Multi-inspection time optimisation for a cracked component based on a updating reliability approach
Keywords:
fatigue crack growth, inspection scheduling, updating reliability, Firstorder reliability method, response surface, optimisationAbstract
It is well acknowledged that Fatigue Crack Growth (FCG) process is one of the main processes that can produce failure of structures and mechanical components. To ensure the survival of these components a maintenance inspection schedule is needed. The aim of this study is to develop a predicting inspection time model for structural FCG life based on updating reliability analysis. The proposed approach takes into account the additional information generated by the previous inspection results. First-order reliability method and surface response method are used to evaluate the reliability. The uncertainties such as material parameters and geometrical parameters that affect the lifespan of the structure were regarded as random variables. Updating reliability assessment based on Bayesian approach was introduced to determine the updating inspection time for target reliability. Moreover, the proposed approach leads to determine the optimal inspection time strategy based on an economic study under the minimal total inspection and detecting costs using a dynamic method. The optimal inspection time for a single and two inspections was determined. A generalisation of this method is carried out for the case of multiple inspections. In order to illustrate and validate this method two applications are carried out: the first one is applied to the crack growth in mode I, and the second one is applied to the crack growth in mixed mode. The results of these applications are in good agreement with the physical results and show that the proposed method is proved to be feasible and applicable in the general complex fatigue loading and able to give accurate updating framework for scheduling inspections.
Downloads
References
Baker, M. J., & Descamps, B. (1999). Reliability-based methods in the inspection planning of
fixed offshore steel structures. Journal of Constructional Steel Research, 52, 117–131.
M. Eltaief et al.
Bea, J. A., Doblaré, M., & Gracia, L. (1999). Evaluation of the probability distribution of crack
propagation life in metal fatigue by means of probabilistic finite element method and B-models.
Engineering Fracture Mechanics, 63, 675–711.
Besterfield, G. H., Liu, W. K., Lawrence, M. A., & Belytschko, T. (1991). Fatigue crack growth
reliability by probabilistic finite elements. Computer Methods in Applied Mechanics and Engineering,
, 297–320.
Cavallini, G., & Lazzeri, R. (2007, December). A probabilistic approach to fatigue risk assessment
in aerospace components. Engineering Fracture Mechanics, 74, 2964–2970.
Chan, S. K., Tuba, I. S., & Wilson, W. K. (1970). On the finite element method in linear fracture
mechanics. Engineering Fracture Mechanics, 2(1), 1–17.
Destuynder, Ph., Djoua, M., & Lescure, S. (1983). Quelques remarques sur la mécanique de la
rupture élastique [Some remarks on the mechanics of elastic fracture]. Journal of Theoretical
And Applied Mechanics, 2, 113–135.
Ditlevsen, O., & Madsen, H. O. (1996). Structural reliability method. New York: John Wiley and
Sons.
Erdogan, F., & Sih, G. C. (1963). On the crack extension in plates under plane loading and transverse
shear. Journal of Basic Engineering, 85, 519–527.
Fourlaris, G., Ellwood, R., & Jones, T. B. (2007). The reliability of test results from simple test
samples in predicting the fatigue performance of automotive components. Materials &
Design, 28, 1198–1210.
Gdoutos, E. E. (2005). Fracture mechanics an introduction (2nd ed.). ISBN 1-4020-3153-X
(e-book) Published by Springer.
Ghonem, H., & Dore, S. (1987). Experimental study of the constant probability crack growth
curves under constant amplitude loading. Engineering Fracture Mechanics, 27, 1–25.
Guinea, G. V., Planas, J., & Eliccs, M. (2000). KI evaluation by the displacement extrapolation
technique. Engineering Fracture Mechanics, 66, 1–17.
Han, P. H. (1999). Inspection and maintenance planning of pipeline under external corrosion considering
generation of new defects. Structural Safety, 21, 203–222.
Hasofer, A. M., & Lind, N. C. (1974). Exact and invariant second moment code format. Journal
of Engineering Mechanics, 100, 111–121.
Jiao, G., & Moan, T. (1990). Methods of reliability model updating through additional events.
Structural Safety, 9, 139–153.
Khaleel, M. A., & Simonen, F. A. (2000). Effects of alternative inspection strategies on piping
reliability. Nuclear Engineering and Design, 197, 115–140.
Kulkarni, S. S., & Achenbach, J. D. (2007). Optimization of inspection schedule for a surfacebreaking
crack subject to fatigue loading. Probabilistic Engineering Mechanics, 22, 301–312.
