Ductility limit prediction using a GTN damage model coupled with localization bifurcation analysis

• A large-strain elastic–plastic–damage GTN model is coupled with the Rice bifurcation theory.
• The resulting GTN–Rice coupling is used to predict ductility limits set by plastic flow localization.
• A sensitivity analysis with respect to model parameters is conducted on selected ductile materials.
• The role of softening in triggering plastic flow localization is shown predominant in this approach.
• The proper identification of damage parameters has a significant impact on the model predictions.

Because the localization of deformation into narrow planar bands is often precursor to material failure, several approaches have been proposed to predict this phenomenon. In this paper, the Gurson–Tvergaard–Needleman (GTN) elastic–plastic–damage model for ductile materials is considered. A large-strain version of this constitutive model is coupled with the Rice localization criterion, which is based on bifurcation theory, to investigate strain localization. The resulting loss of ellipticity condition is then used to determine ellipticity loss diagrams (ELDs) associated with strain paths that are those typically applied to metals under biaxial stretching. A sensitivity analysis is conducted with respect to the model parameters on a representative selection of ductile materials. The analysis shows that the damage parameters have a significant impact on the predicted ELDs, which confirms the predominant role of damage-induced softening in triggering plastic flow localization with the adopted constitutive description combined with the bifurcation approach. As a consequence of this high sensitivity, it appears that the proper identification of damage parameters is a key issue for accurate plastic flow localization predictions using the GTN model coupled with bifurcation theory. The effect of the dense matrix hardening parameters on the strain localization predictions of the voided aggregate, although found much smaller in the whole, is more noticeable for the plane strain tension loading path or, more generally, when the critical hardening modulus required for localization is not strongly negative.