Three-dimensional effects on cracked discs and plates under nominal Mode III loading

Abstract

The existence of three-dimensional effects at cracks has been known for many years, but
understanding has been limited, and for some situations still is. Understanding improved when the existence of
corner point singularities and their implications became known. Increasingly powerful computers made it
possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, threedimensional
effects are sometimes ignored in situations where they may be important. The purpose of the
present contribution is to review the study carried out by the same authors in some recent investigations, in
which a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in
linear elastic discs and plates has been analysed by means of accurate 3D finite element (FE) models.
The results obtained from the highly accurate finite element analyses have improved understanding of the
behaviour of through cracked components under anti-plane loading. The influence of plate bending is
increasingly important as the thickness decreases. It appears that a new field parameter, probably a singularity, is
needed to describe the stresses at the free surfaces. Discussion on whether KIII tends to zero or infinity as a
corner point is approached is futile because KIII is meaningless at a corner point.
The intensity of the local stress and strain state through the thickness of the cracked components has been
evaluated by using the strain energy density (SED) averaged over a control volume embracing the crack tip. The
SED has been considered as a parameter able to control fracture in some previous contributions and can easily
take into account also coupled three-dimensional effects. Calculation of the SED shows that the position of the
maximum SED in the discs case is a function of the thickness. In the plates case instead the position of the
maximum SED is independent of plate thickness, contrary to disc results.