Theoretical analysis of the elastic Kelvin-Helmholtz instability in explosive weldings

By considering the joint effects of the Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instabilities, this paper presents an interpretation of the wavy patterns that occur in explosive welding. It is assumed that the elasticity of the material at the interface effectively determines the wavelength, because explosive welding is basically a solid-state welding process. To this end, an analytical model of elastic hydrodynamic instabilities is proposed, and the most unstable mode is selected in the solid phase. Similar approaches have been widely used to study the interfacial behavior of solid metals in high-energy-density physics. By comparing the experimental and theoretical results, it is concluded that thermal softening, which significantly reduces the shear modulus, is necessary and sufficient for successful welding. The thermal softening is verified by theoretical analysis of the increase in temperature due to the impacting and sliding of the flyer and base plates, and some experimental observations are qualitatively validated. In summary, the combined effect of the KH and RT instabilities in solids determines the wavy morphology, and our theoretical results are in good qualitative agreement with experimental and numerical observations.