###### Abstract  
The hypervelocity impact of space debris causes damage or destruction to spacecraft. The continuous damage caused by space debris creates greater requirements for protective materials. Wave-impedance gradient-protection material is a new type of space-debris-protection material with high kinetic-energy dissipation. However, the relationship between the distribution characteristics of the impedance layer and the protective performance is still unclear. This study provides guidance for the design of high-performance wave-impedance gradient materials by establishing the quantitative relationship between impedance-layer distribution characteristics and protective performance. Based on the one-dimensional shock-wave theory, this paper analyzes the propagation process of shock waves in wave-impedance gradient materials, establishes a transmission model of shock waves with changes in impedance layers, and quantitatively studies the influence of the change in wave impedance on the impact pressure, internal-energy conversion, and projectile- breaking characteristics by means of a numerical simulation. The results show that, when the surface and back of the wave-impedance gradient material are titanium alloy and nylon, respectively, the total transmission coefficient increases from 0.206 to a maximum of 0.339 with the continuous change in the gradient. The reduction amplitude of the shock wave with time under the three working conditions is Ti-Al-Mg-Ny \(>\) Ti-Al-Ny \(>\) Ti-Ny. The relationship of the transformed internal energy is Ti Al-Mg-Ny \(>\) Ti-Al-Ny \(>\) Ti-Ny, and the projectile breaking area is Ti-Al-Mg-Ny \(>\) Ti-Al-Ny \(>\) Ti-Ny. The analysis shows that the continuous change in wave impedance is beneficial to reduce the attenuation of the amplitude of the shock wave in the hypervelocity projectile, to keep the stress amplitude of the shock wave at a higher level, and to improve the internal-energy conversion and impact-breaking degree of the projectile, thereby enhancing the protection performance of the wave-impedance gradient material. hypervelocity impact impedance layer change; shock wave propagation; protection characteristics +
Footnote †: journal: Applied Sciences  
years, with the increasing frequency of human space activities and increasing space debris, space-debris protection has become an important part of spacecraft design [6; 7; 8]. In order to improve the survivability of spacecraft in harsh space-debris environments, since the 1980s, NASA, ESA, JAXA, and China have carried out a large number of hypervelocity-impact experiments based on the traditional Whipple protection structure, and developed a variety of high-performance protection structures. The selected materials are mainly high-strength aluminum alloy plate, aluminum mesh, foam aluminum, honeycomb plate, Nextel ceramic cloth, Kevlar fiber cloth, etc. [9; 10; 11; 12; 13; 14]. Meanwhile, the characteristics of hypervelocity impact have been investigated by many researchers [15; 16; 17; 18; 19]. However, the process of hypervelocity impact is extremely complex, involving dynamic mechanical responses and the dynamic breaking of materials under extremely high pressure, as well as the mixing and transformation of solid, liquid, and gas. Generally, the ideal protective material should have good projectile-breaking ability and lower protective-structure quality, reduce the ability of debris to penetrate the rear wall, create a large diffusion angle for debris clouds, and reduce the splashing of debris [20]. Good projectile-breaking ability requires that the projectile target has higher impact pressure at the moment of impact. The debris produced by the protective material should have a reduced ability to penetrate the rear wall. This requires an easier transformation from the solid state to the liquid and gas state under impact conditions. The lower quality of the protective structure requires that the protective material has excellent comprehensive protection performance under the same surface density.