Laggoune R., Chateauneuf A., & Aissani D. (2009). Opportunistic policy for optimal preventive
maintenance of a multi-component system in continuous operating units. Computers & Chemical
Engineering, 33, 1499–1510.
Lemaire, M., Chateauneuf, A., & Mitteau, J. C. (2005). Fiabilité des structures: couplage mécanofiabiliste
statique. Paris: Edit. Hermes. 620.004 52 LEM.
Leonel, E. D., Chateauneuf, A., Venturini, W. S., & Bressolette, P. (2010, November). Coupled
reliability and boundary element model for probabilistic fatigue life assessment in mixed
mode crack propagation. International Journal of Fatigue, 32, 1823–1834.
Liu, W. K., Chen, Y., Belytschko, T., & Lua, Y. J. (1996). Three reliability methods for fatigue
crack growth. Engineering Fracture Mechanics, 53, 733–752.
Lua, Y. J., Liu, W. K., & Belytschko, T. (1992). A stochastic damage model for the rupture prediction
of a multi-phase solid. Part II: Statistical approach. International Journal of Fracture
Mechanics, 55, 341–361.
Meng, G., Li, F., Sha, L., & Zhou, Z. (2007). Prediction of optimal inspection time for structural
fatigue life. International Journal of Fatigue, 29, 1516–1522.
Myötyri, E., Pulkkienen, U., & Simola, K. (2006). Application of stochastic filtering for lifetime
prediction. Reliability Engineering & System Safety, 91, 200–208.
Nechval, N., Nechval, K., Purgailis, M., & Strelchonok, V. (2011, May). Planning inspections in
the case of damage tolerance approach to service of fatigued aircraft structures. International
Journal of Performability Engineering, 7, 279–290.
Newby, M. J. (1987). Markov models for fatigue crack growth. Engineering Fracture Mechanics,
, 477–482.Papadopoulos, I. V., Davol, P., Gorla, C., Filippini, M., & Bernasconi, A. (1997). A comparative
study of multi-axial high cycle fatigue criteria of metals. International Journal of Fatigue, 19,
–235.
Paris, P. C., & Erdogan, F. (1963). A critical analysis of crack propagation laws. Journal of Basic
Engineering, 85, 528–534.
Parks, M. D. (1974). A stiffness derivative finite element technique of crack tip stress intensity
factors. International Journal of Fracture, 10, 243–255.
Rackwitz, R., & Fiessler, B. (1978). Structural reliability under combined load sequences. Computers
& Structures, 9, 489–494.
Riahi, H., Bressolette, Ph., Chateauneuf, A., Bouraoui, Ch., & Fathallah, R. (2011). Reliability
analysis and inspection updating by stochastic response surface of fatigue cracks in mixed
mode. Engineering Structures, 33, 3392–3401.
Ben Sghaier, R., Bouraoui, Ch., Fathallah, R., & Hassine, T. (2007). Probabilistic high cycle fatigue
behaviour prediction based on global approach criteria. International Journal of Fatigue,
, 209–221.
Shen, M. (1999). Reliability assessment of high cycle fatigue design of gas turbine blades using
the probabilistic Goodman Diagram. International Journal of Fatigue, 21, 699–708.
Straub, D., & Faber, M. H. (2005). Risked based inspection planning for structural systems.
Structure Safety, 27, 335–355.
Tanaka, H., & Toyoda-Makino, M. (1998). Cost-based optimal relation between inspection time
and assessment time for random fatigue crack growth. Probabilistic Engineering Mechanics,
, 69–76.
Webster, G. A., & Ezeilo, A. N. (2001). Residual stress distributions and their influence on fatigue
lifetimes. International Journal of Fatigue, 23, S375–S383.
Wirsching, P. H. (1980). Fatigue reliability in welded joints of offshore structures. International
Journal of Fatigue, 2, 77–83.
Wu, W. F., & Ni, C. C. (2007). Statistical aspects of some fatigue crack growth data. Engineering
Fracture Mechanics, 74, 2952–2963.
Yu, L., Purnendu, K. D., & Zheng, Y. (2009). A response surface approach to fatigue reliability
of ship structures. Ships and Offshore Structures, 4, 253–259.
Yuan H. C. (2007, April). Fatigue analysis of welded joints with the aid of real three-dimensional
weld toe geometry. International Journal of Fatigue, 29, 772–785.
Zhao, Y. G., & Ono, T. (2001). Oment for structural reliability. Structural Safety, 23, 47–75.
