Issue 41

Carpinteri A. et alii, Frattura ed Integrità Strutturale, 41 (2017) 40-44; DOI: 10.3221/IGF-ESIS.41.06 41 by such an input. However, most structures experience a variety of loadings. Therefore, since many load cases are necessary for fatigue analysis, the computational time can become extremely high or even unacceptable [2]. A much more efficient method of analysis, named frequency-domain or spectral analysis, is that to consider the Power Spectral Density (PSD) function of the loading on the structure, which represents the frequency content of the loading time history. Generally, such methods employ an equivalent uniaxial loading to represent the actual multiaxial stress state, opening the possibility to use time- and frequency-domain methods originally proposed for fatigue analysis under uniaxial variable or random amplitude loading. The spectral method employed in this paper was proposed by the authors to determine fatigue damage in structures under multiaxial stationary random Gaussian loading [3]. In the recent past, the method was validated by employing experimental data available in the literature [3-7]. Numerical simulations are here developed, by considering random biaxial loading characterized by different values of the correlation coefficient, zero order moments ratio and central frequencies ratio. F REQUENCY - DOMAIN CRITICAL PLANE (F-D/CP) CRITERION he input data for the fatigue damage calculation is the PSD matrix of the stress tensor (Step 1 in Fig.1). The determination of the expected critical plane orientation constitutes an important part of the algorithm (Step from 2 to 4 in Fig.1). The PSD function of an equivalent stress is defined as a linear combination of the PSD functions of suitable stress components acting on the critical plane. Finally, the expected fatigue damage per unit time is obtained (Step 5 in Fig.1). Details of each step of the F-D/CP criterion are reported in Refs [3-7]. Determination of the PSD matrix S   (  ) Determination of the critical plane orientation 1 1 3 1 2 4 5 xyz Determination of the PSD matrix S  (  ) x'y'z' Determination of the PSD matrix S   (  ) x''y''z'' Calculation of expected fatigue damage rate E[D] Figure 1 : Algorithm for damage determination using the F-D/CP criterion. Random biaxial loading: numerical simulations Let us consider the following stress tensor         xyz 1 2 3 4 5 6 x y z y xz x 0 0 0 0 T T T z xy xy t s , s , s , s , s , s , , , , , , , , , ,            s with respect to the fixed frame XYZ . By assuming that the random features can be described by a two-dimensional ergodic stationary Gaussian stochastic process with zero mean value, the PSD matrix with respect to XYZ is here displayed:   11 16 xyz 61 66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S S S S                       S (1) T