A Damage to Crack Transition Framework for Ductile Failure

Accurate numerical predictions of the entire ductile failure process is still challenging. Indeed, it combines a diffuse damage stage followed by a damage localisation and crack initiation and propagation. On the one hand, continuous damage models are suited for the diffuse damage stage but are inadequate for the description of physical discontinuities. On the other hand, discontinuous approaches, as cohesive zone models, are able to reproduce crack initiation and propagation, but not the damage diffusion. In this work, the presented numerical scheme joins both approaches in a discontinuous Galerkin finite element framework. A non-local implicit damage model computes the initial diffuse damage stage beyond the softening point without mesh-dependency. Then, a crack is introduced using a cohesive band model [1, 2]. Contrarily to classical cohesive models, a 3D state is recreated at the crack interface by considering a small, but finite, fictitious cohesive thickness. As a result, a strain tensor can be recomposed from the cohesive jump and the neighbouring bulk deformation gradient. A stress tensor at the interface, from which the cohesive forces are deduced, is computed using an appropriate local damage law. The framework is applied to ductile failure, modelled by a combination of the Gurson and the Thomason model [3]. The initial diffuse void growth phase is modelled by the (non-local) Gurson model [4] accounting for shear effects [5]. Then, a crack is introduced when the coalescence is reached and the behaviour of the cohesive law is computed from the Thomason model [3]. The framework capabilities are demonstrated by reproducing the slanted and the cup-cone failure respectively of a plane strain specimen and a round bar. REFERENCES [1] J.J.C. Remmers, R. de Borst., C.V. Verhoosel and A. Needleman. The cohesive band model: a cohesive surface formulation with stress triaxiality. Int. J. Fract. (2013). [2] J. Leclerc, L. Wu, V.D. Nguyen and L. Noels. Cohesive band model: a cohesive model with triaxiality for crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework. Int. J. for Num. Methods in Eng. (2018). [3] A.A. Benzerga, J.-B. Leblond, A. Needleman, V. Tvergaard. Ductile failure modelling. Int. J. Fract. (2016). [4] F. Reusch, B. Svendsen and D. Klingbeil. A non-local extension of Gurson-based ductile damage modelling. Comp. Mat. Sci. (2003). [5] K. Nahshon and J.W. Hutchinson. Modi cation of the Gurson Model for shear failure. Eur. J. of Mech. A/Sol. (2008).The research has been funded by the Walloon Region under the agreement no.7581-MRIPF in the context of the 16thMECATECH cal