The University of Southampton
University of Southampton Institutional Repository

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

An approximate, analytical approach to the 'HRR' solution for sharp V notches
An approximate, analytical approach to the 'HRR' solution for sharp V notches
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 π/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.
hrr solution, v-notch, elastoplastic stress distributions
0376-9429
269-286
Flippi, S.
ca3fe987-2590-43c6-b285-a5d4aa7591a1
Ciavarella, M.
d5aa6350-b3d4-4a78-a670-9d78242f58c5
Lazzarin, P.
97044a15-79c0-46a0-9f42-e26556bd8564
Flippi, S.
ca3fe987-2590-43c6-b285-a5d4aa7591a1
Ciavarella, M.
d5aa6350-b3d4-4a78-a670-9d78242f58c5
Lazzarin, P.
97044a15-79c0-46a0-9f42-e26556bd8564

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), 269-286. (doi:10.1023/A:1022057621185).

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 π/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.

Text
fili_02.pdf - Accepted Manuscript
Download (2MB)

More information

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
Last modified: 15 Mar 2024 06:45

Export record

Altmetrics

Contributors

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

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×