Limitations to leading-order asymptotic solutions for elastic-plastic crack growth

Authors
Citation
Wj. Drugan, Limitations to leading-order asymptotic solutions for elastic-plastic crack growth, J MECH PHYS, 46(12), 1998, pp. 2361-2386
Citations number
8
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanical Engineering
Journal title
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
ISSN journal
0022-5096 → ACNP
Volume
46
Issue
12
Year of publication
1998
Pages
2361 - 2386
Database
ISI
SICI code
0022-5096(199812)46:12<2361:LTLASF>2.0.ZU;2-O
Abstract
Previous work has shown that there are significant discrepancies between le ading-order asymptotic analytical solutions for the elastic-plastic fields near growing crack tips and detailed numerical finite element solutions of the same problems. The evidence is dearest in the simplest physically reali stic case: quasistatic anti-plane shear crack growth in homogeneous, isotro pic elastic-ideally plastic material. There, the sore extant asymptotic ana lytical solution involves a plastic loading sector of radial stress charact eristics extending about 20 degrees from ahead of the crack, followed by el astic unloading, whereas detailed numerical finite element solutions show t he presence of an additional sector of plastic loading, extending from abou t 20 to about 50 degrees, that is comprised of non-radial characteristics. To explore how the asymptotic analysis can completely miss this important s olution feature, we derive an exact representation for the stress and defor mation fields in such a propagating region of non-radial characteristics, a s well as in the other allowable solution regions. These exact solutions co ntain arbitrary functions, which are determined by applying asymptotic anal ysis to the solutions and assembling a complete near-tip solution, valid th rough second order, that is in agreement with the numerical finite element results. In so doing, we prove that the angular extent of the sector of non -radial characteristics, while substantial until extremely close to the cra ck tip, vanishes in the limit as the tip is approached, and that the soluti on in this sector is not of variable-separable form. Beyond resolving the a nalytical-numerical discrepancies in this specific anti-plane sheer problem , the analysis serves to caution, by explicit example, that purely leading- order asymptotic solutions to nonlinear crack growth problems cannot in gen eral capture all essential physical features of the near-tip fields, and th at the often-invoked assumption of variable-separable solutions is not alwa ys valid. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.