We consider the response of fluid-filled tubes to internal shock waves and explosions. The emphasis is on the fluid–solid coupling aspects. The coupling of axial wave propagation in the fluid to flexural waves in the tube may be characterized by a single parameter that depends only on the tube and fluid material properties and dimensions. Using this parameter as a figure of merit, we discuss the limiting cases of weak and strong coupling between the fluid wave motion and tube structural motion. Examples discussed include detonation and shock waves in gas and liquid-filled tubes of metal, polymers, and composites. The results of experiments on elastic and plastic deformation are presented as well as selected results on fracture and rupture. Detonation in gas-filled tubes usually falls in the weak coupling regime except for very thin tubes or cases of deformation that lead to tube rupture. Impact generated axial waves in liquid-filled tubes can range from weak-to-strong coupling cases depending on the tube wall thickness and material. These cases include the well-known phenomenon of water hammer and we describe the relationship of impact studies to previous work on wave-propagation in water-filled pipes.

https://shepherd.caltech.edu/EDL/publications/reprints/ShepherdInabaChapter.pdf

Shock Loading and Failure of Fluid-filled Tubular Structures

Elastic response of water-filled fiber composite tubes under shock wave loading

We have experimentally studied the coupling of flexural waves in water-filled tubes with cavitating flow. To examine the cavitation events in the tube, we used a transparent polycarbonate (PC) tube. The flexural waves are generated by stress waves in the water propagating along the tube axis. A steel impactor is accelerated by gravity and strikes a polycarbonate buffer placed on top of the water surface within the tube. Strain gages measure hoop strain along the polycarbonate tube and a piezoelectric pressure gage measures the pressure at the bottom of the tube. The events were visualized by a high-speed video camera synchronized with the strain and pressure measurements. The impact of the projectile creates a stress wave propagating along the tube and coupled to the pressure wave in water. A sequence of traveling waves results and when the pressure in the waves drops below the vapor pressure, cavitation occurs in the tube. When cavitation bubbles are present, the tube vibrates at the natural frequency of the second mode of the circular ring. The duration of the cavitation can be estimated from a balance between the buffer kinetic energy and the work done in accelerating the fluid. Cavitation does not occur uniformly or simultaneously; cavitation events are observed near the bottom surface of the buffer, the middle of the tube, and at the bottom (closed) end. High-speed video of the cavitation events reveals that the cavities are clusters of bubbles that have a rosary or grape-bunch appearance.Copyright © 2010 by ASME

Dynamics of Cavitating Flow and Flexural Waves in Fluid-Filled Tubes Subject to Axial Impact

We experimentally studied the propagation of coupled fluid stress waves and tube flexural waves generated through projectile impact along the axis of a water-filled tube. We tested mild steel tubes, 38–40 mm inner diameter and wall thicknesses of 0.8 mm, 6.4 mm, and 12.7 mm. A steel impactor was accelerated using an air cannon and struck a polycarbonate buffer placed on top of the water surface within the tube. Elastic flexural waves were observed for impact speeds of 5–10 m/s and plastic waves appeared for impact speeds approaching 20 m/s for a 0.8 mm thickness tube. We observed primary wave speeds of 1100 m/s in a 0.8 mm thickness tube, increasing to the water sound speed with 6.4 mm and 12.7 mm thickness tubes. Comparison of our measurements in the 0.8 mm thickness tube with Skalak's water hammer theory indicates reasonable agreement between the predicted and measured peak strains as a function of the impact buffer speed (1956, “An Extension to the Theory of Water Hammer,” Trans. ASME, 78, pp. 105–116). For thick-walled tubes, the correlation between the experimentally determined peak pressures and strains reveals the importance of corrections for the through-wall stress distribution.

/pdf/flexural-waves-in-fluid-filled-tubes-subject-to-axial-impact-2nyks5oasv.pdf

Flexural Waves in Fluid-Filled Tubes Subject to Axial Impact

The use of high-velocity sheet-forming techniques where the strain rates are in excess of 10(2)/s can help us solve many problems that are difficult to overcome with traditional metal-forming techniques. In this investigation, thin metallic plates/foils were subjected to shock wave loading in the newly developed diaphragmless shock tube. The conventional shock tube used in the aerodynamic applications uses a metal diaphragm for generating shock waves. This method of operation has its own disadvantages including the problems associated with repeatable and reliable generation of shock waves. Moreover, in industrial scenario, changing metal diaphragms after every shot is not desirable. Hence, a diaphragmless shock tube is calibrated and used in this study. Shock Mach numbers up to 3 can be generated with a high degree of repeatability (+/- 4 per cent) for the pressure jumps across the primary shock wave. The shock Mach number scatter is within +/- 1.5 per cent. Copper, brass, and aluminium plates of diameter 60 mm and thickness varying from 0.1 to 1 mm are used. The plate peak over-pressures ranging from 1 to 10 bar are used. The midpoint deflection, circumferential, radial, and thickness strains are measured and using these, the Von Mises strain is also calculated. The experimental results are compared with the numerical values obtained using finite element analysis. The experimental results match well with the numerical values. The plastic hinge effect was also observed in the finite element simulations. Analysis of the failed specimens shows that aluminium plates had mode I failure, whereas copper plates had mode II failure.

Theoretical–experimental study of shock wave-assisted metal forming process using a diaphragmless shock tube

The deformation of metal plates and tubes achievable through the use of liquid shock waves generated in a shock tube is studied, with reference to both free-forming and forming the metal in...

Use of a liquid shock tube as a device for the study of material deformation under impulsive loading conditions

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Use of a liquid shock tube as a device for the study of material deformation under impulsive loading conditions