Finite Fracture Mechanics extension to dynamic loading scenarios

Abstract

The coupled criterion of Finite Fracture Mechanics (FFM) has already been successfully applied to assess the brittle failure initiation in cracked and notched structures subjected to quasi-static loading conditions. The FFM originality lies in addressing failure onset through the simultaneous fulfilment of a stress requirement and the energy balance, both computed over a finite distance ahead of the stress raiser. Accordingly, this length results to be a structural parameter, thus able to interact with the geometry under investigation. This work aims at extending the FFM failure criterion to dynamic loadings. To this end, the general requisites of a proper dynamic failure criterion are first shortlisted. The novel Dynamic extension of FFM (DFFM) is then put forward assuming the existence of a material time interval that is related to the coalescence period of microcracks upon macroscopic failure. On this basis, the DFFM model is investigated in case a one-to-one relation between the external solicitation and both the dynamic stress field and energy release rate holds true. Under such a condition, the DFFM is also validated against suitable experimental data on rock materials from the literature and proven to properly catch the increase of the failure load as the loading rate rises, thus proving to be a novel technique suitable for modelling the rate dependence of failure initiation in brittle and quasi-brittle materials.

Strength-based regularization length in phase field fracture

“…First, it is based on the assumption of an existing crack and enables studying its propagation but fails to predict its nucleation. Second, its implementation in a finite element (FE) code to study crack propagation either requires a priori the knowledge of the crack path or robust remeshing methods to update the crack configuration at each propagation step (Chiaruttini et al 2013;Vattré et al 2022). The first limitation was overcome by Leguillon (2002) who developed the coupled criterion in the finite fracture mechanics (FFM) framework (Nairn et al 1993;Hashin 1996), dedicated to study the nucleation of a crack.…”

“…This approach proved to be a robust and efficient way to predict crack initiation in many configurations such as, e.g., weak or strong singularities, non-singular stress raisers (Weißgraeber et al 2016;Doitrand et al 2020b). 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).…”