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IN THIS ISSUE


Foreword

J. Appl. Mech. 2011;78(5):050501-050501-1. doi:10.1115/1.4004308.
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This issue of the Journal of Applied Mechanics contains twenty-three scientific papers presented at the 26th ISB, organized by the National Defense Industrial Association (NDIA, www.ndia.org), under the auspices of the International Ballistics Society (IBS, www.ballistics.org).
  • Symposium Chairman: Dr. Ernest L. Baker, US Army Materiel Command
  • Symposium Vice Chairman: Dr. Douglas Templeton, US Army Materiel Command
  • IBS Chairman: Mr. Jack Riegel III, R3 Technology, Inc., Springfield, VA, USA
Topics: Ballistics
Commentary by Dr. Valentin Fuster

Research Papers

J. Appl. Mech. 2011;78(5):051001-051001-8. doi:10.1115/1.4004279.

The multilevel stepped-wall chamber is designed to study the combustion stability control mechanism of the bulk-loaded liquid propellant gun (BLPG). The cold state experiment of the interaction of the high speed gas jet with liquid medium is conducted by means of high speed digital camera system. The simulated small caliber bulk-loaded liquid propellant combustion propulsion device is designed to study the effect of the stepped-wall chamber size on the combustion stability. The experimental results indicate that, the stepped-wall structure can restrain the expansion randomness of the Taylor cavity and leads smooth expansion at each step. In 4 stepped-wall chamber with ΔD/L = 3/40, the interior ballistic performance of BLPG is stable and the consistency of the p-t curves is good. Two-dimensional unsteady model is developed based on the BLPG combustion propulsion experiment. The numerical simulation results coincide well with the experiment.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051002-051002-6. doi:10.1115/1.4004292.

The traveling charge (TC) concept is theoretically capable of producing higher muzzle velocities without a large increase in maximum operating pressure, compared with the conventional charge. This work presents experimental and numerical studies on a 35 mm test gun system using liquid fuels as traveling charge. Eight firings with 2 different configurations of booster charge and traveling charge are performed in this paper. The firing experimental results indicate that the liquid traveling charge configuration performs better, in terms of increased muzzle velocity, than a conventional propellant charge by approximately 94 m/s, corresponding to about 8% velocity increase. A mathematical model for the two-phase flows in the 35 mm test gun system using liquid fuels as traveling charge is established and simulated by using the two-phase flow method and computational fluid dynamics technology. The mathematical model for the two-phase gas-dynamical processes consists of a system of first-order, nonlinear coupled partial differential equations. An adaptive grid generation algorithm is developed to account for the expansion of the computational domain due to the motion of the system’s payload in the tube. The numerical code is well validated by comparing its predictions with the experimental results. The calculated pressure-time profiles and projectile muzzle velocity are in good agreement with the experimental data. The numerical results show that the mathematical model developed gives the correct trend and can provide useful calculated parameters for the structural design of liquid traveling charge.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051003-051003-9. doi:10.1115/1.4004326.

This article presents a computational constitutive model for glass subjected to large strains, high strain rates and high pressures. The model has similarities to a previously developed model for brittle materials by Johnson, Holmquist and Beissel (JHB model), but there are significant differences. This new glass model provides a material strength that is dependent on the location and/or condition of the material. Provisions are made for the strength to be dependent on whether it is in the interior, on the surface (different surface finishes can be accommodated), adjacent to failed material, or if it is failed. The intact and failed strengths are also dependent on the pressure and the strain rate. Thermal softening, damage softening, time-dependent softening, and the effect of the third invariant are also included. The shear modulus can be constant or variable. The pressure-volume relationship includes permanent densification and bulking. Damage is accumulated based on plastic strain, pressure and strain rate. Simple (single-element) examples are presented to illustrate the capabilities of the model. Computed results for more complex ballistic impact configurations are also presented and compared to experimental data.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051004-051004-10. doi:10.1115/1.4004327.

