Fracture Mechanics of Ductile and Tough Materials and its Applications to Energy Related Structures pp 165-167 | Cite as

# Notch Analysis of Ductile Fracture

Conference paper

## 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:
where n is the strain hardening exponent, ρ* the Neuber micro support effect constant and ε

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

(1)

_{Fαβ}the 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.## Keywords

Ductile Fracture Crack Extension Fracture Strain Trip Steel Void Nucleation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- (1).H. Neuber: Kerbspannungslehre. First Edithion 1937, Second Edition 1958, Berlin, Gottingen, Heidelberg.Google Scholar
- (2).H. Neuber: Theory of Stress Concentration for Shear-Strained Prismatical Bodies With Arbitrary Non-Linear Stress-Strain Law. Trans. Am. Soc. Mech. Eng. J. Appl. Mech., 28 (1961) pp. 544–550.MathSciNetMATHCrossRefGoogle Scholar
- (3).R. Hill: Mathematical Theory of Plasticity. Oxford (1950).MATHGoogle Scholar
- (4).V. Weiss: Notch Analysis of Fracture. In: Liebowitz, H.: Fracture, Vol.
*3*, New York and London, (1971) pp. 227–264.Google Scholar - (5).V. Weiss, Y. Kasai, and K. Sieradzki, & #x201C;Microstructural Aspect of Fracture Toughness, ASTM STP 605, American Society for Testing and Materials, (1976) pp. 16–33.Google Scholar
- (6).V. Weiss and H. Neuber, “Recent Advances in Notch Analysis of Fracture and Fatigue”, Ingenieur-Archiv 45 (1976) S. 281–289, Springer-Verlag (1976).Google Scholar
- (7).H. W. Liu, “An Analysis on Fatigue Crack Propagation, NASA CR-2032 (1972).Google Scholar
- (8).M. Ogasawara, M. Adachi, M. Nagao, and V. Weiss, “Crack Initiation at Notches in Low Cycle Fatigue”, Proc. III Intl. Conf. Fracture, Munich, Germany, V. 4, (April 1973) p. 511.Google Scholar
- (9).S. Argon, J. Im, and R. Safoglu, Metallurgical Transactions, Vol. 6A, (1975) pp. 825–837, pp. 839–851.ADSGoogle Scholar
- (10).F. A. Mlintock, “Plasticity Aspects of Fracture”, In: Liebowitz, H.: Fracture, Vol. 3, New York and London, (1971) pp. 47–225Google Scholar

## Copyright information

© Martinus Nijhoff Publishers, The Hague 1981