13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- 2. Modeling the Material Behavior in the Fracture Process Zone Ductile alloys used in engineering structures often contain impurities such as second-phase particles. Cavities often nucleate at relatively low stress levels due to fracture or decohesion of the large inclusions. For the purpose of analysis, voids are assumed to be present in the material at the outset of loading. These voids enlarge with increased plastic deformation and eventually coalesce with the assistance of the nucleation and growth of secondary microscopic voids. Therefore, material in the fracture process zone can be considered as an array of unit cells. Each cell is a representative material volume (RMV) containing a void nucleated from the inclusion. 2.1. Unit Cell Analysis A straight-forward approach to study the ductile fracture mechanism as well as the effects of material properties and stress state on the material failure process is to conduct the unit cell analysis of a representative material volume (RMV). As an example, Figure 1(a) shows a 1/8-symmetric finite element model for a cubic RMV containing a spherical void and Fig. 1(b) shows the three-dimensional stress state applied on the RMV. The material is assumed to obey a power-law hardening, true stress-strain relation with Young’s modulus E=70.4 GPa, Poisson’s ratio ν=0.3, yield stress σ0=345 MPa and strain hardening exponent N=0.14. The initial void volume fraction (volume of the spherical void / volume of the RMV) is taken as f0 = 0.02. The initial size of the RMV is defined as 0 0 0X X X × × and the deformed lengths in the x-, y- and z-directions are represented by X, Y and Z respectively. Figure 1. (a) A one-eighth symmetric finite element mesh for the RMV containing a centered, spherical void. (b) The stress state applied on the RMV. The stress state subjected by the RMV is characterized by two parameters, the stress triaxiality ratio (T) and the Lode angle ( θ) ( )1 2 1 2 3 3 2 1 3 2 , tan 3 Σ −Σ Σ −Σ −Σ = Σ Σ +Σ +Σ = θ e T (1) where Σe represents the von Mises equivalent stress. Here the numerical analyses are carried out 2Σ 1Σ 3Σ X0/2 x y z (a) (b)
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