Notch Analysis of Ductile Fracture

Abstract

Notch analysis of ductile fracture is based on the stress field analysis of notches by Neuber (1,2) and the slip-line field solution by Hill (3). The work at Syracuse (4–6) has shown that an estimate of a materials resistance to crack extension can be obtained by considering the elastic and plastic deformation processes in the crack tip region. Detailed studies of the strain field in the vicinity of the crack tip, e.g. by Liu and co-workers (7) and by Ogasawara, Adachi, Nagao and Weiss (8) show that the strain field ahead of the crack tip is reasonably well represented by:

$$\varepsilon _{\text{r,}\theta } = \varepsilon = _{F,\alpha ,\beta }^{\frac{2}{{n + 1}}} (\frac{{\rho *}}{{\rho * + 2r}})^{\frac{1}{{n + 1}}} f_{ij} (\theta )$$

((1))

where n is the strain hardening exponent, ρ* the Neuber micro support effect constant and ε_Fαβthe maximum strain at the tip of an extending crack under the stress field, $\alpha = \frac{{\sigma _2 }}{{\sigma 1}}$ and $\beta = \frac{{\sigma _3 }}{{\sigma _1 }}$ in that region.