13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- section. The two-phase polycrystalline model has totally 187 grains and volume fraction of hard Pearlite phase of about 30%. Average grain size is about 25µm, and element size 5µm. Figure 11. Meso-scale 3D FE-model of flat micro-tensile specimen with side notches. The mechanical properties needed for the proposed simulation can be identified from testing for full Ferrite and full Pearlite steels having the same morphological and metallurgical properties as those of each phase in F-P steel used. However, in this work, some assumptions were employed for identifying those properties. As for the stress-strain curves of Ferrite and Pearlite phases, they were estimated in accordance with a rule of mixture from stress-strain curve of two-phase steel used [5]. Figure 12(a) shows the equivalent stress !– equivalent plastic strain !p curves for the Ferrite and Pearlite phase along with that obtained by tension test for F-P steel used. The damage parameters for the each phase can be obtained by conducting tension tests for round-bar specimens with/without circumferential notches in accordance with the proposed procedure (section 2.2). However, these parameters were determined based on the stress triaxiality dependent ductility for the F-P steel as presented in Fig. 12(b). The properties for the Ferrite phase were identified by reverse analysis so that the stress triaxiality dependent ductility for the F-P steel might be reproduced by simulation using a 3D micro-structural model (see Fig. 15(b)). As for the Pearlite phase, the same properties as those for F-P steel were used, because no significant effect of those parameters on simulated result was found in this case. (a) Stress-strain curve (b) Stress triaxiality dependent ductility Figure 12. Mechanical properties of constituent phases of F-P steel needed for damage simulation. Figure 13 shows P–u curves obtained by experiment and simulation. The simulation reproduces critical tensile displacement where load drop due to ductile cracking occurred. Ductile damage evolution behaviors from notch root surface and middle of the specimen obtained by simulation are well consistent with experimental results, and damage localization in Ferrite phase near Ferrite/Pearlite boundary is well simulated as shown in Fig. 14. 0 200 400 600 800 1000 1200 0 0.2 0.4 0.6 0.8 1 Equivalent plastic strain, !p Equivalent stress, " (MPa) Ferrite Pearlite Round-bar tension test (F-P steel) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1 1.2 1.4 1.6 1.8 2 Equivalent plastic strain, !p Stress triaxiality, "m/" Ferrite Pearlite (Ep)i = Aexp B #m # const. $ %& ' () A= 2 a1a2 ln (1*D0)Dc (1*Dc)D0 B=*a2 + , - . - Experiment F-P steel Reverse analysis
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