Research Papers

Different Fatigue Dynamics Under Statistically and Spectrally Similar Deterministic and Stochastic Excitations

[+] Author and Article Information
David Chelidze

e-mail: chelidze@egr.uri.edu
Department of Mechanical,
Industrial and Systems Engineering,
University of Rhode Island,
Kingston, RI 02881

R = σmin/σmax, where σmin is the minimum peak stress and σmax is the maximum peak stress.

1Corresponding author.

Manuscript received May 1, 2013; final manuscript received July 10, 2013; accepted manuscript posted July 29, 2013; published online September 23, 2013. Assoc. Editor: John Lambros.

J. Appl. Mech 81(4), 041004 (Sep 23, 2013) (8 pages) Paper No: JAM-13-1182; doi: 10.1115/1.4025138 History: Received May 01, 2013; Revised July 10, 2013; Accepted July 29, 2013

Estimating and tracking crack growth dynamics is essential for fatigue failure prediction. A new experimental system—coupling structural and crack growth dynamics—was used to show fatigue damage accumulation is different under chaotic (i.e., deterministic) and stochastic (i.e., random) loading, even when both excitations possess the same spectral and statistical signatures. Furthermore, the conventional rain-flow counting method considerably overestimates damage in case of chaotic forcing. Important nonlinear loading characteristics, which can explain the observed discrepancies, are identified and suggested to be included as loading parameters in new macroscopic fatigue models.

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Skorupa, M., 1998, “Load Interaction Effects During Fatigue Crack Growth Under Variable Amplitude Loading—A Literature Review. Part I: Empirical Trends,” Fatigue Fract. Eng. Mater. Struct., 21, pp. 987–1006. [CrossRef]
Skorupa, M., 1999, “Load Interaction Effects During Fatigue Crack Growth Under Variable Amplitude Loading—A Literature Review. Part II. Qualitative Interpretations. Fatigue Fract. Eng. Mater. Struct., 22, pp. 905–926. [CrossRef]
Miner, M., 1945, “Cumulative Damage in Fatigue,” J. Appl. Mech., 67, pp. A159–A164.
Palmgren, A., 1924, “Die Lebensdauer von Kugellagern,” Zeitschrift des Vereines Deutscher Ingenieure, 68(14), pp. 339–341.
Macha, E., Lagoda, T., Nieslony, A., and Kardas, D., 2006, “Fatigue Life Under Variable-Amplitude Loading According to the Cycle-Counting and Spectral Methods,” Mater. Sci., 42(3), pp. 416–425. [CrossRef]
Foong, C.-H., Pavlovskaia, E., Wiercigroch, M., and Deans, W.F., 2003, “Chaos Caused by Fatigue Crack Growth,” Chaos, Solitons Fractals, 16, pp. 651–659. [CrossRef]
Falco, M., Liu, M., and Chelidze, D., 2010, “A New Fatigue Testing Apparatus Model and Parameter Identification,” ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Montreal, QB, Canada, August 15–18, ASME Paper No. DETC2010-29107, pp. 1007–1012. [CrossRef]
ASTM E1820-08a, 2008, “Standard Test Methods for Measurement of Fracture Toughness. Annual Book of ASTM Standards,” ASTM, Philadelphia, PA.
Foong, C. H., Wiercigroch, M., and Deans, W. F., 2006, “Novel Dynamic Fatigue-Testing Device: Design and Measurements,” Meas. Sci. Technol., 17, pp. 2218–2226. [CrossRef]
Jakšić, N., Foong, C. H., Wiercigroch, M., and Boltežar, M., 2008, “Parameter Identification and Modelling of the Fatigue-Testing Rig,” Int. J. Mech. Sci., 50(7), pp. 1142–1152. [CrossRef]
Schreiber, T., and Schmitz, A., 1996, “Improved Surrogate Data for Nonlinearity Tests,” Phys. Rev. Lett., 77, pp. 635–638. [CrossRef] [PubMed]
Kantz, H., and Schreiber, S., 2004, Nonlinear Time Series Analysis, Cambridge University, Cambridge, UK.
Downing, S. D., and Socie, D. F., 1982, “Simple Rainflow Counting Algorithms,” Int. J. Fatigue, 4(1), pp. 31–40. [CrossRef]
ASTM E1049, 1985, “Standard Practices for Cycle Counting in Fatigue Analysis,” ASTM, Philadelphia, PA.
Dingwell, J. B., 2006, “Lyapunov Experiments,” The Wiley Encyclopedia of Biomedical Engineering, M. Akay, ed., John Wiley & Sons, Inc., New York. [CrossRef]
Wolf, A., Swift, J., Swinney, H., and Vastano, J., 1985, “Determining Lyapunov Exponents From a Time Series,” Physica D, 16(3), pp. 285–317. [CrossRef]
Wolf, A., 1986, “Quantifying Chaos With Lyapunov Exponents,” Chaos, A. V. Holden, ed., Princeton University Press, Princeton, NJ.
Grassberger, P., and Procaccia, I., 1983, “Characterization of Strange Attractors,” Phys. Rev. Lett., 50(5), pp. 346–349. [CrossRef]
Grassberger, P., 1983, “Generalized Dimensions of Strange Attractors,” Phys. Lett. A, 97(6), pp. 227–230. [CrossRef]
Grassberger, P., and Procaccia, I., 1983, “Measuring the Strangeness of Strange Attractors,” Physica D, 9, pp. 189–208. [CrossRef]
Rosenstein, M. T., Collins, J. J., and DeLuca, C. J., 1993, “A Practical Method for Calculating Largest Lyapunov Exponents From Small Data Sets,” Physica D, 65, pp. 117–134. [CrossRef]
Fraser, A. M., and Swinney, H. L., 1986, “Independent Coordinates for Strange Attractors From Mutual Information,” Phys. Rev. A, 33, pp. 1134–1140. [CrossRef] [PubMed]
Kennel, M. B., Brown, R., and Abarbanel, H.D.I, 1992, “Determining Embedding Dimension for Phase-Space Reconstruction Using a Geometrical Construction,” Phys. Rev. A., 45, pp. 3403–3411. [CrossRef] [PubMed]
Theiler, J., 1986, “Spurious Dimension From Correlation Algorithms Applied to Limited Time-Series Data,” Phys. Rev. A, 34, pp. 2427–2432. [CrossRef] [PubMed]


