Dynamic cratering of graphite : experimental results and simulations

The cratering process in brittle materials under hypervelocity impact (HVI) is of major relevance for debris shielding in spacecraft or high-power laser applications. Amongst other materials, carbon is of particular interest since it is widely used as elementary component in composite materials. In this paper we study a porous polycrystalline graphite under HVI and laser impact, both leading to strong debris ejection and cratering. First, we report new experimental data for normal impacts at 4100 and 4200 m s 1 of a 500-mm-diameter steel sphere on a thick sample of graphite. In a second step, dynamic loadings have been performed with a high-power nanosecond laser facility. High-resolution X-ray tomographies and observations with a scanning electron microscope have been performed in order to visualize the crater shape and the subsurface cracks. These two post-mortem diagnostics also provide evidence that, in the case of HVI tests, the fragmented steel sphere was buried into the graphite target below the crater surface. The current study aims to propose an interpretation of the results, including projectile trapping. In spite of their efficiency to capture overall trends in crater size and shape, semi-empirical scaling laws do not usually predict these phenomena. Hence, to offer better insight into the processes leading to this observation, the need for a computational damage model is argued. After discussing energy partitioning in order to identify the dominant physical mechanisms occurring in our experiments, we propose a simple damage model for porous and brittle materials. Compaction and fracture phenomena are included in the model. A failure criterion relying on Weibull theory is used to relate material tensile strength to deformation rate and damage. These constitutive relations have been implemented in an Eulerian hydrocode in order to compute numerical simulations and confront them with experiments. In this paper, we propose a simple fitting procedure of the unknown Weibull parameters based on HVI results. Good agreement is found with experimental observations of crater shapes and dimensions, as well as debris velocity. The projectile inclusion below the crater is also reproduced by the model and a mechanism is proposed for the trapping process. At least two sets of Weibull parameters can be used to match the results. Finally, we show that laser experiment simulations may discriminate in favor of one set of parameters.