13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- plane-strain condition. The presence of a plane of symmetry enables a half model, with the displacement degree of freedom for all nodes on the plane of symmetry constrained in the direction normal to that plane. The crack-tip contains a focused mesh with an initial root radius of R0 = 25 μm to facilitate numerical convergence under large deformations, as shown in Figure 2b. The total number of nodes in the FE models with different crack depths varies from 2000 to 3000, with the number of elements ranging from 1000 to 1500. The numerical computation in this study utilizes the FE research code, WARP3D [10]. For the Al-alloy SE(B) specimen with a0/W = 0.222, this study generates thirteen FE models to compute the strain energy at thirteen different crack extensions (Δai), as summarized in Table 1. For the deep cracked SE(B) specimen with a0/W = 0.511, the validation utilizes twelve FE models with various crack lengths to represent twelve different crack extensions (Δai), as shown in Table 1. Table 1. The crack size in the FE models for the two SE(B) specimens made of Al-alloy 5083 H-112. Crack extensions (mm) a0/W a0 (mm) Δa1 Δa2 Δa3 Δa4 to Δa11 Δa12 Δa13 0.222 8.0 0 0.2 0.5 1 to 4.5 @ 0.5 mm increment 5 5.5 0.511 18.5 0 0.2 0.6 1.2 to 5.4 @ 0.6 mm increment 6 - (a) (b) (c) Figure 3. (a) P-Δ curve for SE(B) specimen with a0/W=0.222; (b) U-Δa curves for SE(B) specimen with a0/W=0.222; and (c) comparison of the J-R curves measured in the test and those derived from the CMOD-based hybrid approach for both shallow and deep cracked SE(B) specimens.
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