Coupled fracture mode of a cracked plate under anti-plane loading

• The existence of three-dimensional effects at cracks has been known for many years.
• A coupled fracture mode generated by a nominal anti-plane loading of discs was studied.
• Accurate 3D finite element analyses were performed.
• A new field parameter, probably a singularity, is needed to describe stresses.
• The strain energy density in a control volume at the crack predicts a critical point.

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. Despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. The purpose of the present investigation is to study a coupled fracture mode generated by a nominal anti-plane (Mode III) loading applied to linear elastic plates weakened by a straight through-the-thickness crack. With this aim accurate 3D finite element (FE) analyses have been performed. The results obtained from the highly accurate finite element models have improved understanding of the behaviour of through cracked plates under anti-plane loading. The influence of plate bending is increasingly important as plate thickness decreases. It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the plate 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. Calculation of the strain energy density (SED) in a control volume at the crack tip allows us to predict the most critical point through the plate thickness.