  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, $\sigma_{{\mathrm{eff}}}^{\Delta}
(\mathbf{x})$, which is computed after solving numerically the linear
elasticity equations on the specimen domains using finite element methods.
Here, $\Delta$ is a parameter that characterizes the size of the neighbors
covering the domain boundary. The averaged effective stress, parameterized by
$\Delta$, 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.
