Integral model for the description of the debris cloud structure and impact

• Published in: International journal of impact engineering 2001-12, Vol.26 (1), p.115-128
• Main Authors: Corvonato, Enrico, Destefanis, Roberto, Faraud, Moreno
• Format: Article
• Language: English
• Subjects: Ballistics (projectiles; rockets); Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics
• ISSN: 0734-743X; 1879-3509
• DOI: 10.1016/S0734-743X(01)00074-4

The purpose of the present paper is to introduce a new integral model capable to describe the evolution of the debris clouds originated after normal-impacts of orbital debris over a Whipple shield. This work had been developed at Alenia Spazio in the context of a degree thesis. Several numerical SPH simulations of debris impacts on a Whipple shield configuration were performed to determine the ballistic limit and to compare it with semi-empirical damage equations. In the present paper, the numerical simulations were used to investigate the typical behaviour of experimental debris clouds ([6] and [9]) and to support the development of the integral model. With respect to previous papers ([1], [2], [3], [10]) in which a spherical shell-wise debris cloud was considered, here we try to introduce more realistic assumptions. We approximate the cloud's shape also introducing ejecta veil effects, which produce a multiplication of the deposited momentum upon the underneath wall. In the present model, the most peculiar hypothesis is a cinematic self-similar behaviour that is, whatever the shape is, the debris cloud evolves keeping unchanged its shape. Then, the material is opportunely distributed inside a volume and the choice of that distribution is described taking into account the results of the numerical simulations. Knowing the spatial material distribution and treating the cloud as a fluid, we can estimate the load time history and the drag-unitary force induced by the cloud impacting upon the rear wall. Of course, such a method uncouples the dynamic response of the rear wall from the evolution of the debris cloud. The balances of mass, momentum and energy allow three global and unknown parameters to be determined. The one-dimensional theory of impact ([10]) is used to take into account the conversion of part of the initial kinetic energy into internal thermal energy. No integration of differential equations is performed since complex propagation phenomena are taken into account through the effects they globally produce. The model still presents some free parameters related to the integral formulation. These parameters cannot be calculated through any balance condition, but they must be imposed to get a good, global reproduction of the debris cloud. The choice of these parameters is still the weak aspect of the method, and it depends on the consideration of the results obtained with more sophisticated tools, as, for instance, SPH simulations. The spatially defi