On asymptotes of surface tractions and displacement discontinuities at the crack front

Abstract

Analytical expression between the stress intensity factor and displacement intensity factor is derived for an arbitrary shaped plane crack with a smooth crack front. The crack is placed in a medium with an arbitrary elastic anisotropy. The analysis is based on constructing the outer and inner asymptotes for the corresponding surface tractions and displacement discontinuity fields at the crack front. The closed-form pseudodifferential operator of the crack theory along with the associated amplitudes and symbols is constructed.