A combined numerical and theoretical study on the penetration of a jacketed rod into semi-infinite targets

A combined numerical and theoretical study is conducted herein on the penetration of semi-infinite targets by jacketed rods with different r_j0/r_c0 ratios where r_j0 and r_c0 are the radii of the jacket and the core, respectively. The numerical results show that for smaller r_j0/r_c0 ratios the u–v relationship changes only a little compared to that of unitary long rod penetrator of the same core material, hence, the u–v relationship of unitary (homogeneous) long rod penetration is also applicable for jacketed rod penetration. Model for cratering in semi-infinite targets by jacketed rods is then suggested by using the laws of conversation of mass, momentum and energy, together with the u–v relationship of unitary (homogeneous) long rod penetration and an analytical model for predicting the depth of penetration has also been given for jacketed long rods penetrating semi-infinite targets in co-erosion mode. A new criterion for transition from bi-erosion to co-erosion is proposed. It transpires that the present model is in good agreement with the experimental observations for EN24 steel jacketed tungsten alloy long rods penetrating semi-infinite armor steel targets in terms of crater diameter and penetration depth.     

Experiments with jacketed rods of high fineness ratio

Cylinders of high fineness ratio can show severe integrity and stability problems during acceleration and free-flight phase. The paper describes a method to overcome these problems by adding an envelope to the slender cylinder thereby augmenting the stiffness under flexure. Theoretical considerations treat the pros and cons of jackets with different Young's moduli while looking at various parameters such as maximal deflection, total mass as well as muzzle and impact velocity.

Special emphasis is given to the terminal ballistic efficiency which has been tested using jacketed model penetrators made of tungsten heavy metal with carbon-fibre reinforced plastic (CFRP) and steel envelopes. Some experiments were carried out with cannon-launched CFRP-jacketed tungsten rods of aspect ratios from 45 to 60 being accelerated up to 2000 m/s. In other penetration tests L/D=25 and 40 jacketed penetrators were shot onto homogeneous semi-infinite RHA targets and also spaced targets at 60° incidence at velocities up to 2500 m/s by aid of a light-gas gun.

The experiments with jacketed model penetrators of 3 and 4 mm diameter at high impact velocities showed a good penetration power into homogeneous targets, whereas there is a loss of penetration efficiency into spaced targets of 20% and more. Furthermore it seems that the relative thickness of the jacket should not exceed a certain value in order not to risk a detrimental effect on the penetration performance.     

Comparative analysis of oblique impact on ceramic composite systems

An experimental programme is presented which investigated the performance of oblique, ceramic/metal, bilayer composite armours. The ceramics, alumina and silicon carbide, were backed by either Rolled Homogeneous Armour steel (RHA) or 7000 series aluminium. Using a model scale tungsten penetrator at two velocities (representing current and future ordnance threats) the effect of configuration on ballistic limit or depth of penetration (DOP) areal densities was determined. Areal densities of the DOP targets decreased with increasing ceramic thickness, achieving a minimum at zero residual penetration in the backing. The bilayer targets, loaded at the ballistic limit needed a larger areal density to defeat the penetrator. This areal density also decreased with ceramic thickness but showed a minimum with respect to ceramic thickness, as a result of reduced support by the thinner metallic backing. At 1450ms⁻¹ the most efficient system was found to be a SiC/Al, which demonstrated a 25% weight saving over the monolithic aluminium reference target. The Al-alloy backing performs better than RHA, and SiC better than Al₂O₃.     

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     

Penetration of tungsten alloy rods into shallow-cavity steel targets

This paper presents a combined numerical and experimental study on penetration of tungsten heavy alloy long rods (length-to-diameter ratio of 10) into thick RHA (rolled homogeneous armor) steel plates. The main objective of this study was to establish the effects of a shallow cavity at the front of the steel plate on the penetration process. Three experiments were performed at 1.5 km/s on target plates with a shallow-cavity of 19 mm diameter. These results were compared to existing penetration data obtained for flat plates over a range of 1.1–1.7 km/s. In the code simulations three target configurations were considered: a flat target surface without a cavity and two target plates with different cavity diameters (19 and 11.54 mm). The effect of the target’s free surface on the characteristic time that the penetrator takes to reach quasi-steady-state penetration into the target was investigated for three configurations. Based on the experimental results the effect of the shallow-cavity wall constraint on the penetration process was found to be insignificant. The code results matched the measured depths of penetration within the limits of the experimental accuracy for all configurations examined.     

