Spectral methods to estimate local multiaxial fatigue failure for structures undergoing random vibrations

Abstract

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 consistent results when compared with those obtained in the time domain from Monte‐Carlo simulations of local stress vectors while offering tremendous computer savings. A frequency domain tool indicating whether the principal stress directions do rotate with time or not during the loading at a given location in the structure is also presented.