PSI - Issue 13

Kota Kishi et al. / Procedia Structural Integrity 13 (2018) 1111–1116 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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4. Dynamic crack 4.1. The steel plate model

Figure 8 shows the steel plate model used in this experiment of dynamic crack propagation. In order to model infinite steel plate, the length of the side of global area is long enough for the model not to be influenced by reflected wave.

㻸㼛㼏㼍㼘㻌㻹㼑㼟㼔

㻳㼘㼛㼎㼍㼘㻌㻹㼑㼟㼔

Symmetry plane

㼏㼞㼍㼏㼗

Symmetry plane

Fig. 8 Whole model of dynamic crack analysis

4.2. Transformation of the solution In this experiment, the local area is moved following dynamic crack propagation. When the local area is moved, transformation of the nodal values (displacement, velocity and acceleration) is needed in order to give initial conditions. Fig. 9 shows the method. When the local mesh is moved as shown in Fig. 9, the solution of node C in the step is applied to the initial value of node A in the step + 1 . Global mesh Local mesh Crack

C

C

A

A

End of step n

Begining of step n+ 1

Fig. 9 How to move Local mesh

4.3. Results In this experiment, tensile stress is adopted as evaluation index. Experiment is performed by comparing tensile stress obtained in this experiment against Broberg’s solution (Broberg, 1995) . Broberg’s solution is the exact solution of stress field and crack opening displacement for dynamic crack. As the way of discretization with respect to time, HHT method is used. Each analyses are performed at velocity of 500 m/s, 1000 m/s and 1500 m/s. First, proper ratio of the local mesh size to the global crack area is examined. Fig. 10 shows error on tensile stress vs. distance from the crack tip when the ratio of the local mesh size to global crack area is changed. When the ratio is 1:1 or 1:1.5, error is larger than for 1:2, 1:2.5 or 1:3. The result may be because the interpolation cannot be performed when the local mesh size is too long against the global crack area. Second, the effect of local mesh size is examined. The results are shown in Fig. 11.

-0,15 -0,10 -0,05 0,00 0,05 0,10 0,15

0,20

1.250mm 0.833mm

1.000mm 0.714mm

1:1

1:1.5

0,10

0,00

-0,10

Error on tensile stress

-0,20 Error on tensile stress

0

5

10

15

20

0

5

10

15

20

Distance from the crack tip x [mm]

Distance from the crack tip x [mm]

Fig. 10 Effect of global element size against local crack (V=500m/s)

Fig. 11 Effect of local mesh size (V=500m/s)