Abstract
In this dissertation a non-Paris law based unified fatigue cohesive zone model (CZM) capable of predicting both fatigue crack initiation and propagation of delamination cracks in composites with or without starter cracks or stress concentrators has been formulated and validated. The fatigue CZM incorporates normal and shear degradation mechanisms for pre-crack-initiation strength degradation, and simple power-laws for post-crack-initiation fatigue damage accumulation with damage rates computed directly from the in situ cohesive traction-separation history. A unique procedure to determine the in situ loading profiles and an efficient cycle jump strategy have also been developed. It has been demonstrated, through direct comparisons against experimental results, that the proposed fatigue CZM can successfully predict the crack initiation and the ensuing propagation in pre-cracked as well as in crack-free specimens. Furthermore, as the cracks become sufficiently long, and linear elastic fracture mechanics (LEFM) conditions are met, the model can correctly predict Paris Laws under pure or mixed mode fracture conditions. Also, as an initial effort to integrate the unified fatigue CZM into the augmented finite element method (A-FEM) and allow arbitrary multiple fatigue crack development. A new algorithm has been developed and implemented that facilitates this integration and provides analytic solutions to equilibrium equations for cracked A-FEs. This new algorithm is based on a consistency check between trial cohesive stiffness and resulting displacements to differentiate crack displacements from nodal displacements. Benchmark numerical tests demonstrate that the algorithm yields superior numerical accuracy, efficiency, and robustness over existing methods. The overall improvement in computational efficiency is ~50 times that of the phantom-node based A-FEM in modeling a 4-point shear beam test. For mixed mode composite delamination problems, the A-FEM with the algorithm is 20-30% faster than the standard CZM method, despite the fact that in the CZM method, delamination paths were pre-defined.