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.     

The role of dynamic recrystallization in [001] single-crystal W and W-Ta alloy ballistic rod penetration into steel targets

The microstructures of long rod [001] single-crystal penetrators of W grown by CVD and zone melt processing, and W-5% Ta grown by zone melt (ZM) processing, were examined before and after penetration into RHA steel targets, by optical metallography and transmission electron microscopy. The initial Vickers microhardness values for the CVD-W rods was 417 VHN in contrast to 485 VHN for the ZM-W and W-5% Ta rods as a consequence of an order of magnitude larger dislocation density. Both the CVD-W and ZM-W exhibited less dense head flow associated with adiabatic shear bands and dynamic recrystallization (DRX) than the ZM-W-5% Ta, but all penetrators exhibited erosion tube formation in the penetration channel. These tube and erosion debris particles exhibited dense, overlapping shear bands composed of DRX grains or areas with larger, equiaxed grains resulting from residual grain growth. These observations suggest that controlling the penetrator head flow by solute-induced DRX may control penetration.     

Development of impact model for ceramic-faced semi-infinite armour

A model is presented which predicts the penetration of projectiles into ceramic faced semi-infinite armour. This model facilitates the study of material property and armour configuration changes on penetration. The model results correlate well with previously published experimental data for long-rod penetrator impacts with similar armours. Tests with spherical projectiles against ceramic faced semi-infinite armour were carried out, for which the model results correlated reasonably well.     

Deep penetration of polycarbonate by a cylindrical punch

An experimental and theoretical investigation has been conducted to determine the deep penetration response of polycarbonate (PC). A series of low speed deep penetration tests was performed with steel punches to establish the load versus indentation response, and to enable detailed observation of the penetration processes. The effects of nose shape, lubrication and punch diameter were determined. We found that the average pressure on the indenting end of the penetrator is equal to 4–5 times the tensile yield stress and is independent of nose shape and penetrator diameter. A hackle zone of microcracked material extends to a diameter of 1.4 times that of the penetrator, and this is surrounded by a plastic zone which extends to a diameter of 3.5 times that of the penetrator. A model of deep penetration is developed, based on the assumption that the average pressure on the nose of the penetrator equals the pressure required to expand an infinitely small circular cylindrical void to the diameter of the penetrator. The model assumes the existence of an outer elastic zone, a plastic zone and a hackle zone surrounding the penetrator. The predicted penetration pressure and the diameters of the hackle and plastic zones are reasonably accurate.     

Influence of the film thickness on structural and optical properties of CdTe thin films electrodeposited on stainless steel substrates

CdTe thin films of different thicknesses were deposited by electrodeposition on stainless steel substrates (SS). The dependence of structural and optical properties on film thickness was evaluated for thicknesses in the range 0.17–1.5 μm. When the film is very thin the crystallites lack preferred orientation, however, thicker films showed preference for (111) plane. The results show that structural parameters such as crystallite size, lattice constant, dislocation density and strain show a noticeable dependence on film thickness, however, the variation is significant only when the film thickness is below 0.8 μm. The films were successfully transferred on to glass substrates for optical studies. Optical parameter such as absorption coefficient (α), band gap (E_g), refractive index (n), extinction coefficient (k_e), real (?_r) and imaginary (?_i) parts of the dielectric constant were studied. The results indicate that all the optical parameters strongly depend on film thickness.     

