PSI - Issue 47

M. Iqbal Maulana et al. / Procedia Structural Integrity 47 (2023) 150–158 Maulana et al. / Structural Integrity Procedia 00 (2019) 000 – 000

152

3

ℎ 2 2 + ℎ=( 0 − 0 )

(2) where is material density, is the yield stress, is the inner radius, ℎ is the wall thickness, is the time, is the wall radial displacement, 0 is the peak overpressure, dan is the pulse duration. The analytical procedure evolves a relation for the radial displacement written as: = 0 2 2 ℎ − 0 3 6 ℎ − 2 2 , 0 ≤ ≤ , (3)

After the pressure pulse has passed, the equation of motion reduces to: ℎ 2 2 + ℎ = 0, ≥ .

(4)

Solving Equation 4 by integration gives: = 2 2 + 0 2 ℎ − 0 3 6 ℎ , ≥ .

(5)

Maximum deformation occurs at zero wall velocity for: = 0 2 ℎ (6) Using the impulse relation 2 = 0 and in Equation 5, the maximum radial displacement is given by: ( ) = 2 2 ℎ 2 − 3 ℎ . (7) If the loading approaches an ideal impulse, i.e. the impulse is held constant, the pressure pulse duration reduced and the peak overpressure increased, the maximum hoop strain,, ( ) = , is found to be given by: ( ) = 2 2 ℎ 2 . (8) 3. Benchmark Reference The experiment conducted by Rushton et al. [2008] at the University of Liverpool was used as a reference in this research. Research conducted by Rushton was carried out by using an open-ended pipe that was hung on trestles and slings, then at the midpoint of the pipe was given a cylindrical explosive charge with an interconnected detonator (shown in Figures 1 and 2). Every 100 mm on the pipe wall is installed dynamic pressure gauge to differentiate between pipe ringing and pressure loading. A research was sponsored by Atomic Weapons Establishment (AWE), which the detonation experiment was carried out using only two types of explosive loading, 0.6 kg, and 0.8 kg. In this case, TNT was modeled using the Johnson-Cook model. The Johnson-Cook model has proven suitable for calculating the combined thermal softening due to high-level loading, strain hardening, and plastic-hoop strain on metals. The form of the Johnson-Cook relation is given by Equation 9. = [ + ][1 + ̇ ∗ ][1− ∗ ], (9) where is in the first bracketed term, is the yield stress of the material at the strain rate 1 −1 , is strain hardening constant, is the equivalent plastic and is strain hardening exponential value. and are the material constants