Abstract :
[en] A damage process starts with a diffuse stage followed by a localized stage in which the initiation and propagation of cracks can occur. To model this whole failure process, on the one hand, continuous approaches formulated under the framework of continuum damage models succeed in capturing the material degradation but are unable to represent properly physical discontinuities. On the other hand, discontinuous approaches describe the failure process such as cracks by propagating field discontinuities. However, they usually do not capture the diffuse damage evolution and in-plane stretch effects which are the consequences of stress triaxiality and must be taken into account for accurate ductile failure simulations. Clearly both described approaches cannot separately represent the whole ductile failure process with accuracy. In this work, the advantages of these two approaches are combined in a single one, so-called non-local damage to crack transition. The non-local porous-plastic damage Gurson model [1] is used to reproduce the initial diffuse damage stage without mesh-dependency. In particular, the law governing void growth accounts for large shear effects [2], while the void coalescence mechanism, hence the damage to crack transition criterion is predicted using the Thomason model [3]. At the transition point, a crack is initiated using a cohesive band model represented by a cohesive law including in-plane stretch effects [4]. By assuming that all the damaging process is concentrated within a band of small but finite thickness, the deformation state inside this band is obtained from the one of neighboring material points and from the displacement jump. Then, the underlying constitutive law is still used to compute the stress state from which the cohesive traction across the cohesive
band is estimated. This combined framework is implemented in a discontinuous Galerkin/ extrinsic cohesive zone method finite element framework, which has successfully been applied for elastic-damage problems in which the band thickness was evaluated to ensure the energetic consistency of the damage to crack transition with respect to purely non-local continuum damage mechanics [5]. The proposed framework is shown to capture the damage diffuse stage as well as crack initiation and propagation of the whole ductile failure process.
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[2] Nahshon K., Hutchinson J. W., Modification of the Gurson Model for shear failure, Eur. J. Mech. A Solids, 27, (2008).
[3] Benzerga A.A., Leblond J.-B., Needleman A., Tvergaard V., Ductile failure modelling, Int. J. Fract., 201, (2016).
[4] Remmers J. J. C., de Borst R., Verhoosel C. V., Needleman A., The cohesive band model: a cohesive surface formulation with stress triaxiality, Int. J. Fract., 181, (2013).
[5] Leclerc J., Wu L., Nguyen V.D., Noels L., A damage to crack transition model accounting for stress triaxiality formulated in a hybrid non-local implicit discontinuous Galerkin - cohesive band model framework, Int. J. for Num. Methods in Eng., 113 (3), (2018)
