Molecular-dynamics simulations of the nanoscale Taylor test under extreme loading conditions

Abstract

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.

Phenomenology of the Maximum Fragment Mass Dependence Upon Ballistic Impact Parameters

“…The slender LJ projectile (D0×L0 = 15×110 nm, mp = 7.0×10 -21 kg), prepared at zero temperature, impacts a rough rigid target represented by a set of immovable atoms. The conversion of simulation data generated at the nanoscale level (atomic positions and velocities, and interatomic forces) to macroscopic observables (temperature, stress and strain) is firmly established nowadays (e.g., Wagner et al, 1992;Allen and Tildesley, 1996;Zhou, 2003;Buehler, 2008;Mastilovic, 2016a). The link between two atoms ruptures when their mutual distance exceeds a predetermined critical value.…”

“…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 coordination number of bulk atoms in the reference configuration is six and the potential energy per atom is -2.96 ε, which is slightly in excess of the bulk value (-3 ε) due to the surface effects. Since the shock wave excitation is inherently ultrafast, the Cauchy problem is solved numerically by using the Verlet algorithm with the time step of the order of femtoseconds (Mastilovic, 2016a). This extremely small time resolution (required by the ultrahigh power of the simulated event) in conjunction with necessity to approach asymptotically steady states of fragment mass distributions, makes the MD simulations extremely time-consuming (even for the relatively small model size) and effectively limits the maximum achievable striking velocity.…”

“…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 extremely steep gradients of state variables (e.g., Mastilovic, 2016a), well documented by shock experiments, may cause phase transitions and lead to sequential fractures that culminate eventually in energetic expulsion of fragment debris. Since a shock wave excitation is inherently ultrafast, the present MD method requires a femtosecond time resolution to observe the collective dynamics of material on picosecond time scales, which renders simulations extremely time-consuming.…”