Elastic-plastic Behavior of WC-Co Cemented Carbide Used for Forging Tool Considering Anisotropic Damage and Stress Unilaterality

Abstract

Elastic—plastic constitutive equation of hard metal for cold forging tools such as WC-Co cemented carbide with anisotropic damage is proposed to predict a precise service life of cold forging tools. A second rank symmetric damage tensor is introduced in order to express the anisotropic material damage and damage-induced stress unilaterality, namely a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress tensor, damage tensor, isotropic hardening variable, and kinematic hardening variable tensor. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening, and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix—WC particle interface and by the mechanism of fatigue, i.e., the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile, and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on the behavior of cemented carbide as a die-insert of cold forward extrusion die set was carried out. The proposed constitutive equation was implemented to commercial FE software MSC.Marc2005 using User Subroutines. It is found that the anisotropic damage component can describe the different failure modes of the die-insert, namely fatigue crack and forced rupture.