Experiments on the penetration of thin long-rod projectiles into thick long-cylindrical borosilicate targets under pressure-free polycarbonate,aluminum and steel confinements

It is well established that confinement pressure inhibits comminution and fragment-flow during projectile penetration of ceramics. Here, a high-pressure gas gun is used to investigate the role of confinement wave impedance on the failure kinetics of ceramics during penetration. Tool-steel rods of fixed lengths and L/D ratios of 12, 16 and 24 impact and penetrate unconfined borosilicate cylinders and those under pressure-free polycarbonate, aluminum and steel confinements. The cylinders are all of the same size with projectile–target diameter ratios lying between 12 and 24, and projectile–target length ratio equal to 8. A stress wave controlling confinement is introduced to approximate an elastic waveguide set-up. Penetration depths into the comminuted borosilicate and the corresponding fragment jet diameters are measured between 168 and 1038 m/s impact velocities with high-speed photography and a witness plate. Expectedly, target resistive pressure increases with confinement impedance but decreases with projectile diameter. However, cylinders confined by steel are less resistive to penetration than those confined by aluminum. This anomalous behavior suggests that comminution increases with dynamic compression and it may be related to densification and the failure wave which occur in silica glasses above certain critical pressures. On this basis, comminution threshold conditions are determined and found to depend strongly on the propagation of stress waves across the target–confinement interface. These results are useful for material selection of impact/penetration-resistant structures with ceramic cores.     

Wave propagation in transversely impacted composite laminates

An experimental investigation was conducted to determine wave-propagation characteristics, transient-strain distributions and residual properties for unidirectional and angle-ply boron/epoxy and graphite/epoxy laminates impacted with silicon-rubber projectiles at velocities up to 250 ms^?1 (820 ft/s). Tests were conducted at normal and 45-deg oblique impact. Strain signals obtained from surface and embedded strain gages were recorded and analyzed to determine the types of waves, propagation velocities, peak strains, strain rates and attenuation characteristics. The predominant wave is a flexural on propagating at different velocities in different directions. The flexural wave velocity is higher in the higher-modulus direction. In general, measured wave velocities were higher than theoretically predicted. The amplitude of the in-plane wave is less than ten percent of that of the flexural wave. Peak strains and strain rates in the transverse to the (outer) fiber direction are much higher than those in the direction of the fibers. Strain rates up to 640 s^?1 were measured. Under oblique 45-deg impact, the flexural wave is still the predominant one. Peak strains under this oblique impact range between 36 and 56 percent of those under normal impact of the same velocity. Residual elastic properties and strength were measured around the point of impact. The most significant result was a reduction in the transverse strength of the unidirectional laminates. The dynamics of impact were also studied with high-speed photography. The projectile is completely flattened within 50–70 μs and the total contact time is of the order of 300 μs.     

Synchronous Full-Field Strain and Temperature Measurement in Tensile Tests at Low,Intermediate and High Strain Rates

Tensile tests with simultaneous full-field strain and temperature measurements at the nominal strain rates of 0.01, 0.1, 1, 200 and 3000 s^?1 are presented. Three different testing methods with specimens of the same thin and flat gage-section geometry are utilized. The full-field deformation is measured on one side of the specimen, using the DIC technique with low and high speed visible cameras, and the full-field temperature is measured on the opposite side using an IR camera. Austenitic stainless steel is used as the test material. The results show that a similar deformation pattern evolves at all strain rates with an initial uniform deformation up to the strain of 0.25–0.35, followed by necking with localized deformation with a maximum strain of 0.7–0.95. The strain rate in the necking regions can exceed three times the nominal strain rate. The duration of the tests vary from 57 s at the lowest strain rate to 197 μs at the highest strain rate. The results show temperature rise at all strain rates. The temperature rise increases with strain rate as the test duration shortens and there is less time for the heat to dissipate. At a strain rate of 0.01 s^?1 the temperature rise is small (up to 48 °C) but noticeable. At a strain rate of 0.1 the temperature rises up to 140 °C and at a strain rate of 1 s^?1 up to 260 °C. The temperature increase in the tests at strain rates of 200 s^?1 and 3000 s^?1 is nearly the same with the maximum temperature reaching 375 °C.     

