Shear instability of plastically-deforming metals in high-velocity impact welding

High-speed oblique impact of two metal plates results in the development of an intense shear region at their interface leading to interfacial profile distortion and interatomic bonding. If the relative velocity is sufficient, a distinct wavy morphology with a well-defined amplitude and wavelength is observed. Emergence of this morphology below the melting point of the metal plates is usually taken as evidence of a successful weld. Amongvarious proposed mechanisms, instability owing to large tangential velocity variations near the interface has received significant attention. With one exception, the few quantitative stability analyses of this proposed mechanism have treated an anti-symmetric/shear-layer base profile (i.e., a Kelvin-Helmholtz configuration) and employed an inviscid or Newtonian viscous fluid constitutive relation. The former stipulation implies the energy source for the instability is the presumed relative shearing motion of the two plates, while the latter is appropriate only if melting occurs locally near the interface. In this study, these restrictions, which are at odds with the conditions realized in high-velocity impact welding, are relaxed. A quantitative temporal linear stability analysis is performed to investigate whether the interfacial wave morphology could be the signature of a shear-driven high strain-rate instability of a perfectly plastic material undergoing a jet-like deformation near the interface. The resulting partial differential eigenvalue problem is solved numerically using a spectral collocation method in which customized boundary conditions near the interface are implemented to properly treat the singularity arising from the vanishing of the base flow strain-rate at the symmetry plane of the jet. The solution of the eigenvalue problem yields the wavelength and growth rate of the dominant wave-like disturbances along the interface and confirms that a shear instability of a plastically-deforming material is compatible with the emergent wavy interfacial morphology.