Spatial Poisson processes for fatigue crack initiation

TL;DR

This paper introduces a stochastic spatial Poisson process model that predicts fatigue crack initiation on metallic specimens by integrating stress analysis and experimental data, applicable to various geometries.

Contribution

The novel model combines stress-life curves with spatially averaged effective stress using finite element analysis, enabling crack initiation predictions across different specimen geometries.

Findings

Model accurately predicts crack initiation in aluminum specimens.

Bayesian methods improve survival probability estimates.

Applicable to diverse geometries and fatigue conditions.

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, $\sigma_{{\mathrm{eff}}}^{\Delta} (\mathbf{x})$, 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.