Dynamic cratering of graphite: Experimental results and simulations

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. b s t r a c tThe 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 À1 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.

Simulations of Hypervelocity Impacts into Graphite

“…This graphite is a commercial grade from the POCO company [11] and is macroscopically isotropic with a 1754 kg.m -3 density. The main mechanical characteristics of both materials can be found in [9][10][11][12]. Projectiles were launched by MICA, a two-stage light-gas gun [9], at velocities ranging between 1.1 and 4.5 km.s -1 .…”

“…Published experimental results give crater dimensions in porous graphite for a large variety of projectile materials and velocities [8]. However, it has been shown that in the case of a steel sphere projectile, it remains buried below the surface of the crater [9]. For the highest velocities, i.e.…”

“…For the highest velocities, i.e. above 4000 m/s, hydrodynamic simulations have been used to explain this behavior, likely related to the damage and rupture process in graphite [9]. More recent results have been obtained at lower velocities, down to 1200 m/s, which show that the projectile penetration depth (PPD) follows a non-monotonic evolution, where the plasticity and rupture of the steel sphere are expected to play a major role [10].…”

Penetration and cratering experiments of graphite by 0.5-mm diameter steel spheres at various impact velocities

“…Indeed, projectiles stem from bearings involving a high Rockwell hardness in the 60e65 HRC range. They were launched by MICA, a twostage light-gas gun described in a previous work [21] at velocities from 1.1 to 4.5 km s…”

“…Experimental results have been published giving crater dimensions in porous graphite for a variety of projectile materials and velocities [19,20]. The present authors have attempted to compute numerical models into hydrocodes to reproduce experimental results [21]. However, a large set of experimental data was missing in order to fit the parameters of the models, especially that of the projectile such as elastic limit and strength which may be highly dependent of the strain rate [22].…”