Markov Approximation to Fatigue Crack Propagation

by George P. Solomos, Commission of the European, Communities, Italy,
Alfredo C. Lucia, Commission of the European, Communities, Italy,

Document Type: Proceeding Paper

Part of: Probabilistic Methods in Civil Engineering


The distribution of the time required by a crack to reach a specified length and the distribution of the crack size itself are determined. To this end, the fatigue crack propagation growth equation is randomized and stochastically averaged, allowing thus the modeling of the crack size as a Markov process. The associated Fokker-Planck equation is solved for the appropriate transition density functions, choosing proper boundary conditions and expressing each time the solution in the form of an infinite series. The survival probability of a component and the first two moments of the first-passage time are also determined.

Subject Headings: Cracking | Markov process | Stochastic processes | Probability | Fatigue (material) | Approximation methods | Structural reliability

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