Issue 35

G. Kullmer et alii, Frattura ed Integrità Strutturale, 35 (2016) 368-378; DOI: 10.3221/IGF-ESIS.35.42 374 1.092 1.074 1.085 1.079 1.147 1.146 1.249 1.256 1.268 1.206 1.242 809 854 888 906 938 1.033 ‐1,5 ‐1 ‐0,5 0 0,5 0 1 2 3 4 5 6 7 8 y‐axis in mm x‐axis in mm region outside the thickening region inside the thickening 1.082 1.111 1.134 1.242 1.2401.328 1.418 1.515 2.354 2.300 2.508 2.400 2.2152.224 2.194 2.147 ‐1,5 ‐1 ‐0,5 0 0,5 8 9 10 11 12 13 14 15 16 y‐axis in mm x‐axis in mm region outside the thickening region inside the thickening Figure 9 : K I -values along the crack path through a thickening with orientation angle α = 45°. Fig. 9 exemplarily shows the distribution of the stress intensity factor K I on the path through the thickening with the orientation angle α = 45° using a bubble diagram whereupon the diameter of the bubbles represents the local value of K I . When the crack approaches the stiffening, K I drops although the crack grows, by the reason that the stiffening causes a stress shield at the crack tip. K I reduces about the factor 2 when the crack enters the thickening. Inside the thickening, K I increases. When the crack exits the thickening K I rises about the factor 2 . If in contrast an inclusion with double Young´s modulus causes the stiffening then K I rises about the factor 2 when the cracks enters the inclusion and K I reduces about the factor 2 when crack exits the inclusion [5, 6]. Since the relations for the stress intensity factor EG K I I  and for the energy release rate dA dU G I  , which is the energy release –dU over the increment of the crack surface dA, are valid and since with every section crossing the thickness or Young´s modulus rise or reduce by the factor 2, obviously, the energy release is continuous when the crack crosses the boundaries of the stiffening. The evaluation of the stress intensity factor K II yields that the values of K II are overall small compared to the values of K I . The greatest values of K II occur, where the stiffening causes the greatest local stiffness asymmetry. At the boundaries of the stiffening, the course of K II shows a zero crossing and the sign of K II changes, so that at these points, the crack path has inflexion points and locally mode I-loading exists. C RACK PATHS FOR COMPLIANT CHANGES IN STIFFNESS ig. 10 illustrates the comparison between crack paths due to changes in stiffness with halving Young´s modulus or halving the thickness in partition P3 for the orientation angles α = 45° and α = 60°. Firstly, the cracks grow towards the change in stiffness. With increasing inclination of the change in stiffness, the deflection of the cracks rises, whereby the entrance angle according to Fig. 11 increases. At the transition point into the compliant region, the curvature of the crack paths changes. Inside of the compliant region, the crack extends steadily curved. On the backside of the compliant region, the crack paths deflect more with increasing inclination of the change in stiffness and tend to run tangential to the region boundary. If the compliant region is big enough, the crack leaves this region on the backside, whereat the curvature of the crack path changes again. With greater distance behind the compliant region, the crack paths approach tangentially a parallel to the extension of the initial crack. The offset of this parallel to the initial crack increases with rising inclination of the change in stiffness. In contrast to the crack paths due to a stiffening through doubling Young´s modulus or doubling the thickness as shown in Fig. 8 the crack paths due to a compliant region through halving Young´s modulus or halving the thickness are rather similar. Obviously, this may be reasoned by the fact that inside a cut-out in contrast to a thickening no stress-free regions occur, so that the effective stiffness mismatches due to both methods to generate a compliant change in stiffness are similar. The characteristics of the courses of the stress intensity factors K I and K II for the compliant regions are corresponded to the characteristics of the courses of the stress intensity factors K I and K II for the stiffening. F