PSI - Issue 19

Zhu Li et al. / Procedia Structural Integrity 19 (2019) 528–537

529

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

2

1. Introduction

Frequency-based fatigue damage prediction methods are now widely adapted for fatigue damage assessment of mechanical components subjected to random loadings. Those structural components are increasingly used in more complex and harsh environments. The components are subjected to complex random loadings that are both difficult to model and expensive to test using current fatigue assessment methods [1]. Therefore, more accurate and efficient modeling approaches for the fatigue assessments of structures operating under extreme operational conditions are needed. Experimental vibrational test methods have been increasingly used in mechanical designs of machine systems [2]. Despite their recent widely usage, vibration experiments are regarded to be excessively expensive and time consuming [3,4]. Certain components such as a jet engine usually experience very high loading cycles i.e. more than a billion cycles and may require many months of laboratory tests under normal service conditions [1]. Therefore, accelerated fatigue test methods has been developed to reduce long test time and corresponding high costs [5,6,7,8,9]. Accelerated test methods employ exaggerated random load levels so that the testing time can be reduced into reasonable timeframe to yield equivalent fatigue damage. The vibrational random loadings are generally transformed in the frequency domain by a power spectral density (PSD) to conduct accelerated tests. The PSD loadings are usually described as a random Gaussian process [5,10]. The PSD can characterize the spread of the mean square vibration loadings over a frequency range [10]. Frequency-domain based fatigue damage approaches have been developed to provide fatigue life assessment of structures by connecting the relationship between the response PSD and fatigue damage [11,12,13]. The most of those approaches/ methods are currently based on the stationary Gaussian process represented a stationary PSD function (time invariant PSD function). The PSD are generally classified into narrow-band and wideband processes depending on a frequency band width of the PSD function. A probability density function (PDF) of loadings (e.g. stress ranges) for narrowband and wideband PSD functions can be associated to Rayleigh and D irlik’s distribution [8] respectively. The narrow-band allows for a direct derivation of the cycle distribution, as pointed out by Lutes and Sarkani [14]. As for a wide-band process the relation of the peak distribution and cycle amplitudes can be determined by empirical solutions (e.g., Dirlik [15]). Dirlik [15] has proposed an empirical solution for the probability density function of rainflow stress ranges. The Dirlik method is based on first four moments of the PSD. In the Dirlik method, the PSD versus frequency data is used to find the first four moments of the PSD function and these four moments are used to determine the PDF of stress ranges. Then, fatigue life is obtained by a damage accumulation method, e.g. Palmgren –Miner’s rule [16]. The PDF of stress distributions in Eq. (1) can be derived directly from first moments of the PSD function. The Narrowband method is a modeling approach based on the single moment ( 0 ) of the PSD function which is used to estimate the fatigue damage. In the Narrow-band process, it is assumed that every peak is coincident with a cycle, so the amplitudes of cycles can be associated with Rayleigh distribution. Braccesi et al. [13] proposed a damage modeling criterion which is called Bands method. According to the Bands method, a given PSD function regardless of its shape, can be divided into several bands. If each divided bandwidth is sufficiently narrow, then it can be related to the Rayleigh distribution of the stress cycles. Total fatigue damage for the given PSD function can be determined by summing of the damages of each individual narrowband [17,18]. Despite substantial progress, current frequency based damage assessment methods are based on stationary PSD function where shape and topology of PSD function does not change in time. However, many real systems, such as jet engine, tracked vehicles, helicopters experience complex random loadings where PSD functions are time varying [19]. These types of complex random loadings are defined as random-on-random loadings. Analysis and simulation of structural components need to account for real complex random loadings in order to provide more accurate fatigue predictions results. Therefore, Zhu and Ince [20,21] recently proposed a novel damage modeling approach to deal with complex random-on-random loadings (non-stationary PSD loadings). The modeling approach proposed by the present authors is further discussed to assess the fatigue damage associated with non-stationary PSD loading environments. The proposed modeling approach is numerically and experimentally validated by a finite element method and experiments using three simplified structures made of 5052-H32 aluminum alloy.