Coupled fracture modes of discs and plates under anti-plane loading and a disc under in-plane shear loading

Three-dimensional effects near crack tips have been deeply investigated in the past, but the topic is still ongoing and under investigation. However, the understanding is in some cases limited, and the problem requires further attention. Three-dimensional effects are in fact neglected in situations where they may play an important role. The main aim of this review paper is to summarise some recent results of a study carried out on the coupled in-plane fracture mode induced by a nominal anti-plane (mode III) loading applied to plates and discs weakened by a straight crack. Only linear elastic conditions are considered herein. The results derived by a large bulk of finite element models allow a better understanding of coupled modes generated by anti-plane loading. The influence of plate/disc bending on three-dimensional stress fields is considered in the investigation, showing that it becomes non-negligible as the thickness decreases. Some considerations on the trend of K-III as the corner point is approached are also part of this paper. In addition, the trend of the strain energy density (SED) in a volume surrounding the crack tip is shown and commented on. This parameter allows the precise determination of the weakest point of the component through the thickness becoming a useful tool. Some new results for a disc under in-plane shear loading are included. These results clarify the influence of disc bending under anti-plane loading.