A criterion based on the local strain energy density for the fracture assessment of cracked and V-notched components made of incompressible hyperelastic materials

Abstract

The present contribution is devoted to the theoretical and numerical study of the elasto-static fields at a vertex notch under mode I loading. The analysis is based on the plane deformation hyperelasticity theory for an incompressible Mooney–Rivlin material. While for cracked components some contributions can be found in the recent and past literature, studies on V-notched components are instead very limited. The aim of this paper is to partially fill this lack, providing a fracture criterion for the assessment of components weakened by sharp V-notches. In the first part of the paper, a brief description of the analytical frame available for V-notches in hyperelastic material is reported. A Williams’ type diagram reporting the degree of singularity for a material obeying a Mooney–Rivlin behavior is present. The asymptotic stress field and the local strain energy density are investigated by means of non-linear finite element analyses. In the second part of the paper, a criterion based on the local energy is proposed and successfully applied to a set of experimental data taken from the literature. Future works are surely necessary to validate the criterion considering more sets of data from sharp and blunt V-notches.