13th International Conference on Fracture June 16–21, 2013, Beijing, China 7 As mentioned in the previous sections, Eq. (4) shows the bilinear behavior if κ=0 under the monotonic loading and the initial cohesive strength of σc=σf =1100MPa associated with Δc=Δf =0.2mm. Computational simulation based on the cohesive zone model according to Eq. (4) is shown in Figure 5(a) for monotonic fracture. It confirms that the final displacement jump Δu=2.5mm gives a reasonable prediction in comparing with the experiment. This kind of the cohesive law is popular in simulation of quasi-brittle material failure. Figure 5(b) illustrates the cohesive response of a ruptured element along crack path, the static damage evolution of the element can be seen additionally and this result should be imagined according to Eq. (7) or Eq. (10). 4.2. Crack growth under cyclic loading The crack growth under cyclic loading case is conducted within elasto-plastic region in this section. Considering the cyclic damage equation as mentioned in Eq. (8), the damage accumulation depends on the current cohesive traction and the increment of the displacement jump corresponding to the loading history. We use the concept of the loading cycles to capture the evolution of damage and predict the fatigue life. By recording the crack growth length, Δa, the fatigue crack growth rate can be determined by Δa/ΔN. Since the global loading behavior of the C(T) specimen is represented by the amplitude of the stress intensity factor, ΔK, the numerical simulation by using the cohesive element can be verified through the experimental da/dN vs. ΔK curve. Figure 6. Four loading amplitudes for the CT specimen as a function of load line displacement. As shown in Figure 6, four different loading amplitudes were performed under the displacement control at the loading ratio R=0.1. Because the stainless steel 304 is a cyclic instable material which associates the stress variation as a function of loading cycles, the average stress amplitude ΔKavg is used to express the loading level during the crack growth process. The specimen dimensions and mesh configurations for the fatigue simulation are the same as those for the fracture test. The material parameters for the damage evolution are α=0.00053, β=0.15 and γ=0.0 combined with the monotonic cohesive law which has been determined from the fracture simulation. The damage growth process in an element ahead of the crack-tip is displayed in Figures 7, 8 and 9 under the conditions with ΔKavg=83.1MPa m1/2 and ΔKavg =104.8 MPa m1/2, respectively. In the figures, the traction and displacement jump are non-dimensionalized by σc and Δc, respectively. The negative displacement jump associated the compression of the crack surface is constrained by introducing a
RkJQdWJsaXNoZXIy MjM0NDE=