**Journal of Theoretical**

and Applied Mechanics

and Applied Mechanics

**36**, 1, pp. 3-14, Warsaw 1998

### Weight functions of K_1 and K_2 for a single radial crack emanating from a circular hole

Weight functions of the stress intensity factors $K_1$ and $K_2$ for a single radial crack emanating from a circular hole are derived using the boundary element method (BEM) together with the Bueckner type singular complex stress function $Z(z)$ applied in the vicinity of the crack tip. Both weight functions, corresponding to the loading modes I and II respectively, are valid for any ratio of the crack length $a$ to hole radius $R$. They are represented in the unified form convenient for creating the weight function database. The accuracy of present solutions has appeared to be much better than 99% verified by comparing the values of $K_1$ and $K_2$ obtained by means of the unitary weight function method to the BEM results and to some particular $K_1$ and $K_2$ solutions found in the literature.

*Keywords*: crack; stress intensity factor; weight function; circular hole