The subdetonative propulsion mode using thermal choking has been studied with a one-dimensional (1D) real gas model that included projectile acceleration. Numerical results from a control volume analysis that accounted for unsteady flow effects established that the thrust coefficient versus Mach number profile was lower than that obtained with a quasi-steady model. This deviation correlates with experimental results obtained in a 38-mm-bore ram accelerator at 5.15 MPa fill pressure. Theoretical calculations were initially carried out with the assumption that the combustion process thermally choked the flow about one projectile length behind the projectile base. Thus the control volume length used in this 1D modeling was twice the projectile length, which is consistent with experimental observations at velocities corresponding to Mach number less than 3.5. Yet the choice of the length of the combustion zone and thus the control volume length remains a key issue in the unsteady modeling of the ram accelerator. The present paper provides a refinement of the unsteady one-dimensional model in which the effect of control volume length on the thrust coefficient and the projectile acceleration were investigated. For this purpose the control volume length determined from computational fluid dynamics (CFD) as a function of projectile Mach number was applied. The CFD modeling utilized the Reynolds-averaged Navier-Stokes (RANS) equations to numerically simulate the reacting flow in the ram accelerator. The shear-stress transport turbulence and the eddy dissipation combustion models were used along with a detailed chemical kinetic mechanism with six species and five-step reactions to account for the influence of turbulence and rate of heat release on the length of the combustion zone. These CFD computational results provided Mach number dependent estimates for the control volume length that were implemented in the 1D modeling. Results from the proposed improved 1D unsteady modeling were compared and validated with ram accelerator experimental data with significant improvements in terms of the predicted thrust dependence on Mach number.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051005-051005-7. doi:10.1115/1.4004330.

An overview of the Magnus effect of projectiles and missiles is presented. The first part of the paper is devoted to the description of the physical mechanisms governing the Magnus effect. For yawing and spinning projectiles, at small incidences, the spin induces a weak asymmetry of the boundary layer profiles. At high incidences, increased spin causes the separated vortex sheets to be altered. Vortex asymmetry generates an additional lateral force which gives a vortex contribution to the total Magnus effect. For finned projectiles or missiles, the origin of the Magnus effect on fins is the main issue. There are two principal sources contributing to the Magnus effect. Firstly, the interaction between the asymmetric boundary layer-wake of the body and the fins, and secondly, the spin induced modifications of the local incidences and of the flow topology around the fins. The second part of the paper is devoted to the numerical prediction and validation of these flow phenomena. A state of the art is presented including classical CFD methods based on Reynolds-averaged Navier–Stokes (RANS) and unsteady rans (URANS) equations, and also hybrid RANS/LES approach called ZDES. This last method is a recent advance in turbulence modeling methodologies that allows to take into account the unsteadiness of the flow in the base region. For validation purposes computational results were compared with wind tunnel tests. A wide range of angles of attack, spin rates, Reynolds and Mach numbers (subsonic, transonic and supersonic) have been investigated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051006-051006-11. doi:10.1115/1.4004398.

Explosive reactive armor (ERA) is a type of add-on armor that usually consists of tiles made of two metal plates with an explosive layer in between. The ERA is placed at a certain distance from the main armor to enhance its performance. ERA design is optimized based on the required effectiveness of the tiles. Various methods of defining ERA effectiveness are described. The effectiveness parameters of the mass-flux model and its derivatives, the effect of material properties, the escape length of the jet tip precursor, the explosive layer thickness, and the edge effects are analyzed, and correlations between them are presented. Analysis results are compared with available experimental data and a very good correlation is found.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051007-051007-13. doi:10.1115/1.4004280.

