PSI - Issue 2_A

Gunter Kullmer et al. / Procedia Structural Integrity 2 (2016) 2994–3001 Author name / Structural Integrity Procedia 00 (2016) 000–000

3001

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As shown in Fig. 9 the crack paths in the specimens with inclined second region are in general slightly curved because a certain portion of mode II is present in this case. The absolute values of K II are small compared to the values of K I but not zero. At the region boundaries the sign of K II changes. Comparable to the findings for inclusions with different stiffness in Kullmer 2016 the curvature of the crack path correlates with the portion of mode II. The comparison of the crack paths shows that at the transition from pliable to stiff the crack grows away from the region boundary and thus reduces the entrance angle β as defined in Fig. 11 in comparison to the orientation angle α. At the transition from stiff to pliable the crack tends to grow towards the region boundary and thus increases the entrance angle β in comparison to the orientation angle α. Fig. 11 shows the dependency of the entrance angle β on the stiffness ratio and on the orientation angle α of the region boundary. For the consideration of the stiffness ratio the stiffness mismatch Ē according to Kullmer 2016 is used. In this connection E 1 is Young´s modulus of the first region and E 2 is Young´s modulus of the second region. If E 1 and E 2 are equal the stiffness mismatch is zero. Therefore, the crack does not deflect and the entrance angle β is equal to the orientation angle α. If E 2 is less than E 1 the stiffness mismatch Ē is negative but at least -1. If E 2 is greater than E 1 the stiffness mismatch Ē is positive but not more than +1. If the values of E 1 and E 2 of the both regions are interchanged the sign of Ē changes but the absolute value of Ē remains constant. The results on the left side of Fig. 11 show that dependent on the orientation angle α the entrance angle β becomes zero for certain positive values of Ē. This means that a crack does not enter a sufficiently stiff second region. On the other hand the entrance angle β obviously approaches a maximum at the corresponding negative value of the stiffness mismatch Ē. This can be seen clearly with the results for α = 45° in Fig. 11. 1 2 1 2 E E E E E    (1)

0 10 20 30 40 50 60 70 80 90 -0,5-0,4-0,3-0,2-0,1 0 0,1 0,2 0,3 0,4 0,5 entrance angle β [°] stiffness mismatch Ē

pliable

stiff

α=90° α=67,5° α=45° α=22,5°

β

Initial crack

β

pliable

β stiff

β

Initial crack

Fig. 11. Entrance angle β of the crack path at the region boundary depending on the stiffness mismatch

References

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