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.