Ballistic tests were performed on single-yarn, single-layer and ten-layer targets of Kevlar® KM2 (600 and 850 denier), Dyneema® SK-65 and PBO® (500 denier). The objective was to develop data for validation of numerical models so, multiple diagnostic techniques were used: (1) ultra-high speed photography, (2) high-speed video and (3) nickel-chromium wire technique. These techniques allowed thorough validation of the numerical models through five different paths. The first validation set was at the yarn level, where the transverse wave propagation obtained with analytical and numerical simulations was compared to that obtained in the experiments. The second validation path was at the single-layer level: the propagation of the pyramidal wave observed with the high speed camera was compared to the numerical simulations. The third validation consisted of comparing, for the targets with ten layers, the pyramid apex and diagonal positions from tests and simulations. The fourth validation, which is probably the most relevant, consisted of comparing the numerical and experimental ballistic limits. Finally for the fifth validation set, nickel-chromium wires were used to record electronically the waves propagating in the fabrics. It is shown that for the three materials the waves recorded during the tests match well the waves predicted by the numerical model.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051008-051008-8. doi:10.1115/1.4004333.

An experimental technique is demonstrated whereby the dynamic deflection of a thin plate or combination of plates, impulsively loaded by the blast of an explosive charge, can be characterized. A blast pendulum measures the resulting impulse simultaneously. The technique utilizes a cylindrical adapter that is fixed onto the blast pendulum into which a helical array of laser diode and receiver pairs are fitted. The output of the receivers is electronically coupled and a cascade voltage plot is obtained as the deforming plate interrupts the aligned light beams. It is found that the technique yields good results of the dynamic motion of the plates as long as the deformation of the specimen is symmetrical.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051009-051009-6. doi:10.1115/1.4004277.

Guided projectile terminal phase against target at ground level is investigated using an adjoint simulation. A pseudo-optimal projectile navigation gain is looked for against a target disturbing the projectile guidance. The use of counter-measures is “modeled” as a suddenly detected target abrupt motion during the guidance terminal phase. The miss distances obtained are studied and the projectile optimal navigation gain is chosen based on the maximum tolerated miss distance.

Topics: Projectiles
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051010-051010-12. doi:10.1115/1.4004278.

A series of blast loading experiments are performed with the aim of providing experimental data for the development and adjustment of numerical tools needed in the modeling of concrete elements subjected to blast. To this end, an experimental setup that allows testing up to four concrete elements simultaneously under the same blast load is developed. Altogether four detonation tests are conducted, in which 12 slabs of two different concrete types are subjected to the same blast load. Results of the experimental program are validated by numerical simulation using two different material models for the prediction of concrete behavior. Major assets of the experimental setup presented are the reduction of scattering on detonation tests and its cost effectiveness. Results from tests and numerical simulations suggest that the ability of reinforced concrete structures of withstanding blast loads is primarily governed by their tensile strength.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051011-051011-10. doi:10.1115/1.4004281.

Glass impact experiments were designed at three different scales—0.22-cal, 0.375-cal, and 0.50-cal—named after the diameter of the bullets. Four experimental series were conducted at the three scale sizes: (1) Lexan® -only experiments; (2) monoblock glass experiments; (3) single impact bonded glass experiments, and (4) multi-hit experiments. The experiments were conducted to obtain residual velocity Vr as a function of impact (striking) velocity Vs , including sufficient partial penetrations to calculate a ballistic limit velocity V50 . The Vs – Vr data were fit to the Lambert equation to obtain another estimate of V50 . The objective of the experiments was to investigate whether a time dependency exists in glass damage/failure for ballistic experiments, and if so, quantify this dependence. No scale effect was observed in experimental results for the Lexan® -only experiments. But a variety of scale effects were observed in the glass impact experiments, suggesting that failure is time dependent within the timeframe of ballistic events.

Topics: Glass , Bullets , Failure
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051012-051012-8. doi:10.1115/1.4004282.

This paper describes research into the suitability of the explosive FOX-7 in the development of insensitive munitions. The analysis of experimental cylinder test data to generate a JWL equation of state and Gurney energy is described and the results compared with other published data. The JWL and Gurney energy are then used in analytical and hydrocode simulations to assess FOX-7 performance in fragmenting and slow stretching jet warheads and compared against other high performance explosives. The results of experiments to validate the simulations are presented and discussed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051013-051013-10. doi:10.1115/1.4004283.

