13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Constitutive parameters for the bulk and cohesive elements are listed in Table 1. Both phases are treated as isotropic, elasto-plastic metals. The density, Young’s modulus E, Poisson’s ratio , and flow stress for the two phases are the same as those in [3,4]. The critical energy release rate of the CGL, Ic G , is obtained in terms of its fracture toughness Ic K , which is taken as 100 MPa m. The cohesive strength of the NGIL can be calibrated at different critical energy release rate and failure strain [3,4]. Two types of boundaries between the CGL and the NGIL are considered: i) a tough boundary implying that its cohesive parameters are the same as those of the CGL and ii) a brittle boundary implying that its cohesive parameters are the same as those of the NGIL. NGIL’s failure strain was estimated to be 3.26% [3]. Here, the critical energy release rate of the NGIL is taken as 60 Jm-2 and its cohesive strength is calibrated as 1.89 GPa [3,4]. With the calibrated results, simulations are carried out at two levels of the cohesive strength of the CGL ( mT =1.87 0 and 1.94 0) and for two types of boundaries. Table 1. Constitutive parameters for bulk and cohesive elements of the co-rolled SMATed 304SS Phase Density Yield stress E GPa max T coh G CGL 8000 0 200 0.29 mT Ic G NGIL 8000 ' 0 200 0.29 ' mT ' Ic G 3. Numerical results 3.1 Effect of the shape of bilinear cohesive law 0 m is taken as 10-2 μm and 10-3 μm. When the mesh size is taken as 10 and 5 μm, the simulated results for the co-rolled SMATed 304SS are shown in Figs. 3(a-b) and 4(a-b), respectively. With 0 m decreasing, the computational burden increases obviously, consistent with the finding in [10], and the overall fluctuation in the stress-strain curve also decreases. As 0 m decreases, simulations show that the peak stress around the microcrack nucleation decreases in Figs. 5 and 6, which is in agreement with [7]. 3.2 Effect of the mesh size For refined mesh, the incipient microcrack occurs relatively earlier, more minor branches occur and then arrest after running one or a few elements length, similar with the experimental study [11]. On comparing Figs. 3 with 4, it can be observed that the stress history when the mesh size is 5 μm is more detailed than that when the mesh size is 10 μm. Meanwhile, at each level of 0 m , both the 3 kg /m
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