Plastic Strain Mapping with Sub-micron Resolution Using Digital Image Correlation

Digital image correlation (DIC) of images obtained using scanning electron microscopy has been used to study, quantitatively, the plastic deformation of stainless steel at the microstructural scale. An artificial speckle pattern was generated by the remodelling of a deposited gold layer. A new experimental setup was shown to accelerate the remodelling process and promote the formation of finer nano-scale speckles with sizes ranging 30 nm to 150 nm and of similar spacing. The effects of surface preparation on speckle morphology are discussed. The high density of speckles enabled displacement mapping with resolution of one displacement vector each 0.2?×?0.2 μm² of surface area. It is shown that sub-micron resolution is necessary to capture the plastic deformation associated with the formation of slip bands in stainless steel, which are an important component of the deformation of these materials at the microscale. Electron backscatter diffraction (EBSD) was used to reconstruct the surface grain boundaries and enabled these deformation features to be linked to the microstructure.     

A new membrane model for the ballistic impact response and V50 performance of multi-ply fibrous systems

This paper develops an analytical model for the ballistic impact response of fibrous materials of interest in body armor applications. It focuses on an un-tensioned 2D membrane impacted transversely by a blunt-nosed projectile, a problem that has remained unsolved for a half a century. Membrane properties are assumed characteristic of the best current body armor materials (Kevlar^®, Spectra^®, Zylon^®, S2 glass), which have very high stiffness and strength per unit weight, and low strain-to-failure. Successful comparisons will be made with extensive experimental data on such material systems as reported by Cunniff [Decoupled response of textile body armor. Proc. 18th Int. Symp. of Ballistics, San Antonio, Texas, 1999a, pp. 814–821; V_s–V_r relationships in textile system impact. Proc. 18th Int. Symp. of Ballistics, San Antonio, Texas, 1999b; Dimensional parameters for optimization of textile-based body armor systems, Proc. 18th Int. Symp. of Ballistics, San Antonio, Texas, 1999c, pp. 1303–1310]. Our mathematical formulation draws on the seminal work of Rakhmatulin and Dem’yanov [Strength Under High Transient Loads, 1961, pp. 94–152]. Under constant projectile velocity we first develop self-similar solution forms for the tensile ‘implosion’ wave and the curved cone wave that develops in its wake. Through matching boundary conditions at the cone wave front, we obtain an accurate approximate solution for the membrane response including cone wave speed and strain distribution. We then consider projectile deceleration due to membrane reactive forces, and obtain results on cone velocity, displacement and strain concentration versus time. Other results obtained are the membrane ballistic limit, or V₅₀ velocity, and the residual velocity when penetrated above this limit. We then derive an exact functional representation of a V₅₀ ‘master curve’ found empirically by Cunniff [ibid] to reduce data for a wide variety of fabric systems impacted by blunt cylindrical projectiles. This curve is given in terms two dimensionless parameters based only on fiber mechanical properties and the ratio of the fabric areal density to the projectile mass divided by its area of fabric contact. Our functional representation has no fitting parameters beyond one reflecting uncertainty in the effective diameter of the impact zone relative to the projectile diameter, and even then the values are consistent across several experimental systems. The extremely successful comparison of our analytical model to experimental results in the literature raises fundamental questions about many long-held views on fabric system impact behavior and parameters thought to be important.     

Shear Failure of Inconel 718 under Dynamic Loads

Kinetics of deformation and fracture of nickel–iron alloy Inconel 718 under dynamic shear loading was measured using a split torsional Hopkinson bar facility and high-speed photography. Tubular specimens with a reduced gage length and a starter notch were sheared at strain rates up to 6 × 10³ s⁻¹. High-speed photographs of fiducial lines scribed on the specimen surface showed the development of local strains and cracking. This paper describes the experimental and analytical procedures, illustrates average and local plastic strain evolution, and presents shear crack initiation times and propagation speeds.     

