Multicriteria evaluation and optimization of the ultrasonic sealing performance based on design of experiments and response surface methodology

Proper closure is an essential packaging quality aspect and can, amongst others, be achieved with ultrasonic sealing. The ultrasonic sealing performance depends on the film type, and the seal settings, such as seal time, applied force and ultrasonic amplitude. Because these parameters are less intuitive than heat seal parameters and optimal settings are undefined for many films, this work presents an efficient approach to evaluate the effect of these settings on the ultrasonic sealing performance. An experimental design defines the experiments to perform. A response surface methodology is then used to model the relation between seal settings and sealing performance. Based on these models, the seal settings are optimized. As there are several criteria to express sealing performance, single‐criteria and multicriteria optimizations are described. The approach was illustrated for a polyethylene terephthalate/linear low‐density polyethylene‐C4 film. The seal settings were optimized to obtain high seal strength, limited ultrasonic horn displacement, and low seal energy. The optimum settings were 0.1 seconds (seal time), 4.32 N/mm (force), and 28.75 μm (amplitude). The predicted optimum strength, horn displacement, and energy were 2.32 N/mm, 40 μm, and 11.66 J, respectively. Besides the optimum, the seal window is also of interest. A broad seal window ensures sufficient seal strength for a wide range of settings. For the polyethylene terephthalate/linear low‐density polyethylene‐C4 film, a strength of ≥90% of the optimum was obtained for 39% of the input combinations within the design space. The presented approach is widely applicable (other films and sealing processes) since it is flexible in the input parameters, design, and responses.     

On the optimal performance of long-rod penetrators subjected to transverse accelerations

The paper deals with theoretical considerations on the conception and optimization of long-rod penetrators with regard to bending strain and penetration efficiency. In a first step we describe a method allowing to design long penetrators in such a manner that given values of bending stress and deflection are met if the rods are subjected to lateral forces. On the assumption of a constant lateral acceleration this results in rods with various dimensions; the aspect ratio remarkably does not remain constant. Then these penetrators are examined for maximum penetration efficiency while considering rods of equal energy. For the case studied the procedure results in an optimum velocity of about 2700 m/s. This demonstrates a fundamental difference in comparison to the optimization process with L/D-scaled penetrators where a much lower optimum velocity (2300 m/s) is obtained. In comparison to the reference penetrator (L/D=34, V=1800 m/s) the optimum penetrator — still at constant stress level and at an impact velocity of 2700 m/s — has of course a reduced mass, but also a reduced length and diameter showing an aspect ratio of 40. The perforation power could be increased by some 17%. On the other hand, the linearly scaled penetrator at constant energy only shows an increase of about 7% in penetration capability if the impact velocity reaches its optimum value at 2300 m/s. The optimization procedure of the energy-efficient penetration of constant-stress projectiles leads to an optimal velocity well in the hypervelocity regime. Furthermore, the special design of the penetrators with constant stress level results in a gain of penetration efficiency.     

Processing strategy for consolidating tungsten heavy alloys for ordnance applications

The environmental concern over the use of depleted uranium (DU) alloys as kinetic-energy (KE) penetrator for high strain rate applications has focussed the interest in tungsten alloys. However, in general, tungsten-based alloys exhibit about 10% lower performance than DU at high strain rate. This paper provides an update on some of the processing strategies adopted for fulfilling this objective.     

Rail launchers to reach hypervelocity

In this paper we present a theoretical study of a 80 mm round bore railgun which allows us, by a current distribution along the projectile, to accelerate a long rod penetrator with a fineness ratio of 30 up to a muzzle velocity of 2500 m/s with an overall efficiency greater than 30%.

This study was started because an optimal impact velocity which allows a given depth of penetration to be reached with a minimum kinetic energy exists for all the targets (homogeneous, composite, structured or reactive). Two years ago we showed that this impact velocity is always greater than 2300 m/s for a heavy alloy penetrator with L/D = 30. For these velocities the electromagnetic rail launchers may have efficiencies over 35 % when classical powder guns have efficiencies about 20 %.     

