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The arcticle gives a spatial gas-dynamic formulation of the backpressure problem, which describes the change in pressure in front of an accelerating projectile when it moves along the bore. This takes into account the geometry of the front of the projectile and its influence on the formation of the shock wave. An unsteady spatial flow of the displaced medium ahead of the projectile body without and taking into account the forces of viscosity is considered. The paper considers the solution to the problem of throwing a body using the energy of gunpowder combustion. The internal ballistics problem, which determines the dynamics of the projectile movement, is solved in terms of averaged parameters. A two-step Runge-Kutta scheme with a second order of accuracy is used to numerically integrate a system of ordinary differential equations in time. The control volume method is used for the numerical solution of the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the problem of the decay of an arbitrary discontinuity. A comparison is presented of taking into account the backpressure as the pressure behind the detached shock wave, obtained from the analytical solution of the problem of the supersonic motion of a flat piston in a pipe at a constant velocity, and the pressure acting on the projectile, determined from the solution of nonstationary one-dimensional and spatial (axisymmetric) equations of gas dynamics. It was found that taking into account the viscosity practically does not affect the results of calculating the backpressure, while taking into account the shape of the front part of the projectile leads to a significant difference in the pressure fields behind the front of the shock wave compared to the solution in the framework of the one-dimensional formulation of the problem, where the shape of the front part of the projectile cannot be taken into account. It is concluded that this can significantly affect the results of modeling the ballistics of a shot at high throwing speeds.

This paper is concerned with mathematical model for numerical simulation of meteoroid dynamics. The simulations of bolide ballistics are carried out via hard sphere approximation. System of differential equations for movement and heat transfer is solved in Lagrange variables via Runge-Kutta methods. The drag force of atmospheric air is computed via Henderson formula, valid for wide ranges of Reynolds and Mach numbers. The parameters of surrounding gas are obtained from standard atmosphere model. The impact pressure is computed taking into account entropy jump through bow head shockwave and consequent isentropic deceleration of the flow in the vicinity of streamlined sphere. Meteoroid fragmentation is modeled as sequential division of parent body into two parts using random weighting coefficient for parent mass. The condition for fragmentation event occur when the hemisphere-averaged value of impact pressure exceeds the threshold of relative body strength, which nonlinearly depends on ration of initial meteoroid mass to current mass of considered fragment. To compute trajectory divergence for newly-formed splinters we introduce the repulsive force, dependent on impact pressure, cross sectional areas of mutually repulsing bodies and distances between them. The set of mathematical models is implemented as the program complex. Preliminary computational results show that fragmentation altitude, terminal velocities and maximum splinter masses are in good agreement with corresponding observations and measurements.

The purpose of this research is to formulate a generic analytical model to assess the phenomena of water ricochet for a conical nose shaped projectile. A theoretical model is analyzed to study the critical angle of conical nose shaped projectile entering in water and is extended for different mediums as normal sand and mercury. Numerical Simulation has been carried out to find the effect of tip angle of the conical nose shaped projectile on the critical angle. Critical angle is defined as that angle of impact of the projectile above which ricochet will occur. This angle is obtained by balancing the momentums acting on the projectile at the time of impact on the basis of Newtonian theory. Major factors affecting critical angle are impact velocity, impact angle, density of the projectile and the target. An attempt has been made to study the effect of longitudinal spin of the projectile on the critical angle.

In order to design hybrid rocket engines, we have developed a numerical prediction approach to the internal ballistics. The key point is its cost performance. Therefore simple but efficient models are required. Fluid phenomenon and thermal conduction phenomenon in a solid fuel should be treated time-dependently, because characteristic times of these phenomena are longer than those of other phenomena. Besides, they are solved with the energy-flux balance equation at the solid fuel surface to determine the regression rate. It is confirmed that numerical evaluation of time- and space-averaged regression rate is the same order of magnitude as that in experiments. However, the factors n in ṙ = aG¯oxn differ between calculations and experiments.

The ‘piston effect’, namely the time response of a fluid to an instantaneous change in the temperature of its boundaries, is studied for a rarefied gas confined in a slab. The problem is solved for the entire range of Knudsen numbers in the case where the prescribed temperature jumps at the walls are small. Analytic solutions are obtained in both collisionless and continuum limits and compared with low‐variance direct Monte Carlo simulations (LVDSMC) of the Boltzmann equation. The collisionless analysis captures well the early‐time dynamics of the system (at times t of the order of the mean collision time τcoll), where the gas motion is essentially ballistic, and the continuum‐limit analysis agrees with LVDSMC predictions at times t≥50τcoll, where the system behaviour is dominated by molecular collisions. Between these two limits, the dynamics of the system is governed by the solution of the complete linearized Boltzmann equation. The results supply insight into the mechanism of continuum breakdown in hea...

