13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Figure 6. Delamination width as a function of the nominal strain for different values of interface toughness. While the initiation of wrinkle-induced delamination is independent of the interface toughness, subsequent growth of the delamination crack does depend on the interface toughness. As shown in Figure 6, for an interfacial strength 5 0 5 10 − = × f E σ , the delamination width (b) as a function of the nominal strain is plotted for three different values of interface toughness. The delamination width is determined from the cohesive zone model based on the damage parameters of the cohesive elements. The delamination width remains zero until the critical strain is reached. Upon initiation, the delamination crack grows rapidly, which in turn leads to rapid growth of the buckle amplitude as shown in Fig. 5(a). The growth of the interfacial crack is eventually stabilized with a delamination width depending on the interface toughness. Further increasing the compressive strain, the delamination grows stably. Apparently, under the same nominal strain (greater than the critical strain), the delamination width decreases as the interface toughness increases. 0 0.005 0.01 0.015 0.02 0 2 4 6 8 10 12 Nominal strain, ε Buckle amplitude σ 0 /Ef = 5e-5 Γ/Ef h = 1e-5 0 0.005 0.01 0.015 0.02 0 10 20 30 40 50 60 Nominal strain, ε Delamination width, b/h σ 0 /Ef = 5e-5 Γ/Ef h = 1e-5 Figure 7. (a) Buckle amplitude and (b) delamination width as a function of the nominal strain during a loading-unloading-reloading cycle. The cohesive zone elements as implemented in ABAQUS assume an irreversible damage process, which may be used to simulate damage accumulation under cyclic loading. As an example, numerical simulation of a loading-unloading-reloading process is performed, with 5 0 5 10 − = × f E σ and 5 10− Γ = E h f . Figure 7(a) shows the buckle amplitude versus the nominal strain. Before the first loading, the interface is perfectly bonded with no damage (D = 0). As the nominal strain increases, wrinkling occurs first at point A (ε ~ 0.00556), and wrinkle-induced delamination initiates at B (ε ~ 0.0076). Subsequently, delamination and buckling co-evolve. The corresponding delamination width is shown in Fig. 7(b). Start unloading at point C (ε = 0.01). The delamination (a) (b) A B C D E C E D B
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