Dynamic crack propagation across a perpendicular interface in a glass specimen was investigated to understand the interaction between the crack and the interface under impact loading. The glass specimen was composed of two glass plates in an edge-to-edge configuration with an adhesive layer in between. One of the plates had a notch for a plastic projectile to strike. A single crack developed from the notch tip, and propagated perpendicularly into the interface. The patterns of crack propagation across the interface depend on the adhesive conditions on the interface. Within a range of impact speeds, the crack is arrested at the interface without any adhesive. The crack passes across a firmly bonded interface with little obstruction by the interface. The crack branches into multiple cracks after it passes through a thicker interface filled with adhesive. Projectiles having higher kinetic energies cause more severe crack branching after the crack extends into the second glass plate.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051014-051014-7. doi:10.1115/1.4004284.

In laser ignition systems, to ignite the propellant, the laser has to be transmitted into chamber through an optical window. If the optical window is destroyed by high pressure or high temperature or contaminated by the black powder residue, the ignition system will fail in further firings. The sapphire window can withstand the high pressure and high temperature of the ballistic cycle, but it is necessary to keep the window clean for the laser to transmit repeatedly. In modular charge systems or fully combustible cartridge cases, there is no place to put a shield window as in ammunition with stub base; thus a new contamination prevention method is put forward. In this method, the hydrodynamic force is used to divert the gas flow in a cavity located in the breech to avoid contact with the optical window and prevent it from being contaminated. To verify the effectiveness of this structure, a three-dimensional unsteady discrete phase model (DPM) coupled with an interior ballistic process was established. The simulation results indicated that the flow jet from the direct orifice was diverted, and particle debris did not contaminate the optical window due to the hydrodynamic force. Various factors influencing the contamination prevention effect were discussed, and the structure parameters were optimized.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051015-051015-7. doi:10.1115/1.4004285.

One of the key technologies of stacked projectile weapons is projectile positioning. However, the present projectile positioning structures have their respective advantages and shortcomings. A new structure based on the self-locking principle is put forward in this paper and verified as feasible by static analysis if the proper material and structural parameters are chosen. In order to check the strength and verify the feasibility of the structure under launch conditions, the multibody contact finite element model of the structure is established, coupled with dynamic load in the interior ballistic cycle. According to simulations and analysis, the projectile positioning structure is feasible and the strength of the projectile can meet the strength requirement for launch conditions. For different maximum static friction coefficients, simulations show that an increase in the maximum static friction coefficient between the contact surfaces of the positioning ring and barrel improves the positioning performance, but an increase in the maximum static friction coefficient between the contact surfaces of the positioning ring and projectile worsens. On the basis of great computation, it is found that an increase in the upper thickness and height of the positioning ring improves the positioning performance, but an increase in the lower thickness worsens the positioning performance. Further, a lower thickness affects the positioning performance more greatly. As a result, the positioning ring will be thin and light to improve the positioning performance. Compared with other positioning structures, the new structure has little influence on the ballistic performance and is a good application prospect.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051016-051016-9. doi:10.1115/1.4004293.

Complex phenomena occur in a combustion chamber during a ballistic cycle. From the ignition of the black powder in the primer to the exit of the projectile through the muzzle, two-phase gas-powder mix undertakes various transfers in different forms. A detailed comprehension of these effects is fundamental to predict the behavior of the whole system, considering performances and safety. Although the ignition of the powder bed is three-dimensional due to the primer’s geometry, simulations generally only deal with one- or two-dimensional problem. In this study, we propose a method to simulate the two-phase flows in 1, 2 or 3 dimensions with the same system of partial differential equations. A one-pressure, conditionally hyperbolic model [1] was used and solved by a nonconservative finite volume scheme associated to a fractional step method, where each step is hyperbolic. We extend our study to a two-pressure, unconditionally hyperbolic model [2] in which a relaxation technique was applied in order to recover the one-pressure model by using the granular stress. The second goal of this study is also to propose an improved ignition model of the powder grains, by taking into account simplified chemical kinetics for decomposition reactions in the two phases. Here we consider a 0th -order solid decomposition and an unimolecular, 2nd -order gas reaction. Validation of the algorithm on several test cases is presented.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051017-051017-7. doi:10.1115/1.4004294.

