Conclusion
You've gotten the 'rundown' on the most basic concepts of fracture mechanics. The most important concepts in this page are that if you limit the stress, improve material toughness and lower the number of cycles a structure is exposed to; it's life and performance will be enhanced. Great, but is there more involved with fracture mechanics? Yes.
We looked at fracture and fatigue from a high level of observation. The methods of finding stresses acting around a fracture can be very complicated (for example, using FEM or continuum mechanics) and rather inaccurate. There is can be a large degree of uncertainty in fracture/fatigue mechanics, thus large factors of safety are usually involved when designing a structure. However, understanding the basics is key to diagnostics and important in the design process and maintenance of a structure.
I hope you enjoyed this section and learned a bit. I also hope you didn't mind the different formatting, for the purpose of this page I simply used MS word and copied it over, there were a ton of pictures and equations that made it tedious to do piecewise!