13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Fig. 4 (b) illustrates the crack growth path, from the center to the free surface through the minimum section of the specimen. The void volume fraction at crack initiation is presented in Fig. 4 (c) and the highest void volume fraction site appears in the center of notched bars with no surprise. Damage element Figure 4. The FEM results of R6 notched tensile bar: (a) (b) Damage elements at and after crack initiation; (c) The void volume fraction at crack initiation 3.4. The effect of stress triaxiality For each specimen, stress triaxiality is highest at the center and lowest at the free edge. Fig. 5(a) demonstrates the stress triaxiality value along the minimum section at the loading level corresponding to the onset of crack. Higher values of stress triaxiality together with increased plastic deformation in the center region of notched specimens accelerate crack initiation and growth according to the GT constitutive relationship. Thus, it is not surprising to find that crack initiates at the center of specimens. For specimens with different notch root radii, various stress triaxialities are determined by geometry. Larger notch root radii results in smaller stress trixiality ratio. The curve of stress triaxiality ratio T versus equivalent plastic strain efε at the center of specimen with load proceeding is presented in Fig. 5(b). Various stress triaxialities lead to void coalescence at different plastic deformation measured by equivalent plastic strain, illustrated in Fig. 6. 4. Concluding remarks By incorporating two coalescence criteria, the extended damage models succeed in simulating the ductile failure in round tensile bars and also provide a practical approach to simulate the crack formation and propagation in small-scale tensile specimens. The present predictions show that: (1) The extended damage models with two different coalescence criteria can give almost identical predictions that are very close to the experimental results for all the specimens. (2) For each round tensile bar, crack initiates in the center of specimen where the highest stress triaxiatity and largest void volume fraction appear. In addition, crack propagation along the minimum section in specimens. (3) Distinct geometries represent different stress triaxiatities and different stress triaxiatities lead
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