The present study investigates the effects of in bore-yaw phenomenon on lateral throw-off and aerodynamic jump behavior for small caliber rotational symmetric (both in configuration and mass distribution) projectiles launched horizontally at supersonic firing speeds and various altitudes from high-subsonic air vehicles. The ammunition used is the caliber .50 API M8 bullet type firing from M2 machine automatic gun. The projectile is considered to be eccentrically engraved, tilted as it enters the rifling, and it is assumed that the tilt persists throughout its passage through the rifled barrel of the used weapon system. The modified linear 6-DOF flight simulation modeling is applied for the bullet free-flight trajectory predictions. The coupled epicyclic pitching and yawing motion analysis for the first 100 m of the examined trajectories are taken into account.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051018-051018-8. doi:10.1115/1.4004295.

In the design and development of solid propellant rocket motors, the use of numerical tools able to predict the behavior of a given motor is particularly important in order to decrease the planning times and costs. This paper is devoted to present the results of the internal ballistics numerical simulation of the NAWC tactical motor n. 6, from ignition to burn-out, by means of a quasi-one-dimensional unsteady numerical simulation model, SPINBALL, coupled with a three-dimensional grain burnback model, GREG. In particular, the attention is focused on the effects on the SRM behavior of the erosive burning, total pressure drops and the cause of the pressure overpeak occurring during the last part of the ignition transient. The final objective is to develop an analysis/simulation capability of SRM internal ballistics for the entire combustion time with simplified physical models, in order to have reduced the computational costs, but ensuring an accuracy greater than the one usually given by zero-dimensional models. The results of the simulations indicate a very good agreement with the experimental data, as no attempt of submodels calibration is made, enforcing the ability of the proposed approach to predict the SRMs internal flow-field conditions. The numerical simulations show that NAWC n. 6 internal ballistics is completely led by the erosive burning, that is the root cause of the pressure peak occurring immediately after the SRM start-up.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051019-051019-11. doi:10.1115/1.4004296.

An experimental and numerical study of ballistic impacts on steel plates at various temperatures (700 °C, 400 °C and room temperature) has been carried out. The motivation for this work is the blade-off event that may occur inside a jet engine turbine. However, as a first attempt to understand this complex loading process, a somewhat simpler approach is carried out in the present work. The material used in this study is the FV535 martensitic stainless steel, which is one of the most commonly used materials for turbine casings. Based on material test data, a Modified Johnson-Cook (MJC) model was calibrated for numerical simulations using the LS-DYNA explicit finite element code. To check the mesh size sensitivity, 2D axisymmetric finite element models with three different mesh sizes and configurations were used for the various temperatures. Two fixed meshes with 64 and 128 elements over the 2 mm thick plate and one mesh with 32 elements over the thickness with adaptive remeshing were used in the simulations. Both the formation of adiabatic shear bands in the perforation process and the modeling of the thermal softening effects at high temperatures have been found crucial in order to achieve good results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051020-051020-5. doi:10.1115/1.4004297.

The geometry, density and velocity of a typical small caliber bullet, are the main factors that stabilize its flight path, range and the impact force; thus the weight variations can indicate the presence of geometrical irregularities or damages of the bullet core, affecting its dynamic characteristics. Computational finite element method (FEM) with the computational fluid dynamic (CFD) module was used for the numerical simulation of 7.62 mm bullets with partial core, subjected to different air flow conditions. Schlieren images were obtained and with the flow visualization principle, the behavior of the projectile during its flight path was determined. The results of the simulations and the experiments showed that in certain cases, bullets with partial core maintain a stable spin during flight without a considerable variation in its range, keeping constant speed conditions with respect to the full core bullets. The importance of this analysis is found in the fact that post processing activities can be implemented in certain ammunitions with imperfections to improve their use.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051021-051021-7. doi:10.1115/1.4004328.

