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Using machine learning and a data-driven approach to identify the small fatigue crack driving force in polycrystalline materials

Abstract : The propagation of small cracks contributes to the majority of the fatigue lifetime for structural components. Despite significant interest, criteria for the growth of small cracks, in terms of the direction and speed of crack advancement, have not yet been determined. In this work, a new approach to identify the microstructurally small fatigue crack driving force is presented. Bayesian network and machine learning techniques are utilized to identify relevant micromechanical and microstructural variables that influence the direction and rate of the fatigue crack propagation. A multimodal dataset, combining results from a high-resolution 4D experiment of a small crack propagating in situ within a polycrystalline aggregate and crystal plasticity simulations, is used to provide training data. The relevant variables form the basis for analytical expressions thus representing the small crack driving force in terms of a direction and a rate equation. The ability of the proposed expressions to capture the observed experimental behavior is quantified and compared to the results directly from the Bayesian network and from fatigue metrics that are common in the literature. Results indicate that the direction of small crack propagation can be reliably predicted using the proposed analytical model and compares more favorably than other fatigue metrics. INTRODUCTION Modeling the propagation of small fatigue cracks, especially cracks that are intragranular in nature, requires information about how the underlying microstructure affects the crack behavior. While, crack initiation has been modeled as both stochastic 1,2 and deterministic, 3-6 there is still an open question if the small fatigue crack behavior can be predicted. Small crack propagation follows crystallographic directions and planes, and thus is said to be a slip-mediated process. 7-9 The behavior of long cracks is well described by linear elastic fracture mechanics through the Paris law. 10 While for small cracks, the propagation rate strongly deviates from linear elastic fracture mechanics behavior and exhibits large scatter, 11-13 based on the complex interactions between the small crack and the local microstructure. Several relationships have been proposed to capture the small crack behavior, albeit these theories have not been validated at the appropriate length-scale due to prior limitations in the experimental measurements. With the advent of synchrotron-based x-ray tomography and diffraction techniques combined with in situ loading, the necessary data are available for the crack direction and propagation rate with respect to the microstructure. In this work, experimental data for the evolution of a fatigue crack relative to the local microstructure during in situ loading 14,15 are used as the foundation to build a model for the driving force of small fatigue cracks. Based on the 3D nature and intricacies of the local crack growth process, simple relationships governing the fatigue crack dynamics are very difficult to extract, thus data-driven approaches offer a promising path forward. Specifically, machine-learning
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Andrea Rovinelli, Michael Sangid, Henry Proudhon, Wolfgang Ludwig. Using machine learning and a data-driven approach to identify the small fatigue crack driving force in polycrystalline materials. npj Computational Materials, Springer Nature, 2018, 4 (1), 10 p. ⟨10.1038/s41524-018-0094-7⟩. ⟨hal-01869114⟩



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