13th International Conference on Fracture June 16–21, 2013, Beijing, China 8 penalty equation for contact. Comparing the amplitudes, the higher loading level results in a faster material degradation (Figure 7) and so shorter fatigue life (Figure 8). Actually, ΔKavg=104.8 MPa m1/2 asymptotically approaches the plain strain toughness Kc of 133MPa m1/2 at the loading ratio R=0.1, larger amount of damage accumulation is coincident with that caused by the fracture loading. In Figure 8, the traction against the loading segment (half cycle) is illustrated in both loading and unloading path, no damage growth is assumed in the unloading path including the compression in terms of Eq. (8), as shown in Figure 9. In order to verify the simulation results, the popular crack growth law proposed by Erdogan et al. [19] is used to consider all ranges of cyclic crack growth which is given by th ( ) d dN (1 ) n c a C K K R K K Δ −Δ = − −Δ , (17) where the fracture toughness of Kc=133MPa m1/2, the threshold value of ΔKth is 7.5MPa m1/2 and material constants C=10-5.578 and n=2.697 for correlating the experimental data. The computational result together with the experiment are compared in Figure 10, the prediction gives a better agreement with the test, especially in the region III of fatigue crack growth. Figure 7. The traction vs. displacement jump curves in a cohesive element for ΔKavg=83.1MPa m1/2 and ΔKavg=104.8MPa m1/2. Figure 8. The traction vs. loading segements curves for ΔKavg=83.1MPa m1/2 and ΔKavg=104.8MPa m1/2.
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