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Tuesday, May 15 • 11:30am - 12:00pm
Crack Propagation in a Compact Tension Specimen Subjected to Gaussian Random Vibrations with Occasional Overloads

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It is well known that cracks in structural components subjected to overloads manifest delayed growth for some period of time, slowly reverting to the initial rate on a  curve thereafter. Frequently, constant amplitude fatigue tests with occasional programmed overloads are used to demonstrate the phenomenon. However, in response to random loading in which the sequence of loads is uncertain, different growth rates result from different spectra, even if the distributions from which the loads are taken are identical.

This paper examines variation in the number of fatigue cycles necessary for a crack to pass through the plastic zone after a single overload. A Monte Carlo simulation generates a single initial overload on a compact tension specimen, creating a large plastic zone ahead of the crack. Following the overload both minimum and maximum cyclic loads are simulated from Gaussian distributions. The Forman equation is used to calculate linear crack growth, i.e., without any retardation, and the Generalized Willenborg retardation model is used to calculate the reduction in crack driving potential, KR. The Forman equation is then modified to use the effective stress intensity factor, ?Keff, and the effective load ratio, Reff, to calculate the reduced cyclic growth rate, which is then compared to the linear result. This procedure is repeated for each load cycle until the crack passes through the overload zone and the number of cycles is recorded. The entire process is then repeated a total of 1000 times.

Using standard hypothesis testing, the resulting crack growth data are analyzed to determine which distributions cannot be excluded from consideration at the 5% significance level. 95% two-sided confidence intervals are determined for the distribution parameters. The best candidate distributions are overlaid on the simulation histogram to provide graphical results. Finally, the first four statistical moments calculated from the simulation data are compared to those derived using the distribution's calculated parameters. It was found that lognormal and Birnbaum-Saunders distributions are both good fits.

The underlying basis of the Willenborg model is that large compressive residual stresses, which reduce the effect of applied tensile loads, exist in the vicinity of the crack tip after an overload. Finite Element Analysis was performed on a Ramberg-Osgood material using kinematic hardening, the von Mises yield criterion and an associated flow rule. The results, which verify the presence of a residual compressive stress distribution in the vicinity of the crack tip are presented and discussed.


Peter Liaw

University of Tennessee

Julian Raphael

Principal Engineer, J R Technical Services, LLC

Tuesday May 15, 2018 11:30am - 12:00pm
Cape May