This study aims to characterize the interaction of explosive blast waves through simulated anatomical models. We have developed physical models and a systematic approach for testing traumatic brain injury (TBI) mechanisms and occurrences. A simplified series of models consisting of spherical PMMA shells housing synthetic gelatins as brain simulants have been utilized. A series of experiments was conducted to compare the sensitivity of the system response to mechanical properties of the simulants under high strain‐rate explosive blasts. Small explosive charges were directed at the models to produce a realistic blast wave in a scaled laboratory test cell setting. Blast profiles were measured and analyzed to compare system response severity. High‐speed shadowgraph imaging captured blast wave interaction with the head model while particle tracking captured internal response for displacement and strain correlation. The results suggest amplification of shock waves inside the head near material interfaces due to...

When a projectile approaches the back surface of a target, complicated mechanics and different failure modes ensue that can lead to perforation. There have been a number of attempts to model these different failure modes, for example models due to Ravid and Bodner [1] and Walker [2]. Of particular interest are analytic models (as opposed to hydrocode models) where the model attempts to explicitly identify relevant failure modes and back surface breakout modes. This paper examines back surface breakout and target failure models with different failure modes to see how they are invoked in specific impact geometries and scenarios. Comparisons are made of thresholds and sensitivities for the different failure modes to gain a greater understanding of their usefulness and applicability. The model results are compared to data to ensure reasonableness of the computations. Good agreement is shown with a relatively simple back‐surface‐strain target failure mode for predicting ballistic limit velocity for large aspect‐ratio projectiles and relatively thick targets as compared to the projectile diameter.

A high‐speed digital camera was used to observe the deflection‐time history of a Kevlar® fabric to bullet impact. It was observed, as others have, that the deflecting fabric has the shape of a pyramid. The average apex angle of the pyramid was calculated from the digital images and was found to be constant with time for the first 50 to 70 microseconds. Using this information, a simple momentum transfer model is shown to capture the velocity‐time history of fabric deflection until ply failure. As expected, once ply failure occurs, the model overpredicts deceleration of the bullet.

Flat, hemispherical and ogive-2 nosed mild steel projectiles (10 mm diameter, 100 mm length) were fired at 200 m s{sup -1} into the end face of cylindrically confined dry sand (100 mm diameter, 150 mm length). Projectiles were tracked through the sand using flash radiography and high speed photography. By seeding a horizontal plane of randomly dispersed lead shot (

Constitutive models for brittle materials such as glass can be very complex as they are dependent on strains, strain rates, pressures, temperatures, damage and other parameters. There may also be significant (pressure‐dependent) strength after failure such that the constitutive response is much different for intact material and failed material. A large number of laboratory tests is required to develop a comprehensive constitutive model. Another approach is to develop simple models by using penetration‐velocity data obtained from ballistic experiments. Here various functional forms of simple models (with a limited number of constants) can be used to (computationally) match the penetration velocity over a range of impact velocities. This allows for the determination of the most important parameters and it provides an approximation of the stresses that occur during penetration. This article presents several simple computational models for borosilicate glass, including single‐state models and dual‐state models (that include an intact strength and a failed strength).

Operation of a two‐stage implosion‐driven hypervelocity launcher in which the launch tube is imploded behind the projectile is examined. In particular, techniques to generate a high phase velocity of implosion are explored, and the technique of using a variable thickness flyer plate with a constant thickness layer of explosive is selected for further investigation. An analytic model, based on the Gurney analysis for flyer plate acceleration, is developed to determine the thickness profile necessary to deliver the desired phase velocity. Finite element simulations and experimental implementation of this approach results in the correct increase in phase velocity along the launch tube, however, the velocity profile does not generate the desired constant acceleration profile.

The conventional spacecraft meteoroids and orbital debris shielding system is the Whipple shield. In general there is a threshold velocity that is just sufficient to shatter the projectile for each system consisting of a projectile and bumper. This velocity is known as the fragmentation onset velocity. To determine the fragmentation onset velocity experimentally, a number of experiments have been conducted with different projectile/bumper configuration. The numerical simulations of fragmentation onset velocity of different material projectile hypervelocity impacts on bumpers with different combination of impact velocities and bumper‐thicker‐to‐projectile‐diameter ratios (t/D) have been performed using the SPH technique of AUTODYN. The spherical projectile materials are aluminum, steel and copper. All bumper material is aluminum alloy 6061‐T6. The simulation velocities were in the range of 1 km/s∼7 km/s. The ratios of t/D were varied from 0.01 to 0.8. The material model contains Mie‐Gruneisen (shock) equat...

We present the results of development of explosive systems for investigating multiple action of solid projectiles upon an obstacle at a moderate impact velocity on the order of 1 km/s. Two types of systems are considered, namely: 1) evacuating shock tube with plane high explosive (HE), 2) ballistic gun with distributed shot of plastic HE. In the first system an acceleration of steel spheres are realized in flux of expanding explosive products. The second system provides the acceleration of a “soft” plastic block with steel spheres having certain mutual orientation. The experiments with these explosive systems testify to higher effectiveness of projectiles penetration into obstacles at multiple impact with a moderate velocity.