管-杆伸出式弹芯垂直侵彻半无限靶机理研究

基于管-杆伸出式弹芯材料满足刚-塑性本构关系及该弹芯在侵彻过程中视为准定常运动等假设,通过分别对头部、管体、管与杆重合部及杆体等不同侵彻阶段的理论分析与推导,建立起该弹芯垂直侵彻半无限靶的简化模型。在1300 m/s~1500 m/s的速度范围内,对该弹芯进行了数值模拟与验证试验研究。通过对模型计算、数值模拟及试验结果之间的对比,表明简化模型及数值模拟方法的可靠性,得出了该弹芯垂直侵彻靶板所产生弹坑的形貌特征与形成机制,以及该弹芯在侵彻中的相对优势情况与侵彻深度随速度的变化规律。     

Penetration of semi-infinite AD995 alumina targets by tungsten long rod penetrators from 1.5 to 3.5 km/s

The performance of confined AD995 Alumina against L/D 20 tungsten long rod penetrators was characterized through reverse ballistic testing. The semi-infinite ceramic target was cylindrical with a diameter approximately 30 times the rod diameter. The target configuration included a titanium confinement tube and a thick, aluminum coverplate. The impact conditions ranged from 1.5 to 3.5 km/s with three or four tests performed at each of six nominal impact velocities. Multiple radiographs obtained during the penetration process allowed measurement of the penetration velocity into the ceramic and the consumption velocity, or erosion rate, of the penetrator. The final depth of penetration was also measured.

Primary penetration approaches 75% of the hydrodynamic limit. Secondary penetration is very small, even at 3.5 km/s. The effective R_t value decreased from 90 kbar to 70 kbar with increasing impact velocity over the range of velocities tested.

In tests in which the ratio of target diameter to penetrator diameter was reduced to 15, R_t, dropped by 30% to 50%. When a steel coverplate was used, total interface defeat occurred at 1.5 km/s.     

Optimizing conditions for preparation of MnOx/RHA catalyst particle for the catalytic oxidation of NO

Rice husk ash (RHA) was utilized as support to synthesize MnOx/RHA catalyst by incipient wetness impregnation. In order to detailedly investigate the influence of preparation variables on the catalytic activity of MnOx/RHA for NO oxidation, the quadratic regression orthogonal rotation design (QRROD) was employed. An empirical model was developed to correlate preparation variables with the conversion of NO to NO₂. The surface species and morphology of the catalyst were also analyzed by SEM and XRD, respectively. It was found that most of MnOx supported on RHA were granular with micron-size and in the form of amorphous phase. The preparation variables except for calcination time (x₂) had significant effect on the catalytic activity of MnOx/RHA. The model could accurately describe the relationship between the preparation variables and NO conversion through the analysis of variance (ANOVA) and the comparison of experimental results and predicted results. The particles size of MnOx was increased from 0.1 to 1.0 μm, as the calcination temperature was raised from 200 to 800 °C, and the fraction of crystal MnOx also increased. The surface structure of RHA was markedly affected by incineration temperature. With incineration temperature increasing, the surface structure becomes compacter.     

Nonsteady penetration of longs rods into semi-infinite targets

This paper describes a new one-dimensional theory of nonsteady penetration of long rods into semi-infinite targets. The target is viewed as a “finite mass” that resides within the semi-infinite target space. Thus, an equation of motion for the target was constructed so that together with erosion and penetrator deceleration equations, expressions for penetration rates and depths were obtained. Forces acting on the target and penetrator are defined in terms of only ordinary strength levels usually associated with dynamic properties or work-hardened material states. Also, the concept of critical impact velocity was used to establish the onset of penetration in this formulation. This penetration equation corresponds in exact form to hydrodynamic theory in the limits of small strengths and/or high impact velocity. Results for penetration rates agree well with hydrocode calculations, and predicted penetrations agree with experimental data over an impact velocity range of 0–5,000 m/s.     

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.     

