Christian Yarin

A model of oblique penetration of a rigid projectile into a thick elastic–plastic target has been developed (Roisman et al., Int J Impact Engng 1997; 19: 769–95) which incorporates stress-free boundary conditions at the rear surface of the target. The main objective of the present work is to validate the theoretical model by comparison with new experimental results for normal and oblique penetration of a rigid projectile into a thick plate of Al 6061-T651. Good agreement between theory and experiment is exhibited for the projectile residual velocity and the crater shape.

By adding minute concentrations of a high molecular weight polymer, liquid jets or bridges collapsing under the action of surface tension develop a characteristic shape of uniform threads connecting spherical fluid drops. In this paper, high-precision measurements of this beads-on-string structure are combined with a theoretical analysis of the limiting case of large polymer relaxation times, for which the evolution can be divided into two distinct regimes. This excludes the very late stages of the evolution, for which the polymers have become fully stretched. For times smaller than the polymer relaxation time, over which the beads-on-string structure develops, we give a simplified local description, which still contains the full complexity of the problem. At times much larger than the relaxation time, we show that the solution consists of exponentially thinning threads connecting almost spherical drops. Both experiment and theoretical analysis of a one-dimensional model equation reveal a self-similar structure of the corner where a thread is attached to the neighbouring drops.

The fracture of the target and projectile during normal penetration is described using a model of chaotic disintegration modifying the theory of chaotic disintegration of liquids. The radius of the locally smallest fragment is calculated equating its kinetic energy of deformation with its surface energy of fracture. The probability of lacunae opening in the target and projectile materials increases near the target/projectile interface. The percolation threshold for this probability determines the boundary of the fractured zone. When this fractured zone reaches the rear surface of the target the fragments can leave it. Mass distribution of the fragments was calculated with the help of percolation theory. Then, the shape of the debris cloud and the direction, velocity and range of its propagation are calculated to estimate vulnerability behind the perforated target.The calculations were compared with results of normal impact experiments performed with tungsten sinter alloy rods (D=20 mm, L/D=6) against 40 and 70 mm rolled homogeneous armor (RHA) at an impact velocity of 1700 m/s  and . For observation of the bulging, breakup and fragmentation of the bulge as well as debris cloud formation and expansion, flash X-ray and laser stroboscope techniques have been applied. From the X-ray photographs and soft recovery tests the shape of the debris cloud and velocity field of the fragments as well as the fragment number and mass distributions have been determined, respectively. The calculations predict well the experimental data.