Plastic Deformation and Vibration in a Fluid-Filled Tube Subject to Axial Impact

The goal of the present study is to examine the coupling of large-amplitude (including plastic deformation) flexural waves and precursor waves in water-filled, thin-wall (1.6 mm) steel tubes. To do this, we have compared the coupling created by exciting the stress waves in water versus in the tube wall. To examine the case of coupling from water to the tube, we used projectile impact on the water surface to create pressure waves in the water propagating along the tube axis. We have tested mild steel tubes using a steel impactor accelerated to speeds of up to 80 m/s using an air cannon to strike a polycarbonate buffer placed on top of the water surface within the tube. Strain gages measure hoop and longitudinal stresses at selected locations and a pressure gage measures the reflected pressure at the bottom of the tube. To examine the coupling from the stress waves in the tube to pressure waves in the water, we excited stress waves by axial impact on the tube along using a Hopkinson bar coupled to the tube without making contact with the water. For direct impact on the water surface, propagating plastic deformation flexural waves with more than 2% hoop strain were obtained at an impact speed of 80 m/s. The maximum hoop strain was observed just below the bottom surface of the buffer as a bulge with 16% hoop strain. Hoop and longitudinal strains indicate a steep elastic front followed by a gradual plastic deformation. Initially, the plastic deformation is dominant but the peak amplitude decays as the wave propagates. Since the plastic deformation wave travels much slower than the elastic waves, the initial flexural wave fronts propagate at 1350 m/s and are close to the wave speed of the Korteweg’s elastic theory of water hammer. Stress waves propagated at 5400 m/s in the tube wall and caused a 1–2 MPa pressure fluctuation in the water. Comparing strain histories to those of tubes without water, we observe that the coupling to the water damps high frequency vibrations and reduced peak amplitudes while maintaining the ratio of hoop and longitudinal strains.