Macroscopic damage laws based on analysis of microscopic unit cells

The paper deals with the influence of the stress state on the damage and fracture behavior of ductile metals. A continuum damage model is discussed taking into account the effect of the stress triaxiality and the Lode parameter on damage criteria and on evolution equations of damage strains. To get insight in the complex damage and failure mechanisms on the micro-level and their effect on the macroscopic behavior of material samples series of three-dimensional micro-mechanical numerical analyses of void containing unit cells have been performed with special focus on shear dominated loading cases. In the present analysis periodic boundary conditions have been used to model the deformation behavior of the unit cells. Numerical results are compared with those based on symmetry boundary conditions. The results are also used to develop equations for stress-state-dependent damage criteria and to propose evolution equations of damage strains also depending on the current stress state. The effect of the respective boundary conditions on damage equations on the macro-scale is critically discussed. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim