Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.

Keywords:

• cracks
• dislocations
• fatigue
• crack growth
• fracture mechanics
• dislocation dynamics

Acknowledgments

This research is supported by the Department of Energy, office of Fusion Energy Sciences, grant number DE-FG02-03ER54078, and also by the Air Force Office of Scientific Research (AFOSR), grant number FA9550-11-1-0282 at UCLA.