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arXiv · 1805.03433

Spatial Poisson processes for fatigue crack initiation

Ivo Babuska·Zaid Sawlan·Marco Scavino·Barna Szabó·Raúl Tempone
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Abstract

In this work we propose a stochastic model for estimating the occurrence of crack initiations on the surface of metallic specimens in fatigue problems that can be applied to a general class of geometries. The stochastic model is based on spatial Poisson processes with intensity function that combines stress-life (S-N) curves with averaged effective stress, $σ_{\mathrm{eff}}^Δ (\mathbf{x})$, which is computed after solving numerically the linear elasticity equations on the specimen domains using finite element methods. Here, $Δ$ is a parameter that characterizes the size of the neighbors covering the domain boundary. The averaged effective stress, parameterized by $Δ$, maps the stress tensor to a scalar field upon the specimen domain. Data from fatigue experiments on notched and unnotched sheet specimens of 75S-T6 aluminum alloys are used to calibrate the model parameters for the individual data sets and for their combination. Bayesian and classical approaches are applied to estimate the survival-probability function for any specimen tested under a prescribed fatigue experimental setup. Our proposed model can predict the initiation of cracks in specimens made from the same material with new geometries.

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Ivo Babuska, Zaid Sawlan, Marco Scavino, Barna Szabó, Raúl Tempone. 2018-10-07. Spatial Poisson processes for fatigue crack initiation. https://doi.org/10.1016/j.cma.2018.11.007

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