Fabrics are an extremely important element of body armors and other armors. Understanding fabrics requires understanding how yarns deform. Classical theory has shown very good agreement with the deformation of a single yarn when impacted transversely. However, the impact speed at which a yarn breaks based on this classical theory is not correct; it has been experimentally noted that yarns break when impacted at a lower speed. This paper explores the mechanism of yarn breakage. The problem of the transverse strike of a yarn by a flat-faced projectile is analytically solved for early times. It is rigorously demonstrated that when a flat-faced projectile strikes a yarn, the minimum impact speed that breaks the yarn will always be at least 11% less than the classical-theory result. It is further shown that when the yarn in front of the projectile “bounces” off the projectile face due to the impact, the impact speed that breaks the yarn is further reduced. If the yarn bounces elastically off the projectile face at twice the impact velocity (the theoretical maximum), there is a 40% reduction in the projectile impact speed that breaks the yarn.

Topics: Yarns , Projectiles , Waves
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051022-051022-7. doi:10.1115/1.4004332.

As modern helmets have become quite capable of defeating the penetration capabilities of ballistic threats, Soldiers may experience head injuries due to blunt trauma caused by helmet back face deformation (BFD). Possible resulting injuries include skull fracture, hematoma, concussion, contusion, diffuse axonal injury, etc. Some of these injuries have been associated with traumatic brain injury. In order to assess potential injury mechanisms prior to fielding new helmets, we have developed a means to experimentally replicate and measure helmet BFD that can be correlated to injury criteria. In this study, helmet performance test methodology is developed using a digital image correlation (DIC) technique. DIC provides the capability to measure dynamic displacements, thereby providing the ability to calculate deformation, velocity, and acceleration rates. We have shown that digital image correlation is an experimentation technique that accurately captures BFD area and rate of deformation for impacts against combat helmets. We used the DIC data to calculate a new metric; the available energy that could potentially impact a Soldier’s head. Our study shows that DIC data upholds the hypothesis that helmet BFD mechanically loads the skull similar to a direct impact from a less-than-lethal projectile or blunt object impact. The available energy obtained from DIC measurements was used to calculate the blunt criterion (BC) for helmet standoff distances of 12.7 mm (0.5 in) and 19.1 mm (0.75 in), which in turn can provide a prediction of the probability of abbreviated injury scale (AIS) levels and, in particular, skull fracture. DIC can be used to provide dynamic helmet performance data that will allow increased understanding of BFD and quantitative assessment and validation of helmet performance results. Knowledge of the conditions leading to head trauma obtained through DIC experimentation should enable the selection of new energy-absorbing materials for helmets; thus, allowing new helmet design candidate performances to be objectively evaluated. Test data and characterization of helmet response could then be used to achieve improved warfighter survivability.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2011;78(5):051023-051023-9. doi:10.1115/1.4004310.

Transverse impact response of a linear elastic Kevlar® KM2 fiber yarn was determined at various striking speeds from Hopkinson bar and gas gun experiments incorporated with high-speed photography techniques. Upon transverse impact, a triangle shape was formed in the fiber yarn. Both longitudinal and transverse waves were produced and propagated outwards the fiber yarn. Both the angle of the triangle and Euler transverse wave speed vary with striking speeds. The relationship between the Euler transverse wave speed and the striking speed was determined. The transverse impact response of the fiber yarn was also analyzed with a model, which agrees well with the experimental results. The model shows that the longitudinal wave speed is critical in the ballistic performance of the fiber yarn. At a certain striking speed, a higher longitudinal wave speed produces a higher Euler transverse wave speed, enabling us to spread the load and dissipate the impact energy faster, such that the ballistic performance of the fiber yarn is improved.

Topics: Fibers , Yarns , Waves
Commentary by Dr. Valentin Fuster

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