Impact of a liquid mass on a perfectly plastic solid

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Abstract
The use of steady, normal and oblique shock configurations is explored in calculating the pressure and deformation produced by the impact of a liquid mass on a plane solid surface. Since pressures generated are very large, the change in bulk modulus of the liquid (water) is accounted for by using an equation of state following Field, Lesser & Davies (1979). The impact of a plane-ended liquid mass is analysed using a normal shock for the cases of a rigid surface and a perfectly plastic surface. For the former, it is found that pressures somewhat in excess of the ‘water-hammer’ pressure of linear acoustic theory are predicted, and for the latter there is a critical impact velocity below which no deformation occurs. Above this velocity the surface deforms at a constant rate, producing a pit with maximum depth at the centre.If the liquid mass is wedge-shaped then an oblique shock is formed, which is attached to the contact point provided that the impact Mach number is large enough, as originally shown by Heymann (1969). Pressure and deformation velocity can again be calculated for the cases of rigid and perfectly plastic surfaces respectively. For a rigid surface it is confirmed that pressures considerably in excess of the plane-ended case are produced at shock detachment. For the plastic surface, it is found that there is no critical impact velocity and deformation can occur at any velocity as shock detachment is approached. For a cylindrical liquid mass with a conical tip, the pit produced again has maximum depth at the centre, but with a considerably increased value. The possible use of these models for pitting caused by microjets associated with cavitation bubbles and by impact of liquid drops is discussed.

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