13th International Conference on Fracture June 16-21, 2013, Beijing, China Using discrete cohesive zone model and general continuously cohesive zone model to simulate the crack propagation and comparing the stress intensity factor as shown in Fig.9 0.85 0.9 0.95 1 1.05 1.1 1.15 0 2e-08 4e-08 6e-08 8e-08 1e-07 KI/KIC Extension of Crack ∆a, m Homogeneous CZ Model l=2.0X10 -8 m l=4.0X10 -8 m l=6.0X10 -8 m l=8.0X10 -8 m l=1.0X10 -7 m Figure 9. The stress intensity factor of discrete cohesive zone model of different characteristic lengths comparing with the theoretical value Figure 9 shows the result of different characteristic lengths. The strength of the material increases with the characteristic length. Also, the stress intensity factors of discrete cohesive zone models are all above the one of general continuously cohesive zone model. Therefore, the possibility that the interface morphology of cohesive zone has an impact on the strength of material is illustrated. 4.2. Microscopic Structure with cohesive zone model The average potential energy to make a new fracture surface can be calculated as φ∗n = φn/∆d = 1.28×10−10J/m. Using this data, the theoretical moment in proportion to strength of the bulk material can be obtained as K∗ = √φ∗nEI =9.55×10− 13Nm. By using simulation, the simulate data of the strength of structures with cohesive zone model and the deformation can be obtained. As shown in Fig.10, the strength of discrete structure exceeds the one of hierarchical structure at first and is reversed during the crack propagation . When crack propagates, the strength of discrete structure turns constant while the one of hierarchical structure shows several jump which represents the thorough separation of unit structures. Although theoretical result overwhelms simulation results, since the result of hierarchical structure increases during element separation, the strength of hierarchical structure shows more resistance to crack propagation. When the strength of hierarchical structure jumps as shown in Fig.12, crack propagation occurs. From the deformed hierarchical structure graph, the details of crack propagation can be illustrated. Figures 13(a)- (h) show the details of crack propagation and element separation. The upper graphs represent the total image of deformed structures while the lower ones represent the enlarged view -7-
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