Issue 35

G. Kullmer et alii, Frattura ed Integrità Strutturale, 35 (2016) 368-378; DOI: 10.3221/IGF-ESIS.35.42 373 For α = 90° the crack propagates independently of the inclusion stiffness straight through the inclusion. With increasing inclination angle of the inclusion, the deflection of the crack rises. If the crack penetrates the region influenced by the stiffness mismatch of an inclined inclusion the crack tends to grow around the boundary to the stiff material and to grow towards the boundary to the compliant material. This can be clearly seen with the simulation results for the inclusion with orientation angle α = 30°. In this case, the crack hardly enters the stiff inclusion. Furthermore, the crack grows along the boundary of the compliant inclusion and leaves the inclusion at the farthest corner. In both cases the orientation angle α = 30° seems to be a lower limit so that the crack properly traverses the inclusion. If the crack traverses the inclusion the crack growth behaviour reverses approaching the second material boundary. When the crack leaves the region influenced by the stiffness mismatch the crack approaches tangentially a parallel to the extension line of the initial crack. The offset of the parallel to the extension line increases with the inclination of the inclusion. Where the crack crosses a material boundary, the crack path has an inflexion point and the curvature of the crack path changes. This means that the stress intensity factor K II is zero at the material boundary and the crack locally grows straight under mode I conditions. The maximal magnitude of K II corresponds with the maximal curvature of the crack path and the maximal stiffness asymmetry around the crack tip due to the inclusion. Anyway, K II is small compared to K I leading to slightly curved crack paths. C RACK PATHS FOR STIFF CHANGES IN STIFFNESS ig. 7 shows crack paths through changes in stiffness due to doubling or halving Young´s modulus in partition P3. These results are already discussed in [5, 6]. Fig. 8 presents the comparison between crack paths due to changes in stiffness with double Young´s modulus or double thickness for the orientation angles α = 45° and α = 60°. Figure 8 : Crack paths for different orientation angles of stiffenings The comparison of crack paths in Fig. 8 shows that in the neighbourhood of different kinds of stiffenings the principle characteristics of the crack paths are similar. If the crack enters the region of influence of a stiffening, the crack grows away from the stiffening. With increasing inclination of the stiffening, the deflection of the crack rises with the tendency that the crack tangentially passes by this region, see Fig. 7. If the extent of the stiffening is too big or the inclination of the stiffening is moderate, the crack penetrates the stiffening under a certain angle as defined in Fig. 11. Furthermore, the curvature of the crack paths changes at this point. Inside of the stiffening, the cracks extend steadily curved. On the backside of the stiffening, they grow towards the boundary of the stiffening. Again, the curvature of the crack paths changes where the cracks leave the stiffening. With increasing distance behind the stiffening, the crack paths approach tangentially a parallel to the extension of the initial crack. The offset of this parallel increases with rising inclination of the stiffening. The results show that the influence of the stiffening on the deflection of the crack path depends on the orientation of the stiffening and on the stiffness mismatch of the stiffening as also shown in Fig. 15. Obviously, the effective stiffness mismatch due to a local stiffening through doubling Young´s modulus with constant thickness is greater than due to a local stiffening through doubling the thickness with constant Young´s modulus. Here it becomes noticeable, that a three dimensional FE-model is used for the crack growth simulation. Thus, particularly inside of the thickening, the stresses are not constant over the whole thickness of the specimen but the outer edges of the thickening are stress-free regions. These stress free regions do not participate in the stiffness mismatch. Therefore, obviously the effect on the crack path of a thickening with double thickness is weaker than the effect of a stiff inclusion with double Young´s modulus. F