13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- in Figure 5c and 5d represent the strain energy evaluated at different deformation levels (θi or δVi) as listed in Table 2. The solid lines correspond to the fitted second-order polynomial functions, which are utilized to determine the first-order derivatives at various crack extensions. (a) (b) (c) (d) Figure 4. Typical FE models for the mixed-mode specimens made of Al-alloy 5083 H-112: (a) global FE model of the Mode I dominant specimen AM1; (b) global FE model of the Mode II dominant specimen AM5; (c) a close-up view around the crack tip for AM1; and (d) a close-up view around the crack tip for AM5. Table 2. FE models for the mixed-mode I and II specimens made of Al-alloy 5083 H-112. FE models Specimen Crack Parameters i = 0 i = 1 i = 2 i = 3 i = 4 i = 5 i = 6 i = 7 i = 8 Δa (mm) 0 0.1 0.3 0.7 1.7 2.7 3.7 4.7 5.7 θ (rad) - 0.024 7 0.028 8 0.035 6 0.06 0.081 6 0.092 4 0.106 0.115 AM1 (Mode I dominant) δV (mm) - 0.052 0.09 0.159 0.273 0.486 0.588 0.6720.749 Δa (mm) 0.15 0.5 1.0 2.0 3.0 3.9 4.5 - - θ (rad) - 0.017 0.019 0.021 0.022 0.023 0.024 - - AM5 (Mode II dominant) δV (mm) - 0.604 0.731 0.911 1.050 1.233 1.412 - - Figure 6 compares the fracture resistance curves obtained from the hybrid approach and the test for AM1. Both the JI-Δa and JII-Δa hybrid results agree well with the test data at small crack extension, i.e., Δa < 1 mm, as shown in Figure 6a. Figure 6a also shows that the hybrid approach leads to slightly lower JI-Δa curve when Δa > 1 mm, due to the combined mode I dominant and mode II dominant fracture failure across the thickness of the specimen [11]. In general, the good agreement between the total J versus Δa curves determined using the hybrid approach and that obtained from
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