13th International Conference on Fracture June 16–21, 2013, Beijing, China 0 dæ dFeq , (6) where Feq=σeq·(1- ΣA ), σeq is equivalent stresses related to a material matrix (without voids), ΣA is a relative void area, i.e. void cross-section area related to the cross-section area unit of a unit cell with voids. It should be noted that when analysing conditions in (Eq. 6) stress state triaxiality is taken to be constant [3]. The parameter ΣA is calculated on the basis of following considerations. In the general case α in (Eq. 4) depends on æ and does not depend on a void volume. Then an increase in the volume of vacancy and deformation voids taking into account (Eq. 1) and (Eq. 3) may be calculated by the equation: (æ) ρ (æ dæ) ρ V dæ V 1 f α 3 dV def v def v def nuc Σ Σ , (7) where def nuc V is the volume of a nucleus deformation void. When integrating (Eq. 7) the initial condition is formulated in the form: 0) (æ ρ V S V def v def nuc 0 w Σ , (8) where 0 ΣV is the value of a relative void volume with æ=0, Sw is material swelling. The parameter ΣA is connected with volume of voids by the following manner 2/3 Σ Σ Σ 1 V V A . (9) It is necessary to note that for prediction of material behavior in ductile fracture regime GTN- model [1, 2] is widely used. According to this model the plastic potential introduced by Gurson [1] is presented in the form [1 (q f ) 0 σ σ q 2 3 2f q cosh σ σ Ф * 2 1 S m 2 1 * 2 2 2 eq , (10) where σS is the function describing the yield surface for material without voids, q1, q2,fc and ka are material constants; c c a c c * for f f f k (f f ) for f f f f . (11) The increase of void volume fraction is written growth nucl df df df , (12) where p ii growth f)dε (1 df , (13) In (Eq. 13) is the sum of normal plastic strain. Value of p ii dε dæ dfnucl may be calculated by formula [10] N N N N nucl S ε æ2 1 exp S 2N f dæ df , (14) where SN, fN and εN are material constant. -3-
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