PSI - Issue 6

Tonsho Fumiaki et al. / Procedia Structural Integrity 6 (2017) 269–275 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

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4

the critical condition for the crack propagation and crack branching, detailed stress distribution at running crack tip is investigated by dynamic FEM analysis. 4. FEM analysis FEM analysis is conducted for further investigation about brittle crack propagation. Crack propagation velocity acquired by experiment is used in the analysis. Major analysis conditions are summarized in Table 4. Fig.6 shows the overview of the model used in this analysis. Considering the symmetry, the model of 1/4 size of the actual specimen is used. Mesh size of crack propagation area is 0.1mm, which is smallest of all the mesh. Propagation of the crack is simulated by using nodal force release method. From the result of analysis, opening stress component( yy ) is extracted from the nodes near the crack tip and dynamic stress intensity factor, d is calculated (eq. (1)). d is assumed as a material constant, so the model is modified by changing the crack shape, as shown in Fig. 7, to keep d constant during the crack propagation. Table 4. Analysis conditions Code ABAQUS 6.14-1 Analysis Dynamic, implicit Element 3Dsolid (8nodes-cubic integral) Minimum element size 0.1mm

30mm

crack propag ation

80mm

θ= 31 °

110mm

0.0002m

160mm

0.01m

θ= 30 °

crack propagation θ= 51 °

unit cell

crack propagation

0.015m

0mm 30mm

200mm

0.005m

θ

110mm Fig. 6Overview of the model used in FEM analysis

Fig. 7The shape of crack model

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

1.2

80mm

160mm

#3

#2

#5

1

Fig. 4The point where the crack branches

0.8

0.6

0.4

0.2

Standard deviation

Standard deviation

Standard deviation

0

0

50

100

150

200

250

0

50

100

150

200

250

0

50

100

150

200

250

300

350

Crack length, a [mm]

Crack length, a [mm]

Crack length, a [mm]

Fig. 5Surface roughness