A Non-Local Ductile Failure Model Accounting for Void Growth and Coalescence at Low and High Stress Triaxiality

Ductile failure is controlled by the nucleation, growth, and coalescence of voids combined with an extensive plastic dissipation accumulating before failure. Although the Gurson- Tvergaard- Needleman [1] model, which is the most popular model of the ductile failure, gives a complete computational methodology for all stages of void evolution, the framework remains phenomenological and does not provide a realistic description of the physics of the void coalescence.
In this work, a hyperelastic finite strain multi-surface constitutive model with multiple nonlocal variables is developed for predicting the failure of ductile materials [2]. This model is based on the combination of the three distinct nonlocal solutions of expansion of voids embedded in an elastoplastic matrix. The void growth phase governed by the GTN model considers the diffusion of the plastic deformation around voids. The first coalescence mode considered is by void necking and is governed by a heuristic extension of the Thomason model based on the maximal principle stress. The second coalescence mode considered is by void shearing triggered by the maximal shear stress. In order to avoid the loss of solution uniqueness when material softening occurs whatever the localization mechanism is, an implicit nonlocal formulation with multiple nonlocal variables, including the volumetric and deviatoric parts of the plastic deformation, and the mean plastic deformation of the matrix, regularises the problem.
Macro-scale numerical tests show that the current approach allows capturing complex failure modes such as slant failure for specimens in plane strain and cup-cone failure for cylindrical.