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Stochastic Modeling of Fatigue Crack Growth with Retardation

by Dhirendra Verma, Case Western Reserve Univ, Cleveland, United States,
Dario A. Gasparini, Case Western Reserve Univ, Cleveland, United States,
Fred Moses, Case Western Reserve Univ, Cleveland, United States,



Document Type: Proceeding Paper

Part of: Engineering Mechanics

Abstract:

This paper develops a new methodology for modeling fatigue crack growth accounting for both material inhomogeneity and the random nature of the loading process by modeling the crack growth rate instead of just the crack length itself. There are substantial benefits in doing so since it is the crack growth rate that is retarded while the crack length is still increasing after an overload. This change in crack growth rate can be regarded as a jump discontinuity in the sample path behavior of the growth rate with each of the jumps occurring at the arrival of the overload, which are idealized as Poisson arrivals. The distribution of the magnitude of these jumps can be considered as identically distributed following some general distribution, with a zero value corresponding to the probability of crack arrest. The magnitude of the jumps themselves will be assumed to follow Walker's model for crack growth retardation. Crack growth rate is then modeled as a diffusion process with jump transitions. Since retardation due to overloads is a history dependent phenomenon we cannot model it directly as a Markov process but instead focus on two auxiliary processes which are Markovian in nature to provide upper and lower bounds to the moments of the time to failure. These moments of time to failure are then determined numerically. Correlations with experimental data are also presented.

Subject Headings: Cracking | Markov process | Fatigue tests | Stochastic processes | Material tests | Overloads | Material mechanics

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