Nevertheless we achieve to obtain very similar results than previous authors Fabrikant [3], Kachanov and Laures [5] and Zhan and Wang [8] by choosing a0/b = 0.1, N = 160, δa/a = 0.025 (see figure 4 where phi is the polar angle). We shall use those parameters as reference in the sequel. 1 1.5 2 2.5 3 3.5 0 20 40 60 80 100 120 140 160 K1max/K10 phi ∆/2a =0.05 ∆/2a =0.05 ∆/2a =0.00025 ∆/2a =0.00025 Figure 4: Points corresponds to the values of Kachanov and Laures [5] given in table 1. Lines correspond to our simulations for a0/b = 0.1, N=160, δa/l =0.025. 4. Propagation of two circular cracks in brittle fracture We present here our results for simulations in brittle fracture. For numerical purposes, Irwin’s law can be remedied by a Paris type law provided to choose an exponent β large enough. In practice, above β =30, results are very close and become independent of β. That is why the sole case β = 30 is presented here. Crack deformation is consequent so that we had to set up a remesh procedure to redistribute nodes. Figure (5a) shows the successive positions of the fronts for different values of the dimensionless loadingσ ∞ √b Kc . When the cracks are distant, threshold is reached for the entire set of points because the SIF values are almost uniform along the fronts. When a/b reaches about 1/4, interaction between cracks leads to an increase in SIF of points near the opssite crack. In consequence, the threshold is only achieved at these nodes whence a pronounced front deformation. It should be noted that coalescence couldn’t be reached because of the values larger and larger of the SIF. Indeed, SIF values are asymptotically infinite at the vinicity of the “interaction area”. Figure (5b) represents the real loading in terms of cracks advance, characterized by the dimensionless quantity aint/b for the case of coalescence and for the isolated crack. It can be noticed that the loading strongly decreases during propagation and tends to almost disappear when cracks are close to one another. 5. Conclusion and perspectives The purpose of this work was to apply Lazarus’s numerical code to study the coalecence of circular cracks. To validate the code, we compared the SIF values, obtained for different configurations, with those found in the literature. Good agreements with Fabrikant [3], Kachanov and Laures [5] and Zhan and Wang [8] were achieved. After validation with literature, brittle propagation was experimented. It shoud be emphasized that each front was highly perturbed by the presence of the other crack. Our simulations showed cracks with a strongly elongated profile within the “interaction area”. It can also be observed a significant decrease of the fracture loading as soon as the interaction between cracks was felt. The possibility of extending the code to more complex geometries is considered. 7
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