大长细比结构弹体侵彻2024-O铝靶的弹塑性动力响应

为研究大长细比结构弹体在撞击典型硬目标早期的结构动力学响应,利用57轻气炮进行了直径1.4 cm、量纲一壁厚0.1和0.15、长细比8和12、头部系数3和4.5的卵形空心弹体对2024-O铝靶的侵彻实验研究,利用高速摄影系统记录了弹体撞靶过程,观察到大长细比弹体垂直撞击硬目标过程中的局部墩粗、塑性屈曲2种结构破坏模式,以及斜侵彻过程中的整体塑性弯曲、弯曲与墩粗耦合、弯曲与屈曲耦合3种结构破坏模式和实时动力学响应过程。基于对指数硬化材料的空腔膨胀理论建立了弹体垂直侵彻模型,给出了在轴向及横向载荷交互作用下计算刚塑性自由梁危险截面屈服函数的控制方程,计算值与实验结果吻合较好。     

The development and use of a torsional Hopkinson-bar apparatus

A technique is described by means of which torsional waves of large, essentially constant amplitude can be generated in an elastic bar. Waves with rise times of order 25 μs and maximum angular velocities of order 10³ rad.s^?1 have been achieved and used to test tubular specimens at shear-strain rates up to 15×10³ s^?1. Results are presented for mild steel tested at 2×10³ s^?1, and it is shown that the flow stress correlates well with the trend found at lower rates using conventional methods. The measured drop of stress at yield, however, was considerably smaller in the present tests than in earlier work; this is attributed to the generation of flexural waves which reach the specimen at the same time as the torsional wave.     

高速3D-DIC测试技术在装甲钢贯穿试验中的应用

数字图像相关（digital image correlation, DIC）技术作为一种非接触、非干涉的全场无损光学量测技术,可获取材料表面的动态变形信息和破坏过程。为了评估装甲钢的抗弹性能并探索高速三维数字图像相关（3D-DIC）技术在钢板贯穿试验测试中的应用,基于氢氧爆轰驱动弹道枪开展了7发15 mm口径可变形弹体以不同速度（255～568 m/s）冲击不同厚度（5、8和10 mm）高强高硬装甲钢板的试验,并结合帧率为144 000 s?1的高速3D-DIC测试技术获取了靶板的离面位移和应变时程。随后,基于前期标定并验证的装甲钢本构模型参数,对上述试验进行了数值模拟。通过对比弹体残余速度和长度验证了有限元分析方法的可靠性。进一步通过对比试验与数值模拟得到的靶背离面位移时程曲线和不同时刻靶背的应变云图,验证了高速3D-DIC测试结果的准确性。最后,对比分析了靶板最大离面位移与弹体冲击速度和装甲钢板厚度的关系。高速3D-DIC测试技术的应用可为相关试验测试提供参考,靶板最大离面位移分析结果可为屏障类防护结构的分析验证和优化设计提供试验依据。     

High strain-rate crack growth in rate-dependent plastic solids

At high crack velocities in metallic materials nearly all plastic strain accumulates at very high strain-rates, typically in the range 10³ s^?1 to 10⁵ s^?1. At these rates, dislocation motion is limited by dynamic lattice effects and the plastic strain-rate increases approximately linearly with stress. The problem for a crack growing at high velocity is posed for steady-state, small scale yielding in elastic/rate-dependent plastic solids. A general expression is derived for the near-tip stress intensity factor in terms of the remote intensity factor, or equivalently for the near-tip energy release-rate in terms of the overall release-rate. An approximate calculation of the plastic strain-rates provides this relation in analytical form. Imposition of the condition that the near-tip energy release-rate be maintained at a critical value provides a propagation equation for the growing crack. A single, nondimensional combination of material constants emerges as the controlling parameter. Implications for dynamic crack propagation are discussed.     

Dehydration characteristics and mathematical modelling of lemon slices drying undergoing oven treatment

In this study, the effect of drying temperature on drying behaviour and mass transfer parameters of lemon slices was investigated. The drying experiments were conducted in a laboratory air ventilated oven dryer at temperatures of 50, 60 and 75 °C. It was observed that the drying temperature affected the drying time and drying rate significantly. Drying rate curves revealed that the process at the temperature levels taken place in the falling rate period entirely. The usefulness of eight thin layer models to simulate the drying kinetics was evaluated and the Midilli and Kucuk model showed the best fit to experimental drying curves. The effective moisture diffusivity was determined on the basis of Fick’s second law and obtained to be 1.62 × 10^?11, 3.25 × 10^?11 and 8.11 × 10^?11 m² s^?1 for the temperatures of 50, 60 and 75 °C, respectively. The activation energy and Arrhenius constant were calculated to be 60.08 kJ mol^?1 and 0.08511 m² s^?1, respectively. The average value of convective mass transfer coefficient for the drying temperatures of 50, 60 and 75 °C was calculated to be 5.71 × 10^?7, 1.62 × 10^?6 and 2.53 × 10^?6 m s^?1, respectively.     

