Dow Chemical Co., Central Res. Eng. Lab., Midland, MI 48674
An approximate analysis for penetration of thin-spaced foils is described. When the projectile strikes the first foil, intense pressure ablates projectile and foil materials and a spherical shock forms propagating toward the next foil. As the spherically expanding shock reaches the second foil, it fails when shear stress along the perimeter of the footprint reaches ultimate shear stress. During this stage of impact, propagation has negligible effect on transfer of momentum. When stricken by material from foils above, each foil after the second deforms plastically into a conical shape ending with extensional failure. The cone's radius grows with time at a rate lower than the speed of propagation of shear waves in the foil's material. The effective wave front lags the actual front because of reversal in the direction of displacement close to the front. Since the mode of failure relies on maximum extensional strain, penetration will cease when speed of impact is lower than some critical speed that depends on maximum strain of the foil material. At this point, the circle of influence is expanding faster than transverse motion of the foil and maximum extensional strain in the cone of influence is never reached. It is found that weight efficiency of the shield rises inversely with foil thickness asymptotically as a result of mass entrained by propagation. The most efficient shield requires relatively thin layers of foil with material properties that maximize effective speed of propagation and maximum strain in the foil material.