Stochastic Modeling of Fatigue Crack Growthby B. F. Spencer, Jr., Univ of Notre Dame, United States,
J. Tang, Univ of Notre Dame, United States,
Abstract: A new lognormal fatigue crack propagation model has been presented in which a two-dimensional state vector has been employed to introduce experimentally observed history dependence of fatigue crack growth. Markov process theory has been used to formulate a well-posed boundary-value problem for the statistics of the random time to reach a critical crack size conditional on the initial flaw size. A robust Petrov-Galerkin finite element method was then utilized for the solution of the boundary value problem. In the examples, the commonly used power-law crack propagation model is employed for simplicity, however, more complex models could have been employed with little additional effort. Finally, excellent correlation with the experimental results was found.
Subject Headings: Cracking | Mathematical models | Fatigue (material) | Two-dimensional models | Markov process | Boundary value problem | Finite element method
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