13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- As a case study, effect of second phase (harder phase) distribution of two-phase steel is estimated using a random type and layered type morphology as presented in Fig. 16. Both types have the same volume fraction of the second phase of 30%, and the same average grain size of 25µm. The matrix and second phases are assumed to be Ferrite and Pearlite, respectively, and the mechanical properties given in Fig. 12 are used for damage simulation. Results of simulated damage evolution are presented in Fig. 17. Critical global deformation for ductile cracking from notch root surface, which is defined as Vg where ductile crack growth !a reaches 50µm, can be obtained from the 3-point bending simulation (Fig. 17(a)). Then, in contrast to the FE-analytical results for homogeneous material model of the 3PB specimen, macro-scopic critical local strain (!p tip) cr can be estimated. Figure 17(b) gives evolution of damage fraction D of RVE as a function of macro-scopic equivalent plastic strain Ep . The stress triaxiality dependent ductility that is defined as Ep where D reaches 0.001 (=Dc) can be estimated. (a) For critical local strain (b) For stress triaxiality dependent ductility Figure 17. Damage simulation to estimate the effect of micro-structural morphology of two-phase steel on macro-scopic ductility. Figure 18 summarizes the estimated macro-scopic critical local strain (!p tip) cr and stress triaxiality dependent ductility for the random and layered type morphology of F-P steel. It was predicted that the layered type morphology provided larger macro-scopic ductility than the random type morphology as long as a volume fraction of second phase were the same. Therefore, the layered type morphology could enlarge ductile crack growth resistance of a cracked structural component. Figure 18. Effect of micro-structural morphology of two-phase steel on macro-scopic ductility simulated on the basis of the proposed meso-scopic approach. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.8 1.0 1.2 1.4 1.6 1.8 Layered type Random type Equivalent plastic strain, !p Stress triaxiality, "m/" (Ep)i = Aexp B #m # const. $ % & ' ( ) (!p tip) cr Critical local strain Stress triaxiality dependent ductility 2nd-H
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