Towards predictive modelling for concrete

Simulations are becoming an increasingly important part of the weapon design cycle allowing the investigation of more parameters in warhead concepts. This relies on a thorough verification and validation process for the simulation tools, which enables a cost effective approach to down-selecting concepts for full-scale experiments. A key factor in this process applied to the design of warheads to defeat hard (structural) targets is the development of truly physically based material models for geological materials where constants are either derived or measured. The paper describes this general approach and highlights aspects of its initial application to kinetic energy (KE) penetration and suggests areas for future investigation.     

Hypervelocity impact penetration mechanics

Inert dense metal penetrators having a mass and geometry capable of missile delivery offer significant potential for countering underground facilities at depths of tens of meters in hard rock. The proliferation of such facilities among countries whose support for terrorism and potential possession of Weapons of Mass Destruction (WMD) constitutes threats to world peace and U.S. Security. The Defense Threat Reduction Agency (DTRA), in cooperation with the U.S. Army Corps of Engineers, the Department of Energy National Laboratories and private sector R&D firms have pursued an aggressive research effort to explore the attributes of high velocity impact penetrators for countering such facilities. The penetration of crustal rocks with metal rods (such as tungsten or steel alloys) at high velocities involves complex wave propagation phenomena within the rod and inelastic response of both the penetrator and target material. In this paper we examine the sensitivity of penetration depth (for a fixed tungsten alloy mass impacting a limestone target) to impactor velocity, strength and geometry. Analyses are based upon a matrix of first principle finite difference calculations using the Sandia CTH (release 7.1) Shock Physics Code. Results indicate that impact velocity, penetrator yield strength and target yield strength strongly influence the penetration depth. Maximum penetration depth is achieved by a delicate trade off between penetrator kinetic energy and penetrator inelastic deformation (erosion). Numerical analyses for the parameter variations exercised in this study (impact velocities 1–3.5 km/s and penetrator yield strengths of 1–4 GPa) produced penetration depths of a tungsten alloy rod (length 200 cm, diameter 20 cm) which varied from 5.1 m to 28 m in a homogeneous limestone target.     

Hypervelocity penetration modeling: momentum vs. energy and energy transfer mechanisms

Analytic penetration modeling usually relies on either a momentum balance or an energy-rate balance to predict depth of penetration by a penetrator based on initial geometry and impact velocity. In recent years, fairly sophisticated models of penetration have arisen that develop the three-dimensional flow field within a target. Based on the flow field and constitutive assumptions, it is then possible to derive a momentum or an energy-rate balance. This paper examines the use of assumed flow fields within a target created by impact and then examines the resulting predicted behavior based on either momentum conservation or energy conservation. It is shown that for the energy-rate balance to work, the details of the energy transfer mechanisms must be included in the model. In particular, how the projectile energy is initially transferred into target kinetic energy and elastic compression energy must be included. As impact velocity increases, more and more energy during the penetration event is temporarily deposited within the target as elastic compression and target kinetic energy. This energy will be dissipated by the target at a later time, but at the time of penetration it is this transfer of energy that defines the forces acting on the projectile. Thus, for an energy rate balance approach to successfully model penetration, it must include the transfer of energy into kinetic energy within the target and the storage of energy by elastic compression. Understanding the role of energy dissipation in the target clarifies the various terms in analytic models and identifies their origin in terms of the fundamental physics. Understanding the modes of energy transfer also assists in understanding the hypervelocity result that penetration depth only slowly increases with increasing velocity even though the kinetic energy increases as the square of the velocity.     

Novel Flow-Softening and Flow-Anisotropy Approaches to Developing Improved Tungsten Kinetic Energy Penetrator Materials

The penetration performance of uranium alloy kinetic energy (long rod) projectiles are superior to that of equivalent projectiles manufactured from high-density tungsten-based composites. Prior research efforts seeking improvements in the penetration capabilities of tungsten penetrator materials have focussed on increases in the strength, ductility, and toughness of the composites and have not been successful.

