The Energetic Approach of Elastoplastic Fracture MechanicsApplied to the Problem of Unloading

摘要

In this paper, a cleavage parameter G_p, based on energetic considerations, is defined to characterise crack initiation in arnbrittle elastoplastic medium, and discussed in the context of the famous ? Rice’s paradox ?. We start from Francfort-Marigornelastic fracture theory, based on a minimum energy principle, which generalises Griffith’s theory. In this theory, the energyrndepends on the displacement field as well as the geometrical crack surface. The cleavage parameter is defined and determinedrnas the value of the discrete gradient of an incremental elastoplastic potential. For that purpose, it is necessary to compute twornsolutions : the solution of the problem with the initial crack, and the solution of the problem after a finite crack propagationrn?Δ1? taking into account the local unloading due to this propagation.rnThis parameter G_p is applied to the analysis of a centred cracked plate submitted to a loading first increasing (to open therncrack) and then decreasing (to close the crack). The constitutive law is elastoplastic with an isotropic hardening. A very finernmesh is used in the area of the crack tip, and a parametric analysis is realised to study the effect of this mesh and of the Δ1rnpropagation. Therefore an important result is obtained : the G_p parameter is neither mesh dependent, nor Δ1 dependent.rnDuring the unloading, G_p decreases very quickly from a maximum value to zero, and we can affirm then that no propagationrnis possible, although the value of the J-integral is non zero.rnThe G_p parameter can be related to the G~Δ parameter proposed by Kfouri & Miller in 1976. As suggested by Rice, thernvalue of this parameter seems to vanish to zero with the length Δ1 of the finite crack propagation. It means that, for anrnelastoplastic media, there would be no energy available for crack propagation. We will show that we would have obtained thernsame result for the G_p parameter with a standard mesh, but also that, if the mesh is sufficiently refined, the final result is notrnzero. Therefore, this G_p parameter can be used as a cleavage fracture parameter.