PSI - Issue 2_A

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

3000

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0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 10 y-coordinate [mm] x-coordinate [mm] crack path α = 90° crack path α = 67,5° crack path α = 45° crack path α = 22,5° region boundary α = 90° region boundary α = 67,5° region boundary α = 45° region boundary α = 22,5°

-5 -4 -3 -2 -1 0 0 1 2 3 4 5 6 7 8 9 10 y-coordinate [mm] x-coordinate [mm] crack path α = 90° crack path α = 67,5° crack path α = 45° crack path α = 22,5° region boundary α = 90° region boundary α = 67,5° region boundary α = 45° region boundary α = 22,5°

E 1 = 100GPa; E 2 = 150GPa

E 1 = 150GPa; E 2 = 100GPa

Fig. 9. Crack paths for different orientations of the second region

The left side of the Fig. 10 illustrates the courses of the stress intensity factor K I plotted over the projection of the crack length on the x-axis in the case that the crack starts in the pliable region and grows towards the stiffer region. This type of illustration is used, since by plotting the results over the x-coordinate of the crack tip position a direct comparison of all results for the investigated orientations of the region boundary including the reference results for the homogeneous specimen is possible. If the crack is still sufficiently far away from the region border, the simulation results show that the courses of K I for all specimens with two regions are equal but smaller than the reference results for the homogeneous specimen. In the vicinity of the region boundary the deviations of K I from the reference results increase and K I reaches almost constant values. Apparently, the stiffer region shields the stress intensity at the crack as long as the crack grows in the pliable region. This influence is strongest when the crack grows perpendicular towards the region boundary. When the crack crosses the region boundary, the stress intensity factor increases abruptly and approximates the reference solution. Since the energy release rate is continuous when the crack crosses the region boundary and the relation ܭ ூ ൌ ඥ ܩ ூ ܧ is valid the height of the jump of K I depends on the ratio of the Young´s moduli of both regions. A similar observation is described in Kullmer 2016. The simulation results also show that for K I the crack length projected on the x-axis is essential, if the crack has entered the obliquely oriented second region, although the crack path is significantly different from the x-axis. An exception is the course of K I for the specimen with α = 22.5°. In this case, K I is always smaller than the reference solution and has no jump because the crack stays in the pliable region and does not cross the region boundary. The left side of the Fig. 10 illustrates the courses of the stress intensity factor K I plotted over the projection of the crack length on the x-axis in the second case that the crack starts in the stiffer region and grows towards the pliable region. The simulation results show that the courses of K I are complementary to the first case. If the crack is still sufficiently far away from the region border, the courses of K I for all specimens with two regions are equal but greater than the reference results for the homogeneous specimen. In the vicinity of the region boundary the deviations of K I from the reference results increase progressively. When the crack crosses the region boundary, K I decreases abruptly and approximates the reference solution.

5000

5000

α = 90° α = 67,5° α = 45° α = 22,5° homogeneous specimen

α = 90° α = 67,5° α = 45° α = 22,5° homogeneous specimen

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1000 K I [MPa(mm)

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K I [MPa(mm)

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0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

x-coordinate [mm]

x-coordinate [mm]

E 1 = 100GPa; E 2 = 150GPa

E 1 = 150GPa; E 2 = 100GPa

Fig. 10. Courses of K I for the crack growth starting in the pliable region