Recent studies at the U.S. Army Research Laboratory, however, have established that it is the rate at which the penetrator material softens, under the high-rate, high-pressure deformation it must undergo in the penetration process, not the material's initial strength or ductility, which governs its performance. The rapid flow-softening behavior of uranium alloys, a function of both their mechanical (strain-hardening, strain rate-hardening) and thermal (thermal-softening, etc.) properties, was shown to be responsible for their superior ballistic performances. Other tests demonstrated analogous differences in the performance of different orientations of monocrystal tungsten penetrators, due to the anisotropics in their flow-strengthening and flow-softening behaviors. These results have indicated two novel and promising directions for tungsten penetrator research, broadly categorized as (1) flow-softening and (2) flow-anisotropy approaches. The flow-softening approach seeks to develop an isotropic, plastically unstable behavior, similar to that exhibited by uranium alloys, in new tungsten composites. This approach relies primarily on modifications or replacements of the nickel-based matrix in the currently produced tungsten composites with thermomechanically less stable alloys. Critical issues include the roles and interactions between matrix and tungsten particle phases in the thermomechanical properties of the overall composite, and the nucleation and growth of plastic localizations in these materials. The flow-anisotropy approach seeks to develop directional flow-softening behavior in tungsten-based composites by orienting the tungsten phase.

These efforts to develop tungsten penetrator materials, with performance equalling or surpassing that of depleted uranium, but without the environmental and political concerns associated with producing and fielding uranium ammunition, are reviewed.     

Modeling the high strain rate behavior of titanium undergoing ballistic impact and penetration

Titanium is an important candidate in the search for lighter weight armors. Increasingly, it is being considered as a replacement for steel components. It is also an important component in the application of ceramics to armor systems, especially in armor modules that are capable of defeating kinetic energy penetrators while sustaining little or no penetration of the ceramic element. The best alloy available today for ballistic applications is Ti-6Al-4V, an aerospace grade titanium alloy. The principal deterrent to widespread use of this alloy as an armor material is cost, and a significant portion of the cost is in processing. Consequently, the U.S. Army Research Laboratory undertook a program to study a particular lower cost processing technique [1].

The objectives of this work are to characterize the low-cost titanium alloy by generating constants for the Johnson-Cook (JC) and Zerilli-Armstrong (ZA) strength models, and to use and compare these two models in simulations of ballistic experiments. High strain rate strength data for the low-cost titanium alloy are used to generate parameters for the two models. The approach to fitting the JC parameters follows one previously used successfully to model 2-in thick rolled homogeneous armor (RHA) [2]. The approach to fitting the ZA parameters is based on a method described by Gray et al. [3]. The resulting model parameters are used in the shock physics code CTH [4] to model a Ti-6Al-4V penetrator penetrating a Ti-6Al-4V semi-infinite block at impact velocities up to 2,000 m/s. Similar experiments are performed, and the predictions of the two models are compared to each other and to the experimental results.     

A computational study of the influence of projectile strength on the performance of long-rod penetrators

Two-dimensional numerical simulations were used to explore the penetration capability of long-rods as a function of their strength. Tungsten alloy rods of varying strengths were ‘shot’ at semi-infinite armor steel targets in the velocity range of 1.4–2.2 km/s. It is found that penetration depths versus penetrator strength curves have a maximum which depends on the impact velocity. This effect which, to our best knowledge, has not been reported previously can be explained, at least qualitatively, by considering the deceleration of the rear part of the rod, as its strength increases. This deceleration can lead to a substantial decrease in the velocity of the rear part of the penetrator with the result that its penetration capability is reduced beyond that of a nondecelerating penetrator. The deceleration is a direct consequence of the elastic waves travelling along the back part of the rod with an amplitude which is equal to the strength of the penetrator material.     

Steady state penetration of rigid perfectly plastic targets

The problem of steady penetration by a semi-infinite, rigid penetrator into an infinite, rigid/perfectly plastic target has been studied. The rod is assumed to be cylindrical, with a hemispherical nose, and the target is assumed to obey the Von-Mises yield criterion with the associated flow rule. Contact between target and penetrator has been assumed to be smooth and frictionless. Results computed and presented graphically include the velocity field in the target, the tangential velocity of target particles on the penetrator nose, normal pressure over the penetrator nose, and the dependence of the axial resisting force on penetrator speed and target strength.     

