscope enabled verification of the crack trajectory modeling approach. The isothermal constant amplitude fatigue crack growth results fills a much needed void in currently available data. While the temperature and load interaction fatigue crack growth results reveal the acceleration and retardation that is present in cracks growing in single crystal turbine blade materials under TMF conditions. This research also provides a deeper understanding of the failure and deformation mechanisms responsible for crack growth during thermo-mechanical fatigue. The crack path trajectory modeling will help enable "Retirement for Cause" to be used for critical turbine engine components, a drastic improvement over the standard "safe-life" calculations while also reducing the risk of catastrophic failure due to "chunk liberation" as a function of time. Leveraging off this work there exists the possibility of developing a "local approach" to define a crack growth forcing function in single crystal superalloys.

The objective of this study is to develop crack growth analysis methods for functionally graded materials under mode I cyclic loading by using finite element technique. The study starts with the analysis of test specimens which are given in ASTM standard E399. The material properties of specimens are assumed to be changing along the thickness direction according to a presumed variation function used for the modeling of functionally graded materials. The results of the study reveal the influence of different material variation functions on the crack growth behavior. In the second part, the growth of an elliptical crack which is a common case in engineering applications is analyzed. First, mode I cycling loading is applied perpendicular to the crack plane and crack growth profiles for a certain number of cycles are obtained for homogeneous materials. Then, the code is extended for the analysis functionally graded materials. The material properties are assumed to vary as an exponential function along the major or minor axis direction of the crack. The results can be used to examine the crack profile and material constants&rsquo / influence for a certain number of cyclic loading.

The fatigue of materials and structures is a subject that has been under investigation for almost 160 years; yet reliable fatigue life predictions are still more of an empirical art than a science. The traditional safe-life approach to fatigue design is based upon the total time to failure of a virtually defect free component. This approach is heavily reliant on the use of safety factors and empirical equations, and therefore much scatter in the fatigue life predictions is normally observed. Furthermore, the safe-life approach is unsuitable for many important applications such as aircraft, pressure vessels, welded structures, and microelectronic devices. In these applications the existence of initial defects is practically unavoidable and the time of propagation from an initial defect to final failure is comparable with the total life of the component. In the early 1970’s, the aircraft industry pioneered a new approach for the analysis of fatigue crack growth, known as damage tolerant design. This approach utilises fracture mechanics principles to consider the propagation of fatigue cracks from an initial crack length until final fracture, or a critical crack length, is reached. Since the first implementation of damage tolerant design, much research and development has been undertaken. In particular, theoretical and experimental fracture mechanics techniques have been utilised for the investigation of a wide variety of fatigue crack growth phenomena. One such example is the retardation and acceleration in crack growth rate caused by spike overloads or underloads. It is generally accepted, however, that the current level of understanding of fatigue crack growth phenomena and the adequacy of fatigue life prediction techniques are still far from satisfactory. This thesis theoretically investigates various non-linear individual and interaction phenomena associated with fatigue crack growth. Specifically, the effect of plate thickness on crack growth under constant amplitude loading, crack growth retardation due to an overload cycle, and small crack growth from sharp notches are considered. A new semianalytical method is developed for the investigations, which utilises the distributed dislocation technique and the well-known concept of plasticity-induced crack closure. The effects of plate thickness are included through the use of first-order plate theory and a fundamental solution for an edge dislocation in plate of arbitrary thickness. Numerical results are obtained via the application of Gauss-Chebyshev quadrature and an iterative procedure. The developed methods are verified against previously published theoretical and experimental data. The elastic out-of-plane stress and displacement fields are first investigated using the developed method and are found to be in very good agreement with past experimental results and finite element simulations. Crack tip plasticity is then introduced by way of a strip-yield model. The effects of thickness on the crack tip plasticity zone and plasticity-induced crack closure are studied for both small and large-scale yielding conditions. It is shown that, in general, an increase in plate thickness will lead to a reduction in the extent of the plasticity and associated crack closure, and therefore an increase in the crack growth rates. This observation is in agreement with many findings of past experimental and theoretical studies. An incremental crack growth scheme is implemented into the developed method to allow for the investigation of variable amplitude loading and small fatigue crack growth. The case of a single tensile overload is first investigated for a range of overload ratios and plate thicknesses. This situation is of practical importance as an overload cycle can significantly increase the service life of a cracked component by temporarily retarding the crack growth. Next to be studied is growth of physically small cracks from sharp notches. Fatigue cracks typically initiate from stress concentrations, such as notches, and can grow at rates higher than as predicted for a long established crack. This can lead to non-conservative estimates for the total fatigue life of a structural component. For both the overload and small crack cases, the present theoretical predictions correlate well with past experimental results for a range of materials. Furthermore, trends observed in the experiments match those of the predictions and can be readily explained through use of crack closure arguments. This thesis is presented in the form of a collection of published or submitted journal articles that are the result of research by the author. These nine articles have been chosen to best demonstrate the development and application of the new theoretical techniques. Additional background information and an introduction into the chosen field of research are provided in order to establish the context and significance of this work. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1349588 / Thesis (Ph.D.) - University of Adelaide, School of Mechanical Engineering, 2008