Analysis of Fatigue Crack Initiation and Propagation in Cold Forging Tools by Local Approach of Fracture

Abstract

The local approach of fracture based on continuum damage mechanics (CDM) combined with the finite element method (FEM) was applied to establish a more precise method of estimation of service life of cold forging tools by simulating the initiation and growth of a fatigue crack. After a brief explanation on the local approach of fracture based on CDM combined with FEM, modeling of elastic-plastic-damage behavior of tool steel was conducted in the framework of thermodynamics. In the modeling, the salient unilateral property of the tool material is considered by introducing a modified stress tensor. The proposed constitutive equations can be found to describe the experimental behaviors under uniaxial tension and compression properly. Then, the initiation and propagation of a fatigue crack in the cold forward extrusion die was analyzed by the local approach of fracture. The initiation of the fatigue crack in the vicinity of the die radius was found to occur when the number of extrusion increased. Then, the crack propagated along the direction perpendicular to the surface of the die radius. Furthermore, the proposed approach was found to estimate the actual behavior of the fatigue crack growth in good agreement with the calculated change of the rate of crack propagation to the number of extrusion. The calculated crack propagation rate also tended to decrease due to a decrease in tensile principal stress at the crack tip as the crack propagates.

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

“…In the present paper, the behavior of the WC-Co cemented carbides material is modeled by the elasticplastic constitutive equations coupled with anisotropic damage based on the framework of the irreversible thermodynamics theory for the constitutive equation [6][7][8].…”

“…In the present paper, we employ the second rank symmetric damage tensor D for the description of the mechanical effect of the three dimensionally distributed microcracks in the material as [7,8] …”

“…Acording to the conventional procedure of the irreversible thermodynamic formulation [6][7][8], the elastic constitutive equation of the damaged material can be obtained as follows:…”

“…The conventional framework of thermodynamic theory is employed for the formulation [6][7][8]. The anisotropic damage is considered to express the salient stress unilateral behavior of cemented carbide material.…”

Application of continuum damage mechanics model in terms of fatigue life assessment for low cycle and quasi static loadings

“…As far as the fatigue itself is concerned, this approach is used in two areas of fatigue: In low-fatigue and in high cycle fatigue [8,12]. In the case of low fatigue modeling it is important that this approach allows to estimate fatigue not only at the stage of crack initiation and also during the crack propagation [13,14]. The continuum damage methods make it possible to determine fatigue life for different materials; apart from steel it can be used for other materials including titanium alloy, concrete, rubber, composites and different structural components e. g. aeroengine blade, bridges, steam turbine rotor, plexiglas resist [8,11,[15][16][17][18][19][20].…”