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 language||English (US)|
|Number of pages||22|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Nov 16 2018|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): 2281, 2584
Acknowledgements: Z. Sawlan, M. Scavino and R. Tempone are members of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering. R. Tempone received support from the KAUST CRG3 Award Ref: 2281 and the KAUST CRG4 Award Ref: 2584.