Hydrodynamic Kelvin-Helmholtz instability on metallic surface.

Kelvin-Helmholtz instability on metallic surface is relevant to intense oblique impact in many physical processes such as explosive welding, Inertial Confinement Fusion and planetary impact events. Evolution of instability results in the formation of wavy morphology leading to material bonding or even mixing. However, mostly due to lack method to describe the dynamic behavior, instability mechanism controlled by elastoplastic properties of metal remains elusive. Here, we introduce a theory to reveal the evolution characteristics aroused by tangential velocity. Our simulations find that the unstable metallic surfaces exhibit amplitude growth and tangential motion by overcoming the depression of yield strength to generate wavy morphology. For diverse loading velocities, corrugated surfaces and material properties, an instability boundary distinguishes all unstable evolutions. Our analytical method with scale-independent variables reproducing numerical findings reveals plentiful characteristics of instability in strength materials. For designed loading velocities and material in oblique impact experiment in laboratory, the property of corrugated surfaces becomes an important factor to determine instability evolution.

Linear analysis of Atwood number effects on shear instability in the elastic-plastic solids.

The evolution of shear instability between elastic-plastic solid and ideal fluid which is concerned in oblique impact is studied by developing an approximate linear theoretical model. With the velocities expressed by the velocity potentials from the incompressible and irrotational continuity equations and the pressures obtained by integrating momentum equations with arbitrary densities, the motion equations of the interface amplitude are deduced by considering the continuity of normal velocities and the force equilibrium with the perfectly elastic-plastic properties of solid at interface. The completely analytical formulas of the growth rate and the amplitude evolution are achieved by solving the motion equations. Consistent results are performed by the model and 2D Lagrange simulations. The characteristics of the amplitude development and Atwood number effects on the growth are discussed. The growth of the amplitude is suppressed by elastic-plastic properties of solids in purely elastic stage or after elastic-plastic transition, and the amplitude oscillates if the interface is stable. The system varies from stable to unstable state as Atwood number decreasing. For large Atwood number, elastic-plastic properties play a dominant role on the interface evolution which may influence the formation of the wavy morphology of the interface while metallic plates are suffering obliquely impact.