Efficient probabilistic methods for real-time fatigue damage prognosis



Yibing Xiang Yongming Liu


A general probabilistic fatigue crack growth prediction methodology for accurate and efficient damage prognosis is proposed in this paper. This methodology consists two major parts. First, the realistic random loading is transformed to an equivalent constant amplitude loading process based on a recently developed mechanism model. This transformation avoids the cycle-by-cycle calculation of fatigue crack growth under variable amplitude loading. Following this, an inverse first-order reliability method (IFORM) is used to evaluate the fatigue crack growth at an arbitrary reliability level. Inverse FORM method does not require a large number of function evaluations compared to the direct Monte Carlo simulation. Computational cost is significantly reduced and the proposed method is very suitable for real-time damage prognosis. Numerical examples are used to demonstrate the proposed method. Various experimental data under variable amplitude loading are collected and model predictions are compared with experimental data for model validation.

How to Cite

Xiang, Y. ., & Liu, Y. . (2010). Efficient probabilistic methods for real-time fatigue damage prognosis. Annual Conference of the PHM Society, 2(1). https://doi.org/10.36001/phmconf.2010.v2i1.1895
Abstract 73 | PDF Downloads 33



fatigue crack growth, probabilistic, variable amplitude, equivalent stress level

Bhaumik, S. K., Sujata, M., & Venkataswamy, M. A. (2008) Fatigue failure of aircraft components. Engineering Failure Analysis, 15, 675-694.

Cheng, J., & Li, Q. S. (2009) Reliability analysis of a long span steel arch bridge against wind-induced stability failure during construction. Journal of Constructional Steel Research, 65, 552-558.

Cizelj, L., Mavko, B., & Riesch-Oppermann, H. (1994) Application of first and second order reliability methods in the safety assessment of cracked steam generator tubing. Nuclear Engineering and Design, 147, 359-368.

Corbly, D. M., & Packman, P. F. (1973) On the influence of single and multiple peak overloads on fatigue crack propagation in 7075-T6511 aluminum. Engineering Fracture Mechanics, 5, 479-497.

de Koning AU, v. d. L. H. (1981). Prediction of fatigue crack growth rates under variable loading using a simple crack closure model. Amsterdam: NLR MP 81023U

Der Kiureghian, A., Zhang, Y., & Li, C.-C. (1994) Inverse reliability problem. Journal of Engineering Mechanics, ASCE, 120(5).

Dowling, N. E. (2007). Mechanical behavior of materials : engineering methods for deformation, fracture and fatigue. Upper Saddle River, NJ
London: Pearson Prentice Hall ;Pearson Education.

Elber, W. (1971). The significance of fracture crack closure. Philadelphia.

Haldar, A., & Mahadevan, S. (2000). Probability,reliability, and statistical methods in engineering design. New York ; Chichester [England]: John Wiley.

Kam, T. Y., Chu, K. H., & Tsai, S. Y. (1998) Fatigue reliability evaluation for composite laminates via a direct numerical integration technique. International Journal of Solids and Structures, 35, 1411-1423.

Koning, A. U. d. (1981). A simple crack closure model for prediction of fatigue crack growth rates under variable-amplitude loading. Fracture Mechanics: Thirteenth Conference, ASTM STP 743 (pp. 63-85): American Society for Testing and Materials.

Liao, M., Xu, X., & Yang, Q.-X. (1995) Cumulative fatigue damage dynamic interference statistical model. International Journal of Fatigue, 17, 559-566.

Liu, Y., & Mahadevan, S. (2007) Stochastic fatigue damage modeling under variable amplitude loading. International Journal of Fatigue, 29, 1149-1161.

Liu, Y., & Mahadevan, S. (2009a) Efficient methods for time-dependent fatigue reliability analysis. AIAA Journal, 47, 494-504.

Liu, Y., & Mahadevan, S. (2009b) Probabilistic fatigue life prediction using an equivalent initial flaw size distribution. International Journal of Fatigue, 31, 476-487.

Liu, Y., Mahadevan, S (2009) Efficient methods for time-dependent fatigue reliability analysis. AIAA Journal, 47, 494-504.

Lu, Z., & Liu, Y. (2010) Small time scale fatigue crack growth analysis. International Journal of Fatigue, 32, 1306-1321.

Mikheevskiy, S., & Glinka, G. (2009) Elastic-plastic fatigue crack growth analysis under variable amplitude loading spectra. International Journal of Fatigue, 31, 1828-1836.

Mohanty, J. R., Verma, B. B., & Ray, P. K. (2009) Prediction of fatigue crack growth and residual life using an exponential model: Part II (mode-I overload induced retardation). International Journal of Fatigue, 31, 425-432.

NASA (2000) Fatigue crack growth computer program NASGRO Version 3.0-Reference manual. JSC- 22267B, NASA, Lyndon B. Johnson Space Center, Texas.

Newman, J. C. (1981). A crack closure model for predicting fatigue crack growth under aircraft spectrum loading. Philadelphia

Noroozi, A. H., Glinka, G., & Lambert, S. (2007) A study of the stress ratio effects on fatigue crack growth using the unified two-parameter fatigue crack growth driving force. International Journal of Fatigue, 29, 1616.

Noroozi, A. H., Glinka, G., & Lambert, S. (2008) Prediction of fatigue crack growth under constant amplitude loading and a single overload based on elasto-plastic crack tip stresses and strains. Engineering Fracture Mechanics, 75, 188-206.

Pommier, S. (2003) Cyclic plasticity and variable amplitude fatigue. International Journal of Fatigue, 25, 983-997.

Porter, T. R. (1972) Method of analysis and prediction for variable amplitude fatigue crack growth. Eng. Fract. Mech, 4, 717-736.

Rackwitz, R. a. F., B (1978) Structural Reliablity Under Combined Random Load Sequences. Computers & Structures, 9, 484-494.

Rackwitz, R. a. F., B (June 1976) Note on Discrete Safety Checking When Using Non-Normal Stochastic Models for Basic Variables. Load Project Working Session,MIT,Cambridge,MA.

Ray, A. (2000). A state-space model of fatigue crack growth for real-time structural health management. Digital Avionics Systems Conferences, Vol. 2 (pp. 6C1/1 - 6C1/8).

Skaggs, T. H., & Barry, D. A. (1996) Assessing uncertainty in subsurface solute transport: efficient first-order reliability methods. Environmental Software, 11, 179-184.

Thorndahl, S., & Willems, P. (2008) Probabilistic modelling of overflow, surcharge and flooding in urban drainage using the first-order reliability method and parameterization of local rain series. Water Research, 42, 455-466.

Val, D. V., Stewart, M. G., & Melchers, R. E. (1998) Effect of reinforcement corrosion on reliability of highway bridges. Engineering Structures, 20, 1010- 1019.

Venkateswara Rao, K. T., & Ritchie, R. O. (1988) Mechanisms for the retardation of fatigue cracks following single tensile overloads: behavior in aluminum-lithium alloys. Acta Metallurgica, 36, 2849- 2862.

Wheeler, O. E. (1972) Spectrum loading and crack growth J. Basic Eng., Trans. ASME, 94, 181-186.

Willenborg J, E. R., Wood RA (1971). A Crack Growth Retardation Model Using an Effective Stress Concept. Wright-Patterson Air Force Base, Ohio: Air Force Flight Dynamics Laboratory.

Xiang, Y., & Liu, Y. (2010 (accepted) ) Inverse first-order reliability method for probabilistic fatigue life prediction of composite laminates under multiaxial loading. ASCE Journal of Aerospace Engineering.
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