Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 101 (2015) 347 – 354
3rd International Conference on Material and Component Performance under Variable Amplitude Loading, VAL2015
Mean stress effect correction in frequency-domain methods for fatigue life assessment Adam Niesáonya,*, Michaá Böhma a
Opole University of Technology, Department of Mechanics and Machine Design, Mikoáajczyka 5, Opole 45-271, Poland
Abstract Two fatigue life calculation methods are presented. One defined in the time domain and the second one defined in the frequency domain – both supplemented with a mean stress effect correction. The method is verified on the basis of own results for the S355JR steel. The authors analyze six models for the designation of the probability density function (PDF) of stress amplitudes used in the calculation process. The results are presented in the form of probability distributions before and after PSD transformation and the calculated fatigue life’s are being compared with the experimental ones in fatigue comparison graphs. © Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 2015The The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Czech Society for Mechanics. Peer-review under responsibility of the Czech Society for Mechanics
Keywords:mean stress, spectral method, random loading, PSD, fatigue;
1. Introduction The phenomenon of material fatigue, which occurs due to the impact of time varying forces is one of the main reasons for material failure. The variable forces which are the main reason for this effect can be divided into two groups with constant amplitude loading and random loading. Those loads can be described with the use of deterministic formulas or with the use of stochastic theory [1]. The mean stress effect in fatigue life assessment is a well-known issue discussed widely in the literature. The mean stress is an extra static load in the form of an additional load applied to the construction or its self-weight [2]. Engineers have to take into account those kind of extra loads and prevent early fatigue failure or other construction defects. Although the literature presents solutions for the correction of mean
* Corresponding author. Tel.: +48 77 400 83 99; fax: +48 77 449 99 06. E-mail address:
[email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Czech Society for Mechanics
doi:10.1016/j.proeng.2015.02.042
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Adam Niesłony and Michał Böhm / Procedia Engineering 101 (2015) 347 – 354
stress in the time domain (cycle counting methods), it is rare to find a solution in the frequency domain (spectral method) [3]. The authors have presented a mean stress correction method that can be used in the frequency domain. For this cause a power spectral density transformation is used [4]. The transformation process is realized with the use of well-known mean stress compensation models. The fatigue life is being calculated with the use of probability density functions as well as damage accumulation hypothesis. The presented correction method is verified with own test results for the S355JR steel for narrowband and broadband loading characteristics. The method is being compared with the method proposed by Kihl and Sarkani [5]. The proposed calculation procedure can be used for narrowband as well as for broadband loading characteristics, independently from the spectral method for determination of the probability density function (PDF) of amplitudes. Nomenclature K(ım) GV( f ) ıa ım ımax ımin ı’f ǻı p(ıa) R Rm Tcal Texp
mean stress compensation coefficient, power spectral density of a centered stress course, stress amplitude, mean stress, maximum stress, minimum stress, fatigue strength coefficient, stress range, stress amplitude probability density function, stress ratio, tensile strength, calculated fatigue life, experimental fatigue life.
The mean stress value used in the process of fatigue life assessment is presented as the static component of the stress history according to the formula: T
Vm
1 V (t ) dt . T of T 0 lim
³
(1)
For the constant amplitude loading the mean stress value is defined as the algebraic mean of the maximum and minimum stress value in one cycle. When discussing the mean stress value we refer to some basic formulas: x Stress range
'V Vmax Vmin ,
(2)
where ımax and ımin are respectively maximum and minimum stress. x Stress amplitude Va
V max V min 2
.
(3)
x Mean stress Vm
V max V min 2
.
(4)
Adam Niesłony and Michał Böhm / Procedia Engineering 101 (2015) 347 – 354
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Adam Niesłony and Michał Böhm / Procedia Engineering 101 (2015) 347 – 354
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Adam Niesłony and Michał Böhm / Procedia Engineering 101 (2015) 347 – 354
for PDF estimation. The theoretical assumed universal application has been confirmed for both narrowband and broadband signal stress characteristics. We can summarize that: x the proposed method for correction of mean stress in the frequency domain has been correctly verified, x it can be used for both narrow and broadband signals, x the procedure directly operates on the power spectral density of the signal, x not every probability density function describes the amplitude distribution in a correct way in comparison with the rainflow amplitude distribution, x nevertheless every probability density function that has been used for calculations gave satisfying fatigue calculation results. a
b
6
10
Rayleigh Rice Dirlik Zhao-Baker Benasciutti-Tovo Lalanne
5
Rayleigh Rice Dirlik Zhao-Baker Benasciutti-Tovo Lalanne
5
Tcal , cycle
10
Tcal , cycle
10
6
10
4
4
10
10
3
3 3
3
3
3
10 3 10
4
5
10
10 Texp , cycle
6
10
10 3 10
4
5
10
10
6
10
Texp , cycle
Fig. 7. Comparison of experimental results with calculation results (a) narrowband; (b) broadband.
Acknowledgements The Project was financed from a Grant by National Science Centre (Decision No. DEC-2012/05/B/ST8/02520). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
A. Niesáony, E. Macha, Spectral Method in Multiaxial Random Fatigue, Springer, Berlin Heidelberg, 2007. A. Niesáony, M. Böhm, Mean stress effect correction using constant stress ratio S-N curves, Int. J. Fatigue 52 (2013) 49–56. T. àagoda, E. Macha, A. Niesáony, Fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading, Fatigue Fract. Eng. M. 28 (2005) 409–420. A. Niesáony, M. Böhm, Mean stress value in spectral method for the determination of fatigue life, Acta Mechanica et Automatica 6 (2012) 71–74. D.P. Kihl, S. Sarkani, Mean stress effects in fatigue of welded steel joints, Probabilist. Eng. Mech. 14 (1999) 97–104. T. àagoda, E. Macha, R. Pawliczek, The influence of the mean stress on fatigue life of 10HNAP steel under random loading, Int. J. Fatigue 23 (2001) 283–291. E. Haibach, Betriebsfestigkeit - Verfahren und Daten zur Bauteilberechnung, Springer, Berlin Heidelberg, 2006. A. Niesáony, Comparison of some selected multiaxial fatigue failure criteria dedicated for spectral method, J. Theor. Appl. Mech. 48 (2010) 233–254. J. S. Bendat, Random data: analysis and measurement procedures, 4th ed. Hoboken, N.J: Wiley, 2010. C. Lalanne, Mechanical Vibration and Shock Analysis, Random Vibration. John Wiley & Sons, 2013. D. Benasciutti, R. Tovo, Frequency-based fatigue analysis of non-stationary switching random loads, Fatigue Fract. Eng. M. 30 (2007) 1016–1029. D. Benasciutti, R. Tovo, Comparison of spectral methods for fatigue analysis of broad-band Gaussian random processes, Probabilist. Eng. Mech. 21 (2006) 287–299. D. Benasciutti, R. Tovo, Spectral methods for lifetime prediction under wide-band stationary random processes, Int. J. Fatigue 27 (2005) 867–877. C. Braccesi, F. Cianetti, G. Lori, D. Pioli, An equivalent uniaxial stress process for fatigue life estimation of mechanical components under multiaxial stress conditions, Int. J. Fatigue 30 (2008) 1479–1497. C. Braccesi, F. Cianetti, G. Lori, D. Pioli, Fatigue behaviour analysis of mechanical components subject to random bimodal stress process: frequency domain approach, Int. J. Fatigue 27 (2005) 335–345.
