13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 7. Application to materials with heterogeneous toughness . The case of heterogeneous fracture properties is investigated, in particular when one single flaw may upset the crack kinematics. If the flaw is weaker than the safe material, the crack may jump over it. This phenomenon, called “pop-in” [8] is investigated here with the following parameters : the flaw position, and its toughness. Conversely, tougher inclusions inside the test material may slow down or stop the crack, or reduce the crack arrest length. 7.1. One single weak flaw ahead the initial crack tip. In a first case, a e length single flaw, located just ahead the initial crack tip, is considered (see fig. 5). The flaw toughness value is 1 0 / R Γ =Γ and the material recovers its original toughness 0Γ beyond the flaw. The aim is to check if the crack will stop just after the flaw or deeper in the original material, and in this latter case, which is the arrest length, depending of e and R. Fig. 5. One single weak inclusion ahead the initial crack tip in the test material. The figure 6 displays the ratio crack arrest length over flaw length, versus the ratio flaw length over initial crack length, for a range of 1.5 4 R< < . It is noteworthy that for 0 0.2 / 0.4 e L ≤ ≤ (this range of 0 / e L and R is usual for industrial components, the crack arrest occurs around the flaw tip, and the crack does not deeply penetrate inside the safe material. Fig. 6. Crack arrest length on flaw length, versus flaw length on initial crack length. 0 l A l 0 Γ e 1Γ 0Γ Crack arrest increment versus flaw width e (computed with 4 modes) 0 1 2 3 4 5 6 7 8 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 e/L0 (La-L0)/e R=1.5 R=2 R=2.5 R=3 R=4 Usual zone of interest
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