Finite fracture Mechanics at the micro-scale. Application to bending tests of micro cantilever beams

In the framework of Finite Fracture Mechanics theory, the Coupled Criterion predicts crack onset based, totally or partially according to the situation, on an energy condition. Due to the smallness of the specimens at the micro-scale, this condition may become difficult to be satisfied given the very small volume of the structures, leading to an apparent strengthening. The aim of this work is to analyze how the answer brought by the Coupled Criterion evolves when descending the scales from the cm-scale, to the mu m-scale and even nm-scale. It is based on case studies and on comparisons with experiments found in the literature. Obviously, the Coupled Criterion still works at the micro-scale. However, due to the lack of energy caused by the smallness of the specimens, it is in general much sensitive to the toughness whereas it is little sensitive to the tensile strength, making it sometimes difficult to identify this latter parameter. In parallel, the difference between displacement and force controlled loading modes increases when descending the scales and a notch insensitivity appears.