Multiaxial fatigue damage estimation of structures under random vibrations using Matsubara’s criterion

Abstract The purpose of such a multiaxial fatigue damage criterion is to estimate the life time of structures subject to multiaxial loads. Therefore, several methods are developed to achieve this purpose. Comparing with other criteria, Matsubara’s criterion predicts the fatigue damage with higher accuracy. However, this method has been applied only for constant amplitude loading. But, in real mechanical application structures are subject to random vibrations. So, in this paper we propose an extension of this criterion in the case of random structures under random vibrations, using a computationally efficient multiaxial fatigue damage strategy developed in frequency domain. Matsubara’s criterion is constituted of two parameters: one governing crack initiation, and the other governing crack growth. Each parameter will be calculated from the stresses Power Spectral Densities determined at each point of the structure. A time domain formulation is also proposed in order to compare the two strategies. Two numerical applications are then used, at the end of this paper, to present the advantages of the frequency domain strategy of Matsubara’s criterion for treating problem of multiaxial fatigue damage of structures under random loads.