Novel KE penetrator performance against a steel/ceramic/steel target at 0° over the velocity range 1800 to 2900 m/s

This paper presents scale size firings of two novel shape KE penetrators into a steel/ceramic/steel target at four velocities between 1.8 and 2.9 km/s. The two novel shapes were a three piece segmented rod and a telescopic rod/tube. Two unitary rod designs were also included in the assessment. All the penetrators had a similar mass of 60 grams. Test data against semi-infinite RHA was used to obtain the mass effectiveness (E_m) of the ceramic target for each rod shape and velocity. The performance rankings of the penetrators against the ceramic target were found to be similar to those for semi-infinite RHA. In ascending order of penetration depth the ranking was the 10.6 mm unitary rod, segmented rod, telescopic rod and 6.5 mm unitary rod. It was found that the E_m reached a maximum between 2.3 and 2.6 km/s depending on the penetrator type. The E_m values ranged from 1.8 to 2.4. Hydrocode analysis of the experiments gave some valuable insights into the penetration processes of the two novel penetrator designs. Predicted depth of penetration compared very well with experimental values, but enhancements to the physics of the ceramic model are needed in order to simulate cover plate effects. Crown copyright     

动能弹侵彻多层陶瓷靶板数值模拟研究

结合试验对钨合金长杆弹垂直侵彻多层陶瓷靶板进行了三维数值模拟,得出了侵彻的物理图像及各种参量的变化规律。模拟结果中,后置钢靶剩余穿深和陶瓷破碎锥形状与试验基本一致。对于多层陶瓷靶板,每一层都会有漏斗形的破碎锥出现,且这些破碎锥的形状基本一致。随着陶瓷层数的增多,弹体的速度和动能下降速率逐渐变小。比较了相同厚度的多层和单层陶瓷靶板的抗弹性能,结果表明两者的陶瓷破坏形式不同,多层靶板的抗弹性能要优于相同厚度的单层陶瓷靶板,且仅在一定厚度范围内这种优势才较为明显。     

Numerical simulation of segmented penetrator impact

The performance of segmented and continuous penetrators impacting semi-infinite and spaced armor is studied using both the EPIC-2 and HULL hydrocodes. First the performance of a segmented rod is studied, striking semi-infinite armor, for various parameters such as striking velocity, segment spacing and number of segments. Then an actual penetrator configuration proposed by A. Charters is analyzed and the use of normalized penetration is discussed. Finally three-dimensional simulations are presented for segmented and continuous penetrators impacting oblique spaced armor varying such parameters as striking velocity, segment spacing, number of segments, and target thickness.     

Theoretical considerations on the penetration of powdered metal jets

This paper explores some of the theoretical issues encountered when interpreting the penetration behavior of an oilwell perforating charge, whose jet forms from an unsintered powdered metal (PM) liner. Appropriate treatments of the jet's porous compressible nature fill the gap between classical “continuous” and “fully particulated” jet penetration models. Within certain constraints, increasing a penetrator's length (even if by distension) increases its hydrodynamic penetration depth, while reducing its impact pressure; and a porous penetrator penetrates deeper than a non-porous penetrator of the same density, length, and velocity. Dynamic target pressure considerations lead to the conclusion that highly distended, low-velocity, PM jets should penetrate moderate-strength geologic targets effectively. After demonstrating that initial transient shock pressures may be much higher than steady-state penetration pressures, we suggest that initial penetration rates may be higher than the steady-state rates. This, in conjunction with the well-known “residual penetration” phenomenon, indicates that a non-continuous jet's penetration may be strongly influenced by transient effects.     

