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# An approximate, analytical approach to the 'HRR' solution for sharp V notches

Flippi, S., Ciavarella, M. and Lazzarin, P. (2002) An approximate, analytical approach to the 'HRR' solution for sharp V notches International Journal of Fracture, 117, (3), pp. 269-286.

Record type: Article

## Abstract

The well-known so-called HRR-solution' (Hutchinson, 1968 and Rice and Rosengren, 1968) considers the elasto-plastic stress field in a power-law strain hardening material near a sharp crack. It provides a closed form explicit expression for the stress singularity as a function of the power-law exponent n' of the material, but the stress angular variation functions are not found in closed form. More recently, similar formulations have appeared in the literature for sharp V-notches under mode I and II loading conditions. In such cases not only is the angular variation of the stress fields obtained numerically, but so is the singularity exponent of the stress field. In the present paper, approximate but accurate closed form solutions are first reported for sharp V-notches with an included angle greater than /6 radians. Such solutions, limited here to Mode I loading conditions, allow a very satisfactory estimate of the angular stress components in the neighbourhood of the notch tip, in the entire range of notch angles and for the most significant values of n (i.e. from 1 to 15). When the notch opening angle tends towards zero, and the notch approaches the crack case, the solution becomes much more complex and a precise evaluation of the parameters involved requires a best-fitting procedure which, however, can be carried out in an automatic way. This solution is also reported in the paper and its degree of accuracy is discussed in detail.

PDF fili_02.pdf - Accepted Manuscript

Published date: 2002
Keywords: hrr solution, v-notch, elastoplastic stress distributions

## Identifiers

Local EPrints ID: 23228
URI: http://eprints.soton.ac.uk/id/eprint/23228
ISSN: 0376-9429
PURE UUID: f0d97612-f66c-4413-93fb-271563426fe3

## Catalogue record

Date deposited: 27 Mar 2006

## Contributors

Author: S. Flippi
Author: M. Ciavarella
Author: P. Lazzarin