Modelling and Numerical Simulation of Ductile Damage in Bulk Metal Forming

Abstract

A complete set of fully coupled constitutive equations accounting for both combined isotropic and kinematic hardening as well as the ductile damage under anisothermal conditions at finite (visco)plastic strain is developed and implemented into the general purpose Finite Element code for metal forming simulation. First, the fully coupled anisotropic constitutive equations in the framework of Continuum Damage Mechanics are presented. Attention is paid to the strong coupling between the main thermomechanical fields as thermal effects, elasto-viscoplasticity, mixed hardening, ductile isotropic damage and contact with friction. The associated numerical aspects concerning both the local integration of the coupled constitutive equations as well as the (global) equilibrium integration schemes are presented. The local integration is outlined thanks to the Newton iterative scheme applied to a reduced system of two differential equations. For the global resolution of the equilibrium problem, the classical dynamic explicit (DE) scheme with an adaptive time step control is used. A fully adaptive 2D methodology with mesh and loading sequences adaptation based on some appropriate error estimates is used. For 3D simulations only a constant appropriately refined 3D mesh is used. Various 2D and 3D examples are given in order to show the capability of the methodology to predict the ductile damage initiation and growth during metal forming processes.