# Finite Elements Applications

Numerical Tools and Specific Fatigue Problems
• H. Maitournam
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 392)

## Abstract

A systematic methodology for designing structures against high-cycle fatigue is developed. It relies upon: (i) computational methods for the calculation of the limit response of structures subjected to cyclic loading; (ii) numerical implementation of efficient high-cycle fatigue criteria. The first step in the prediction of high-cycle fatigue damage is the determination of stress cycles. In this paper we present three finite element procedures for the calculation of elastic-plastic structures subjected to cyclic loading (repeated moving contacts, small oscillatory contacts, etc.), namely the direct cyclic method, the stationary method and the simplified analysis of inelastic structures. These methods lead to easy determination of the possible stabilised response. Therefore, they avoid the lengthy repeated calculations performed with the classical finite element method and an incremental treatment of the loading history. The second step is the use of high-cycle fatigue criteria. We review some numerical tools for their implementations. Finally, some applications are presented. The first one is a problem of a cylinder subjected to an elliptical rotating pressure. The direct stationary method is used to determine the stabilised stress cycle and a macro-meso high-cycle fatigue criterion is used to detect crack initiation. The second application is the numerical simulation of a fretting fatigue map in relation with material fatigue properties.

## Keywords

Multiaxial Fatigue Slip Regime Fatigue Criterion Inelastic Structure Incremental Treatment
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