A Mesh Independent GTN Damage Model and Its Application in Simulation of Ductile Fracture Behaviour

Ductile fracture process involves the typical stages of nucleation, growth and coalescence of voids in the micro-scale. In order to take the effects of these voids on the stress carrying capability of a mechanical continuum during simulation, damage mechanics models, such as those of Rousselier and Gurson-Tvergaard-Needleman (GTN) are widely used. These have been highly successful in simulating the fracture resistance behaviour of different specimens and components made of a wide spectrum of engineering steels. However, apart from the material parameters, a characteristic length parameter has to be used as a measure of the size of the discretisation in the zone of crack propagation. This inherent limitation of these local damage models prevents them from simulating the stress distribution near the sharp stress gradients satisfactorily, especially at transition temperature regime. There have been efforts in literature to overcome the effect of mesh-dependency by development of nonlocal and gradient damage models. A nonlocal measure (weighted average of a quantity over a characteristics volume) of damage is usually used in the material constitutive equation. In this paper, the authors have extended the GTN model to its nonlocal form using damage parameter ‘d’ as a degree of freedom in the finite element (FE) formulation. The evolution of the nonlocal damage is related to the actual void volume faction ‘f’ in ductile fracture using a diffusion type equation. The coupled mechanical equilibrium and damage diffusion equations have been discretised using FE method. In order to demonstrate the mesh independent nature of the new formulation, a standard fracture mechanics specimen (i.e., 1T compact tension) has been analysed using different mesh sizes near the crack tip and the results have been compared with those of experiment. The results of the nonlocal model have also been compared with those of the local model. The effect of different GTN parameters on the fracture resistance behaviour of this specimen has been studied for the nonlocal model and these results have been compared with those of experiment.