Spectral Methods to Estimate Local Multiaxial Fatigue Failure Criteria for Structures Undergoing Random Vibrations

Xavier Pitoiset, Igor Rychlik and André Preumont

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
This paper proposes computationally efficient frequency domain formulations for two well-known multiaxial fatigue failure criteria, namely Matake's critical plane criterion and Crossland's criterion. For that purpose, it is shown how fatigue related variables involved in both criteria can be estimated from the power spectral density matrix of the local stress vector. The finite element model of an example structure is then used to illustrate the application of the proposed frequency domain approaches. It is observed that both frequency domain formulations produce accurate results when compared to those obtained in the time domain from Monte-Carlo simulations of local stress vectors
while offering tremendous computer savings. A frequency domain tool indicating if the principal stress directions do rotate with time or not during the loading at a given location in the structure is also presented.
Key words:
multiaxial fatigue, failure criterion, random vibrations, finite elements