PSI - Issue 2_B

Fuminori Yanagimoto et al. / Procedia Structural Integrity 2 (2016) 395–402 Author name / Structural Integrity Procedia 00 (2016) 000–000

399

5

-0,008 -0,006 -0,004 -0,002 0,000 0,002 0,004

0,002

0,000

-0,002

118mm 126mm 134mm 142mm 150mm 158mm 166mm 174mm 182mm 190mm Position of strain gages

strain

strain

Position of strain gages

-0,004

126mm 134mm 142mm 150mm 158mm 166mm

-0,006

0,0005

0,0007

0,0009

0,0005

0,0007

0,0009

time [s]

time [s]

Test 1 Test 2 Fig.5 Strain history obtained in test 1 and 2 obtained by strain gages

0 100 200 300 400 500 600 700 800 900 1000

Test 1 Experiment Test 1 Approximation curve Test 2 Experiment Test 2 Approximation curve

0,05 0,07 0,09 0,11 0,13 0,15 0,17 0,19

Test 1 Test 2

Crack velocity [m/s]

crack tip position [m]

0,05

0,10

0,15

0,20

0,0005

0,0007

0,0009

time t [s]

Crack length[m]

Fig.6 Strain peak time and strain gage position

Fig.7 Crack velocity

far from the path, the peak would not necessarily correspond to the crack passing. On the other hand, in this study, time of the peak of obtained strain is regarded as time of crack tip passing because the strain gages were pasted much near from the path of crack. The strain histories obtained from test 1 and test 2 by strain gages are shown in Fig.5. They have not been filtered by anything. The relationships between time of the peaks and the position of the gages are shown in Fig.6. 0.0010 second in figures is the time when crack finished propagating and penetrating over the specimen. 0 second means the initiation of logging the strain. We approximated these relationship as the form of Eq.(1) by least-square method. We differentiated each equation to get the crack velocities. The velocities against the crack length are shown in Fig.7. = ( 1000 ) + (1) l is the position of the crack tip corresponding to the crack length at the peak time and t is time of crack passing. a, b, and c in Eq.(1) are fitting parameters to approximate the experimental data.

3. FEM analysis

3.1. Finite element model

There are some methods to represent crack propagation in FEM, such as X-FEM (Moes et al. (1999)), PDS-FEM (Hori et al. (2005)) and so on. In this study, because the crack path and crack velocity were obtained from above