13th International Conference on Fracture June 16–21, 2013, Beijing, China -13- Figure 33. Comparison curves between simulation and test, punch, 3.5 m/s Figure 34. Stress triaxiality evolution curve, punch, 3.5 m/s 8. Construction of ductile failure criteria 8.1. Failure locus under static loading Figure 35. Stress triaxiality evolution at 0.01/s Figure 36. Failure locus from average stress triaxiality at 0.01/s Figure 35 shows stress triaxiality evolution curves of shear, notched tension and punch under static loading. Using average stress triaxiality, we can obtain failure locus at 0.01/s shown in Fig. 36. However, since stress triaxiality varies greatly during the whole loading process in shear test, equivalent failure strain at stress triaxiality of 0 is not accurate enough. Besides, since we directly obtained equivalent failure from test via digital image correlation method in tensile test, equivalent failure strain at stress triaxiality of 0.33 is questionable as well. Therefore, damage evolution rule was used to optimize failure locus under static loading. We selected quadratic function (Eq. (7)) as optimization function. The reason we selected quadratic function partly referred to acquired four failure points in Fig. 36. Table 2 summarizes existing functions used to fitting failure locus in the equivalent strain and stress triaxiality space. And most of them are for metallic materials [3]. ( )= 0 + 1 + 2 2 (7) Table 2. Equivalent failure strain, Average stress triaxiality Function of ( ) Linear function ( )= 1 + 2 0 5 10 15 20 25 30 0 2000 4000 6000 Force (N) Displacement (mm) Test result Modeling result 0.0 0.2 0.4 0.6 -0.2 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 -0.2 0.0 0.2 0.4 0.6 0.8 Stress triaxiality Equivalent plastic strain Punch, 3.5m/s 0.0 0.4 0.8 1.2 -0.2 0.0 0.2 0.4 0.6 0.8 0.0 0.4 0.8 1.2 -0.2 0.0 0.2 0.4 0.6 0.8 Equaivalent plastic strain Stress triaxiality Simple shear Notched tension Punch 0.0 0.2 0.4 0.6 0.8 0.6 0.8 1.0 1.2 1.4 1.6 Equivalent plastic failure strain Stress triaxiality To be modified
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