Issue 35

G. Kullmer et alii, Frattura ed Integrità Strutturale, 35 (2016) 368-378; DOI: 10.3221/IGF-ESIS.35.42 376 C RACK PATHS DEPENDING ON THE DISTANCE OF THE CHANGE IN STIFFNESS FROM THE STARTER NOTCH he crack paths for a stiff inclusion and a compliant inclusion with constant orientation angle α = 45° and varying distance to the starter notch are represented in Fig. 13. The distance varies in steps of 2.5mm from 9.7mm to 19.7mm. Figure 13 : Crack paths for stiff inclusions (top image) and compliant inclusions (lower image) with constant orientation angle α = 45° and varying distance from the starter notch As shown in Fig. 13 the characteristics of the particular crack paths for the stiff inclusions and the compliant inclusions are equal. In the region of influence of the inclusion, the crack deflects and the deviation of the crack path from the initial crack increases with the distance from the starter notch. Behind the inclusion, the crack grows parallel to the initial crack with a certain offset. The parallel offset behind the stiff inclusion is the bigger the greater the distance of the inclusion from the starter notch. Whereas, the parallel offset behind the compliant inclusion is the smaller the greater the distance of the inclusion from the starter notch. Superposing the crack paths, so that the entry points and the exit points coincide, shows that the crack paths through the inclusions and the transition angles according to Fig. 11 are independent of the distance of the inclusion from the initial crack but dependent on the stiffness mismatch. This is represented exemplarily in Fig. 14 for crack paths through the compliant inclusions. The dependence of the transition angles on the stiffness mismatch represents Fig. 15. Here the transition angles for an inclusion with constant distance d = 14.7mm from the starter notch and constant orientation angle α = 45° and varying Young´s modulus are plotted over the stiffness mismatch. The stiffness mismatch Ē is defined as follows: D I D I EE EEE    (3) Whereat E I is Young´s modulus of the inclusion and E D is the default Young´s modulus. If E I and E D are equal the stiffness mismatch is zero. Therefore, the crack does not deflect and the transition angles are equal to the orientation angle. If E I is less than E D the stiffness mismatch Ē is negative but at least -1. If E I is greater than E D the stiffness mismatch Ē is positive but not more than +1. The course of the entrance angle and the course of the exit angle over Ē show a counter similar behaviour. If Ē is less than a critical negative value, the entrance angle reaches a constant value and T