13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- (b). Case 1: left notch elongates 0.5mm, right notches shrinks 0.5mm (c). Case 2: the two notches get close to each other by 0.5mm (d). Case 3.a: the two notches rotates 5°in the same direction (e). Case 3.b: the two notches rotates 5°in the opposite direction 30 t s 90 t s 120 t s final state Figure 3. The near field crack path comparison with reference model Fig. 3 shows the crack growth process and final states of this dynamic analysis with and without disturbance in notches’ configuration. Although the modification is small, the crack path solutions of investigated cases show significant difference except for Case 2. The anti-symmetry property of crack paths solution from the analytical analysis becomes lost [15]. 4. Far field disturbance modeling and simulation 4.1. Effect of the degree of heterogeneity Since the observation technology has its limitation, the boundary condition of analysis model is often proposed in a stochastic way, say, the average with some variances is applied. The variances are used to represent the degree of heterogeneity. The boundary condition with larger variances has stronger effects on crack propagation. The first part of section 4 carries out a series of simulations to numerically examine the effect of the heterogeneity. The model property is the same as Fig. 2, except that the height is changed to 40mm with the notches still located in the center. In order to avoid element failure near the boundary for the sudden changes caused by the disturbances, the strength of elements within 10mm to the top surface is set to be infinite. The initial tension displacement is 0.075mm for reference model, and the loading rate is set to be uniformly 126mm/s for all the cases. The time step is 5.0×10−9 s. Four kinds of disturbance are designed as shown in Table 2. In these formulations, “y” is the Y-axis coordinate of the nodes on top surfaces. The disturbances are added only to the magnitude of nodal displacement boundary condition on top surface along +Z direction. The first one is a half period of sine wave, whose wavelength is 16mm. Case 2 and 3 are two and four periods of sine waves, respectively. The 4th case generates a random number between -0.05mm and 0.05mm for each node on top surface. Except for case 4, the disturbance is set to be uniform along X direction. From Fig. 4, it can be observed that it becomes more and more homogeneous from ud1 to ud4 (the boundary disturbances are added with 0.075mm in this figure.) For case 4, for a specified area, the average of the disturbance on a certain area tends to be 0. By comparing the stress distribution of models with only
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