Phenomenology of the Maximum Fragment Mass Dependence Upon Ballistic Impact Parameters

Abstract

Molecular dynamics simulations of the ballistic Taylor test are used to explore correlation between the largest fragment mass and the impact energy of a projectile as well as a set of selected state variables. Flat-ended, monocrystalline, nanoscale bars collide with a rigid wall with striking velocities ranging from 0.27 km/s to 60 km/s. The investigation emphasis is on two border regions of the emerging nonlinear phenomenological model identified with two transitions: the damage-fragmentation transition and the shattering transition. In between these two nonlinear regions, the maximum fragment mass is largely inversely proportional to the impact energy, and the maximum values of the pressure, temperature, and the square of the effective strain. A reverse-sigmoid phenomenological model is proposed to capture the unifying features of this nonlinear and saturable dependence. A crystallographic orientation dependence of the damage-fragmentation transition parameters is investigated.

Some sigmoid and reverse-sigmoid response patterns emerging from high-power loading of solids

“…The temperature definition (3.4) has the firm statistical-mechanics foundations since it follows from the canonical ensemble maximum-probability distribution. It was verified by the statistical hypothesis testing that the vibrational velocities obtained from these MD simulations represent a random sample corresponding to the Maxwell-Boltzmann distribution [12]. The temperature evolution in time and space can be vividly presented with a very high-resolution [11].…”

“…MD is a convenient tool to investigate dynamic response of solids under extreme loading conditions by high-resolution virtual testing. Therefore, it frequently assumes a role of a "computational microscope" to explore evolution of discrete systems at spatial and temporal scales that go beyond the current experimental limits (e.g., [3,[10][11][12]). The present approach is limited to the classic MD simulation technique in which the dynamic state of an atomic system is defined by laws of Newtonian mechanics with atomic motions being uniquely determined by empirical potentials.…”

“…Thus, a monatomic system (mimicking a monocrystalline sample) is comprised of atoms of equal masses = 0 ( = 1, ) that form an ideal triangular lattice and interact with their nearest neighbors according to the L-J (Lennard-Jones) potential. The Cauchy problem is solved numerically by using the Verlet algorithm and the neighbor-list method [9,13,14] with the time step as low as a fraction of femtosecond [11,12]. The extremely small time step, necessitated by the ultrahigh power of the simulated events, makes the simulations painstakingly time-consuming even for the relatively small model size.…”

“…and illustrated by Figure 6 [12]. The phenomenological model (4.9) is developed based on the reverse-sigmoid form of the Weibull equation (1.1b), where the three uppercase alphabetic letters ( , , ), as in the preceding cases, designate the fitting parameters (for example, in Figure 6a, = 4, = 7, = 2.2).…”

Simulation of Fragmentation Characteristics of Projectile Jacket Made of Tungsten Alloy after Penetrating Metal Target Plate using SPH Method

“…The issue of dynamic fragmentation of solid material under impact loading is a long-term research topic in the fields of elastic-plastic mechanics, dynamic mechanical properties of material, aerospace and weapon science. At present, the main methods to simulate the dynamic fracture of solid material are finite element method (FEM) 2 , discrete element method (DEM) 3 , finite element method combined with discrete element method [4][5] , level set method 6 , molecular dynamics method 7 and smooth particle hydrodynamics (SPH) method [8][9][10] . The finite element method is difficult to display the discontinuity accurately such as crack, for it is difficult to deal with the contact problem of the crack surface and crack propagation on multiple elements 11 .…”