Variable amplitude fatigue analysis using surrogate models and exact XFEM reanalysis

Fatigue crack growth occurs as the result of repeated cyclic loading well below the stress levels which typically would cause failure. The number of cycles to failure for high-cycle fatigue is commonly of the order of 10 4–108 cycles to failure. Fatigue is characterized by a differential equation which gives the crack growth rate as a function of material properties and the stress intensity factor. Analytical relationships for the stress intensity factor are limited to simple geometries. A numerical method is commonly used to find the stress intensity factor for a given geometry under certain loading.;The use of kriging to assist higher-order approximations is introduced. Here stress intensity factor data is fit using a surrogate. This surrogate is used to extrapolate for the purpose of integration, which enables larger step sizes to be taken without a loss in accuracy for the solution of the governing differential equation. Furthermore, it was observed that for the extended finite element method a small portion of the global stiffness matrix is changed as a result of crack growth. It is possible to use this small portion to save on both the assembly and solution of the resulting system of linear equations. This results in savings in both the assembly and factorization of the stiffness matrix for repeated simulations reducing the computational cost associated with numerical fatigue crack growth.;The use of the XFEM reanalysis algorithm allow for the analysis of nonproportional mixed-mode variable amplitude loading upon an airplane wing to be considered. An airplane wing box was analyzed using Abaqus®. The Abaqus ® stress solution was used in coordination with airplane flight data provided by the Air Force Research Laboratory. This stress history is converted into a cyclic loading history through the use of the rainflow counting method. The resulting analysis is one where approximately 30,000 cycles elapse. Due to the non-proportional loading, each cycle must be modeled independently as the direction of crack propagation will be cycledependent creating a solution which would be very expensive with existing techniques. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html).