The effects of blast‐fragmentation warheads need to be carefully characterized in a variety of applications like passive and active vehicle protection or hard target defeat and TBM defense. With these applications in mind, we have developed a collection of tools called FI‐BLAST (Fast Interface for Blast‐Fragment Load Analysis of Structures). In the present paper we describe the essential part of these tools, namely the close range blast‐fragment model. The meaning of “close range” is here defined as the standoff to a charge at which blast effects can inflict serious damage on massive structures. In order to quantify our model’s range of validity, examples of measured and calculated momentum of bare and confined charges are given in the present paper. Short (L/D = 0.5) and long (L/D = 5) cylindrical charges are included as well as spherical charges. The presented examples demonstrate that the model gives reasonable results in the intended domains of application.

The response of U and Ti alloys has been studied in planar and ballistic impact experiments performed with a 25 mm light‐gas gun. Free surface velocities were monitored by VISAR. The velocity profiles and the damage maps were simulated using 2D AUTODYN™ finite differences code. A modified Steinberg‐Cochran‐Guinan constitutive model was calibrated by simulating planar impact experiments. Bauschinger effect and a single‐parameter spall model were added to describe the unloading and the tensile paths. The ballistic experiments were simulated by using the calibrated model. Softly recovered samples revealed different degrees of spall fracture (planar impact) and of adiabatic shear bands (ballistic experiments). The results demonstrate a possibility to combine experimental and numerical techniques, VISAR and AUTODYN, to calibrate constitutive models of solids in a wide range of shock‐induced strain.

Computational solid mechanics (CSM) for ballistics, as it exists today, does not have predictive capabilities that are comparable to those of computational fluid dynamics (CFD). The most important reason for this is the lack of high quality physical models for the damage and failure processes that occur during high‐speed impact. An approach for modeling impact damage in metals, based on physical modeling of adiabatic shear bands and voids, will be presented. Scaling laws for damage from shear bands have been developed over the past decade from detailed analysis of the thermomechanical processes, and are being adapted for efficient use in large‐scale computations. A similar approach for ductile void growth and spall has also been initiated. This approach is expected to lead to models that are based on the essence of the physics, rather than on fitting of phenomenological models to large databases.

The paper introduces with schemes of possible electromagnetic armor augmentation. The interaction of projectile with a main wall of target after penetration across the pre‐defense layer is of interest here. The same problem is of interest for the current‐carrying elements of electric guns. The theoretical analysis is done in the paper for the impact when the kinetic energy of projectile is enough to create the liquid layer in the crater of the wall’s metal. Spherical head of projectile and right angle of inclination have been taken for consideration. The solution of problem for the liquid layer of metal around the projectile head has resulted a reduction of the resistant properties of wall material under current influence, in view of electromagnetic pressure appearance, what is directed towards the wall likely the projectile velocity vector.

Some of the recent efforts to improve the ballistic performance of lightweight armors utilize functionally graded materials to provide a continuous transition in properties between dissimilar materials. It has been conjectured that the elimination of abrupt acoustic impedance changes may result in beneficial stress wave attenuation. We examine this issue for some idealized one‐dimensional problems in which all materials are linear elastic. Exact solutions are compared with DYNA3D simulations of the same problems.

Walker [1] developed an analytical model for the dynamic response of fabrics to ballistic impact. In the model the force on the bullet is a function of fabric displacement (h) along the axis of impact and the radius (R) of the fabric deformation or ‘bulge”. Ballistic tests against Zylon™ fabric have been performed to measure h and R as a function of time. The results of these experiments are presented and analyzed in the context of the Walker model.

We present a model for the steady-state penetration phase of yawed long rods. The projectile-target interaction is comprised of axial deceleration and erosion due to frontal pressure, and lateral deceleration due to cavity expansion pressure. By solving the resulting ODEs through time-stepping, the evolution of the projectile/crater shape is obtained.

It is well known that impact inclination is detrimental to penetration performance for long-rod projectiles into semi-infinite targets. The drop-off in performance, measured as the depth of penetration normalized by the initial projectile length, is generally attributed to interference of the tail of the projectile with the side walls of the penetration cavity. However, little has been done to study the effect of impact inclination on the performance of long rods penetrating finite targets. A reverse ballistic experiment and three-dimensional numerical simulations are used to examine the effect of impact inclination against an oblique plate. In particular, the interaction of the projectile with the plate, to include asymmetric enlargement of the penetration channel and side loading of the projectile, are examined in the simulations, and compared to experimental results.

When a long-rod penetrator impacts a target at a high yaw angle, interference of the penetrator with the sidewall of a crater is the mechanism for the degraded penetration performance. The yawed penetrator is described as a series of cylindrical elements. Using this assumption, the model considers the effective diameters of the penetrator whether or not it interacts with the crater wall and a revised crater profile is calculated with the effective diameters.

We present a numerical method as applied to flows generated by ignition and combustion of reactive solid particles. Strong shock waves are characteristic features of these flows and must be correctly resolved. For configurations that are typical of Interior Ballistics we adopt a two‐phase, two‐dimensional, axially‐symmetry and unsteady mathematical model. Numerical results for test problems are presented.