Analytic Ballistic Performance Model of Whipple Shields
The dual-wall Whipple shield is the shield of choice for lightweight, long-duration flight. The shield uses an initial sacrificial wall to initiate fragmentation and melt an impacting threat that expands over a void before hitting a subsequent shield wall of a critical component. The key parameters to this type of shield are the rear wall and its mass which stops the debris, as well as the minimum pressure generated under threat particle impact of the sacrificial wall and the amount of void that is available for expansion. Ensuring the minimum pressure is sufficiently high to achieve large scale fragmentation/melt of the threat particle enables the expansion of the threat and reduces the momentum flux of the debris on the rear wall. Three key factors in the minimum pressure achieved are the thickness of the sacrificial wall relative to the characteristic dimension of the impacting particle, the density and material cohesion contrast of the sacrificial wall relative to the threat particle and the impact speed. The mass of the rear wall and the sacrificial wall are desirable to minimize for launch costs and dynamic concerns making it important to have an understanding of the effects of density contrast and impact speed. In this paper a fourth key parameter is identified related to fragmentation, which corresponds to the ratio of the size of the projectile relative to the transition from brittle to ductile hole growth in the projectile. Ballistic limit equations have been developed to define the failure limits of a MMOD shield, generally in terms of projectile diameter (or mass), impact velocity, and angle. Within the range of impact velocities relevant for Earth-orbiting spacecraft, three distinct regions of penetration phenomenology have been identified for Whipple shields: center dot Low velocity: the projectile is eroded (and possibly deformed) during its passage through the bumper plate, but is not fragmented. Thus, perforation of the rear wall is by a fragment with a mass and speed equal to or less than the original impactor. center dot Intermediate (shatter) velocity: impact velocities are sufficient to induce projectile fragmentation upon impact with the bumper plate, resulting in a coarse debris cloud with large solid fragments. Increasing velocity within the shatter regime results in increased fragmentation, and eventually melting, of the projectile and bumper fragments, generating a finer and more evenly dispersed debris cloud. Failure of the rear wall is a complicated combination of modes observed at low- and hypervelocity. center dot Hypervelocity: the projectile and holed-out bumper material is completely, or nearly completely, melted and/or vaporized by the initial impact. The resultant debris cloud impacts over a dispersed area of the rear wall, loading it impulsively and inducing failure through rupture or petalling. While each of these regimes are well observed with extensive empirical methods to describe these regions, differences in impactor materials, configurations of shields and questions about the limitations of the attainable impact speeds have left questions that are difficult to answer from completely empirical methods.