Elastic-Plastic Constitutive Equation of WC-Co Cemented Carbides with Anisotropic Damage

Abstract

Elastic‐plastic constitutive equation of WC‐Co cemented carbides with anisotropic damage is proposed to predict a precise service life of cold forging tools. A 2nd rank symmetric tensor damage tensor is introduced in order to express the stress unilaterality; 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, damage tensor, isotropic hardening variable and kinematic hardening variable. 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 cold forward extrusion was carried out, in which the proposed constitutive equation was employed as die insert material.