PSI - Issue 2_A

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

2998

5

stress intensity factors along the crack front with an appropriate polynomial regression is considered because Dibblee 2016 showed, that this method stabilizes crack growth simulations with ADAPCRACK3D. Further, numerical fluctuations and the deviations from the reference solutions of the stress intensity factor curves are reduced for growing crack lengths.

1.100

1.050

0,5 ]

1.000

Raw data Adaption with 4th degree polynomial regression mean value

950 K I [MPa(mm)

900

-1

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0,8

1

z-coordinate [mm]

Fig. 6. Course of K I along the crack front over the thickness of the specimen

The comparison of the courses of K I along the crack front in Fig. 6 shows that the evaluation of the stress intensity factor curves using the mean value for every crack increment is obviously possible since specimen with constant thickness are investigated.

2500

1000 1500 2000 2500 3000 3500

2000

0,5 ]

1500

0,5 ]

1000 K I [MPa(mm)

Evaluation with 4th degree polynomial regression Evaluation with mean value

Evaluation with 4th degree polynomial regression Evaluation with mean value

K I [MPa(mm)

500

0 500

0

0 1 2 3 4 5

0

2

4

6

8

x-coordinate [mm]

x-coordinate [mm]

α = 45°; E 1 = 100GPa; E 2 = 150GPa

α = 22.5°; E 1 = 150GPa; E 2 = 100GPa

Fig. 7. Courses of K I for different fracture mechanical evaluations

In Fig. 7 the courses of K I along the crack path, evaluated with a 4 th degree polynomial regression and evaluated using the mean value, are plotted over the projection of the crack length on the x-axis. Fig. 7 compares two cases. In the first case the crack starts in the region with lower Young´s modulus and runs towards the region with higher Young´s modulus and the orientation angle of the stiffer region is α = 45°. In the second case the crack starts in the region with higher Young´s modulus and runs towards the region with lower Young´s modulus and the orientation angle of the pliable region is α = 22.5°. Both comparisons show that the courses of K I are in principle the same for the two types of evaluation and have similar characteristics. However, by evaluating the course of K I along the crack path using mean values numerical fluctuations are significantly reduced and the curves are much smoother than using a 4 th degree polynomial regression.