Stochastic Modeling of Fatigue Crack Damage for Risk Analysis and Remaining Life Prediction

This paper presents a stochastic model of fatigue crack damage in metallic materials that are commonly encountered in structures and machinery components of complex mechanical systems (e.g., aircraft, spacecraft, and power plants). The constitutive equation of the damage model is based on the physics of fracture mechanics and is validated by Karhunen-Loeve analysis of test data. The (nonstationary) probability distribution function (PDF) of fatigue crack damage is generated in a closed form without numerically solving stochastic differential equations in the Wiener integral or Ito integral setting. The crack damage model thus allows real-time execution of decision algorithms for risk assessment and life prediction on inexpensive platforms such as a Pentium processor. The model predictions are in close agreement with experimental data of fatigue crack growth statistics for 2024-T3 and 7075-T6 aluminum alloys.

[1]  Keinosuke Fukunaga,et al.  Introduction to statistical pattern recognition (2nd ed.) , 1990 .

[2]  S. Suresh.  Fatigue of materials , 1991 .

[3]  L. Faravelli,et al.  Fatigue crack size probability distribution via a filter technique , 1992 .

[4]  Y. K. Lin,et al.  A stochastic theory of fatigue crack propagation , 1985 .

[5]  P. Goel,et al.  The Statistical Nature of Fatigue Crack Propagation , 1979 .

[6]  H. Saunders,et al.  Probabilistic models of cumulative damage , 1985 .

[7]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[8]  Asok Ray,et al.  A nonlinear stochastic model of fatigue crack dynamics , 1997 .

[9]  Ove Ditlevsen,et al.  Random fatigue crack growth—a first passage problem , 1986 .

[10]  Hiroshi Ishikawa,et al.  Reliability assessment of structures based upon probabilistic fracture mechanics , 1994 .

[11]  Asok Ray,et al.  Hybrid life-extending control of mechanical systems: experimental validation of the concept , 2000, Autom..

[12]  Min Liao,et al.  A probabilistic model for fatigue crack growth , 1992 .

[13]  J Schijve.  Observations on the Prediction of Fatigue Crack Growth Propagation Under Variable-Amplitude Loading , 1976 .

[14]  W. F. Wu,et al.  Stochastic Modeling of Fatigue Crack Propagation , 1985 .

[15]  Süleyman Özekici,et al.  Reliability and Maintenance of Complex Systems , 2010, NATO ASI Series.

[16]  Asok Ray,et al.  A State-Space Model of Fatigue Crack Growth , 1998 .

[17]  Asok Ray,et al.  Stochastic modeling of fatigue crack dynamics for on-line failure prognostics , 1996, IEEE Trans. Control. Syst. Technol..

[18]  Asok Ray,et al.  State-space supervisory control of reconfigurable discrete event systems , 1996 .

[19]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[20]  S. D. Manning,et al.  A simple second order approximation for stochastic crack growth analysis , 1996 .

[21]  J. Newman.  A crack opening stress equation for fatigue crack growth , 1984 .

[22]  B. F. Spencer,et al.  Stochastic approach to modeling fatigue crack growth , 1989 .

[23]  A. Ray,et al.  Stochastic modeling of fatigue crack propagation , 1998 .

[24]  T. Topper,et al.  A study of the effect of mechanical variables on fatigue crack closure and propagation , 1986 .

[25]  Asok Ray,et al.  A stochastic model of fatigue crack propagation under variable-amplitude loading , 1999 .

[26]  Asok Ray,et al.  Fuzzy Damage Mitigating Control of Mechanical Structures , 1998 .

[27]  Akira Tsurui,et al.  Application of the Fokker-Planck equation to a stochastic fatigue crack growth model , 1986 .

[28]  Hui Fan,et al.  Prediction of Service Life for Machines and Structures , 1990 .

[29]  P. C. Paris,et al.  A Critical Analysis of Crack Propagation Laws , 1963 .

[30]  S. Mall,et al.  Dugdale plastic zone size and CTOD equations for the compact specimen , 1984 .

[31]  Hamouda Ghonem,et al.  Experimental study of the constant-probability crack growth curves under constant amplitude loading , 1987 .

[32]  Asok Ray,et al.  Life-extending control of fossil fuel power plants , 1997, Autom..