A Damage to Crack Transition Framework for Ductile Materials Accounting for Stress Triaxiality

Predicting the entire ductile failure process is still a challenge task since it involves different processes: damage first diffuses before localizing, eventually leading to a micro-crack initiation and propagation. On the one hand, discontinuous approaches can describe localised processes such as crack propagation but fail in capturing diffuse damage evolution. On the other hand, continuous approaches such as continuum damage models are suited for diffuse damage modelling, but cannot represent properly physical discontinuities.
In this work both approaches are combined in a hybrid implicit non-local damage model combined with an extrinsic cohesive law in a discontinuous Galerkin finite element framework [1]. The implicit non-local damage model reproduces the initial diffuse damage stage without mesh-dependency. Upon transition at void coalescence or intensive plastic localisation, a crack is introduced using a cohesive band model. Contrarily to cohesive elements, cohesive band models capture in-plane stretch effects, and thus account for stress triaxiality [2]. Indeed, by considering a band of small but finite thickness ahead of the crack surface, the strain field inside this band is evaluated from the neighbouring strains and from the cohesive jump [2]. Then, an appropriate damage model is used to compute the stress-state inside the band and the cohesive traction forces on the crack lips.
The approach is first applied in the case of elastic damage for which the band thickness is evaluated to ensure the energetic consistency of the damage to crack transition with respect to purely non-local continuum damage mechanics [1]. Then, the scheme is formulated to the case of a non-local porous-plastic damage Gurson model. In particular, the law governing void growth accounts for shear effects, while the void coalescence mechanism, hence the damage to crack transition criterion, is predicted using the Thomason model [3].
References:
[1] Leclerc J., Wu L., Nguyen V.D., Noels L. 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. (2017): In press.
[2] 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).
[3] Benzerga A.A., Leblond J.-B., Needleman A., Tvergaard V. Ductile failure modelling. Int J Fract 201 (2016).