Fatigue of metals is a problem that affects almost all sectors of industry, from energy to transportation, and failures to account for fatigue or incorrect estimations of service life have cost many lives. To mitigate such fatigue failures, engineers must be able to reliably predict the fatigue life of components under service conditions. Great progress has been made in this regard in the past 40 years; however one aspect of fatigue that is still being actively researched is the behavior of microstructurally small cracks (MSCs), which can diverge significantly from that of long cracks. The portion of life spent nucleating and growing a MSC over the first few grains/phases can consume over 90% of the total fatigue life under High Cycle Fatigue (HCF) conditions and is the primary source of the scatter in fatigue lives. Therefore, the development of robust fatigue design methodologies requires that the MSC regime of crack growth can be adequately modeled. The growth of microstructurally small cracks is dominated by influence of the local heterogeneity of the microstructure and is a highly complex process. In order to successfully model the growth of these microstructurally small cracks (MSCs), two computational frameworks are necessary. First, the local behavior of the material must be modeled, necessitating a constitutive relation with resolution on the scale of grain size. Second, a physically based model for the nucleation and growth of microstructurally small fatigue cracks is needed. The overall objective of this thesis is best summarized as the introduction these two computational frameworks, a crystal plasticity constitutive model and fatigue model, specifically for aluminum alloy 7075-T6, a high-strength, low density, precipitation hardened alloy used extensively in aerospace applications. Results are presented from simulations conducted to study the predicted crack growth under a variety of loading conditions and applied strain ratios, including uniaxial tension-compression and simple shear at a range of applied strain amplitudes. Results from the model are compared to experimental results obtained by other researchers under similar loading conditions. A modified fatigue crack growth algorithm that captures the early transition to Stage II growth in this alloy will also be presented.

This thesis focuses on the growth of cracks which are small in relation to the material microstructure especially the situation of clusters of small cracks grown from smooth surfaces, termed micro-multi-site cracking, as is frequently the case for components in service. A proper understanding of this regime of crack growth will allow for less conservative maintenance schedules as well as the application of more sensitive health monitoring systems which are currently under development. To address the problem a significant experimental investigation of micro-multi-site cracking was conducted on 7075-T7351 aluminum alloy. Using the resulting data a micro-structurally based transition crack length is defined to determine the point which separates small and long crack growth. This definition is based upon the observed evolution of scatter in the growth rates of growing small cracks. It is shown that this scatter falls with growth until the transition point is reached where it assumes a constant value for the growth of long cracks. It is then shown that the total population of cracks within the clusters can be considered as bi-modal. One distribution consists of primary cracks which can grow and ultimately cause specimen failure. The second distribution consists of secondary cracks, the growth of which ultimately arrests. Several methods for experimentally separating the two distributions have been developed. The first method relies upon the defined transition point between small and long crack behavior. A second method based upon the second derivative of the crack length versus cycle count data has also been developed. Since the secondary cracks cannot lead to failure their data must be discarded prior to any analysis. It is then shown that failure to do so will lead to erroneous non-conservative predictions of crack growth.

This thesis discusses plasticity-induced crack closure based finite element simulations of small fatigue cracks in three dimensions utilizing crystal plasticity theory. Previously, modeling has been performed in two dimensions using a double-slip crystal plasticity material model. The goal of this work is to extend that research using a full three-dimensional FCC crystal plasticity material model implementation that accounts for all twelve FCC slip systems. Discussions of Python scripts that were written to perform analyses with the commercial finite element code ABAQUS are given. A detailed description of the modeling methodology is presented along with results for single crystals and bicrystals. The results are compared with finite element and experimental results from the literature. A discussion of preliminary work for the analysis of crack growth around an intermetallic particle is also presented.

In spite of its significance in industrial applications, the prediction of the influence of microstructure on the early stages of crack formation and growth in engineering alloys remains underdeveloped. The formation and early growth of fatigue cracks in the high cycle fatigue regime lasts for much of the fatigue life, and it is strongly influenced by microstructural features such as grain size, twins and morphological and crystallographic texture. However, most fatigue models do not predict the influence of the microstructure on early stages of crack formation, or they employ parameters that should be calibrated with experimental data from specimens with microstructures of interest. These post facto strategies are adequate to characterize materials, but they are not fully appropriate to aid in the design of fatigue-resistant engineering alloys. This thesis considers finite element computational models that explicitly render the microstructure of selected FCC metallic systems and introduces a fatigue methodology that estimates transgranular and intergranular fatigue growth for microstructurally small cracks. The driving forces for both failure modes are assessed by means of fatigue indicators, which are used along with life correlations to estimate the fatigue life. Furthermore, cracks with meandering paths are modeled by considering crack growth on a grain-by-grain basis with a damage model embedded analytically to account for stress and strain redistribution as the cracks extend. The methodology is implemented using a crystal plasticity constitutive model calibrated for studying the effect of microstructure on early fatigue life of a powder processed Ni-base RR1000 superalloy at elevated temperature under high cycle fatigue conditions. This alloy is employed for aircraft turbine engine disks, which undergo a thermomechanical production process to produce a controlled bimodal grain size distribution. The prediction of the fatigue life for this complex microstructure presents particular challenges that are discussed and addressed. The conclusions of this work describe the mechanistic of microstructural small crack. In particular, the fatigue crack growth driving force has been characterized as it evolves within grains and crosses to other grains. Furthermore, the computational models serve as a tool to assess the effects of microstructural features on early stages of fatigue crack formation and growth, such as distributions of grain size and twins.