The study of fatigue crack closure is very important for the prediction of fatigue crack growth behavior. The closure behavior of fatigue cracks has been investigated mainly from experiments. However, when experimental method cannot be applied, an analytical or numerical simulation methods could be used as an alternative. In particular, the finite element (FE) method has long been used for the analysis of crack closure behavior.
Useful FE analysis results have been obtained for crack closure behavior under plane stress state. However, there are a few results for plane strain state and some researchers have found that crack opening stress, $S_op$, obtained by FE analysis under plane strain state are much lower than those of plane stress state.
In this thesis, an elastic-plastic FE analyses are preformed using the general purpose finite element code ABAQUS to examine crack closure behavior under plane strain state and the numerical results are compared with experimental ones. The theory of incremental rate independent classical plasticity and von Mises criteria are used. To sufficiently simulate the Bauschinger effect associated with reversed yielding, nonlinear kinematic hardening rule of Prager-Ziegler implemented in the ABAQUS is chosen. Several FORTRAN and UNIX shell programs are written to perform the fatigue crack closure analysis with 4-node bilinear reduced-integration element(CPE4R) implemented in the ABAQUS.
The effects of several parameters such as element size, kinds of elements, initial crack length, load step increment, nodal coupling, force convergence tolerance etc. are investigated and then compared with the results published by others.
The crack opening load stabilized after the crack grew beyond the four times of the monotonic plastic zone size induced by the initial crack length for plane strain condition. Based on the results of the stabilization of crack opening load, the crack opening load that is observed after a crack grows by 4 or more was chosen as the representative value.
The ratio of the element size to the plastic zone size, $Δa^*/W_p$ is used as a criterion to determine the most appropriate mesh size to provide good numerical results. It has been shown that the mesh size has to be changed continuously as the maximum stress intensity factor, $K_{max}$ increases under plane strain state.
A procedure to predict the most appropriate mesh size for different stress ratio is suggested. Crack opening loads predicted by the FE analysis based on the procedure suggested resulted in good agreement with experimental ones within the error of 5 %.
Effect of the distance behind the crack tip on the crack opening load determined by the ASTM compliance offset method based on the load-displacement relation and by the rotational offset method based on the load-differential displacement relation was investigated. Optimal gage location and method to determine the crack opening load was suggested.
