Finite element implementation of Field Crack Mechanics for brittle and ductile fracture

Abstract

In this work, a Finite Element (FE) implementation of a Field Crack Mechanics (FCM) model is presented for the first time. The implementation includes general boundary conditions and application to bulk plasticity as well. The current numerical investigation adopts the standard Galerkin finite element formulation to solve the equation of linear momentum balance and finite difference framework for crack evolution. Our preliminary investigation includes the modes-I and II loading conditions, where their respective normal stress fields are compared against their analytical counterparts. The fundamental questions in classical fracture mechanics, e.g. the existence of threshold stress for the crack to move, and various stages associated with the crack propagation are investigated. Additionally, this study explores two distinct strain energy functions based on the crack surface normal and hydrostatic deviatoric energy split. Crack irreversibility is a natural phenomenon in the FCM model, and it does not require satisfying any extra irreversibility constraints. The model shows good agreement against literature and analytical framework. The current FCM implementation also recovers the basic notion of fracture propagation which satisfies both energy and stress criterion. The study also explores the crack motion under the effect of plasticity in ductile materials. The results thus obtained for both brittle and ductile fracture cases are consistent with the predictions of classical fracture mechanics. The current implementation of the FCM effectively demonstrates stable crack propagation, eliminating the requirement for surfing boundary conditions.