A nonlocal model for ductile failure incorporating void growth and coalescence

Ductile failure is known to be governed by nucleation, growth, and coalescence of voids, together with extensive plastic dissipation accumulated before failure. Modelling of the ductile failure requires the development of robust constitutive models able to represent both the hardening phase during which large deformation gradients of several tens of percent arise in combination with nucleation and growth of micro-voids, as well as the softening phase characterized by high critical energy release rate and during in which coalescence of micro-voids develops. Although the Gurson- Tvergaard- Needleman (so-called GTN) model, which is the most popular model of the ductile failure, gives a complete computational methodology for all stages of void evolution, the underlying phenomenological concept of void coalescence, in which a critical value of porosity is used to predict the onset of void coalescence beyond which the porosity growth rate is artificially accelerated through an effective porosity, 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. This model is based on the three distinct nonlocal solutions of expansion of voids embedded in an elastoplastic matrix: the void growth phase governed by the GTN model, the void necking coalescence phase governed by a heuristic extension of the Thomason model based on the maximal principle stress, and the void shearing coalescence triggered by the maximal shear stress. The first solution considers the diffusion of the plastic deformation around voids while the last two solutions correspond to the localization of the plastic deformation between neighboring voids. This combination allows accounting for effects of the Lode variable and shear stress, which play important roles in the ductile failure. The 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, provides an efficient regularization of the problem of the loss of solution uniqueness when material softening occurs whatever the localization mechanism. It is shown that this approach allows recovering complex failure patterns such as slant and cup-cone of respectively plane strain and axisymmetric samples tests.