Progressive failure of ductile materials: Description via a three-dimensional coupled CZM-XFEM approach
Résumé
The context of the present work is the design of naval and aeronautical, engineering structures regarding accidental overloading encountered notably during collision, shock, blast or impact. The aim is to predict the residual resistance of the structure made of ductile materials such as steel, aluminum alloy, titanium alloy, etc. This implies to be able to reproduce the successive steps of the progressive structural failure including typically (i) more or less diffuse micro-voiding induced damage, (ii) strain/damage localization in a narrow band and (iii) crack formation and propagation, as well as defining transition criteria while ensuring the mesh objectivity of the numerical results. In the approach developed, in the first step (i) the material is assumed to obey the Gurson micro-porous plasticity continuous model, while in the third step (iii) the kinematics of the discontinuous crack is described within the XFEM framework. The intermediate step (ii) of localization, which is probably the most complex to reproduce from the physical and numerical perspectives, is described via a cohesive zone model (CZM) within the XFEM framework. The CZM describes the progressive degradation of the thermomechanical properties of the localization band material induced by an increase in the micro-voids coalescence and leading ultimately to the formation of the traction-free crack. The unified three-dimensional methodology has been implemented as a user element subroutine (UEL) within the commercial finite element computation code ABAQUS and its performances are assessed considering 3D numerical simulations of boundary value problems with an increasing complexity. The transition criteria, the stress continuity, the integration of the rate and equilibrium equations, the mesh objectivity and the interest of the CZM-XFEM coupling will be discussed in details.