13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- void growth model that was originally proposed by Gurson [6], was derived so that the relation between the critical strain (Ep)i for micro-voids formation and the stress triaxiality can be in accordance with an exponential function as expressed in Eq. (2). (Ep)i =Aexp B !m ! const. ! " # $ % &, A= 2 a1a2 ln (1!D0)Dc (1!Dc)D0 B=!a2 " # $ % $ (2) Therefore, the material parameters a1 and a2 can be identified only from the stress triaxiality dependent ductility of steel. The (Ep)i is generally set to be 80% of ductile cracking strain (!p)cr for the steel which exhibits mico-voids nucleation controlled ductile failure behavior. 2.2.2. Simulation of ductile crack growth resistance of a cracked component. In the light of two types of ductility of each steel presented in Fig. 3, critical local strain (!p tip) cr and damage parameters a1 and a2 were identified. Table 2 summarizes these parameters for all the steels used: D0, Dc and K are fixed as 0.0001, 0.001 and 4, respectively. Table 2. Materials parameters used for simulation. Initiation D0 Dc K a1 a2 Steel A 1.6 1.54 1.28 Steel B 1.6 0.66 1.59 Steel C 1.4 0.72 1.78 0.0001 0.001 4 Extension Critical local strain Damage process based variables Ductility based variables Figure 4 exhibits a FE-model of 3-point bend specimen with a deep crack (a0/W=0.5) used for simulation, which has the same configuration and size as used in experiments. The simulated ductile crack growth resistance curves, that are CTOD-R curve, were compared with experimental results. As shown in Fig. 5, it was demonstrated that the proposed simulation method could predict CTOD-R curve of the cracked 3PB specimen with high accuracy even for the high strength steel C. Consequently, by means of the proposed simulation method, a ductile crack growth resistance of a cracked component can be quantitatively correlated with the mechanical properties obtained by laboratory tests. Figure 4. FE-mesh division and simulation model. Figure 5. Comparison between CTOD-R curves obtained by experiment and simulation for steels A, B and C. a0/W=0.5 0.0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1 CTOD, ! (mm) Maximum ductile crack extension, "amax (mm) Steel A Steel B Steel C at R.T. Experiments Simulations
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