Impact fragmentation of nanoscale projectiles at ultrahigh striking velocities

Abstract

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.

Phenomenology of the Maximum Fragment Mass Dependence Upon Ballistic Impact Parameters

“…A series of two-dimensional (2D) traditional MD (molecular dynamics) simulations of this classic experiment is performed in this study by using nanoscale projectiles made of the Lennard-Jones 6-12 (LJ) monocrystalline solid, under a tacit assumption that this, admittedly rather simple, model is sufficient to capture some essential features of the investigated phenomenon. An extension and refinement of an earlier analysis (Mastilovic, 2015a) result in collision of nanoscale projectiles with a rough rigid wall with impact velocities (v) varying in a wide range from 0.27 km/s to 60 km/s that reveal a nonlinear and saturable character of the maximum fragment mass dependence upon selected ballistic parameters. The resulting reverse-sigmoid phenomenological model, suggested in the present article, consists of two nonlinear border regions identified with two phase transitions: the damage-fragmentation transition (v = v0) and the shattering transition (v = v1), with largely linear region in between.…”

“…The resulting reverse-sigmoid phenomenological model, suggested in the present article, consists of two nonlinear border regions identified with two phase transitions: the damage-fragmentation transition (v = v0) and the shattering transition (v = v1), with largely linear region in between. The accompanying hyper-exponential fragment mass distribution typical of instantaneous fragmentation of the ductile solids was discussed earlier (Mastilovic, 2015a) within a narrower striking velocity range. The ultrafast flat-end collision of the projectile with the rigid target is an extremely intense loading event belonging to the realm of akrology within the study of materials' physics.…”

“…The model is described in detail in preceding studies (Mastilovic, 2015a(Mastilovic, , 2016a(Mastilovic, , 2016b, thus, a succinct summary is deemed sufficient herein. A monatomic system is comprised of atoms of equal masses mi = m0 that form an ideal defect-free triangular lattice (without any quenched disorder) and interact with their nearest neighbors according to the LJ potential to mimic a monocrystalline, flat-nosed projectile.…”

“…The cut-off interatomic distance, R ≈ 1.7 r0, is selected herein to be between the first and second nearest neighbors in the reference configuration (the perfect crystal prepared at zero temperature). A fragment is defined as a self-bound cluster of atoms with interatomic distance less than the cut-off distance (rij ≤ R) in a sequential atom-by-atom search for the nearest neighbors (Mastilovic, 2015a(Mastilovic, , 2016a). …”

“…The investigation of dependence of the maximum fragment mass upon various state variables is extended and considerably refined in the present article in comparison to the preceding investigation which resulted in the piecewise-linear approximation (Mastilovic, 2015a). First, the analysis of the onset of the damage-fragmentation transition for slender projectiles, based on the maximum and average fragment mass, is refined to identify more transparently this continuous phase transition (Kun and Herrmann, 1999;Timar et al, 2012).…”