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.

Random multiaxial fatigue: A comparative analysis among selected frequency and time domain fatigue evaluation methods

“…However when the frequency translation is successful, the computational application of the method is improved, because of the well know synthesis properties of the frequency domain with respect to the time domain. In general the state of stress s(t) assumes the wellknown symmetric form with all non-zero components; however it is often accepted and adopted in literature the simplification of plane tensor [54], based on the experimental evidence that the fatigue failure occurs on the surface of the component [13,14]. Under such hypothesis the reconstruction of the state of stress gives the definition of three distinct components and then a reduced matrix S(x) of dimension 3 Â 3.…”

“…Even under these conditions the frequency translation, under the form implemented by Preumont et al [54], introduces an important beneficial effect on the computational effort, by the fast individuation of the critical plane.…”

Time and frequency domain models for multiaxial fatigue life estimation under random loading

“…he verification plane orientation, named critical plane, is here assumed to be dependent on the PSD matrix of the stress vector [13], as is explained in the following.…”

Random fatigue. A new frequency domain criterion for the damage evaluation of mechanical components

“…When the stress state satisfies the hypothesis of Gaussian stationary ergodic signal and is synthesized by a single Power Spectral Density function (uniaxial stress state) [20][21][22][23][24], the literature shows a whole series of approaches that, starting from its Power Spectral Density function (PSD), allow to directly obtain an estimation of the damage [7][8][9][10][11][12][13].…”