Strain-induced damage of metals under large plastic deformation: Theoretical framework and experiments

• The constitutive equations for ductile damage of metals are presented.
• Two normalized measures represent the kinetic process of strain-induced damage.
• The evolution of damage is determined in uniaxial tensile and upsetting tests.
• The equilibrium point for kinetics of the damage growth and healing is revealed.
• The connection of the damage measure with the fracture locus is shown.

Based on a micromechanical concept of the void growth and a change in the void shape the 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 including the limit conditions for the onset of void coalescence and ductile fracture. A relation of the equivalent damage measure to the well-known criteria is shown. The evolution of damage is experimentally determined in uniaxial tensile and upsetting tests for three ductile metals: steel DC01, aluminum–magnesium alloy AlMg3 and pure copper. Void distribution, growth and changes in shapes are analyzed using scanning electron microscopy. The equilibrium point for the kinetics of damage growth and healing is revealed. It is shown that if the strain does not reach the limit value prior to that equilibrium point then the further compression of the material is accompanied by the growing effect of negative stress triaxiality on closure and healing of defects which prevents the fracture. A tensorial framework for strain-induced damage and its thermodynamically consistent mathematical models can be applied to the analysis of metal forming processes in which materials are subjected to large plastic deformations and non-proportional loading paths.