Finite fracture mechanics and cohesive crack model: Weight functions vs. cohesive laws

The present work represents the prosecution of a previous paper [Short cracks and V-notches: Finite Frac- ture Mechanics vs. Cohesive Crack Model (2016). P. Cornetti, A. Sapora, A. Carpinteri. Engineering Fracture Mechanics 168:2–12] aiming to corroborate the use of Finite Fracture Mechanics by showing that its fail- ure load estimates are very close to the ones provided by the well-established Cohesive Crack Model. While the above paper focused only on the Dugdale cohesive law and the original Finite Fracture Me- chanics approach, here we consider generic cohesive laws of power law type and propose an extension of Finite Fracture Mechanics based on stress weight functions. We argue that excellent agreement be- tween the models is found provided proper correspondence rules between the shape of the cohesive laws and of the weight functions are given. As a test bench for this conjecture, we choose the Griffith crack geometry, where we are able to achieve the solutions in a semi-analytical way for both the models. Finally, we show that similar results can be obtained also by varying the domain of the weight function while keeping fixed its shape

Crack onset and propagation at fibre-matrix elastic interfaces under biaxial loading using finite fracture mechanics

A new fracture criterion able to predict crack onset and propagation at interfaces between solids is formulated, implemented in a computational code and applied to a particular problem in composites on a microscale. More specifically, this criterion is used to study the debond onset and propagation in mixed mode in the case of a single fibre subjected to a biaxial remote loading. The fracture criterion formulation is based on the Linear Elastic-(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Each of these criteria is a necessary but not sufficient condition for crack onset and propagation. Two empirical mixed-mode fracture criteria are considered and tested: the interface fracture toughness law by Hutchinson and Suo and the quadratic stress criterion. The FFM + LEBIM approach developed offers an adequate characterization of the interface stiffness in contrast to the too restrictive, original LEBIM formulation