Spatial Poisson processes for fatigue crack initiation

Ivo Babuška, Zaid A Sawlan, Marco Scavino, Barna Szabó, Raul Tempone

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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, σeffΔ(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 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.
Original languageEnglish (US)
Pages (from-to)454-475
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Nov 16 2018


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