A frequency-domain formulation of MCE method for multi-axial random loadings

Many multi-axial fatigue limit criteria are formalized as a linear combination of a shear stress amplitude and a normal stress. To identify the shear stress amplitude, appropriate conventional definitions, as the minimum circumscribed circle (MCC) or ellipse (MCE) proposals, are in use. Despite computational improvements, deterministic algorithms implementing the MCC/MCE methods are exceptionally time-demanding when applied to "coiled" random loading paths resulting from in-service multi-axial loadings and they may also provide insufficiently robust and reliable results. It would be then preferable to characterize multi-axial random loadings by statistical re-formulations of the deterministic MCC/MCE methods. Following an early work of Pitoiset et al., this paper presents a statistical re-formulation for the MCE method. Numerical simulations are used to compare both statistical re-formulations with their deterministic counterparts. The observed general good trend, with some better performance of the statistical approach, confirms the validity, reliability and robustness of the proposed formulation.