Constitutive equations of a tensorial model for ductile damage of metals

Based on a micromechanical concept of void growth and change in void shape, a dissipation potential and constitutive equations for ductile damage of metals are presented. Multiplicative decomposition of the metric transformation tensor and thermodynamic formulation of the constitutive equations lead to a symmetric second-order tensor of damage which is physically meaningful. Its first invariant defines the damage related to plastic dilatation of the material due to the void growth. The second invariant of the deviatoric tensor accounts for the damage associated with a change in the void shape. Two physically motivated normalized measures allow us to represent the kinetic process of strain-induced damage by using the equivalent parameter of damage including the limit conditions for the onset of void coalescence and ductile failure. An experimental analysis of the evolution of ductile damage is presented for the case of uniaxial tension of sheet steel specimens with artificial defects.