Ultrasonic inspection of a welded stainless steel pipe to evaluate residual stresses through thickness

This study investigates ultrasonic method in axial and hoop stress measurement through thickness of an austenitic stainless steel pipe. Longitudinal critically refracted (L_CR) waves are employed to measure the welding residual stresses while outer and inner surfaces of the pipe are inspected by using different frequency range of ultrasonic transducers. The acoustoelastic constant is measured on a plate with the same material and thickness of the investigated pipe to keep the pipe intact. Welding process of the pipe is simulated by a 3D finite element (FE) model which is validated by hole-drilling method performed on 25 points. The residual stresses calculated by FE simulation are then compared with those obtained from the ultrasonic measurement while a good agreement is observed. It is demonstrated that the residual stresses through thickness of the stainless steel pipe can be evaluated by combining FE and L_CR method (known as FEL_CR method).     

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.     

Influence of the melt thermal conductivity on temperature fields in aluminum oxide upon heating by concentrated laser radiation

The influence of the melt thermal conductivity Λ_m on the formation of temperature fields upon heating and melting of a plane aluminum oxide layer by CO₂ laser radiation with a flux density q from 200 to 3000 W/cm² is investigated using a rigorous model of transient combined radiative and conductive energy transfer. The maximum heating time is 100 s. Parameter Λ_m varies from 1.5 to 3 W/(m K). Absorption coefficient k _l for the laser radiation is assumed to be 1000 cm^–1. The formation of a two-phase region,which exists for a short time, has been observed in the initial melting stage at a depth less than the penetration depth of the heating laser radiation. Maxima of the heated-surface temperature and melt thickness (not coinciding in time) are found at q < 600 W/cm². The melt thickness and its value at the maximum depend only slightly on q, while parameter Λ_m significantly affects the melt thickness at the maximum and during the entire heating process. It is shown that similar temperature profiles are established in the solid phase at different Λ_m values while approaching the quasi-steady state due to large values of the melt absorption coefficient in the wavelength range that is most energetically important for radiative transfer. The melt thermal conductivity affects only slightly the temperature of the “cold” surface that is opposite the melt.     

Stress induced and concentration dependent diffusion of nitrogen in plasma nitrided austenitic stainless steel

The nitrogen transport mechanism in austenitic stainless steel during plasma nitriding at moderate temperatures (around 400 °C) is considered by stress induced diffusion model. The model involves diffusion of nitrogen in presence of internal stresses gradient induced by penetrating nitrogen as the next driving force of diffusion after concentration gradient. Furthermore, in the present work it was found that nitrogen diffusion coefficient vary with nitrogen concentration according to well-known Einstein-Smoluchowski relation D(C_N) = f(1/C_N). Nitrogen depth profiles in nitided AISI 316L steel at T = 400 °C for 1, 3 and 8 h calculated on the basis of this model are in good agreement with experimental nitrogen profiles. The dependencies of nitrogen flux and nitriding time on nitrogen concentration, nitrogen surface concentration and penetration depth are analyzed by proposed model. It is shown that, with the increase of nitriding time the compositionally-induced stresses and thickness of stressed steel layer increases.     

The influence of projectile hardness on ballistic performance

The ballistic performance of 17 penetrator materials, representing 5 distinct steel alloys treated to various hardnesses along with one tungsten alloy, has been investigated. Residual lengths and velocities, as well as the ballistic limit velocities, were determined experimentally for each of the alloy types for length-to-diameter (L/D) ratio 10 projectiles against finite-thick armor steel targets. The target thickness normalized by the projectile diameter (T/D) was 3.55. For some of the projectile types, a harder target, with the same thickness, was also used. It was found that the ballistic limit velocity decreases significantly when the projectile hardness exceeds that of the target. Numerical simulations are used to investigate some of the observed trends. It is shown that the residual projectile length is sensitive to projectile hardness; the numerical simulations reproduce this experimental observation. However, the observed trend in residual velocity as a function of projectile hardness is not reproduced in the numerical simulations unless a material model is invoked. It is assumed that the plastic work per unit volume is approximately a constant, that is, there is a trade off between strength and ductility. Using this model, the numerical simulations reproduce the experimentally observed trend.