Three-dimensional X-FEM modeling of crack coalescence phenomena in the Smart CutTM technology

A new 3D X-FEM approach is proposed to model crack coalescence phenomena in the Smart CutTM technology. An adaptive mesh is developed based on a 3D fractal mesh allowing a significant gain in computing time compared to regular meshes. In order to calculate stress intensity factors (SIFs), the term corresponding to internal pressure, that is normal loading on crack faces has been determined, added to the interaction integral and the results of SIFs in mode I have been compared to their analytical values with mean error less than 1%. An implicit algorithm is implemented to predict the evolution of the internal pressure for growing cracks of any shape; a constitutive law in pressure correlated with the equation of state of ideal gases has therefore been used. Compared to the analytical solution, numerically evaluated pressure is accurate with maximum errors less than 1% for relevant convergence tolerance. Finally, the coalescence of two cracks is taken into account in the model. Qualitative local stress analysis makes it possible to explain some phenomena experimentally observed in the Smart CutTM such as neighboring effects of growing cracks, the outgrowth of nearby cracks or influence of the presence of concave areas at a front on growth.