PSI - Issue 38

Arvid Trapp et al. / Procedia Structural Integrity 38 (2022) 260–270 A. Trapp / Structural Integrity Procedia 00 (2021) 1–11

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A lifetime prediction on the basis of a load spectrum generally consists of linear damage accumulation of the stress cycles under the consideration of the corresponding material resp. component properties. They are generally provided in the form of stress-life-curves (S-N curves) [17]. An S-N-curve given by the elemen tary Palmgren-Miner rule is fully defined by the constant C and the Miner exponent k . It relates the number of cycles n with amplitude s to failure by C = s k n . Therefore, to compare load spectra of variable amplitudes s j with count n j to other spectra by its e ff ects on lifetime estimates, Eq. (11) defines the equivalent response amplitude s eq = 1 n eq J j = 1 n j s k j 1 k (11) Equation (11) sums all stress cycles as partial damages, from which an equivalent response amplitude s eq is derived, causing the same damage considering n eq cycles under linear damage accumulation. This can be interpreted as transforming the load spectrum of variable amplitudes into a single-level spectrum of n eq cycles for a Miner exponent k . In the form of the equivalent response amplitude, reconstructed stress series can be compared to the original series in a compact and meaningful way. The equivalent response amplitude finds common use by the notation pseudo damage. Intuitively, the closer a relevant frequency component locates to the Nyquist frequency f Ny the more probable is that its peaks are not well resolved by the sampling. Therefore, the following investigation analyzes individual harmonics (exemplary in Fig. 2a) for di ff erent ratios of f f Ny via the pseudo damage (Eq. 11). The central idea is to visualize the tendency for errors due to insu ffi cient sampling — foremost as a function of frequency (Fig. 2b) but also in the form of load spectra (Fig. 2c,d). Hereby it is of interest whether and how the Miner exponent k — the inverse of the S-N slope — may interfere with the deviations 3.2. Analysis of individual harmonics

(a) schematic analysis of sampled harmonics with ratio f / f Ny = 40%

(b) pseudo damage for di ff erent Miner exponents

(d) load spectrum for f / f Ny = 50%

(c) load spectrum for f / f Ny = 40%

Fig. 2: Sampling analysis for individual harmonics with given ratio f / f Ny