Finite Element Simulations Of Fatigue Crack Stages In Aa 7075-T651 Microstructure

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This dissertation is organized as three independent chapters. Each chapter is intended to be, or has been, submitted as a journal article and has a specific topic of focus. However, they all address the use of finite element simulation in modeling the initial stages of microstructurally small fatigue cracks (MSFCs) in aluminum alloy (AA) 7075-T651. A detailed abstract is provided at the beginning of each chapter. Fatigue experiments of AA 7075-T651 double edge-notched specimens have illustrated that a very small percentage of second-phase particles incubate a crack and lead to life-limiting cracks. Many of the incubating particles eventually nucleate cracks into the surrounding microstructure, but the number of cycles to nucleation varies widely among them. The goal here is to develop an understanding of the mechanics underpinning the observed stochasticity so that more reliable fatigue life predictions can be made. This is motivated by recent experimental observations and statistical analyses that suggest that microstructural hotspots - the combination of features that initiate life-limiting cracks - can not be determined solely from the statistics of microstructural features, e.g. particle diameter. However, the mechanics of MSFCs are complex and detailed finite element simulations are necessary for accurate modeling. The objective of the first chapter is to study the hypothesis that nucleation can be predicted by determining slip accumulation near the crack front. The main contribution is the development of five slip-based nucleation metrics to aid in the study of the effect of slip localization and accumulation on nucleation. Each of the five slip-based metrics is derived from an elastic-viscoplastic crystal plasticity formulation. Two non-local regularization approaches for the slip-based metrics near the crack front are studied because of local numerical divergence of slip fields upon mesh refinement. The limited validation conducted in the first chapter suggests that slip accumulation governs if nucleation will occur. Furthermore, crystallographic orientation, with respect to an incubated crack, is found to play a dominant role in the localization and accumulation of slip, and can also influence the direction of crack nucleation. The second chapter uses the five slip-based metrics and non-local regularization techniques in 11 finite element models of replicated microstructures under fatigue loading. Each model is generated by replicating grain and particle geometry where each grain's measured orientation is defined using an elastic-viscoplastic crystal plasticity model. A high slip localization and accumulation rate is found to be a necessary, but not sufficient, condition for nucleation from cracked particles. Furthermore, the simulation results elucidate that the local stress required to drive nucleation reduces as slip is accumulated. A semi-empirical model for the number of cycles required to nucleate a crack is found. The observed nucleation direction did not coalign with the directions of slip localization and accumulation, but were orthogonal to the computed local maximum tangential stress direction. This indicates that nucleation in this alloy is a stage-II process. A probabilistic approach to model the complex, stochastic mechanical interplay among the various microstructural features and the MSFC stages is presented in the third chapter. The developed incubation and nucleation models are used in a Monte Carlo simulation to filter out statistically insiginificant realizations of candidate hotspots. Validation of this process is analyzed by comparing the statistics of observed hotspot features with the statistics of the predicted hotspot features. The determination of MSFC hotspots provides a distribution of initial crack sizes and locations in a digital microstructure for subsequent simulations of propagation. Collectively, this dissertation constitutes an extensive study of the ability to enhance fatigue life modeling philosophies by incorporating mechanics-based modeling of the MSFC stages. The outcome of the incubation and nucleation filters is a prediction of the statistical variation in MSFC behavior, as dependent on the local microstructural features. The mechanics-based models developed herein could also be used to predict a deterministic set of incubation and nucleation events based on a particular instance of a microstructure, on a component-by-component basis. This approach would enhance the safe-life philosophy, where a worst-case scenario is enforced among a fleet of components. Lastly, useful information for the design of more fatigue-resistant materials is obtained using the modeling and simulation approaches presented.

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