PSI - Issue 13

Yasuyuki Furuta et al. / Procedia Structural Integrity 13 (2018) 110–115 Furuta / Structural Integrity Procedia 00 (2018) 000 – 000

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Fig.5 Histories of crack velocity, 0 = 0.006, 0.0067 MPa. Fig.6 Histories of crack velocity, 0 = 0.012 MPa. Figure 7 shows distribution of pressure in a tube with a propagating crack, schematically. If the crack velocity is higher than the sound velocity, the initial pressure is maintained at crack-tip position and membrane force in the circumferential direction of the tube is expected to be maintained at the initial value. If the crack velocity is smaller than the sound velocity, on the other hand, the crack-tip pressure decreases with time and membrane force drops. At a position in the axial direction, , time of crack-tip arrival after the decompression wave passed through this position can be expressed as ′ = − / 0 (1) where is time of crack-tip arrival at position and can be determined from the high-speed camera measurement.

Fig.7 Schematic of gas decompression and crack propagation in rubber tube. Figure 8 shows change of crack velocity versus ′ , corresponding to Fig.5. The both curves coincide with each other. This result indicates that a crack passes through a position at relatively short time after the decompression wave passed through this point in the test with gas medium with slow sound velocity, like the air in the present case. Although the pressure at crack-tip becomes close to the atmospheric pressure quickly, the circumferential membrane force remains during some time period due to the inertial effect of the membrane movement in the radial direction. If the sound velocity of gas medium is high, the crack-tip arrives at this position after longer time period, in which case the membrane force becomes lower. The decreasing trend of the crack velocity in Fig.8 reflects this phenomenon. Figure 9 shows a similar graph corresponding to Fig. 6. In this case, the initial crack velocity was higher than the sound velocity of the air, therefore, the value of ′ is always 0, i.e. , no pressure drop is expected to take place. However, the pressure drop can take place in the helium gas test, even at this high initial pressure. From the above discussions, it is clear that the crack velocity tends to decrease more quickly with gas medium having higher sound velocity but the sound velocity can have no influence on crack velocity if the initial crack velocity is higher than the sound velocity.