Damage Mechanisms Perspective on Superior Ballistic Performance of Spinel over Sapphire

Sapphire and magnesium spinel are two commonly used transparent armor materials. Although it is commonly believed that better mechanical properties often result in better field performance, the ballistic performance of spinel is reported to be superior to sapphire despite its inferior mechanical properties. The above discrepancy has been rationalized on the basis of mechanisms of deformation during impact loading. After reviewing the reported ballistic performance results on spinel and sapphire, we will discuss the relevant mechanical properties and their inability to explain the observed paradoxical behavior. We will then present differences in static (15 s duration) and dynamic (100 μs duration) indentation fracture characteristics and compare these observations to fracture modes witnessed during ball-on-rod impact tests. Lastly, the energy absorbed in various deformation mechanisms for each material is compared to draw a rationale for the intriguing behavior of spinel. Fracture along crystallographic planes in sapphire during ball impact allows large fragments to be ejected causing a significant loss in structural integrity and deeper projectile penetration, whereas the mixed mode fracture in spinel produces fine debris which opposes the incoming projectile and causes severe deceleration and erosion of the ball. Thus a mechanism based rationale has been provided to describe the superior performance of spinel over sapphire.     

Effect of elastic target material on Taylor model

A theoretical model is proposed for a semi-infinite elastic bar struck axially by a flat-ended cylindrical projectile. The model is actually developed from the classical Taylor model except that the target is a semi-infinite bar with elastic behavior being considered. Particular attention is paid to the influence due to elastic wave propagation in the target bar on the energy partitioning between the projectile and target, which may result in the final length of the cylinder significantly different from the predictions of the classical Taylor model. The theoretical model is verified by numerical simulations, and the effects of several key non-dimensional parameters on the residual deformation and energy dissipation are discussed in detail. It is shown that the elastic effect of the target bar plays an important role in the prediction of plastic deformation of the cylindrical projectile.     

Relationship between Local Strain Jumps and Temperature Bursts Due to the Portevin-Le Chatelier Effect in an Al-Mg Alloy

Local strain and temperature of an AA5754-O aluminum alloy sheet have been full-field measured during monotonous tensile tests carried out at room temperature. Sharp strain increases and temperature bursts which are locally generated by the Portevin-Le Chatelier phenomenon have been measured at the same point for two strain rates: V2?=?1.9?×?10^?3?s^?1 and V10?=?9.7?×?10^?3?s^?1. A relationship, which is based on the underlying physical mechanisms, has been established between the strain and the temperature and experimentally verified for the highest strain rate V10. The discrepancy between the theoretical and experimental results for the lowest strain rate V2 suggests that the localized plastic deformations do not follow an adiabatic transformation. Such a set-up seems to offer a direct and experimental method to check the adiabatic character of localized plastic deformations.     

Drying characteristics of garlic (Allium sativum L) slices in a convective hot air dryer

The effects of drying temperatures on the drying kinetics of garlic slices were investigated using a cabinet-type dryer. The experimental drying data were fitted best to the Page and Modified Page models apart from other theoretical models to predict the drying kinetics. The effective moisture diffusivities varied from 4.214 × 10^?10 to 2.221 × 10^?10 m² s^?1 over the temperature range studied, and activation energy was 30.582 kJ mol^?1.     

