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

Abstract

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 µm-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. Nomenclaturea Notch depth , * A A Scaling coefficients involved in the Coupled Criterion d Notch width E Young's modulus F Applied force c F Critical applied force at failure exp i F Measured applied force on specimen i sim i F Predicted applied force on specimen i using the coupled criterion G Energy release rate c

Strength-based regularization length in phase field fracture

“…Initially developed under small deformation assumption and linear elastic 2D framework, it has since then been extended to 3D (Leguillon et al 2014;Yosibash et al 2016;García et al 2016;Doitrand et al 2018a;Doitrand et al 2018b), to consider material or geometry nonlinearities (Leguillon et al 2017;Li et al 2019;Rosendahl et al 2019;Doitrand et al 2020c;Leite et al 2021), as well as dynamic crack initiation (Doitrand et al 2022;Chao Correas et al 2022). It also revealed efficient for small scale fracture assessment (Doitrand et al 2020a;Gallo et al 2020;Jimenez Alfaro et al 2021). The second limitation of Griffith's approach was solved by first reconsidering the local energy criterion as a global minimization problem (Francfort et al 1998), which was the first step towards a variational formulation of fracture problems.…”