Numerical prediction of discontinuous central bursting in axisymmetric forward extrusion by continuum damage mechanics

Abstract

The prediction of the central burst defects in axisymmetric cold extrusion is analyzed numerically by using 2D finite element analysis (FEA) accounting for the ductile damage effect. The coupling between the ductile damage and the thermoelastoplastic constitutive equations is formulated in the framework of the thermodynamics of irreversible processes together with the continuum damage mechanics (CDM) theory. A simple isotropic ductile damage model is fully coupled with thermoelastoplastic constitutive equations of Prandtl–Reuss type including non-linear isotropic hardening and thermal effects. A modified ductile damage criterion based on linear combination of the stress tensor invariants is proposed in order to predict the occurrence of micro-crack initiation as a discontinuous central bursts along the bar axis. The implicit integration scheme of the fully coupled constitutive equations and the iterative resolution scheme to solve the associated thermomechanical equilibrium problem are presented. A three fields (velocity, hydrostatic pressure and temperature) variational formulation is used to solve the resulting algebraic system. The effects of various process parameters, namely, the diameter reduction ratio, the die semi-angle, the friction coefficient and the material ductility, …, on the central bursts occurrence are discussed. The quantitative effects of ductile damage on the extrusion parameters are studied and qualitative comparison with some available experimental data are given.