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Molecular-dynamics simulations of the classic Taylor experiment are performed to investigate some general trends of impact fragmentation at ultra-high striking velocities. The striking velocities of flat-ended, monocrystalline, nanoscale pillars (nanoprojectiles) range from 0.34 km/s (Mach 1) to 30 km/s to explore qualitative effects on the fragment mass distribution. These atomistic simulations offer insight into evolution of the fragment distribution and its dependence upon the striking velocity. According to the simulation results, distribution of the fragment masses following hypervelocity impacts of energy sufficient to ensure that the fragmentation problem is statistically well posed, is well represented by the bilinear (bimodal) exponential distribution commonly observed during high-energy homogeneous fragmentation events. At more moderate striking velocities, a mixing of fragments from different fragmentation intensity events-that is, the more pronounced statistical heterogeneity-results in the distribution of fragment masses that appears to follow the trilinear (trimodal) exponential distribution due to the occurrence of a large-fragment tail in addition to the bilinear exponential part. The maximum fragment mass is studied from the standpoint of the striking velocity as well as a set of state parameters: the instantaneous kinetic temperature and the selected stress and strain invariants; corresponding phenomenological relationships are suggested for the investigated hypervelocity impact range.

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A series of molecular-dynamics simulations of the classic Taylor impact test is performed by using a flat-ended monocrystalline nanoscale projectile made of the Lennard-Jones two-dimensional solid. The nanoprojectile striking velocities range from 0.75 to 7 km/s. These atomistic simulations offer insight into nature of fragment distributions and evolution of state parameters. According to the simulation results, the cumulative distribution of fragment sizes in the course of this non-homogeneous fragmentation process for hypervelocity impacts appears to be well represented by the bimodal-exponential distribution commonly observed during high-energy uniform fragmentation events. For more moderate impact velocities, the cumulative distribution of fragment sizes, in addition to the bimodal-exponential part, exhibits a large-fragment tail. Temporal evolutions on instantaneous kinetic temperature, stress and strain invariants are presented and discussed. Scaling relations between temperature/temperature rate and kinematic rates of deformation are suggested.

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It had been long recognized that the tensile strength of brittle materials increases with increase of the loading rate. In the present article, a statistical approach to rupture of a disordered 2D triangular truss lattice consisting of fragile nonlinear springs is attempted in hope to elucidate some generic effects of structural and geometrical disorder on the tensile strength and the (stress-peak and post-peak) damage energy rates. The simulation results reveal increase of the mean and decrease of the standard deviation of the macroscopic tensile strength with increase of the structural and geometrical order till the ‘theoretical strength’ saturation. At the same time, the increase in lattice disorder results in increase of the mean and standard deviation of the stress-peak damage energy rate, followed by the decrease of the same in the softening regime.

This article illuminates some general features and provides elementary interpretations of the deformation, damage, and failure of brittle solids characterized by very low fracture energy. The dynamic response of these materials is determined to a large extent by stochastic and random factors. The investigation emphasis is on the moderate-to-extremely high rate range (10 s À1 , 1 Â 10 9 s À1 ), explored under practically identical in-plane stress conditions. The statistical approach is based on repeated particle dynamics simulations for different physical realizations of micromechanical disorder of a 2D brittle discrete system. The proposed strategy is computationally intensive, which necessitates simplicity of the laws governing the interparticular interaction. Based on the simulation results, an expression is proposed to model the mean tensile strength dependence on the strain rate. The linearity of the rate dependence of the stress-peak macroscopic response parameters is observed and discussed.KEY WORDS: brittle systems, dynamic strength, damage energy rate, time to failure, disorder.