Modelling of ductile failure over multiple scales

This thesis investigates damage development through void growth in porous, ductile materials, both for conventional isotropic materials and materials exhibiting gradient strengthening. Two types of modelling approaches are used for the numerical analyses. The first is a local approach based on the classical micro-mechanical Gurson-Tvergaard model that accounts for porosity driven material damage through an averaged void volume fraction. Niordson and Tvergaard
[1] have extended the model to account for gradient strengthening effects by introducing an intrinsic material length parameter in the constitutive equations. The aim is to investigate the possibility of simulating plastic strain gradient effects on damage evolution at the micron scale by employing an intrinsic length scale parameter in the continuum model's constitutive equations. The gradient enriched Gurson-Tvergaard model accurately predicts the elevated
yield point and suppressed void growth associated with gradient strengthening in a parametric study. However, void shape and inter-void ligament sizes affect the load-carrying capacity more than the void volume fraction itself. A well-known extension to the Gurson-Tvergaard model accounting for the void shape evolution's effect on material damage, namely the Gologanu- Leblond-Devaux model, has also applied to conventional isotropic, porous, ductile materials.
Current work is being done to extend this model to capture the effects of plastic strain gradients in gradient hardening materials, allowing for combined investigation of void size and shape on the macroscopic material response.

The second of the two modelling approaches consists of analysing discrete voids embedded in unit cells through finite element simulation. The finite element mesh consists of elements with a strain gradient plasticity theory incorporated in the element property definition. Accounting for the role of the plastic strain gradients in the constitutive equations naturally introduces a material length scale parameter for dimensional consistency. This non-local approach allows for an immediate investigation of the effects of inter-void ligament sizes and void distribution inhomogeneity on the void growth and the subsequent damage, as their presence is not determined by an averaging parameter, such as the void volume fraction. A study on the combination of void size and inter-void ligament size has been conducted. The results showed that a smaller intervoid ligament size would reduce the material's load-carrying capacity unless the microstructure is small enough to induce large plastic strain gradients in the inter-void ligaments, inhibiting localisation of plastic ow. The material response will be independent of inter-void ligament size for materials with a large length scale parameter. Ongoing work to further investigate the effect of the randomness of void distributions is being conducted. The combined eects of void clustering and microstructure size under different loading conditions are investigated by analysing the response of representative volume elements with a random distribution of voids. The method for such an investigation has been established, and some preliminary results presented