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Fig. 4

Delay coordinate reconstruction of phase portraits for the stochastic (a) and original chaotic (b) signals

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Fig. 3

Histogram and power spectrum of the original chaotic (a) and stochastic (b) signals

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Fig. 2

Model of a specimen. The machined notch can be seen in the center, as well as the round hole on the left and the oblong slot on the right.

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Fig. 1

(a): Experimental apparatus. (b): Schematic of the apparatus: 1. shaker; 2. granite base; 3. slip table; 4. linear bearings for the slip table; 5. back mass; 6. specimen supports; 7. pneumatic cylinder supports; 8. slip table rails; 9. front cylinder; 10. front mass; 11. the specimen; 12. linear bearings for the masses; 13. central rail for the masses; 14. back cylinder; and 15. flexible axial coupling.

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Fig. 5

Histogram and power spectrum of the table acceleration data of the random (a) and chaotic (b) signals

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Fig. 6

Reconstructed phase portrait of the table acceleration data for the random (a) and chaotic (b) signals

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Fig. 7

Beam diagram with applied forces

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Fig. 8

Histograms of cycle amplitudes counted by the rainflow counting method in random (a) and chaotic (b) tests

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Fig. 9

Estimation of embedding dimension for the random (a) and chaotic (b) signals

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Fig. 10

Average trajectory divergence rates for all records in random loading (a) and chaotic loading (b)

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Fig. 11

Average trajectory divergence rates for all tests using random loading (a) and chaotic loading (b)

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Fig. 12

Correlation sum for all ten tests



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