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Probabilistic considerations for growth and detection of cracks from rivet holes in a lap joint

Published online by Cambridge University Press:  27 January 2016

M. L. Cohen  and
J. D. Achenbach
M. L. Cohen
Affiliation:
Center for Quality Engineering and Failure Prevention, Northwestern University, Evanston, Illinois, USA
J. D. Achenbach*
Affiliation:
Center for Quality Engineering and Failure Prevention, Northwestern University, Evanston, Illinois, USA
*
[email protected]
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Abstract

In this paper, probabilistic considerations are introduced in a model for fatigue life prediction for a riveted lap joint using Paris’ law. Initial crack sizes are distributed according to a truncated lognormal distribution, which is chosen to avoid known complications due to Paris’ law. The stress intensity factor for a single rivet hole is calculated, and is generalized to a lap joint. The probability of the existence of a crack in two domains of interest are evaluated, and the effect of a single inspection, modeled using the Probability of Detection, is studied. Additionally, the probability of detection concept is extended by linking it to applied stress and number of elapsed cycles using Bayes’ theorem and ramifications are explored.

Type
Research Article
Information
The Aeronautical Journal , Volume 117 , Issue 1193 , July 2013 , pp. 727 - 740
Copyright
Copyright © Royal Aeronautical Society 2013 

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References

1. Sobczyk, K. and Spencer, B.F. Random Fatigue: From Data to Theory, 1992, Academic Press, New York, USA.Google Scholar
2. Liu, Y. and Mahadevan, S. Probabilistic fatigue life prediction using an equivalent initial flaw size distribution, Int J Fatigue, 2009, 31, (3), pp 476–487.Google Scholar
3. White, P., Molent, L. and Barter, S. Interpreting fatigue test results using a probabilistic fracture approach, Int J Fatigue, 2005, 27, (7), pp 752–767.Google Scholar
4. Cobb, A.C., Michaels, J.E. and Michaels, T.E. An integrated approach to local ultrasonic monitoring of fastener hole fatigue cracks, Aeronaut J, December 2009, 113, (1144), pp 775–788.Google Scholar
5. Bowie, O.L. Analysis of an infinite plate containing radial cracks originating at the boundary of an internal circular hole, J Mathematics and Physics, 1956, 35, (1), pp 60–71.Google Scholar
6. Newman, J.C. An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries, 1971, Technical Report TN D-6376, National Aeronautics and Space Administration, Washington, DC, USA.Google Scholar
7. Grandt, A.F. Stress intensity factors for some through-cracked fastener holes, Int J Fatigue, 1975, 11, (2), pp 283–294.Google Scholar
8. Cartwright, D.J. and Parker, A.P. Opening mode stress intensity factors for cracks in pin-loads and joints, Intl J Fracture, 1982, 18, (1), pp 65–78.Google Scholar
9. Yen, S.W. and Smillie, D.G. Computer analysis of fastener load distribution in a multi-row joint, Computers & Structures, 1973, 3, (6), pp 1293–1320.Google Scholar
10. Atluri, S.N. Structural Integrity & Durability, 1997, Tech Science Press, Forsyth, GA, USA.Google Scholar
11. Harris, H.G., Ojalvo, I.U. and Hooson, R.E. Stress and deflection analysis of mechanically fastened points, Air Force Flight Dynamics Laboratory Technical Report AFFDL-TR-70-49.Google Scholar
12. Tada, , 1970, Paris, H., P.C., and Irwin, G.R. The Stress Analysis of Cracks Handbook, 3rd Edition, 2000, American Society of Mechanical Engineers, New York, USA.Google Scholar
13. Broek, D. Elementary Engineering Fracture Mechanics, 1974, Noordhoff International Publishing, Leyden, The Netherlands.Google Scholar
14. Rooke, D.P. Stress intensity factors for cracks at a row of holes, Intl J Fracture, 1982, 18, (2), pp R31– R36.Google Scholar
15. Bickley, W.G. The distribution of stress round a circular hole in a plate, Phil Trans Roy Soc Lon Series A, 1928, 227, (647-658), pp 383–415.Google Scholar
16. Petroski, H.J. and Achenbach, J.D. Computation of the weight function from a stress intensity factor, Engineering Fracture Mechanics, 1978, 10, (2), pp 257–266.Google Scholar
17. Paris, P.C. and Erdogan, F. Critical analysis of propagation laws, J Basic Engineering, 1963, 85, pp 528–534.Google Scholar
18. Virkler, D.A., Hillberry, B.M., and Goel, P.K. The statistical nature of fatigue crack propagation, 1978, Air Force Flight Dynamics Laboratory Technical Report AFFDL-TR-78-43.Google Scholar
19. Annis, C. Probabilistic life prediction isn’t as easy as it looks, J ASTM Intl, 2004, 1, (2), p 12.Google Scholar
20. Cohen, M.L., kulkarni, S.S. and Achenbach, J.D. Probabilistic approach to growth and detection of a truncated distribution of initial crack lengths based on Paris law, Structural Health Monitoring, 2012, 11, (2), pp 225–236.Google Scholar
21. Kulkarni, S.S. and Achenbach, J.D. Structural health monitoring and damage prognosis in fatigue, Structural Health Monitoring, 2008, 7, (1), pp 37–49.Google Scholar
22. Kulkarni, S.S. and Achenbach, J.D. Optimization of inspection schedule for a surface-breaking crack subject to fatigue loading, Probabilistic Engineering Mechanics, 2007, 22, (4), pp 301–312.Google Scholar