Digital Repository, Giornata IGF Forni di Sopra (UD) 2011

Font Size: 
Sharp Notch Roots; The length scale implicit in the solution
D.A. Hills, D. Dini

Last modified: 2011-02-25


Reentrant notches whose internal angle exceeds about 257o induce two singular eigensolutions,
from the classical Williams procedure, where the symmetric term is always more strongly singular than the
antisymmetric term. This implies the presence of a length scale within the singular solution, and it means that
notch root process zones are not self-similar but vary in character according to their size; small ones will be
mode-I like, larger ones mode-II like, larger ones still not existing under small scale yielding conditions. Here
we explore explicitly within the framework of the singular solution (i.e. a semi-infinite notch) the conditions
under which mode I type behaviour exists, or mode II behaviour, or the solution is mixed in character. These
general results are then applied to example finite problems, and used to show the range of loads under which
pure mode I, small scale yielding singular behaviour is to be expected. This is of practical relevance because it
means that, even if both eigenmodes are excited in a particular example problem, the process zone may
practically be considered to be mode I in nature. It is shown that, in each of the example problems examined so
far, there is a wide range of conditions where this is so, and this property may be used to simplify the way we
treat the effects of sharp corners, whether at notches or at the edges of complete contacts, as characterizers of
the local process zone.

Full Text: PDF