Finnie's Notes on Fracture Mechanics pp 63-94 | Cite as

# Some Solutions That Are Useful in Fracture Prediction

## Abstract

Our primary objective is to use solutions that have been developed for elastic, elastic–plastic, and fully plastic behavior to predict fracture. The detailed development of these solutions and a discussion of techniques, analytical and numerical, used to obtain them are beyond the scope of this work. However, for completeness, some of the analytical techniques that have been used to obtain stress fields for sharp cracks and other configurations will be described. We consider first the elastic solutions for sharp cracks, circular holes, and elliptical holes in flat plates. Also, the elastic solutions for cylindrical inclusions, for spherical holes, and inclusions will be summarized. Then, approximate and more exact solutions, based on elastic–plastic behavior for sharp and blunted cracks, will be described. Finally, solutions for notched members will be presented, both for the initial elastic stress distribution and for the case in which yielding has occurred over the entire cross section. A few solutions have been omitted from this chapter because it seems more appropriate to treat them at a later stage. These are the Dugdale model for the plastic zone ahead of a crack for plane stress (Chap. 5), the solutions for stresses and strains (in terms) of the J integral (Chap. 6), and the solutions for void growth in ductile fracture (Chap. 7).

### Keywords

Strain Hardening### References

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