Fatigue Crack Growth Analysis with Finite Element Methods and a Monte Carlo Simulation


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Virginia Tech


Fatigue crack growth in engineered structures reduces the structures load carrying capacity and will eventually lead to failure. Cycles required to grow a crack from an initial length to the critical length is called the fatigue fracture life. In this thesis, five different methods for analyzing the fatigue fracture life of a center cracked plate were compared to experimental data previously collected by C.M. Hudson in a 1969 NASA report studying the R-ratio effects on crack growth in 7075-T6 aluminum alloy. The Paris, Walker, and Forman fatigue crack growth models were fit the experimental data. The Walker equation best fit the data since it incorporated R-ratio effects and had a similar Root Mean Square Error (RMSE) compared to the other models. There was insufficient data in the unstable region of crack growth to adequately fit the Forman equation.

Analytical models were used as a baseline for all fatigue fracture life comparisons. Life estimates from AFGROW and finite elements with mid-side nodes moved to their quarter point location compared very with the analytical model with errors less than 3%. The Virtual Crack Closure Technique (VCCT) was selected as a method for crack propagation along a predefined path. Stress intensity factors (SIFs) for shorter crack lengths were found to be low, resulting in an overestimated life of about 8%. The eXtended Finite Element Method with Phantom Nodes (XFEM-PN) was used, allowing crack propagation along a solution dependent path, independent of the mesh. Low SIFs throughout growth resulted in life estimates 20% too large. All finite element analyses were performed in Abaqus 6-13.3. An integrated polynomial method was developed for calculating life based on Abaqus' results, leading to coarser meshes with answers closer to the analytical estimate. None of the five methods for estimating life compared well with the experimental data, with analytical errors on life ranging from 10-20%. These errors were attributed to the limited number of crack growth experiments run at each R-ratio, and the large variability typically seen in growth rates.

Monte Carlo simulations were run to estimate the distribution on life. It was shown that material constants in the Walker model must be selected based on their interrelation with a multivariate normal probability density function. Both analytical and XFEM-PN simulations had similar coefficients of variation on life of approximately 3% with similar normal distributions.

It was concluded that Abaqus' XFEM-PN is a reasonable means of estimating fatigue fracture life and its variation, and this method could be extended to other geometries and three-dimensional analyses.



Fracture, eXtended Finite Element Method, Phantom Nodes, Monte Carlo