A model for deformation and fragmentation in crushable brittle solids

A unified framework of continuum elasticity, inelasticity, damage mechanics, and fragmentation in crushable solid materials is presented. A free energy function accounts for thermodynamics of elastic deformation and damage, and thermodynamically admissible kinetic relations are given for inelastic rates (i.e., irreversible strain and damage evolution). The model is further specialized to study concrete subjected to ballistic loading. Numerical implementation proceeds within a finite element context in which standard continuum elements represent the intact solid and particle methods capture eroded material. The impact of a metallic, spherical projectile upon a planar concrete target and the subsequent motion of the resulting cloud of concrete debris are simulated. Favorable quantitative comparisons are made between the results of simulations and experiments regarding residual velocity of the penetrator, mass of destroyed material, and crater and hole sizes in the target. The model qualitatively predicts aspects of the fragment cloud observed in high-speed photographs of the impact experiment, including features of the size and velocity distributions of the fragments. Additionally, two distinct methods are evaluated for quantitatively characterizing the mass and velocity distributions of the debris field, with one method based upon a local energy balance and the second based upon global entropy maximization. Finally, the model is used to predict distributions of fragment masses produced during impact crushing of a concrete sphere, with modest quantitative agreement observed between results of simulation and experiment.     

Impact behaviour of PELE projectiles perforating thin target plates

The first experiments with a penetrator with enhanced lateral efficiency (PELE) were carried out in 1996. The unusual behaviour of the penetrator as it perforates a target can generally be described in three main stages. In the first stage the different kinetic energies of the jacket and the filling lead to the enclosure of the filling material. This induces a pressure rise in the filling, which dilates the surrounding jacket in the second stage. During the last stage the high-density jacket breaks into pieces. When a thin target, as in our case, is perforated, a fourth stage must be added to the other three. This new stage describes the interaction between the filling and the plug, which is produced during the impact. For the lateral efficiency of the PELE, the second stage is the important one. The behaviour in this stage (pressure build-up and radial expansion of the jacket) is dominated by only a few physical parameters. For weak shock waves, these parameters are determined by theoretical consideration. A number of experiments were carried out in the velocity range between 900 and 3000 m/s in order to obtain an experimental database. In the last section a comparison between the physical model and experimental data gives a short outline of the complex impact behaviour of the PELE projectile. The physical model and the experimental data are in good agreement for impact velocities under 1400 m/s. For higher velocities causing stronger shock waves, the theory has to be modified; but the set of physical parameters influencing the terminal ballistic behaviour of PELE remains valid.     

Microscopic models of hardness

Recent developments in the field of microscopic hardness models have been reviewed. In these models, the theoretical hardness is described as a function of the bond density and bond strength. The bond strength may be characterized by energy gap, reference potential, electron-holding energy or Gibbs free energy, and different expressions of bond strength may lead to different hardness models. In particular, the hardness model based on the chemical bond theory of complex crystals has been introduced in detail. The examples of the hardness calculations of typical crystals, such as spinel Si₃N₄, stishovite SiO₂, B₁₂O₂, ReB₂, OsB₂, RuB₂, and PtN₂, are presented. These microscopic models of hardness would play an important role in search for new hard materials.     

Novel penetrator study for defeat of ballistic missile payloads

Aimable kinetic energy rod (KER) warheads are one of the most efficient types of kill enhancement concepts for missile interceptors that exist today. This is because these devices contain minimal explosive, allowing most of its warhead weight to be designed as lethal penetrators. These projectiles are deployed at low velocity and rely on the relative velocity for the penetration power. Static rod deployment testing was performed to investigate the spatial distribution of the spray pattern as well as its deployment velocity. Raytheon's test program deployed over 900 hexagon and cruciform rods in order to understand the physics of their deployment. In conjunction with deployment tests, novel penetrator studies were conducted that determined that novel projectiles are better penetrators when compared with traditional cylindrical rods. A new endgame simulation was developed that predicts damage from closely spaced tumbling rods. This new simulation predicts the synergistic effects from any collateral damage against submunition and bomblet payloads. This new endgame model will allow for an analyst to optimize the rod mass, size, cross-section and L/D ratio against ballistic missile payloads.