An implicit gradient type of static failure criterion for mixed-mode loading

Abstract

This paper proposes a new criterion for the prediction of static failure load of structural components made of linear brittle-elastic material affected by high stress concentrations. The static failure criterion is based on the definition of a non-local equivalent stress scalar. The approach starts with the definition of a spatial weighted average of a local stress scalar, called non-local equivalent stress. The non-local equivalent stress is then approximated through a spatial gradient expansion containing the Laplacian of the local equivalent stress multiplied by a non-local length. Thus the non-local equivalent stress is expressed as an implicit differential equation. We develop an analytical solution in the case of a one-dimensional stress state at a crack tip, assuming Neumann’s boundary conditions. Two-dimensional V-notched components are then considered and a numerical solution is found via a standard finite element procedure. We also relate the non-local length of the model to the ultimate tensile stress and fracture toughness of the material. Finally, we consider experimentally measured failure loads reported in the literature for brittle-elastic PMMA specimens. The failure loads numerically calculated for mode I and mixed-mode loading are compared with experimental data. For this purpose, different definitions of the local equivalent stress are taken into account. The accuracies of the numerically estimated failure loads are satisfactory for the considered loading modes.