3D effects on Fracture Mechanics: corner point singularities

Abstract

Plane elasticity has allowed the development of the current knowledge on fracture mechanics since the dawn of this discipline. Linear elastic fracture mechanics (LEFM) has taken advantage of the possibility to obtain analytical closed-form solutions. Indeed, three dimensional effects, related basically to the Poisson’s ratio and the plate thickness, have been mostly neglected for a long time. The proof of the existence of corner point singularities, i.e. stress singularity at the intersection of crack front with a free surface, has contributed to explain fracture phenomena, such as the bowed crack fronts and the behavior of stress intensity factors along the thickness of a cracked/notched body. Although fatigue crack growth is Mode I dominated and corner point singularities become insignificant, for the estimation of brittle failure of cracked/notched they may represent a substantial source of error, both in terms of magnitude of the stress field and failure location. In this paper we provide before a brief overview on 3D corner point singularities. By exploiting of 3D finite element (FE) modeling, to understand the theoretical basis of this phenomenon, numerical experiments on sharply-V-notched linear elastic plates under mode 1 loading are performed. A quantitative and qualitative description of the causes and effects of 3D vertex singularities under mode 1 in relation with Poisson’s ratio is given, including negative values of this latter material parameter, never before investigated. Besides, by means of numerical simulations of the same notched plates subjected to mode 3 loading, observations on the possible connection between 3D corner point singularities and the out-of-plane shear stress distribution near the model surface are discussed. Finally, future perspectives on this research field are addressed.