DYNAMIC RESPONSE OF A RIGID,PERFECTLY PLASTIC FREE-FREE BEAM STRUCK BY A PROJECTILE ATANY CROSS-SECTION ALONG ITS SPAN

I. INTRODUCTION The dynamic plastic response of free-free beams subjected to intense dynamic loading is a subject ofinterest for aerospace engineering applications. For example, when a rocket is attacked by a missile, itslarge plastic deformation behav…     

Stable Speckle Patterns for Nano-scale Strain Mapping up to 700 °C

The digital image correlation (DIC) of speckle patterns obtained by vapour-assisted gold remodelling at 200 – 350 °C has already been used to map plastic strains with submicron resolution. However, it has not so far proved possible to use such patterns for testing at high temperatures. Here we demonstrate how a gold speckle pattern can be made that is stable at 700 °C, to study deformation in a commercial TiAl alloy (Ti-45Al-2Nb-2Mn(at%)-0.8 vol% TiB₂). The pattern is made up of a uniformly sized random array of Au islands as small as 15 nm in diameter, depending on reconstruction parameters, with a sufficiently small spacing to be suitable for nano-scale, nDIC, strain mapping at a subset size of 60 × 60 nm². It can be used at temperatures up to 700 °C for many hours, for high cycle fatigue testing for instance. There is good particle attachment to the substrate. It can withstand ultra-sound cleaning, is thermally stable and has a high atomic number contrast for topography-free backscatter electron imaging.     

Annular Pulse Shaping Technique for Large-Diameter Kolsky Bar Experiments on Concrete

The goal of this study is to design a novel annular pulse shaping technique for large-diameter Kolsky bars for investigating the dynamic compressive response of concretes. The purpose of implementing an annular pulse shaper design is to alleviate inertia-induced stresses in the pulse shaper material that would otherwise superpose unwanted oscillations on the incident wave. This newly developed pulse shaping technique led to well-controlled testing conditions enabling dynamic stress equilibrium, uniform deformation, and constant strain-rate in the testing of a chosen concrete material. The observed dynamic deformation rate of the concrete is highly consistent (8 % variation) with the stress in the specimen well equilibrated confirming the validity of this new technique. Experimental results at both quasi-static (10^?4 s^?1) and dynamic (100 s^?1, 240 s^?1) strain rates showed that the failure strength of this concrete is rate-sensitive.     

The surface-forming energy release rate based fracture criterion for elastic–plastic crack propagation

The J-integral based criterion is widely used in elastic–plastic fracture mechanics. However, it is not rigorously applicable when plastic unloading appears during crack propagation. One difficulty is that the energy density with plastic unloading in the J-integral cannot be defined unambiguously. In this paper, we alternatively start from the analysis on the power balance, and propose a surface-forming energy release rate (ERR), which represents the energy available for separating the crack surfaces during the crack propagation and excludes the loading-mode-dependent plastic dissipation. Therefore the surface-forming ERR based fracture criterion has wider applicability, including elastic–plastic crack propagation problems. Several formulae are derived for calculating the surface-forming ERR. From the most concise formula, it is interesting to note that the surface-forming ERR can be computed using only the stress and deformation of the current moment, and the definition of the energy density or work density is avoided. When an infinitesimal contour is chosen, the expression can be further simplified. For any fracture behaviors, the surface-forming ERR is proven to be path-independent, and the path-independence of its constituent term, so-called J_s-integral, is also investigated. The physical meanings and applicability of the proposed surface-forming ERR, traditional ERR, J_s-integral and J-integral are compared and discussed. Besides, we give an interpretation of Rice paradox by comparing the cohesive fracture model and the surface-forming ERR based fracture criterion.     

Effect of projectile nose shape,impact velocity and target thickness on deformation behavior of aluminum plates

The present study deals with the experimental and numerical investigations of aluminum target plates impacted by blunt, ogive and hemispherical nosed steel projectiles. The projectiles were normally impacted on the target plates of 0.5, 0.71, 1, 1.5, 2, 2.5 and 3 mm thicknesses at different velocities with the help of a pneumatic gun. Effect of projectile nose shape, impact velocity and plate thickness on the deformation of the target plates was studied. Hemispherical nosed projectile caused highest global deformation (dishing) of the target plates. Ogive nosed projectiles were found to be the most efficient penetrator for the case of plates of thicknesses 0.5, 0.71, 1.0 and 1.5 mm. For the case of plates of thicknesses 2.0, 2.5 and 3.0 mm however, blunt nosed projectiles required least energy to perforate the target plates. The ballistic limit velocity of hemispherical nosed projectiles was found to be highest as compared to the other two projectiles. Finite element analysis of the problem was carried out using ABAQUS finite element code. Results of the numerical analysis were compared with the experiments and good correlation between the two was found.